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CoVAMPnet: Comparative Markov State Analysis for Studying Effects of Drug Candidates on Disordered Biomolecules
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  • Sérgio M. Marques
    Sérgio M. Marques
    Loschmidt Laboratories, Department of Experimental Biology and RECETOX, Faculty of Science, Masaryk University, Kamenice 5, Brno 625 00, Czech Republic
    International Clinical Research Center, St. Anne’s University Hospital Brno, Pekarska 53, Brno 656 91, Czech Republic
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  • Petr Kouba
    Petr Kouba
    Loschmidt Laboratories, Department of Experimental Biology and RECETOX, Faculty of Science, Masaryk University, Kamenice 5, Brno 625 00, Czech Republic
    Czech Institute of Informatics, Robotics and Cybernetics, Czech Technical University in Prague, Jugoslavskych partyzanu 1580/3, Dejvice, Praha 6 160 00, Czech Republic
    Faculty of Electrical Engineering, Czech Technical University in Prague, Technicka 2, Dejvice, Praha 6 166 27, Czech Republic
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    Orcidhttps://orcid.org/0000-0002-9979-4159
  • Anthony Legrand
    Anthony Legrand
    Loschmidt Laboratories, Department of Experimental Biology and RECETOX, Faculty of Science, Masaryk University, Kamenice 5, Brno 625 00, Czech Republic
    International Clinical Research Center, St. Anne’s University Hospital Brno, Pekarska 53, Brno 656 91, Czech Republic
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  • Jiri Sedlar
    Jiri Sedlar
    Czech Institute of Informatics, Robotics and Cybernetics, Czech Technical University in Prague, Jugoslavskych partyzanu 1580/3, Dejvice, Praha 6 160 00, Czech Republic
    More by Jiri Sedlar
    Orcidhttps://orcid.org/0000-0002-4704-3388
  • Lucas Disson
    Lucas Disson
    Czech Institute of Informatics, Robotics and Cybernetics, Czech Technical University in Prague, Jugoslavskych partyzanu 1580/3, Dejvice, Praha 6 160 00, Czech Republic
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  • Joan Planas-Iglesias
    Joan Planas-Iglesias
    Loschmidt Laboratories, Department of Experimental Biology and RECETOX, Faculty of Science, Masaryk University, Kamenice 5, Brno 625 00, Czech Republic
    International Clinical Research Center, St. Anne’s University Hospital Brno, Pekarska 53, Brno 656 91, Czech Republic
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    Orcidhttps://orcid.org/0000-0002-6279-2483
  • Zainab Sanusi
    Zainab Sanusi
    Loschmidt Laboratories, Department of Experimental Biology and RECETOX, Faculty of Science, Masaryk University, Kamenice 5, Brno 625 00, Czech Republic
    International Clinical Research Center, St. Anne’s University Hospital Brno, Pekarska 53, Brno 656 91, Czech Republic
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  • Antonin Kunka
    Antonin Kunka
    Loschmidt Laboratories, Department of Experimental Biology and RECETOX, Faculty of Science, Masaryk University, Kamenice 5, Brno 625 00, Czech Republic
    International Clinical Research Center, St. Anne’s University Hospital Brno, Pekarska 53, Brno 656 91, Czech Republic
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  • Jiri Damborsky
    Jiri Damborsky
    Loschmidt Laboratories, Department of Experimental Biology and RECETOX, Faculty of Science, Masaryk University, Kamenice 5, Brno 625 00, Czech Republic
    International Clinical Research Center, St. Anne’s University Hospital Brno, Pekarska 53, Brno 656 91, Czech Republic
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    Orcidhttps://orcid.org/0000-0002-7848-8216
  • Tomas Pajdla
    Tomas Pajdla
    Czech Institute of Informatics, Robotics and Cybernetics, Czech Technical University in Prague, Jugoslavskych partyzanu 1580/3, Dejvice, Praha 6 160 00, Czech Republic
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  • Zbynek Prokop
    Zbynek Prokop
    Loschmidt Laboratories, Department of Experimental Biology and RECETOX, Faculty of Science, Masaryk University, Kamenice 5, Brno 625 00, Czech Republic
    International Clinical Research Center, St. Anne’s University Hospital Brno, Pekarska 53, Brno 656 91, Czech Republic
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    Orcidhttps://orcid.org/0000-0001-9358-4081
  • Stanislav Mazurenko*
    Stanislav Mazurenko
    Loschmidt Laboratories, Department of Experimental Biology and RECETOX, Faculty of Science, Masaryk University, Kamenice 5, Brno 625 00, Czech Republic
    International Clinical Research Center, St. Anne’s University Hospital Brno, Pekarska 53, Brno 656 91, Czech Republic
    *E-mail: [email protected]
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  • Josef Sivic*
    Josef Sivic
    Czech Institute of Informatics, Robotics and Cybernetics, Czech Technical University in Prague, Jugoslavskych partyzanu 1580/3, Dejvice, Praha 6 160 00, Czech Republic
    *E-mail: [email protected]
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  • David Bednar*
    David Bednar
    Loschmidt Laboratories, Department of Experimental Biology and RECETOX, Faculty of Science, Masaryk University, Kamenice 5, Brno 625 00, Czech Republic
    International Clinical Research Center, St. Anne’s University Hospital Brno, Pekarska 53, Brno 656 91, Czech Republic
    *E-mail: [email protected]
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    Orcidhttps://orcid.org/0000-0002-6803-0340
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JACS Au

Cite this: JACS Au 2024, 4, 6, 2228–2245
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https://doi.org/10.1021/jacsau.4c00182
Published May 28, 2024

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Abstract

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Computational study of the effect of drug candidates on intrinsically disordered biomolecules is challenging due to their vast and complex conformational space. Here, we developed a comparative Markov state analysis (CoVAMPnet) framework to quantify changes in the conformational distribution and dynamics of a disordered biomolecule in the presence and absence of small organic drug candidate molecules. First, molecular dynamics trajectories are generated using enhanced sampling, in the presence and absence of small molecule drug candidates, and ensembles of soft Markov state models (MSMs) are learned for each system using unsupervised machine learning. Second, these ensembles of learned MSMs are aligned across different systems based on a solution to an optimal transport problem. Third, the directional importance of inter-residue distances for the assignment to different conformational states is assessed by a discriminative analysis of aggregated neural network gradients. This final step provides interpretability and biophysical context to the learned MSMs. We applied this novel computational framework to assess the effects of ongoing phase 3 therapeutics tramiprosate (TMP) and its metabolite 3-sulfopropanoic acid (SPA) on the disordered Aβ42 peptide involved in Alzheimer’s disease. Based on adaptive sampling molecular dynamics and CoVAMPnet analysis, we observed that both TMP and SPA preserved more structured conformations of Aβ42 by interacting nonspecifically with charged residues. SPA impacted Aβ42 more than TMP, protecting α-helices and suppressing the formation of aggregation-prone β-strands. Experimental biophysical analyses showed only mild effects of TMP/SPA on Aβ42 and activity enhancement by the endogenous metabolization of TMP into SPA. Our data suggest that TMP/SPA may also target biomolecules other than Aβ peptides. The CoVAMPnet method is broadly applicable to study the effects of drug candidates on the conformational behavior of intrinsically disordered biomolecules.

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Introduction

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Alzheimer’s disease (AD) is globally the fifth leading cause of death and fourth cause of disability in people aged 75 years and above and thus represents an enormous societal burden. (1) Amyloid-beta (Aβ) peptides play a major role in the development of AD, although the mechanism behind their toxicity is still debated. (2,3) A model of toxicity known as the oligomer hypothesis states that Aβ oligomerizes into toxic pore-forming oligomers at the neuronal plasma membrane, which ultimately leads to cell death. Among the different Aβ peptides, the 42-residue long peptide (Aβ42; Figure 1A) is the most aggregation-prone isoform. (4,5)

Figure 1

Figure 1. Structures of Aβ42 peptide and the studied small molecules, and properties of the ensembles from the adaptive simulations for the free Aβ42, Aβ42 + TMP, and Aβ42 + SPA. A) Sequence of the Aβ42 peptide and chemical structures of tramiprosate (TMP) and 3-sulfopropanoic acid (SPA) in the dominant protonation states at the physiological pH 7.4. The sequence residues are color-coded as follows: red for negatively charged; blue for positively charged; green for hydrophobic; and black for polar neutral residues. B) Total secondary structural propensity (% SS) of Aβ42 during the adaptive MDs, in the original NMR ensemble (PDB 1Z0Q with 30 structures), and from the experimental measurements of free Aβ42 in aqueous solution. C) Secondary structure propensity of Aβ42 by residue, obtained for the global ensembles from the adaptive simulations. The certainty of the secondary structure assignment was obtained by the statistical variance among ten randomized bins of frames and is represented by the saturation of the secondary structure color (the more saturated the color, the more certain the assignment, as indicated by the legend). D) Distribution of the radius of gyration (Rg) of the ensembles from the same adaptive simulations. E) Time evolution of the secondary structure of Aβ42 during the time-based aligned adaptive sampling MD simulations. The secondary elements are aggregated across all 42 residues, averaged at each time over all the trajectories parallel in time according to the time-based alignment. Only the timespan covering at least 20 parallel trajectories is plotted.

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The Aβ peptides are intrinsically disordered, which makes them difficult to study both experimentally and computationally. Intrinsically disordered proteins do not adopt a single well-defined structure, but rather exist as ensembles of conformations with similar energies. These ensembles are best characterized by their population distributions and probabilities of several properties or descriptors (e.g., radius of gyration and secondary structure). (6,7) The disordered nature of Aβ42 significantly complicates the analysis of its molecular dynamics (MD) trajectories, namely, the definition of conformational states, which is an important step toward a deeper understanding of the system and its slowest transitions. (8) A popular approach for identifying notable conformational states in MD simulations involves building so-called Markov state models (MSMs). Under the assumption of the dynamics being Markovian (memoryless), these models cluster the conformational space into states preserving the Markovianity of the transitions and estimate the equilibrium distribution and transition rates between the states. The conventional methods for building MSMs typically rely on a selection of collective variables, compressing the high-dimensional MD data and simplifying the clustering. Recent progress in variational approaches for conformational dynamics has further allowed scoring different MSMs, e.g., based on their ability to approximate the slowest modes of the dynamics, thus facilitating the development of automatic frameworks for the identification of Markov states. (9) Although some of these procedures are quite advanced and enable, e.g., an accurate estimation of transition rates even from biased simulation data, (10) the manual selection of the collective variables is typically laborious and can often cause the resulting models to fail the tests for Markovianity. While MSMs are extremely valuable tools, they possess certain limitations, such as the assumption of Markovianity, constraints on state representation granularity, reliance on extensive sampling, and relatively rapid relaxation dynamics. (11−14) Several alternative methodologies exist to address these shortcomings. These include hidden Markov models (HMMs) to relax the Markovian assumption, (12) approaches incorporating memory effects such as the generalized master equation (GME) and the generalized Langevin equation (GLE) for more effective dynamic property assessment, (11) and methods rooted in deep learning. (15)
A powerful framework based on deep learning is VAMPnet, a neural network that learns a probabilistic assignment of each simulation frame to individual states in an unsupervised manner by maximizing a variational score. (16) In contrast to the other methods, the VAMPnet approach does not relax the Markovianity assumption but rather combines the search of collective variables with the optimization of a cost function to efficiently identify the slowest modes of the system. The application of VAMPnets to the analysis of Aβ42 trajectories has already shown great potential in producing robust MSMs for quantification of the Aβ42 kinetics and equilibrium properties. (17) Several recent methods build on the VAMPnet approach to address the efficiency of protein representation, (18,19) scalability to multidomain protein systems, (20) stability of the training process, (21) sampling of rare conformations, (22) or the importance of residues based on the attention mechanism. (18,23) However, to the best of our knowledge, a method for aligning and comparing ensembles of learned MSMs across different systems that would simplify the biophysical interpretation of the conformational states by identifying their distinctive features is still missing. In this work, we have developed such a method to help understand and quantify the effects of drug candidates on the conformational space of the analyzed system.
This problem is important in many fields of research, particularly in AD. Due to the prevalence and severity of the disease, there is a growing interest in pharmaceuticals capable of preventing the early stages of the Aβ42 oligomerization and stopping the pathogenic amyloid cascade. (3,4,24) Tramiprosate (TMP), also known as homotaurine or 3-amino-1-propanesulfonic acid, is a naturally occurring aminosulfonate. Even at high concentrations, it is well tolerated in the human brain, where it is metabolized into 3-sulfopropanoic acid (SPA) (Figure 1A). TMP has been reported to prevent the formation of fibrillar forms of Aβ, reduce the Aβ-induced death rate of neuronal cell cultures, and lower the amyloid plaque deposition in the brain. (25−27) Clinical trials have shown its ability to slow down the cognitive decline in patients with homozygous expression of the apolipoprotein E gene APOE4, similarly to FDA-approved aducanumab. (24,28) TMP can act not only on Aβ, but also on other pathways that contribute to cognitive impairment in AD and other neurologic disorders. (29,30) ALZ-801 is a valine-conjugated prodrug of TMP that is currently in phase 3 of clinical trials for early stage AD patients bearing the APOE4/4 genotype (NCT04770220). (31,32) Preliminary in vitro and in silico studies suggested that both TMP and SPA can lock the Aβ peptides in monomeric conformations that are less prone to oligomerization, thus inhibiting the first step in the pathological pathway of Aβ. (33−35) However, these studies do not provide sufficient insights to fully explain the mechanism of action of these molecules on Aβ. At the moment, it is still unclear whether TMP or its metabolite SPA can exert a stronger biological effect, and this was one of our motivations to carry out this study.
To analyze the effect of TMP and SPA on Aβ and understand how these small molecules may prevent the formation of Aβ oligomers and fibrils, we developed a new computational framework called comparative Markov state analysis (CoVAMPnet). The CoVAMPnet framework reveals the impact of a small molecule (in our case, TMP or SPA) on the conformational space and dynamics of an intrinsically disordered biomolecule (in our case, Aβ) in three steps. First, molecular dynamic trajectories are generated using enhanced sampling, and an ensemble of soft MSMs is computed for each system by training VAMPnet neural networks. (17) In particular, we simulated the monomeric Aβ42 peptide in its free form and in the presence of drug candidates TMP or SPA. Second, using our novel alignment method, these ensembles are aligned to identify similar conformational states across the different systems based on a solution to an optimal transport problem. This proved useful in quantifying the similarities and differences in Aβ42 conformations in response to the presence or absence of the small molecules. Finally, our new approach based on analyzing gradients of the trained neural networks is used to elucidate the patterns underlying the learned MSMs and to understand the biophysical relevance of the molecular features, namely, the directional inter-residue distances, for the classification into each state. To our knowledge, this is the first time that such a biomolecular relevance analysis has been used to compare and interpret MSMs built by unsupervised machine learning methods and quantify the effects of drug candidates on the conformational space of a disordered protein. Experimental comparison of Aβ42 in its free form and in the presence of TMP or SPA by circular dichroism (CD), Fourier-transform infrared spectroscopy (FTIR), nuclear magnetic resonance (NMR), and fluorometry has further shown the effects of the small molecules on longer time scales, complementing our computational findings.

Materials and Methods

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Here, we present only a concise description of the methods used, focusing mainly on the novel methodology. A complete and detailed description is provided in Supporting Information and Methods.

Molecular Dynamics (MD) Simulations

System Preparation

The structures of tramiprosate (TMP) and 3-sulfopropanoic acid (SPA) were constructed and minimized using Avogadro 2. (36) During the calculation of partial charges, the structures were further optimized by Gaussian 09, (37) and the antechamber module of AmberTools 16 (38) was then used to prepare the force field-compatible parameters. The three-dimensional structural data of the Aβ42 peptide were obtained from the RCSB Protein Data Bank (39) (PDB entry 1Z0Q). It resulted from NMR experiments and contains 30 structures, which were saved separately. The Aβ42 peptide was protonated using PROPKA (40) at physiological pH 7.4, the small molecules were embedded (when appropriate), the systems solvated, and their topologies built using high-throughput molecular dynamics (HTMD) (41) in combination with the CHARMM36m (42) (C36m) force field. We used a stoichiometry of 100 molecules of TMP or SPA per molecule of Aβ42. This ratio approximates the experimental conditions (1000:1) without compromising the computational costs of the simulations.

MD Simulation Protocols

All the systems were equilibrated using HTMD. (41) The end point of the equilibration cycle was taken as a starting point for subsequent MD simulations, either classic or adaptive sampling ones. The simulations employed the same settings as the last step of the equilibration, and their trajectories were saved every 0.1 ns. HTMD was used to perform adaptive sampling of the Aβ42 conformations. Due to the conformational complexity of Aβ42, three protocols (namely, A, B, and C) were assessed. Each protocol differed from the others in the starting structure set, the adaptive metric, the number of adaptive epochs and replicas, and the total cumulative MD time (Table S1). Protocols A and B were only applied to free Aβ42, while protocol C was applied to free Aβ42, Aβ42 + TMP, and Aβ42 + SPA.
Classical MD simulations were also performed using HTMD, where only the structure of the first model of the PDB entry 1Z0Q was used as the starting point. The free Aβ42, Aβ42 + TMP, and Aβ42 + SPA systems were prepared and equilibrated as described above. These MDs were performed using only the C36m force field. Each MD was run in sequential batches of 200 ns each, for a total of 5 μs, and 10 independent replicates were performed for each system.

Analyses of Properties in Combined MD Ensembles

In order to analyze the produced MD simulations, their topologies were converted from CHARMM to AMBER using ParmEd (43) when required. Water molecules and ions were filtered out from the resulting MDs, which were then compiled into a simulation list using HTMD. The cpptraj (44) module of AmberTools 16 (38) was used to compute several properties in the combined ensembles: root-mean square deviation (RMSD), radius of gyration (Rg), and linear interaction energy (LIE) (45) between Aβ42 and TMP or SPA. DSSP 3.0 (46) was used to assign a secondary structure to every residue in every snapshot of the combined trajectories, and the default DSSP seven-letter alphabet was converted to the three main secondary elements (α-helix, β-strand, and coil, see MD analysis section in Supporting Information and Methods). Accounting for all the residues of each secondary structure type in the peptide for all the analyzed snapshots resulted in the total secondary structure content of the ensemble. Mechanics/generalized Born solvent accessible surface area (MM/GBSA) (47,48) calculations were performed with the MMPBSA.py.MPI (47) module of AmberTools 14 to obtain the free energy of the peptide for every frame of the ensemble, from which the peptide intramolecular interactions were derived.

Comparative Markov State Model Analysis (CoVAMPnet)

This section describes our comparative Markov state analysis (CoVAMPnet) of adaptive sampling MD simulations of the free Aβ42, Aβ42 + TMP, and Aβ42 + SPA systems. CoVAMPnet builds on the variational approach to Markov processes by VAMPnet neural networks, followed by two new analyses: (i) alignment of the learned MSM ensembles across different systems based on a solution to an optimal transport problem and (ii) characterization of the learned states by the inter-residue distances based on the neural network gradients.

Learning Markov State Models Using Neural Networks

The variational approach to Markov processes (VAMP) (49) was used to learn Markov state models (MSMs) via unsupervised training of VAMP neural networks (VAMPnets) (16) with physical constraints. (50) VAMPnet learns a nonlinear function that maps the peptide tertiary structure to a vector of state probabilities. The physical constraints ensure that the learned MSM is reversible and that the elements of the matrix representing the governing Koopman operator (16) (a linear operator propagating the state probabilities in time) are non-negative. In this work, we used the VAMPnet implementation by Löhr et al., (17) including the self-normalizing setup. (51)
The VAMPnet architecture consists of two parallel weight-sharing lobes: one for a frame at time t and the other for a frame at time t + τ in the same trajectory, where τ is a fixed lag time. Each frame was represented on the input as a vector (780 elements) of the upper triangular part of the peptide inter-residue heavy atom distance matrix without the diagonal and the first two subdiagonals (i.e., without the distances to the first and second neighboring residues). The output nodes in each lobe measure the probabilities of the constructed MSM states for the input frame. The network was trained on pairs of MD simulation frames separated by a selected lag time τ. To obtain the probabilities of the learned states, the frames were run through one of the lobes. For each system, an ensemble of 20 models was built. The pairs of frames were divided into 20 random splits (90% training and 10% validation) and for each split, three VAMPnet models were trained with different initialization and the one with the highest VAMP-E score (49) was selected for the MSM ensemble. The soft assignment of a frame was defined as the average of its state probabilities across the ensemble, whereas the hard assignment was defined as the state with the highest probability in the soft assignment of the frame. Throughout this work, the soft assignments were used everywhere unless it was necessary to select example frames from a particular state (such as the example structures in Figure 2A or the frames representing the states for the columns of the matrix in Figures S22). Further details on our VAMPnet setup are described in Supporting Information and Methods.

Figure 2

Figure 2. Analysis of conformational states learned using the variational approach to Markov processes on the adaptive simulations and their evolution in time. A) Properties of the states. For each system, we report: (i) the free energy surface (FES) projected on the first two tICA dimensions (gray maps), where darker shades correspond to more negative energy regions; (ii) flux diagrams overlapping the FES and projected on the same tICA space, where each state is represented by a colored circle with the area proportional to the state probability, and the arrows indicate the mean first-passage times TM between the states, with the thickness proportional to the transition probability; (iii) equilibrium distribution of the states (bottom-left corner of FES; the bars represent the 95th percentile of values centered around the median from the ensemble of 20 learned models; see Supplementary Note 7 for details); (iv) superimposition of 20 representative structures from each state, selected based on the highest assignment probability (below FES, enclosed in colored circles); (v) global mean secondary structure content of each state (below the respective structures). B) Distribution of the learned states in time (top) and the number of frames available at each time point (bottom). The adaptive sampling trajectories were aligned in time and concatenated. The state probability at a given time point was computed as the average soft assignment of all available frames at this time point. From left to right, the state assignments evolve from the beginning to the end of the simulation time. All plots are shown for the free Aβ (left), Aβ + TMP (middle), and Aβ + SPA (right). The states are numbered and color-coded consistently across the entire panel; the same colors across different systems indicate aligned states.

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Alignment of Learned States for Comparative Analysis

The order of the states on the output of a trained VAMPnet is not well-defined and may thus vary. To construct an MSM from multiple models or compare MSMs of different systems, a correspondence between states across the models had to be established. In this work, we generalized the approach from Löhr et al. (17) for the alignment of states within a single system to obtain an ensemble of aligned MSMs. Then, we introduced a new method for the alignment of ensembles of MSMs between different systems to compare the systems and further understand the effects of the small molecules on the conformational dynamics of Aβ42.
Aligning States within a Single System
The states from the 20 models within an ensemble were aligned by a constrained k-means clustering algorithm (52) using the average inter-residue distance matrices Dmn, where n indexes the models in the ensemble and m indexes the states in each model. The cluster centers were initialized by the Dmn0 matrices of a randomly selected model n0 in the ensemble. The clustering iterated in two steps: 1) for each model n, its states were sequentially assigned to different clusters in the order of the proximity of the Dmn matrix to the closest unassigned cluster center and respecting the constraint that two matrices from the same model cannot be assigned to the same cluster; 2) each cluster center was recomputed as the mean of the Dmn matrices of the corresponding states. These two steps were iterated until the cluster assignment did not change. The states in each model were then renumbered according to the final assigned cluster. The method by Löhr et al. (17) is equivalent to performing only one iteration of our method. Our approach is thus less susceptible to incorrect initialization and can lead to a better alignment.
Aligning Ensembles of Markov State Models Between Different Systems
With each system described by an ensemble of N mutually aligned MSMs after the single system state alignment (see above), we proposed a novel method for aligning ensembles of MSMs across different systems. In particular, we (i) characterized each state of the given system by a nonparametric distribution over the ensemble, (ii) defined a distance metric to compare such distributions, and finally, (iii) computed an alignment of the ensembles of MSMs between the two systems by solving an optimal matching problem. Details of these steps are given next. The N instances of the VAMPnet network learned for a given system s output N different feature matrices {Dmsn}n=1N (average inter-residue matrices, see Supporting Information and Methods for a formal definition of the feature matrix) describing each of the M states of the system. Each state m was, therefore, characterized by the distribution θms(ξ) of the features over the different VAMPnet instances as
θms(ξ)=1N∑n=1Nδ(ξ−Dmsn)
(1)
where δ is the Dirac delta function defined over the feature space of inter residue distances in which the simulation frames are represented and Dmsn is the inter-residue distance matrix representing state m of the learned model n for system s. θms thus represents the state m of system s with a nonparametric distribution given by the set of Dirac functions centered at the feature matrices Dmsn obtained by the instances of the learned ensemble.
To exploit the entire distribution of the features of each state, the distance between two different states was evaluated by comparing their respective distributions. In particular, we employed the Wasserstein distance of two distributions as a distance measure quantifying the cost of aligning two states from different MSMs as
cmls1s2=dW(θms1,θls2)
(2)
where cmls1s2 is the cost of aligning state m of system s1 with state l of system s2 and dW(θms1,θls2) is the Wasserstein-1 distance of the two respective distributions defined as
dW(θms1,θls2)=infγ∈Γ(θmS1,θls2)∫||ξ,ξ′||γ(ξ,ξ′)
(3)
where Γ(θms1,θls2) is the set of joint distributions whose left and right marginals are θms1 and θls2, respectively, and ||ξ, ξ′|| is the Euclidean distance of the two feature vectors ξ, ξ′ distributed according to the joint distribution γ(ξ, ξ′). In the case of empirical nonparametric distributions (such as in our case), the problem of Wasserstein-1 distance computation has an equivalent linear program formulation and it was solved using an optimal transport algorithm. (53)
Finally, the alignment of MSM ensembles was formulated as an optimization problem. Without the loss of generality, let us assume that the MSM representing system s1 does not have more states than the MSM representing system s2. The problem was defined as
π^s1s2=arg⁡minπs1s2∈Πs1s2∑m=1Ms1cmπ(m)s1s2
(4)
where Ms1 is the number of states of the MSM estimated for system s1, Πs1s2 is the set of all bijections from the states of system s1 into any Ms1-sized subset of states of system s2, and the bijection π^s1s2 is the optimal mapping of states of system s1 onto the states of system s2. This optimization problem, and thus also the alignment of MSM ensembles, was solved using the Hungarian algorithm. (54)

Gradient-Based Characterization of Learned States

The differentiability of the VAMPnet model enables interpretation of the states by investigating the feature importance, which is hard to do using classical Markov state models. This analysis aimed to understand how important the different parts of the protein structure (here represented by the peptide inter-residue distances) are for the definition of different states. While there exist different methods to investigate the importance of features in neural networks, (55,56) they are usually applied to single models for simple tasks, such as the classification of individual images. The challenge of adopting those methods for the current study was in calculating the feature importance for an ensemble of MSMs. We proposed a method to identify which features were important for the classification of the simulation frames into the learned states, building on the gradient-based method proposed for image classification. (56) In our approach, we computed the gradients for each of the models in the MSM ensemble separately and aggregated their results over the ensemble. To this end, the MSMs produced by the models needed to be aligned, which we did by using our state alignment method discussed earlier (see Aligning states within a single system). The gradients for individual Markov states were computed as follows:
gm(ξ)=1N∑n=1N∇ξχnm
(5)
where gm is a 780-dimensional vector containing the ensemble-averaged gradient of the output probability of state m computed with respect to the input features ξ; N is the number of models in the ensemble; ∇ξ is the operator of gradient with respect to the coordinates of the network input features ξ; and χnm represents the output node corresponding to state m of nth VAMPnet model in the ensemble. Here, the 780-dimensional network input vector was obtained by vectorizing the upper triangular inter-residue distance matrix and removing the diagonal and two subdiagonals. The intuition is that the ith entry of vector gm expresses the change in the probability of the assignment of the given frame of the simulation to state m induced by an increase in the distance of the ith pair of residues at the input of the VAMPnet network. The above definition computes the gradient value for an individual frame of the system. To aggregate the gradient value over a representative set of frames from the investigated system, we evaluated the gradient vector gm^ as the average of gm over 10,000 randomly selected simulation frames ξ. For visualization purposes, we took the 780-dimensional vector of evaluated gradients {gm^}m=1M and arranged it back into a 42 × 42 matrix corresponding to the shape of the inter-residue distance matrix. These gradients evaluated and averaged over randomly selected frames should express the importance of particular residues on average for the classification into a specific state without any particular assumptions about the input frame.

Estimation of the Free Energy Landscape

We estimated the free energy landscape of Aβ42 for each of the studied systems, projected on the first 2 time-lagged independent component analysis (tICA) dimensions, by performing Gaussian kernel density estimation on 10% of the simulated frames. (17)

Experimental Validation

Aβ42 in its monomeric form (N-methionine-Aβ42 or N-Met-Aβ42) was produced and purified following an adapted version of the protocol by Cohen et al. (57) Spectroscopic properties of N-Met-Aβ42 alone or in the presence of TMP, SPA, and the membrane-mimicking hexafluoroisopropanol (HFIP) were measured using circular dichroism (CD), Fourier-transformed infrared spectroscopy (FTIR), and nuclear magnetic resonance (NMR). Aggregation kinetics were recorded using thioflavin T (ThT) assays. (58) A 1000-fold molar excess of TMP or SPA with respect to the concentration of N-Met-Aβ42 was used, to replicate the experimental conditions previously reported to exert biological effects from those molecules. (33)

Results

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Selection of the Computational Protocol for the Simulation of Aβ42

We aimed to query, by molecular dynamics (MD) simulations, the conformational diversity and dynamics of Aβ42 (the most aggregation-prone and the second-most abundant isoform of Aβ (4,5)) and the effect of small molecules on such dynamics. The molar excess of small molecules with respect to Aβ42 was lower in the simulations (100-fold) than in the experiments (1000-fold), but it ensured sufficient interactions with the peptide (see Supplementary Note 1). Some of the key parameters to consider in any MD simulation are (i) the starting conformation, (ii) the MD technique and its length, and (iii) the force field. For the starting conformation, we chose a structure of the full-length peptide obtained from liquid state NMR (PDB ID 1Z0Q; (59) see Supplementary Note 2 and Figure S1). Because of its enhanced ability to sample events occurring in longer timescales, (60−62) we applied adaptive sampling. This method consists of several MD trajectories simulated in parallel and over multiple consecutive epochs, in an adaptive approach. The MDs from each epoch are iteratively seeded from selected snapshots from previous MDs, according to a predefined criterion. This criterion defines a feature (also called metric or collective variable), and the objective is to maximize the variability of that feature sampled in the overall simulation (in this case, the secondary structures). (41,63) Based on the literature, (64) we explored the AMBER ff14SB (65) (hereafter termed A14SB) and CHARMM36m (42) (C36m) force fields as the ones likely to provide reasonable ensembles to study Aβ42. Notably, C36m was developed specifically for intrinsically disordered proteins and has already been used with Aβ42. (35) We tested different combinations of parameters in three adaptive sampling protocols and compared the results to the initial structure, experimental data, (59,66) and previous reports. (8) The goal was to obtain conformations of Aβ42 diverging from the initial NMR structure (membrane-like environment) and to reach average secondary structure ratios that approximate the experimental ones (in aqueous environment). The selected protocol used the C36m force field and A14SB was discarded (protocol C; see Supplementary Note 2, Table S1, and Figures S2–S4). The respective MD ensembles seemed to be well converged (Figure S5).

Secondary Structure Content in Simulations of Free Aβ42 and Aβ42 with Ligands

To compare the simulations of Aβ42 alone and in the presence of an excess of TMP and SPA (Figure 1A), we first analyzed the global secondary structure content of the peptide in the three systems (Figure 1B). In the adaptive simulations of free Aβ42, the peptide showed a larger ratio of coils (77.5%), followed by the α-helices (16.8%) and finally the β-strands (5.7%). In the presence of TMP, the α-helix content of Aβ42 peptide increased by 11.1 p.p. to 27.9%, while the ratio of β-strands remained unchanged (5.8% vs 5.7%). In the presence of SPA, the differences in the secondary structure were more striking. In this case, the content of α-helices was nearly the same as in the original NMR structure (41.6% vs 42.1%), the ratio of coils was slightly lower (56.1% vs 57.9%), and the β-strands were half of those in free Aβ42 (2.3% vs 5.7%). This remarkable result suggests a strong effect of SPA in preserving the α-helical structures of Aβ42.
We analyzed the secondary structures in more detail, dissecting the different propensities by the sequence residues (Figure 1C). The results showed that Aβ42 could adopt a coiled structure over its entire sequence, with the highest fractions in the N-terminal residues 1–8. Helical structures were most significant for residues 10–20, with α-helical structures near and above 40% and decreasing in further residues. The β-strands were the least frequent element, present at the C-terminal tail of the peptide (residues 30–41) and, to a lesser degree, also around residues 2–8 and 17–20. This is in agreement with Tomaselli et al., who reported the formation of an antiparallel β-sheet made of two β-strands containing amino acids 18–22 and 37–41. (59) TMP had little effect on the secondary structure distribution, only slightly increasing the frequency of helical structures in the regions that already had a propensity for it (residues 9–28) and reducing the β-strands in the N-terminal residues 2–8. However, the inclusion of SPA resulted in a substantial reduction of the β-strand content in residues 2–20 and 30–41 and in a significant increase of helical propensity in residues 9–28 and 30–37. Thus, we observed that both studied Aβ modulators (TMP and SPA) could increase the regular structures, specifically protecting the α-helix content of the Aβ42 peptide. The effect was notably stronger with SPA, which also prevented or slowed down the transitions from helices into coils and β-strands.
We further analyzed the different MD ensembles and calculated the radius of gyration (Rg) to assess the compactness of the Aβ42 peptide in the three systems. We found that the free Aβ42 alone had a significantly (with p value < 10–4 from the t-test) broader and more skewed distribution of Rg (average Rg = 14.2 ± 4.3 Å) than in the presence of TMP or SPA (Rg = 13.3 ± 3.1 and 11.8 ± 2.1 Å, respectively; Figure 1D). This indicates that the free Aβ42 had a population of extended conformations that was not found in the presence of TMP or SPA. SPA showed a particularly strong effect on shifting Aβ42 toward more compact conformations, compared to the other two systems. Interestingly, Löhr and coworkers recently reported an aggregation inhibitor that presented the opposite effect and stabilized the extended, higher-entropy conformations of Aβ42. (67)

Effects of Ligands on the Evolution of Secondary Structure Elements Over Time

To understand the evolution of secondary structure elements in the adaptive sampling simulations, we first performed the time-based alignment and concatenation of the MDs (Supplementary Note 3 and Figure S6). We computed the evolution of the mean secondary structure content along the continuous simulation time of the aligned and concatenated simulations (Figure 1E). We observed that the different secondary structure ratios evolved quickly in the free Aβ42, decreasing for α-helices and increasing for coils and β-strands. In the presence of TMP, those values changed similarly but more slowly, while SPA induced the slowest changes. Classical MDs showed similar trends toward the apparition of coils and strands over time. However, the capacity of the small molecules to preserve helical elements was not as pronounced as in adaptive-sampling MDs (Supplementary Note 4, Figures S7–S9, Table S2). We can speculate that performing longer simulation times might result in a further decrease in the levels of α-helices and an increase of β-strands.

Conformational Analysis of Ligand Effects Using Markov State Models

Initially, we tried to construct conventional Markov state models (MSMs) to analyze the adaptive sampling simulations and characterize the conformational states of Aβ42. Different metrics and settings were tested, namely, the RMSD of the Cα atoms, the secondary-structure, the self-distance of all Cα atoms, and combinations of those metrics (Supporting Information and Methods). However, none of these analyses produced reliable models (see example in Figures S10–S12), so we decided to use the recently published method for MSM construction using artificial neural networks. We further extended that method with new analyses, which proved highly useful for comparing different systems and improving the interpretability of the results.

Construction of Variational Markov State Models

We approached the construction of MSMs with VAMPnet (16) by testing several lag times (25, 50, 75, and 100 ns) and different numbers of Markov states (2, 3, 4, and 5). Since we are interested in identifying the major differences among the three systems (free Aβ42, Aβ42 + TMP, Aβ42 + SPA), we prioritized the characterization of a few major macrostates rather than many microstates. For this reason, we explored only a relatively small number of states, as done previously by Löhr et al. (17) According to the implied time scales plots (Figure S13) and the Chapman–Kolmogorov tests (Figure S14), we selected τ = 25 ns as the final lag time. By evaluating the impact of the additional states on the change in the frame classification (Figure S15), together with considering the transition rates for each state, we decided to use the 3-state MSM for all the studied systems. Using the selected parameters, we re-estimated the MSMs for MD simulations generated by protocol C. We first constructed 16 subsets of data by gradual addition of epochs to the training and validation data. From the models, we calculated the exact transition probabilities, mean first-passage times, and transition rates (Figure S16), as well as the respective structural propensities (Figures 2A and S17). Finally, we verified that additional data did not significantly affect the estimated implied time scales and that the size of our data sets was thus sufficient for VAMPnet training (Figure S18).

Evaluation of the Effect of Using the Soft versus the Hard Assignment

Interestingly, we found the models to be quite certain about the classification of frames into the learned states, thus diminishing the differences between the hard and soft assignment. For free Aβ42, Aβ42 + TMP, and Aβ42 + SPA, we found 99%, 99%, and 98% of the frames, respectively, to be classified into one of the states with probability higher than 95%.

Alignment of Learned States Across Systems with and without Ligands

To automatically detect similar conformational states across different systems and compare the estimated MSMs, we developed and applied a novel alignment method. This method aligns different states, by minimizing the global cost of alignment of MSM ensembles and produces alignment costs for each pair of matched states Te (see Alignment of learned states). To distinguish truly aligned states from those without a counterpart in the other system, we considered two states as aligned only if their alignment cost was lower than the threshold Te = 6 (see Supplementary Note 5). This threshold was selected empirically by comparing the visualized structures (Figure 2A), the secondary structure content, and contact maps (Figure S17) of the states proposed for mutual alignment. This approach allowed us to find two similar states between free Aβ42 and Aβ42 + TMP (states 1 and 2), and one similar state between free Aβ42 and Aβ42 + SPA (state 1; see Figure S19).

Comparison of Learned States Across Systems with and without Ligands

The evolution and kinetics of the constructed MSMs for the studied systems are shown in Figure 2, as well as a representative ensemble of structures for every state. The free Aβ42 system (Figure 2, left) was characterized by a sparsely populated source state (state 1, pink, 10% equilibrium probability), a dominant sink state (state 2, orange, 86% equilibrium probability), and a metastable transition state between them that was the least populated of all (state 3, green, 4% equilibrium probability). The kinetic roles (source and sink) were derived from the transition kinetic rates and the mean first-passage times, and from the secondary structure contents of each state. Hence, the source state (1, pink), with the structural content most resembling the starting NMR structure (ca. 58% coil, 40% α-helices, and 2% β-strands), converted fast into the sink state (2, orange; TM = 2.6 μs), and could be reasonably formed from the transition state (3, green; TM = 14.6 μs). The sink state was characterized by disorder, with the highest contents of coils and β-strands and the lowest contents of α-helices. The transition state represented a middle point in terms of secondary structure content, and it converted faster into the source or sink states than it was formed. This kinetic ensemble is in good agreement with the results previously described by Löhr et al. for the monomeric Aβ42, namely, in terms of microsecond transition times between the states, the presence of one dominant state that was mainly disordered, and the inexistence of long-lived folded states. (17)
According to our alignment method, the Aβ42 + TMP system (Figure 2, center) had counterparts in the free Aβ42, namely, the disordered sink state (orange) and the helical-rich source state (pink). The equilibrium probability of the sink was slightly reduced (state 2, orange, 75%), and the more helical source was slightly increased (state 1, pink, 12%). A new transition state appeared in this system (lime, 14% equilibrium probability), with intermediate secondary structure propensities and a higher α-helical content compared to the transition state in the free Aβ42. Perhaps for this reason, the cost of their alignment was above the selected threshold (Figure S19), and the state was thus considered a newly formed state. This was supported by the visualized structures (Figure 2A) and the detailed secondary structure and contact maps for the respective states (Figure S17). Overall, the MSM ensemble for the Aβ42 + TMP system showed higher variability of the equilibrium distribution. Interestingly, the kinetics of this system was rather similar to that of the free Aβ42 but significantly slower, generally with higher transition mean-times. As in the case of the free Aβ42, the formation rates of the disordered sink state 1 were higher than its conversion into the other states.
The simulations of Aβ42 + SPA produced a clearly distinct MSM (Figure 2, right), with the equilibrium distribution more uniform than in the other two systems. Furthermore, the confidence intervals of the equilibrium probabilities were even wider, and the free energy landscape appeared more homogeneous, implying that the states in Aβ42 + SPA were less clearly defined compared to the other systems. According to our alignment procedure, only the source state of Aβ42 + SPA (state 1, pink, 46% equilibrium probability) found its counterpart in the free Aβ42 system. The secondary structure content of this state was similar to the corresponding one in the free Aβ42 and the starting NMR structure (61% coil, 36% α-helices, and 3% β-strands). It is noteworthy how the addition of SPA disrupted the kinetic ensemble: the remaining two states differed significantly from those of the free Aβ42, as demonstrated by the high alignment costs (Figure S19) and the secondary structure contents. Strikingly, in contrast with the previous two systems, the unstructured sink state disappeared as the two new unmatched states with high α-helix contents occurred. This was especially the case of state 2 (blue, 23% equilibrium probability), which contained more α-helices (48.7%) and fewer coils (50.6%) than the initial NMR structure (42.1% and 57.9%, respectively). This state 2 evolved over time into state 3 (purple, 31% equilibrium probability; Figure 2B), which had the fastest conversion to the source state, and thus could hardly be considered a “sink” state. All three states interconverted between each other rather quickly, with TM values in the low microsecond range, suggesting a dynamical metastable equilibrium around the source state. All these observations are supported by the study of the time-evolution of the states in the different simulations (Supplementary Note 6, Figure S20).
We also calculated the radius of gyration (Rg) of the different states (Figure S21). The free Aβ42 system presented the largest dispersion of Rg values, with its states showing peaks at higher values, while for Aβ42 + SPA, all the states displayed low Rg dispersion and peaks at low values (between 10.6 and 11.0 Å). This observation is in agreement with the Rg calculations on the global MD ensembles, discussed above, suggesting that the systems differ intrinsically in their degrees of structural order and compactness.

Characterization of Learned Conformational States via Network Gradients

To better understand the differences between the states in each MSM, we attempted to interpret the molecular features that were determinant to the assignment of each state. For that, we visualized the ensemble-averaged gradients of the state assignment probabilities obtained from the learned neural network models. Figure 3 shows that the elements near the diagonal were the most important for the classification into the respective states. As our representation does not consider the distances of the residues to their first and second neighbors in the primary sequence, the colored pixels along the empty diagonal in each heatmap correspond to the distances of the residues to their third neighbors in the sequence. Since this roughly corresponds to the length of one turn in an α-helix (ca. 4 residues), the consistently red or blue color of the two subdiagonals closest to the white diagonal to the presence or absence of helices, respectively. This interpretation is also supported by the average secondary structure content per residue and the average contact maps (Figure S17).

Figure 3

Figure 3. Gradients of the state assignment probabilities of the learned variational Markov state models. Each 42 × 42 heatmap shows the ensemble-averaged gradients of the model probabilities for the corresponding system and state with respect to the input inter-residue Cα distances. The color indicates how the probability of the particular state would change for an input frame if the distance between the particular pair of residues increased: blue indicates that the probability of the state assignment would increase if the distance between the Cα atoms increased whereas red indicates that the probability would increase if that distance decreased. The presented visualizations correspond to ensemble-averaged gradients evaluated and aggregated over 10,000 randomly selected simulation frames. Columns: MSMs for the free Aβ42 (left), Aβ42 + TMP (middle), and Aβ42 + SPA (right) systems. Rows: states 1 (top), 2 (middle), and 3 (bottom) of each model.

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For the free Aβ42 system, the peptide residues around positions 10–25 seem to be crucial for the state classification. The results in the free Aβ42 state 1 heatmap imply that if the red colored residues in this region got closer to their third and fourth sequence neighbors in a particular snapshot, the probability of classifying that snapshot into state 1 (source state) would increase. This means that state 1 prefers a helical conformation in this region. On the contrary, the “state 2” heatmap shows that the probability of classification into state 2 would increase if the blue-colored residues in this region got farther from their third and fourth sequence neighbors, i.e., state 2 (sink state) prefers disorder in this region. The classification into state 3 relies on the same region (residues 10–25) but is split into two parts: residues 13–19 (red) and the rest (gray). This implies that state 3 (transition state) prefers a short helix only in residues 13–19.
For the Aβ42 + TMP system, the corresponding heatmaps show that the presence (red) or lack (blue) of a helix at positions 29–36 are important for distinguishing between states 1 and 3, respectively, while state 2 can be discriminated based on the lack of a helix at positions 10–25. For Aβ42 + SPA, the lack (blue) or presence (red) of a helix at positions 3–12 is relevant for discriminating states 1 and 3, respectively. State 2 differs by the presence of two helices at positions 20–27 and 30–35 (red) as well as by long distances between residues in positions 10–17 (blue pattern).
The states can be compared in more detail by evaluating the gradients on sets of state-specific frames (Figure S22). Conversely, the gradient matrices can also be aggregated by residue into simpler but still very informative plots (Figure S23). These can help to readily assess the most influential regions defining the states, compare different systems, and potentially cross-validate the results with other residue-based analyses, e.g., from experimental data (see below).

Molecular Interactions

Ligand–Peptide Interactions

The interactions of TMP and SPA with Aβ42 were assessed by the linear interaction energy (LIE) (45) and computed for all the 100 ligand molecules with each peptide residue during the adaptive sampling simulations. For this purpose, all the snapshots in the simulations were used. The electrostatic component (ΔGbindelec) dominated the interactions formed by Aβ42 with both TMP and SPA, overshadowing the van der Waals component (Figure S24). Those interactions were, on average, much stronger with the charged residues (Figures 4 and S25). This was expected, considering that both TMP and SPA bear two charges at physiological pH, separated by only a short alkyl chain (positive and negative charges in TMP, and two negative charges in SPA). SPA showed both attractive and repulsive interactions (respectively, positive and negative ΔGbindelec; Figure 4); TMP showed mostly favorable interactions (negative ΔGbindelec; Figure S25). The absolute mean interaction energies were also higher with SPA (from −114 to 71 kcal/mol) than with TMP (from −50 to 0 kcal/mol). Moreover, the interactions were highly variable due to the rapid exchange of the TMP and SPA molecules, which formed unspecific short-lived interactions with Aβ42. This explains the large populations of snapshots with a lower range of interaction energies and the smaller populations of snapshots with strong interactions with the charged residues.

Figure 4

Figure 4. Interactions of SPA with Aβ42 studied by molecular dynamics. A) Violin plot of the binding energy of SPA with each residue of Aβ42. The electrostatic component (ΔGbindelec) was calculated for all the 100 molecules in every snapshot of the adaptive simulation of Aβ42 + SPA. The plot shows the distribution of the energy values; the black dots show the mean values; the y-axis uses a quasi-logarithmic scale based on the inverse hyperbolic sine to highlight the higher absolute values. The residue labels are colored by charge: black for neutral, blue for positive, and red for negative. The chemical structure of SPA is shown in the upper-right corner. B) Structure of Aβ42 with the main interacting residues. Aβ42 is shown as the putty cartoon, and the main interacting residues are represented by sticks (structure from PDB ID 1Z0Q). The colors reflect the mean ΔGbindelec (in kcal/mol) and range from the most positive (blue) to the most negative (red) values obtained for SPA.

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Although TMP and SPA have quite similar structures, the global effects of SPA on Aβ42 were more striking than those of TMP. This is probably due to the fact that SPA has a double negative charge, which reverses the charge of positive groups it interacts with. Conversely, TMP is zwitterionic (with positive and negative charges) and thus preserves the charge around the interacting residues. A comprehensive comparison of the properties of TMP and SPA and their effects on the simulations of Aβ42 is presented in Table S3.

Intramolecular Interactions of Aβ42

The interactions within the Aβ42 peptide were calculated using the molecular mechanics/generalized Born solvent accessible surface area (MM/GBSA) method. (47,48) Interestingly, the electrostatic energy prevailed over the van der Waals, but the polar solvation energy outweighed all the other contributions to the internal free energy of Aβ42 (Table S4 and Supplementary Note 8). The peptide was more stable (lower mean total free energy) in the presence of TMP or SPA than alone in solution. This stabilization was mainly due to the solvation energy, which indicates a higher exposure of polar residues to the solvent than the free Aβ42. This effect is concomitant with an increase of the internal hydrophobic contacts in the presence of TMP or SPA, which is consistent with an increase of the compactness of the peptide, according to the Rg values reported above (Figure 1D). Intramolecular salt bridges E22-K28 and D23-K28 have been reported to be important for the conformational transition, oligomerization, and toxicity of Aβ42. (68,69) Analysis of the three ensembles showed that these salt bridges occurred considerably less often in the presence of TMP than in the free Aβ42, and even less with SPA (Figure S26). This suggests a lower propensity of Aβ42 to form oligomers in the presence of those small molecules. Due to their charged moieties, TMP and SPA induce electrostatic dispersion on the residues involved in the salt bridges, thus weakening those interactions (Table S3). Similar observations have previously been reported for apolipoprotein E (ApoE) interacting with SPA. (70)

Experimental Validation

To validate our computational findings described above, we experimentally characterized the conformations of N-methionine-Aβ42 (N-Met-Aβ42) alone and in the presence of TMP and SPA. The presence of N-terminal methionine was necessary for the Aβ42 recombinant expression and does not influence its aggregation behavior. This is demonstrated by the routine use of N-Met-Aβ42 in aggregation studies. (71,72) Circular dichroism (CD) of N-Met-Aβ42 in aqueous buffer revealed that the peptide was mainly disordered (68% of coils, 29% of β-strands, and 3% of α-helices; Figures 5A and S27A). To replicate the NMR structure obtained in 20% (v/v) of hexafluoroisopropanol (HFIP), used herein as the starting conformation for the computational analysis, we titrated the N-Met-Aβ42 with increasing concentrations of HFIP. At 20% HFIP, the secondary structure content of N-Met-Aβ42 was heavily changed in favor of the α-helices, in agreement with the literature (59) (Figure S28). We repeated the titrations in the presence of a 1000-fold excess of TMP or SPA. In all cases, no major changes in the CD spectra were induced by the small molecules during the titrations (Figures S27A and S28). N-Met-Aβ42 remained mostly disordered at 0% HFIP and had almost similar helical and strand content at 20% HFIP, independently of the presence of TMP or SPA. This is not in agreement with the computational results, which predicted a significant increase of the helical content of Aβ42 with the small molecules, especially with SPA.

Figure 5

Figure 5. Experimental validation of computational data using biophysical techniques. A) Circular dichroism spectra of Aβ42. N-Met-Aβ42 (37 μM) was studied in the absence (black) or presence of a 1000-fold excess of TMP (green), SPA (blue), or 20% HFIP (dashed curves). The curves for SPA were trimmed below 205 nm to remove the signal from SPA. B) FTIR spectra of Aβ42. N-Met-Aβ42 (60 μM) was studied in the absence (black) or presence of a 1000-fold excess of TMP (green) or SPA (blue). The bars represent the standard deviations from successive acquisitions. The second derivatives are drawn as dashed curves. Offset was shifted to improve readability. C) NMR analysis of Aβ42. 1H–15N HMQC NMR spectra of 15N-labeled N-Met-Aβ42 were determined alone (black, 69 μM) and in the presence of a 1000-fold excess of TMP (green, 58 μM) or SPA (blue, 55 μM). Assignment is given for free N-Met-Aβ42 (black); the assignment of His6 was ambiguous, thus no CSP was calculated for this residue. D) NMR chemical shift perturbation (CSP) of Aβ42. N-Met-Aβ42 in the presence of a 1000-fold excess of TMP (green), or SPA (blue) with respect to the free N-Met-Aβ42. The red dashed line represents the threshold for significance, taken as the standard deviation of all CSPs. E) Summary of the effects of small molecules on Aβ42 conformations studied by three different biophysical techniques: - indicates that no significant effect was detected, + indicates a mild effect, and ++ a stronger effect.

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To determine whether the molecules induced subtle changes in secondary structure that are below the resolution limit of CD spectroscopy, we analyzed the N-Met-Aβ42 in buffer and in the presence of the small molecules using Fourier-transformed infrared spectroscopy (FTIR). Based on the secondary structure deconvolution of the amide I bands, (73) the FTIR spectra of free N-Met-Aβ42 and N-Met-Aβ42 + SPA showed fingerprints from both helical (peak at around 1660 cm–1) and strand contributions (peak below 1650 cm–1) (Figures 5B and S27B and S29). At 1000-fold excess of TMP, a shift of the peak wavenumbers was observed (Figure 5B). The spectrum for N-Met-Aβ42 + TMP had one peak centered around 1650 cm–1 instead of 1660 cm–1, which might suggest more random conformation (coils) of N-Met-Aβ42 in the presence of TMP compared to the free peptide. Nonetheless, the large overlap of the two peaks casts doubts on such interpretations. Further remarks on differences in secondary structure propensities are discussed in Supplementary Note 9.
To gain deeper insights into conformational changes of N-Met-Aβ42 upon the addition of the small molecules, we employed nuclear magnetic resonance (NMR). The 1H–15N HMQC spectral fingerprint of N-Met-Aβ42 revealed a narrow distribution in δ(1H) of the backbone amides (from 7.5 to 8.5 ppm), a characteristic of intrinsically disordered peptides (Figures 5C and S30). Using 1H–1H NOESY and 1H–1H–15N NOESY-HMQC spectra, we assigned the spectral fingerprint and computed the secondary structure propensities using chemical shift indexing. (74,75) This method is based on the published NMR statistics, where each residue is expected to have a chemical shift within a certain region of the spectrum that is a function of its local secondary structure. The resulting global secondary structure propensity was much higher in α-helices than what was previously obtained by CD (29.6% vs 3%, respectively; Figure S27A,C). The secondary structure probabilities of the different residues showed the highest β-strand propensity for the C-terminal tail, and the highest helical propensity of residues 15–25 (Figure S27D). This is in agreement with the results from our simulations for the free Aβ42 (Figure 1C). We titrated N-Met-Aβ42 with increasing concentrations of TMP or SPA, up to a 1000-fold excess (Figures 5C and S30) and measured the chemical shift perturbation (CSP) in the 1H–15N HMQC spectral fingerprint (Figure 5D). The threshold for the CSP significance was taken as the standard deviation of all chemical shifts. (76) Only small CSPs were observed when adding SPA, which were not sufficient to indicate a shift in the global secondary structure (Figure S27C). This is not unprecedented, as others have also reported minimal changes in the NMR spectrum of Aβ42 upon the binding of small molecules. (77) CSP was observed across most of the peptide sequence in the presence of SPA, namely in regions 2–7, 11–17, 20, 22–27, and 32–37. Strikingly, these regions correspond to peptide ranges that emerged in the gradient-based analysis of learned conformational states (namely, regions 3–12, 10–17, 20–27, 30–35; Figures 3 and S23). In the presence of SPA, close distances (structural order) between residues 2–7 are characteristic of the transition between states 1 (pink in Figure 2A) and 3 (purple in Figure 2A). Similarly, close distances in residues 22–27 and 32–37 are characteristic hallmarks of state 2 (blue), which is also determined by long distances (disorder) in the range 11–17. It is noteworthy that states 2 and 3 in this system are distinctively different from the other two systems. Thus, gradient-based analysis of learned states was able to pinpoint similar conformational events as the ones captured by NMR. Moreover, regions 22–27 are neighboring the salt bridges between 22 and 28 and 23–28, which are relevant to the conformational transition, oligomerization, and toxicity of Aβ42, (68,69) as pinpointed in the Intramolecular interactions of Aβ42 section.
Finally, we assessed the fibril formation of N-Met-Aβ42 using the well-known thioflavin T (ThT) fluorometric assay with and without the small molecules. We found that neither TMP nor SPA seemed to significantly reduce the N-Met-Aβ42 fibril formation rates, as observed by other groups. (78) This is in contrast with HFIP, which is a known solubilizing agent of Aβ42 and a crude membrane mimetic (59) (Figure S31). In fact, a change in the CD spectrum was observed in the presence of HFIP and either TMP or SPA (Figures 5A,E and S28).

Discussion

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Alzheimer’s disease drug candidate TMP and its metabolite SPA are thought to modify the conformational dynamics of the Aβ42 peptide and decrease its propensity to form toxic oligomers. (33,34) The conformational diversity of Aβ42 has been previously explored by exploiting the variational approach to Markov processes in VAMPnets (16) to construct Markov state models (MSMs), to better capture the slowest processes in MD simulations. (17,67) However, the exact mechanism of action of TMP, and particularly SPA, on Aβ42 was still unclear. To fill this gap, we first applied the variational approach to Markov processes on adaptive sampling MD simulations using VAMPnets, (17) and then ran our newly developed comparative Markov state analysis (CoVAMPnet) pipeline to (1) align the learned conformational states across ensembles of different MSMs, and (2) based on the learned VAMPnet gradients, to characterize these states by the inter-residue distances. The CoVAMPnet alignment method proved a powerful approach to (i) quantitatively compare the different conformational states of Aβ42, (ii) identify which states were preserved across different systems, and (iii) identify which states were unique. The CoVAMPnet gradient-based characterization of the learned ensembles of Markov states utilizes the end-to-end differentiability of the neural network-based MSMs, i.e., a property that the conventional methods for MSM estimation lack. The analysis of gradients allowed us to reason, at the molecular level, which residues are responsible for the assignment to a specific state obtained from the variational Markov state analysis. We expect these newly developed methods, i.e., (i) the alignment of ensembles of variational Markov state models across different systems, and (ii) the gradient-based characterization of learned states, to become valuable for studying the impact of small molecules on the conformational dynamics of intrinsically disordered proteins and peptides. (79,80)
The newly developed analyses were applied to MD simulations of Aβ42. It is known that the sampling protocol (namely, the force field, the length of the simulations, the adaptive metrics, and the simulation method) can highly influence the global results. (81,82) This is largely due to the intrinsically disordered nature of the Aβ42 peptide, which has a rather shallow energy landscape with many energy minima separated by small energy barriers. (6,79) For this reason, the conformational sampling of Aβ42 remains a challenge. (81,82) Starting from a helix-rich Aβ42 structure, biased toward the conformation in the membrane environment (59,83) (PDB ID 1Z0Q), we identified the most suitable adaptive protocol to simulate Aβ42, according to the secondary structure contents expected in aqueous phase (dominated by coils and β-strands). In this way, we sampled the conformations and transitions occurring immediately after the release of Aβ42 from the transmembrane region to the extracellular fluid. After approximately 64 μs of adaptive MDs, the free Aβ42 diverged substantially from the initial structure, increasing the total amount of random coils and β-strands (as expected) while decreasing the ratio of α-helices, and became closer to experimental values and previous reports. (59,66,84) We identified two regions of Aβ42 that were more prone to form β-strands (mainly residues 2–8, 17–20, and 30–41). The MSMs learned from the variational Markov state analysis revealed that the most populated state of Aβ42 is highly disordered and contains some β-strands. This state is in equilibrium with two other states with higher contents of α-helices, but still bearing mainly coils. These results are in good agreement with recent reports by Löhr et al., obtained from much longer simulation times (315 μs). (17)
The presence of TMP and SPA shifted Aβ42 toward more structured conformations (less coils and higher content of α-helices) and reduced the propensity of regions 2–8, 17–20, and 30–41 to form β-strands. This behavior is similar to what has previously been reported for some aggregation inhibitors (85−87) and is in contrast with some others. (67) The variational Markov state analysis showed that TMP and SPA induced a change in the equilibrium distribution and interconversion rates of the Aβ42 conformational states. SPA exerted a much stronger effect, stabilizing new conformational states that were richer in α-helices than in the other systems. Since β-strand structures lead to the formation of β-sheets, the precursors that prompt the oligomerization and fibrillation of Aβ, (2,4,5) these results suggest the potential of TMP and SPA to inhibit or delay both processes. This can be particularly relevant if we consider previous studies suggesting that oligomers may start by the formation of β-hairpins made of β-strands of residues 16–24 and 28–35, (88) and that α-helices in regions 10–21 (84) or 17–21 (89) may prevent the formation of higher oligomers and aggregation. While Aβ42 is preserved in its monomeric form, it should not be harmful until it is cleared from the brain, namely, through the binding to apolipoprotein E (ApoE). (90−92) Our simulations suggest that TMP and SPA may affect the conformational equilibrium of Aβ42 in the brain and prolong its monomeric soluble state, thus allowing to extend the effective time of the clearance mechanisms. Due to their charged terminal moieties, both TMP and SPA formed mainly electrostatic interactions with the charged residues of Aβ42. These interactions were nonspecific and short-lived, but they promoted the exposure of polar residues (similar to a “solvation” effect), induced Aβ42 to be more compact, and weakened intramolecular electrostatic interactions (as previously observed (70)). Importantly, some of the intramolecular salt bridges (E22-K28, D23-K28) considered to promote the formation of β-sheets, aggregation, and neurotoxicity of Aβ42 (68,69,88) were disrupted by the presence of those small molecules. The difference between TMP and SPA in terms of charge distribution (zwitterionic and doubly negative, respectively) is likely the main factor responsible for the overall stronger effects of SPA (see Table S3). The reasons for the stronger stabilization of α-helices by SPA are not clear. However, it may be due to competition of the densely charged ligand with the water molecules, which may lead to preventing their destabilizing action on the peptide, as previously described for a series of ions at higher concentrations. (93)
The CoVAMPnet algorithm developed for identification of structural features in the learned variational MSMs based on network gradients proved useful. We were able to identify the peptide regions with preferential order or disorder in the different states and pinpoint major differences across the different systems. Remarkably, this analysis showed good agreement with the CSPs in the NMR spectra, correctly predicting the peptide regions most affected by the presence of SPA. These computational findings were in agreement with previous studies involving Aβ, TMP, and SPA, namely: (i) the unstructured nature of the peptide, (ii) shift of the Aβ42 conformations by those ligands toward more compact structures, (iii) reduction of the β-strand propensity, and (iv) nonspecific interactions with charged residues. (33−35) Reports also have shown that both small molecules can interact with the soluble Aβ40 or Aβ42, change their dominant conformation, inhibit the formation of oligomers and fibrils, decrease the Aβ-induced neuronal cell death, (25,33,34) and have protective effects in vivo. (30)
We applied several experimental biophysical techniques to validate the computational results described above. Although the experimental outcomes showed only a mild influence of both TMP and SPA on N-Met-Aβ42, several relevant effects were observed (Figure 5E). FTIR revealed slight changes in secondary structure upon the addition of TMP, suggesting higher coil conformation propensity for the peptide. On the other hand, NMR showed a stronger impact of SPA on the 1H–15N NMR spectral fingerprint of N-Met-Aβ42, indicating either direct ligand–peptide interactions, subtle changes in secondary structure, or both. Strikingly, these perturbations were observed in the same peptide regions highlighted by our network gradient analysis. TMP did not produce significant CSPs. Altogether, these results suggest a stronger effect of SPA on Aβ42 than TMP. Yet, the fibril formation kinetics of N-Met-Aβ42 seemed unaffected by TMP or SPA.
The experimental results corroborated several computational findings: (i) the intrinsically disordered Aβ42 interacts with TMP or SPA molecules through many weak interactions, (ii) these interactions induce conformational changes on the peptide, (iii) SPA has stronger influence on Aβ42 than TMP, and (iv) the regions affected could be predicted by the gradient analysis of the learned state probabilities. On the other hand, not all the predictions from our molecular modeling were confirmed experimentally: (i) Aβ42 showed higher β-strand content compared to the computational results, and (ii) TMP and SPA did not change significantly the global secondary structure propensities of Aβ42 and did not prevent fibril formation. The differences in the time scales sampled by the simulations (microseconds) and the experiments (minutes/hours) and the peptide concentration effects may have contributed to this discrepancy. Moreover, the membrane mimetic HFIP modulated the impact of TMP and SPA on N-Met-Aβ42, which may deserve further investigation. An extended discussion of these phenomena is provided in Supplementary Note 10. In further works, the development of specific binders able to stabilize α-helices in the regions of Aβ42 mentioned above could be a better approach for designing drugs targeting the neurotoxic oligomerization of Aβ. The interaction of TMP and SPA with other proteins participating in the amyloid cascade, (94) which has been demonstrated in the case of ApoE (especially ApoE4), (70,95) should also be considered and evaluated in future studies. Particularly, we have recently shown the strong impact of TMP and SPA on ApoE4, shifting its structure and properties toward those of ApoE3 and significantly reducing its aggregation. (70) The observation of significant effects of TMP and SPA on ApoE4, but weaker ones on Aβ, is also important in the context of a recently published paper reporting the existence of five subtypes of AD. (96) All subtypes showed a higher prevalence of the APOE e4 genotype, while only selected ones are characterized by modified levels of Aβ. In the future, it will be interesting to relate this information to the data collected within phase 3 of clinical trials, which will reveal the efficacy of TMP on the different subtypes.
In summary, in this work, we introduced CoVAMPnet to compare and interpret learned MSMs across different systems. CoVAMPnet is composed of two methods: (i) the alignment of Markov state models and (ii) characterization of learned conformational states based on network gradients. The CoVAMPnet approach can be applied to study and compare any related molecular systems and extract valuable information. It can be especially useful to study the impact of small molecules on intrinsically disordered proteins and peptides, whose quantitative analysis can be extremely difficult. Furthermore, we applied CoVAMPnet to study molecular effects of potential anti-Alzheimer’s drugs on hallmark peptide Aβ42. Our computational results suggested that TMP, and particularly SPA, in short dynamic time windows can stabilize structured helical conformations of Aβ42, potentially preventing its oligomerization. In vitro validation confirmed the stronger impact of SPA on Aβ42 and the peptide regions affected by this molecule. However, in long time ranges, the global secondary structure was not significantly modified, neither was the Aβ42 aggregation propensity under the experimental conditions. This suggests the potential existence of additional mechanisms, such as the suppression of ApoE4 aggregation, (81) contributing to the mode of action and the clinical effects of TMP/SPA in AD besides the conformational shift of Aβ42.

Data Availability

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The sampled stripped trajectories and intermediate data, including the trained neural network weights, are available at https://data.ciirc.cvut.cz/public/projects/2023CoVAMPnet/. The code and example data are available at https://github.com/KoubaPetr/CoVAMPnet.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacsau.4c00182.

  • Detailed materials and methods, complementary to the concise descriptions in this main text, Supplementary discussions (Notes 1–10), Supplementary figures: structure of Aβ42 (Figure S1), comparison of the Amber ff14SB and CHARMM36m force fields (Figures S2 and S3), comparison of different adaptive sampling protocols (Figures S4 and S5), temporal alignment and concatenation of the adaptive sampling and classical MDs (Figures S6–S9), conventional Markov state model analysis (Figures S10–S12), variational Markov state analysis using VAMPnets (Figures S13–S18), comparative Markov state model analysis (Figure S19), time-based evolution of the states (Figure S20), radius of gyration by state (Figure S21), characterization of learned conformational states via network gradients (Figures S22 and S23), interactions of Aβ42 with the small molecules (Figures S24–S26), experimental validation (Figures S27–S31), Supplementary tables: comparison of computational protocols for the simulation of Aβ42 (Table S1), analysis of classical MDs (Table S2), summary of the effects of small molecules (Table S3), and intramolecular interactions of Aβ42 (Table S4) (PDF)

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Author Information

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  • Corresponding Authors
    • Stanislav Mazurenko - Loschmidt Laboratories, Department of Experimental Biology and RECETOX, Faculty of Science, Masaryk University, Kamenice 5, Brno 625 00, Czech Republic;  International Clinical Research Center, St. Anne’s University Hospital Brno, Pekarska 53, Brno 656 91, Czech Republic;  Email: [email protected]
    • Josef Sivic - Czech Institute of Informatics, Robotics and Cybernetics, Czech Technical University in Prague, Jugoslavskych partyzanu 1580/3, Dejvice, Praha 6 160 00, Czech Republic;  Email: [email protected]
    • David Bednar - Loschmidt Laboratories, Department of Experimental Biology and RECETOX, Faculty of Science, Masaryk University, Kamenice 5, Brno 625 00, Czech Republic;  International Clinical Research Center, St. Anne’s University Hospital Brno, Pekarska 53, Brno 656 91, Czech Republic;  Orcidhttps://orcid.org/0000-0002-6803-0340;  Email: [email protected]
  • Authors
    • Sérgio M. Marques - Loschmidt Laboratories, Department of Experimental Biology and RECETOX, Faculty of Science, Masaryk University, Kamenice 5, Brno 625 00, Czech Republic;  International Clinical Research Center, St. Anne’s University Hospital Brno, Pekarska 53, Brno 656 91, Czech Republic
    • Petr Kouba - Loschmidt Laboratories, Department of Experimental Biology and RECETOX, Faculty of Science, Masaryk University, Kamenice 5, Brno 625 00, Czech Republic;  Czech Institute of Informatics, Robotics and Cybernetics, Czech Technical University in Prague, Jugoslavskych partyzanu 1580/3, Dejvice, Praha 6 160 00, Czech Republic;  Faculty of Electrical Engineering, Czech Technical University in Prague, Technicka 2, Dejvice, Praha 6 166 27, Czech Republic;  Orcidhttps://orcid.org/0000-0002-9979-4159
    • Anthony Legrand - Loschmidt Laboratories, Department of Experimental Biology and RECETOX, Faculty of Science, Masaryk University, Kamenice 5, Brno 625 00, Czech Republic;  International Clinical Research Center, St. Anne’s University Hospital Brno, Pekarska 53, Brno 656 91, Czech Republic
    • Jiri Sedlar - Czech Institute of Informatics, Robotics and Cybernetics, Czech Technical University in Prague, Jugoslavskych partyzanu 1580/3, Dejvice, Praha 6 160 00, Czech Republic;  Orcidhttps://orcid.org/0000-0002-4704-3388
    • Lucas Disson - Czech Institute of Informatics, Robotics and Cybernetics, Czech Technical University in Prague, Jugoslavskych partyzanu 1580/3, Dejvice, Praha 6 160 00, Czech Republic
    • Joan Planas-Iglesias - Loschmidt Laboratories, Department of Experimental Biology and RECETOX, Faculty of Science, Masaryk University, Kamenice 5, Brno 625 00, Czech Republic;  International Clinical Research Center, St. Anne’s University Hospital Brno, Pekarska 53, Brno 656 91, Czech Republic;  Orcidhttps://orcid.org/0000-0002-6279-2483
    • Zainab Sanusi - Loschmidt Laboratories, Department of Experimental Biology and RECETOX, Faculty of Science, Masaryk University, Kamenice 5, Brno 625 00, Czech Republic;  International Clinical Research Center, St. Anne’s University Hospital Brno, Pekarska 53, Brno 656 91, Czech Republic
    • Antonin Kunka - Loschmidt Laboratories, Department of Experimental Biology and RECETOX, Faculty of Science, Masaryk University, Kamenice 5, Brno 625 00, Czech Republic;  International Clinical Research Center, St. Anne’s University Hospital Brno, Pekarska 53, Brno 656 91, Czech Republic
    • Jiri Damborsky - Loschmidt Laboratories, Department of Experimental Biology and RECETOX, Faculty of Science, Masaryk University, Kamenice 5, Brno 625 00, Czech Republic;  International Clinical Research Center, St. Anne’s University Hospital Brno, Pekarska 53, Brno 656 91, Czech Republic;  Orcidhttps://orcid.org/0000-0002-7848-8216
    • Tomas Pajdla - Czech Institute of Informatics, Robotics and Cybernetics, Czech Technical University in Prague, Jugoslavskych partyzanu 1580/3, Dejvice, Praha 6 160 00, Czech Republic
    • Zbynek Prokop - Loschmidt Laboratories, Department of Experimental Biology and RECETOX, Faculty of Science, Masaryk University, Kamenice 5, Brno 625 00, Czech Republic;  International Clinical Research Center, St. Anne’s University Hospital Brno, Pekarska 53, Brno 656 91, Czech Republic;  Orcidhttps://orcid.org/0000-0001-9358-4081
  • Author Contributions

    S.M.M., P.K., and A.L. contributed equally to this study. CRediT: Sérgio M. Marques conceptualization, data curation, investigation, methodology, validation, visualization, writing-original draft, writing-review & editing; Petr Kouba data curation, methodology, software, validation, writing-original draft; Anthony Legrand data curation, investigation, validation, writing-original draft; Jiri Sedlar conceptualization, methodology, software, visualization, supervision, writing-review & editing; Lucas Disson methodology, software, visualization; Joan Planas-Iglesias data curation, investigation, visualization, writing-original draft; Zainab Sanusi investigation, validation; Antonin Kunka investigation, methodology, validation, writing-original draft; Jiří Damborský conceptualization, funding acquisition, project administration, supervision, writing-review & editing; Tomas Pajdla conceptualization, supervision; Zbyněk Prokop conceptualization, methodology, supervision, writing-review & editing; Stanislav Mazurenko conceptualization, data curation, methodology, supervision, writing-review & editing; Josef Sivic conceptualization, funding acquisition, project administration, supervision, writing-review & editing; David Bednar conceptualization, funding acquisition, project administration, supervision, writing-review & editing.

  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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This work was supported by the Ministry of Education, Youth and Sports of the Czech Republic (grants ESFRI RECETOX RI LM2023069, e-INFRA CZ LM2018140, ESFRI ELIXIR CZ LM2023055, TEAMING CZ CZ.02.1.01/0.0/0.0/17_043/0009632), the European Regional Development Fund under the project IMPACT (reg. no. CZ.02.1.01/0.0/0.0/15_003/0000468), the National Institute for Neurology Research (EXCELES Neuro nr. LX22NPO5107 MEYS), and the European Union (Next Generation EU, SinFonia 814418, TEAMING 857560 and ERC FRONTIER 101097822). Views and opinions expressed are those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them. Petr Kouba is a holder of the Brno Ph.D. Talent scholarship funded by the Brno City Municipality and the JCMM.

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    A review. Conformational changes underpin function and encode complex biomol. mechanisms. Gaining at.-level detail of how such changes occur has the potential to reveal these mechanisms and is of crit. importance in identifying drug targets, facilitating rational drug design, and enabling bioengineering applications. While the past two decades have brought Markov state model techniques to the point where practitioners can regularly use them to glimpse the long-time dynamics of slow conformations in complex systems, many systems are still beyond their reach. In this Perspective, we discuss how including memory (i.e., non-Markovian effects) can reduce the computational cost to predict the long-time dynamics in these complex systems by orders of magnitude and with greater accuracy and resoln. than state-of-the-art Markov state models. We illustrate how memory lies at the heart of successful and promising techniques, ranging from the Fokker-Planck and generalized Langevin equations to deep-learning recurrent neural networks and generalized master equations. We delineate how these techniques work, identify insights that they can offer in biomol. systems, and discuss their advantages and disadvantages in practical settings. We show how generalized master equations can enable the investigation of, for example, the gate-opening process in RNA polymerase II and demonstrate how our recent advances tame the deleterious influence of statistical underconvergence of the mol. dynamics simulations used to parameterize these techniques. This represents a significant leap forward that will enable our memory-based techniques to interrogate systems that are currently beyond the reach of even the best Markov state models. We conclude by discussing some current challenges and future prospects for how exploiting memory will open the door to many exciting opportunities.
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  12. 12
    Noé, F.; Wu, H.; Prinz, J.-H.; Plattner, N. Projected and Hidden Markov Models for Calculating Kinetics and Metastable States of Complex Molecules. J. Chem. Phys. 2013, 139 (18), 184114,  DOI: 10.1063/1.4828816
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    12
    Projected and hidden Markov models for calculating kinetics and metastable states of complex molecules
    Noe, Frank; Wu, Hao; Prinz, Jan-Hendrik; Plattner, Nuria
    Journal of Chemical Physics (2013), 139 (18), 184114/1-184114/17CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Markov state models (MSMs) have been successful in computing metastable states, slow relaxation timescales and assocd. structural changes, and stationary or kinetic exptl. observables of complex mols. from large amts. of mol. dynamics simulation data. However, MSMs approx. the true dynamics by assuming a Markov chain on a clusters discretization of the state space. This approxn. is difficult to make for high-dimensional biomol. systems, and the quality and reproducibility of MSMs has, therefore, been limited. Here, we discard the assumption that dynamics are Markovian on the discrete clusters. Instead, we only assume that the full phase-space mol. dynamics is Markovian, and a projection of this full dynamics is obsd. on the discrete states, leading to the concept of Projected Markov Models (PMMs). Robust estn. methods for PMMs are not yet available, but we derive a practically feasible approxn. via Hidden Markov Models (HMMs). It is shown how various mol. observables of interest that are often computed from MSMs can be computed from HMMs/PMMs. The new framework is applicable to both, simulation and single-mol. exptl. data. We demonstrate its versatility by applications to educative model systems, a 1 ms Anton MD simulation of the bovine pancreatic trypsin inhibitor protein, and an optical tweezer force probe trajectory of an RNA hairpin. (c) 2013 American Institute of Physics.
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  13. 13
    Suárez, E.; Wiewiora, R. P.; Wehmeyer, C.; Noé, F.; Chodera, J. D.; Zuckerman, D. M. What Markov State Models Can and Cannot Do: Correlation versus Path-Based Observables in Protein-Folding Models. J. Chem. Theory Comput. 2021, 17 (5), 3119– 3133,  DOI: 10.1021/acs.jctc.0c01154
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    Dominic, A. J.; Sayer, T.; Cao, S.; Markland, T. E.; Huang, X.; Montoya-Castillo, A. Building Insightful, Memory-Enriched Models to Capture Long-Time Biochemical Processes from Short-Time Simulations. Proc. Natl. Acad. Sci. U. S. A. 2023, 120 (12), e2221048120  DOI: 10.1073/pnas.2221048120
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    Wehmeyer, C.; Noé, F. Time-Lagged Autoencoders: Deep Learning of Slow Collective Variables for Molecular Kinetics. J. Chem. Phys. 2018, 148 (24), 241703,  DOI: 10.1063/1.5011399
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    Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics
    Wehmeyer, Christoph; Noe, Frank
    Journal of Chemical Physics (2018), 148 (24), 241703/1-241703/9CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Inspired by the success of deep learning techniques in the phys. and chem. sciences, we apply a modification of an autoencoder type deep neural network to the task of dimension redn. of mol. dynamics data. We can show that our time-lagged autoencoder reliably finds low-dimensional embeddings for high-dimensional feature spaces which capture the slow dynamics of the underlying stochastic processes - beyond the capabilities of linear dimension redn. techniques. (c) 2018 American Institute of Physics.
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  16. 16
    Mardt, A.; Pasquali, L.; Wu, H.; Noé, F. VAMPnets for Deep Learning of Molecular Kinetics. Nat. Commun. 2018, 9 (1), 5,  DOI: 10.1038/s41467-017-02388-1
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    16
    VAMPnets for deep learning of molecular kinetics
    Mardt Andreas; Pasquali Luca; Wu Hao; Noe Frank
    Nature communications (2018), 9 (1), 5 ISSN:.
    There is an increasing demand for computing the relevant structures, equilibria, and long-timescale kinetics of biomolecular processes, such as protein-drug binding, from high-throughput molecular dynamics simulations. Current methods employ transformation of simulated coordinates into structural features, dimension reduction, clustering the dimension-reduced data, and estimation of a Markov state model or related model of the interconversion rates between molecular structures. This handcrafted approach demands a substantial amount of modeling expertise, as poor decisions at any step will lead to large modeling errors. Here we employ the variational approach for Markov processes (VAMP) to develop a deep learning framework for molecular kinetics using neural networks, dubbed VAMPnets. A VAMPnet encodes the entire mapping from molecular coordinates to Markov states, thus combining the whole data processing pipeline in a single end-to-end framework. Our method performs equally or better than state-of-the-art Markov modeling methods and provides easily interpretable few-state kinetic models.
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    Löhr, T.; Kohlhoff, K.; Heller, G. T.; Camilloni, C.; Vendruscolo, M. A Kinetic Ensemble of the Alzheimer’s Aβ Peptide. Nat. Comput. Sci. 2021, 1 (1), 71– 78,  DOI: 10.1038/s43588-020-00003-w
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    Ghorbani, M.; Prasad, S.; Klauda, J. B.; Brooks, B. R. GraphVAMPNet, using graph neural networks and variational approach to Markov processes for dynamical modeling of biomolecules. J. Chem. Phys. 2022, 156 (18), 184103,  DOI: 10.1063/5.0085607
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    18
    GraphVAMPNet, using graph neural networks and variational approach to Markov processes for dynamical modeling of biomolecules
    Ghorbani, Mahdi; Prasad, Samarjeet; Klauda, Jeffery B.; Brooks, Bernard R.
    Journal of Chemical Physics (2022), 156 (18), 184103CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Finding a low dimensional representation of data from long-timescale trajectories of biomol. processes, such as protein folding or ligand-receptor binding, is of fundamental importance, and kinetic models, such as Markov modeling, have proven useful in describing the kinetics of these systems. Recently, an unsupervised machine learning technique called VAMPNet was introduced to learn the low dimensional representation and the linear dynamical model in an end-to-end manner. VAMPNet is based on the variational approach for Markov processes and relies on neural networks to learn the coarse-grained dynamics. In this paper, we combine VAMPNet and graph neural networks to generate an end-to-end framework to efficiently learn high-level dynamics and metastable states from the long-timescale mol. dynamics trajectories. This method bears the advantages of graph representation learning and uses graph message passing operations to generate an embedding for each datapoint, which is used in the VAMPNet to generate a coarse-grained dynamical model. This type of mol. representation results in a higher resoln. and a more interpretable Markov model than the std. VAMPNet, enabling a more detailed kinetic study of the biomol. processes. Our GraphVAMPNet approach is also enhanced with an attention mechanism to find the important residues for classification into different metastable states. (c) 2022 American Institute of Physics.
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    Liu, B.; Xue, M.; Qiu, Y.; Konovalov, K. A.; O’Connor, M. S.; Huang, X. GraphVAMPnets for Uncovering Slow Collective Variables of Self-Assembly Dynamics. J. Chem. Phys. 2023, 159 (9), 094901,  DOI: 10.1063/5.0158903
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    Mardt, A.; Hempel, T.; Clementi, C.; Noé, F. Deep Learning to Decompose Macromolecules into Independent Markovian Domains. Nat. Commun. 2022, 13 (1), 7101,  DOI: 10.1038/s41467-022-34603-z
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    Deep learning to decompose macromolecules into independent Markovian domains
    Mardt, Andreas; Hempel, Tim; Clementi, Cecilia; Noe, Frank
    Nature Communications (2022), 13 (1), 7101CODEN: NCAOBW; ISSN:2041-1723. (Nature Portfolio)
    The increasing interest in modeling the dynamics of ever larger proteins has revealed a fundamental problem with models that describe the mol. system as being in a global configuration state. This notion limits our ability to gather sufficient statistics of state probabilities or state-to-state transitions because for large mol. systems the no. of metastable states grows exponentially with size. In this manuscript, we approach this challenge by introducing a method that combines our recent progress on independent Markov decompn. (IMD) with VAMPnets, a deep learning approach to Markov modeling. We establish a training objective that quantifies how well a given decompn. of the mol. system into independent subdomains with Markovian dynamics approximates the overall dynamics. By constructing an end-to-end learning framework, the decompn. into such subdomains and their individual Markov state models are simultaneously learned, providing a data-efficient and easily interpretable summary of the complex system dynamics. While learning the dynamical coupling between Markovian subdomains is still an open issue, the present results are a significant step towards learning Ising models of large mol. complexes from simulation data.
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    Chen, W.; Sidky, H.; Ferguson, A. L. Nonlinear Discovery of Slow Molecular Modes Using State-Free Reversible VAMPnets. J. Chem. Phys. 2019, 150 (21), 214114,  DOI: 10.1063/1.5092521
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    21
    Nonlinear discovery of slow molecular modes using state-free reversible VAMPnets
    Chen, Wei; Sidky, Hythem; Ferguson, Andrew L.
    Journal of Chemical Physics (2019), 150 (21), 214114/1-214114/16CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    The success of enhanced sampling mol. simulations that accelerate along collective variables (CVs) is predicated on the availability of variables coincident with the slow collective motions governing the long-time conformational dynamics of a system. It is challenging to intuit these slow CVs for all but the simplest mol. systems, and their data-driven discovery directly from mol. simulation trajectories has been a central focus of the mol. simulation community to both unveil the important phys. mechanisms and drive enhanced sampling. In this work, we introduce state-free reversible VAMPnets (SRV) as a deep learning architecture that learns nonlinear CV approximants to the leading slow eigenfunctions of the spectral decompn. of the transfer operator that evolves equil.-scaled probability distributions through time. Orthogonality of the learned CVs is naturally imposed within network training without added regularization. The CVs are inherently explicit and differentiable functions of the input coordinates making them well-suited to use in enhanced sampling calcns. We demonstrate the utility of SRVs in capturing parsimonious nonlinear representations of complex system dynamics in applications to 1D and 2D toy systems where the true eigenfunctions are exactly calculable and to mol. dynamics simulations of alanine dipeptide and the WW domain protein. (c) 2019 American Institute of Physics.
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    Kleiman, D. E.; Shukla, D. Active Learning of the Conformational Ensemble of Proteins Using Maximum Entropy VAMPNets. J. Chem. Theory Comput. 2023, 19 (14), 4377– 4388,  DOI: 10.1021/acs.jctc.3c00040
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    Mardt, A.; Noé, F. Progress in Deep Markov State Modeling: Coarse Graining and Experimental Data Restraints. J. Chem. Phys. 2021, 155 (21), 214106,  DOI: 10.1063/5.0064668
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    Tolar, M.; Abushakra, S.; Hey, J. A.; Porsteinsson, A.; Sabbagh, M. Aducanumab, Gantenerumab, BAN2401, and ALZ-801─the First Wave of Amyloid-Targeting Drugs for Alzheimer’s Disease with Potential for near Term Approval. Alzheimer’s Res. Ther. 2020, 12 (1), 95,  DOI: 10.1186/s13195-020-00663-w
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    Gervais, F.; Paquette, J.; Morissette, C.; Krzywkowski, P.; Yu, M.; Azzi, M.; Lacombe, D.; Kong, X.; Aman, A.; Laurin, J. Targeting Soluble Aβ Peptide with Tramiprosate for the Treatment of Brain Amyloidosis. Neurobiol. Aging 2007, 28 (4), 537– 547,  DOI: 10.1016/j.neurobiolaging.2006.02.015
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    25
    Targeting soluble Aβ peptide with Tramiprosate for the treatment of brain amyloidosis
    Gervais, Francine; Paquette, Julie; Morissette, Celine; Krzywkowski, Pascale; Yu, Mathilde; Azzi, Mounia; Lacombe, Diane; Kong, Xianqi; Aman, Ahmed; Laurin, Julie; Szarek, Walter A.; Tremblay, Patrick
    Neurobiology of Aging (2007), 28 (4), 537-547CODEN: NEAGDO; ISSN:0197-4580. (Elsevier)
    Amyloid β-peptide (Aβ) is a major constituent of senile plaques in Alzheimer's disease (AD). Neurotoxicity results from the conformational transition of Aβ from random-coil to β-sheet and its oligomerization. Among a series of ionic compds. able to interact with sol. Aβ, Tramiprosate (3-amino-1-propanesulfonic acid; 3APS; Alzhemed) was found to maintain Aβ in a non-fibrillar form, to decrease Aβ42-induced cell death in neuronal cell cultures, and to inhibit amyloid deposition. Tramiprosate crosses the murine blood-brain barrier (BBB) to exert its activity. Treatment of TgCRND8 mice with Tramiprosate resulted in significant redn. (∼30%) in the brain amyloid plaque load and a significant decrease in the cerebral levels of sol. and insol. Aβ40 and Aβ42 (∼20-30%). A dose-dependent redn. (up to 60%) of plasma Aβ levels was also obsd., suggesting that Tramiprosate influences the central pool of Aβ, changing either its efflux or its metab. in the brain. We propose that Tramiprosate, which targets sol. Aβ, represents a new and promising therapeutic class of drugs for the treatment of AD.
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    Caltagirone, C.; Ferrannini, L.; Marchionni, N.; Nappi, G.; Scapagnini, G.; Trabucchi, M. The Potential Protective Effect of Tramiprosate (Homotaurine) against Alzheimer’s Disease: A Review. Aging: Clin. Exp. Res. 2012, 24 (6), 580– 587,  DOI: 10.1007/BF03654836
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    Zou, X.; Himbert, S.; Dujardin, A.; Juhasz, J.; Ros, S.; Stöver, H. D. H.; Rheinstädter, M. C. Curcumin and Homotaurine Suppress Amyloid-Β25–35 Aggregation in Synthetic Brain Membranes. ACS Chem. Neurosci. 2021, 12 (8), 1395– 1405,  DOI: 10.1021/acschemneuro.1c00057
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    Abushakra, S.; Porsteinsson, A.; Vellas, B.; Cummings, J.; Gauthier, S.; Hey, J. A.; Power, A.; Hendrix, S.; Wang, P.; Shen, L.; Sampalis, J.; Tolar, M. Clinical Benefits of Tramiprosate in Alzheimer’s Disease Are Associated with Higher Number of APOE4 Alleles: The “APOE4 Gene-Dose Effect. J. Prev. Alzheimers Dis. 2016, 3 (4), 219– 228,  DOI: 10.14283/jpad.2016.115
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    Tian, J.; Dang, H.; Wallner, M.; Olsen, R.; Kaufman, D. L. Homotaurine, a Safe Blood-Brain Barrier Permeable GABAA-R-Specific Agonist, Ameliorates Disease in Mouse Models of Multiple Sclerosis. Sci. Rep. 2018, 8 (1), 16555,  DOI: 10.1038/s41598-018-32733-3
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    29
    Homotaurine, a safe blood-brain barrier permeable GABAA-R-specific agonist, ameliorates disease in mouse models of multiple sclerosis
    Tian Jide; Dang Hoa; Wallner Martin; Olsen Richard; Kaufman Daniel L
    Scientific reports (2018), 8 (1), 16555 ISSN:.
    There is a need for treatments that can safely promote regulatory lymphocyte responses. T cells express GABA receptors (GABAA-Rs) and GABA administration can inhibit Th1-mediated processes such as type 1 diabetes and rheumatoid arthritis in mouse models. Whether GABAA-R agonists can also inhibit Th17-driven processes such as experimental autoimmune encephalomyelitis (EAE), a model of multiple sclerosis (MS), is an open question. GABA does not pass through the blood-brain barrier (BBB) making it ill-suited to inhibit the spreading of autoreactivity within the CNS. Homotaurine is a BBB-permeable amino acid that antagonizes amyloid fibril formation and was found to be safe but ineffective in long-term Alzheimer's disease clinical trials. Homotaurine also acts as GABAA-R agonist with better pharmacokinetics than that of GABA. Working with both monophasic and relapsing-remitting mouse models of EAE, we show that oral administration of homotaurine can (1) enhance CD8(+)CD122(+)PD-1(+) and CD4(+)Foxp3(+) Treg, but not Breg, responses, (2) inhibit autoreactive Th17 and Th1 responses, and (3) effectively ameliorate ongoing disease. These observations demonstrate the potential of BBB-permeable GABAA-R agonists as a new class of treatment to enhance CD8(+) and CD4(+) Treg responses and limit Th17 and Th1-medaited inflammation in the CNS.
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    Manzano, S.; Agüera, L.; Aguilar, M.; Olazarán, J. A Review on Tramiprosate (Homotaurine) in Alzheimer’s Disease and Other Neurocognitive Disorders. Front. Neurol. 2020, 11, 614,  DOI: 10.3389/fneur.2020.00614
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    30
    A Review on Tramiprosate (Homotaurine) in Alzheimer's Disease and Other Neurocognitive Disorders
    Manzano Sagrario; Aguera Luis; Aguilar Miquel; Olazaran Javier
    Frontiers in neurology (2020), 11 (), 614 ISSN:1664-2295.
    Alzheimer's disease (AD) is the most prevalent neurodegenerative condition, especially among elderly people. The presence of cortical β-amyloid deposition, together with tau phosphorylation and intracellular accumulation of neurofibrillary tangles (NFT) is the main neuropathologic criteria for AD diagnosis. Additionally, a role of inflammatory, mitochondrial, and metabolic factors has been suggested. Tramiprosate binds to soluble amyloid, thus inhibiting its aggregation in the brain. It reduced oligomeric and fibrillar (plaque) amyloid, diminished hippocampal atrophy, improved cholinergic transmission, and stabilized cognition in preclinical and clinical studies. In this narrative review, current information on the efficacy and safety of tramiprosate, both in AD and in other neurocognitive disorders, is presented. Possible directions for future studies with tramiprosate are also discussed.
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    Hey, J. A.; Yu, J. Y.; Versavel, M.; Abushakra, S.; Kocis, P.; Power, A.; Kaplan, P. L.; Amedio, J.; Tolar, M. Clinical Pharmacokinetics and Safety of ALZ-801, a Novel Prodrug of Tramiprosate in Development for the Treatment of Alzheimer’s Disease. Clin. Pharmacokinet. 2018, 57 (3), 315– 333,  DOI: 10.1007/s40262-017-0608-3
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    31
    Clinical Pharmacokinetics and Safety of ALZ-801, a Novel Prodrug of Tramiprosate in Development for the Treatment of Alzheimer's Disease
    Hey, John A.; Yu, Jeremy Y.; Versavel, Mark; Abushakra, Susan; Kocis, Petr; Power, Aidan; Kaplan, Paul L.; Amedio, John; Tolar, Martin
    Clinical Pharmacokinetics (2018), 57 (3), 315-333CODEN: CPKNDH; ISSN:0312-5963. (Springer International Publishing AG)
    ALZ-801 is an orally available, valine-conjugated prodrug of tramiprosate. Tramiprosate, the active agent, is a small-mol. β-amyloid (Aβ) anti-oligomer and aggregation inhibitor that was evaluated extensively in preclin. and clin. investigations for the treatment of Alzheimer's disease (AD). Tramiprosate has been found to inhibit β-amyloid oligomer formation by a multi-ligand enveloping mechanism of action that stabilizes Aβ42 monomers, resulting in the inhibition of formation of oligomers and subsequent aggregation. Although promising as an AD treatment, tramiprosate exhibited two limiting deficiencies: high intersubject pharmacokinetic (PK) variability likely due to extensive gastrointestinal metab., and mild-to-moderate incidence of nausea and vomiting. To address these, we developed an optimized prodrug, ALZ-801, which retains the favorable efficacy attributes of tramiprosate while improving oral PK variability and gastrointestinal tolerability. In this study, we summarize the phase I bridging program to evaluate the safety, tolerability and PK for ALZ-801 after single and multiple rising dose administration in healthy volunteers. Randomized, placebo-controlled, phase I studies in 127 healthy male and female adult and elderly volunteers included [1] a single ascending dose (SAD) study; [2] a 14-day multiple ascending dose (MAD) study; and [3] a single-dose tablet food-effect study. This program was conducted with both a loose-filled capsule and an immediate-release tablet formulation, under both fasted and fed conditions. Safety and tolerability were assessed, and plasma and urine were collected for liq. chromatog.-mass spectrometry (LC-MS) detn. and non-compartmental PK anal. In addn., we defined the target dose of ALZ-801 that delivers a steady-state plasma area under the curve (AUC) exposure of tramiprosate equiv. to that studied in the tramiprosate phase III study. ALZ-801 was well tolerated and there were no severe or serious adverse events (AEs) or lab. findings. The most common AEs were transient mild nausea and some instances of vomiting, which were not dose-related and showed development of tolerance after continued use. ALZ-801 produced dose-dependent max. plasma concn. (Cmax) and AUC exposures of tramiprosate, which were equiv. to that after oral tramiprosate, but with a substantially reduced intersubject variability and a longer elimination half-life. Administration of ALZ-801 with food markedly reduced the incidence of gastrointestinal symptoms compared with the fasted state, without affecting plasma tramiprosate exposure. An immediate-release tablet formulation of ALZ-801 displayed plasma exposure and low variability similar to the loose-filled capsule. ALZ-801 also showed excellent dose-proportionality without accumulation or decrease in plasma exposure of tramiprosate over 14 days. Based on these data, 265 mg of ALZ-801 twice daily was found to achieve a steady-state AUC exposure of tramiprosate equiv. to 150 mg twice daily of oral tramiprosate in the previous phase III trials. ALZ-801, when administered in capsule and tablet forms, showed excellent oral safety and tolerability in healthy adults and elderly volunteers, with significantly improved PK characteristics over oral tramiprosate. A clin. dose of ALZ-801 (265 mg twice daily) was established that achieves the AUC exposure of 150 mg of tramiprosate twice daily, which showed pos. cognitive and functional improvements in apolipoprotein E4/4 homozygous AD patients. These bridging data support the phase III development of ALZ-801 in patients with AD.
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    A Phase 3, Multicenter, Randomized, Double-Blind, Placebo-Controlled Study of the Efficacy, Safety and Biomarker Effects of ALZ-801 in Subjects With Early Alzheimer’s Disease and APOE4/4 Genotype, ClinicalTrials.gov ID; Clinical trial registration NCT04770220; https://clinicaltrials.gov/ct2/show/NCT04770220 (accessed 2022–07–21).
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    Kocis, P.; Tolar, M.; Yu, J.; Sinko, W.; Ray, S.; Blennow, K.; Fillit, H.; Hey, J. A. Elucidating the Aβ42 Anti-Aggregation Mechanism of Action of Tramiprosate in Alzheimer’s Disease: Integrating Molecular Analytical Methods, Pharmacokinetic and Clinical Data. CNS Drugs 2017, 31 (6), 495– 509,  DOI: 10.1007/s40263-017-0434-z
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    Hey, J. A.; Kocis, P.; Hort, J.; Abushakra, S.; Power, A.; Vyhnálek, M.; Yu, J. Y.; Tolar, M. Discovery and Identification of an Endogenous Metabolite of Tramiprosate and Its Prodrug ALZ-801 That Inhibits Beta Amyloid Oligomer Formation in the Human Brain. CNS Drugs 2018, 32 (9), 849– 861,  DOI: 10.1007/s40263-018-0554-0
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    Liang, C.; Savinov, S. N.; Fejzo, J.; Eyles, S. J.; Chen, J. Modulation of Amyloid-Β42 Conformation by Small Molecules Through Nonspecific Binding. J. Chem. Theory Comput. 2019, 15 (10), 5169– 5174,  DOI: 10.1021/acs.jctc.9b00599
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    35
    Modulation of Amyloid-β42 Conformation by Small Molecules Through Nonspecific Binding
    Liang, Chungwen; Savinov, Sergey N.; Fejzo, Jasna; Eyles, Stephen J.; Chen, Jianhan
    Journal of Chemical Theory and Computation (2019), 15 (10), 5169-5174CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    Aggregation of amyloid-β (Aβ) peptides is a crucial step in the progression of Alzheimer's disease (AD). Identifying aggregation inhibitors against AD has been a great challenge. We report an atomistic simulation study of the inhibition mechanism of two small mols., homotaurine and scyllo-inositol, which are AD drug candidates currently under investigation. We show that both small mols. promote a conformational change of the Aβ42 monomer toward a more collapsed phase through a nonspecific binding mechanism. This finding provides atomistic-level insights into designing potential drug candidates for future AD treatments.
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    Hanwell, M. D.; Curtis, D. E.; Lonie, D. C.; Vandermeersch, T.; Zurek, E.; Hutchison, G. R. Avogadro: An Advanced Semantic Chemical Editor, Visualization, and Analysis Platform. J. Cheminf. 2012, 4 (1), 17,  DOI: 10.1186/1758-2946-4-17
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    Avogadro: an advanced semantic chemical editor, visualization, and analysis platform
    Hanwell, Marcus D.; Curtis, Donald E.; Lonie, David C.; Vandermeersch, Tim; Zurek, Eva; Hutchison, Geoffrey R.
    Journal of Cheminformatics (2012), 4 (), 17CODEN: JCOHB3; ISSN:1758-2946. (Chemistry Central Ltd.)
    Background: The Avogadro project has developed an advanced mol. editor and visualizer designed for cross-platform use in computational chem., mol. modeling, bioinformatics, materials science, and related areas. It offers flexible, high quality rendering, and a powerful plugin architecture. Typical uses include building mol. structures, formatting input files, and analyzing output of a wide variety of computational chem. packages. By using the CML file format as its native document type, Avogadro seeks to enhance the semantic accessibility of chem. data types. Results: The work presented here details the Avogadro library, which is a framework providing a code library and application programming interface (API) with three-dimensional visualization capabilities; and has direct applications to research and education in the fields of chem., physics, materials science, and biol. The Avogadro application provides a rich graphical interface using dynamically loaded plugins through the library itself. The application and library can each be extended by implementing a plugin module in C++ or Python to explore different visualization techniques, build/manipulate mol. structures, and interact with other programs. We describe some example extensions, one which uses a genetic algorithm to find stable crystal structures, and one which interfaces with the PackMol program to create packed, solvated structures for mol. dynamics simulations. The 1.0 release series of Avogadro is the main focus of the results discussed here. Conclusions: Avogadro offers a semantic chem. builder and platform for visualization and anal. For users, it offers an easy-to-use builder, integrated support for downloading from common databases such as PubChem and the Protein Data Bank, extg. chem. data from a wide variety of formats, including computational chem. output, and native, semantic support for the CML file format. For developers, it can be easily extended via a powerful plugin mechanism to support new features in org. chem., inorg. complexes, drug design, materials, biomols., and simulations.
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    Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A., Gaussian 09. In Revision E.01, Gaussian, Inc., 2009.
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    Case, D. A.; Betz, R. M.; Cerutti, D. S.; Cheatham, III, T. E.; Darden, T. A.; Duke, R. E.; Giese, T. J.; Gohlke, H.; Goetz, A. W.; Homeyer, N., ; AMBER 16, University of California, San Francisco, 2016.
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    Rose, P. W.; Bi, C.; Bluhm, W. F.; Christie, C. H.; Dimitropoulos, D.; Dutta, S.; Green, R. K.; Goodsell, D. S.; Prlić, A.; Quesada, M. The RCSB Protein Data Bank: New Resources for Research and Education. Nucleic Acids Res. 2012, 41 (D1), D475– D482,  DOI: 10.1093/nar/gks1200
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    Bas, D. C.; Rogers, D. M.; Jensen, J. H. Very fast prediction and rationalization of pKa values for protein–ligand complexes. Proteins: Struct., Funct., Bioinf. 2008, 73 (3), 765– 783,  DOI: 10.1002/prot.22102
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    Very fast prediction and rationalization of pKa values for protein-ligand complexes
    Bas, Delphine C.; Rogers, David M.; Jensen, Jan H.
    Proteins: Structure, Function, and Bioinformatics (2008), 73 (3), 765-783CODEN: PSFBAF ISSN:. (Wiley-Liss, Inc.)
    The PROPKA method for the prediction of the pKa values of ionizable residues in proteins is extended to include the effect of non-proteinaceous ligands on protein pKa values as well as predict the change in pKa values of ionizable groups on the ligand itself. This new version of PROPKA (PROPKA 2.0) is, as much as possible, developed by adapting the empirical rules underlying PROPKA 1.0 to ligand functional groups. Thus, the speed of PROPKA is retained, so that the pKa values of all ionizable groups are computed in a matter of seconds for most proteins. This adaptation is validated by comparing PROPKA 2.0 predictions to exptl. data for 26 protein-ligand complexes including trypsin, thrombin, three pepsins, HIV-1 protease, chymotrypsin, xylanase, hydroxynitrile lyase, and dihydrofolate reductase. For trypsin and thrombin, large protonation state changes (|n| > 0.5) have been obsd. exptl. for 4 out of 14 ligand complexes. PROPKA 2.0 and Klebe's PEOE approach both identify three of the four large protonation state changes. The protonation state changes due to plasmepsin II, cathepsin D and endothiapepsin binding to pepstatin are predicted to within 0.4 proton units at pH 6.5 and 7.0, resp. The PROPKA 2.0 results indicate that structural changes due to ligand binding contribute significantly to the proton uptake/release, as do residues far away from the binding site, primarily due to the change in the local environment of a particular residue and hence the change in the local hydrogen bonding network. Overall the results suggest that PROPKA 2.0 provides a good description of the protein-ligand interactions that have an important effect on the pKa values of titratable groups, thereby permitting fast and accurate detn. of the protonation states of key residues and ligand functional groups within the binding or active site of a protein.
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    Doerr, S.; Harvey, M. J.; Noé, F.; De Fabritiis, G. HTMD: High-Throughput Molecular Dynamics for Molecular Discovery. J. Chem. Theory Comput. 2016, 12 (4), 1845– 1852,  DOI: 10.1021/acs.jctc.6b00049
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    HTMD: High-Throughput Molecular Dynamics for Molecular Discovery
    Doerr, S.; Harvey, M. J.; Noe, Frank; De Fabritiis, G.
    Journal of Chemical Theory and Computation (2016), 12 (4), 1845-1852CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    Recent advances in mol. simulations have allowed scientists to investigate slower biol. processes than ever before. Together with these advances came an explosion of data that has transformed a traditionally computing-bound into a data-bound problem. Here, we present HTMD, a programmable, extensible platform written in Python that aims to solve the data generation and anal. problem as well as increase reproducibility by providing a complete workspace for simulation-based discovery. So far, HTMD includes system building for CHARMM and AMBER force fields, projection methods, clustering, mol. simulation prodn., adaptive sampling, an Amazon cloud interface, Markov state models, and visualization. As a result, a single, short HTMD script can lead from a PDB structure to useful quantities such as relaxation time scales, equil. populations, metastable conformations, and kinetic rates. In this paper, we focus on the adaptive sampling and Markov state modeling features.
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    Huang, J.; Rauscher, S.; Nawrocki, G.; Ran, T.; Feig, M.; de Groot, B. L.; Grubmüller, H.; MacKerell, A. D. CHARMM36m: An Improved Force Field for Folded and Intrinsically Disordered Proteins. Nat. Methods 2017, 14 (1), 71– 73,  DOI: 10.1038/nmeth.4067
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    CHARMM36m: an improved force field for folded and intrinsically disordered proteins
    Huang, Jing; Rauscher, Sarah; Nawrocki, Grzegorz; Ran, Ting; Feig, Michael; de Groot, Bert L.; Grubmuller, Helmut; MacKerell, Alexander D. Jr
    Nature Methods (2017), 14 (1), 71-73CODEN: NMAEA3; ISSN:1548-7091. (Nature Publishing Group)
    The all-atom additive CHARMM36 protein force field is widely used in mol. modeling and simulations. We present its refinement, CHARMM36m (http://mackerell.umaryland.edu/charmm_ff.shtml), with improved accuracy in generating polypeptide backbone conformational ensembles for intrinsically disordered peptides and proteins.
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    Roe, D. R.; Cheatham, T. E. PTRAJ and CPPTRAJ: Software for Processing and Analysis of Molecular Dynamics Trajectory Data. J. Chem. Theory Comput. 2013, 9 (7), 3084– 3095,  DOI: 10.1021/ct400341p
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    PTRAJ and CPPTRAJ: Software for Processing and Analysis of Molecular Dynamics Trajectory Data
    Roe, Daniel R.; Cheatham, Thomas E.
    Journal of Chemical Theory and Computation (2013), 9 (7), 3084-3095CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    We describe PTRAJ and its successor CPPTRAJ, two complementary, portable, and freely available computer programs for the anal. and processing of time series of three-dimensional at. positions (i.e., coordinate trajectories) and the data therein derived. Common tools include the ability to manipulate the data to convert among trajectory formats, process groups of trajectories generated with ensemble methods (e.g., replica exchange mol. dynamics), image with periodic boundary conditions, create av. structures, strip subsets of the system, and perform calcns. such as RMS fitting, measuring distances, B-factors, radii of gyration, radial distribution functions, and time correlations, among other actions and analyses. Both the PTRAJ and CPPTRAJ programs and source code are freely available under the GNU General Public License version 3 and are currently distributed within the AmberTools 12 suite of support programs that make up part of the Amber package of computer programs (see http://ambermd.org). This overview describes the general design, features, and history of these two programs, as well as algorithmic improvements and new features available in CPPTRAJ.
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    Aqvist, J.; Medina, C.; Samuelsson, J. E. A New Method for Predicting Binding Affinity in Computer-Aided Drug Design. Protein Eng. 1994, 7 (3), 385– 391,  DOI: 10.1093/protein/7.3.385
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    A new method for predicting binding affinity in computer-aided drug design
    Aqvist J; Medina C; Samuelsson J E
    Protein engineering (1994), 7 (3), 385-91 ISSN:0269-2139.
    A new semi-empirical method for calculating free energies of binding from molecular dynamics (MD) simulations is presented. It is based on standard thermodynamic cycles and on a linear approximation of polar and non-polar free energy contributions from the corresponding MD averages. The method is tested on a set of endothiapepsin inhibitors and found to give accurate results both for absolute as well as relative free energies.
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    Kabsch, W.; Sander, C. Dictionary of Protein Secondary Structure: Pattern Recognition of Hydrogen-Bonded and Geometrical Features. Biopolymers 1983, 22 (12), 2577– 2637,  DOI: 10.1002/bip.360221211
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    Dictionary of protein secondary structure: pattern recognition of hydrogen-bonded and geometrical features
    Kabsch, Wolfgang; Sander, Christian
    Biopolymers (1983), 22 (12), 2577-637CODEN: BIPMAA; ISSN:0006-3525.
    For a successful anal. of the relation between amino acid sequence and protein structure, an unambiguous and phys. meaningful definition of secondary structure is essential. A set of simple and phys. motivated criteria for secondary structure, programmed as a pattern-recognition process of H-bonded and geometrical features extd. from x-ray coordinates were developed. Cooperative secondary structure is recognized as repeats of the elementary H-bonding patterns turn and bridge. Repeating turns are helixes, repeating bridges are ladders, connected ladders are sheets. Geometric structure is defined in terms of the concepts torsion and curvature of differential geometry. Local chain chirality is the torsional handedness of 4 consecutive Cα positions and is pos. for right-handed helixes and neg. for ideal twisted β-sheets. Curved pieces are defined as bends. Solvent exposure is given as the no. of H2O mols. in possible contact with a residue. The end result is a compilation of the primary structure, including SS bonds, secondary structure, and solvent exposure of 62 different globular proteins. The presentation is in linear form: strip graphs for an overall view and strip tables for the details of each of 10,925 residues. The dictionary is also available in computer-readable form for protein structure prediction work.
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    Miller, B. R.; McGee, T. D.; Swails, J. M.; Homeyer, N.; Gohlke, H.; Roitberg, A. E. MMPBSA.Py: An Efficient Program for End-State Free Energy Calculations. J. Chem. Theory Comput. 2012, 8, 3314– 3321,  DOI: 10.1021/ct300418h
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    MMPBSA.py: An Efficient Program for End-State Free Energy Calculations
    Miller, Bill R., III; McGee, T. Dwight, Jr.; Swails, Jason M.; Homeyer, Nadine; Gohlke, Holger; Roitberg, Adrian E.
    Journal of Chemical Theory and Computation (2012), 8 (9), 3314-3321CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    MM-PBSA is a post-processing end-state method to calc. free energies of mols. in soln. MMPBSA.py is a program written in Python for streamlining end-state free energy calcns. using ensembles derived from mol. dynamics (MD) or Monte Carlo (MC) simulations. Several implicit solvation models are available with MMPBSA.py, including the Poisson-Boltzmann Model, the Generalized Born Model, and the Ref. Interaction Site Model. Vibrational frequencies may be calcd. using normal mode or quasi-harmonic anal. to approx. the solute entropy. Specific interactions can also be dissected using free energy decompn. or alanine scanning. A parallel implementation significantly speeds up the calcn. by dividing frames evenly across available processors. MMPBSA.py is an efficient, user-friendly program with the flexibility to accommodate the needs of users performing end-state free energy calcns. The source code can be downloaded at http://ambermd.org/ with AmberTools, released under the GNU General Public License.
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    Genheden, S.; Ryde, U. The MM/PBSA and MM/GBSA Methods to Estimate Ligand-Binding Affinities. Expert Opin. Drug Discovery 2015, 10 (5), 449– 461,  DOI: 10.1517/17460441.2015.1032936
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    The MM/PBSA and MM/GBSA methods to estimate ligand-binding affinities
    Genheden, Samuel; Ryde, Ulf
    Expert Opinion on Drug Discovery (2015), 10 (5), 449-461CODEN: EODDBX; ISSN:1746-0441. (Informa Healthcare)
    Introduction: The mol. mechanics energies combined with the Poisson-Boltzmann or generalized Born and surface area continuum solvation (MM/PBSA and MM/GBSA) methods are popular approaches to est. the free energy of the binding of small ligands to biol. macromols. They are typically based on mol. dynamics simulations of the receptor-ligand complex and are therefore intermediate in both accuracy and computational effort between empirical scoring and strict alchem. perturbation methods. They have been applied to a large no. of systems with varying success. Areas covered: The authors review the use of MM/PBSA and MM/GBSA methods to calc. ligand-binding affinities, with an emphasis on calibration, testing and validation, as well as attempts to improve the methods, rather than on specific applications. Expert opinion: MM/PBSA and MM/GBSA are attractive approaches owing to their modular nature and that they do not require calcns. on a training set. They have been used successfully to reproduce and rationalize exptl. findings and to improve the results of virtual screening and docking. However, they contain several crude and questionable approxns., for example, the lack of conformational entropy and information about the no. and free energy of water mols. in the binding site. Moreover, there are many variants of the method and their performance varies strongly with the tested system. Likewise, most attempts to ameliorate the methods with more accurate approaches, for example, quantum-mech. calcns., polarizable force fields or improved solvation have deteriorated the results.
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    Fong, R.; Vedaldi, A. Explanations for Attributing Deep Neural Network Predictions. In Explainable AI: Interpreting, Explaining and Visualizing Deep Learning. In Lecture Notes in Computer Science, Samek, W.; Montavon, G.; Vedaldi, A.; Hansen, L. K.; Müller, K.-R.; Springer International Publishing: Cham, 2019; pp. 149 167. DOI:  DOI: 10.1007/978-3-030-28954-6_8 .
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    Cohen, S. I. A.; Linse, S.; Luheshi, L. M.; Hellstrand, E.; White, D. A.; Rajah, L.; Otzen, D. E.; Vendruscolo, M.; Dobson, C. M.; Knowles, T. P. J. Proliferation of Amyloid-Β42 Aggregates Occurs through a Secondary Nucleation Mechanism. Proc. Natl. Acad. Sci. U. S. A. 2013, 110 (24), 9758– 9763,  DOI: 10.1073/pnas.1218402110
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    Proliferation of amyloid-β42 aggregates occurs through a secondary nucleation mechanism
    Cohen, Samuel I. A.; Linse, Sara; Luheshi, Leila M.; Hellstrand, Erik; White, Duncan A.; Rajah, Luke; Otzen, Daniel E.; Vendruscolo, Michele; Dobson, Christopher M.; Knowles, Tuomas P. J.
    Proceedings of the National Academy of Sciences of the United States of America (2013), 110 (24), 9758-9763, S9758/1-S9758/11CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
    The generation of toxic oligomers during the aggregation of the amyloid-β (Aβ) peptide Aβ42 into amyloid fibrils and plaques has emerged as a central feature of the onset and progression of Alzheimer's disease, but the mol. pathways that control pathol. aggregation have proved challenging to identify. Here, the authors used a combination of kinetic studies, selective radiolabeling expts., and cell viability assays to detect directly the rates of formation of both fibrils and oligomers and the resulting cytotoxic effects. The results showed that once a small but crit. concn. of amyloid fibrils had accumulated, the toxic oligomeric species were predominantly formed from monomeric peptide mols. through a fibril-catalyzed secondary nucleation reaction, rather than through a classical mechanism of homogeneous primary nucleation. This catalytic mechanism coupled together the growth of insol. amyloid fibrils and the generation of diffusible oligomeric aggregates that are implicated as neurotoxic agents in Alzheimer's disease. These results revealed that the aggregation of Aβ42 is promoted by a pos. feedback loop that originates from the interactions between the monomeric and fibrillar forms of this peptide. These findings bring together the main mol. species implicated in the Aβ aggregation cascade and suggest that perturbation of the secondary nucleation pathway identified in this study could be an effective strategy to control the proliferation of neurotoxic Aβ42 oligomers.
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    Arosio, P.; Knowles, T. P. J.; Linse, S. On the Lag Phase in Amyloid Fibril Formation. Phys. Chem. Chem. Phys. 2015, 17 (12), 7606– 7618,  DOI: 10.1039/C4CP05563B
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    On the lag phase in amyloid fibril formation
    Arosio, Paolo; Knowles, Tuomas P. J.; Linse, Sara
    Physical Chemistry Chemical Physics (2015), 17 (12), 7606-7618CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
    A review. The formation of nanoscale amyloid fibrils from normally sol. peptides and proteins is a common form of self-assembly phenomenon that has fundamental connections with biol. functions and human diseases. The kinetics of this process has been widely studied and exhibits on a macroscopic level three characteristic stages: (1) a lag phase; (2) a growth phase; and (3) a final plateau regime. The question of which mol. events take place during each one of these phases has been a central element in the quest for a mechanism of amyloid formation. Here, the authors discuss the nature and mol. origin of the lag-phase in amyloid formation by making use of tools and concepts from phys. chem., in particular from chem. reaction kinetics. The authors discuss how, in macroscopic samples, it has become apparent that the lag-phase is not a waiting time for nuclei to form. Rather, multiple parallel processes exist and typically millions of primary nuclei form during the lag phase from monomers in soln. Thus, the lag-time represents a time that is required for the nuclei that are formed early on in the reaction to grow and proliferate in order to reach an aggregate concn. that is readily detected in bulk assays. In many cases, this proliferation takes place through secondary nucleation, where fibrils may present a catalytic surface for the formation of new aggregates. Fibrils may also break (fragmentation) and thereby provide new ends for elongation. Thus, at least 2 (primary nucleation and elongation) and in many systems at least 4 (primary nucleation, elongation, secondary nucleation, and fragmentation) microscopic processes occur during the lag phase. Moreover, these same processes occur during all 3 phases of the macroscopic aggregation process, albeit at different rates as governed by rate consts. and by the concn. of reacting species at each point in time.
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    Tomaselli, S.; Esposito, V.; Vangone, P.; van Nuland, N. A. J.; Bonvin, A. M. J. J.; Guerrini, R.; Tancredi, T.; Temussi, P. A.; Picone, D. The α-to-β Conformational Transition of Alzheimer’s Aβ-(1–42) Peptide in Aqueous Media Is Reversible: A Step by Step Conformational Analysis Suggests the Location of β Conformation Seeding. ChemBiochem 2006, 7 (2), 257– 267,  DOI: 10.1002/cbic.200500223
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    The α-to-β conformational transition of Alzheimer's Aβ-(1-42) peptide in aqueous media is reversible: a step by step conformational analysis suggests the location of β conformation seeding
    Tomaselli, Simona; Esposito, Veronica; Vangone, Paolo; van Nuland, Nico A. J.; Bonvin, Alexandre M. J. J.; Guerrini, Remo; Tancredi, Teodorico; Temussi, Piero A.; Picone, Delia
    ChemBioChem (2006), 7 (2), 257-267CODEN: CBCHFX; ISSN:1439-4227. (Wiley-VCH Verlag GmbH & Co. KGaA)
    Current views of the role of β-amyloid (Aβ) peptide fibrils range from regarding them as the cause of Alzheimer's pathol. to having a protective function. In the last few years, it has also been suggested that sol. oligomers might be the most important toxic species. In all cases, the study of the conformational properties of Aβ peptides in sol. form constitutes a basic approach to the design of mols. with "antiamyloid" activity. We exptl. investigated the conformational 'path' that can lead the Aβ-(1-42) peptide from the native state, which is represented by an α helix embedded in the membrane, to the final state in the amyloid fibrils, which is characterized by sheet structures. The conformational steps were monitored by using CD and NMR spectroscopy in media of varying polarities. This was achieved by changing the compn. of water and hexafluoroisopropanol (HFIP). In the presence of HFIP, β conformations can be obsd. in solns. that have very high water content (up to 99% water; vol./vol.). These can be turned back to α helixes simply by adding the appropriated amt. of HFIP. The transition of Aβ-(1-42) from α to β conformation occurs when the amt. of water is higher that 80% (vol./vol.). The NMR structure solved in HFIP/H2O with high water content showed that, on going from very apolar to polar environments, the long N-terminal helix is essentially retained, whereas the shorter C-terminal helix is lost. The complete conformational path was investigated in detail with the aid of mol. dynamics simulations in explicit solvent, which led to the localization of residues that might seed β conformations. The structures obtained might help to find regions that are more affected by environmental conditions in vivo. This could in turn aid the design of mols. able to inhibit fibril deposition or revert oligomerization processes.
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  60. 60
    Shamsi, Z.; Moffett, A. S.; Shukla, D. Enhanced Unbiased Sampling of Protein Dynamics Using Evolutionary Coupling Information. Sci. Rep. 2017, 7 (1), 12700,  DOI: 10.1038/s41598-017-12874-7
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    Zimmerman, M. I.; Porter, J. R.; Sun, X.; Silva, R. R.; Bowman, G. R. Choice of Adaptive Sampling Strategy Impacts State Discovery, Transition Probabilities, and the Apparent Mechanism of Conformational Changes. J. Chem. Theory Comput. 2018, 14 (11), 5459– 5475,  DOI: 10.1021/acs.jctc.8b00500
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    61
    Choice of Adaptive Sampling Strategy Impacts State Discovery, Transition Probabilities, and the Apparent Mechanism of Conformational Changes
    Zimmerman, Maxwell I.; Porter, Justin R.; Sun, Xianqiang; Silva, Roseane R.; Bowman, Gregory R.
    Journal of Chemical Theory and Computation (2018), 14 (11), 5459-5475CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    Interest in atomically detailed simulations has grown significantly with recent advances in computational hardware and Markov state modeling (MSM) methods, yet outstanding questions remain that hinder their widespread adoption. Namely, how do alternative sampling strategies explore conformational space and how might this influence predictions generated from the data. Here, we seek to answer these questions for four commonly used sampling methods: (1) a single long simulation, (2) many short simulations run in parallel, (3) adaptive sampling, and (4) our recently developed goal-oriented sampling algorithm, FAST. We first develop a theor. framework for anal. calcg. the probability of discovering select states on simple landscapes, where we uncover the drastic effects of varying the no. and length of simulations. We then use kinetic Monte Carlo simulations on a variety of phys. inspired landscapes to characterize the probability of discovering particular states and transition pathways for each of the four methods. Consistently, we find that FAST simulations discover each target state with the highest probability, while traversing realistic pathways. Furthermore, we uncover the potential pathol. that short parallel simulations sometimes predict an incorrect transition pathway by crossing large energy barriers that long simulations would typically circumnavigate. We refer to this pathol. as "pathway tunneling". To protect against this phenomenon when using adaptive-sampling and FAST simulations, we introduce the FAST-string method. This method enhances sampling along the highest-flux transition paths to refine an MSMs transition probabilities and discriminate between competing pathways. Addnl., we compare the performance of a variety of MSM estimators in describing accurate thermodn. and kinetics. For adaptive sampling, we recommend simply normalizing the transition counts out of each state after adding small pseudocounts to avoid creating sources or sinks. Lastly, we evaluate whether our insights from simple landscapes hold for all-atom mol. dynamics simulations of the folding of the λ-repressor protein. Remarkably, we find that FAST-contacts predicts the same folding pathway as a set of long simulations but with orders of magnitude less simulation time.
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  62. 62
    Betz, R. M.; Dror, R. O. How Effectively Can Adaptive Sampling Methods Capture Spontaneous Ligand Binding?. J. Chem. Theory Comput. 2019, 15 (3), 2053– 2063,  DOI: 10.1021/acs.jctc.8b00913
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    62
    How Effectively Can Adaptive Sampling Methods Capture Spontaneous Ligand Binding?
    Betz, Robin M.; Dror, Ron O.
    Journal of Chemical Theory and Computation (2019), 15 (3), 2053-2063CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    Mol. dynamics (MD) simulations that capture the spontaneous binding of drugs and other ligands to their target proteins can reveal a great deal of useful information, but most drug-like ligands bind on time scales longer than those accessible to individual MD simulations. Adaptive sampling methods-in which one performs multiple rounds of simulation, with the initial conditions of each round based on the results of previous rounds-offer a promising potential soln. to this problem. No comprehensive anal. of the performance gains from adaptive sampling is available for ligand binding, however, particularly for protein-ligand systems typical of those encountered in drug discovery. Moreover, most previous work presupposes knowledge of the ligand's bound pose. Here the authors outline existing methods for adaptive sampling of the ligand-binding process and introduce several improvements, with a focus on methods that do not require prior knowledge of the binding site or bound pose. The authors then evaluate these methods by comparing them to traditional, long MD simulations for realistic protein-ligand systems. The authors find that adaptive sampling simulations typically fail to reach the bound pose more efficiently than traditional MD. However, adaptive sampling identifies multiple potential binding sites more efficiently than traditional MD and also provides better characterization of binding pathways. The authors explain these results by showing that protein-ligand binding is an example of an exploration-exploitation dilemma. Existing adaptive sampling methods for ligand binding in the absence of a known bound pose vastly favor the broad exploration of protein-ligand space, sometimes failing to sufficiently exploit intermediate states as they are discovered. The authors suggest potential avenues for future research to address this shortcoming.
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    Kleiman, D. E.; Nadeem, H.; Shukla, D. Adaptive Sampling Methods for Molecular Dynamics in the Era of Machine Learning. J. Phys. Chem. B 2023, 127 (50), 10669– 10681,  DOI: 10.1021/acs.jpcb.3c04843
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    Man, V. H.; He, X.; Derreumaux, P.; Ji, B.; Xie, X.-Q.; Nguyen, P. H.; Wang, J. Effects of All-Atom Molecular Mechanics Force Fields on Amyloid Peptide Assembly: The Case of Aβ16–22 Dimer. J. Chem. Theory Comput. 2019, 15 (2), 1440– 1452,  DOI: 10.1021/acs.jctc.8b01107
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    64
    Effects of all-atom molecular mechanics force fields on amyloid peptide assembly: The case of Aβ16-22 dimer
    Man, Viet Hoang; He, Xibing; Derreumaux, Philippe; Ji, Beihong; Xie, Xiang-Qun; Nguyen, Phuong H.; Wang, Junmei
    Journal of Chemical Theory and Computation (2019), 15 (2), 1440-1452CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    We investigated the effects of 17 widely used atomistic mol. mechanics force fields (MMFFs) on the structures and kinetics of amyloid peptide assembly. To this end, we performed large-scale all-atom mol. dynamics simulations in explicit water on the dimer of the 7-residue fragment of Alzheimer amyloid-β peptide, Aβ16-22, for a total time of 0.34 ms. We compared the effects of these MMFFs by analyzing various global reaction coordinates, secondary structure contents, the fibril population, the in-register and out-of-register architectures, and the fibril formation time at 310 K. While the AMBER94, AMBER99, and AMBER12SB force fields did not predict any β-sheets, the 7 force fields (AMBER96, GROMOS45a3, GROMOS53a5, GROMOS53a6, GROMOS43a1, GROMOS43a2, and GROMOS54a7) formed β-sheets rapidly. In contrast, the following 5 force fields (AMBER99-ILDN, AMBER14SB, CHARMM22*, CHARMM36, and CHARMM36m) were the best candidates for studying amyloid peptide assembly, as they provided good balances in terms of structures and kinetics. We also investigated the assembly mechanisms of dimeric Aβ16-22 and found that the fibril formation rate was predominantly controlled by the total β-strand content.
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    Maier, J. A.; Martinez, C.; Kasavajhala, K.; Wickstrom, L.; Hauser, K. E.; Simmerling, C. ff14SB: Improving the Accuracy of Protein Side Chain and Backbone Parameters from ff99SB. J. Chem. Theory Comput. 2015, 11 (8), 3696– 3713,  DOI: 10.1021/acs.jctc.5b00255
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    65
    ff14SB: Improving the Accuracy of Protein Side Chain and Backbone Parameters from ff99SB
    Maier, James A.; Martinez, Carmenza; Kasavajhala, Koushik; Wickstrom, Lauren; Hauser, Kevin E.; Simmerling, Carlos
    Journal of Chemical Theory and Computation (2015), 11 (8), 3696-3713CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    Mol. mechanics is powerful for its speed in atomistic simulations, but an accurate force field is required. The Amber ff99SB force field improved protein secondary structure balance and dynamics from earlier force fields like ff99, but weaknesses in side chain rotamer and backbone secondary structure preferences have been identified. Here, we performed a complete refit of all amino acid side chain dihedral parameters, which had been carried over from ff94. The training set of conformations included multidimensional dihedral scans designed to improve transferability of the parameters. Improvement in all amino acids was obtained as compared to ff99SB. Parameters were also generated for alternate protonation states of ionizable side chains. Av. errors in relative energies of pairs of conformations were under 1.0 kcal/mol as compared to QM, reduced 35% from ff99SB. We also took the opportunity to make empirical adjustments to the protein backbone dihedral parameters as compared to ff99SB. Multiple small adjustments of φ and ψ parameters were tested against NMR scalar coupling data and secondary structure content for short peptides. The best results were obtained from a phys. motivated adjustment to the φ rotational profile that compensates for lack of ff99SB QM training data in the β-ppII transition region. Together, these backbone and side chain modifications (hereafter called ff14SB) not only better reproduced their benchmarks, but also improved secondary structure content in small peptides and reprodn. of NMR χ1 scalar coupling measurements for proteins in soln. We also discuss the Amber ff12SB parameter set, a preliminary version of ff14SB that includes most of its improvements.
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    Harada, T.; Kuroda, R. CD Measurements of β-Amyloid (1–40) and (1–42) in the Condensed Phase. Biopolymers 2011, 95 (2), 127– 134,  DOI: 10.1002/bip.21543
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    Löhr, T.; Kohlhoff, K.; Heller, G. T.; Camilloni, C.; Vendruscolo, M. A Small Molecule Stabilizes the Disordered Native State of the Alzheimer’s Aβ Peptide. ACS Chem. Neurosci. 2022, 13 (12), 1738– 1745,  DOI: 10.1021/acschemneuro.2c00116
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    67
    A Small Molecule Stabilizes the Disordered Native State of the Alzheimer's Aβ Peptide
    Lohr, Thomas; Kohlhoff, Kai; Heller, Gabriella T.; Camilloni, Carlo; Vendruscolo, Michele
    ACS Chemical Neuroscience (2022), 13 (12), 1738-1745CODEN: ACNCDM; ISSN:1948-7193. (American Chemical Society)
    The stabilization of native states of proteins is a powerful drug discovery strategy. It is still unclear, however, whether this approach can be applied to intrinsically disordered proteins. Here, the authors report a small mol. that stabilizes the native state of the Aβ42 peptide, an intrinsically disordered protein fragment assocd. with Alzheimer's disease. This stabilization takes place by a dynamic binding mechanism, in which both the small mol. and the Aβ42 peptide remain disordered. This disordered binding mechanism involves enthalpically favorable local -stacking interactions coupled with entropically advantageous global effects. Small mols. can stabilize disordered proteins in their native states through transient non-specific interactions that provide enthalpic gain while simultaneously increasing the conformational entropy of the proteins.
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  68. 68
    Reddy, G.; Straub, J. E.; Thirumalai, D. Influence of Preformed Asp23-Lys28 Salt Bridge on the Conformational Fluctuations of Monomers and Dimers of Aβ Peptides with Implications for Rates of Fibril Formation. J. Phys. Chem. B 2009, 113 (4), 1162– 1172,  DOI: 10.1021/jp808914c
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    68
    Influence of Preformed Asp23-Lys28 Salt Bridge on the Conformational Fluctuations of Monomers and Dimers of Aβ Peptides with Implications for Rates of Fibril Formation
    Reddy, Govardhan; Straub, John E.; Thirumalai, D.
    Journal of Physical Chemistry B (2009), 113 (4), 1162-1172CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
    Recent expts. have shown that the congener Aβ1-40[D23-K28], in which the side chains of charged residues Asp23 and Lys28 are linked by a lactam bridge, forms amyloid fibrils that are structurally similar to the wild type (WT) Aβ peptide, but at a rate that is nearly 1000 times faster. We used all atom mol. dynamics simulations in explicit water, and two force fields, of the WT dimer, a monomer with the lactam bridge (Aβ10-35-lactam[D23-K28]), and the monomer and dimers with harmonically constrained D23-K28 salt bridge (Aβ10-35[D23-K28]) to understand the origin of the enhanced fibril rate formation. The simulations show that the assembly-competent fibril-like monomer (N*) structure, which is present among the conformations sampled by the isolated monomer, with strand conformations in the residues spanning the N and C termini and a bend involving residues D23VGSNKG29, are populated to a much greater extent in Aβ10-35[D23-K28] and Aβ10-35-lactam[D23-K28] than in the WT, which has negligible probability of forming N*. The salt bridge in N* of Aβ10-35[D23-K28], whose topol. is similar to that found in the fibril, is hydrated. The redn. in the free energy barrier to fibril formation in Aβ10-35[D23-K28] and in Aβ10-35-lactam[D23-K28], compared to the WT, arises largely due to entropic restriction which enables the bend formation. A decrease in the entropy of the unfolded state and the lesser penalty for conformational rearrangement including the formation of the salt bridge in Aβ peptides with D23-K28 constraint results in a redn. in the kinetic barrier in the Aβ1-40-lactam[D23-K28] congener compared to the WT. The decrease in the barrier, which is related to the free energy cost of forming a bend, is estd. to be in the range (4-7)kBT. Although a no. of factors det. the growth of fibrils, the decrease in the free energy barrier, relative to the WT, to N* formation is a major factor in the rate enhancement in the fibril formation of Aβ1-40[D23-K28] congener. Qual. similar results were obtained using simulations of Aβ9-40 peptides and various constructs related to the Aβ10-35 systems that were probed using OPLS and CHARMM force fields. We hypothesize that mutations or other constraints that preferentially enhance the population of the N* species would speed up aggregation rates. Conversely, ligands that lock it in the fibril-like N* structure would prevent amyloid formation.
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    Chandra, B.; Bhowmik, D.; Maity, B. K.; Mote, K. R.; Dhara, D.; Venkatramani, R.; Maiti, S.; Madhu, P. K. Major Reaction Coordinates Linking Transient Amyloid-β Oligomers to Fibrils Measured at Atomic Level. Biophys. J. 2017, 113 (4), 805– 816,  DOI: 10.1016/j.bpj.2017.06.068
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    69
    Major reaction coordinates linking transient amyloid-β oligomers to fibrils measured at atomic level
    Chandra, Bappaditya; Bhowmik, Debanjan; Maity, Barun Kumar; Mote, Kaustubh R.; Dhara, Debabrata; Venkatramani, Ravindra; Maiti, Sudipta; Madhu, Perunthiruthy K.
    Biophysical Journal (2017), 113 (4), 805-816CODEN: BIOJAU; ISSN:0006-3495. (Cell Press)
    The structural underpinnings for the higher toxicity of the oligomeric intermediates of amyloidogenic peptides, compared to the mature fibrils, remain unknown at present. The transient nature and heterogeneity of the oligomers make it difficult to follow their structure. Here, using vibrational and solid-state NMR spectroscopy, and mol. dynamics simulations, we show that freely aggregating Aβ40 oligomers in physiol. solns. have an intramol. antiparallel configuration that is distinct from the intermol. parallel β-sheet structure obsd. in mature fibrils. The intramol. hydrogen-bonding network flips nearly 90°, and the two β-strands of each monomeric unit move apart, to give rise to the well-known intermol. in-register parallel β-sheet structure in the mature fibrils. Solid-state NMR distance measurements capture the interstrand sepn. within monomer units during the transition from the oligomer to the fibril form. We further find that the D23-K28 salt-bridge, a major feature of the Aβ40 fibrils and a focal point of mutations linked to early onset Alzheimer's disease, is not detectable in the small oligomers. Mol. dynamics simulations capture the correlation between changes in the D23-K28 distance and the flipping of the monomer secondary structure between antiparallel and parallel β-sheet architectures. Overall, we propose interstrand sepn. and salt-bridge formation as key reaction coordinates describing the structural transition of the small Aβ40 oligomers to fibrils.
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  70. 70
    Nemergut, M.; Marques, S. M.; Uhrik, L.; Vanova, T.; Nezvedova, M.; Gadara, D. C.; Jha, D.; Tulis, J.; Novakova, V.; Planas-Iglesias, J. Domino-like Effect of C112R Mutation on ApoE4 Aggregation and Its Reduction by Alzheimer’s Disease Drug Candidate. Mol. Neurodegener. 2023, 18 (1), 38,  DOI: 10.1186/s13024-023-00620-9
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    Domino-like effect of C112R mutation on ApoE4 aggregation and its reduction by Alzheimer's Disease drug candidate
    Nemergut, Michal; Marques, Sergio M.; Uhrik, Lukas; Vanova, Tereza; Nezvedova, Marketa; Gadara, Darshak Chandulal; Jha, Durga; Tulis, Jan; Novakova, Veronika; Planas-Iglesias, Joan; Kunka, Antonin; Legrand, Anthony; Hribkova, Hana; Pospisilova, Veronika; Sedmik, Jiri; Raska, Jan; Prokop, Zbynek; Damborsky, Jiri; Bohaciakova, Dasa; Spacil, Zdenek; Hernychova, Lenka; Bednar, David; Marek, Martin
    Molecular Neurodegeneration (2023), 18 (1), 38CODEN: MNOEAZ; ISSN:1750-1326. (BioMed Central Ltd.)
    Apolipoprotein E (ApoE) ε4 genotype is the most prevalent risk factor for late-onset Alzheimers Disease (AD). Although ApoE4 differs from its non-pathol. ApoE3 isoform only by the C112R mutation, the mol. mechanism of its proteinopathy is unknown. Here, we reveal the mol. mechanism of ApoE4 aggregation using a combination of exptl. and computational techniques, including X-ray crystallog., site-directed mutagenesis, hydrogen-deuterium mass spectrometry (HDX-MS), static light scattering and mol. dynamics simulations. Treatment of ApoE ε3/ε3 and ε4/ε4 cerebral organoids with tramiprosate was used to compare the effect of tramiprosate on ApoE4 aggregation at the cellular level. We found that C112R substitution in ApoE4 induces long-distance (> 15 A) conformational changes leading to the formation of a V-shaped dimeric unit that is geometrically different and more aggregation-prone than the ApoE3 structure. AD drug candidate tramiprosate and its metabolite 3-sulfopropanoic acid induce ApoE3-like conformational behavior in ApoE4 and reduce its aggregation propensity. Anal. of ApoE ε4/ε4 cerebral organoids treated with tramiprosate revealed its effect on cholesteryl esters, the storage products of excess cholesterol. Our results connect the ApoE4 structure with its aggregation propensity, providing a new druggable target for neurodegeneration and ageing.
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    Walsh, D. M.; Thulin, E.; Minogue, A. M.; Gustavsson, N.; Pang, E.; Teplow, D. B.; Linse, S. A Facile Method for Expression and Purification of the Alzheimer’s Disease-Associated Amyloid Beta-Peptide. FEBS J. 2009, 276 (5), 1266– 1281,  DOI: 10.1111/j.1742-4658.2008.06862.x
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    71
    A facile method for expression and purification of the Alzheimer's disease-associated amyloid β-peptide
    Walsh, Dominic M.; Thulin, Eva; Minogue, Aedin M.; Gustavsson, Niklas; Pang, Eric; Teplow, David B.; Linse, Sara
    FEBS Journal (2009), 276 (5), 1266-1281CODEN: FJEOAC; ISSN:1742-464X. (Wiley-Blackwell)
    The authors report the development of a high-level bacterial expression system for the Alzheimer's disease-assocd. amyloid β-peptide (Aβ), together with a scalable and inexpensive purifn. procedure. Aβ(1-40) and Aβ(1-42) coding sequences together with added ATG codons were cloned directly into a Pet vector to facilitate prodn. of Met-Aβ(1-40) and Met-Aβ(1-42), referred to as Aβ(M1-40) and Aβ(M1-42), resp. The expression sequences were designed using codons preferred by Escherichia coli, and the two peptides were expressed in this host in inclusion bodies. Peptides were purified from inclusion bodies using a combination of anion-exchange chromatog. and centrifugal filtration. The method described requires little specialized equipment and provides a facile and inexpensive procedure for prodn. of large amts. of very pure Aβ peptides. Recombinant peptides generated using this protocol produced amyloid fibrils that were indistinguishable from those formed by chem. synthesized Aβ1-40 and Aβ1-42. Formation of fibrils by all peptides was concn.-dependent, and exhibited kinetics typical of a nucleation-dependent polymn. reaction. Recombinant and synthetic peptides exhibited a similar toxic effect on hippocampal neurons, with acute treatment causing inhibition of MTT redn., and chronic treatment resulting in neuritic degeneration and cell loss.
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    Thacker, D.; Sanagavarapu, K.; Frohm, B.; Meisl, G.; Knowles, T. P. J.; Linse, S. The Role of Fibril Structure and Surface Hydrophobicity in Secondary Nucleation of Amyloid Fibrils. Proc. Natl. Acad. Sci. U. S. A. 2020, 117 (41), 25272– 25283,  DOI: 10.1073/pnas.2002956117
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    72
    The role of fibril structure and surface hydrophobicity in secondary nucleation of amyloid fibrils
    Thacker, Dev; Sanagavarapu, Kalyani; Frohm, Birgitta; Meisl, Georg; Knowles, Tuomas P. J.; Linse, Sara
    Proceedings of the National Academy of Sciences of the United States of America (2020), 117 (41), 25272-25283CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
    Crystals, nanoparticles, and fibrils catalyze the generation of new aggregates on their surface from the same type of monomeric building blocks as the parent assemblies. This secondary nucleation process can be many orders of magnitude faster than primary nucleation. In the case of amyloid fibrils assocd. with Alzheimer's disease, this process leads to the multiplication and propagation of aggregates, whereby short-lived oligomeric intermediates cause neurotoxicity. Understanding the catalytic activity is a fundamental goal in elucidating the mol. mechanisms of Alzheimer's and assocd. diseases. Here the authors explore the role of fibril structure and hydrophobicity by asking whether the V18, A21, V40, and A42 side chains which are exposed on the Aβ42 fibril surface as continuous hydrophobic patches play a role in secondary nucleation. Single, double, and quadruple serine substitutions were made. Kinetic analyses of aggregation data at multiple monomer concns. reveal that all seven mutants retain the dominance of secondary nucleation as the main mechanism of fibril proliferation. This finding highlights the generality of secondary nucleation and its independence of the detailed mol. structure. Cryo-electron micrographs reveal that the V18S substitution causes fibrils to adopt a distinct morphol. with longer twist distance than variants lacking this substitution. Self- and cross-seeding data show that surface catalysis is only efficient between peptides of identical morphol., indicating a templating role of secondary nucleation with structural conversion at the fibril surface. The authors' findings thus provide clear evidence that the propagation of amyloid fibril strains is possible even in systems dominated by secondary nucleation rather than fragmentation.
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    Yang, H.; Yang, S.; Kong, J.; Dong, A.; Yu, S. Obtaining Information about Protein Secondary Structures in Aqueous Solution Using Fourier Transform IR Spectroscopy. Nat. Protoc. 2015, 10 (3), 382– 396,  DOI: 10.1038/nprot.2015.024
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    Obtaining information about protein secondary structures in aqueous solution using Fourier transform IR spectroscopy
    Yang, Huayan; Yang, Shouning; Kong, Jilie; Dong, Aichun; Yu, Shaoning
    Nature Protocols (2015), 10 (3), 382-396CODEN: NPARDW; ISSN:1750-2799. (Nature Publishing Group)
    Fourier transform IR (FTIR) spectroscopy is a nondestructive technique for structural characterization of proteins and polypeptides. The IR spectral data of polymers are usually interpreted in terms of the vibrations of a structural repeat. The repeat units in proteins give rise to nine characteristic IR absorption bands (amides A, B and I-VII). Amide I bands (1,700-1,600 cm-1) are the most prominent and sensitive vibrational bands of the protein backbone, and they relate to protein secondary structural components. In this protocol, we have detailed the principles that underlie the detn. of protein secondary structure by FTIR spectroscopy, as well as the basic steps involved in protein sample prepn., instrument operation, FTIR spectra collection and spectra anal. in order to est. protein secondary-structural components in aq. (both H2O and deuterium oxide (D2O)) soln. using algorithms, such as second-deriv., deconvolution and curve fitting. Small amts. of high-purity (>95%) proteins at high concns. (>3 mg ml-1) are needed in this protocol; typically, the procedure can be completed in 1-2 d.
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    Hafsa, N. E.; Arndt, D.; Wishart, D. S. CSI 3.0: A Web Server for Identifying Secondary and Super-Secondary Structure in Proteins Using NMR Chemical Shifts. Nucleic Acids Res. 2015, 43 (W1), W370– W377,  DOI: 10.1093/nar/gkv494
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    Borcherds, W. M.; Daughdrill, G. W. Using NMR Chemical Shifts to Determine Residue-Specific Secondary Structure Populations for Intrinsically Disordered Proteins. Methods Enzymol. 2018, 611, 101– 136,  DOI: 10.1016/bs.mie.2018.09.011
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    Schumann, F. H.; Riepl, H.; Maurer, T.; Gronwald, W.; Neidig, K.-P.; Kalbitzer, H. R. Combined Chemical Shift Changes and Amino Acid Specific Chemical Shift Mapping of Protein–Protein Interactions. J. Biomol. NMR 2007, 39 (4), 275– 289,  DOI: 10.1007/s10858-007-9197-z
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    Heller, G. T.; Aprile, F. A.; Michaels, T. C. T.; Limbocker, R.; Perni, M.; Ruggeri, F. S.; Mannini, B.; Löhr, T.; Bonomi, M.; Camilloni, C. Small-Molecule Sequestration of Amyloid-β as a Drug Discovery Strategy for Alzheimer’s Disease. Sci. Adv. 2020, 6 (45), eabb5924  DOI: 10.1126/sciadv.abb5924
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    Habchi, J.; Arosio, P.; Perni, M.; Costa, A. R.; Yagi-Utsumi, M.; Joshi, P.; Chia, S.; Cohen, S. I. A.; Müller, M. B. D.; Linse, S. An Anticancer Drug Suppresses the Primary Nucleation Reaction That Initiates the Production of the Toxic Aβ42 Aggregates Linked with Alzheimer’s Disease. Sci. Adv. 2016, 2 (2), e1501244  DOI: 10.1126/sciadv.1501244
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    An anticancer drug suppresses the primary nucleation reaction that initiates the production of the toxic Ab42 aggregates linked with Alzheimer's disease
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    The conversion of the β-amyloid (Aβ) peptide into pathogenic aggregates is linked to the onset and progression of Alzheimer's disease. Although this observation has prompted an extensive search for therapeutic agents to modulate the concn. of Aβ or inhibit its aggregation, all clin. trials with these objectives have so far failed, at least in part because of a lack of understanding of the mol. mechanisms underlying the process of aggregation and its inhibition. To address this problem, we describe a chem. kinetics approach for rational drug discovery, in which the effects of small mols. on the rates of specific microscopic steps in the self-assembly of Aβ42, the most aggregation-prone variant of Aβ, are analyzed quant. By applying this approach, we report that bexarotene, an anticancer drug approved by the U.S. Food and Drug Administration, selectively targets the primary nucleation step in Aβ42 aggregation, delays the formation of toxic species in neuroblastoma cells, and completely suppresses Aβ42 deposition and its consequences in a Caenorhabditis elegans model of Aβ42-mediated toxicity. These results suggest that the prevention of the primary nucleation of Aβ42 by compds. such as bexarotene could potentially reduce the risk of onset of Alzheimer's disease and, more generally, that our strategy provides a general framework for the rational identification of a range of candidate drugs directed against neurodegenerative disorders.
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    Understanding the conformational dynamics of proteins and peptides involved in important functions is still a difficult task in computational structural biology. Because such conformational transitions in β-amyloid (Aβ) forming peptides play a crucial role in many neurological disorders, researchers from different scientific fields have been trying to address issues related to the folding of Aβ forming peptides together. Many theoretical models have been proposed in the recent years for studying Aβ peptides using mathematical, physicochemical, and molecular dynamics simulation, and machine learning approaches. In this article, we have comprehensively reviewed the developmental advances in the theoretical models for Aβ peptide folding and interactions, particularly in the context of neurological disorders. Furthermore, we have extensively reviewed the advances in molecular dynamics simulation as a tool used for studying the conversions between polymorphic amyloid forms and applications of using machine learning approaches in predicting Aβ peptides and aggregation-prone regions in proteins. We have also provided details on the theoretical advances in the study of Aβ peptides, which would enhance our understanding of these peptides at the molecular level and eventually lead to the development of targeted therapies for certain acute neurological disorders such as Alzheimer's disease in the future.
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    Several neurodegenerative disorders arise from the abnormal protein aggregation in the nervous tissue lead- ing tointracellular inclusions or extracellular aggregates in specific brain areas. In case of Alzheimer Disease, the accumulation of the Amyloid Beta peptide in the brain is proposed to be an early important event in the pathogenesis. Despite significant research efforts in this field, the mol. mechanisms of protein misfolding and aggregation remain somewhat unrevealed.Within this framework, computer simulations represent a power- ful tool able to connect macroscopic exptl. fiend- ings to nanoscale mol. events.However, from the computational point of View, insufficient sampling often limits the ability of computer simulations to fully address this point. One of the main challenges of MD simulations is the ability to sample exptl. relevant millise- cond to second timescales.The present review describes the applications of mol. dynamics techniques to elucidate the conformational states and the aggregation pathway of the Amyloid Beta peptide responsible for AD. Moreover, the computational studies focused on the impact of Amyloid Beta assemblies on cell membranes will be also described. Finally, the interaction mechanisms between promising small mols. and Amyloid Beta assemblies will be discussed within the field of designing new efficient drugs against neurodegenerative disorders.
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    A review. Accumulations of insol. deposits of amyloid β-peptide are major pathol. hallmarks of Alzheimer disease. Amyloid β-peptide is derived by sequential proteolytic processing from a large type 1 trans-membrane protein, the β-amyloid precursor protein. The proteolytic enzymes involved in its processing are named secretases. β- And γ-secretase liberate by sequential cleavage the neurotoxic amyloid β-peptide, whereas α-secretase prevents its generation by cleaving within the middle of the amyloid domain. In this chapter we describe the cell biol. and biochem. characteristics of the three secretase activities involved in the proteolytic processing of the precursor protein. In addn. we outline how the precursor protein maturates and traffics through the secretory pathway to reach the subcellular locations where the individual secretases are preferentially active. Furthermore, we illuminate how neuronal activity and mutations which cause familial Alzheimer disease affect amyloid β-peptide generation and therefore disease onset and progression.
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    Aβ42 peptides can form helix and sheet structure under different conditions. The conformational conversion is closely assocd. with Aβ peptides aggregation and their neurotoxicity. But the transition from helix to sheet is not be clearly understood. In this study we performed microsecond timescale MD simulations of Aβ42 peptide to investigate the conformation transition from α-helix to β-sheet. Markov state model (MSM) was built to facilitate identification of crucial intermediate states and possible transition pathway. Based on the anal., we found that the region Y10-A21 in the middle of Aβ42 peptide plays an initial role in this transition. MSM model revealed that the collapse of helical structure in this region might trigger the formation of sheet structure. Moreover, we further simulated the aggregation of Aβ42 peptides with different conformations. We found that the Aβ42 peptides forming sheet structure have higher aggregation potential compared with peptides with helix structure. These results demonstrate that we can prevent the aggregation of Aβ42 peptides by stabilizing the helix structure in the region of Y10-A21. In addn., this study provides new insight into better understanding the conformational transition and aggregation of Aβ42 peptides.
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    Early oligomerization during amyloid-β (Aβ) aggregation is essential for Aβ neurotoxicity. Understanding how unstructured Aβs assemble into oligomers, esp. those rich in β-sheets, is essential but remains challenging as the assembly process is too transient for exptl. characterization and too slow for mol. dynamics simulations. So far, at. simulations are limited only to studies of either oligomer structures or assembly pathways for short Aβ segments. Here, to overcome the computational challenge, we combined in this study a hybrid-resoln. model and adaptive sampling techniques to perform over 2.7 ms of simulations of formation of full-length Aβ40 dimers that are the earliest toxic oligomeric species. The Markov state model was further employed to characterize the transition pathways and assocd. kinetics. The results showed that for 2 major forms of β-sheet-rich structures reported exptl., the corresponding assembly mechanisms were markedly different. Hairpin-contg. structures were formed by direct binding of sol. Aβ in β-hairpin-like conformations. The formation of parallel, in-register structures resembling fibrils occurred ∼100-fold more slowly and involved a rapid encounter of Aβ in arbitrary conformations followed by a slow structural conversion. The structural conversion proceeded via diverse pathways but always required transient unfolding of encounter complexes. We found that the transition kinetics could be affected differently by intramol./intermol. interactions involving individual residues in a conformation-dependent manner. In particular, the interactions involving Aβ's N-terminal part promoted the assembly into hairpin-contg. structures but delayed the formation of fibril-like structures, thus explaining puzzling observations reported previously regarding the roles of this region in the early assembly process.
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    The β amyloid (Aβ) peptide aggregates to form β-rich structures that are known to trigger Alzheimer's disease. Expts. suggest that an α-helical intermediate precedes the formation of these aggregates. However, a description at the mol. level of the α-to-β transition has not been obtained. Because it has been proposed that the transition might be initiated in the amino-terminal region of Aβ, we studied the aggregation of the 28-residue amino-terminal fragment of Aβ (Aβ1-28) using mol. dynamics (MD) and a coarse-grained force field. Simulations starting from extended and helical conformations showed that oligomerization is initiated by the formation of intermol. β-sheets between the residues in the N-terminal regions. In simulations starting from the α-helical conformation, forcing residues 17-21 to remain in the initial (helical) conformation prevents aggregation but allows for the formation of dimers, indicating that oligomerization, initiated along the nonhelical N-terminal regions, cannot progress without the α-to-β transition propagating along the chains.
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  • Abstract

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    Figure 1

    Figure 1. Structures of Aβ42 peptide and the studied small molecules, and properties of the ensembles from the adaptive simulations for the free Aβ42, Aβ42 + TMP, and Aβ42 + SPA. A) Sequence of the Aβ42 peptide and chemical structures of tramiprosate (TMP) and 3-sulfopropanoic acid (SPA) in the dominant protonation states at the physiological pH 7.4. The sequence residues are color-coded as follows: red for negatively charged; blue for positively charged; green for hydrophobic; and black for polar neutral residues. B) Total secondary structural propensity (% SS) of Aβ42 during the adaptive MDs, in the original NMR ensemble (PDB 1Z0Q with 30 structures), and from the experimental measurements of free Aβ42 in aqueous solution. C) Secondary structure propensity of Aβ42 by residue, obtained for the global ensembles from the adaptive simulations. The certainty of the secondary structure assignment was obtained by the statistical variance among ten randomized bins of frames and is represented by the saturation of the secondary structure color (the more saturated the color, the more certain the assignment, as indicated by the legend). D) Distribution of the radius of gyration (Rg) of the ensembles from the same adaptive simulations. E) Time evolution of the secondary structure of Aβ42 during the time-based aligned adaptive sampling MD simulations. The secondary elements are aggregated across all 42 residues, averaged at each time over all the trajectories parallel in time according to the time-based alignment. Only the timespan covering at least 20 parallel trajectories is plotted.

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    Figure 2

    Figure 2. Analysis of conformational states learned using the variational approach to Markov processes on the adaptive simulations and their evolution in time. A) Properties of the states. For each system, we report: (i) the free energy surface (FES) projected on the first two tICA dimensions (gray maps), where darker shades correspond to more negative energy regions; (ii) flux diagrams overlapping the FES and projected on the same tICA space, where each state is represented by a colored circle with the area proportional to the state probability, and the arrows indicate the mean first-passage times TM between the states, with the thickness proportional to the transition probability; (iii) equilibrium distribution of the states (bottom-left corner of FES; the bars represent the 95th percentile of values centered around the median from the ensemble of 20 learned models; see Supplementary Note 7 for details); (iv) superimposition of 20 representative structures from each state, selected based on the highest assignment probability (below FES, enclosed in colored circles); (v) global mean secondary structure content of each state (below the respective structures). B) Distribution of the learned states in time (top) and the number of frames available at each time point (bottom). The adaptive sampling trajectories were aligned in time and concatenated. The state probability at a given time point was computed as the average soft assignment of all available frames at this time point. From left to right, the state assignments evolve from the beginning to the end of the simulation time. All plots are shown for the free Aβ (left), Aβ + TMP (middle), and Aβ + SPA (right). The states are numbered and color-coded consistently across the entire panel; the same colors across different systems indicate aligned states.

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    Figure 3

    Figure 3. Gradients of the state assignment probabilities of the learned variational Markov state models. Each 42 × 42 heatmap shows the ensemble-averaged gradients of the model probabilities for the corresponding system and state with respect to the input inter-residue Cα distances. The color indicates how the probability of the particular state would change for an input frame if the distance between the particular pair of residues increased: blue indicates that the probability of the state assignment would increase if the distance between the Cα atoms increased whereas red indicates that the probability would increase if that distance decreased. The presented visualizations correspond to ensemble-averaged gradients evaluated and aggregated over 10,000 randomly selected simulation frames. Columns: MSMs for the free Aβ42 (left), Aβ42 + TMP (middle), and Aβ42 + SPA (right) systems. Rows: states 1 (top), 2 (middle), and 3 (bottom) of each model.

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    Figure 4

    Figure 4. Interactions of SPA with Aβ42 studied by molecular dynamics. A) Violin plot of the binding energy of SPA with each residue of Aβ42. The electrostatic component (ΔGbindelec) was calculated for all the 100 molecules in every snapshot of the adaptive simulation of Aβ42 + SPA. The plot shows the distribution of the energy values; the black dots show the mean values; the y-axis uses a quasi-logarithmic scale based on the inverse hyperbolic sine to highlight the higher absolute values. The residue labels are colored by charge: black for neutral, blue for positive, and red for negative. The chemical structure of SPA is shown in the upper-right corner. B) Structure of Aβ42 with the main interacting residues. Aβ42 is shown as the putty cartoon, and the main interacting residues are represented by sticks (structure from PDB ID 1Z0Q). The colors reflect the mean ΔGbindelec (in kcal/mol) and range from the most positive (blue) to the most negative (red) values obtained for SPA.

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    Figure 5

    Figure 5. Experimental validation of computational data using biophysical techniques. A) Circular dichroism spectra of Aβ42. N-Met-Aβ42 (37 μM) was studied in the absence (black) or presence of a 1000-fold excess of TMP (green), SPA (blue), or 20% HFIP (dashed curves). The curves for SPA were trimmed below 205 nm to remove the signal from SPA. B) FTIR spectra of Aβ42. N-Met-Aβ42 (60 μM) was studied in the absence (black) or presence of a 1000-fold excess of TMP (green) or SPA (blue). The bars represent the standard deviations from successive acquisitions. The second derivatives are drawn as dashed curves. Offset was shifted to improve readability. C) NMR analysis of Aβ42. 1H–15N HMQC NMR spectra of 15N-labeled N-Met-Aβ42 were determined alone (black, 69 μM) and in the presence of a 1000-fold excess of TMP (green, 58 μM) or SPA (blue, 55 μM). Assignment is given for free N-Met-Aβ42 (black); the assignment of His6 was ambiguous, thus no CSP was calculated for this residue. D) NMR chemical shift perturbation (CSP) of Aβ42. N-Met-Aβ42 in the presence of a 1000-fold excess of TMP (green), or SPA (blue) with respect to the free N-Met-Aβ42. The red dashed line represents the threshold for significance, taken as the standard deviation of all CSPs. E) Summary of the effects of small molecules on Aβ42 conformations studied by three different biophysical techniques: - indicates that no significant effect was detected, + indicates a mild effect, and ++ a stronger effect.

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      Thermodynamics and kinetics of the amyloid-β peptide revealed by Markov state models based on MD data in agreement with experiment
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      Chemical Science (2021), 12 (19), 6652-6669CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)
      The amlyoid-β peptide (Aβ) is closely linked to the development of Alzheimer's disease. Mol. dynamics (MD) simulations have become an indispensable tool for studying the behavior of this peptide at the atomistic level. General key aspects of MD simulations are the force field used for modeling the peptide and its environment, which is important for accurate modeling of the system of interest, and the length of the simulations, which dets. whether or not equil. is reached. In this study we address these points by analyzing 30-μs MD simulations acquired for Aβ40 using seven different force fields. We assess the convergence of these simulations based on the convergence of various structural properties and of NMR and fluorescence spectroscopic observables. Moreover, we calc Markov state models for the different MD simulations, which provide an unprecedented view of the thermodn. and kinetics of the amyloid-β peptide. This further allows us to provide answers for pertinent questions, like: which force fields are suitable for modeling Aβ (a99SB-UCB and a99SB-ILDN/TIP4P-D); what does Aβ peptide really look like (mostly extended and disordered) and; how long does it take MD simulations of Aβ to attain equil. (at least 20-30μs). We believe the analyses presented in this study will provide a useful ref. guide for important questions relating to the structure and dynamics of Aβ in particular, and by extension other similar disordered proteins.
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      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXovVaqtrk%253D&md5=53401b7f733acd3039b84361fe413cbc
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      Journal of Chemical Physics (2015), 142 (12), 124105/1-124105/12CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      Markov state models are a widely used method for approximating the eigenspectrum of the mol. dynamics propagator, yielding insight into the long-timescale statistical kinetics and slow dynamical modes of biomol. systems. However, the lack of a unified theor. framework for choosing between alternative models has hampered progress, esp. for non-experts applying these methods to novel biol. systems. Here, we consider cross-validation with a new objective function for estimators of these slow dynamical modes, a generalized matrix Rayleigh quotient (GMRQ), which measures the ability of a rank-m projection operator to capture the slow subspace of the system. It is shown that a variational theorem bounds the GMRQ from above by the sum of the first m eigenvalues of the system's propagator, but that this bound can be violated when the requisite matrix elements are estd. subject to statistical uncertainty. This overfitting can be detected and avoided through cross-validation. These result make it possible to construct Markov state models for protein dynamics in a way that appropriately captures the tradeoff between systematic and statistical errors. (c) 2015 American Institute of Physics.
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      Dominic, A. J. I.; Cao, S.; Montoya-Castillo, A.; Huang, X. Memory Unlocks the Future of Biomolecular Dynamics: Transformative Tools to Uncover Physical Insights Accurately and Efficiently. J. Am. Chem. Soc. 2023, 145 (18), 9916– 9927,  DOI: 10.1021/jacs.3c01095
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      Memory Unlocks the Future of Biomolecular Dynamics: Transformative Tools to Uncover Physical Insights Accurately and Efficiently
      Dominic, Anthony J.; Cao, Siqin; Montoya-Castillo, Andres; Huang, Xuhui
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      A review. Conformational changes underpin function and encode complex biomol. mechanisms. Gaining at.-level detail of how such changes occur has the potential to reveal these mechanisms and is of crit. importance in identifying drug targets, facilitating rational drug design, and enabling bioengineering applications. While the past two decades have brought Markov state model techniques to the point where practitioners can regularly use them to glimpse the long-time dynamics of slow conformations in complex systems, many systems are still beyond their reach. In this Perspective, we discuss how including memory (i.e., non-Markovian effects) can reduce the computational cost to predict the long-time dynamics in these complex systems by orders of magnitude and with greater accuracy and resoln. than state-of-the-art Markov state models. We illustrate how memory lies at the heart of successful and promising techniques, ranging from the Fokker-Planck and generalized Langevin equations to deep-learning recurrent neural networks and generalized master equations. We delineate how these techniques work, identify insights that they can offer in biomol. systems, and discuss their advantages and disadvantages in practical settings. We show how generalized master equations can enable the investigation of, for example, the gate-opening process in RNA polymerase II and demonstrate how our recent advances tame the deleterious influence of statistical underconvergence of the mol. dynamics simulations used to parameterize these techniques. This represents a significant leap forward that will enable our memory-based techniques to interrogate systems that are currently beyond the reach of even the best Markov state models. We conclude by discussing some current challenges and future prospects for how exploiting memory will open the door to many exciting opportunities.
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      Projected and hidden Markov models for calculating kinetics and metastable states of complex molecules
      Noe, Frank; Wu, Hao; Prinz, Jan-Hendrik; Plattner, Nuria
      Journal of Chemical Physics (2013), 139 (18), 184114/1-184114/17CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      Markov state models (MSMs) have been successful in computing metastable states, slow relaxation timescales and assocd. structural changes, and stationary or kinetic exptl. observables of complex mols. from large amts. of mol. dynamics simulation data. However, MSMs approx. the true dynamics by assuming a Markov chain on a clusters discretization of the state space. This approxn. is difficult to make for high-dimensional biomol. systems, and the quality and reproducibility of MSMs has, therefore, been limited. Here, we discard the assumption that dynamics are Markovian on the discrete clusters. Instead, we only assume that the full phase-space mol. dynamics is Markovian, and a projection of this full dynamics is obsd. on the discrete states, leading to the concept of Projected Markov Models (PMMs). Robust estn. methods for PMMs are not yet available, but we derive a practically feasible approxn. via Hidden Markov Models (HMMs). It is shown how various mol. observables of interest that are often computed from MSMs can be computed from HMMs/PMMs. The new framework is applicable to both, simulation and single-mol. exptl. data. We demonstrate its versatility by applications to educative model systems, a 1 ms Anton MD simulation of the bovine pancreatic trypsin inhibitor protein, and an optical tweezer force probe trajectory of an RNA hairpin. (c) 2013 American Institute of Physics.
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      Suárez, E.; Wiewiora, R. P.; Wehmeyer, C.; Noé, F.; Chodera, J. D.; Zuckerman, D. M. What Markov State Models Can and Cannot Do: Correlation versus Path-Based Observables in Protein-Folding Models. J. Chem. Theory Comput. 2021, 17 (5), 3119– 3133,  DOI: 10.1021/acs.jctc.0c01154
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      Dominic, A. J.; Sayer, T.; Cao, S.; Markland, T. E.; Huang, X.; Montoya-Castillo, A. Building Insightful, Memory-Enriched Models to Capture Long-Time Biochemical Processes from Short-Time Simulations. Proc. Natl. Acad. Sci. U. S. A. 2023, 120 (12), e2221048120  DOI: 10.1073/pnas.2221048120
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      Wehmeyer, C.; Noé, F. Time-Lagged Autoencoders: Deep Learning of Slow Collective Variables for Molecular Kinetics. J. Chem. Phys. 2018, 148 (24), 241703,  DOI: 10.1063/1.5011399
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      Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics
      Wehmeyer, Christoph; Noe, Frank
      Journal of Chemical Physics (2018), 148 (24), 241703/1-241703/9CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      Inspired by the success of deep learning techniques in the phys. and chem. sciences, we apply a modification of an autoencoder type deep neural network to the task of dimension redn. of mol. dynamics data. We can show that our time-lagged autoencoder reliably finds low-dimensional embeddings for high-dimensional feature spaces which capture the slow dynamics of the underlying stochastic processes - beyond the capabilities of linear dimension redn. techniques. (c) 2018 American Institute of Physics.
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      Mardt, A.; Pasquali, L.; Wu, H.; Noé, F. VAMPnets for Deep Learning of Molecular Kinetics. Nat. Commun. 2018, 9 (1), 5,  DOI: 10.1038/s41467-017-02388-1
      16
      VAMPnets for deep learning of molecular kinetics
      Mardt Andreas; Pasquali Luca; Wu Hao; Noe Frank
      Nature communications (2018), 9 (1), 5 ISSN:.
      There is an increasing demand for computing the relevant structures, equilibria, and long-timescale kinetics of biomolecular processes, such as protein-drug binding, from high-throughput molecular dynamics simulations. Current methods employ transformation of simulated coordinates into structural features, dimension reduction, clustering the dimension-reduced data, and estimation of a Markov state model or related model of the interconversion rates between molecular structures. This handcrafted approach demands a substantial amount of modeling expertise, as poor decisions at any step will lead to large modeling errors. Here we employ the variational approach for Markov processes (VAMP) to develop a deep learning framework for molecular kinetics using neural networks, dubbed VAMPnets. A VAMPnet encodes the entire mapping from molecular coordinates to Markov states, thus combining the whole data processing pipeline in a single end-to-end framework. Our method performs equally or better than state-of-the-art Markov modeling methods and provides easily interpretable few-state kinetic models.
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      Löhr, T.; Kohlhoff, K.; Heller, G. T.; Camilloni, C.; Vendruscolo, M. A Kinetic Ensemble of the Alzheimer’s Aβ Peptide. Nat. Comput. Sci. 2021, 1 (1), 71– 78,  DOI: 10.1038/s43588-020-00003-w
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      Ghorbani, M.; Prasad, S.; Klauda, J. B.; Brooks, B. R. GraphVAMPNet, using graph neural networks and variational approach to Markov processes for dynamical modeling of biomolecules. J. Chem. Phys. 2022, 156 (18), 184103,  DOI: 10.1063/5.0085607
      18
      GraphVAMPNet, using graph neural networks and variational approach to Markov processes for dynamical modeling of biomolecules
      Ghorbani, Mahdi; Prasad, Samarjeet; Klauda, Jeffery B.; Brooks, Bernard R.
      Journal of Chemical Physics (2022), 156 (18), 184103CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      Finding a low dimensional representation of data from long-timescale trajectories of biomol. processes, such as protein folding or ligand-receptor binding, is of fundamental importance, and kinetic models, such as Markov modeling, have proven useful in describing the kinetics of these systems. Recently, an unsupervised machine learning technique called VAMPNet was introduced to learn the low dimensional representation and the linear dynamical model in an end-to-end manner. VAMPNet is based on the variational approach for Markov processes and relies on neural networks to learn the coarse-grained dynamics. In this paper, we combine VAMPNet and graph neural networks to generate an end-to-end framework to efficiently learn high-level dynamics and metastable states from the long-timescale mol. dynamics trajectories. This method bears the advantages of graph representation learning and uses graph message passing operations to generate an embedding for each datapoint, which is used in the VAMPNet to generate a coarse-grained dynamical model. This type of mol. representation results in a higher resoln. and a more interpretable Markov model than the std. VAMPNet, enabling a more detailed kinetic study of the biomol. processes. Our GraphVAMPNet approach is also enhanced with an attention mechanism to find the important residues for classification into different metastable states. (c) 2022 American Institute of Physics.
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      Liu, B.; Xue, M.; Qiu, Y.; Konovalov, K. A.; O’Connor, M. S.; Huang, X. GraphVAMPnets for Uncovering Slow Collective Variables of Self-Assembly Dynamics. J. Chem. Phys. 2023, 159 (9), 094901,  DOI: 10.1063/5.0158903
      There is no corresponding record for this reference.
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      Mardt, A.; Hempel, T.; Clementi, C.; Noé, F. Deep Learning to Decompose Macromolecules into Independent Markovian Domains. Nat. Commun. 2022, 13 (1), 7101,  DOI: 10.1038/s41467-022-34603-z
      20
      Deep learning to decompose macromolecules into independent Markovian domains
      Mardt, Andreas; Hempel, Tim; Clementi, Cecilia; Noe, Frank
      Nature Communications (2022), 13 (1), 7101CODEN: NCAOBW; ISSN:2041-1723. (Nature Portfolio)
      The increasing interest in modeling the dynamics of ever larger proteins has revealed a fundamental problem with models that describe the mol. system as being in a global configuration state. This notion limits our ability to gather sufficient statistics of state probabilities or state-to-state transitions because for large mol. systems the no. of metastable states grows exponentially with size. In this manuscript, we approach this challenge by introducing a method that combines our recent progress on independent Markov decompn. (IMD) with VAMPnets, a deep learning approach to Markov modeling. We establish a training objective that quantifies how well a given decompn. of the mol. system into independent subdomains with Markovian dynamics approximates the overall dynamics. By constructing an end-to-end learning framework, the decompn. into such subdomains and their individual Markov state models are simultaneously learned, providing a data-efficient and easily interpretable summary of the complex system dynamics. While learning the dynamical coupling between Markovian subdomains is still an open issue, the present results are a significant step towards learning Ising models of large mol. complexes from simulation data.
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    21. 21
      Chen, W.; Sidky, H.; Ferguson, A. L. Nonlinear Discovery of Slow Molecular Modes Using State-Free Reversible VAMPnets. J. Chem. Phys. 2019, 150 (21), 214114,  DOI: 10.1063/1.5092521
      21
      Nonlinear discovery of slow molecular modes using state-free reversible VAMPnets
      Chen, Wei; Sidky, Hythem; Ferguson, Andrew L.
      Journal of Chemical Physics (2019), 150 (21), 214114/1-214114/16CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      The success of enhanced sampling mol. simulations that accelerate along collective variables (CVs) is predicated on the availability of variables coincident with the slow collective motions governing the long-time conformational dynamics of a system. It is challenging to intuit these slow CVs for all but the simplest mol. systems, and their data-driven discovery directly from mol. simulation trajectories has been a central focus of the mol. simulation community to both unveil the important phys. mechanisms and drive enhanced sampling. In this work, we introduce state-free reversible VAMPnets (SRV) as a deep learning architecture that learns nonlinear CV approximants to the leading slow eigenfunctions of the spectral decompn. of the transfer operator that evolves equil.-scaled probability distributions through time. Orthogonality of the learned CVs is naturally imposed within network training without added regularization. The CVs are inherently explicit and differentiable functions of the input coordinates making them well-suited to use in enhanced sampling calcns. We demonstrate the utility of SRVs in capturing parsimonious nonlinear representations of complex system dynamics in applications to 1D and 2D toy systems where the true eigenfunctions are exactly calculable and to mol. dynamics simulations of alanine dipeptide and the WW domain protein. (c) 2019 American Institute of Physics.
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      Kleiman, D. E.; Shukla, D. Active Learning of the Conformational Ensemble of Proteins Using Maximum Entropy VAMPNets. J. Chem. Theory Comput. 2023, 19 (14), 4377– 4388,  DOI: 10.1021/acs.jctc.3c00040
      There is no corresponding record for this reference.
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      Mardt, A.; Noé, F. Progress in Deep Markov State Modeling: Coarse Graining and Experimental Data Restraints. J. Chem. Phys. 2021, 155 (21), 214106,  DOI: 10.1063/5.0064668
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      Tolar, M.; Abushakra, S.; Hey, J. A.; Porsteinsson, A.; Sabbagh, M. Aducanumab, Gantenerumab, BAN2401, and ALZ-801─the First Wave of Amyloid-Targeting Drugs for Alzheimer’s Disease with Potential for near Term Approval. Alzheimer’s Res. Ther. 2020, 12 (1), 95,  DOI: 10.1186/s13195-020-00663-w
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      Gervais, F.; Paquette, J.; Morissette, C.; Krzywkowski, P.; Yu, M.; Azzi, M.; Lacombe, D.; Kong, X.; Aman, A.; Laurin, J. Targeting Soluble Aβ Peptide with Tramiprosate for the Treatment of Brain Amyloidosis. Neurobiol. Aging 2007, 28 (4), 537– 547,  DOI: 10.1016/j.neurobiolaging.2006.02.015
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      Targeting soluble Aβ peptide with Tramiprosate for the treatment of brain amyloidosis
      Gervais, Francine; Paquette, Julie; Morissette, Celine; Krzywkowski, Pascale; Yu, Mathilde; Azzi, Mounia; Lacombe, Diane; Kong, Xianqi; Aman, Ahmed; Laurin, Julie; Szarek, Walter A.; Tremblay, Patrick
      Neurobiology of Aging (2007), 28 (4), 537-547CODEN: NEAGDO; ISSN:0197-4580. (Elsevier)
      Amyloid β-peptide (Aβ) is a major constituent of senile plaques in Alzheimer's disease (AD). Neurotoxicity results from the conformational transition of Aβ from random-coil to β-sheet and its oligomerization. Among a series of ionic compds. able to interact with sol. Aβ, Tramiprosate (3-amino-1-propanesulfonic acid; 3APS; Alzhemed) was found to maintain Aβ in a non-fibrillar form, to decrease Aβ42-induced cell death in neuronal cell cultures, and to inhibit amyloid deposition. Tramiprosate crosses the murine blood-brain barrier (BBB) to exert its activity. Treatment of TgCRND8 mice with Tramiprosate resulted in significant redn. (∼30%) in the brain amyloid plaque load and a significant decrease in the cerebral levels of sol. and insol. Aβ40 and Aβ42 (∼20-30%). A dose-dependent redn. (up to 60%) of plasma Aβ levels was also obsd., suggesting that Tramiprosate influences the central pool of Aβ, changing either its efflux or its metab. in the brain. We propose that Tramiprosate, which targets sol. Aβ, represents a new and promising therapeutic class of drugs for the treatment of AD.
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    26. 26
      Caltagirone, C.; Ferrannini, L.; Marchionni, N.; Nappi, G.; Scapagnini, G.; Trabucchi, M. The Potential Protective Effect of Tramiprosate (Homotaurine) against Alzheimer’s Disease: A Review. Aging: Clin. Exp. Res. 2012, 24 (6), 580– 587,  DOI: 10.1007/BF03654836
      There is no corresponding record for this reference.
    27. 27
      Zou, X.; Himbert, S.; Dujardin, A.; Juhasz, J.; Ros, S.; Stöver, H. D. H.; Rheinstädter, M. C. Curcumin and Homotaurine Suppress Amyloid-Β25–35 Aggregation in Synthetic Brain Membranes. ACS Chem. Neurosci. 2021, 12 (8), 1395– 1405,  DOI: 10.1021/acschemneuro.1c00057
      There is no corresponding record for this reference.
    28. 28
      Abushakra, S.; Porsteinsson, A.; Vellas, B.; Cummings, J.; Gauthier, S.; Hey, J. A.; Power, A.; Hendrix, S.; Wang, P.; Shen, L.; Sampalis, J.; Tolar, M. Clinical Benefits of Tramiprosate in Alzheimer’s Disease Are Associated with Higher Number of APOE4 Alleles: The “APOE4 Gene-Dose Effect. J. Prev. Alzheimers Dis. 2016, 3 (4), 219– 228,  DOI: 10.14283/jpad.2016.115
      There is no corresponding record for this reference.
    29. 29
      Tian, J.; Dang, H.; Wallner, M.; Olsen, R.; Kaufman, D. L. Homotaurine, a Safe Blood-Brain Barrier Permeable GABAA-R-Specific Agonist, Ameliorates Disease in Mouse Models of Multiple Sclerosis. Sci. Rep. 2018, 8 (1), 16555,  DOI: 10.1038/s41598-018-32733-3
      29
      Homotaurine, a safe blood-brain barrier permeable GABAA-R-specific agonist, ameliorates disease in mouse models of multiple sclerosis
      Tian Jide; Dang Hoa; Wallner Martin; Olsen Richard; Kaufman Daniel L
      Scientific reports (2018), 8 (1), 16555 ISSN:.
      There is a need for treatments that can safely promote regulatory lymphocyte responses. T cells express GABA receptors (GABAA-Rs) and GABA administration can inhibit Th1-mediated processes such as type 1 diabetes and rheumatoid arthritis in mouse models. Whether GABAA-R agonists can also inhibit Th17-driven processes such as experimental autoimmune encephalomyelitis (EAE), a model of multiple sclerosis (MS), is an open question. GABA does not pass through the blood-brain barrier (BBB) making it ill-suited to inhibit the spreading of autoreactivity within the CNS. Homotaurine is a BBB-permeable amino acid that antagonizes amyloid fibril formation and was found to be safe but ineffective in long-term Alzheimer's disease clinical trials. Homotaurine also acts as GABAA-R agonist with better pharmacokinetics than that of GABA. Working with both monophasic and relapsing-remitting mouse models of EAE, we show that oral administration of homotaurine can (1) enhance CD8(+)CD122(+)PD-1(+) and CD4(+)Foxp3(+) Treg, but not Breg, responses, (2) inhibit autoreactive Th17 and Th1 responses, and (3) effectively ameliorate ongoing disease. These observations demonstrate the potential of BBB-permeable GABAA-R agonists as a new class of treatment to enhance CD8(+) and CD4(+) Treg responses and limit Th17 and Th1-medaited inflammation in the CNS.
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    30. 30
      Manzano, S.; Agüera, L.; Aguilar, M.; Olazarán, J. A Review on Tramiprosate (Homotaurine) in Alzheimer’s Disease and Other Neurocognitive Disorders. Front. Neurol. 2020, 11, 614,  DOI: 10.3389/fneur.2020.00614
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      A Review on Tramiprosate (Homotaurine) in Alzheimer's Disease and Other Neurocognitive Disorders
      Manzano Sagrario; Aguera Luis; Aguilar Miquel; Olazaran Javier
      Frontiers in neurology (2020), 11 (), 614 ISSN:1664-2295.
      Alzheimer's disease (AD) is the most prevalent neurodegenerative condition, especially among elderly people. The presence of cortical β-amyloid deposition, together with tau phosphorylation and intracellular accumulation of neurofibrillary tangles (NFT) is the main neuropathologic criteria for AD diagnosis. Additionally, a role of inflammatory, mitochondrial, and metabolic factors has been suggested. Tramiprosate binds to soluble amyloid, thus inhibiting its aggregation in the brain. It reduced oligomeric and fibrillar (plaque) amyloid, diminished hippocampal atrophy, improved cholinergic transmission, and stabilized cognition in preclinical and clinical studies. In this narrative review, current information on the efficacy and safety of tramiprosate, both in AD and in other neurocognitive disorders, is presented. Possible directions for future studies with tramiprosate are also discussed.
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    31. 31
      Hey, J. A.; Yu, J. Y.; Versavel, M.; Abushakra, S.; Kocis, P.; Power, A.; Kaplan, P. L.; Amedio, J.; Tolar, M. Clinical Pharmacokinetics and Safety of ALZ-801, a Novel Prodrug of Tramiprosate in Development for the Treatment of Alzheimer’s Disease. Clin. Pharmacokinet. 2018, 57 (3), 315– 333,  DOI: 10.1007/s40262-017-0608-3
      31
      Clinical Pharmacokinetics and Safety of ALZ-801, a Novel Prodrug of Tramiprosate in Development for the Treatment of Alzheimer's Disease
      Hey, John A.; Yu, Jeremy Y.; Versavel, Mark; Abushakra, Susan; Kocis, Petr; Power, Aidan; Kaplan, Paul L.; Amedio, John; Tolar, Martin
      Clinical Pharmacokinetics (2018), 57 (3), 315-333CODEN: CPKNDH; ISSN:0312-5963. (Springer International Publishing AG)
      ALZ-801 is an orally available, valine-conjugated prodrug of tramiprosate. Tramiprosate, the active agent, is a small-mol. β-amyloid (Aβ) anti-oligomer and aggregation inhibitor that was evaluated extensively in preclin. and clin. investigations for the treatment of Alzheimer's disease (AD). Tramiprosate has been found to inhibit β-amyloid oligomer formation by a multi-ligand enveloping mechanism of action that stabilizes Aβ42 monomers, resulting in the inhibition of formation of oligomers and subsequent aggregation. Although promising as an AD treatment, tramiprosate exhibited two limiting deficiencies: high intersubject pharmacokinetic (PK) variability likely due to extensive gastrointestinal metab., and mild-to-moderate incidence of nausea and vomiting. To address these, we developed an optimized prodrug, ALZ-801, which retains the favorable efficacy attributes of tramiprosate while improving oral PK variability and gastrointestinal tolerability. In this study, we summarize the phase I bridging program to evaluate the safety, tolerability and PK for ALZ-801 after single and multiple rising dose administration in healthy volunteers. Randomized, placebo-controlled, phase I studies in 127 healthy male and female adult and elderly volunteers included [1] a single ascending dose (SAD) study; [2] a 14-day multiple ascending dose (MAD) study; and [3] a single-dose tablet food-effect study. This program was conducted with both a loose-filled capsule and an immediate-release tablet formulation, under both fasted and fed conditions. Safety and tolerability were assessed, and plasma and urine were collected for liq. chromatog.-mass spectrometry (LC-MS) detn. and non-compartmental PK anal. In addn., we defined the target dose of ALZ-801 that delivers a steady-state plasma area under the curve (AUC) exposure of tramiprosate equiv. to that studied in the tramiprosate phase III study. ALZ-801 was well tolerated and there were no severe or serious adverse events (AEs) or lab. findings. The most common AEs were transient mild nausea and some instances of vomiting, which were not dose-related and showed development of tolerance after continued use. ALZ-801 produced dose-dependent max. plasma concn. (Cmax) and AUC exposures of tramiprosate, which were equiv. to that after oral tramiprosate, but with a substantially reduced intersubject variability and a longer elimination half-life. Administration of ALZ-801 with food markedly reduced the incidence of gastrointestinal symptoms compared with the fasted state, without affecting plasma tramiprosate exposure. An immediate-release tablet formulation of ALZ-801 displayed plasma exposure and low variability similar to the loose-filled capsule. ALZ-801 also showed excellent dose-proportionality without accumulation or decrease in plasma exposure of tramiprosate over 14 days. Based on these data, 265 mg of ALZ-801 twice daily was found to achieve a steady-state AUC exposure of tramiprosate equiv. to 150 mg twice daily of oral tramiprosate in the previous phase III trials. ALZ-801, when administered in capsule and tablet forms, showed excellent oral safety and tolerability in healthy adults and elderly volunteers, with significantly improved PK characteristics over oral tramiprosate. A clin. dose of ALZ-801 (265 mg twice daily) was established that achieves the AUC exposure of 150 mg of tramiprosate twice daily, which showed pos. cognitive and functional improvements in apolipoprotein E4/4 homozygous AD patients. These bridging data support the phase III development of ALZ-801 in patients with AD.
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    32. 32
      A Phase 3, Multicenter, Randomized, Double-Blind, Placebo-Controlled Study of the Efficacy, Safety and Biomarker Effects of ALZ-801 in Subjects With Early Alzheimer’s Disease and APOE4/4 Genotype, ClinicalTrials.gov ID; Clinical trial registration NCT04770220; https://clinicaltrials.gov/ct2/show/NCT04770220 (accessed 2022–07–21).
      There is no corresponding record for this reference.
    33. 33
      Kocis, P.; Tolar, M.; Yu, J.; Sinko, W.; Ray, S.; Blennow, K.; Fillit, H.; Hey, J. A. Elucidating the Aβ42 Anti-Aggregation Mechanism of Action of Tramiprosate in Alzheimer’s Disease: Integrating Molecular Analytical Methods, Pharmacokinetic and Clinical Data. CNS Drugs 2017, 31 (6), 495– 509,  DOI: 10.1007/s40263-017-0434-z
      There is no corresponding record for this reference.
    34. 34
      Hey, J. A.; Kocis, P.; Hort, J.; Abushakra, S.; Power, A.; Vyhnálek, M.; Yu, J. Y.; Tolar, M. Discovery and Identification of an Endogenous Metabolite of Tramiprosate and Its Prodrug ALZ-801 That Inhibits Beta Amyloid Oligomer Formation in the Human Brain. CNS Drugs 2018, 32 (9), 849– 861,  DOI: 10.1007/s40263-018-0554-0
      There is no corresponding record for this reference.
    35. 35
      Liang, C.; Savinov, S. N.; Fejzo, J.; Eyles, S. J.; Chen, J. Modulation of Amyloid-Β42 Conformation by Small Molecules Through Nonspecific Binding. J. Chem. Theory Comput. 2019, 15 (10), 5169– 5174,  DOI: 10.1021/acs.jctc.9b00599
      35
      Modulation of Amyloid-β42 Conformation by Small Molecules Through Nonspecific Binding
      Liang, Chungwen; Savinov, Sergey N.; Fejzo, Jasna; Eyles, Stephen J.; Chen, Jianhan
      Journal of Chemical Theory and Computation (2019), 15 (10), 5169-5174CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      Aggregation of amyloid-β (Aβ) peptides is a crucial step in the progression of Alzheimer's disease (AD). Identifying aggregation inhibitors against AD has been a great challenge. We report an atomistic simulation study of the inhibition mechanism of two small mols., homotaurine and scyllo-inositol, which are AD drug candidates currently under investigation. We show that both small mols. promote a conformational change of the Aβ42 monomer toward a more collapsed phase through a nonspecific binding mechanism. This finding provides atomistic-level insights into designing potential drug candidates for future AD treatments.
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    36. 36
      Hanwell, M. D.; Curtis, D. E.; Lonie, D. C.; Vandermeersch, T.; Zurek, E.; Hutchison, G. R. Avogadro: An Advanced Semantic Chemical Editor, Visualization, and Analysis Platform. J. Cheminf. 2012, 4 (1), 17,  DOI: 10.1186/1758-2946-4-17
      36
      Avogadro: an advanced semantic chemical editor, visualization, and analysis platform
      Hanwell, Marcus D.; Curtis, Donald E.; Lonie, David C.; Vandermeersch, Tim; Zurek, Eva; Hutchison, Geoffrey R.
      Journal of Cheminformatics (2012), 4 (), 17CODEN: JCOHB3; ISSN:1758-2946. (Chemistry Central Ltd.)
      Background: The Avogadro project has developed an advanced mol. editor and visualizer designed for cross-platform use in computational chem., mol. modeling, bioinformatics, materials science, and related areas. It offers flexible, high quality rendering, and a powerful plugin architecture. Typical uses include building mol. structures, formatting input files, and analyzing output of a wide variety of computational chem. packages. By using the CML file format as its native document type, Avogadro seeks to enhance the semantic accessibility of chem. data types. Results: The work presented here details the Avogadro library, which is a framework providing a code library and application programming interface (API) with three-dimensional visualization capabilities; and has direct applications to research and education in the fields of chem., physics, materials science, and biol. The Avogadro application provides a rich graphical interface using dynamically loaded plugins through the library itself. The application and library can each be extended by implementing a plugin module in C++ or Python to explore different visualization techniques, build/manipulate mol. structures, and interact with other programs. We describe some example extensions, one which uses a genetic algorithm to find stable crystal structures, and one which interfaces with the PackMol program to create packed, solvated structures for mol. dynamics simulations. The 1.0 release series of Avogadro is the main focus of the results discussed here. Conclusions: Avogadro offers a semantic chem. builder and platform for visualization and anal. For users, it offers an easy-to-use builder, integrated support for downloading from common databases such as PubChem and the Protein Data Bank, extg. chem. data from a wide variety of formats, including computational chem. output, and native, semantic support for the CML file format. For developers, it can be easily extended via a powerful plugin mechanism to support new features in org. chem., inorg. complexes, drug design, materials, biomols., and simulations.
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    37. 37
      Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A., Gaussian 09. In Revision E.01, Gaussian, Inc., 2009.
      There is no corresponding record for this reference.
    38. 38
      Case, D. A.; Betz, R. M.; Cerutti, D. S.; Cheatham, III, T. E.; Darden, T. A.; Duke, R. E.; Giese, T. J.; Gohlke, H.; Goetz, A. W.; Homeyer, N., ; AMBER 16, University of California, San Francisco, 2016.
      There is no corresponding record for this reference.
    39. 39
      Rose, P. W.; Bi, C.; Bluhm, W. F.; Christie, C. H.; Dimitropoulos, D.; Dutta, S.; Green, R. K.; Goodsell, D. S.; Prlić, A.; Quesada, M. The RCSB Protein Data Bank: New Resources for Research and Education. Nucleic Acids Res. 2012, 41 (D1), D475– D482,  DOI: 10.1093/nar/gks1200
      There is no corresponding record for this reference.
    40. 40
      Bas, D. C.; Rogers, D. M.; Jensen, J. H. Very fast prediction and rationalization of pKa values for protein–ligand complexes. Proteins: Struct., Funct., Bioinf. 2008, 73 (3), 765– 783,  DOI: 10.1002/prot.22102
      40
      Very fast prediction and rationalization of pKa values for protein-ligand complexes
      Bas, Delphine C.; Rogers, David M.; Jensen, Jan H.
      Proteins: Structure, Function, and Bioinformatics (2008), 73 (3), 765-783CODEN: PSFBAF ISSN:. (Wiley-Liss, Inc.)
      The PROPKA method for the prediction of the pKa values of ionizable residues in proteins is extended to include the effect of non-proteinaceous ligands on protein pKa values as well as predict the change in pKa values of ionizable groups on the ligand itself. This new version of PROPKA (PROPKA 2.0) is, as much as possible, developed by adapting the empirical rules underlying PROPKA 1.0 to ligand functional groups. Thus, the speed of PROPKA is retained, so that the pKa values of all ionizable groups are computed in a matter of seconds for most proteins. This adaptation is validated by comparing PROPKA 2.0 predictions to exptl. data for 26 protein-ligand complexes including trypsin, thrombin, three pepsins, HIV-1 protease, chymotrypsin, xylanase, hydroxynitrile lyase, and dihydrofolate reductase. For trypsin and thrombin, large protonation state changes (|n| > 0.5) have been obsd. exptl. for 4 out of 14 ligand complexes. PROPKA 2.0 and Klebe's PEOE approach both identify three of the four large protonation state changes. The protonation state changes due to plasmepsin II, cathepsin D and endothiapepsin binding to pepstatin are predicted to within 0.4 proton units at pH 6.5 and 7.0, resp. The PROPKA 2.0 results indicate that structural changes due to ligand binding contribute significantly to the proton uptake/release, as do residues far away from the binding site, primarily due to the change in the local environment of a particular residue and hence the change in the local hydrogen bonding network. Overall the results suggest that PROPKA 2.0 provides a good description of the protein-ligand interactions that have an important effect on the pKa values of titratable groups, thereby permitting fast and accurate detn. of the protonation states of key residues and ligand functional groups within the binding or active site of a protein.
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    41. 41
      Doerr, S.; Harvey, M. J.; Noé, F.; De Fabritiis, G. HTMD: High-Throughput Molecular Dynamics for Molecular Discovery. J. Chem. Theory Comput. 2016, 12 (4), 1845– 1852,  DOI: 10.1021/acs.jctc.6b00049
      41
      HTMD: High-Throughput Molecular Dynamics for Molecular Discovery
      Doerr, S.; Harvey, M. J.; Noe, Frank; De Fabritiis, G.
      Journal of Chemical Theory and Computation (2016), 12 (4), 1845-1852CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      Recent advances in mol. simulations have allowed scientists to investigate slower biol. processes than ever before. Together with these advances came an explosion of data that has transformed a traditionally computing-bound into a data-bound problem. Here, we present HTMD, a programmable, extensible platform written in Python that aims to solve the data generation and anal. problem as well as increase reproducibility by providing a complete workspace for simulation-based discovery. So far, HTMD includes system building for CHARMM and AMBER force fields, projection methods, clustering, mol. simulation prodn., adaptive sampling, an Amazon cloud interface, Markov state models, and visualization. As a result, a single, short HTMD script can lead from a PDB structure to useful quantities such as relaxation time scales, equil. populations, metastable conformations, and kinetic rates. In this paper, we focus on the adaptive sampling and Markov state modeling features.
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    42. 42
      Huang, J.; Rauscher, S.; Nawrocki, G.; Ran, T.; Feig, M.; de Groot, B. L.; Grubmüller, H.; MacKerell, A. D. CHARMM36m: An Improved Force Field for Folded and Intrinsically Disordered Proteins. Nat. Methods 2017, 14 (1), 71– 73,  DOI: 10.1038/nmeth.4067
      42
      CHARMM36m: an improved force field for folded and intrinsically disordered proteins
      Huang, Jing; Rauscher, Sarah; Nawrocki, Grzegorz; Ran, Ting; Feig, Michael; de Groot, Bert L.; Grubmuller, Helmut; MacKerell, Alexander D. Jr
      Nature Methods (2017), 14 (1), 71-73CODEN: NMAEA3; ISSN:1548-7091. (Nature Publishing Group)
      The all-atom additive CHARMM36 protein force field is widely used in mol. modeling and simulations. We present its refinement, CHARMM36m (http://mackerell.umaryland.edu/charmm_ff.shtml), with improved accuracy in generating polypeptide backbone conformational ensembles for intrinsically disordered peptides and proteins.
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    43. 43
      Swails, J.; ParmEd, GitHub, Inc, 2010. https://github.com/ParmEd/ParmEd. (accessed 2018–03–08).
      There is no corresponding record for this reference.
    44. 44
      Roe, D. R.; Cheatham, T. E. PTRAJ and CPPTRAJ: Software for Processing and Analysis of Molecular Dynamics Trajectory Data. J. Chem. Theory Comput. 2013, 9 (7), 3084– 3095,  DOI: 10.1021/ct400341p
      44
      PTRAJ and CPPTRAJ: Software for Processing and Analysis of Molecular Dynamics Trajectory Data
      Roe, Daniel R.; Cheatham, Thomas E.
      Journal of Chemical Theory and Computation (2013), 9 (7), 3084-3095CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      We describe PTRAJ and its successor CPPTRAJ, two complementary, portable, and freely available computer programs for the anal. and processing of time series of three-dimensional at. positions (i.e., coordinate trajectories) and the data therein derived. Common tools include the ability to manipulate the data to convert among trajectory formats, process groups of trajectories generated with ensemble methods (e.g., replica exchange mol. dynamics), image with periodic boundary conditions, create av. structures, strip subsets of the system, and perform calcns. such as RMS fitting, measuring distances, B-factors, radii of gyration, radial distribution functions, and time correlations, among other actions and analyses. Both the PTRAJ and CPPTRAJ programs and source code are freely available under the GNU General Public License version 3 and are currently distributed within the AmberTools 12 suite of support programs that make up part of the Amber package of computer programs (see http://ambermd.org). This overview describes the general design, features, and history of these two programs, as well as algorithmic improvements and new features available in CPPTRAJ.
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    45. 45
      Aqvist, J.; Medina, C.; Samuelsson, J. E. A New Method for Predicting Binding Affinity in Computer-Aided Drug Design. Protein Eng. 1994, 7 (3), 385– 391,  DOI: 10.1093/protein/7.3.385
      45
      A new method for predicting binding affinity in computer-aided drug design
      Aqvist J; Medina C; Samuelsson J E
      Protein engineering (1994), 7 (3), 385-91 ISSN:0269-2139.
      A new semi-empirical method for calculating free energies of binding from molecular dynamics (MD) simulations is presented. It is based on standard thermodynamic cycles and on a linear approximation of polar and non-polar free energy contributions from the corresponding MD averages. The method is tested on a set of endothiapepsin inhibitors and found to give accurate results both for absolute as well as relative free energies.
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    46. 46
      Kabsch, W.; Sander, C. Dictionary of Protein Secondary Structure: Pattern Recognition of Hydrogen-Bonded and Geometrical Features. Biopolymers 1983, 22 (12), 2577– 2637,  DOI: 10.1002/bip.360221211
      46
      Dictionary of protein secondary structure: pattern recognition of hydrogen-bonded and geometrical features
      Kabsch, Wolfgang; Sander, Christian
      Biopolymers (1983), 22 (12), 2577-637CODEN: BIPMAA; ISSN:0006-3525.
      For a successful anal. of the relation between amino acid sequence and protein structure, an unambiguous and phys. meaningful definition of secondary structure is essential. A set of simple and phys. motivated criteria for secondary structure, programmed as a pattern-recognition process of H-bonded and geometrical features extd. from x-ray coordinates were developed. Cooperative secondary structure is recognized as repeats of the elementary H-bonding patterns turn and bridge. Repeating turns are helixes, repeating bridges are ladders, connected ladders are sheets. Geometric structure is defined in terms of the concepts torsion and curvature of differential geometry. Local chain chirality is the torsional handedness of 4 consecutive Cα positions and is pos. for right-handed helixes and neg. for ideal twisted β-sheets. Curved pieces are defined as bends. Solvent exposure is given as the no. of H2O mols. in possible contact with a residue. The end result is a compilation of the primary structure, including SS bonds, secondary structure, and solvent exposure of 62 different globular proteins. The presentation is in linear form: strip graphs for an overall view and strip tables for the details of each of 10,925 residues. The dictionary is also available in computer-readable form for protein structure prediction work.
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    47. 47
      Miller, B. R.; McGee, T. D.; Swails, J. M.; Homeyer, N.; Gohlke, H.; Roitberg, A. E. MMPBSA.Py: An Efficient Program for End-State Free Energy Calculations. J. Chem. Theory Comput. 2012, 8, 3314– 3321,  DOI: 10.1021/ct300418h
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      MMPBSA.py: An Efficient Program for End-State Free Energy Calculations
      Miller, Bill R., III; McGee, T. Dwight, Jr.; Swails, Jason M.; Homeyer, Nadine; Gohlke, Holger; Roitberg, Adrian E.
      Journal of Chemical Theory and Computation (2012), 8 (9), 3314-3321CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      MM-PBSA is a post-processing end-state method to calc. free energies of mols. in soln. MMPBSA.py is a program written in Python for streamlining end-state free energy calcns. using ensembles derived from mol. dynamics (MD) or Monte Carlo (MC) simulations. Several implicit solvation models are available with MMPBSA.py, including the Poisson-Boltzmann Model, the Generalized Born Model, and the Ref. Interaction Site Model. Vibrational frequencies may be calcd. using normal mode or quasi-harmonic anal. to approx. the solute entropy. Specific interactions can also be dissected using free energy decompn. or alanine scanning. A parallel implementation significantly speeds up the calcn. by dividing frames evenly across available processors. MMPBSA.py is an efficient, user-friendly program with the flexibility to accommodate the needs of users performing end-state free energy calcns. The source code can be downloaded at http://ambermd.org/ with AmberTools, released under the GNU General Public License.
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    48. 48
      Genheden, S.; Ryde, U. The MM/PBSA and MM/GBSA Methods to Estimate Ligand-Binding Affinities. Expert Opin. Drug Discovery 2015, 10 (5), 449– 461,  DOI: 10.1517/17460441.2015.1032936
      48
      The MM/PBSA and MM/GBSA methods to estimate ligand-binding affinities
      Genheden, Samuel; Ryde, Ulf
      Expert Opinion on Drug Discovery (2015), 10 (5), 449-461CODEN: EODDBX; ISSN:1746-0441. (Informa Healthcare)
      Introduction: The mol. mechanics energies combined with the Poisson-Boltzmann or generalized Born and surface area continuum solvation (MM/PBSA and MM/GBSA) methods are popular approaches to est. the free energy of the binding of small ligands to biol. macromols. They are typically based on mol. dynamics simulations of the receptor-ligand complex and are therefore intermediate in both accuracy and computational effort between empirical scoring and strict alchem. perturbation methods. They have been applied to a large no. of systems with varying success. Areas covered: The authors review the use of MM/PBSA and MM/GBSA methods to calc. ligand-binding affinities, with an emphasis on calibration, testing and validation, as well as attempts to improve the methods, rather than on specific applications. Expert opinion: MM/PBSA and MM/GBSA are attractive approaches owing to their modular nature and that they do not require calcns. on a training set. They have been used successfully to reproduce and rationalize exptl. findings and to improve the results of virtual screening and docking. However, they contain several crude and questionable approxns., for example, the lack of conformational entropy and information about the no. and free energy of water mols. in the binding site. Moreover, there are many variants of the method and their performance varies strongly with the tested system. Likewise, most attempts to ameliorate the methods with more accurate approaches, for example, quantum-mech. calcns., polarizable force fields or improved solvation have deteriorated the results.
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    49. 49
      Wu, H.; Noé, F. Variational Approach for Learning Markov Processes from Time Series Data. J. Nonlinear Sci. 2020, 30 (1), 23– 66,  DOI: 10.1007/s00332-019-09567-y
      There is no corresponding record for this reference.
    50. 50
      Mardt, A.; Pasquali, L.; Noé, F.; Wu, H. Deep Learning Markov and Koopman Models with Physical Constraints. In Proceedings of The First Mathematical and Scientific Machine Learning Conference; PMLR, 2020; pp. 451 475.
      There is no corresponding record for this reference.
    51. 51
      Klambauer, G.; Unterthiner, T.; Mayr, A.; Hochreiter, S.; Self-Normalizing Neural Networks. In Advances in Neural Information Processing Systems, Curran Associates, Inc, 2017, Vol. 30.
      There is no corresponding record for this reference.
    52. 52
      MacQueen, J. Some Methods for Classification and Analysis of Multivariate Observations Proceedings of the Fifth Berkeley Symposium On Mathematical Statistics And Probability, Volume 1: Statistics Le Cam, L. M.; Neyman, J. Project Euclid 1967, 5; 281 298.
      There is no corresponding record for this reference.
    53. 53
      Bonneel, N.; van de Panne, M.; Paris, S.; Heidrich, W. Displacement Interpolation Using Lagrangian Mass Transport. ACM Trans. Graph. 2011, 30 (6), 1– 12,  DOI: 10.1145/2070781.2024192
      There is no corresponding record for this reference.
    54. 54
      Kuhn, H. W. The Hungarian Method for the Assignment Problem. Naval Res. Logistics Quarterly 1955, 2 (1–2), 83– 97,  DOI: 10.1002/nav.3800020109
      There is no corresponding record for this reference.
    55. 55
      Fong, R.; Vedaldi, A. Explanations for Attributing Deep Neural Network Predictions. In Explainable AI: Interpreting, Explaining and Visualizing Deep Learning. In Lecture Notes in Computer Science, Samek, W.; Montavon, G.; Vedaldi, A.; Hansen, L. K.; Müller, K.-R.; Springer International Publishing: Cham, 2019; pp. 149 167. DOI:  DOI: 10.1007/978-3-030-28954-6_8 .
      There is no corresponding record for this reference.
    56. 56
      Simonyan, K.; Vedaldi, A.; Zisserman, A. Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps, arXiv 2014 DOI: 10.48550/arXiv.1312.6034 .
      There is no corresponding record for this reference.
    57. 57
      Cohen, S. I. A.; Linse, S.; Luheshi, L. M.; Hellstrand, E.; White, D. A.; Rajah, L.; Otzen, D. E.; Vendruscolo, M.; Dobson, C. M.; Knowles, T. P. J. Proliferation of Amyloid-Β42 Aggregates Occurs through a Secondary Nucleation Mechanism. Proc. Natl. Acad. Sci. U. S. A. 2013, 110 (24), 9758– 9763,  DOI: 10.1073/pnas.1218402110
      57
      Proliferation of amyloid-β42 aggregates occurs through a secondary nucleation mechanism
      Cohen, Samuel I. A.; Linse, Sara; Luheshi, Leila M.; Hellstrand, Erik; White, Duncan A.; Rajah, Luke; Otzen, Daniel E.; Vendruscolo, Michele; Dobson, Christopher M.; Knowles, Tuomas P. J.
      Proceedings of the National Academy of Sciences of the United States of America (2013), 110 (24), 9758-9763, S9758/1-S9758/11CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
      The generation of toxic oligomers during the aggregation of the amyloid-β (Aβ) peptide Aβ42 into amyloid fibrils and plaques has emerged as a central feature of the onset and progression of Alzheimer's disease, but the mol. pathways that control pathol. aggregation have proved challenging to identify. Here, the authors used a combination of kinetic studies, selective radiolabeling expts., and cell viability assays to detect directly the rates of formation of both fibrils and oligomers and the resulting cytotoxic effects. The results showed that once a small but crit. concn. of amyloid fibrils had accumulated, the toxic oligomeric species were predominantly formed from monomeric peptide mols. through a fibril-catalyzed secondary nucleation reaction, rather than through a classical mechanism of homogeneous primary nucleation. This catalytic mechanism coupled together the growth of insol. amyloid fibrils and the generation of diffusible oligomeric aggregates that are implicated as neurotoxic agents in Alzheimer's disease. These results revealed that the aggregation of Aβ42 is promoted by a pos. feedback loop that originates from the interactions between the monomeric and fibrillar forms of this peptide. These findings bring together the main mol. species implicated in the Aβ aggregation cascade and suggest that perturbation of the secondary nucleation pathway identified in this study could be an effective strategy to control the proliferation of neurotoxic Aβ42 oligomers.
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    58. 58
      Arosio, P.; Knowles, T. P. J.; Linse, S. On the Lag Phase in Amyloid Fibril Formation. Phys. Chem. Chem. Phys. 2015, 17 (12), 7606– 7618,  DOI: 10.1039/C4CP05563B
      58
      On the lag phase in amyloid fibril formation
      Arosio, Paolo; Knowles, Tuomas P. J.; Linse, Sara
      Physical Chemistry Chemical Physics (2015), 17 (12), 7606-7618CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      A review. The formation of nanoscale amyloid fibrils from normally sol. peptides and proteins is a common form of self-assembly phenomenon that has fundamental connections with biol. functions and human diseases. The kinetics of this process has been widely studied and exhibits on a macroscopic level three characteristic stages: (1) a lag phase; (2) a growth phase; and (3) a final plateau regime. The question of which mol. events take place during each one of these phases has been a central element in the quest for a mechanism of amyloid formation. Here, the authors discuss the nature and mol. origin of the lag-phase in amyloid formation by making use of tools and concepts from phys. chem., in particular from chem. reaction kinetics. The authors discuss how, in macroscopic samples, it has become apparent that the lag-phase is not a waiting time for nuclei to form. Rather, multiple parallel processes exist and typically millions of primary nuclei form during the lag phase from monomers in soln. Thus, the lag-time represents a time that is required for the nuclei that are formed early on in the reaction to grow and proliferate in order to reach an aggregate concn. that is readily detected in bulk assays. In many cases, this proliferation takes place through secondary nucleation, where fibrils may present a catalytic surface for the formation of new aggregates. Fibrils may also break (fragmentation) and thereby provide new ends for elongation. Thus, at least 2 (primary nucleation and elongation) and in many systems at least 4 (primary nucleation, elongation, secondary nucleation, and fragmentation) microscopic processes occur during the lag phase. Moreover, these same processes occur during all 3 phases of the macroscopic aggregation process, albeit at different rates as governed by rate consts. and by the concn. of reacting species at each point in time.
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    59. 59
      Tomaselli, S.; Esposito, V.; Vangone, P.; van Nuland, N. A. J.; Bonvin, A. M. J. J.; Guerrini, R.; Tancredi, T.; Temussi, P. A.; Picone, D. The α-to-β Conformational Transition of Alzheimer’s Aβ-(1–42) Peptide in Aqueous Media Is Reversible: A Step by Step Conformational Analysis Suggests the Location of β Conformation Seeding. ChemBiochem 2006, 7 (2), 257– 267,  DOI: 10.1002/cbic.200500223
      59
      The α-to-β conformational transition of Alzheimer's Aβ-(1-42) peptide in aqueous media is reversible: a step by step conformational analysis suggests the location of β conformation seeding
      Tomaselli, Simona; Esposito, Veronica; Vangone, Paolo; van Nuland, Nico A. J.; Bonvin, Alexandre M. J. J.; Guerrini, Remo; Tancredi, Teodorico; Temussi, Piero A.; Picone, Delia
      ChemBioChem (2006), 7 (2), 257-267CODEN: CBCHFX; ISSN:1439-4227. (Wiley-VCH Verlag GmbH & Co. KGaA)
      Current views of the role of β-amyloid (Aβ) peptide fibrils range from regarding them as the cause of Alzheimer's pathol. to having a protective function. In the last few years, it has also been suggested that sol. oligomers might be the most important toxic species. In all cases, the study of the conformational properties of Aβ peptides in sol. form constitutes a basic approach to the design of mols. with "antiamyloid" activity. We exptl. investigated the conformational 'path' that can lead the Aβ-(1-42) peptide from the native state, which is represented by an α helix embedded in the membrane, to the final state in the amyloid fibrils, which is characterized by sheet structures. The conformational steps were monitored by using CD and NMR spectroscopy in media of varying polarities. This was achieved by changing the compn. of water and hexafluoroisopropanol (HFIP). In the presence of HFIP, β conformations can be obsd. in solns. that have very high water content (up to 99% water; vol./vol.). These can be turned back to α helixes simply by adding the appropriated amt. of HFIP. The transition of Aβ-(1-42) from α to β conformation occurs when the amt. of water is higher that 80% (vol./vol.). The NMR structure solved in HFIP/H2O with high water content showed that, on going from very apolar to polar environments, the long N-terminal helix is essentially retained, whereas the shorter C-terminal helix is lost. The complete conformational path was investigated in detail with the aid of mol. dynamics simulations in explicit solvent, which led to the localization of residues that might seed β conformations. The structures obtained might help to find regions that are more affected by environmental conditions in vivo. This could in turn aid the design of mols. able to inhibit fibril deposition or revert oligomerization processes.
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    60. 60
      Shamsi, Z.; Moffett, A. S.; Shukla, D. Enhanced Unbiased Sampling of Protein Dynamics Using Evolutionary Coupling Information. Sci. Rep. 2017, 7 (1), 12700,  DOI: 10.1038/s41598-017-12874-7
      There is no corresponding record for this reference.
    61. 61
      Zimmerman, M. I.; Porter, J. R.; Sun, X.; Silva, R. R.; Bowman, G. R. Choice of Adaptive Sampling Strategy Impacts State Discovery, Transition Probabilities, and the Apparent Mechanism of Conformational Changes. J. Chem. Theory Comput. 2018, 14 (11), 5459– 5475,  DOI: 10.1021/acs.jctc.8b00500
      61
      Choice of Adaptive Sampling Strategy Impacts State Discovery, Transition Probabilities, and the Apparent Mechanism of Conformational Changes
      Zimmerman, Maxwell I.; Porter, Justin R.; Sun, Xianqiang; Silva, Roseane R.; Bowman, Gregory R.
      Journal of Chemical Theory and Computation (2018), 14 (11), 5459-5475CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      Interest in atomically detailed simulations has grown significantly with recent advances in computational hardware and Markov state modeling (MSM) methods, yet outstanding questions remain that hinder their widespread adoption. Namely, how do alternative sampling strategies explore conformational space and how might this influence predictions generated from the data. Here, we seek to answer these questions for four commonly used sampling methods: (1) a single long simulation, (2) many short simulations run in parallel, (3) adaptive sampling, and (4) our recently developed goal-oriented sampling algorithm, FAST. We first develop a theor. framework for anal. calcg. the probability of discovering select states on simple landscapes, where we uncover the drastic effects of varying the no. and length of simulations. We then use kinetic Monte Carlo simulations on a variety of phys. inspired landscapes to characterize the probability of discovering particular states and transition pathways for each of the four methods. Consistently, we find that FAST simulations discover each target state with the highest probability, while traversing realistic pathways. Furthermore, we uncover the potential pathol. that short parallel simulations sometimes predict an incorrect transition pathway by crossing large energy barriers that long simulations would typically circumnavigate. We refer to this pathol. as "pathway tunneling". To protect against this phenomenon when using adaptive-sampling and FAST simulations, we introduce the FAST-string method. This method enhances sampling along the highest-flux transition paths to refine an MSMs transition probabilities and discriminate between competing pathways. Addnl., we compare the performance of a variety of MSM estimators in describing accurate thermodn. and kinetics. For adaptive sampling, we recommend simply normalizing the transition counts out of each state after adding small pseudocounts to avoid creating sources or sinks. Lastly, we evaluate whether our insights from simple landscapes hold for all-atom mol. dynamics simulations of the folding of the λ-repressor protein. Remarkably, we find that FAST-contacts predicts the same folding pathway as a set of long simulations but with orders of magnitude less simulation time.
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    62. 62
      Betz, R. M.; Dror, R. O. How Effectively Can Adaptive Sampling Methods Capture Spontaneous Ligand Binding?. J. Chem. Theory Comput. 2019, 15 (3), 2053– 2063,  DOI: 10.1021/acs.jctc.8b00913
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      How Effectively Can Adaptive Sampling Methods Capture Spontaneous Ligand Binding?
      Betz, Robin M.; Dror, Ron O.
      Journal of Chemical Theory and Computation (2019), 15 (3), 2053-2063CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      Mol. dynamics (MD) simulations that capture the spontaneous binding of drugs and other ligands to their target proteins can reveal a great deal of useful information, but most drug-like ligands bind on time scales longer than those accessible to individual MD simulations. Adaptive sampling methods-in which one performs multiple rounds of simulation, with the initial conditions of each round based on the results of previous rounds-offer a promising potential soln. to this problem. No comprehensive anal. of the performance gains from adaptive sampling is available for ligand binding, however, particularly for protein-ligand systems typical of those encountered in drug discovery. Moreover, most previous work presupposes knowledge of the ligand's bound pose. Here the authors outline existing methods for adaptive sampling of the ligand-binding process and introduce several improvements, with a focus on methods that do not require prior knowledge of the binding site or bound pose. The authors then evaluate these methods by comparing them to traditional, long MD simulations for realistic protein-ligand systems. The authors find that adaptive sampling simulations typically fail to reach the bound pose more efficiently than traditional MD. However, adaptive sampling identifies multiple potential binding sites more efficiently than traditional MD and also provides better characterization of binding pathways. The authors explain these results by showing that protein-ligand binding is an example of an exploration-exploitation dilemma. Existing adaptive sampling methods for ligand binding in the absence of a known bound pose vastly favor the broad exploration of protein-ligand space, sometimes failing to sufficiently exploit intermediate states as they are discovered. The authors suggest potential avenues for future research to address this shortcoming.
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    63. 63
      Kleiman, D. E.; Nadeem, H.; Shukla, D. Adaptive Sampling Methods for Molecular Dynamics in the Era of Machine Learning. J. Phys. Chem. B 2023, 127 (50), 10669– 10681,  DOI: 10.1021/acs.jpcb.3c04843
      There is no corresponding record for this reference.
    64. 64
      Man, V. H.; He, X.; Derreumaux, P.; Ji, B.; Xie, X.-Q.; Nguyen, P. H.; Wang, J. Effects of All-Atom Molecular Mechanics Force Fields on Amyloid Peptide Assembly: The Case of Aβ16–22 Dimer. J. Chem. Theory Comput. 2019, 15 (2), 1440– 1452,  DOI: 10.1021/acs.jctc.8b01107
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      Effects of all-atom molecular mechanics force fields on amyloid peptide assembly: The case of Aβ16-22 dimer
      Man, Viet Hoang; He, Xibing; Derreumaux, Philippe; Ji, Beihong; Xie, Xiang-Qun; Nguyen, Phuong H.; Wang, Junmei
      Journal of Chemical Theory and Computation (2019), 15 (2), 1440-1452CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      We investigated the effects of 17 widely used atomistic mol. mechanics force fields (MMFFs) on the structures and kinetics of amyloid peptide assembly. To this end, we performed large-scale all-atom mol. dynamics simulations in explicit water on the dimer of the 7-residue fragment of Alzheimer amyloid-β peptide, Aβ16-22, for a total time of 0.34 ms. We compared the effects of these MMFFs by analyzing various global reaction coordinates, secondary structure contents, the fibril population, the in-register and out-of-register architectures, and the fibril formation time at 310 K. While the AMBER94, AMBER99, and AMBER12SB force fields did not predict any β-sheets, the 7 force fields (AMBER96, GROMOS45a3, GROMOS53a5, GROMOS53a6, GROMOS43a1, GROMOS43a2, and GROMOS54a7) formed β-sheets rapidly. In contrast, the following 5 force fields (AMBER99-ILDN, AMBER14SB, CHARMM22*, CHARMM36, and CHARMM36m) were the best candidates for studying amyloid peptide assembly, as they provided good balances in terms of structures and kinetics. We also investigated the assembly mechanisms of dimeric Aβ16-22 and found that the fibril formation rate was predominantly controlled by the total β-strand content.
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    65. 65
      Maier, J. A.; Martinez, C.; Kasavajhala, K.; Wickstrom, L.; Hauser, K. E.; Simmerling, C. ff14SB: Improving the Accuracy of Protein Side Chain and Backbone Parameters from ff99SB. J. Chem. Theory Comput. 2015, 11 (8), 3696– 3713,  DOI: 10.1021/acs.jctc.5b00255
      65
      ff14SB: Improving the Accuracy of Protein Side Chain and Backbone Parameters from ff99SB
      Maier, James A.; Martinez, Carmenza; Kasavajhala, Koushik; Wickstrom, Lauren; Hauser, Kevin E.; Simmerling, Carlos
      Journal of Chemical Theory and Computation (2015), 11 (8), 3696-3713CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      Mol. mechanics is powerful for its speed in atomistic simulations, but an accurate force field is required. The Amber ff99SB force field improved protein secondary structure balance and dynamics from earlier force fields like ff99, but weaknesses in side chain rotamer and backbone secondary structure preferences have been identified. Here, we performed a complete refit of all amino acid side chain dihedral parameters, which had been carried over from ff94. The training set of conformations included multidimensional dihedral scans designed to improve transferability of the parameters. Improvement in all amino acids was obtained as compared to ff99SB. Parameters were also generated for alternate protonation states of ionizable side chains. Av. errors in relative energies of pairs of conformations were under 1.0 kcal/mol as compared to QM, reduced 35% from ff99SB. We also took the opportunity to make empirical adjustments to the protein backbone dihedral parameters as compared to ff99SB. Multiple small adjustments of φ and ψ parameters were tested against NMR scalar coupling data and secondary structure content for short peptides. The best results were obtained from a phys. motivated adjustment to the φ rotational profile that compensates for lack of ff99SB QM training data in the β-ppII transition region. Together, these backbone and side chain modifications (hereafter called ff14SB) not only better reproduced their benchmarks, but also improved secondary structure content in small peptides and reprodn. of NMR χ1 scalar coupling measurements for proteins in soln. We also discuss the Amber ff12SB parameter set, a preliminary version of ff14SB that includes most of its improvements.
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    66. 66
      Harada, T.; Kuroda, R. CD Measurements of β-Amyloid (1–40) and (1–42) in the Condensed Phase. Biopolymers 2011, 95 (2), 127– 134,  DOI: 10.1002/bip.21543
      There is no corresponding record for this reference.
    67. 67
      Löhr, T.; Kohlhoff, K.; Heller, G. T.; Camilloni, C.; Vendruscolo, M. A Small Molecule Stabilizes the Disordered Native State of the Alzheimer’s Aβ Peptide. ACS Chem. Neurosci. 2022, 13 (12), 1738– 1745,  DOI: 10.1021/acschemneuro.2c00116
      67
      A Small Molecule Stabilizes the Disordered Native State of the Alzheimer's Aβ Peptide
      Lohr, Thomas; Kohlhoff, Kai; Heller, Gabriella T.; Camilloni, Carlo; Vendruscolo, Michele
      ACS Chemical Neuroscience (2022), 13 (12), 1738-1745CODEN: ACNCDM; ISSN:1948-7193. (American Chemical Society)
      The stabilization of native states of proteins is a powerful drug discovery strategy. It is still unclear, however, whether this approach can be applied to intrinsically disordered proteins. Here, the authors report a small mol. that stabilizes the native state of the Aβ42 peptide, an intrinsically disordered protein fragment assocd. with Alzheimer's disease. This stabilization takes place by a dynamic binding mechanism, in which both the small mol. and the Aβ42 peptide remain disordered. This disordered binding mechanism involves enthalpically favorable local -stacking interactions coupled with entropically advantageous global effects. Small mols. can stabilize disordered proteins in their native states through transient non-specific interactions that provide enthalpic gain while simultaneously increasing the conformational entropy of the proteins.
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    68. 68
      Reddy, G.; Straub, J. E.; Thirumalai, D. Influence of Preformed Asp23-Lys28 Salt Bridge on the Conformational Fluctuations of Monomers and Dimers of Aβ Peptides with Implications for Rates of Fibril Formation. J. Phys. Chem. B 2009, 113 (4), 1162– 1172,  DOI: 10.1021/jp808914c
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      Influence of Preformed Asp23-Lys28 Salt Bridge on the Conformational Fluctuations of Monomers and Dimers of Aβ Peptides with Implications for Rates of Fibril Formation
      Reddy, Govardhan; Straub, John E.; Thirumalai, D.
      Journal of Physical Chemistry B (2009), 113 (4), 1162-1172CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
      Recent expts. have shown that the congener Aβ1-40[D23-K28], in which the side chains of charged residues Asp23 and Lys28 are linked by a lactam bridge, forms amyloid fibrils that are structurally similar to the wild type (WT) Aβ peptide, but at a rate that is nearly 1000 times faster. We used all atom mol. dynamics simulations in explicit water, and two force fields, of the WT dimer, a monomer with the lactam bridge (Aβ10-35-lactam[D23-K28]), and the monomer and dimers with harmonically constrained D23-K28 salt bridge (Aβ10-35[D23-K28]) to understand the origin of the enhanced fibril rate formation. The simulations show that the assembly-competent fibril-like monomer (N*) structure, which is present among the conformations sampled by the isolated monomer, with strand conformations in the residues spanning the N and C termini and a bend involving residues D23VGSNKG29, are populated to a much greater extent in Aβ10-35[D23-K28] and Aβ10-35-lactam[D23-K28] than in the WT, which has negligible probability of forming N*. The salt bridge in N* of Aβ10-35[D23-K28], whose topol. is similar to that found in the fibril, is hydrated. The redn. in the free energy barrier to fibril formation in Aβ10-35[D23-K28] and in Aβ10-35-lactam[D23-K28], compared to the WT, arises largely due to entropic restriction which enables the bend formation. A decrease in the entropy of the unfolded state and the lesser penalty for conformational rearrangement including the formation of the salt bridge in Aβ peptides with D23-K28 constraint results in a redn. in the kinetic barrier in the Aβ1-40-lactam[D23-K28] congener compared to the WT. The decrease in the barrier, which is related to the free energy cost of forming a bend, is estd. to be in the range (4-7)kBT. Although a no. of factors det. the growth of fibrils, the decrease in the free energy barrier, relative to the WT, to N* formation is a major factor in the rate enhancement in the fibril formation of Aβ1-40[D23-K28] congener. Qual. similar results were obtained using simulations of Aβ9-40 peptides and various constructs related to the Aβ10-35 systems that were probed using OPLS and CHARMM force fields. We hypothesize that mutations or other constraints that preferentially enhance the population of the N* species would speed up aggregation rates. Conversely, ligands that lock it in the fibril-like N* structure would prevent amyloid formation.
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    69. 69
      Chandra, B.; Bhowmik, D.; Maity, B. K.; Mote, K. R.; Dhara, D.; Venkatramani, R.; Maiti, S.; Madhu, P. K. Major Reaction Coordinates Linking Transient Amyloid-β Oligomers to Fibrils Measured at Atomic Level. Biophys. J. 2017, 113 (4), 805– 816,  DOI: 10.1016/j.bpj.2017.06.068
      69
      Major reaction coordinates linking transient amyloid-β oligomers to fibrils measured at atomic level
      Chandra, Bappaditya; Bhowmik, Debanjan; Maity, Barun Kumar; Mote, Kaustubh R.; Dhara, Debabrata; Venkatramani, Ravindra; Maiti, Sudipta; Madhu, Perunthiruthy K.
      Biophysical Journal (2017), 113 (4), 805-816CODEN: BIOJAU; ISSN:0006-3495. (Cell Press)
      The structural underpinnings for the higher toxicity of the oligomeric intermediates of amyloidogenic peptides, compared to the mature fibrils, remain unknown at present. The transient nature and heterogeneity of the oligomers make it difficult to follow their structure. Here, using vibrational and solid-state NMR spectroscopy, and mol. dynamics simulations, we show that freely aggregating Aβ40 oligomers in physiol. solns. have an intramol. antiparallel configuration that is distinct from the intermol. parallel β-sheet structure obsd. in mature fibrils. The intramol. hydrogen-bonding network flips nearly 90°, and the two β-strands of each monomeric unit move apart, to give rise to the well-known intermol. in-register parallel β-sheet structure in the mature fibrils. Solid-state NMR distance measurements capture the interstrand sepn. within monomer units during the transition from the oligomer to the fibril form. We further find that the D23-K28 salt-bridge, a major feature of the Aβ40 fibrils and a focal point of mutations linked to early onset Alzheimer's disease, is not detectable in the small oligomers. Mol. dynamics simulations capture the correlation between changes in the D23-K28 distance and the flipping of the monomer secondary structure between antiparallel and parallel β-sheet architectures. Overall, we propose interstrand sepn. and salt-bridge formation as key reaction coordinates describing the structural transition of the small Aβ40 oligomers to fibrils.
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    70. 70
      Nemergut, M.; Marques, S. M.; Uhrik, L.; Vanova, T.; Nezvedova, M.; Gadara, D. C.; Jha, D.; Tulis, J.; Novakova, V.; Planas-Iglesias, J. Domino-like Effect of C112R Mutation on ApoE4 Aggregation and Its Reduction by Alzheimer’s Disease Drug Candidate. Mol. Neurodegener. 2023, 18 (1), 38,  DOI: 10.1186/s13024-023-00620-9
      70
      Domino-like effect of C112R mutation on ApoE4 aggregation and its reduction by Alzheimer's Disease drug candidate
      Nemergut, Michal; Marques, Sergio M.; Uhrik, Lukas; Vanova, Tereza; Nezvedova, Marketa; Gadara, Darshak Chandulal; Jha, Durga; Tulis, Jan; Novakova, Veronika; Planas-Iglesias, Joan; Kunka, Antonin; Legrand, Anthony; Hribkova, Hana; Pospisilova, Veronika; Sedmik, Jiri; Raska, Jan; Prokop, Zbynek; Damborsky, Jiri; Bohaciakova, Dasa; Spacil, Zdenek; Hernychova, Lenka; Bednar, David; Marek, Martin
      Molecular Neurodegeneration (2023), 18 (1), 38CODEN: MNOEAZ; ISSN:1750-1326. (BioMed Central Ltd.)
      Apolipoprotein E (ApoE) ε4 genotype is the most prevalent risk factor for late-onset Alzheimers Disease (AD). Although ApoE4 differs from its non-pathol. ApoE3 isoform only by the C112R mutation, the mol. mechanism of its proteinopathy is unknown. Here, we reveal the mol. mechanism of ApoE4 aggregation using a combination of exptl. and computational techniques, including X-ray crystallog., site-directed mutagenesis, hydrogen-deuterium mass spectrometry (HDX-MS), static light scattering and mol. dynamics simulations. Treatment of ApoE ε3/ε3 and ε4/ε4 cerebral organoids with tramiprosate was used to compare the effect of tramiprosate on ApoE4 aggregation at the cellular level. We found that C112R substitution in ApoE4 induces long-distance (> 15 A) conformational changes leading to the formation of a V-shaped dimeric unit that is geometrically different and more aggregation-prone than the ApoE3 structure. AD drug candidate tramiprosate and its metabolite 3-sulfopropanoic acid induce ApoE3-like conformational behavior in ApoE4 and reduce its aggregation propensity. Anal. of ApoE ε4/ε4 cerebral organoids treated with tramiprosate revealed its effect on cholesteryl esters, the storage products of excess cholesterol. Our results connect the ApoE4 structure with its aggregation propensity, providing a new druggable target for neurodegeneration and ageing.
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    71. 71
      Walsh, D. M.; Thulin, E.; Minogue, A. M.; Gustavsson, N.; Pang, E.; Teplow, D. B.; Linse, S. A Facile Method for Expression and Purification of the Alzheimer’s Disease-Associated Amyloid Beta-Peptide. FEBS J. 2009, 276 (5), 1266– 1281,  DOI: 10.1111/j.1742-4658.2008.06862.x
      71
      A facile method for expression and purification of the Alzheimer's disease-associated amyloid β-peptide
      Walsh, Dominic M.; Thulin, Eva; Minogue, Aedin M.; Gustavsson, Niklas; Pang, Eric; Teplow, David B.; Linse, Sara
      FEBS Journal (2009), 276 (5), 1266-1281CODEN: FJEOAC; ISSN:1742-464X. (Wiley-Blackwell)
      The authors report the development of a high-level bacterial expression system for the Alzheimer's disease-assocd. amyloid β-peptide (Aβ), together with a scalable and inexpensive purifn. procedure. Aβ(1-40) and Aβ(1-42) coding sequences together with added ATG codons were cloned directly into a Pet vector to facilitate prodn. of Met-Aβ(1-40) and Met-Aβ(1-42), referred to as Aβ(M1-40) and Aβ(M1-42), resp. The expression sequences were designed using codons preferred by Escherichia coli, and the two peptides were expressed in this host in inclusion bodies. Peptides were purified from inclusion bodies using a combination of anion-exchange chromatog. and centrifugal filtration. The method described requires little specialized equipment and provides a facile and inexpensive procedure for prodn. of large amts. of very pure Aβ peptides. Recombinant peptides generated using this protocol produced amyloid fibrils that were indistinguishable from those formed by chem. synthesized Aβ1-40 and Aβ1-42. Formation of fibrils by all peptides was concn.-dependent, and exhibited kinetics typical of a nucleation-dependent polymn. reaction. Recombinant and synthetic peptides exhibited a similar toxic effect on hippocampal neurons, with acute treatment causing inhibition of MTT redn., and chronic treatment resulting in neuritic degeneration and cell loss.
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    72. 72
      Thacker, D.; Sanagavarapu, K.; Frohm, B.; Meisl, G.; Knowles, T. P. J.; Linse, S. The Role of Fibril Structure and Surface Hydrophobicity in Secondary Nucleation of Amyloid Fibrils. Proc. Natl. Acad. Sci. U. S. A. 2020, 117 (41), 25272– 25283,  DOI: 10.1073/pnas.2002956117
      72
      The role of fibril structure and surface hydrophobicity in secondary nucleation of amyloid fibrils
      Thacker, Dev; Sanagavarapu, Kalyani; Frohm, Birgitta; Meisl, Georg; Knowles, Tuomas P. J.; Linse, Sara
      Proceedings of the National Academy of Sciences of the United States of America (2020), 117 (41), 25272-25283CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
      Crystals, nanoparticles, and fibrils catalyze the generation of new aggregates on their surface from the same type of monomeric building blocks as the parent assemblies. This secondary nucleation process can be many orders of magnitude faster than primary nucleation. In the case of amyloid fibrils assocd. with Alzheimer's disease, this process leads to the multiplication and propagation of aggregates, whereby short-lived oligomeric intermediates cause neurotoxicity. Understanding the catalytic activity is a fundamental goal in elucidating the mol. mechanisms of Alzheimer's and assocd. diseases. Here the authors explore the role of fibril structure and hydrophobicity by asking whether the V18, A21, V40, and A42 side chains which are exposed on the Aβ42 fibril surface as continuous hydrophobic patches play a role in secondary nucleation. Single, double, and quadruple serine substitutions were made. Kinetic analyses of aggregation data at multiple monomer concns. reveal that all seven mutants retain the dominance of secondary nucleation as the main mechanism of fibril proliferation. This finding highlights the generality of secondary nucleation and its independence of the detailed mol. structure. Cryo-electron micrographs reveal that the V18S substitution causes fibrils to adopt a distinct morphol. with longer twist distance than variants lacking this substitution. Self- and cross-seeding data show that surface catalysis is only efficient between peptides of identical morphol., indicating a templating role of secondary nucleation with structural conversion at the fibril surface. The authors' findings thus provide clear evidence that the propagation of amyloid fibril strains is possible even in systems dominated by secondary nucleation rather than fragmentation.
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    73. 73
      Yang, H.; Yang, S.; Kong, J.; Dong, A.; Yu, S. Obtaining Information about Protein Secondary Structures in Aqueous Solution Using Fourier Transform IR Spectroscopy. Nat. Protoc. 2015, 10 (3), 382– 396,  DOI: 10.1038/nprot.2015.024
      73
      Obtaining information about protein secondary structures in aqueous solution using Fourier transform IR spectroscopy
      Yang, Huayan; Yang, Shouning; Kong, Jilie; Dong, Aichun; Yu, Shaoning
      Nature Protocols (2015), 10 (3), 382-396CODEN: NPARDW; ISSN:1750-2799. (Nature Publishing Group)
      Fourier transform IR (FTIR) spectroscopy is a nondestructive technique for structural characterization of proteins and polypeptides. The IR spectral data of polymers are usually interpreted in terms of the vibrations of a structural repeat. The repeat units in proteins give rise to nine characteristic IR absorption bands (amides A, B and I-VII). Amide I bands (1,700-1,600 cm-1) are the most prominent and sensitive vibrational bands of the protein backbone, and they relate to protein secondary structural components. In this protocol, we have detailed the principles that underlie the detn. of protein secondary structure by FTIR spectroscopy, as well as the basic steps involved in protein sample prepn., instrument operation, FTIR spectra collection and spectra anal. in order to est. protein secondary-structural components in aq. (both H2O and deuterium oxide (D2O)) soln. using algorithms, such as second-deriv., deconvolution and curve fitting. Small amts. of high-purity (>95%) proteins at high concns. (>3 mg ml-1) are needed in this protocol; typically, the procedure can be completed in 1-2 d.
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    74. 74
      Hafsa, N. E.; Arndt, D.; Wishart, D. S. CSI 3.0: A Web Server for Identifying Secondary and Super-Secondary Structure in Proteins Using NMR Chemical Shifts. Nucleic Acids Res. 2015, 43 (W1), W370– W377,  DOI: 10.1093/nar/gkv494
      There is no corresponding record for this reference.
    75. 75
      Borcherds, W. M.; Daughdrill, G. W. Using NMR Chemical Shifts to Determine Residue-Specific Secondary Structure Populations for Intrinsically Disordered Proteins. Methods Enzymol. 2018, 611, 101– 136,  DOI: 10.1016/bs.mie.2018.09.011
      There is no corresponding record for this reference.
    76. 76
      Schumann, F. H.; Riepl, H.; Maurer, T.; Gronwald, W.; Neidig, K.-P.; Kalbitzer, H. R. Combined Chemical Shift Changes and Amino Acid Specific Chemical Shift Mapping of Protein–Protein Interactions. J. Biomol. NMR 2007, 39 (4), 275– 289,  DOI: 10.1007/s10858-007-9197-z
      There is no corresponding record for this reference.
    77. 77
      Heller, G. T.; Aprile, F. A.; Michaels, T. C. T.; Limbocker, R.; Perni, M.; Ruggeri, F. S.; Mannini, B.; Löhr, T.; Bonomi, M.; Camilloni, C. Small-Molecule Sequestration of Amyloid-β as a Drug Discovery Strategy for Alzheimer’s Disease. Sci. Adv. 2020, 6 (45), eabb5924  DOI: 10.1126/sciadv.abb5924
      There is no corresponding record for this reference.
    78. 78
      Habchi, J.; Arosio, P.; Perni, M.; Costa, A. R.; Yagi-Utsumi, M.; Joshi, P.; Chia, S.; Cohen, S. I. A.; Müller, M. B. D.; Linse, S. An Anticancer Drug Suppresses the Primary Nucleation Reaction That Initiates the Production of the Toxic Aβ42 Aggregates Linked with Alzheimer’s Disease. Sci. Adv. 2016, 2 (2), e1501244  DOI: 10.1126/sciadv.1501244
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      An anticancer drug suppresses the primary nucleation reaction that initiates the production of the toxic Ab42 aggregates linked with Alzheimer's disease
      Habchi, Johnny; Arosio, Paolo; Perni, Michele; Costa, Ana Rita; Yagi-Utsumi, Maho; Joshi, Priyanka; Chia, Sean; Cohen, Samuel I. A.; Muller, Martin B. D.; Linse, Sara; Nollen, Ellen A. A.; Dobson, Christopher M.; Knowles, Tuomas P. J.; Vendruscolo, Michele
      Science Advances (2016), 2 (2), e1501244/1-e1501244/14CODEN: SACDAF; ISSN:2375-2548. (American Association for the Advancement of Science)
      The conversion of the β-amyloid (Aβ) peptide into pathogenic aggregates is linked to the onset and progression of Alzheimer's disease. Although this observation has prompted an extensive search for therapeutic agents to modulate the concn. of Aβ or inhibit its aggregation, all clin. trials with these objectives have so far failed, at least in part because of a lack of understanding of the mol. mechanisms underlying the process of aggregation and its inhibition. To address this problem, we describe a chem. kinetics approach for rational drug discovery, in which the effects of small mols. on the rates of specific microscopic steps in the self-assembly of Aβ42, the most aggregation-prone variant of Aβ, are analyzed quant. By applying this approach, we report that bexarotene, an anticancer drug approved by the U.S. Food and Drug Administration, selectively targets the primary nucleation step in Aβ42 aggregation, delays the formation of toxic species in neuroblastoma cells, and completely suppresses Aβ42 deposition and its consequences in a Caenorhabditis elegans model of Aβ42-mediated toxicity. These results suggest that the prevention of the primary nucleation of Aβ42 by compds. such as bexarotene could potentially reduce the risk of onset of Alzheimer's disease and, more generally, that our strategy provides a general framework for the rational identification of a range of candidate drugs directed against neurodegenerative disorders.
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    79. 79
      Granata, D.; Baftizadeh, F.; Habchi, J.; Galvagnion, C.; De Simone, A.; Camilloni, C.; Laio, A.; Vendruscolo, M. The Inverted Free Energy Landscape of an Intrinsically Disordered Peptide by Simulations and Experiments. Sci. Rep. 2015, 5 (1), 15449,  DOI: 10.1038/srep15449
      There is no corresponding record for this reference.
    80. 80
      Chong, S.-H.; Ham, S. Folding Free Energy Landscape of Ordered and Intrinsically Disordered Proteins. Sci. Rep. 2019, 9 (1), 14927,  DOI: 10.1038/s41598-019-50825-6
      80
      Folding Free Energy Landscape of Ordered and Intrinsically Disordered Proteins
      Chong Song-Ho; Ham Sihyun
      Scientific reports (2019), 9 (1), 14927 ISSN:.
      Folding funnel is the essential concept of the free energy landscape for ordered proteins. How does this concept apply to intrinsically disordered proteins (IDPs)? Here, we address this fundamental question through the explicit characterization of the free energy landscapes of the representative α-helical (HP-35) and β-sheet (WW domain) proteins and of an IDP (pKID) that folds upon binding to its partner (KIX). We demonstrate that HP-35 and WW domain indeed exhibit the steep folding funnel: the landscape slope for these proteins is ca. -50 kcal/mol, meaning that the free energy decreases by ~5 kcal/mol upon the formation of 10% native contacts. On the other hand, the landscape of pKID is funneled but considerably shallower (slope of -24 kcal/mol), which explains why pKID is disordered in free environments. Upon binding to KIX, the landscape of pKID now becomes significantly steep (slope of -54 kcal/mol), which enables otherwise disordered pKID to fold. We also show that it is the pKID-KIX intermolecular interactions originating from hydrophobic residues that mainly confer the steep folding funnel. The present work not only provides the quantitative characterization of the protein folding free energy landscape, but also establishes the usefulness of the folding funnel concept to IDPs.
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    81. 81
      Saravanan, K. M.; Zhang, H.; Zhang, H.; Xi, W.; Wei, Y. On the Conformational Dynamics of β-Amyloid Forming Peptides: A Computational Perspective. Front. Bioeng. Biotechnol. 2020, 8, 532,  DOI: 10.3389/fbioe.2020.00532
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      On the Conformational Dynamics of β-Amyloid Forming Peptides: A Computational Perspective
      Saravanan Konda Mani; Zhang Haiping; Zhang Huiling; Xi Wenhui; Wei Yanjie
      Frontiers in bioengineering and biotechnology (2020), 8 (), 532 ISSN:2296-4185.
      Understanding the conformational dynamics of proteins and peptides involved in important functions is still a difficult task in computational structural biology. Because such conformational transitions in β-amyloid (Aβ) forming peptides play a crucial role in many neurological disorders, researchers from different scientific fields have been trying to address issues related to the folding of Aβ forming peptides together. Many theoretical models have been proposed in the recent years for studying Aβ peptides using mathematical, physicochemical, and molecular dynamics simulation, and machine learning approaches. In this article, we have comprehensively reviewed the developmental advances in the theoretical models for Aβ peptide folding and interactions, particularly in the context of neurological disorders. Furthermore, we have extensively reviewed the advances in molecular dynamics simulation as a tool used for studying the conversions between polymorphic amyloid forms and applications of using machine learning approaches in predicting Aβ peptides and aggregation-prone regions in proteins. We have also provided details on the theoretical advances in the study of Aβ peptides, which would enhance our understanding of these peptides at the molecular level and eventually lead to the development of targeted therapies for certain acute neurological disorders such as Alzheimer's disease in the future.
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    82. 82
      Grasso, G.; Danani, A. Molecular Simulations of Amyloid Beta Assemblies. Adv. Phys.: x 2020, 5 (1), 1770627,  DOI: 10.1080/23746149.2020.1770627
      82
      Molecular simulations of amyloid beta assemblies
      Grasso, Gianvito; Danani, Andrea
      Advances in Physics: X (2020), 5 (1), 1770627CODEN: APXDAR; ISSN:2374-6149. (Taylor & Francis Ltd.)
      Several neurodegenerative disorders arise from the abnormal protein aggregation in the nervous tissue lead- ing tointracellular inclusions or extracellular aggregates in specific brain areas. In case of Alzheimer Disease, the accumulation of the Amyloid Beta peptide in the brain is proposed to be an early important event in the pathogenesis. Despite significant research efforts in this field, the mol. mechanisms of protein misfolding and aggregation remain somewhat unrevealed.Within this framework, computer simulations represent a power- ful tool able to connect macroscopic exptl. fiend- ings to nanoscale mol. events.However, from the computational point of View, insufficient sampling often limits the ability of computer simulations to fully address this point. One of the main challenges of MD simulations is the ability to sample exptl. relevant millise- cond to second timescales.The present review describes the applications of mol. dynamics techniques to elucidate the conformational states and the aggregation pathway of the Amyloid Beta peptide responsible for AD. Moreover, the computational studies focused on the impact of Amyloid Beta assemblies on cell membranes will be also described. Finally, the interaction mechanisms between promising small mols. and Amyloid Beta assemblies will be discussed within the field of designing new efficient drugs against neurodegenerative disorders.
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    83. 83
      Haass, C.; Kaether, C.; Thinakaran, G.; Sisodia, S. Trafficking and Proteolytic Processing of APP. Cold Spring Harbor Perspect. Med. 2012, 2 (5), a006270,  DOI: 10.1101/cshperspect.a006270
      83
      Trafficking and proteolytic processing of APP
      Haass, Christian; Kaether, Christoph; Thinakaran, Copal; Sisodia, Sangram
      Cold Spring Harbor Perspectives in Medicine (2012), 2 (5), a006270/1-a006270/25CODEN: CSHPFV; ISSN:2157-1422. (Cold Spring Harbor Laboratory Press)
      A review. Accumulations of insol. deposits of amyloid β-peptide are major pathol. hallmarks of Alzheimer disease. Amyloid β-peptide is derived by sequential proteolytic processing from a large type 1 trans-membrane protein, the β-amyloid precursor protein. The proteolytic enzymes involved in its processing are named secretases. β- And γ-secretase liberate by sequential cleavage the neurotoxic amyloid β-peptide, whereas α-secretase prevents its generation by cleaving within the middle of the amyloid domain. In this chapter we describe the cell biol. and biochem. characteristics of the three secretase activities involved in the proteolytic processing of the precursor protein. In addn. we outline how the precursor protein maturates and traffics through the secretory pathway to reach the subcellular locations where the individual secretases are preferentially active. Furthermore, we illuminate how neuronal activity and mutations which cause familial Alzheimer disease affect amyloid β-peptide generation and therefore disease onset and progression.
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    84. 84
      Zhou, M.; Wen, H.; Lei, H.; Zhang, T. Molecular Dynamics Study of Conformation Transition from Helix to Sheet of Aβ42 Peptide. J. Mol. Graphics Modell. 2021, 109, 108027,  DOI: 10.1016/j.jmgm.2021.108027
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      Molecular dynamics study of conformation transition from helix to sheet of Aβ42 peptide
      Zhou, Min; Wen, Huilin; Lei, Huimin; Zhang, Tao
      Journal of Molecular Graphics & Modelling (2021), 109 (), 108027CODEN: JMGMFI; ISSN:1093-3263. (Elsevier Ltd.)
      Aβ42 peptides can form helix and sheet structure under different conditions. The conformational conversion is closely assocd. with Aβ peptides aggregation and their neurotoxicity. But the transition from helix to sheet is not be clearly understood. In this study we performed microsecond timescale MD simulations of Aβ42 peptide to investigate the conformation transition from α-helix to β-sheet. Markov state model (MSM) was built to facilitate identification of crucial intermediate states and possible transition pathway. Based on the anal., we found that the region Y10-A21 in the middle of Aβ42 peptide plays an initial role in this transition. MSM model revealed that the collapse of helical structure in this region might trigger the formation of sheet structure. Moreover, we further simulated the aggregation of Aβ42 peptides with different conformations. We found that the Aβ42 peptides forming sheet structure have higher aggregation potential compared with peptides with helix structure. These results demonstrate that we can prevent the aggregation of Aβ42 peptides by stabilizing the helix structure in the region of Y10-A21. In addn., this study provides new insight into better understanding the conformational transition and aggregation of Aβ42 peptides.
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    85. 85
      Shuaib, S.; Goyal, B. Scrutiny of the Mechanism of Small Molecule Inhibitor Preventing Conformational Transition of Amyloid-Β42 Monomer: Insights from Molecular Dynamics Simulations. J. Biomol. Struct. Dyn. 2018, 36 (3), 663– 678,  DOI: 10.1080/07391102.2017.1291363
      There is no corresponding record for this reference.
    86. 86
      Liu, F.; Ma, Z.; Sang, J.; Lu, F. Edaravone Inhibits the Conformational Transition of Amyloid-Β42: Insights from Molecular Dynamics Simulations. J. Biomol. Struct. Dyn. 2020, 38 (8), 2377– 2388,  DOI: 10.1080/07391102.2019.1632225
      There is no corresponding record for this reference.
    87. 87
      Narang, S. S.; Goyal, D.; Goyal, B. Inhibition of Alzheimer’s Amyloid-Β42 Peptide Aggregation by a Bi-Functional Bis-Tryptoline Triazole: Key Insights from Molecular Dynamics Simulations. J. Biomol. Struct. Dyn. 2020, 38 (6), 1598– 1611,  DOI: 10.1080/07391102.2019.1614093
      There is no corresponding record for this reference.
    88. 88
      Cao, Y.; Jiang, X.; Han, W. Self-Assembly Pathways of β-Sheet-Rich Amyloid-β(1–40) Dimers: Markov State Model Analysis on Millisecond Hybrid-Resolution Simulations. J. Chem. Theory Comput. 2017, 13 (11), 5731– 5744,  DOI: 10.1021/acs.jctc.7b00803
      88
      Self-Assembly Pathways of β-Sheet-Rich Amyloid-β(1-40) Dimers: Markov State Model Analysis on Millisecond Hybrid-Resolution Simulations
      Cao, Yang; Jiang, Xuehan; Han, Wei
      Journal of Chemical Theory and Computation (2017), 13 (11), 5731-5744CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      Early oligomerization during amyloid-β (Aβ) aggregation is essential for Aβ neurotoxicity. Understanding how unstructured Aβs assemble into oligomers, esp. those rich in β-sheets, is essential but remains challenging as the assembly process is too transient for exptl. characterization and too slow for mol. dynamics simulations. So far, at. simulations are limited only to studies of either oligomer structures or assembly pathways for short Aβ segments. Here, to overcome the computational challenge, we combined in this study a hybrid-resoln. model and adaptive sampling techniques to perform over 2.7 ms of simulations of formation of full-length Aβ40 dimers that are the earliest toxic oligomeric species. The Markov state model was further employed to characterize the transition pathways and assocd. kinetics. The results showed that for 2 major forms of β-sheet-rich structures reported exptl., the corresponding assembly mechanisms were markedly different. Hairpin-contg. structures were formed by direct binding of sol. Aβ in β-hairpin-like conformations. The formation of parallel, in-register structures resembling fibrils occurred ∼100-fold more slowly and involved a rapid encounter of Aβ in arbitrary conformations followed by a slow structural conversion. The structural conversion proceeded via diverse pathways but always required transient unfolding of encounter complexes. We found that the transition kinetics could be affected differently by intramol./intermol. interactions involving individual residues in a conformation-dependent manner. In particular, the interactions involving Aβ's N-terminal part promoted the assembly into hairpin-contg. structures but delayed the formation of fibril-like structures, thus explaining puzzling observations reported previously regarding the roles of this region in the early assembly process.
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    89. 89
      Rojas, A. V.; Liwo, A.; Scheraga, H. A. A Study of the α-Helical Intermediate Preceding the Aggregation of the Amino-Terminal Fragment of the β Amyloid Peptide (Aβ1–28). J. Phys. Chem. B 2011, 115 (44), 12978– 12983,  DOI: 10.1021/jp2050993
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      A Study of the α-Helical Intermediate Preceding the Aggregation of the Amino-Terminal Fragment of the β Amyloid Peptide (Aβ1-28)
      Rojas, Ana V.; Liwo, Adam; Scheraga, Harold A.
      Journal of Physical Chemistry B (2011), 115 (44), 12978-12983CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
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  • Supporting Information

    Supporting Information

    The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacsau.4c00182.

    • Detailed materials and methods, complementary to the concise descriptions in this main text, Supplementary discussions (Notes 1–10), Supplementary figures: structure of Aβ42 (Figure S1), comparison of the Amber ff14SB and CHARMM36m force fields (Figures S2 and S3), comparison of different adaptive sampling protocols (Figures S4 and S5), temporal alignment and concatenation of the adaptive sampling and classical MDs (Figures S6–S9), conventional Markov state model analysis (Figures S10–S12), variational Markov state analysis using VAMPnets (Figures S13–S18), comparative Markov state model analysis (Figure S19), time-based evolution of the states (Figure S20), radius of gyration by state (Figure S21), characterization of learned conformational states via network gradients (Figures S22 and S23), interactions of Aβ42 with the small molecules (Figures S24–S26), experimental validation (Figures S27–S31), Supplementary tables: comparison of computational protocols for the simulation of Aβ42 (Table S1), analysis of classical MDs (Table S2), summary of the effects of small molecules (Table S3), and intramolecular interactions of Aβ42 (Table S4) (PDF)


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