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Training Neural Network Models Using Molecular Dynamics Simulation Results to Efficiently Predict Cyclic Hexapeptide Structural Ensembles

Cite this: J. Chem. Theory Comput. 2023, 19, 14, 4757–4769
Publication Date (Web):May 26, 2023
https://doi.org/10.1021/acs.jctc.3c00154

Copyright © 2023 The Authors. Published by American Chemical Society. This publication is licensed under

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Abstract

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Cyclic peptides have emerged as a promising class of therapeutics. However, their de novo design remains challenging, and many cyclic peptide drugs are simply natural products or their derivatives. Most cyclic peptides, including the current cyclic peptide drugs, adopt multiple conformations in water. The ability to characterize cyclic peptide structural ensembles would greatly aid their rational design. In a previous pioneering study, our group demonstrated that using molecular dynamics results to train machine learning models can efficiently predict structural ensembles of cyclic pentapeptides. Using this method, which was termed StrEAMM (Structural Ensembles Achieved by Molecular Dynamics and Machine Learning), linear regression models were able to predict the structural ensembles for an independent test set with R2 = 0.94 between the predicted populations for specific structures and the observed populations in molecular dynamics simulations for cyclic pentapeptides. An underlying assumption in these StrEAMM models is that cyclic peptide structural preferences are predominantly influenced by neighboring interactions, namely, interactions between (1,2) and (1,3) residues. Here we demonstrate that for larger cyclic peptides such as cyclic hexapeptides, linear regression models including only (1,2) and (1,3) interactions fail to produce satisfactory predictions (R2 = 0.47); further inclusion of (1,4) interactions leads to moderate improvements (R2 = 0.75). We show that when using convolutional neural networks and graph neural networks to incorporate complex nonlinear interaction patterns, we can achieve R2 = 0.97 and R2 = 0.91 for cyclic pentapeptides and hexapeptides, respectively.

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SPECIAL ISSUE

This article is part of the Machine Learning for Molecular Simulation special issue.

1. Introduction

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Protein–protein interactions regulate many key biological processes, and the ability to target specific protein–protein interactions is of great therapeutic interest. While biologics can target large protein surfaces (∼1500 to 3000 Å2) involved in protein–protein interactions, these molecules typically exhibit poor cell membrane permeability and thus are unable to reach intracellular targets. (1,2) Conversely, small-molecule drugs can better cross cell membranes and engage intracellular targets. However, small molecules are often too small to target such large, flat protein surfaces. Cyclic peptides are candidate molecules with unique properties that can address the limitations of small molecules and biologics. Ranging from 500 to 1500 Da, cyclic peptides have the potential to target protein–protein interactions while still possessing good membrane permeabilty. (1,3,4) Thus, cyclic peptides have emerged as a promising drug modality, and within the past 20 years, 18 cyclic peptide drugs have been approved by the FDA. (5,6) Unfortunately, many of these recently approved cyclic peptide drugs are natural products or their derivatives, and the de novo design of cyclic peptide therapeutics remains difficult. The ability to efficiently characterize or predict cyclic peptide structures could greatly enhance cyclic peptide development but is currently hard to achieve. For example, characterizing cyclic peptide structures can be difficult using analytical methods like solution NMR spectroscopy because cyclic peptides often adopt multiple conformations in solution. (7−9) The use of computational methods like molecular dynamics (MD) simulations, density functional theory (DFT) calculations, and the NMR Analysis of Molecular Flexibility in Solution (NAMFIS) algorithm (10) can help interpret solution NMR spectroscopy results, i.e., these methods can generate an ensemble of conformers that can be compared to experimental observables from NMR spectroscopy such as chemical shifts. (7,11) Aside from using MD simulation as a means for NMR spectroscopy interpretation, the use of MD simulation itself has proved useful in characterizing cyclic peptide structural ensembles. (12−17) Because cyclic peptides can have many solvent-exposed backbone hydrogen-bond donors and acceptors available to interact with polar solvent molecules like water, these interactions must be accounted for. Thus, the inclusion of explicit solvent in order to accurately elucidate cyclic peptide structures is necessary. (18−20) Unfortunately, MD simulations using explicit solvent are computationally expensive, making them inefficient and unfeasible for large-scale screening.
Recently, machine learning (ML) models such as AlphaFold2 and RoseTTAFold have shown exciting successes in predicting structures of folded proteins. (21−24) In theory, these models can be used to predict the structures of cyclic peptides, especially when the cyclic peptides have a clear fold and adopt structural motifs observed in folded proteins. (25) However, it should be noted that cyclic peptides typically contain between 5 and 15 residues, (5,26) and thus they are generally unable to adopt regular secondary structures and most of the time lack a highly populated “fold”. Currently, it is difficult to use these ML models to predict structural ensembles adopted by non-well-behaved peptides in aqueous solution. Furthermore, these state-of-the-art ML models for protein structure prediction are trained on the extensive structural and evolutionary data available for proteins. In contrast, there are very thin structural and evolutionary data available for cyclic peptides because of the scarcity of NOE signals, the general lack of a highly populated structure, and the fact that cyclic peptides are often synthesized through nonribosomal pathways, (27−30) making it potentially challenging to improve the models using a similar strategy. Lastly, since these models are trained using structural and evolutionary data for proteins, they are unable to make predictions for peptides composed of unnatural amino acids.
Recently, our group developed a method that trains ML models for cyclic peptide structure prediction using MD simulation results and called this method StrEAMM (Structural Ensembles Achieved by Molecular Dynamics and Machine Learning). (31) The method was applied to a simple cyclic pentapeptide system with a 15 amino acid library as a proof-of-concept study. In brief, our group performed MD simulations of 705 cyclic pentapeptides and obtained the structural ensembles, i.e., a collection of different structures and their associated populations, to form the training dataset. Then we trained linear regression models that could predict the structural ensembles for new cyclic pentapeptide sequences in an independent test dataset. While the initial simulations to generate the training dataset were time-consuming, the resulting trained model could make a structural ensemble prediction in less than 1 s per sequence, and the trained model could provide simulation-quality structural ensemble predictions for all the sequences in their sequence space (which was ∼150,000 for cyclic pentapeptides consisting of a 15 amino acid library).
In this work, we aim to assess whether the StrEAMM methodology can be extended to larger cyclic peptides, as many cyclic peptide drugs are larger than just five residues. The original StrEAMM linear regression models for cyclic pentapeptides predicted the natural logarithm of the population of sequence cyclo-(X1X2X3X4X5) adopting the structure S1S2S3S4S5 in the ensemble (Figure 1). Here the structure of a cyclic pentapeptide was described using five “structural digits”, which were assigned based on each residue’s backbone (ϕ, ψ) dihedrals (Figure 2A,B). The linear regression models used weights to represent the contributions of (1,2) and (1,3) neighboring interactions to the natural logarithm of the population of a specific structure. While including (1,2) and (1,3) neighboring interactions was found to be sufficient to describe the structural preferences of cyclic pentapeptides, longer-range interactions (such as (1,4) neighbors) and other complex, multibody interactions may be required to accurately describe the structural preferences of larger cyclic peptides.

Figure 1

Figure 1. StrEAMM linear regression models are constructed using contributions from neighboring interactions. For example, the natural logarithm of the population of cyclic pentapeptide cyclo-(X1X2X3X4X5) adopting a specific structure S1S2S3S4S5 is the sum of the interaction weights for each (1,2) and (1,3) neighbor present. Xi is an amino acid; Si is a structural digit that represents a region of (ϕ, ψ) space (see Figure 2); wSiSi+1XiXi+1 is the weight for residues XiXi+1 adopting structure SiSi+1; wSiSi+1Si+2Xi_Xi+2 is the weight for residues Xi and Xi+2 adopting substructure SiSi+1Si+2; and wQX1X2X3X4X5 is related to the partition function, Q, for sequence X1X2X3X4X5 and ensures that all the structures’ populations sum to 1 for a given sequence. This equation was first proposed by Miao et al. (31)

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Figure 2

Figure 2. Structural binning maps divide the (ϕ, ψ) space of cyclic pentapeptides into 10 regions and the (ϕ, ψ) space of cyclic hexapeptides into six regions. (A) The (ϕ, ψ) population density of cyclo-(GGGGG) and (B) the resulting binning map when all the grid points are assigned to their closest centroid to form the final binning map. (C) The (ϕ, ψ) population density of cyclo-(GGGGGG) and (D) the resulting binning map using the same binning protocol.

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Here we extend the StrEAMM methodology to predict the structural ensembles of cyclic hexapeptides. We first show that the current StrEAMM linear regression models did not perform well in predicting cyclic hexapeptide structural ensembles when trained on cyclic hexapeptide simulation results and using (1,2) and (1,3) neighboring interaction weights. We show that upon adding additional two-body interactions, the (1,4) neighboring interactions, the model achieved moderate performance. We then propose using the StrEAMM methodology with other ML models such as convolutional neural networks (CNNs) and graph neural networks (GNNs). These neural network models can easily embed nonlinear relationships and have found success in biologically relevant applications such as secondary structure prediction, protein fold family predictions, and binding affinity predictions. (32−36) Lastly, we show that when using the StrEAMM neural network models, we can successfully and efficiently predict the structural ensembles for both cyclic pentapeptides and cyclic hexapeptides.

2. Methods

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2.1. Datasets

We prepared our training and test datasets for our ML models by generating diverse cyclic peptide sequences, performing MD simulations of these sequences, and analyzing their MD results. For cyclic pentapeptides, to enable comparison with our previously published StrEAMM linear regression models, we used the same 705 cyclic pentapeptide training dataset from that study (31) to train our StrEAMM neural network models. These cyclic pentapeptide sequences were generated from a library of 15 amino acids including G, A, V, F, N, S, D, R, a, v, f, n, s, d, and r, where the lowercase letters represent the d-amino acids. These 15 amino acids were selected to be a diverse and representative subset of the canonical amino acids and their d forms: G is achiral and the smallest amino acid; A is the simplest chiral amino acid, with only a methyl group side chain; V has a β branch in its side chain; F has an aromatic ring in its side chain; N has an amide group in its side chain; S has a hydroxyl group in its side chain; D has a negatively charged side chain; and R has a positively charged side chain. Their d forms are also considered, as including d-amino acids in cyclic peptide design can expand the accessible structural space beyond what is achievable using only l-amino acids. Additionally, including d-amino acids in the peptide sequence can improve the peptide’s stability against enzymatic degradation. (38,39) The cyclic pentapeptide training sequences were generated in a semirandom protocol which efficiently produced diverse sequences that allowed us to observe all the possible XiXi+1Xi+2 subsequences (where Xi is one of the 15 amino acids) at least once. This protocol resulted in 705 cyclic pentapeptide training sequences. Fifty random cyclic pentapeptide sequences were used as the test set to evaluate the performance of the models. For cyclic hexapeptides, using the same 15 amino acid library and following a similar sequence generation protocol, we generated and performed MD simulations of 581 cyclic hexapeptide training sequences (List S1). For the test dataset, we followed the same procedure to obtain 50 random cyclic hexapeptide sequences (List S2).

2.2. Molecular Dynamics Simulations

To characterize the structural ensembles of the cyclic hexapeptides, we performed two parallel bias-exchange metadynamics (BE-META) simulations starting with two different initial structures for each cyclic hexapeptide. (40−42) BE-META, and more generally metadynamics, is an enhanced sampling technique that biases collective variables which ideally describe the slow degrees of freedom. During a metadynamics simulation, Gaussian potentials are deposited along each collective variable to push the conformation away from spots along the collective variable. (41) When there are multiple collective variables of interest, BE-META can be used, where multiple replicas of the simulation, each biased along one collective variable, are all simulated in parallel; periodically during the simulations, structures of different replicas can exchange with each other based on the Metropolis criterion, effectively enhancing sampling in all collective variables. (43)
In principle, one set of BE-META simulations should be able to sample the conformational space of a cyclic peptide when the simulations have been run long enough. To monitor and verify simulation convergence, for each cyclic peptide sequence, we performed two sets of BE-META simulations, starting from two different initial structures. Each set of BE-META simulations explored the conformational space independently, and the conformational sampling was considered sufficient when the two sets of BE-META simulations provided similar structural ensembles for the same cyclic peptide. For each cyclic hexapeptide in our training and test datasets, we prepared two initial structures (referred to as s1 and s2) using the UCSF Chimera package. (44) To ensure that the two initial structures were sufficiently different, we required that the backbone root-mean-square deviation (RMSD) between the two structures must be larger than 1.5 Å. For head-to-tail cyclized hexapeptides with all-trans peptide bonds, a backbone RMSD of 1.5 Å is fairly large, and it is likely geometrically impossible for two conformations to have a backbone RMSD greater than 2.0 Å. Therefore, we considered the conformations of two cyclic hexapeptides significantly different when they had a backbone RMSD greater than 1.5 Å.
All the MD simulations were performed with GROMACS 2018.6 (45) using the residue-specific force field 2 (RSFF2) (46) and TIP3P water. (47) We chose the RSFF2 force field because it was reported to have the best performance in recapitulating the crystal structures of 20 cyclic peptides (from length 5 to 12 amino acids) among RSFF1, (48) RSFF2, (46) Amber99sb-ildn, (49) and OPLS-AA/L. (50,51) Each initial structure was energy-minimized in vacuum using the steepest descent algorithm. Then, each structure was solvated in a box of water, with a minimum distance of 1.0 nm between the cyclic peptide and the walls of the box. If the total charge of the system was nonzero, counterions were added to neutralize the system. The solvated system was then energy-minimized using the steepest descent algorithm. Following energy minimization, two stages of equilibration were performed on the solvated system. First, the solvent molecules were allowed to equilibrate while the heavy atoms of the cyclic peptide were restrained using a harmonic potential with a force constant of 1000 kJ·mol–1·nm–2. This first stage of equilibration began with a 50 ps NVT simulation at 300 K followed by a 50 ps NPT simulation at 300 K and 1 bar. In the second equilibration stage, the restraints on the heavy atoms were removed to allow the whole system to equilibrate. This second stage of equilibration began with a 100 ps NVT simulation at 300 K followed by a 100 ps NPT simulation at 300 K and 1 bar. The production simulations were at least 200 ns NPT simulations at 300 K and 1 bar. The leapfrog algorithm with a time step of 2 fs was used to integrate the equations of motion. Bonds involving hydrogen were constrained with the LINCS algorithm during production. Nonbonded interactions (electrostatic and Lennard-Jones interactions) were truncated at 1.0 nm. For long-range electrostatic interactions, the particle mesh Ewald method (52) with a Fourier grid spacing of 0.12 nm and an interpolation order of 4 was applied. To account for the truncation of Lennard-Jones interactions, a long-range dispersion correction for energy and pressure was applied. An additional improper dihedral related to the H, N, C, and O atoms for each peptide bond was also included to maintain the trans amide configuration, and data used in our analysis contained only trans peptide bonds.
We performed two parallel BE-META simulations of the two initial structures for each cyclic hexapeptide using GROMACS 2018.6 (45) patched by the PLUMED 2.5.1 plugin. (53) For each BE-META simulation, there were six replicas biasing the 2D collective variables (ϕi, ψi) and six replicas biasing the 2D collective variables (ψi, ϕi+1), as it was previously observed that conformational changes of cyclic peptides involve coupled changes of these dihedral pairs. (42) In addition to the 12 biased replicas, five neutral replicas were also included to obtain the unbiased structural ensemble that was used for analysis. The trajectories were analyzed using dihedral principal component analysis. (54) We calculated the 3D density distributions of s1 and s2 simulations projected in the top three principal components, and we monitored simulation convergence by calculating the normalized integrated products (NIPs) between the s1 and s2 density distributions, where a NIP value of 1.0 represents perfect similarity. (55) Most BE-META simulations of our cyclic hexapeptides were performed for 200 ns, and when the last 100 ns of the neutral replicas was used for structural analysis, the density distributions between the s1 and s2 simulations had a NIP of ≥0.9. In these cases, trajectories of the last 100 ns of the neutral replicas of both s1 and s2 simulations were combined for each cyclic peptide and used for further structural analysis. However, some simulations did not reach a NIP of 0.9 when using the last 100 ns of 200 ns BE-META simulations. We extended these simulations to 300 ns and used the last 200 ns of the neutral replicas to calculate the NIP. To ensure that we only included high-quality data, sequences that still did not converge in 300 ns were discarded from the dataset. The final cyclic hexapeptide datasets included 555 (out of 581) sequences for training and 49 (out of 50) for testing (the sequences that did not reach convergence are colored gray in Lists S1 and S2). Files describing how to run BE-META simulations of cyclic peptides and scripts to perform dihedral principal component analysis can be found on GitHub (https://github.com/ysl-lab/CP_tutorial).

2.3. Structural Analysis

We described cyclic peptide conformations using the backbone dihedral angles (ϕ, ψ) for each residue, which are typically represented in the continuous range between −180° and 180°. In order to further simplify the structure definitions, the (ϕ, ψ) space can be separated into discrete regions, and each region can be assigned a “structural digit” (denoted by Greek letters here). (31,37,56) For example, in our previous work on cyclic pentapeptides, we used the (ϕ, ψ) distribution of cyclo-(GGGGG) to guide the discretization of the (ϕ, ψ) space for cyclic pentapeptides (Figure 2A,B). (31) First, the (ϕ, ψ) distribution of cyclo-(GGGGG) was binned into a 100 × 100 grid, and the probability density of each grid point was calculated. Then all of the grid points with a probability density larger than 0.00001 were clustered using a grid-based and density-peak-based method, resulting in 10 clusters. (57) For each cluster, the centroid was defined by the grid point with the smallest average of distances to the remaining grid points of the cluster, where the distances were also weighted by the probability density of each remaining grid point. Then, all the grid points were assigned to their closest centroid to form the final binning map (Figure 2B). Each of the 10 regions was assigned a “structural digit” (Greek letter Λ, λ, Γ, γ, B, β, Π, π, Ζ, or ζ). In the end, a cyclic pentapeptide structure could be described using a string of five structural digits based on the (ϕ, ψ) of each residue. For example, if the sequence sasFr (lowercase letters denote d-amino acids) had a structure represented using the five-digit structural code ζλβΠλ, it meant that ser1 had dihedral angles within the region assigned to the structural digit “ζ” in Figure 2B, ala2 had dihedral angles within the “λ” region, ser3 had dihedral angles within the “β” region, Phe4 had dihedral angles within the “Π” region, and arg5 had dihedral angles within the “λ” region. In this work, we performed the same protocol using cyclo-(GGGGGG) to obtain the binning map for cyclic hexapeptides (Figure 2C,D). These maps (Figures 2B and 2D) are herein called “Map 1” maps.
Given the significance of this structural analysis and discretization method in defining the structural ensembles used to train our models, here we also explored two variations to this protocol. In one variation, instead of performing our clustering protocol on only grid points with a probability density larger than 0.00001, we performed cluster analysis on all 100 × 100 grid points. The inclusion of all grid points in the clustering protocol eliminated the need to calculate the distances between the grid points to all the cluster centroids and assign grid points to their nearest centroid. This modification changed the shape of the clusters for both the cyclic pentapeptide and cyclic hexapeptide binning maps (Figure S1A, bottom). The resulting binning maps from this modified protocol are herein called “Map 2” maps.
Previously, it was assumed that cyclic polyglycines could provide a representative binning map for both d- and l-amino acids because glycine is achiral and the most flexible amino acid. In the second variation to the protocol, instead of clustering the (ϕ, ψ) distributions of cyclic polyglycines (Figure 2A,C and Figure S1A, top), we clustered the (ϕ, ψ) distributions of the cyclic peptides in our training datasets (Figure S1B, top). The (ϕ, ψ) distributions of the cyclic pentapeptide training dataset and the cyclic hexapeptide training dataset were clustered using all 100 × 100 grid points. The resulting binning maps are herein called “Map 3” maps (Figure S1B, bottom). A MATLAB script to perform grid-based and density-based clustering is available on GitHub (https://github.com/ysl-lab/CP_tutorial).

2.4. Linear Regression Models

In our group’s previous work on cyclic pentapeptides, the StrEAMM linear regression models were built to predict the (natural logarithm of) population for a sequence cyclo-(X1X2X3X4X5) adopting the structure S1S2S3S4S5. (31) We first hypothesized that neighboring interactions contribute to cyclic peptide structural preferences and that these interactions were additive like energy terms. This assumption, along with the exponential relationship between energies and population in the Boltzmann distribution (pi=e−Ei/kBTQ, where Q=∑ie−Ei/kBT) motivated our proposed exponential relationship between the sum of the neighboring interactions and the predicted population. We explicitly included (1,2) and (1,3) interactions, and they were represented by different “weight” terms (w). Thus, the population of a cyclic pentapeptide sequence cyclo-(X1X2X3X4X5) adopting the structure S1S2S3S4S5 is
pS1S2S3S4S5X1X2X3X4X5=exp(wS1S2X1X2+wS2S3X2X3+wS3S4X3X4+wS4S5X4X5+wS5S1X5X1+wS1S2S3X1_X3+wS2S3S4X2_X4+wS3S4S5X3_X5+wS4S5S1X4_X1+wS5S1S2X5_X2)/Q
in which the partition function, Q, is the sum of the exponential terms for all the structures in the ensemble for cyclo-(X1X2X3X4X5) and was used to calculate the exact populations for the structures.
To convert this exponential relationship to a linear relationship that could ultimately be used for our linear regression model, we applied a natural logarithm operation. This operation resulted in a linear equation between ln pS1S2S3S4S5X1X2X3X4X5 and the specific (1,2) and (1,3) weights and a weight that represented Q (Figure 1). To train the linear regression model, we first formulated the linear equation describing ln pS1S2S3S4S5X1X2X3X4X5 using the 11 corresponding weights, for every sequence and structure pair (X1X2X3X4X5 adopting a structure S1S2S3S4S5) in the training dataset. The set of linear equations for describing all the ln pS1S2S3S4S5X1X2X3X4X5 in the training dataset was represented as a matrix Aw. The coefficient matrix A contains the coefficients for the weights w and was used to select the needed weights for predicting ln pS1S2S3S4S5X1X2X3X4X5. For example, the linear equation for ln pζλβΠλsasFr is
ln⁡pζλβΠλsasFr=(1×wζλsa)+(1×wλβas)+(1×wβΠsF)+(1×wλΠFr)+(1×wζλrs)+(1×wζλβs_s)+(1×wλβΠa_F)+(1×wβΠλs_r)+(1×wΠλζF_s)+(1×wλζλr_a)+(1×wQsasFr)
In the row of the coefficient matrix A that corresponds to this specific sequence–structure population, the coefficients for these 11 weights are 1, while all of the other coefficients are 0. The linear regression model updated the (1,2) and (1,3) weights to minimize the difference between the predicted ln pS1S2S3S4S5X1X2X3X4X5 and the actual ln pS1S2S3S4S5X1X2X3X4X5 observed in the MD simulations. We used least-squares fitting to minimize our weighted loss function L(w):
L(w)=∑i=1Npi|∑j=1MAijwj−ln⁡pi|2
where M is the number of weights, N is the number of sequence–structure pairs, and pi is the population observed in the MD simulation. The loss function was weighted by the population such that there was a larger contribution to the calculated loss from highly populated structures.

2.5. Neural Network Models

2.5.1. Amino Acid Feature Representation and Data Augmentation for Neural Networks

To represent a cyclic peptide sequence, we first encoded each amino acid in our library using circular topological molecular fingerprints (i.e., Morgan fingerprints) (58) with RDKit version 2021.03.05. (59) A molecular fingerprint breaks down molecules into a set of substructures, and then those resulting substructures can be represented as an N-bit vector, where the 1s and 0s correspond to the presence and absence of each substructure, respectively. We generated fingerprints using a radius of 3 (i.e., atoms up to three bonds away are considered in the substructure search), considering chirality, and using a fingerprint length of N = 2048 bits.
We also performed cyclic permutations of our datasets to give our models examples of the cyclic nature of our peptides. For example, if the cyclic peptide sequence sasFr had an observed structure ζλβΠλ in MD with 69.35% population, then we also supplied the model with the following additional four examples whose sequences and structural digits were cyclically permuted: sequence asFrs with the structure λβΠλζ with 69.35% population, sequence sFrsa with the structure βΠλζλ with 69.35% population, sequence Frsas with the structure Πλζλβ with 69.35% population, and sequence rsasF with the structure λζλβΠ with 69.35% population.
Additionally, we leveraged the enantiomeric nature of amino acids and the centrosymmetry of the structural digit binning maps (Figures 2B and 2D) to add the enantiomers of the cyclic peptides that we simulated to the datasets. When swapping an l-amino acid for a d-amino acid or vice versa, its corresponding structural digits would be capitalized if previously lowercase and lowercase if previously capitalized. Here, when we report performance of the neural network models on the training and test datasets, we take the model’s structural ensemble prediction for a sequence to be the average of the predictions for all of the cyclic permutations and the enantiomers of the sequence.

2.5.2. StrEAMM Convolutional Neural Networks

For our CNNs, we aimed to design architectures that would perform convolutions on combinations of (1,2), (1,3), and (1,4) neighboring residues, analogous to the StrEAMM linear regression models. To achieve so, we represented one sequence with N residues as a matrix with N columns and 2048 rows, where 2048 is the dimension of the fingerprint encoding (Figure 3A). Then, in the case of a (1,2) architecture, we generated a similar 2048 × N matrix representation for the original sequence permutated by one position. We concatenated these two matrices to create a 4096 × N matrix, such that the fingerprint encodings representing the residues in a (1,2) neighboring pair are in the same column (Figure 3B). Other architectures were created by modifying the permutation step (i.e., for a (1,3) architecture, the 2048 × N matrix representation for the original sequence and the 2048 × N matrix representation for the original sequence permutated by two positions were concatenated).

Figure 3

Figure 3. Convolutional neural network and graph neural network architectures. (A) Cartoon example of the cyclic pentapeptide sequence cyclo-(sasFr) represented using a matrix with N = 5 columns and 2048 rows, where the 2048 bits come from the fingerprint encoding of each amino acid. (B) The representations of cyclo-(sasFr) and cyclo-(asFrs) are concatenated such that the (1,2) neighboring residues are spatially close together, enabling the 1D convolutional filter (blue box representing a (4096 × 1) vector of learnable model parameters) to encompass all the fingerprint features that define residues s and a. (C) The top graph represents a cyclic pentapeptide, where the (1,2) edge types are denoted with blue arrows and the (1,3) edge types are denoted with green arrows. The bottom graph represents a cyclic hexapeptide, where in addition to the (1,2) and (1,3) edge types we also can include (1,4) edge types, as denoted with purple arrows. Note: The purple (1,4) edges appear to be double-arrowed, but there are really two unique single-arrowed edges. For example, the forward edge in dark purple that starts at ser1 would be directed to Phe4, and the forward edge in dark purple that starts at Phe4 would be directed to ser1.

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The input to the CNN model was this resulting feature matrix representing the cyclic peptide, and the output of the model was a structural ensemble prediction in the form of an array of structure populations. Only structures whose populations were larger than 0.1% in at least one of the cyclic peptides in the training dataset were considered, along with their permutations and enantiomers. The feature matrix of the cyclic peptide was input to the convolutional layer of the CNN model. Here the convolutions were dot product calculations performed between each column of the matrix and the 1D convolutional filter, which is a vector containing 4096 parameters that are updated during model training. After the convolutions were performed, the resulting learned representation of the cyclic peptide sequence was fully connected to the hidden layer of a multilayer perceptron (MLP), followed by the output layer (which has a number of nodes equal to the number of structures in the structural ensemble). A rectified linear unit (ReLU) activation function (60) was applied to the node representations to apply nonlinearity during the forward pass through the MLP. The SoftMax activation function was applied to the output layer to ensure that the output structural ensemble was normalized. All models were trained using the Adam optimizer (61) and summation of the squared errors loss function (L = ∑i = 1N(pi,learned – pi)2, where N is the number of populations in the training dataset, pi,learned is the population learned by the network, and pi is the actual population observed in MD simulations). The number of filters, the number of nodes in the hidden layer, and the learning rate were tuned using a grid search with three-fold cross-validation for up to 2500 epochs and saving the model results every 100 epochs (Figures S2 and S3). Neural network training was performed using PyTorch 1.9.0 (62) and PyTorch Geometric 1.7.2 (63) software. The models that had the best-performing hyperparameters were selected based on comparing the average (across the three folds) mean square error (MSE) loss on the validation datasets. The optimal number of epochs was selected using an overfitting criterion based on percentage change and generalized error calculations using the average MSE loss at every 100 epochs (Figure S4). (64)

2.5.3. StrEAMM Graph Neural Networks (GNNs)

We represented a cyclic pentapeptide or a cyclic hexapeptide as a graph with one node for each amino acid in the sequence, and the initial node representation was set using an amino acid’s 2048-bit molecular fingerprint. In a cyclic pentapeptide graph representation, the nodes can be connected by up to four types of directed edges, where two types of edges (forward and backward with respect to peptide sequence) connect (1,2) neighbor nodes and two types of edges connect (1,3) neighbor nodes (Figure 3C). We included two directional edges to prevent a sequence and its retroisomer (reverse ordering sequence, i.e., sasFr and rFsas) from being encoded as identical graphs. Thus, a cyclic pentapeptide was represented by a graph with five nodes and up to 20 edges. We refer to the models built with the inclusion of different sets of these edges as the StrEAMM GNN (1,2), StrEAMM GNN (1,3), and StrEAMM GNN (1,2)+(1,3) models depending on whether the models connect (1,2) neighbor nodes only, (1,3) neighbor nodes only, or both (1,2) and (1,3) neighbor nodes. The cyclic hexapeptide graph representation was constructed in similar fashion, but we also included the option for (1,4) edge types, such that the resulting graph had six nodes and up to 36 directed edges (Figure 3C).
The aim of the GNN models is to input a cyclic peptide graph and output a structural ensemble prediction in the same format as the CNN models. Starting with the input graph, the network underwent one message passing operation using the RGCNConv operator through PyTorch Geometric. (63,65) This operator updated each node’s representation by summing the node’s transformed initial representation and the transformed representations of any nodes it was connected to by an edge. Each different edge type had its own weights because of their unique learned transformations. The ReLU activation function (60) was applied to the node representations, and the resulting node representations were concatenated. This concatenated vector was a learned representation of the cyclic peptide sequence that was then passed through an MLP architecture with a single hidden layer. The ReLU activation function (60) was also applied at the hidden layer, and a SoftMax activation function was applied to the output layer in a similar fashion to the CNN models. The hyperparameters, such as the number of nodes in the hidden layer and the learning rate, were tuned using a grid search with three-fold cross-validation in the same approach as the CNNs (Figures S5 and S6). The GNN models were trained with the same sum of squared errors loss function and the Adam optimizer, (61) and the PyTorch 1.9.0 (62) and PyTorch Geometric 1.7.2 (63) software packages were used for the GNN training.

3. Results and Discussion

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3.1. StrEAMM Linear Regression (1,2)+(1,3) Models Cannot Predict the Structural Ensembles of Cyclic Hexapeptides

In our previously published proof-of-concept study, the StrEAMM linear regression model incorporated weights related to (1,2) and (1,3) neighboring interactions and could efficiently and accurately predict the structural ensembles of cyclic pentapeptides. (31) Specifically, the StrEAMM linear regression (1,2)+(1,3) model had R2 = 0.94 and an average weighted error (WE) of 1.54 in percent population between the predicted and observed populations for cyclic pentapeptide sequences in the test dataset (Figure 4A). Here, the scatter plots compare the predicted and observed percent population in MD for each structure in a cyclic peptide’s structural ensemble, and all the cyclic peptides within the training or test dataset are included in the corresponding scatter plot. We then tried to build an analogous StrEAMM linear regression (1,2)+(1,3) model to predict cyclic hexapeptide structural ensembles. Unfortunately, the resulting model showed poor performance when evaluated on the test dataset, with R2 = 0.47 and WE = 5.99 (Figure 4B). We hypothesized that (1,2) and (1,3) interactions may not be sufficient to describe the structural preferences of cyclic hexapeptides. Thus, we trained a linear regression model to also explicitly incorporate (1,4) interactions, i.e., the StrEAMM linear regression (1,2)+(1,3)+(1,4) model. Although the addition of (1,4) interactions did improve the performance of the StrEAMM linear regression model, with R2 = 0.75 and WE = 3.66 (Figure 4C), the StrEAMM linear regression (1,2)+(1,3)+(1,4) model for cyclic hexapeptides could not achieve the performance we previously observed for the StrEAMM linear regression (1,2)+(1,3) model on cyclic pentapeptides. While both the cyclic pentapeptide (1,2)+(1,3) model and hexapeptide (1,2)+(1,3)+(1,4) model were able to fit the training data, unlike the pentapeptide model, the performance of the hexapeptide model was unable to generalize to the test dataset. We hypothesized that there might exist more complex, nonlinear relationships between the amino acids that influence the structural ensemble of cyclic hexapeptides beyond simple two-body interactions. To this end, we built StrEAMM neural network models that can easily incorporate complex interaction patterns but are less interpretable than the StrEAMM linear regression models.

Figure 4

Figure 4. Performance of StrEAMM linear regression models on the training dataset (top) and test dataset (bottom) for (A) cyclic pentapeptides and (B, C) cyclic hexapeptides. (A) Performance of StrEAMM linear regression model on cyclic pentapeptides using (1,2) and (1,3) interactions. (B) Performance of StrEAMM linear regression model on cyclic hexapeptides using (1,2) and (1,3) interactions. (C) Performance of StrEAMM linear regression model on cyclic hexapeptides using (1,2), (1,3), and (1,4) interactions. The black dashed line represents y = x. R2 is the coefficient of determination. WE is the weighted error, given by WE=∑ipi,observed|pi,observed−pi,predicted|∑ipi,observed, where pi,observed and pi,predicted are the populations observed in MD simulation and predicted by StrEAMM, respectively. Each point on the plot represents the predicted versus the observed percent population in MD for a structure in the structural ensemble of a cyclic peptide. All the structures in the structural ensembles for all the cyclic peptides in the training or test dataset with a predicted or observed percent population in MD of >1% are plotted.

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3.2. StrEAMM Neural Network Models Can Predict Cyclic Pentapeptide Structural Ensembles

We aimed to train StrEAMM CNN and GNN models and evaluate whether they could learn complex interaction patterns that may be missing in the StrEAMM linear regression models. As a first step, in section 3.2, we verified that these neural network models could accurately predict cyclic pentapeptide structural ensembles as well as, or even better than, the StrEAMM linear regression model. Then, in section 3.3, we moved on to evaluate the performance of the neural network models for cyclic hexapeptides.

3.2.1. StrEAMM CNN Models for Cyclic Pentapeptides

The StrEAMM linear regression (1,2)+(1,3) model had R2 = 0.94 and WE = 1.54 for cyclic pentapeptides (Figure 4A). The StrEAMM CNN (1,2)+(1,3) model had R2 = 0.96 and WE = 1.25, showing a similar or slightly better performance than the StrEAMM linear regression (1,2)+(1,3) model (Figure 5A; for results on the training dataset, see Figure S7A). The similar performances between the StrEAMM linear regression and StrEAMM CNN models for cyclic pentapeptides is consistent with the assumption that cyclic pentapeptides are small enough that their structural preference is determined by their (1,2) and (1,3) neighboring interactions. Therefore, the linear regression model using simply (1,2) and (1,3) weights is sufficient in summarizing the interactions that influence cyclic pentapeptide structural preferences.

Figure 5

Figure 5. Performance of (A–C) StrEAMM CNN models and (D–F) StrEAMM GNN models on the test dataset for (A, D) cyclic pentapeptides and the models incorporating (1,2) and (1,3) filters/edges, (B, E) cyclic hexapeptides and the models incorporating (1,2) and (1,3) filters/edges, and (C, F) cyclic hexapeptides and the models incorporating (1,2), (1,3), and (1,4) filters/edges. See Figure S7 for the model performances on the corresponding training datasets. All the structures in the structural ensembles for all the cyclic peptides in the training or test dataset with a predicted or observed percent population in MD of >1% are plotted.

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For StrEAMM linear regression models, including both (1,2) and (1,3) interactions was critical for the performance in predicting cyclic pentapeptide structural ensembles. When only (1,2) or (1,3) interactions were included, StrEAMM linear regression models showed poorer performance, especially when only (1,2) interactions were included, with R2 = 0.63 and WE = 4.32 (Figure 6A, red bars; Figure S8A). On the other hand, StrEAMM CNN (1,2), StrEAMM CNN (1,3), and StrEAMM CNN (1,2)+(1,3) all showed very similar performances (Figure 6A, green bars; Figure S8B). In other words, including multiple “neighbor-inspired” convolutions did not affect the model performance as significantly as it did for the linear regression models. We suspected that the neural networks did not necessarily need to incorporate all of our “neighbor-inspired” convolutions because the model was still learning with information contributed by all of the residues in the sequence when the training data were propagated through MLP layers, which were present in both our CNN and GNN models. Therefore, while we designed convolutional filters and edge types to combine features for select neighboring residues, the explicit inclusion of all the important interactions may not be necessary for the CNN and GNN models.

Figure 6

Figure 6. Comparison of the StrEAMM linear regression and neural network models’ performances on the (A) cyclic pentapeptide and (B) cyclic hexapeptide test datasets. The coefficient of determination, R2, and weighted error, WE, are shown for each model (the linear regression in red with diagonal slash pattern, CNN in green with dotted pattern, and GNN in blue with vertical line pattern) including different neighboring interactions.

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3.2.2. StrEAMM GNN Models for Cyclic Pentapeptides

The StrEAMM GNN (1,2)+(1,3) model had R2 = 0.97 and WE = 1.19 (Figure 5D; for results on the training dataset, see Figure S7D), showing a similar or slightly better performance than the StrEAMM linear regression (1,2)+(1,3) model. This observation was consistent with the CNN models’ performances also having been comparable to those of the linear regression models. Also similar to the trend observed for the various CNN models, the StrEAMM GNN (1,2), StrEAMM GNN (1,3), and StrEAMM GNN (1,2)+(1,3) models showed very similar performances to each other (Figure 6A, blue bars; Figure S8C). This trend is again consistent with our hypothesis that the explicit inclusion of all “neighbor-inspired” convolutions may not be necessary for the neural networks.

3.3. StrEAMM Neural Network Models Can Predict Cyclic Hexapeptide Structural Ensembles

After we observed that our StrEAMM neural network models could accurately predict the structural ensembles of cyclic pentapeptides, we turned our attention to developing neural network models to predict the structural ensembles of cyclic hexapeptides. Our StrEAMM linear regression (1,2)+(1,3) model failed at this prediction task for cyclic hexapeptides in the test dataset, with R2 = 0.47 and WE = 5.99 (Figure 4B). While the addition of the (1,4) neighboring interactions in the StrEAMM linear regression (1,2)+(1,3)+(1,4) model improved the model’s performance, the model was still not very accurate (R2 = 0.75 and WE = 3.66; Figure 4C). Here we evaluated whether the StrEAMM neural network models could be more accurate than the current StrEAMM linear regression models at predicting cyclic hexapeptide structural ensembles.

3.3.1. StrEAMM CNN Models for Cyclic Hexapeptides

The StrEAMM CNN (1,2)+(1,3) model had R2 = 0.90 and WE = 2.05 (Figure 5B), and the StrEAMM CNN (1,2)+(1,3)+(1,4) model had R2 = 0.89 and WE = 2.12 (Figure 5C), both showing much better performance than the StrEAMM linear regression models.
As was observed for the models trained on cyclic pentapeptides, the performance of the linear regression models trained on cyclic hexapeptides strongly depended on which interactions were explicitly included in the models (Figure 6B, red bars; Figure S9A), while the performance of the CNN models did not (Figure 6B, green bars; Figure S9B). Furthermore, when considering the three-fold cross-validation results of the CNN models incorporating (1,2)-only, (1,3)-only, (1,4)-only, (1,2)+(1,3), and (1,2)+(1,3)+(1,4) interactions, we observed that they all performed similarly (Figure S3).

3.3.2. StrEAMM GNN Models for Cyclic Hexapeptides

The StrEAMM GNN (1,2)+(1,3) model had R2 = 0.91 and WE = 1.95 (Figure 5E), and the StrEAMM GNN (1,2)+(1,3)+(1,4) model had R2 = 0.91 and WE = 1.96 (Figure 5F), showing an improved performance for cyclic hexapeptides compared to the StrEAMM linear regression models. Again, while the explicit inclusion of specific neighboring interactions strongly impacted the performance of the linear regression models (Figure 6B, red bars; Figure S9A), we did not observe this dependence on the performance of the GNN models (Figure 6B, blue bars; Figure S9C). Similar to the CNN model cross-validation results, the GNN models using (1,2)-only, (1,3)-only, (1,4)-only, (1,2)+(1,3), and (1,2)+(1,3)+(1,4) interactions reported similar model performance (Figure S6). This observation suggests that due to the convolutions and operations in the neural network models, explicit inclusion of all types of neighboring interactions is not necessary for good model performance.

3.4. Using Alternative Binning Maps Does Not Improve the StrEAMM Model Performance Trained on Either Cyclic Pentapeptides or Cyclic Hexapeptides

All the models we had trained and presented results for thus far had used datasets prepared from the “Map 1” structural binning maps (Figure 2). These maps were generated by analyzing the (ϕ, ψ) density distributions of cyclic polyglycines, clustering the high-density grid points, and using the resulting cluster centroids to assign all the grid points. To evaluate how sensitive the model performance was to the binning map, we developed two new maps. For one map, the (ϕ, ψ) density distributions of cyclic polyglycines were still used, but all 100 × 100 grid points were used in the clustering protocol (“Map 2” maps; Figure S1A). The other map used the (ϕ, ψ) density distributions of the training sequences instead of those of cyclic polyglycines; again, all 100 × 100 grid points were used in the clustering protocol (“Map 3” maps; Figure S1B). The results showed that the model performance was not sensitive to the choice of the maps (Figure S10). This observation was rather surprising to us, as one might assume that a map that was more fine-tuned and based on the training sequences (i.e., “Map 3” maps) would provide more accurate binning of the structures, thus constructing more accurate structural ensembles. These results likely suggest that the differences in these maps did not alter the majority of the structural assignments, thus only leading to minor differences in the model performance.

3.5. StrEAMM Neural Network Models Can Predict Structural Ensembles of Cyclic Peptide Sequences Containing Amino Acids That Were Absent in the Training Dataset Sequences

Thus far, we had found that the StrEAMM neural network models could outperform the StrEAMM linear regression models for both cyclic pentapeptide and hexapeptide datasets. We also report here an additional benefit of using our neural network models: the encoding scheme we used to describe the features of our cyclic peptide sequences allowed our models to predict the structural ensembles of sequences composed of amino acids that were not originally included in the training dataset (i.e., amino acids that the model had never “seen” during training). We had chosen to represent peptide sequences using molecular fingerprints with the intention that our trained models could also make predictions for cyclic peptide sequences containing amino acids not present in the training dataset as long as the new amino acids shared some bit information with the amino acids that were already in the training dataset. This ability is not a feature of all encoding schemes. For example, a typical one-hot encoding scheme requires that each amino acid is represented by a bit vector. This bit vector has the length of the number of amino acids in the library and contains a single 1 at a position that is unique for each amino acid in the library. Therefore, given the uniqueness of these bit vectors and the fact that the length of the bit vector depends on the size of the original amino acid library, it would be impossible to make predictions for new amino acids. In a similar fashion, the StrEAMM linear regression models could not make predictions for sequences containing “new” amino acids because there would be no corresponding weights containing the new amino acid.
With the aid of the molecular fingerprint encodings, we extended the StrEAMM neural network models and observed that they were able to predict cyclic peptide structural ensembles for cyclic peptide sequences containing amino acids that were not originally included in the training dataset (Figure 7). We simulated an additional 25 cyclic pentapeptide and 25 cyclic hexapeptide sequences that were composed of a larger amino acid library (37 amino acids, including all the canonical amino acids in their d and l forms, with the exception of proline; Lists S3 and S4). However, it is to be noted that only 21 cyclic hexapeptide sequences were used to compose the new test dataset due to failure to reach our convergence criterion of having a NIP value ≥ 0.90 after 300 ns of simulation. For the CNN models, we chose the architectures that performed best during hyperparameter tuning, which were the CNN (1,2) model for the cyclic pentapeptide dataset and the CNN (1,2)+(1,3)+(1,4) model for the cyclic hexapeptide dataset (Figures S2 and S3). When trained using the cyclic peptide datasets containing only 15 amino acids in the library, the CNN models could only reach a mediocre performance of R2 = 0.49 for both the cyclic pentapeptide and cyclic hexapeptide test datasets containing amino acids from the 37 amino acid library (Figure 7A,B). Similarly, the GNN models reported R2 = 0.46 and R2 = 0.51 for the cyclic pentapeptide and cyclic hexapeptide test datasets, respectively (Figure 7C,D). To improve the model performances, we simulated an additional 50 training sequences, which we termed “booster” sequences, which contain amino acids from the 37 amino acid library, for the cyclic pentapeptide and cyclic hexapeptide training datasets. It is to be noted that only 48 training booster sequences were added to the cyclic hexapeptide training dataset due to our convergence criterion (Lists S5 and S6). When we supplemented the training datasets with these booster sequences, we saw a great increase in model performances across both the CNNs and GNNs: the CNN models were able to reach performances of R2 = 0.90 and R2 = 0.86 for the cyclic pentapeptide and cyclic hexapeptide test datasets, respectively (Figure 7E,F); similarly, the GNN models reported R2 = 0.88 and R2 = 0.86 for the cyclic pentapeptide and cyclic hexapeptide test datasets, respectively (Figure 7G,H). This result demonstrates that supplementing the training dataset with some additional training sequences is a viable approach to access predictions for larger amino acid libraries. With the addition of only ∼50 sequences built from a 37 amino acid library, we were able to achieve good performance on the test dataset with sequences generated from the 37 amino acid library. This addition is more efficient than if we were to build a training dataset using our current protocol for generating the cyclic hexapeptide sequences from a 15 amino acid library (which requires observing all possible XiXi+1Xi+2 subsequences), as applying this protocol to generate cyclic hexapeptide sequences from a 37 amino acid library would require ∼8500 sequences.

Figure 7

Figure 7. The StrEAMM neural network models can predict structural ensembles for cyclic pentapeptides and cyclic hexapeptides that contain amino acids that were absent in the training dataset. (A–D) Performances of the (A, B) CNN and (C, D) GNN models on cyclic pentapeptide and cyclic hexapeptide datasets containing sequences composed of the 37 amino acid library, when the models were trained using only sequences composed of the 15 amino acid library. (E–H) Performances of the (E, F) CNN and (G, H) GNN models on cyclic pentapeptide and cyclic hexapeptide datasets containing sequences composed of the 37 amino acid library, when the models were trained using sequences composed of the 15 amino acid library and “booster” sequences composed of the 37 amino acid library.

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4. Conclusions and Future Directions

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The StrEAMM methodology can efficiently predict cyclic peptide structural ensembles by leveraging MD results to train ML models. The newly proposed StrEAMM neural network models can easily embed complicated interaction patterns that may be necessary to learn the structural preferences of cyclic peptides larger than the simple cyclic pentapeptide systems. Our StrEAMM neural network models can accurately predict the structural ensembles for cyclic hexapeptides, which is an improvement from the original StrEAMM linear regression models. The new neural network models can also enable predictions for cyclic peptides with amino acids that were not originally present in the training dataset, suggesting that we can access a larger sequence space without having to spend computational resources on performing more simulations.
While we have described the advantages of using the neural network models, we acknowledge that overall, although the models perform well for cyclic hexapeptides (in general, R2 > 0.90; Figure 6B), they did not reach the same excellent performance as for cyclic pentapeptides (R2 ≥ 0.97; Figure 6A). We plan to focus our future directions on exploring different feature representations, such as physicochemical properties, in addition to the molecular fingerprints to help improve the models’ performance on the cyclic hexapeptide set. We also suspect that a possible reason for the worse performance of the cyclic hexapeptide models compared to the cyclic pentapeptide models is related to the number of training instances. Recall that the training dataset was constructed such that we observe every XiXi+1Xi+2 subsequence. In the cyclic pentapeptide dataset, there were 705 sequences in the training dataset, but in the cyclic hexapeptide dataset, there were only 555 sequences because the increased size of the cyclic hexapeptide allows for an additional triplet subsequence per cyclic peptide sequence. Therefore, we will also evaluate how collecting more training sequences for the cyclic hexapeptide dataset or better designing the training sequences can further improve the model performance. We are also eager to extend the StrEAMM models to larger cyclic peptides and cyclic peptides beyond head-to-tail cyclization, as our neural network models can efficiently predict structural ensembles without the need to explicitly include various neighboring interactions that may influence the structural preferences of such larger, more complex systems. We envision that the implementation of these StrEAMM neural network models can provide the structural information that can greatly aid the rational design and development of cyclic peptides.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jctc.3c00154.

  • Lists of sequences in the training and test datasets; structural binning maps 2 and 3; hyperparameter tuning schemes; neural network model performances on the training datasets for cyclic pentapeptides and cyclic hexapeptides; performances of linear regression and neural network models including only (1,2) or only (1,3) interactions on training and test datasets for cyclic pentapeptides; performances of linear regression and neural network models including only (1,2), only (1,3), or only (1,4) interactions on training and test datasets for cyclic hexapeptides; comparison of model performances using different binning maps (PDF)

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Author Information

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  • Corresponding Author
  • Authors
    • Tiffani Hui - Department of Chemistry, Tufts University, Medford, Massachusetts 02155, United States
    • Marc L. Descoteaux - Department of Chemistry, Tufts University, Medford, Massachusetts 02155, United States
    • Jiayuan Miao - Department of Chemistry, Tufts University, Medford, Massachusetts 02155, United States;  Orcidhttps://orcid.org/0000-0003-1112-1927
  • Author Contributions

    T.H., M.L.D., and J.M. contributed equally.

  • Notes
    The authors declare the following competing financial interest(s): Y.-S.L. has an equity interest in and is a founding scientist of Speed Cycles, Inc. A patent application (PCT/US2022/072941, Cyclic peptide structure prediction via structural ensembles achieved by molecular dynamics and machine learning) was filed on June 14, 2022.

Acknowledgments

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This work was supported by the National Institute of General Medical Sciences of the National Institutes of Health under Award R01GM124160 (PI: Y.-S.L.). We are grateful for the support from the Tufts Technology Services and for the computing resources at the Tufts Research Cluster. Initial structures for the simulations were built using UCSF Chimera, developed by the Resource for Biocomputing, Visualization, and Informatics at the University of California, San Francisco, with support from NIH Grant P41-GM103311.

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    Dougherty, P. G.; Sahni, A.; Pei, D. Understanding Cell Penetration of Cyclic Peptides. Chem. Rev. 2019, 119, 10241– 10287,  DOI: 10.1021/acs.chemrev.9b00008
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    Understanding Cell Penetration of Cyclic Peptides
    Dougherty, Patrick G.; Sahni, Ashweta; Pei, Dehua
    Chemical Reviews (Washington, DC, United States) (2019), 119 (17), 10241-10287CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
    A review. Approx. 75% of all disease-relevant human proteins, including those involved in intracellular protein-protein interactions (PPIs), are undruggable with the current drug modalities (i.e., small mols. and biologics). Macrocyclic peptides provide a potential soln. to these undruggable targets because their larger sizes (relative to conventional small mols.) endow them the capability of binding to flat PPI interfaces with antibody-like affinity and specificity. Powerful combinatorial library technologies have been developed to routinely identify cyclic peptides as potent, specific inhibitors against proteins including PPI targets. However, with the exception of a very small set of sequences, the vast majority of cyclic peptides are impermeable to the cell membrane, preventing their application against intracellular targets. This Review examines common structural features that render most cyclic peptides membrane impermeable, as well as the unique features that allow the minority of sequences to enter the cell interior by passive diffusion, endocytosis/endosomal escape, or other mechanisms. We also present the current state of knowledge about the mol. mechanisms of cell penetration, the various strategies for designing cell-permeable, biol. active cyclic peptides against intracellular targets, and the assay methods available to quantify their cell-permeability.
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  5. 5
    Zhang, H.; Chen, S. Cyclic peptide drugs approved in the last two decades (2001–2021). RSC Chem. Biol. 2022, 3, 18– 31,  DOI: 10.1039/D1CB00154J
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    Cyclic peptide drugs approved in the last two decades (2001-2021)
    Zhang Huiya; Chen Shiyu
    RSC chemical biology (2022), 3 (1), 18-31 ISSN:.
    In contrast to the major families of small molecules and antibodies, cyclic peptides, as a family of synthesizable macromolecules, have distinct biochemical and therapeutic properties for pharmaceutical applications. Cyclic peptide-based drugs have increasingly been developed in the past two decades, confirming the common perception that cyclic peptides have high binding affinities and low metabolic toxicity as antibodies, good stability and ease of manufacture as small molecules. Natural peptides were the major source of cyclic peptide drugs in the last century, and cyclic peptides derived from novel screening and cyclization strategies are the new source. In this review, we will discuss and summarize 18 cyclic peptides approved for clinical use in the past two decades to provide a better understanding of cyclic peptide development and to inspire new perspectives. The purpose of the present review is to promote efforts to resolve the challenges in the development of cyclic peptide drugs that are more effective.
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    Zorzi, A.; Deyle, K.; Heinis, C. Cyclic peptide therapeutics: past, present and future. Curr. Opin. Chem. Biol. 2017, 38, 24– 29,  DOI: 10.1016/j.cbpa.2017.02.006
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    Cyclic peptide therapeutics: past, present and future
    Zorzi, Alessandro; Deyle, Kaycie; Heinis, Christian
    Current Opinion in Chemical Biology (2017), 38 (), 24-29CODEN: COCBF4; ISSN:1367-5931. (Elsevier B.V.)
    Cyclic peptides combine several favorable properties such as good binding affinity, target selectivity and low toxicity that make them an attractive modality for the development of therapeutics. Over 40 cyclic peptide drugs are currently in clin. use and around one new cyclic peptide drug enters the market every year on av. The vast majority of clin. approved cyclic peptides are derived from natural products, such as antimicrobials or human peptide hormones. New powerful techniques based on rational design and in vitro evolution have enabled the de novo development of cyclic peptide ligands to targets for which nature does not offer solns. A look at the cyclic peptides currently under clin. evaluation shows that several have been developed using such techniques. This new source for cyclic peptide ligands introduces a freshness to the field, and it is likely that de novo developed cyclic peptides will be in clin. use in the near future.
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  7. 7
    Nguyen, Q. N. N.; Schwochert, J.; Tantillo, D. J.; Lokey, R. S. Using 1H and 13C NMR chemical shifts to determine cyclic peptide conformations: a combined molecular dynamics and quantum mechanics approach. Phys. Chem. Chem. Phys. 2018, 20, 14003– 14012,  DOI: 10.1039/C8CP01616J
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    Using 1H and 13C NMR chemical shifts to determine cyclic peptide conformations: a combined molecular dynamics and quantum mechanics approach
    Nguyen, Q. Nhu N.; Schwochert, Joshua; Tantillo, Dean J.; Lokey, R. Scott
    Physical Chemistry Chemical Physics (2018), 20 (20), 14003-14012CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
    Solving conformations of cyclic peptides can provide insight into structure-activity and structure-property relationships, which can help in the design of compds. with improved bioactivity and/or ADME characteristics. The most common approaches for detg. the structures of cyclic peptides are based on NMR-derived distance restraints obtained from NOESY or ROESY cross-peak intensities, and 3J-based dihedral restraints using the Karplus relationship. Unfortunately, these observables are often too weak, sparse, or degenerate to provide unequivocal, high-confidence soln. structures, prompting us to investigate an alternative approach that relies only on 1H and 13C chem. shifts as exptl. observables. This method, which we call conformational anal. from NMR and d.-functional prediction of low-energy ensembles (CANDLE), uses mol. dynamics (MD) simulations to generate conformer families and d. functional theory (DFT) calcns. to predict their 1H and 13C chem. shifts. Iterative conformer searches and DFT energy calcns. on a cyclic peptide-peptoid hybrid yielded Boltzmann ensembles whose predicted chem. shifts matched the exptl. values better than any single conformer. For these compds., CANDLE outperformed the classic NOE- and 3J-coupling-based approach by disambiguating similar β-turn types and also enabled the structural elucidation of the minor conformer. Through the use of chem. shifts, in conjunction with DFT and MD calcns., CANDLE can help illuminate conformational ensembles of cyclic peptides in soln.
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    Ball, K. A.; Wemmer, D. E.; Head-Gordon, T. Comparison of Structure Determination Methods for Intrinsically Disordered Amyloid-β Peptides. J. Phys. Chem. B 2014, 118, 6405– 6416,  DOI: 10.1021/jp410275y
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    Comparison of Structure Determination Methods for Intrinsically Disordered Amyloid-β Peptides
    Ball, K. Aurelia; Wemmer, David E.; Head-Gordon, Teresa
    Journal of Physical Chemistry B (2014), 118 (24), 6405-6416CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
    Intrinsically disordered proteins (IDPs) represent a new frontier in structural biol. since the primary characteristic of IDPs is that structures need to be characterized as diverse ensembles of conformational substates. We compare two general but very different ways of combining NMR spectroscopy with theor. methods to derive structural ensembles for the disease IDPs amyloid-β 1-40 and amyloid-β 1-42, which are assocd. with Alzheimer's Disease. We analyze the performance of de novo mol. dynamics and knowledge-based approaches for generating structural ensembles by assessing their ability to reproduce a range of NMR exptl. observables. In addn. to the comparison of computational methods, we also evaluate the relative value of different types of NMR data for refining or validating the IDP structural ensembles for these important disease peptides.
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  9. 9
    Fisher, C. K.; Stultz, C. M. Constructing ensembles for intrinsically disordered proteins. Curr. Opin. Struct. Biol. 2011, 21, 426– 431,  DOI: 10.1016/j.sbi.2011.04.001
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    Constructing ensembles for intrinsically disordered proteins
    Fisher, Charles K.; Stultz, Collin M.
    Current Opinion in Structural Biology (2011), 21 (3), 426-431CODEN: COSBEF; ISSN:0959-440X. (Elsevier Ltd.)
    A review. The relatively flat energy landscapes assocd. with intrinsically disordered proteins makes modeling these systems esp. problematic. A comprehensive model for these proteins requires one to build an ensemble consisting of a finite collection of structures, and their corresponding relative stabilities, which adequately capture the range of accessible states of the protein. In this regard, methods that use computational techniques to interpret exptl. data in terms of such ensembles are an essential part of the modeling process. In this review, we critically assess the advantages and limitations of current techniques and discuss new methods for the validation of these ensembles.
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  10. 10
    Cicero, D. O.; Barbato, G.; Bazzo, R. NMR Analysis of Molecular Flexibility in Solution: A New Method for the Study of Complex Distributions of Rapidly Exchanging Conformations. Application to a 13-Residue Peptide with an 8-Residue Loop. J. Am. Chem. Soc. 1995, 117, 1027– 1033,  DOI: 10.1021/ja00108a019
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    10
    NMR Analysis of Molecular Flexibility in Solution: A New Method for the Study of Complex Distributions of Rapidly Exchanging Conformations. Application to a 13-Residue Peptide with an 8-Residue Loop
    Cicero, D. O.; Barbato, G.; Bazzo, R.
    Journal of the American Chemical Society (1995), 117 (3), 1027-33CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    A new methodol., called NAMFIS (NMR anal. of mol. flexibility in soln.), is described for the anal. of flexible mols. in soln. Once a complete set of conformations is generated and is able to encompass all the possible states of the mol. that are not a priori incompatible with the available exptl. NMR evidence, NAMFIS allows for the examn. of the occurrence and relevance of arbitrary elements of secondary structure, even when extensive conformational averaging defies a detailed exptl. characterization. The anal. is based on the available exptl. NMR data. The method is demonstrated in the conformational anal. of peptide I (R = Lys-Aib-Lys-OH; Aib = α-aminoisobutyric acid, Mhe = 2-amino-6-mercaptohexanoic acid).
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  11. 11
    Ge, Y.; Zhang, S.; Erdelyi, M.; Voelz, V. A. Solution-State Preorganization of Cyclic β-Hairpin Ligands Determines Binding Mechanism and Affinities for MDM2. J. Chem. Inf. Model. 2021, 61, 2353– 2367,  DOI: 10.1021/acs.jcim.1c00029
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    11
    Solution-State Preorganization of Cyclic β-Hairpin Ligands Determines Binding Mechanism and Affinities for MDM2
    Ge, Yunhui; Zhang, Si; Erdelyi, Mate; Voelz, Vincent A.
    Journal of Chemical Information and Modeling (2021), 61 (5), 2353-2367CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
    Understanding mechanisms of protein folding and binding is crucial to designing their mol. function. Mol. dynamics (MD) simulations and Markov state model (MSM) approaches provide a powerful way to understand complex conformational change that occurs over long time scales. Such dynamics are important for the design of therapeutic peptidomimetic ligands, whose affinity and binding mechanism are dictated by a combination of folding and binding. To examine the role of preorganization in peptide binding to protein targets, the authors performed massively parallel explicit-solvent MD simulations of cyclic β-hairpin ligands designed to mimic the p53 transactivation domain and competitively bind mouse double minute 2 homolog (MDM2). Disrupting the MDM2-p53 interaction is a therapeutic strategy to prevent degrdn. of the p53 tumor suppressor in cancer cells. MSM anal. of over 3 ms of aggregate trajectory data enabled the authors to build a detailed mechanistic model of coupled folding and binding of four cyclic peptides which the authors compare to exptl. binding affinities and rates. The results show a striking relation between the relative preorganization of each ligand in soln. and its affinity for MDM2. Specifically, changes in peptide conformational populations predicted by the MSMs suggest that entropy loss upon binding is the main factor influencing affinity. The MSMs also enable detailed examn. of non-native interactions which lead to misfolded states and comparison of structural ensembles with exptl. NMR measurements. In contrast to an MSM study of p53 transactivation domain (TAD) binding to MDM2, MSMs of cyclic β-hairpin binding show a conformational selection mechanism. Finally, the authors make progress toward predicting accurate off rates of cyclic peptides using multi-ensemble Markov models (MEMMs) constructed from unbiased and biased simulated trajectories.
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  12. 12
    Slough, D. P.; McHugh, S. M.; Cummings, A. E.; Dai, P.; Pentelute, B. L.; Kritzer, J. A.; Lin, Y.-S. Designing Well-Structured Cyclic Pentapeptides Based on Sequence-Structure Relationships. J. Phys. Chem. B 2018, 122, 3908– 3919,  DOI: 10.1021/acs.jpcb.8b01747
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    12
    Designing well-structured cyclic pentapeptides based on sequence-structure relationships
    Slough, Diana P.; McHugh, Sean M.; Cummings, Ashleigh E.; Dai, Peng; Pentelute, Bradley L.; Kritzer, Joshua A.; Lin, Yu-Shan
    Journal of Physical Chemistry B (2018), 122 (14), 3908-3919CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
    Cyclic peptides are a promising class of mols. for unique applications. Unfortunately, cyclic peptide design is severely limited by the difficulty in predicting the conformations they will adopt in soln. In this work, we use explicit-solvent mol. dynamics simulations to design well-structured cyclic peptides by studying their sequence-structure relationships. Crit. to our approach is an enhanced sampling method that exploits the essential transitional motions of cyclic peptides to efficiently sample their conformational space. We simulated a range of cyclic pentapeptides from all-glycine to a library of cyclo-(X1X2AAA) peptides to map their conformational space and det. cooperative effects of neighboring residues. By combining the results from all cyclo-(X1X2AAA) peptides, we developed a scoring function to predict the structural preferences for X1-X2 residues within cyclic pentapeptides. Using this scoring function, we designed a cyclic pentapeptide, cyclo-(GNSRV), predicted to be well structured in aq. soln. Subsequent CD and NMR spectroscopy revealed that this cyclic pentapeptide is indeed well structured in water, with a nuclear Overhauser effect and J-coupling values consistent with the predicted structure.
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  13. 13
    Cummings, A. E.; Miao, J.; Slough, D. P.; McHugh, S. M.; Kritzer, J. A.; Lin, Y. S. β-Branched Amino Acids Stabilize Specific Conformations of Cyclic Hexapeptides. Biophys. J. 2019, 116, 433– 444,  DOI: 10.1016/j.bpj.2018.12.015
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    13
    β-Branched Amino Acids Stabilize Specific Conformations of Cyclic Hexapeptides
    Cummings, Ashleigh E.; Miao, Jiayuan; Slough, Diana P.; McHugh, Sean M.; Kritzer, Joshua A.; Lin, Yu-Shan
    Biophysical Journal (2019), 116 (3), 433-444CODEN: BIOJAU; ISSN:0006-3495. (Cell Press)
    Cyclic peptides (CPs) are a promising class of mols. for drug development, particularly as inhibitors of protein-protein interactions. Predicting low-energy structures and global structural ensembles of individual CPs is crit. for the design of bioactive mols., but these are challenging to predict and difficult to verify exptl. In our previous work, we used explicit-solvent mol. dynamics simulations with enhanced sampling methods to predict the global structural ensembles of cyclic hexapeptides contg. different permutations of glycine, alanine, and valine. One peptide, cyclo-(VVGGVG) or P7, was predicted to be unusually well structured. In this work, we synthesized P7, along with a less well-structured control peptide, cyclo-(VVGVGG) or P6, and characterized their global structural ensembles in water using NMR spectroscopy. The NMR data revealed a structural ensemble similar to the prediction for P7 and showed that P6 was indeed much less well-structured than P7. We then simulated and exptl. characterized the global structural ensembles of several P7 analogs and discovered that β-branching at one crit. position within P7 is important for overall structural stability. The simulations allowed deconvolution of thermodn. factors that underlie this structural stabilization. Overall, the excellent correlation between simulation and exptl. data indicates that our simulation platform will be a promising approach for designing well-structured CPs and also for understanding the complex interactions that control the conformations of constrained peptides and other macrocycles.
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    Wakefield, A. E.; Wuest, W. M.; Voelz, V. A. Molecular Simulation of Conformational Pre-Organization in Cyclic RGD Peptides. J. Chem. Inf. Model. 2015, 55, 806– 813,  DOI: 10.1021/ci500768u
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    Molecular Simulation of Conformational Pre-Organization in Cyclic RGD Peptides
    Wakefield, Amanda E.; Wuest, William M.; Voelz, Vincent A.
    Journal of Chemical Information and Modeling (2015), 55 (4), 806-813CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
    To test the ability of mol. simulations to accurately predict the soln.-state conformational properties of peptidomimetics, we examd. a test set of 18 cyclic RGD peptides selected from the literature, including the anticancer drug candidate cilengitide, whose favorable binding affinity to integrin has been ascribed to its pre-organization in soln. For each design, we performed all-atom replica-exchange mol. dynamics simulations over several microseconds and compared the results to extensive published NMR data. We find excellent agreement with exptl. NOE distance restraints, suggesting that mol. simulation can be a useful tool for the computational design of pre-organized soln.-state structure. Moreover, our anal. of conformational populations ests. that, despite the potential for increased flexibility due to backbone amide isomerizaton, N-methylation provides about 0.5 kcal/mol of reduced conformational entropy to cyclic RGD peptides. The combination of pre-organization and binding-site compatibility explains the strong binding affinity of cilengitide to integrin.
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    Damjanovic, J.; Miao, J.; Huang, H.; Lin, Y.-S. Elucidating Solution Structures of Cyclic Peptides Using Molecular Dynamics Simulations. Chem. Rev. 2021, 121, 2292– 2324,  DOI: 10.1021/acs.chemrev.0c01087
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    Elucidating Solution Structures of Cyclic Peptides Using Molecular Dynamics Simulations
    Damjanovic, Jovan; Miao, Jiayuan; Huang, He; Lin, Yu-Shan
    Chemical Reviews (Washington, DC, United States) (2021), 121 (4), 2292-2324CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
    A review. Protein-protein interactions are vital to biol. processes, but the shape and size of their interfaces make them hard to target using small mols. Cyclic peptides have shown promise as protein-protein interaction modulators, as they can bind protein surfaces with high affinity and specificity. Dozens of cyclic peptides are already FDA approved, and many more are in various stages of development as immunosuppressants, antibiotics, antivirals, or anticancer drugs. However, most cyclic peptide drugs so far have been natural products or derivs. thereof, with de novo design having proven challenging. A key obstacle is structural characterization: cyclic peptides frequently adopt multiple conformations in soln., which are difficult to resolve using techniques like NMR spectroscopy. The lack of soln. structural information prevents a thorough understanding of cyclic peptides' sequence-structure-function relationship. Here we review recent development and application of mol. dynamics simulations with enhanced sampling to studying the soln. structures of cyclic peptides. We describe novel computational methods capable of sampling cyclic peptides' conformational space and provide examples of computational studies that relate peptides' sequence and structure to biol. activity. We demonstrate that mol. dynamics simulations have grown from an explanatory technique to a full-fledged tool for systematic studies at the forefront of cyclic peptide therapeutic design.
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    Ono, S.; Naylor, M. R.; Townsend, C. E.; Okumura, C.; Okada, O.; Lokey, R. S. Conformation and Permeability: Cyclic Hexapeptide Diastereomers. J. Chem. Inf. Model. 2019, 59, 2952– 2963,  DOI: 10.1021/acs.jcim.9b00217
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    Conformation and Permeability: Cyclic Hexapeptide Diastereomers
    Ono, Satoshi; Naylor, Matthew R.; Townsend, Chad E.; Okumura, Chieko; Okada, Okimasa; Lokey, R. Scott
    Journal of Chemical Information and Modeling (2019), 59 (6), 2952-2963CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
    Conformational ensembles of eight cyclic hexapeptide diastereomers in explicit cyclohexane, chloroform, and water were analyzed by multicanonical mol. dynamics (McMD) simulations. Free-energy landscapes (FELs) for each compd. and solvent were obtained from the mol. shapes and principal component anal. at T = 300 K; detailed anal. of the conformational ensembles and flexibility of the FELs revealed that permeable compds. have different structural profiles even for a single stereoisomeric change. The av. solvent-accessible surface area (SASA) in cyclohexane showed excellent correlation with the cell permeability, whereas this correlation was weaker in chloroform. The av. SASA in water correlated with the aq. soly. The av. polar surface area did not correlate with cell permeability in these solvents. A possible strategy for designing permeable cyclic peptides from FELs obtained from McMD simulations is proposed.
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  17. 17
    Wang, S.; König, G.; Roth, H.-J.; Fouché, M.; Rodde, S.; Riniker, S. Effect of Flexibility, Lipophilicity, and the Location of Polar Residues on the Passive Membrane Permeability of a Series of Cyclic Decapeptides. J. Med. Chem. 2021, 64, 12761– 12773,  DOI: 10.1021/acs.jmedchem.1c00775
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    Effect of Flexibility, Lipophilicity, and the Location of Polar Residues on the Passive Membrane Permeability of a Series of Cyclic Decapeptides
    Wang, Shuzhe; Konig, Gerhard; Roth, Hans-Jorg; Fouche, Marianne; Rodde, Stephane; Riniker, Sereina
    Journal of Medicinal Chemistry (2021), 64 (17), 12761-12773CODEN: JMCMAR; ISSN:0022-2623. (American Chemical Society)
    Cyclic peptides have received increasing attention over the recent years as potential therapeutics for "undruggable" targets. One major obstacle is, however, their often relatively poor bioavailability. Here, we investigate the structure-permeability relationship of 24 cyclic decapeptides that share the same backbone N-methylation pattern but differ in their side chains. The peptides cover a large range of values for passive membrane permeability as well as lipophilicity and soly. To rationalize the obsd. differences in permeability, we extd. for each peptide the population of the membrane-permeable conformation in water from extensive explicit-solvent mol. dynamics simulations and used this as a metric for conformational rigidity or "prefolding.". The insights from the simulations together with lipophilicity measurements highlight the intricate interplay between polarity/lipophilicity and flexibility/rigidity and the possible compensating effects on permeability. The findings allow us to better understand the structure-permeability relationship of cyclic peptides and ext. general guiding principles.
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    El Tayar, N.; Mark, A. E.; Vallat, P.; Brunne, R. M.; Testa, B.; van Gunsteren, W. F. Solvent-dependent conformation and hydrogen-bonding capacity of cyclosporin A: evidence from partition coefficients and molecular dynamics simulations. J. Med. Chem. 1993, 36, 3757– 3764,  DOI: 10.1021/jm00076a002
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    Solvent-dependent conformation and hydrogen-bonding capacity of cyclosporin A: evidence from partition coefficients and molecular dynamics simulations
    El Tayar, Nabil; Mark, Alan E.; Vallat, Philippe; Brunne, Roger M.; Testa, Bernard; van Gunsteren, Wilfred F.
    Journal of Medicinal Chemistry (1993), 36 (24), 3757-64CODEN: JMCMAR; ISSN:0022-2623.
    The partition coeff. of cyclosporin A (CsA) was measured in octanol/water and heptane/water by centrifugal partition chromatog. By comparison with results from model compds., it was deduced that the hydrogen-bonding capacity of CsA changed dramatically from an apolar solvent (where it is internally H-bonded) to polar solvents (where it exposes its H-bonding groups to the solvent). Mol. dynamics simulations in water and CCl4 support the suggestion that CsA undergoes a solvent-dependent conformational changes and that the interconversion process is slow on the mol. dynamics time scale.
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    Merten, C.; Li, F.; Bravo-Rodriguez, K.; Sanchez-Garcia, E.; Xu, Y.; Sander, W. Solvent-induced conformational changes in cyclic peptides: a vibrational circular dichroism study. Phys. Chem. Chem. Phys. 2014, 16, 5627– 5633,  DOI: 10.1039/C3CP55018D
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    Solvent-induced conformational changes in cyclic peptides: a vibrational circular dichroism study
    Merten, Christian; Li, Fee; Bravo-Rodriguez, Kenny; Sanchez-Garcia, Elsa; Xu, Yunjie; Sander, Wolfram
    Physical Chemistry Chemical Physics (2014), 16 (12), 5627-5633CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
    The three-dimensional structure of a peptide is strongly influenced by its solvent environment. In the present study, we study three cyclic tetrapeptides which serve as model peptides for β-turns. They are of the general structure cyclo(Boc-Cys-Pro-X-Cys-OMe) with the amino acid X being either glycine, or L- or D-leucine. Using vibrational CD (VCD) spectroscopy, we confirm previous NMR results which showed that cyclo(Boc-Cys-Pro-D-Leu-Cys-OMe) adopts predominantly a βII turn structure in apolar and polar solvents. Our results for cyclo(Boc-Cys-Pro-Leu-Cys-OMe) (Boc = tert-nutoxycarbonyl) indicate a preference for a βI structure over βII. With increasing solvent polarity, the preference for cyclo(Boc-Cys-Pro-Gly-Cys-OMe) is shifted from βII towards βI. This conformational change goes along with the breaking of an intramol. hydrogen bond which stabilizes the βII conformation. Instead, a hydrogen bond with a solvent mol. can stabilize the βI turn conformation.
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  20. 20
    Quartararo, J. S.; Eshelman, M. R.; Peraro, L.; Yu, H.; Baleja, J. D.; Lin, Y.-S.; Kritzer, J. A. A bicyclic peptide scaffold promotes phosphotyrosine mimicry and cellular uptake. Bioorg. Med. Chem. 2014, 22, 6387– 6391,  DOI: 10.1016/j.bmc.2014.09.050
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    17
    A bicyclic peptide scaffold promotes phosphotyrosine mimicry and cellular uptake
    Quartararo, Justin S.; Eshelman, Matthew R.; Peraro, Leila; Yu, Hongtao; Baleja, James D.; Lin, Yu-Shan; Kritzer, Joshua A.
    Bioorganic & Medicinal Chemistry (2014), 22 (22), 6387-6391CODEN: BMECEP; ISSN:0968-0896. (Elsevier B.V.)
    While peptides are promising as probes and therapeutics, targeting intracellular proteins will require greater understanding of highly structured, cell-internalized scaffolds. We recently reported BC1, an 11-residue bicyclic peptide that inhibits the Src homol. 2 (SH2) domain of growth factor receptor-bound protein 2 (Grb2). In this work, we describe the unique structural and cell uptake properties of BC1 and similar cyclic and bicyclic scaffolds. These constrained scaffolds are taken up by mammalian cells despite their net neutral or neg. charges, while unconstrained analogs are not. The mechanism of uptake is shown to be energy-dependent and endocytic, but distinct from that of Tat. The soln. structure of BC1 was investigated by NMR and MD simulations, which revealed discrete water-binding sites on BC1 that reduce exposure of backbone amides to bulk water. This represents an original and potentially general strategy for promoting cell uptake.
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  21. 21
    Baek, M.; DiMaio, F.; Anishchenko, I.; Dauparas, J.; Ovchinnikov, S.; Lee, G. R.; Wang, J.; Cong, Q.; Kinch, L. N.; Schaeffer, R. D.; Millán, C.; Park, H.; Adams, C.; Glassman, C. R.; DeGiovanni, A.; Pereira, J. H.; Rodrigues, A. V.; van Dijk, A. A.; Ebrecht, A. C.; Opperman, D. J.; Sagmeister, T.; Buhlheller, C.; Pavkov-Keller, T.; Rathinaswamy, M. K.; Dalwadi, U.; Yip, C. K.; Burke, J. E.; Garcia, K. C.; Grishin, N. V.; Adams, P. D.; Read, R. J.; Baker, D. Accurate prediction of protein structures and interactions using a three-track neural network. Science 2021, 373, 871– 876,  DOI: 10.1126/science.abj8754
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    18
    Accurate prediction of protein structures and interactions using a three-track neural network
    Baek, Minkyung; DiMaio, Frank; Anishchenko, Ivan; Dauparas, Justas; Ovchinnikov, Sergey; Lee, Gyu Rie; Wang, Jue; Cong, Qian; Kinch, Lisa N.; Schaeffer, R. Dustin; Millan, Claudia; Park, Hahnbeom; Adams, Carson; Glassman, Caleb R.; DeGiovanni, Andy; Pereira, Jose H.; Rodrigues, Andria V.; van Dijk, Alberdina A.; Ebrecht, Ana C.; Opperman, Diederik J.; Sagmeister, Theo; Buhlheller, Christoph; Pavkov-Keller, Tea; Rathinaswamy, Manoj K.; Dalwadi, Udit; Yip, Calvin K.; Burke, John E.; Garcia, K. Christopher; Grishin, Nick V.; Adams, Paul D.; Read, Randy J.; Baker, David
    Science (Washington, DC, United States) (2021), 373 (6557), 871-876CODEN: SCIEAS; ISSN:1095-9203. (American Association for the Advancement of Science)
    DeepMind presented notably accurate predictions at the recent 14th Crit. Assessment of Structure Prediction (CASP14) conference. We explored network architectures that incorporate related ideas and obtained the best performance with a three-track network in which information at the one-dimensional (1D) sequence level, the 2D distance map level, and the 3D coordinate level is successively transformed and integrated. The three-track network produces structure predictions with accuracies approaching those of DeepMind in CASP14, enables the rapid soln. of challenging x-ray crystallog. and cryo-electron microscopy structure modeling problems, and provides insights into the functions of proteins of currently unknown structure. The network also enables rapid generation of accurate protein-protein complex models from sequence information alone, short-circuiting traditional approaches that require modeling of individual subunits followed by docking. We make the method available to the scientific community to speed biol. research.
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  22. 22
    Bryant, P.; Pozzati, G.; Elofsson, A. Improved prediction of protein-protein interactions using AlphaFold2. Nat. Commun. 2022, 13, 1265,  DOI: 10.1038/s41467-022-28865-w
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    20
    Improved prediction of protein-protein interactions using AlphaFold2
    Bryant, Patrick; Pozzati, Gabriele; Elofsson, Arne
    Nature Communications (2022), 13 (1), 1265CODEN: NCAOBW; ISSN:2041-1723. (Nature Portfolio)
    Predicting the structure of interacting protein chains is a fundamental step towards understanding protein function. Unfortunately, no computational method can produce accurate structures of protein complexes. AlphaFold2, has shown unprecedented levels of accuracy in modeling single chain protein structures. Here, we apply AlphaFold2 for the prediction of heterodimeric protein complexes. We find that the AlphaFold2 protocol together with optimized multiple sequence alignments, generate models with acceptable quality (DockQ ≥ 0.23) for 63% of the dimers. From the predicted interfaces we create a simple function to predict the DockQ score which distinguishes acceptable from incorrect models as well as interacting from non-interacting proteins with state-of-art accuracy. We find that, using the predicted DockQ scores, we can identify 51% of all interacting pairs at 1% FPR.
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    Bryant, P.; Pozzati, G.; Zhu, W.; Shenoy, A.; Kundrotas, P.; Elofsson, A. Predicting the structure of large protein complexes using AlphaFold and Monte Carlo tree search. Nat. Commun. 2022, 13, 6028,  DOI: 10.1038/s41467-022-33729-4
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    21
    Predicting the structure of large protein complexes using AlphaFold and Monte Carlo tree search
    Bryant, Patrick; Pozzati, Gabriele; Zhu, Wensi; Shenoy, Aditi; Kundrotas, Petras; Elofsson, Arne
    Nature Communications (2022), 13 (1), 6028CODEN: NCAOBW; ISSN:2041-1723. (Nature Portfolio)
    AlphaFold can predict the structure of single- and multiple-chain proteins with very high accuracy. However, the accuracy decreases with the no. of chains, and the available GPU memory limits the size of protein complexes which can be predicted. Here we show that one can predict the structure of large complexes starting from predictions of subcomponents. We assemble 91 out of 175 complexes with 10-30 chains from predicted subcomponents using Monte Carlo tree search, with a median TM-score of 0.51. There are 30 highly accurate complexes (TM-score ≥0.8, 33% of complete assemblies). We create a scoring function, mpDockQ, that can distinguish if assemblies are complete and predict their accuracy. We find that complexes contg. symmetry are accurately assembled, while asym. complexes remain challenging.
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  24. 24
    Jumper, J.; Evans, R.; Pritzel, A.; Green, T.; Figurnov, M.; Ronneberger, O.; Tunyasuvunakool, K.; Bates, R.; Žídek, A.; Potapenko, A.; Bridgland, A.; Meyer, C.; Kohl, S. A. A.; Ballard, A. J.; Cowie, A.; Romera-Paredes, B.; Nikolov, S.; Jain, R.; Adler, J.; Back, T.; Petersen, S.; Reiman, D.; Clancy, E.; Zielinski, M.; Steinegger, M.; Pacholska, M.; Berghammer, T.; Bodenstein, S.; Silver, D.; Vinyals, O.; Senior, A. W.; Kavukcuoglu, K.; Kohli, P.; Hassabis, D. Highly accurate protein structure prediction with AlphaFold. Nature 2021, 596, 583– 589,  DOI: 10.1038/s41586-021-03819-2
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    Highly accurate protein structure prediction with AlphaFold
    Jumper, John; Evans, Richard; Pritzel, Alexander; Green, Tim; Figurnov, Michael; Ronneberger, Olaf; Tunyasuvunakool, Kathryn; Bates, Russ; Zidek, Augustin; Potapenko, Anna; Bridgland, Alex; Meyer, Clemens; Kohl, Simon A. A.; Ballard, Andrew J.; Cowie, Andrew; Romera-Paredes, Bernardino; Nikolov, Stanislav; Jain, Rishub; Adler, Jonas; Back, Trevor; Petersen, Stig; Reiman, David; Clancy, Ellen; Zielinski, Michal; Steinegger, Martin; Pacholska, Michalina; Berghammer, Tamas; Bodenstein, Sebastian; Silver, David; Vinyals, Oriol; Senior, Andrew W.; Kavukcuoglu, Koray; Kohli, Pushmeet; Hassabis, Demis
    Nature (London, United Kingdom) (2021), 596 (7873), 583-589CODEN: NATUAS; ISSN:0028-0836. (Nature Portfolio)
    Proteins are essential to life, and understanding their structure can facilitate a mechanistic understanding of their function. Through an enormous exptl. effort, the structures of around 100,000 unique proteins have been detd., but this represents a small fraction of the billions of known protein sequences. Structural coverage is bottlenecked by the months to years of painstaking effort required to det. a single protein structure. Accurate computational approaches are needed to address this gap and to enable large-scale structural bioinformatics. Predicting the three-dimensional structure that a protein will adopt based solely on its amino acid sequence-the structure prediction component of the 'protein folding problem'-has been an important open research problem for more than 50 years. Despite recent progress, existing methods fall far short of at. accuracy, esp. when no homologous structure is available. Here we provide the first computational method that can regularly predict protein structures with at. accuracy even in cases in which no similar structure is known. We validated an entirely redesigned version of our neural network-based model, AlphaFold, in the challenging 14th Crit. Assessment of protein Structure Prediction (CASP14), demonstrating accuracy competitive with exptl. structures in a majority of cases and greatly outperforming other methods. Underpinning the latest version of AlphaFold is a novel machine learning approach that incorporates phys. and biol. knowledge about protein structure, leveraging multi-sequence alignments, into the design of the deep learning algorithm.
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  25. 25
    Rettie, S. A.; Campbell, K. V.; Bera, A. K.; Kang, A.; Kozlov, S.; De La Cruz, J.; Adebomi, V.; Zhou, G.; DiMaio, F.; Ovchinnikov, S.; Bhardwaj, G. Cyclic peptide structure prediction and design using AlphaFold. bioRxiv 2023,  DOI: 10.1101/2023.02.25.529956v1
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    Gang, D.; Kim, D. W.; Park, H. S. Cyclic Peptides: Promising Scaffolds for Biopharmaceuticals. Genes 2018, 9, 557,  DOI: 10.3390/genes9110557
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    Cyclic peptides: promising scaffolds for biopharmaceuticals
    Gang, Donghyeok; Kim, Do Wook; Park, Hee-Sung
    Genes (2018), 9 (11), 557/1-557/15CODEN: GENEG9; ISSN:2073-4425. (MDPI AG)
    A review. To date, small mols. and macromols., including antibodies, have been the most pursued substances in drug screening and development efforts. Despite numerous favorable features as a drug, these mols. still have limitations and are not complementary in many regards. Recently, peptide-based chem. structures that lie between these two categories in terms of both structural and functional properties have gained increasing attention as potential alternatives. In particular, peptides in a circular form provide a promising scaffold for the development of a novel drug class owing to their adjustable and expandable ability to bind a wide range of target mols. In this review, we discuss recent progress in methodologies for peptide cyclization and screening and use of bioactive cyclic peptides in various applications.
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    Iacovelli, R.; Bovenberg, R. A. L.; Driessen, A. J. M. Nonribosomal peptide synthetases and their biotechnological potential in Penicillium rubens. J. Ind. Microbiol. Biotechnol. 2021, 48, kuab045,  DOI: 10.1093/jimb/kuab045
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    Marahiel, M. A. Working outside the protein-synthesis rules: insights into non-ribosomal peptide synthesis. J. Pept. Sci. 2009, 15, 799– 807,  DOI: 10.1002/psc.1183
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    Working outside the protein-synthesis rules: Insights into non-ribosomal peptide synthesis
    Marahiel, Mohamed A.
    Journal of Peptide Science (2009), 15 (12), 799-807CODEN: JPSIEI; ISSN:1075-2617. (John Wiley & Sons Ltd.)
    A review. Non-ribosomally synthesized microbial peptides show remarkable structural diversity and constitute a widespread class of the most potent antibiotics and other important pharmaceuticals that range from penicillin to the immunosuppressant cyclosporine. They are assembled independent of the ribosome in a nucleic acid-independent way by a group of multimodular megaenzymes called non-ribosomal peptide synthetases. These biosynthetic machineries rely not only on the 20 canonical amino acids, but also use several different building blocks, including D-configured- and β-amino acids, methylated, glycosylated and phosphorylated residues, heterocyclic elements and even fatty acid building blocks. This structural diversity leads to a high d. of functional groups, which are often essential for the bioactivity. Recent biochem. and structural studies on several non-ribosomal peptide synthetase assembly lines have substantially contributed to the understanding of the mol. mechanisms and dynamics of individual catalytic domains underlying substrate recognition and substrate shuffling among the different active sites as well as peptide bond formation and the regio- and stereoselective product release. Copyright © 2009 European Peptide Society and John Wiley & Sons, Ltd.
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    Martínez-Núñez, M. A.; López y López, V. E. Nonribosomal peptides synthetases and their applications in industry. Sustainable Chem. Processes 2016, 4, 13,  DOI: 10.1186/s40508-016-0057-6
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    Nonribosomal peptides synthetases and their applications in industry
    Martinez-Nunez, Mario Alberto; Lopez y Lopez, Victor Eric
    Sustainable Chemical Processes (2016), 4 (), 13/1-13/8CODEN: SCPUCB; ISSN:2043-7129. (Chemistry Central Ltd.)
    A review. X. Nonribosomal peptides are products that fall into the class of secondary metabolites with diverse properties as toxins, siderophores, pigments, or antibiotics, among others. Unlike other proteins, its biosynthesis is independent of ribosomal machinery. Nonribosomal peptides are synthesized on large nonribosomal peptide synthetase (NRPS) enzyme complexes. NRPSs are defined as multimodular enzymes, consisting of repeated modules. The NRPS enzymes are at operons and their regulation can be pos. or neg. at transcriptional or post-translational level. The presence of NRPS enzymes has been reported in the 3 domains of life, being prevalent in bacteria. Nonribosomal peptides are used in human medicine, crop protection, or environment restoration; and their use as com. products has been approved by the U.S. Food and Drug Administration and the Environmental Protection Agency. Here, the key features of nonribosomal peptides and NRPS enzymes, and some of their applications in industry are summarized.
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    Sieber, S. A.; Marahiel, M. A. Learning from Nature’s Drug Factories: Nonribosomal Synthesis of Macrocyclic Peptides. J. Bacteriol. 2003, 185, 7036– 7043,  DOI: 10.1128/JB.185.24.7036-7043.2003
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    Learning from nature's drug factories: Nonribosomal synthesis of macrocyclic peptides
    Sieber, Stephan A.; Marahiel, Mohamed A.
    Journal of Bacteriology (2003), 185 (24), 7036-7043CODEN: JOBAAY; ISSN:0021-9193. (American Society for Microbiology)
    A review. The family of enzymes, nonribosomal peptide peptide synthetases/ cyclases, are discussed.
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    Miao, J.; Descoteaux, M. L.; Lin, Y.-S. Structure prediction of cyclic peptides by molecular dynamics + machine learning. Chem. Sci. 2021, 12, 14927– 14936,  DOI: 10.1039/D1SC05562C
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    Structure prediction of cyclic peptides by molecular dynamics + machine learning
    Miao, Jiayuan; Descoteaux, Marc L.; Lin, Yu-Shan
    Chemical Science (2021), 12 (44), 14927-14936CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)
    Recent computational methods have made strides in discovering well-structured cyclic peptides that preferentially populate a single conformation. However, many successful cyclic-peptide therapeutics adopt multiple conformations in soln. In fact, the chameleonic properties of some cyclic peptides are likely responsible for their high cell membrane permeability. Thus, we require the ability to predict complete structural ensembles for cyclic peptides, including the majority of cyclic peptides that have broad structural ensembles, to significantly improve our ability to rationally design cyclic-peptide therapeutics. Here, we introduce the idea of using mol. dynamics simulation results to train machine learning models to enable efficient structure prediction for cyclic peptides. Using mol. dynamics simulation results for several hundred cyclic pentapeptides as the training datasets, we developed machine-learning models that can provide mol. dynamics simulation-quality predictions of structural ensembles for all the hundreds of thousands of sequences in the entire sequence space. The prediction for each individual cyclic peptide can be made using less than 1 s of computation time. Even for the most challenging classes of poorly structured cyclic peptides with broad conformational ensembles, our predictions were similar to those one would normally obtain only after running multiple days of explicit-solvent mol. dynamics simulations. The resulting method, termed StrEAMM (Structural Ensembles Achieved by Mol. Dynamics and Machine Learning), is the first technique capable of efficiently predicting complete structural ensembles of cyclic peptides without relying on addnl. mol. dynamics simulations, constituting a seven-order-of-magnitude improvement in speed while retaining the same accuracy as explicit-solvent simulations.
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    Jurtz, V. I.; Johansen, A. R.; Nielsen, M.; Almagro Armenteros, J. J.; Nielsen, H.; Sønderby, C. K.; Winther, O.; Sønderby, S. K. An introduction to deep learning on biological sequence data: examples and solutions. Bioinformatics 2017, 33, 3685– 3690,  DOI: 10.1093/bioinformatics/btx531
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    An introduction to deep learning on biological sequence data: Examples and solutions
    Jurtz, Vanessa Isabell; Johansen, Alexander Rosenberg; Nielsen, Morten; Armenteros, Jose Juan Almagro; Nielsen, Henrik; Soenderby, Casper Kaae; Winther, Ole; Soenderby, Soeren Kaae
    Bioinformatics (2017), 33 (22), 3685-3690CODEN: BOINFP; ISSN:1367-4811. (Oxford University Press)
    Motivation: Deep neural network architectures such as convolutional and long short-term memory networks have become increasingly popular as machine learning tools during the recent years. The availability of greater computational resources, more data, new algorithms for training deep models and easy to use libraries for implementation and training of neural networks are the drivers of this development. The use of deep learning has been esp. successful in image recognition; and the development of tools, applications and code examples are in most cases centered within this field rather than within biol. Results: Here, we aim to further the development of deep learning methods within biol. by providing application examples and ready to apply and adapt code templates. Given such examples, we illustrate how architectures consisting of convolutional and long short-term memory neural networks can relatively easily be designed and trained to state-of-the-art performance on three biol. sequence problems: prediction of subcellular localization, protein secondary structure and the binding of peptides to MHC Class II mols.
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    Hou, J.; Adhikari, B.; Cheng, J. DeepSF: deep convolutional neural network for mapping protein sequences to folds. Bioinformatics 2018, 34, 1295– 1303,  DOI: 10.1093/bioinformatics/btx780
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    DeepSF: deep convolutional neural network for mapping protein sequences to folds
    Hou, Jie; Adhikari, Badri; Cheng, Jianlin
    Bioinformatics (2018), 34 (8), 1295-1303CODEN: BOINFP; ISSN:1367-4811. (Oxford University Press)
    Motivation: Protein fold recognition is an important problem in structural bioinformatics. Almost all traditional fold recognition methods use sequence (homol.) comparison to indirectly predict the fold of a target protein based on the fold of a template protein with known structure, which cannot explain the relationship between sequence and fold. Only a few methods had been developed to classify protein sequences into a small no. of folds due to methodol. limitations, which are not generally useful in practice. Results: We develop a deep 1D-convolution neural network (DeepSF) to directly classify any protein sequence into one of 1195 known folds, which is useful for both fold recognition and the study of sequence-structure relationship. Different from traditional sequence alignment (comparison) based methods, our method automatically exts. fold-related features from a protein sequence of any length and maps it to the fold space. We train and test our method on the datasets curated from SCOP1.75, yielding an av. classification accuracy of 75.3%. On the independent testing dataset curated from SCOP2.06, the classification accuracy is 73.0%. We compare our method with a top profile-profile alignment method-HHSearch on hard template-based and template-free modeling targets of CASP9-12 in terms of fold recognition accuracy. The accuracy of our method is 12.63-26.32% higher than HHSearch on template-free modeling targets and 3.39-17.09% higher on hard template-based modeling targets for top 1, 5 and 10 predicted folds. The hidden features extd. from sequence by our method is robust against sequence mutation, insertion, deletion and truncation, and can be used for other protein pattern recognition problems such as protein clustering, comparison and ranking.
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    Cheng, J.; Liu, Y.; Ma, Y. Protein secondary structure prediction based on integration of CNN and LSTM model. J. Vis. Commun. Image Representation. 2020, 71, 102844,  DOI: 10.1016/j.jvcir.2020.102844
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    Chen, Z.; Min, M. R.; Ning, X. Ranking-Based Convolutional Neural Network Models for Peptide-MHC Class I Binding Prediction. Front. Mol. Biosci. 2021, 8, 634836,  DOI: 10.3389/fmolb.2021.634836
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    Ranking-based convolutional neural network models for peptide-MHC class I binding prediction
    Chen, Ziqi; Min, Martin Renqiang; Ning, Xia
    Frontiers in Molecular Biosciences (2021), 8 (), 634836CODEN: FMBRBS; ISSN:2296-889X. (Frontiers Media S.A.)
    T-cell receptors can recognize foreign peptides bound to major histocompatibility complex (MHC) class-I proteins, and thus trigger the adaptive immune response. Therefore, identifying peptides that can bind to MHC class-I mols. plays a vital role in the design of peptide vaccines. Many computational methods, for example, the state-of-the-art allele-specific method mhcflurry, have been developed to predict the binding affinities between peptides and MHC mols. In this manuscript, we develop two allele-specific Convolutional Neural Network-based methods named convm and spconvm to tackle the binding prediction problem. Specifically, we formulate the problem as to optimize the rankings of peptide-MHC bindings via ranking-based learning objectives. Such optimization is more robust and tolerant to the measurement inaccuracy of binding affinities, and therefore enables more accurate prioritization of binding peptides. In addn., we develop a new position encoding method in convm and spconvm to better identify the most important amino acids for the binding events. We conduct a comprehensive set of expts. using the latest Immune Epitope Database (IEDB) datasets. Our exptl. results demonstrate that our models significantly outperform the state-of-the-art methods including mhcflurry with an av. percentage improvement of 6.70% on AUC and 17.10% on ROC5 across 128 alleles.
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    Gelman, S.; Fahlberg, S. A.; Heinzelman, P.; Romero, P. A.; Gitter, A. Neural networks to learn protein sequence─function relationships from deep mutational scanning data. Proc. Natl. Acad. Sci. U.S.A. 2021, 118, e2104878118  DOI: 10.1073/pnas.2104878118
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    Neural networks to learn protein sequence-function relationships from deep mutational scanning data
    Gelman, Sam; Fahlberg, Sarah A.; Heinzelman, Pete; Romero, Philip A.; Gitter, Anthony
    Proceedings of the National Academy of Sciences of the United States of America (2021), 118 (48), e2104878118CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
    The mapping from protein sequence to function is highly complex, making it challenging to predict how sequence changes will affect a protein's behavior and properties. We present a supervised deep learning framework to learn the sequence-function mapping from deep mutational scanning data and make predictions for new, uncharacterized sequence variants. We test multiple neural network architectures, including a graph convolutional network that incorporates protein structure, to explore how a network's internal representation affects its ability to learn the sequence-function mapping. Our supervised learning approach displays superior performance over physics-based and unsupervised prediction methods. We find that networks that capture nonlinear interactions and share parameters across sequence positions are important for learning the relationship between sequence and function. Further anal. of the trained models reveals the networks' ability to learn biol. meaningful information about protein structure and mechanism. Finally, we demonstrate the models' ability to navigate sequence space and design new proteins beyond the training set. We applied the protein G B1 domain (GB1) models to design a sequence that binds to IgG with substantially higher affinity than wild-type GB1.
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  37. 37
    Hosseinzadeh, P.; Bhardwaj, G.; Mulligan, V. K.; Shortridge, M. D.; Craven, T. W.; Pardo-Avila, F.; Rettie, S. A.; Kim, D. E.; Silva, D.-A.; Ibrahim, Y. M.; Webb, I. K.; Cort, J. R.; Adkins, J. N.; Varani, G.; Baker, D. Comprehensive computational design of ordered peptide macrocycles. Science 2017, 358, 1461– 1466,  DOI: 10.1126/science.aap7577
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    Comprehensive computational design of ordered peptide macrocycles
    Hosseinzadeh, Parisa; Bhardwaj, Gaurav; Mulligan, Vikram Khipple; Shortridge, Matthew D.; Craven, Timothy W.; Pardo-Avila, Fatima; Rettie, Stephen A.; Kim, David E.; Silva, Daniel-Adriano; Ibrahim, Yehia M.; Webb, Ian K.; Cort, John R.; Adkins, Joshua N.; Varani, Gabriele; Baker, David
    Science (Washington, DC, United States) (2017), 358 (6369), 1461-1466CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
    Mixed-chirality peptide macrocycles such as cyclosporine are among the most potent therapeutics identified to date, but there is currently no way to systematically search the structural space spanned by such compds. Natural proteins do not provide a useful guide: Peptide macrocycles lack regular secondary structures and hydrophobic cores, and can contain local structures not accessible with L-amino acids. Here, we enumerate the stable structures that can be adopted by macrocyclic peptides composed of L- and D-amino acids by near-exhaustive backbone sampling followed by sequence design and energy landscape calcns. We identify more than 200 designs predicted to fold into single stable structures, many times more than the no. of currently available unbound peptide macrocycle structures. NMR structures of 9 of 12 designed 7- to 10-residue macrocycles, and three 11- to 14-residue bicyclic designs, are close to the computational models. Our results provide a nearly complete coverage of the rich space of structures possible for short peptide macrocycles and vastly increase the available starting scaffolds for both rational drug design and library selection methods.
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  38. 38
    Li, X.; Du, X.; Li, J.; Gao, Y.; Pan, Y.; Shi, J.; Zhou, N.; Xu, B. Introducing d-Amino Acid or Simple Glycoside into Small Peptides to Enable Supramolecular Hydrogelators to Resist Proteolysis. Langmuir 2012, 28, 13512– 13517,  DOI: 10.1021/la302583a
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    36
    Introducing d-Amino Acid or Simple Glycoside into Small Peptides to Enable Supramolecular Hydrogelators to Resist Proteolysis
    Li, Xinming; Du, Xuewen; Li, Jiayang; Gao, Yuan; Pan, Yue; Shi, Junfeng; Zhou, Ning; Xu, Bing
    Langmuir (2012), 28 (37), 13512-13517CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
    Here we report the examn. of two convenient strategies, the use of a d-amino acid residue or a glycoside segment, for increasing the proteolytic resistance of supramol. hydrogelators based on small peptides. Our results show that the introduction of d-amino acid or glycoside to the peptides significantly increases the resistance of the hydrogelators against proteinase K, a powerful endopeptidase. The insertion of d-amino acid in the peptide backbone, however, results relatively low storage moduli of the hydrogels, likely due to the disruption of the superstructures of the mol. assembly. In contrast, the introduction of a glycoside to the C-terminal of peptide enhances the biostability of the hydrogelators without the significant decrease of the storage moduli of the hydrogels. This work suggests that the inclusion of a simple glycogen in hydrogelators is a useful approach to increase their biostability, and the gained understanding from the work may ultimately lead to development of hydrogels of functional peptides for biomedical applications that require long-term biostability.
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  39. 39
    Liu, J.; Liu, J.; Chu, L.; Zhang, Y.; Xu, H.; Kong, D.; Yang, Z.; Yang, C.; Ding, D. Self-Assembling Peptide of d-Amino Acids Boosts Selectivity and Antitumor Efficacy of 10-Hydroxycamptothecin. ACS Appl. Mater. Interfaces 2014, 6, 5558– 5565,  DOI: 10.1021/am406007g
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    Self-Assembling Peptide of d-Amino Acids Boosts Selectivity and Antitumor Efficacy of 10-Hydroxycamptothecin
    Liu, Jianfeng; Liu, Jinjian; Chu, Liping; Zhang, Yumin; Xu, Hongyan; Kong, Deling; Yang, Zhimou; Yang, Cuihong; Ding, Dan
    ACS Applied Materials & Interfaces (2014), 6 (8), 5558-5565CODEN: AAMICK; ISSN:1944-8244. (American Chemical Society)
    D-Peptides, which consist of D-amino acids and can resist the hydrolysis catalyzed by endogenous peptidases, are one of the promising candidates for construction of peptide materials with enhanced biostability in vivo. In this paper, we report on a self-assembling supramol. nanostructure of D-amino acid-based peptide Nap-GDFDFDYGRGD (D-fiber, DF meant D-phenylalanine, DY meant D-tyrosine), which were used as carriers for 10-hydroxycamptothecin (HCPT). Transmission electron microscopy observations demonstrated the filamentous morphol. of the HCPT-loaded peptides (D-fiber-HCPT). The better selectivity and antitumor activity of D-fiber-HCPT than L-fiber-HCPT were found in the in vitro and in vivo antitumor studies. These results highlight that this model D-fiber system holds great promise as vehicles of hydrophobic drugs for cancer therapy.
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    Piana, S.; Laio, A. A bias-exchange approach to protein folding. J. Phys. Chem. B 2007, 111, 4553– 4559,  DOI: 10.1021/jp067873l
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    A Bias-Exchange Approach to Protein Folding
    Piana, Stefano; Laio, Alessandro
    Journal of Physical Chemistry B (2007), 111 (17), 4553-4559CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
    By suitably extending a recent approach [Bussi, G., et al., 2006] the authors introduce a powerful methodol. that allows the parallel reconstruction of the free energy of a system in a virtually unlimited no. of variables. Multiple metadynamics simulations of the same system at the same temp. are performed, biasing each replica with a time-dependent potential constructed in a different set of collective variables. Exchanges between the bias potentials in the different variables are periodically allowed according to a replica exchange scheme. Due to the efficaciously multidimensional nature of the bias the method allows exploring complex free energy landscapes with high efficiency. The usefulness of the method is demonstrated by performing an atomistic simulation in explicit solvent of the folding of a Triptophane cage miniprotein. It is shown that the folding free energy landscape can be fully characterized starting from an extended conformation with use of only 40 ns of simulation on 8 replicas.
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    Laio, A.; Parrinello, M. Escaping free-energy minima. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 12562– 12566,  DOI: 10.1073/pnas.202427399
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    Escaping free-energy minima
    Laio, Alessandro; Parrinello, Michele
    Proceedings of the National Academy of Sciences of the United States of America (2002), 99 (20), 12562-12566CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
    We introduce a powerful method for exploring the properties of the multidimensional free energy surfaces (FESs) of complex many-body systems by means of coarse-grained non-Markovian dynamics in the space defined by a few collective coordinates. A characteristic feature of these dynamics is the presence of a history-dependent potential term that, in time, fills the min. in the FES, allowing the efficient exploration and accurate detn. of the FES as a function of the collective coordinates. We demonstrate the usefulness of this approach in the case of the dissocn. of a NaCl mol. in water and in the study of the conformational changes of a dialanine in soln.
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    McHugh, S. M.; Rogers, J. R.; Yu, H.; Lin, Y.-S. Insights into How Cyclic Peptides Switch Conformations. J. Chem. Theory Comput. 2016, 12, 2480– 2488,  DOI: 10.1021/acs.jctc.6b00193
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    Insights into How Cyclic Peptides Switch Conformations
    McHugh, Sean M.; Rogers, Julia R.; Yu, Hongtao; Lin, Yu-Shan
    Journal of Chemical Theory and Computation (2016), 12 (5), 2480-2488CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    Cyclic peptides have recently emerged as promising modulators of protein-protein interactions. However, it is currently highly difficult to predict the structures of cyclic peptides owing to their rugged conformational free energy landscape, which prevents sampling of all thermodynamically relevant conformations. In this article, we first investigate how a relatively flexible cyclic hexapeptide switches conformations. It is found that, although the circular geometry of small cyclic peptides of size 6-8 may require rare, coherent dihedral changes to sample a new conformation, the changes are rather local, involving simultaneous changes of .vphi.i and ψi or ψi and .vphi.i+1. The understanding of how these cyclic peptides switch conformations enables the use of metadynamics simulations with reaction coordinates specifically targeting such coupled two-dihedral changes to effectively sample cyclic peptide conformational space.
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    Sugita, Y.; Kitao, A.; Okamoto, Y. Multidimensional replica-exchange method for free-energy calculations. J. Chem. Phys. 2000, 113, 6042– 6051,  DOI: 10.1063/1.1308516
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    Multidimensional replica-exchange method for free-energy calculations
    Sugita, Yuji; Kitao, Akio; Okamoto, Yuko
    Journal of Chemical Physics (2000), 113 (15), 6042-6051CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    We have developed a new simulation algorithm for free-energy calcns. The method is a multidimensional extension of the replica-exchange method. While pairs of replicas with different temps. are exchanged during the simulation in the original replica-exchange method, pairs of replicas with different temps. and/or different parameters of the potential energy are exchanged in the new algorithm. This greatly enhances the sampling of the conformational space and allows accurate calcns. of free energy in a wide temp. range from a single simulation run, using the weighted histogram anal. method.
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    Pettersen, E. F.; Goddard, T. D.; Huang, C. C.; Couch, G. S.; Greenblatt, D. M.; Meng, E. C.; Ferrin, T. E. UCSF Chimera-a visualization system for exploratory research and analysis. J. Comput. Chem. 2004, 25, 1605– 1612,  DOI: 10.1002/jcc.20084
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    UCSF Chimera-A visualization system for exploratory research and analysis
    Pettersen, Eric F.; Goddard, Thomas D.; Huang, Conrad C.; Couch, Gregory S.; Greenblatt, Daniel M.; Meng, Elaine C.; Ferrin, Thomas E.
    Journal of Computational Chemistry (2004), 25 (13), 1605-1612CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
    The design, implementation, and capabilities of an extensible visualization system, UCSF Chimera, are discussed. Chimera is segmented into a core that provides basic services and visualization, and extensions that provide most higher level functionality. This architecture ensures that the extension mechanism satisfies the demands of outside developers who wish to incorporate new features. Two unusual extensions are presented: Multiscale, which adds the ability to visualize large-scale mol. assemblies such as viral coats, and Collab., which allows researchers to share a Chimera session interactively despite being at sep. locales. Other extensions include Multalign Viewer, for showing multiple sequence alignments and assocd. structures; ViewDock, for screening docked ligand orientations; Movie, for replaying mol. dynamics trajectories; and Vol. Viewer, for display and anal. of volumetric data. A discussion of the usage of Chimera in real-world situations is given, along with anticipated future directions. Chimera includes full user documentation, is free to academic and nonprofit users, and is available for Microsoft Windows, Linux, Apple Mac OS X, SGI IRIX, and HP Tru64 Unix from http://www.cgl.ucsf.edu/chimera/.
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    Abraham, M. J.; Murtola, T.; Schulz, R.; Páll, S.; Smith, J. C.; Hess, B.; Lindahl, E. GROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputers. SoftwareX 2015, 1–2, 19– 25,  DOI: 10.1016/j.softx.2015.06.001
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    Zhou, C.-Y.; Jiang, F.; Wu, Y.-D. Residue-Specific Force Field Based on Protein Coil Library. RSFF2: Modification of AMBER ff99SB. J. Phys. Chem. B 2015, 119, 1035– 1047,  DOI: 10.1021/jp5064676
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    Residue-Specific Force Field Based on Protein Coil Library. RSFF2: Modification of AMBER ff99SB
    Zhou, Chen-Yang; Jiang, Fan; Wu, Yun-Dong
    Journal of Physical Chemistry B (2015), 119 (3), 1035-1047CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
    Recently, we developed a residue-specific force field (RSFF1) based on conformational free-energy distributions of the 20 amino acid residues from a protein coil library. Most parameters in RSFF1 were adopted from the OPLS-AA/L force field, but some van der Waals and torsional parameters that effectively affect local conformational preferences were introduced specifically for individual residues to fit the coil library distributions. Here a similar strategy has been applied to modify the Amber ff99SB force field, and a new force field named RSFF2 is developed. It can successfully fold α-helical structures such as polyalanine peptides, Trp-cage miniprotein, and villin headpiece subdomain and β-sheet structures such as Trpzip-2, GB1 β-hairpins, and the WW domain, simultaneously. The properties of various popular force fields in balancing between α-helix and β-sheet are analyzed based on their descriptions of local conformational features of various residues, and the anal. reveals the importance of accurate local free-energy distributions. Unlike the RSFF1, which overestimates the stability of both α-helix and β-sheet, RSFF2 gives melting curves of α-helical peptides and Trp-cage in good agreement with exptl. data. Fitting to the two-state model, RSFF2 gives folding enthalpies and entropies in reasonably good agreement with available exptl. results.
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    Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. Comparison of simple potential functions for simulating liquid water. J. Chem. Phys. 1983, 79, 926– 935,  DOI: 10.1063/1.445869
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    Comparison of simple potential functions for simulating liquid water
    Jorgensen, William L.; Chandrasekhar, Jayaraman; Madura, Jeffry D.; Impey, Roger W.; Klein, Michael L.
    Journal of Chemical Physics (1983), 79 (2), 926-35CODEN: JCPSA6; ISSN:0021-9606.
    Classical Monte Carlo simulations were carried out for liq. H2O in the NPT ensemble at 25° and 1 atm using 6 of the simpler intermol. potential functions for the dimer. Comparisons were made with exptl. thermodn. and structural data including the neutron diffraction results of Thiessen and Narten (1982). The computed densities and potential energies agree with expt. except for the original Bernal-Fowler model, which yields an 18% overest. of the d. and poor structural results. The discrepancy may be due to the correction terms needed in processing the neutron data or to an effect uniformly neglected in the computations. Comparisons were made for the self-diffusion coeffs. obtained from mol. dynamics simulations.
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    Jiang, F.; Zhou, C.-Y.; Wu, Y.-D. Residue-Specific Force Field Based on the Protein Coil Library. RSFF1: Modification of OPLS-AA/L. J. Phys. Chem. B 2014, 118, 6983– 6998,  DOI: 10.1021/jp5017449
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    Residue-Specific Force Field Based on the Protein Coil Library. RSFF1: Modification of OPLS-AA/L
    Jiang, Fan; Zhou, Chen-Yang; Wu, Yun-Dong
    Journal of Physical Chemistry B (2014), 118 (25), 6983-6998CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
    Traditional protein force fields use one set of parameters for most of the 20 amino acids (AAs), allowing transferability of the parameters. However, a significant shortcoming is the difficulty to fit the Ramachandran plots of all AA residues simultaneously, affecting the accuracy of the force field. In this Feature Article, the authors report a new strategy for protein force field parametrization. Backbone and side-chain conformational distributions of all 20 AA residues obtained from protein coil library were used as the target data. The dihedral angle (torsion) potentials and some local nonbonded (1-4/1-5/1-6) interactions in OPLS-AA/L force field were modified such that the target data can be excellently reproduced by mol. dynamics simulations of dipeptides (blocked AAs) in explicit water, resulting in a new force field with AA-specific parameters, RSFF1. An efficient free energy decompn. approach was developed to sep. the corrections on φ and ψ from the two-dimensional Ramachandran plots. RSFF1 is shown to reproduce the exptl. NMR 3J-coupling consts. of AA dipeptides better than other force fields. It has a good balance between α-helical and β-sheet secondary structures. It can successfully fold a set of α-helix proteins (Trp-cage and Homeodomain) and β-hairpins (Trpzip-2, GB1 hairpin), which cannot be consistently stabilized by other state-of-the-art force fields. The RSFF1 force field systematically overestimates the melting temp. (and the stability of native state) of these peptides/proteins. It has a potential application in the simulation of protein folding and protein structure refinement.
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    Lindorff-Larsen, K.; Piana, S.; Palmo, K.; Maragakis, P.; Klepeis, J. L.; Dror, R. O.; Shaw, D. E. Improved side-chain torsion potentials for the Amber ff99SB protein force field. Proteins: Struct., Funct., Bioinf. 2010, 78, 1950– 1958,  DOI: 10.1002/prot.22711
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    Improved side-chain torsion potentials for the Amber ff99SB protein force field
    Lindorff-Larsen, Kresten; Piana, Stefano; Palmo, Kim; Maragakis, Paul; Klepeis, John L.; Dror, Ron O.; Shaw, David E.
    Proteins: Structure, Function, and Bioinformatics (2010), 78 (8), 1950-1958CODEN: PSFBAF ISSN:. (Wiley-Liss, Inc.)
    Recent advances in hardware and software have enabled increasingly long mol. dynamics (MD) simulations of biomols., exposing certain limitations in the accuracy of the force fields used for such simulations and spurring efforts to refine these force fields. Recent modifications to the Amber and CHARMM protein force fields, for example, have improved the backbone torsion potentials, remedying deficiencies in earlier versions. Here, the authors further advance simulation accuracy by improving the amino acid side-chain torsion potentials of the Amber ff99SB force field. First, the authors used simulations of model alpha-helical systems to identify the four residue types whose rotamer distribution differed the most from expectations based on Protein Data Bank statistics. Second, the authors optimized the side-chain torsion potentials of these residues to match new, high-level quantum-mech. calcns. Finally, the authors used microsecond-timescale MD simulations in explicit solvent to validate the resulting force field against a large set of exptl. NMR measurements that directly probe side-chain conformations. The new force field, which the authors have termed Amber ff99SB-ILDN, exhibits considerably better agreement with the NMR data. Proteins 2010. © 2010 Wiley-Liss, Inc.
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    Geng, H.; Jiang, F.; Wu, Y.-D. Accurate Structure Prediction and Conformational Analysis of Cyclic Peptides with Residue-Specific Force Fields. J. Phys. Chem. Lett. 2016, 7, 1805– 1810,  DOI: 10.1021/acs.jpclett.6b00452
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    Accurate Structure Prediction and Conformational Analysis of Cyclic Peptides with Residue-Specific Force Fields
    Geng, Hao; Jiang, Fan; Wu, Yun-Dong
    Journal of Physical Chemistry Letters (2016), 7 (10), 1805-1810CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
    Cyclic peptides (CPs) are promising candidates for drugs, chem. biol. tools, and self-assembling nanomaterials. However, the development of reliable and accurate computational methods for their structure prediction has been challenging. Here, 20 all-trans CPs of 5-12 residues selected from Cambridge Structure Database have been simulated using replica-exchange mol. dynamics with four different force fields. The authors' recently developed residue-specific force fields RSFF1 and RSFF2 can correctly identify the crystal-like conformations of more than half CPs as the most populated conformation. The RSFF2 performs the best, which consistently predicts the crystal structures of 17 out of 20 CPs with RMSD < 1.1 Å. The authors also compared the backbone (φ,ψ) sampling of residues in CPs which those in short linear peptides and in globular proteins. In general, unlike linear peptides, CPs have local conformational free energies and entropies quite similar to globular proteins.
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    Kaminski, G. A.; Friesner, R. A.; Tirado-Rives, J.; Jorgensen, W. L. Evaluation and Reparametrization of the OPLS-AA Force Field for Proteins via Comparison with Accurate Quantum Chemical Calculations on Peptides. J. Phys. Chem. B 2001, 105, 6474– 6487,  DOI: 10.1021/jp003919d
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    Evaluation and Reparametrization of the OPLS-AA Force Field for Proteins via Comparison with Accurate Quantum Chemical Calculations on Peptides
    Kaminski, George A.; Friesner, Richard A.; Tirado-Rives, Julian; Jorgensen, William L.
    Journal of Physical Chemistry B (2001), 105 (28), 6474-6487CODEN: JPCBFK; ISSN:1089-5647. (American Chemical Society)
    We present results of improving the OPLS-AA force field for peptides by means of refitting the key Fourier torsional coeffs. The fitting technique combines using accurate ab initio data as the target, choosing an efficient fitting subspace of the whole potential-energy surface, and detg. wts. for each of the fitting points based on magnitudes of the potential-energy gradient. The av. energy RMS deviation from the LMP2/cc-pVTZ(-f)//HF/6-31G** data is reduced by ∼40% from 0.81 to 0.47 kcal/mol as a result of the fitting for the electrostatically uncharged dipeptides. Transferability of the parameters is demonstrated by using the same alanine dipeptide-fitted backbone torsional parameters for all of the other dipeptides (with the appropriate side-chain refitting) and the alanine tetrapeptide. Parameters of nonbonded interactions have also been refitted for the sulfur-contg. dipeptides (cysteine and methionine), and the validity of the new Coulombic charges and the van der Waals σ's and ε's is proved through reproducing gas-phase energies of complex formation heats of vaporization and densities of pure model liqs. Moreover, a novel approach to fitting torsional parameters for electrostatically charged mol. systems has been presented and successfully tested on five dipeptides with charged side chains.
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    Essmann, U.; Perera, L.; Berkowitz, M. L.; Darden, T.; Lee, H.; Pedersen, L. G. A smooth particle mesh Ewald method. J. Chem. Phys. 1995, 103, 8577– 8593,  DOI: 10.1063/1.470117
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    A smooth particle mesh Ewald method
    Essmann, Ulrich; Perera, Lalith; Berkowitz, Max L.; Darden, Tom; Lee, Hsing; Pedersen, Lee G.
    Journal of Chemical Physics (1995), 103 (19), 8577-93CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    The previously developed particle mesh Ewald method is reformulated in terms of efficient B-spline interpolation of the structure factors. This reformulation allows a natural extension of the method to potentials of the form 1/rp with p ≥ 1. Furthermore, efficient calcn. of the virial tensor follows. Use of B-splines in the place of Lagrange interpolation leads to analytic gradients as well as a significant improvement in the accuracy. The authors demonstrate that arbitrary accuracy can be achieved, independent of system size N, at a cost that scales as N log(N). For biomol. systems with many thousands of atoms and this method permits the use of Ewald summation at a computational cost comparable to that of a simple truncation method of 10 Å or less.
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    Tribello, G. A.; Bonomi, M.; Branduardi, D.; Camilloni, C.; Bussi, G. PLUMED 2: New feathers for an old bird. Comput. Phys. Commun. 2014, 185, 604– 613,  DOI: 10.1016/j.cpc.2013.09.018
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    PLUMED 2: New feathers for an old bird
    Tribello, Gareth A.; Bonomi, Massimiliano; Branduardi, Davide; Camilloni, Carlo; Bussi, Giovanni
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    Enhancing sampling and analyzing simulations are central issues in mol. simulation. Recently, we introduced PLUMED, an open-source plug-in that provides some of the most popular mol. dynamics (MD) codes with implementations of a variety of different enhanced sampling algorithms and collective variables (CVs). The rapid changes in this field, in particular new directions in enhanced sampling and dimensionality redn. together with new hardware, require a code that is more flexible and more efficient. We therefore present PLUMED 2 here-a complete rewrite of the code in an object-oriented programming language (C++). This new version introduces greater flexibility and greater modularity, which both extends its core capabilities and makes it far easier to add new methods and CVs. It also has a simpler interface with the MD engines and provides a single software library contg. both tools and core facilities. Ultimately, the new code better serves the ever-growing community of users and contributors in coping with the new challenges arising in the field.
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  • Abstract

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    Figure 1

    Figure 1. StrEAMM linear regression models are constructed using contributions from neighboring interactions. For example, the natural logarithm of the population of cyclic pentapeptide cyclo-(X1X2X3X4X5) adopting a specific structure S1S2S3S4S5 is the sum of the interaction weights for each (1,2) and (1,3) neighbor present. Xi is an amino acid; Si is a structural digit that represents a region of (ϕ, ψ) space (see Figure 2); wSiSi+1XiXi+1 is the weight for residues XiXi+1 adopting structure SiSi+1; wSiSi+1Si+2Xi_Xi+2 is the weight for residues Xi and Xi+2 adopting substructure SiSi+1Si+2; and wQX1X2X3X4X5 is related to the partition function, Q, for sequence X1X2X3X4X5 and ensures that all the structures’ populations sum to 1 for a given sequence. This equation was first proposed by Miao et al. (31)

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    Figure 2

    Figure 2. Structural binning maps divide the (ϕ, ψ) space of cyclic pentapeptides into 10 regions and the (ϕ, ψ) space of cyclic hexapeptides into six regions. (A) The (ϕ, ψ) population density of cyclo-(GGGGG) and (B) the resulting binning map when all the grid points are assigned to their closest centroid to form the final binning map. (C) The (ϕ, ψ) population density of cyclo-(GGGGGG) and (D) the resulting binning map using the same binning protocol.

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    Figure 3

    Figure 3. Convolutional neural network and graph neural network architectures. (A) Cartoon example of the cyclic pentapeptide sequence cyclo-(sasFr) represented using a matrix with N = 5 columns and 2048 rows, where the 2048 bits come from the fingerprint encoding of each amino acid. (B) The representations of cyclo-(sasFr) and cyclo-(asFrs) are concatenated such that the (1,2) neighboring residues are spatially close together, enabling the 1D convolutional filter (blue box representing a (4096 × 1) vector of learnable model parameters) to encompass all the fingerprint features that define residues s and a. (C) The top graph represents a cyclic pentapeptide, where the (1,2) edge types are denoted with blue arrows and the (1,3) edge types are denoted with green arrows. The bottom graph represents a cyclic hexapeptide, where in addition to the (1,2) and (1,3) edge types we also can include (1,4) edge types, as denoted with purple arrows. Note: The purple (1,4) edges appear to be double-arrowed, but there are really two unique single-arrowed edges. For example, the forward edge in dark purple that starts at ser1 would be directed to Phe4, and the forward edge in dark purple that starts at Phe4 would be directed to ser1.

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    Figure 4

    Figure 4. Performance of StrEAMM linear regression models on the training dataset (top) and test dataset (bottom) for (A) cyclic pentapeptides and (B, C) cyclic hexapeptides. (A) Performance of StrEAMM linear regression model on cyclic pentapeptides using (1,2) and (1,3) interactions. (B) Performance of StrEAMM linear regression model on cyclic hexapeptides using (1,2) and (1,3) interactions. (C) Performance of StrEAMM linear regression model on cyclic hexapeptides using (1,2), (1,3), and (1,4) interactions. The black dashed line represents y = x. R2 is the coefficient of determination. WE is the weighted error, given by WE=∑ipi,observed|pi,observed−pi,predicted|∑ipi,observed, where pi,observed and pi,predicted are the populations observed in MD simulation and predicted by StrEAMM, respectively. Each point on the plot represents the predicted versus the observed percent population in MD for a structure in the structural ensemble of a cyclic peptide. All the structures in the structural ensembles for all the cyclic peptides in the training or test dataset with a predicted or observed percent population in MD of >1% are plotted.

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    Figure 5

    Figure 5. Performance of (A–C) StrEAMM CNN models and (D–F) StrEAMM GNN models on the test dataset for (A, D) cyclic pentapeptides and the models incorporating (1,2) and (1,3) filters/edges, (B, E) cyclic hexapeptides and the models incorporating (1,2) and (1,3) filters/edges, and (C, F) cyclic hexapeptides and the models incorporating (1,2), (1,3), and (1,4) filters/edges. See Figure S7 for the model performances on the corresponding training datasets. All the structures in the structural ensembles for all the cyclic peptides in the training or test dataset with a predicted or observed percent population in MD of >1% are plotted.

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    Figure 6

    Figure 6. Comparison of the StrEAMM linear regression and neural network models’ performances on the (A) cyclic pentapeptide and (B) cyclic hexapeptide test datasets. The coefficient of determination, R2, and weighted error, WE, are shown for each model (the linear regression in red with diagonal slash pattern, CNN in green with dotted pattern, and GNN in blue with vertical line pattern) including different neighboring interactions.

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    Figure 7

    Figure 7. The StrEAMM neural network models can predict structural ensembles for cyclic pentapeptides and cyclic hexapeptides that contain amino acids that were absent in the training dataset. (A–D) Performances of the (A, B) CNN and (C, D) GNN models on cyclic pentapeptide and cyclic hexapeptide datasets containing sequences composed of the 37 amino acid library, when the models were trained using only sequences composed of the 15 amino acid library. (E–H) Performances of the (E, F) CNN and (G, H) GNN models on cyclic pentapeptide and cyclic hexapeptide datasets containing sequences composed of the 37 amino acid library, when the models were trained using sequences composed of the 15 amino acid library and “booster” sequences composed of the 37 amino acid library.

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  • References

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      Cyclic peptides combine several favorable properties such as good binding affinity, target selectivity and low toxicity that make them an attractive modality for the development of therapeutics. Over 40 cyclic peptide drugs are currently in clin. use and around one new cyclic peptide drug enters the market every year on av. The vast majority of clin. approved cyclic peptides are derived from natural products, such as antimicrobials or human peptide hormones. New powerful techniques based on rational design and in vitro evolution have enabled the de novo development of cyclic peptide ligands to targets for which nature does not offer solns. A look at the cyclic peptides currently under clin. evaluation shows that several have been developed using such techniques. This new source for cyclic peptide ligands introduces a freshness to the field, and it is likely that de novo developed cyclic peptides will be in clin. use in the near future.
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    7. 7
      Nguyen, Q. N. N.; Schwochert, J.; Tantillo, D. J.; Lokey, R. S. Using 1H and 13C NMR chemical shifts to determine cyclic peptide conformations: a combined molecular dynamics and quantum mechanics approach. Phys. Chem. Chem. Phys. 2018, 20, 14003– 14012,  DOI: 10.1039/C8CP01616J
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      7
      Using 1H and 13C NMR chemical shifts to determine cyclic peptide conformations: a combined molecular dynamics and quantum mechanics approach
      Nguyen, Q. Nhu N.; Schwochert, Joshua; Tantillo, Dean J.; Lokey, R. Scott
      Physical Chemistry Chemical Physics (2018), 20 (20), 14003-14012CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      Solving conformations of cyclic peptides can provide insight into structure-activity and structure-property relationships, which can help in the design of compds. with improved bioactivity and/or ADME characteristics. The most common approaches for detg. the structures of cyclic peptides are based on NMR-derived distance restraints obtained from NOESY or ROESY cross-peak intensities, and 3J-based dihedral restraints using the Karplus relationship. Unfortunately, these observables are often too weak, sparse, or degenerate to provide unequivocal, high-confidence soln. structures, prompting us to investigate an alternative approach that relies only on 1H and 13C chem. shifts as exptl. observables. This method, which we call conformational anal. from NMR and d.-functional prediction of low-energy ensembles (CANDLE), uses mol. dynamics (MD) simulations to generate conformer families and d. functional theory (DFT) calcns. to predict their 1H and 13C chem. shifts. Iterative conformer searches and DFT energy calcns. on a cyclic peptide-peptoid hybrid yielded Boltzmann ensembles whose predicted chem. shifts matched the exptl. values better than any single conformer. For these compds., CANDLE outperformed the classic NOE- and 3J-coupling-based approach by disambiguating similar β-turn types and also enabled the structural elucidation of the minor conformer. Through the use of chem. shifts, in conjunction with DFT and MD calcns., CANDLE can help illuminate conformational ensembles of cyclic peptides in soln.
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    8. 8
      Ball, K. A.; Wemmer, D. E.; Head-Gordon, T. Comparison of Structure Determination Methods for Intrinsically Disordered Amyloid-β Peptides. J. Phys. Chem. B 2014, 118, 6405– 6416,  DOI: 10.1021/jp410275y
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      8
      Comparison of Structure Determination Methods for Intrinsically Disordered Amyloid-β Peptides
      Ball, K. Aurelia; Wemmer, David E.; Head-Gordon, Teresa
      Journal of Physical Chemistry B (2014), 118 (24), 6405-6416CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
      Intrinsically disordered proteins (IDPs) represent a new frontier in structural biol. since the primary characteristic of IDPs is that structures need to be characterized as diverse ensembles of conformational substates. We compare two general but very different ways of combining NMR spectroscopy with theor. methods to derive structural ensembles for the disease IDPs amyloid-β 1-40 and amyloid-β 1-42, which are assocd. with Alzheimer's Disease. We analyze the performance of de novo mol. dynamics and knowledge-based approaches for generating structural ensembles by assessing their ability to reproduce a range of NMR exptl. observables. In addn. to the comparison of computational methods, we also evaluate the relative value of different types of NMR data for refining or validating the IDP structural ensembles for these important disease peptides.
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    9. 9
      Fisher, C. K.; Stultz, C. M. Constructing ensembles for intrinsically disordered proteins. Curr. Opin. Struct. Biol. 2011, 21, 426– 431,  DOI: 10.1016/j.sbi.2011.04.001
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      9
      Constructing ensembles for intrinsically disordered proteins
      Fisher, Charles K.; Stultz, Collin M.
      Current Opinion in Structural Biology (2011), 21 (3), 426-431CODEN: COSBEF; ISSN:0959-440X. (Elsevier Ltd.)
      A review. The relatively flat energy landscapes assocd. with intrinsically disordered proteins makes modeling these systems esp. problematic. A comprehensive model for these proteins requires one to build an ensemble consisting of a finite collection of structures, and their corresponding relative stabilities, which adequately capture the range of accessible states of the protein. In this regard, methods that use computational techniques to interpret exptl. data in terms of such ensembles are an essential part of the modeling process. In this review, we critically assess the advantages and limitations of current techniques and discuss new methods for the validation of these ensembles.
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    10. 10
      Cicero, D. O.; Barbato, G.; Bazzo, R. NMR Analysis of Molecular Flexibility in Solution: A New Method for the Study of Complex Distributions of Rapidly Exchanging Conformations. Application to a 13-Residue Peptide with an 8-Residue Loop. J. Am. Chem. Soc. 1995, 117, 1027– 1033,  DOI: 10.1021/ja00108a019
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      10
      NMR Analysis of Molecular Flexibility in Solution: A New Method for the Study of Complex Distributions of Rapidly Exchanging Conformations. Application to a 13-Residue Peptide with an 8-Residue Loop
      Cicero, D. O.; Barbato, G.; Bazzo, R.
      Journal of the American Chemical Society (1995), 117 (3), 1027-33CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      A new methodol., called NAMFIS (NMR anal. of mol. flexibility in soln.), is described for the anal. of flexible mols. in soln. Once a complete set of conformations is generated and is able to encompass all the possible states of the mol. that are not a priori incompatible with the available exptl. NMR evidence, NAMFIS allows for the examn. of the occurrence and relevance of arbitrary elements of secondary structure, even when extensive conformational averaging defies a detailed exptl. characterization. The anal. is based on the available exptl. NMR data. The method is demonstrated in the conformational anal. of peptide I (R = Lys-Aib-Lys-OH; Aib = α-aminoisobutyric acid, Mhe = 2-amino-6-mercaptohexanoic acid).
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    11. 11
      Ge, Y.; Zhang, S.; Erdelyi, M.; Voelz, V. A. Solution-State Preorganization of Cyclic β-Hairpin Ligands Determines Binding Mechanism and Affinities for MDM2. J. Chem. Inf. Model. 2021, 61, 2353– 2367,  DOI: 10.1021/acs.jcim.1c00029
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      11
      Solution-State Preorganization of Cyclic β-Hairpin Ligands Determines Binding Mechanism and Affinities for MDM2
      Ge, Yunhui; Zhang, Si; Erdelyi, Mate; Voelz, Vincent A.
      Journal of Chemical Information and Modeling (2021), 61 (5), 2353-2367CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
      Understanding mechanisms of protein folding and binding is crucial to designing their mol. function. Mol. dynamics (MD) simulations and Markov state model (MSM) approaches provide a powerful way to understand complex conformational change that occurs over long time scales. Such dynamics are important for the design of therapeutic peptidomimetic ligands, whose affinity and binding mechanism are dictated by a combination of folding and binding. To examine the role of preorganization in peptide binding to protein targets, the authors performed massively parallel explicit-solvent MD simulations of cyclic β-hairpin ligands designed to mimic the p53 transactivation domain and competitively bind mouse double minute 2 homolog (MDM2). Disrupting the MDM2-p53 interaction is a therapeutic strategy to prevent degrdn. of the p53 tumor suppressor in cancer cells. MSM anal. of over 3 ms of aggregate trajectory data enabled the authors to build a detailed mechanistic model of coupled folding and binding of four cyclic peptides which the authors compare to exptl. binding affinities and rates. The results show a striking relation between the relative preorganization of each ligand in soln. and its affinity for MDM2. Specifically, changes in peptide conformational populations predicted by the MSMs suggest that entropy loss upon binding is the main factor influencing affinity. The MSMs also enable detailed examn. of non-native interactions which lead to misfolded states and comparison of structural ensembles with exptl. NMR measurements. In contrast to an MSM study of p53 transactivation domain (TAD) binding to MDM2, MSMs of cyclic β-hairpin binding show a conformational selection mechanism. Finally, the authors make progress toward predicting accurate off rates of cyclic peptides using multi-ensemble Markov models (MEMMs) constructed from unbiased and biased simulated trajectories.
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    12. 12
      Slough, D. P.; McHugh, S. M.; Cummings, A. E.; Dai, P.; Pentelute, B. L.; Kritzer, J. A.; Lin, Y.-S. Designing Well-Structured Cyclic Pentapeptides Based on Sequence-Structure Relationships. J. Phys. Chem. B 2018, 122, 3908– 3919,  DOI: 10.1021/acs.jpcb.8b01747
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      12
      Designing well-structured cyclic pentapeptides based on sequence-structure relationships
      Slough, Diana P.; McHugh, Sean M.; Cummings, Ashleigh E.; Dai, Peng; Pentelute, Bradley L.; Kritzer, Joshua A.; Lin, Yu-Shan
      Journal of Physical Chemistry B (2018), 122 (14), 3908-3919CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
      Cyclic peptides are a promising class of mols. for unique applications. Unfortunately, cyclic peptide design is severely limited by the difficulty in predicting the conformations they will adopt in soln. In this work, we use explicit-solvent mol. dynamics simulations to design well-structured cyclic peptides by studying their sequence-structure relationships. Crit. to our approach is an enhanced sampling method that exploits the essential transitional motions of cyclic peptides to efficiently sample their conformational space. We simulated a range of cyclic pentapeptides from all-glycine to a library of cyclo-(X1X2AAA) peptides to map their conformational space and det. cooperative effects of neighboring residues. By combining the results from all cyclo-(X1X2AAA) peptides, we developed a scoring function to predict the structural preferences for X1-X2 residues within cyclic pentapeptides. Using this scoring function, we designed a cyclic pentapeptide, cyclo-(GNSRV), predicted to be well structured in aq. soln. Subsequent CD and NMR spectroscopy revealed that this cyclic pentapeptide is indeed well structured in water, with a nuclear Overhauser effect and J-coupling values consistent with the predicted structure.
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    13. 13
      Cummings, A. E.; Miao, J.; Slough, D. P.; McHugh, S. M.; Kritzer, J. A.; Lin, Y. S. β-Branched Amino Acids Stabilize Specific Conformations of Cyclic Hexapeptides. Biophys. J. 2019, 116, 433– 444,  DOI: 10.1016/j.bpj.2018.12.015
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      13
      β-Branched Amino Acids Stabilize Specific Conformations of Cyclic Hexapeptides
      Cummings, Ashleigh E.; Miao, Jiayuan; Slough, Diana P.; McHugh, Sean M.; Kritzer, Joshua A.; Lin, Yu-Shan
      Biophysical Journal (2019), 116 (3), 433-444CODEN: BIOJAU; ISSN:0006-3495. (Cell Press)
      Cyclic peptides (CPs) are a promising class of mols. for drug development, particularly as inhibitors of protein-protein interactions. Predicting low-energy structures and global structural ensembles of individual CPs is crit. for the design of bioactive mols., but these are challenging to predict and difficult to verify exptl. In our previous work, we used explicit-solvent mol. dynamics simulations with enhanced sampling methods to predict the global structural ensembles of cyclic hexapeptides contg. different permutations of glycine, alanine, and valine. One peptide, cyclo-(VVGGVG) or P7, was predicted to be unusually well structured. In this work, we synthesized P7, along with a less well-structured control peptide, cyclo-(VVGVGG) or P6, and characterized their global structural ensembles in water using NMR spectroscopy. The NMR data revealed a structural ensemble similar to the prediction for P7 and showed that P6 was indeed much less well-structured than P7. We then simulated and exptl. characterized the global structural ensembles of several P7 analogs and discovered that β-branching at one crit. position within P7 is important for overall structural stability. The simulations allowed deconvolution of thermodn. factors that underlie this structural stabilization. Overall, the excellent correlation between simulation and exptl. data indicates that our simulation platform will be a promising approach for designing well-structured CPs and also for understanding the complex interactions that control the conformations of constrained peptides and other macrocycles.
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    14. 14
      Wakefield, A. E.; Wuest, W. M.; Voelz, V. A. Molecular Simulation of Conformational Pre-Organization in Cyclic RGD Peptides. J. Chem. Inf. Model. 2015, 55, 806– 813,  DOI: 10.1021/ci500768u
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      14
      Molecular Simulation of Conformational Pre-Organization in Cyclic RGD Peptides
      Wakefield, Amanda E.; Wuest, William M.; Voelz, Vincent A.
      Journal of Chemical Information and Modeling (2015), 55 (4), 806-813CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
      To test the ability of mol. simulations to accurately predict the soln.-state conformational properties of peptidomimetics, we examd. a test set of 18 cyclic RGD peptides selected from the literature, including the anticancer drug candidate cilengitide, whose favorable binding affinity to integrin has been ascribed to its pre-organization in soln. For each design, we performed all-atom replica-exchange mol. dynamics simulations over several microseconds and compared the results to extensive published NMR data. We find excellent agreement with exptl. NOE distance restraints, suggesting that mol. simulation can be a useful tool for the computational design of pre-organized soln.-state structure. Moreover, our anal. of conformational populations ests. that, despite the potential for increased flexibility due to backbone amide isomerizaton, N-methylation provides about 0.5 kcal/mol of reduced conformational entropy to cyclic RGD peptides. The combination of pre-organization and binding-site compatibility explains the strong binding affinity of cilengitide to integrin.
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    15. 15
      Damjanovic, J.; Miao, J.; Huang, H.; Lin, Y.-S. Elucidating Solution Structures of Cyclic Peptides Using Molecular Dynamics Simulations. Chem. Rev. 2021, 121, 2292– 2324,  DOI: 10.1021/acs.chemrev.0c01087
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      Elucidating Solution Structures of Cyclic Peptides Using Molecular Dynamics Simulations
      Damjanovic, Jovan; Miao, Jiayuan; Huang, He; Lin, Yu-Shan
      Chemical Reviews (Washington, DC, United States) (2021), 121 (4), 2292-2324CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
      A review. Protein-protein interactions are vital to biol. processes, but the shape and size of their interfaces make them hard to target using small mols. Cyclic peptides have shown promise as protein-protein interaction modulators, as they can bind protein surfaces with high affinity and specificity. Dozens of cyclic peptides are already FDA approved, and many more are in various stages of development as immunosuppressants, antibiotics, antivirals, or anticancer drugs. However, most cyclic peptide drugs so far have been natural products or derivs. thereof, with de novo design having proven challenging. A key obstacle is structural characterization: cyclic peptides frequently adopt multiple conformations in soln., which are difficult to resolve using techniques like NMR spectroscopy. The lack of soln. structural information prevents a thorough understanding of cyclic peptides' sequence-structure-function relationship. Here we review recent development and application of mol. dynamics simulations with enhanced sampling to studying the soln. structures of cyclic peptides. We describe novel computational methods capable of sampling cyclic peptides' conformational space and provide examples of computational studies that relate peptides' sequence and structure to biol. activity. We demonstrate that mol. dynamics simulations have grown from an explanatory technique to a full-fledged tool for systematic studies at the forefront of cyclic peptide therapeutic design.
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    16. 16
      Ono, S.; Naylor, M. R.; Townsend, C. E.; Okumura, C.; Okada, O.; Lokey, R. S. Conformation and Permeability: Cyclic Hexapeptide Diastereomers. J. Chem. Inf. Model. 2019, 59, 2952– 2963,  DOI: 10.1021/acs.jcim.9b00217
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      65
      Conformation and Permeability: Cyclic Hexapeptide Diastereomers
      Ono, Satoshi; Naylor, Matthew R.; Townsend, Chad E.; Okumura, Chieko; Okada, Okimasa; Lokey, R. Scott
      Journal of Chemical Information and Modeling (2019), 59 (6), 2952-2963CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
      Conformational ensembles of eight cyclic hexapeptide diastereomers in explicit cyclohexane, chloroform, and water were analyzed by multicanonical mol. dynamics (McMD) simulations. Free-energy landscapes (FELs) for each compd. and solvent were obtained from the mol. shapes and principal component anal. at T = 300 K; detailed anal. of the conformational ensembles and flexibility of the FELs revealed that permeable compds. have different structural profiles even for a single stereoisomeric change. The av. solvent-accessible surface area (SASA) in cyclohexane showed excellent correlation with the cell permeability, whereas this correlation was weaker in chloroform. The av. SASA in water correlated with the aq. soly. The av. polar surface area did not correlate with cell permeability in these solvents. A possible strategy for designing permeable cyclic peptides from FELs obtained from McMD simulations is proposed.
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    17. 17
      Wang, S.; König, G.; Roth, H.-J.; Fouché, M.; Rodde, S.; Riniker, S. Effect of Flexibility, Lipophilicity, and the Location of Polar Residues on the Passive Membrane Permeability of a Series of Cyclic Decapeptides. J. Med. Chem. 2021, 64, 12761– 12773,  DOI: 10.1021/acs.jmedchem.1c00775
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      66
      Effect of Flexibility, Lipophilicity, and the Location of Polar Residues on the Passive Membrane Permeability of a Series of Cyclic Decapeptides
      Wang, Shuzhe; Konig, Gerhard; Roth, Hans-Jorg; Fouche, Marianne; Rodde, Stephane; Riniker, Sereina
      Journal of Medicinal Chemistry (2021), 64 (17), 12761-12773CODEN: JMCMAR; ISSN:0022-2623. (American Chemical Society)
      Cyclic peptides have received increasing attention over the recent years as potential therapeutics for "undruggable" targets. One major obstacle is, however, their often relatively poor bioavailability. Here, we investigate the structure-permeability relationship of 24 cyclic decapeptides that share the same backbone N-methylation pattern but differ in their side chains. The peptides cover a large range of values for passive membrane permeability as well as lipophilicity and soly. To rationalize the obsd. differences in permeability, we extd. for each peptide the population of the membrane-permeable conformation in water from extensive explicit-solvent mol. dynamics simulations and used this as a metric for conformational rigidity or "prefolding.". The insights from the simulations together with lipophilicity measurements highlight the intricate interplay between polarity/lipophilicity and flexibility/rigidity and the possible compensating effects on permeability. The findings allow us to better understand the structure-permeability relationship of cyclic peptides and ext. general guiding principles.
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    18. 18
      El Tayar, N.; Mark, A. E.; Vallat, P.; Brunne, R. M.; Testa, B.; van Gunsteren, W. F. Solvent-dependent conformation and hydrogen-bonding capacity of cyclosporin A: evidence from partition coefficients and molecular dynamics simulations. J. Med. Chem. 1993, 36, 3757– 3764,  DOI: 10.1021/jm00076a002
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      15
      Solvent-dependent conformation and hydrogen-bonding capacity of cyclosporin A: evidence from partition coefficients and molecular dynamics simulations
      El Tayar, Nabil; Mark, Alan E.; Vallat, Philippe; Brunne, Roger M.; Testa, Bernard; van Gunsteren, Wilfred F.
      Journal of Medicinal Chemistry (1993), 36 (24), 3757-64CODEN: JMCMAR; ISSN:0022-2623.
      The partition coeff. of cyclosporin A (CsA) was measured in octanol/water and heptane/water by centrifugal partition chromatog. By comparison with results from model compds., it was deduced that the hydrogen-bonding capacity of CsA changed dramatically from an apolar solvent (where it is internally H-bonded) to polar solvents (where it exposes its H-bonding groups to the solvent). Mol. dynamics simulations in water and CCl4 support the suggestion that CsA undergoes a solvent-dependent conformational changes and that the interconversion process is slow on the mol. dynamics time scale.
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    19. 19
      Merten, C.; Li, F.; Bravo-Rodriguez, K.; Sanchez-Garcia, E.; Xu, Y.; Sander, W. Solvent-induced conformational changes in cyclic peptides: a vibrational circular dichroism study. Phys. Chem. Chem. Phys. 2014, 16, 5627– 5633,  DOI: 10.1039/C3CP55018D
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      Solvent-induced conformational changes in cyclic peptides: a vibrational circular dichroism study
      Merten, Christian; Li, Fee; Bravo-Rodriguez, Kenny; Sanchez-Garcia, Elsa; Xu, Yunjie; Sander, Wolfram
      Physical Chemistry Chemical Physics (2014), 16 (12), 5627-5633CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      The three-dimensional structure of a peptide is strongly influenced by its solvent environment. In the present study, we study three cyclic tetrapeptides which serve as model peptides for β-turns. They are of the general structure cyclo(Boc-Cys-Pro-X-Cys-OMe) with the amino acid X being either glycine, or L- or D-leucine. Using vibrational CD (VCD) spectroscopy, we confirm previous NMR results which showed that cyclo(Boc-Cys-Pro-D-Leu-Cys-OMe) adopts predominantly a βII turn structure in apolar and polar solvents. Our results for cyclo(Boc-Cys-Pro-Leu-Cys-OMe) (Boc = tert-nutoxycarbonyl) indicate a preference for a βI structure over βII. With increasing solvent polarity, the preference for cyclo(Boc-Cys-Pro-Gly-Cys-OMe) is shifted from βII towards βI. This conformational change goes along with the breaking of an intramol. hydrogen bond which stabilizes the βII conformation. Instead, a hydrogen bond with a solvent mol. can stabilize the βI turn conformation.
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    20. 20
      Quartararo, J. S.; Eshelman, M. R.; Peraro, L.; Yu, H.; Baleja, J. D.; Lin, Y.-S.; Kritzer, J. A. A bicyclic peptide scaffold promotes phosphotyrosine mimicry and cellular uptake. Bioorg. Med. Chem. 2014, 22, 6387– 6391,  DOI: 10.1016/j.bmc.2014.09.050
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      17
      A bicyclic peptide scaffold promotes phosphotyrosine mimicry and cellular uptake
      Quartararo, Justin S.; Eshelman, Matthew R.; Peraro, Leila; Yu, Hongtao; Baleja, James D.; Lin, Yu-Shan; Kritzer, Joshua A.
      Bioorganic & Medicinal Chemistry (2014), 22 (22), 6387-6391CODEN: BMECEP; ISSN:0968-0896. (Elsevier B.V.)
      While peptides are promising as probes and therapeutics, targeting intracellular proteins will require greater understanding of highly structured, cell-internalized scaffolds. We recently reported BC1, an 11-residue bicyclic peptide that inhibits the Src homol. 2 (SH2) domain of growth factor receptor-bound protein 2 (Grb2). In this work, we describe the unique structural and cell uptake properties of BC1 and similar cyclic and bicyclic scaffolds. These constrained scaffolds are taken up by mammalian cells despite their net neutral or neg. charges, while unconstrained analogs are not. The mechanism of uptake is shown to be energy-dependent and endocytic, but distinct from that of Tat. The soln. structure of BC1 was investigated by NMR and MD simulations, which revealed discrete water-binding sites on BC1 that reduce exposure of backbone amides to bulk water. This represents an original and potentially general strategy for promoting cell uptake.
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    21. 21
      Baek, M.; DiMaio, F.; Anishchenko, I.; Dauparas, J.; Ovchinnikov, S.; Lee, G. R.; Wang, J.; Cong, Q.; Kinch, L. N.; Schaeffer, R. D.; Millán, C.; Park, H.; Adams, C.; Glassman, C. R.; DeGiovanni, A.; Pereira, J. H.; Rodrigues, A. V.; van Dijk, A. A.; Ebrecht, A. C.; Opperman, D. J.; Sagmeister, T.; Buhlheller, C.; Pavkov-Keller, T.; Rathinaswamy, M. K.; Dalwadi, U.; Yip, C. K.; Burke, J. E.; Garcia, K. C.; Grishin, N. V.; Adams, P. D.; Read, R. J.; Baker, D. Accurate prediction of protein structures and interactions using a three-track neural network. Science 2021, 373, 871– 876,  DOI: 10.1126/science.abj8754
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      18
      Accurate prediction of protein structures and interactions using a three-track neural network
      Baek, Minkyung; DiMaio, Frank; Anishchenko, Ivan; Dauparas, Justas; Ovchinnikov, Sergey; Lee, Gyu Rie; Wang, Jue; Cong, Qian; Kinch, Lisa N.; Schaeffer, R. Dustin; Millan, Claudia; Park, Hahnbeom; Adams, Carson; Glassman, Caleb R.; DeGiovanni, Andy; Pereira, Jose H.; Rodrigues, Andria V.; van Dijk, Alberdina A.; Ebrecht, Ana C.; Opperman, Diederik J.; Sagmeister, Theo; Buhlheller, Christoph; Pavkov-Keller, Tea; Rathinaswamy, Manoj K.; Dalwadi, Udit; Yip, Calvin K.; Burke, John E.; Garcia, K. Christopher; Grishin, Nick V.; Adams, Paul D.; Read, Randy J.; Baker, David
      Science (Washington, DC, United States) (2021), 373 (6557), 871-876CODEN: SCIEAS; ISSN:1095-9203. (American Association for the Advancement of Science)
      DeepMind presented notably accurate predictions at the recent 14th Crit. Assessment of Structure Prediction (CASP14) conference. We explored network architectures that incorporate related ideas and obtained the best performance with a three-track network in which information at the one-dimensional (1D) sequence level, the 2D distance map level, and the 3D coordinate level is successively transformed and integrated. The three-track network produces structure predictions with accuracies approaching those of DeepMind in CASP14, enables the rapid soln. of challenging x-ray crystallog. and cryo-electron microscopy structure modeling problems, and provides insights into the functions of proteins of currently unknown structure. The network also enables rapid generation of accurate protein-protein complex models from sequence information alone, short-circuiting traditional approaches that require modeling of individual subunits followed by docking. We make the method available to the scientific community to speed biol. research.
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    22. 22
      Bryant, P.; Pozzati, G.; Elofsson, A. Improved prediction of protein-protein interactions using AlphaFold2. Nat. Commun. 2022, 13, 1265,  DOI: 10.1038/s41467-022-28865-w
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      20
      Improved prediction of protein-protein interactions using AlphaFold2
      Bryant, Patrick; Pozzati, Gabriele; Elofsson, Arne
      Nature Communications (2022), 13 (1), 1265CODEN: NCAOBW; ISSN:2041-1723. (Nature Portfolio)
      Predicting the structure of interacting protein chains is a fundamental step towards understanding protein function. Unfortunately, no computational method can produce accurate structures of protein complexes. AlphaFold2, has shown unprecedented levels of accuracy in modeling single chain protein structures. Here, we apply AlphaFold2 for the prediction of heterodimeric protein complexes. We find that the AlphaFold2 protocol together with optimized multiple sequence alignments, generate models with acceptable quality (DockQ ≥ 0.23) for 63% of the dimers. From the predicted interfaces we create a simple function to predict the DockQ score which distinguishes acceptable from incorrect models as well as interacting from non-interacting proteins with state-of-art accuracy. We find that, using the predicted DockQ scores, we can identify 51% of all interacting pairs at 1% FPR.
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    23. 23
      Bryant, P.; Pozzati, G.; Zhu, W.; Shenoy, A.; Kundrotas, P.; Elofsson, A. Predicting the structure of large protein complexes using AlphaFold and Monte Carlo tree search. Nat. Commun. 2022, 13, 6028,  DOI: 10.1038/s41467-022-33729-4
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      21
      Predicting the structure of large protein complexes using AlphaFold and Monte Carlo tree search
      Bryant, Patrick; Pozzati, Gabriele; Zhu, Wensi; Shenoy, Aditi; Kundrotas, Petras; Elofsson, Arne
      Nature Communications (2022), 13 (1), 6028CODEN: NCAOBW; ISSN:2041-1723. (Nature Portfolio)
      AlphaFold can predict the structure of single- and multiple-chain proteins with very high accuracy. However, the accuracy decreases with the no. of chains, and the available GPU memory limits the size of protein complexes which can be predicted. Here we show that one can predict the structure of large complexes starting from predictions of subcomponents. We assemble 91 out of 175 complexes with 10-30 chains from predicted subcomponents using Monte Carlo tree search, with a median TM-score of 0.51. There are 30 highly accurate complexes (TM-score ≥0.8, 33% of complete assemblies). We create a scoring function, mpDockQ, that can distinguish if assemblies are complete and predict their accuracy. We find that complexes contg. symmetry are accurately assembled, while asym. complexes remain challenging.
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    24. 24
      Jumper, J.; Evans, R.; Pritzel, A.; Green, T.; Figurnov, M.; Ronneberger, O.; Tunyasuvunakool, K.; Bates, R.; Žídek, A.; Potapenko, A.; Bridgland, A.; Meyer, C.; Kohl, S. A. A.; Ballard, A. J.; Cowie, A.; Romera-Paredes, B.; Nikolov, S.; Jain, R.; Adler, J.; Back, T.; Petersen, S.; Reiman, D.; Clancy, E.; Zielinski, M.; Steinegger, M.; Pacholska, M.; Berghammer, T.; Bodenstein, S.; Silver, D.; Vinyals, O.; Senior, A. W.; Kavukcuoglu, K.; Kohli, P.; Hassabis, D. Highly accurate protein structure prediction with AlphaFold. Nature 2021, 596, 583– 589,  DOI: 10.1038/s41586-021-03819-2
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      22
      Highly accurate protein structure prediction with AlphaFold
      Jumper, John; Evans, Richard; Pritzel, Alexander; Green, Tim; Figurnov, Michael; Ronneberger, Olaf; Tunyasuvunakool, Kathryn; Bates, Russ; Zidek, Augustin; Potapenko, Anna; Bridgland, Alex; Meyer, Clemens; Kohl, Simon A. A.; Ballard, Andrew J.; Cowie, Andrew; Romera-Paredes, Bernardino; Nikolov, Stanislav; Jain, Rishub; Adler, Jonas; Back, Trevor; Petersen, Stig; Reiman, David; Clancy, Ellen; Zielinski, Michal; Steinegger, Martin; Pacholska, Michalina; Berghammer, Tamas; Bodenstein, Sebastian; Silver, David; Vinyals, Oriol; Senior, Andrew W.; Kavukcuoglu, Koray; Kohli, Pushmeet; Hassabis, Demis
      Nature (London, United Kingdom) (2021), 596 (7873), 583-589CODEN: NATUAS; ISSN:0028-0836. (Nature Portfolio)
      Proteins are essential to life, and understanding their structure can facilitate a mechanistic understanding of their function. Through an enormous exptl. effort, the structures of around 100,000 unique proteins have been detd., but this represents a small fraction of the billions of known protein sequences. Structural coverage is bottlenecked by the months to years of painstaking effort required to det. a single protein structure. Accurate computational approaches are needed to address this gap and to enable large-scale structural bioinformatics. Predicting the three-dimensional structure that a protein will adopt based solely on its amino acid sequence-the structure prediction component of the 'protein folding problem'-has been an important open research problem for more than 50 years. Despite recent progress, existing methods fall far short of at. accuracy, esp. when no homologous structure is available. Here we provide the first computational method that can regularly predict protein structures with at. accuracy even in cases in which no similar structure is known. We validated an entirely redesigned version of our neural network-based model, AlphaFold, in the challenging 14th Crit. Assessment of protein Structure Prediction (CASP14), demonstrating accuracy competitive with exptl. structures in a majority of cases and greatly outperforming other methods. Underpinning the latest version of AlphaFold is a novel machine learning approach that incorporates phys. and biol. knowledge about protein structure, leveraging multi-sequence alignments, into the design of the deep learning algorithm.
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    25. 25
      Rettie, S. A.; Campbell, K. V.; Bera, A. K.; Kang, A.; Kozlov, S.; De La Cruz, J.; Adebomi, V.; Zhou, G.; DiMaio, F.; Ovchinnikov, S.; Bhardwaj, G. Cyclic peptide structure prediction and design using AlphaFold. bioRxiv 2023,  DOI: 10.1101/2023.02.25.529956v1
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      There is no corresponding record for this reference.
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      Gang, D.; Kim, D. W.; Park, H. S. Cyclic Peptides: Promising Scaffolds for Biopharmaceuticals. Genes 2018, 9, 557,  DOI: 10.3390/genes9110557
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      Cyclic peptides: promising scaffolds for biopharmaceuticals
      Gang, Donghyeok; Kim, Do Wook; Park, Hee-Sung
      Genes (2018), 9 (11), 557/1-557/15CODEN: GENEG9; ISSN:2073-4425. (MDPI AG)
      A review. To date, small mols. and macromols., including antibodies, have been the most pursued substances in drug screening and development efforts. Despite numerous favorable features as a drug, these mols. still have limitations and are not complementary in many regards. Recently, peptide-based chem. structures that lie between these two categories in terms of both structural and functional properties have gained increasing attention as potential alternatives. In particular, peptides in a circular form provide a promising scaffold for the development of a novel drug class owing to their adjustable and expandable ability to bind a wide range of target mols. In this review, we discuss recent progress in methodologies for peptide cyclization and screening and use of bioactive cyclic peptides in various applications.
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    27. 27
      Iacovelli, R.; Bovenberg, R. A. L.; Driessen, A. J. M. Nonribosomal peptide synthetases and their biotechnological potential in Penicillium rubens. J. Ind. Microbiol. Biotechnol. 2021, 48, kuab045,  DOI: 10.1093/jimb/kuab045
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      Marahiel, M. A. Working outside the protein-synthesis rules: insights into non-ribosomal peptide synthesis. J. Pept. Sci. 2009, 15, 799– 807,  DOI: 10.1002/psc.1183
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      Working outside the protein-synthesis rules: Insights into non-ribosomal peptide synthesis
      Marahiel, Mohamed A.
      Journal of Peptide Science (2009), 15 (12), 799-807CODEN: JPSIEI; ISSN:1075-2617. (John Wiley & Sons Ltd.)
      A review. Non-ribosomally synthesized microbial peptides show remarkable structural diversity and constitute a widespread class of the most potent antibiotics and other important pharmaceuticals that range from penicillin to the immunosuppressant cyclosporine. They are assembled independent of the ribosome in a nucleic acid-independent way by a group of multimodular megaenzymes called non-ribosomal peptide synthetases. These biosynthetic machineries rely not only on the 20 canonical amino acids, but also use several different building blocks, including D-configured- and β-amino acids, methylated, glycosylated and phosphorylated residues, heterocyclic elements and even fatty acid building blocks. This structural diversity leads to a high d. of functional groups, which are often essential for the bioactivity. Recent biochem. and structural studies on several non-ribosomal peptide synthetase assembly lines have substantially contributed to the understanding of the mol. mechanisms and dynamics of individual catalytic domains underlying substrate recognition and substrate shuffling among the different active sites as well as peptide bond formation and the regio- and stereoselective product release. Copyright © 2009 European Peptide Society and John Wiley & Sons, Ltd.
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    29. 29
      Martínez-Núñez, M. A.; López y López, V. E. Nonribosomal peptides synthetases and their applications in industry. Sustainable Chem. Processes 2016, 4, 13,  DOI: 10.1186/s40508-016-0057-6
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      Nonribosomal peptides synthetases and their applications in industry
      Martinez-Nunez, Mario Alberto; Lopez y Lopez, Victor Eric
      Sustainable Chemical Processes (2016), 4 (), 13/1-13/8CODEN: SCPUCB; ISSN:2043-7129. (Chemistry Central Ltd.)
      A review. X. Nonribosomal peptides are products that fall into the class of secondary metabolites with diverse properties as toxins, siderophores, pigments, or antibiotics, among others. Unlike other proteins, its biosynthesis is independent of ribosomal machinery. Nonribosomal peptides are synthesized on large nonribosomal peptide synthetase (NRPS) enzyme complexes. NRPSs are defined as multimodular enzymes, consisting of repeated modules. The NRPS enzymes are at operons and their regulation can be pos. or neg. at transcriptional or post-translational level. The presence of NRPS enzymes has been reported in the 3 domains of life, being prevalent in bacteria. Nonribosomal peptides are used in human medicine, crop protection, or environment restoration; and their use as com. products has been approved by the U.S. Food and Drug Administration and the Environmental Protection Agency. Here, the key features of nonribosomal peptides and NRPS enzymes, and some of their applications in industry are summarized.
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    30. 30
      Sieber, S. A.; Marahiel, M. A. Learning from Nature’s Drug Factories: Nonribosomal Synthesis of Macrocyclic Peptides. J. Bacteriol. 2003, 185, 7036– 7043,  DOI: 10.1128/JB.185.24.7036-7043.2003
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      Learning from nature's drug factories: Nonribosomal synthesis of macrocyclic peptides
      Sieber, Stephan A.; Marahiel, Mohamed A.
      Journal of Bacteriology (2003), 185 (24), 7036-7043CODEN: JOBAAY; ISSN:0021-9193. (American Society for Microbiology)
      A review. The family of enzymes, nonribosomal peptide peptide synthetases/ cyclases, are discussed.
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    31. 31
      Miao, J.; Descoteaux, M. L.; Lin, Y.-S. Structure prediction of cyclic peptides by molecular dynamics + machine learning. Chem. Sci. 2021, 12, 14927– 14936,  DOI: 10.1039/D1SC05562C
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      29
      Structure prediction of cyclic peptides by molecular dynamics + machine learning
      Miao, Jiayuan; Descoteaux, Marc L.; Lin, Yu-Shan
      Chemical Science (2021), 12 (44), 14927-14936CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)
      Recent computational methods have made strides in discovering well-structured cyclic peptides that preferentially populate a single conformation. However, many successful cyclic-peptide therapeutics adopt multiple conformations in soln. In fact, the chameleonic properties of some cyclic peptides are likely responsible for their high cell membrane permeability. Thus, we require the ability to predict complete structural ensembles for cyclic peptides, including the majority of cyclic peptides that have broad structural ensembles, to significantly improve our ability to rationally design cyclic-peptide therapeutics. Here, we introduce the idea of using mol. dynamics simulation results to train machine learning models to enable efficient structure prediction for cyclic peptides. Using mol. dynamics simulation results for several hundred cyclic pentapeptides as the training datasets, we developed machine-learning models that can provide mol. dynamics simulation-quality predictions of structural ensembles for all the hundreds of thousands of sequences in the entire sequence space. The prediction for each individual cyclic peptide can be made using less than 1 s of computation time. Even for the most challenging classes of poorly structured cyclic peptides with broad conformational ensembles, our predictions were similar to those one would normally obtain only after running multiple days of explicit-solvent mol. dynamics simulations. The resulting method, termed StrEAMM (Structural Ensembles Achieved by Mol. Dynamics and Machine Learning), is the first technique capable of efficiently predicting complete structural ensembles of cyclic peptides without relying on addnl. mol. dynamics simulations, constituting a seven-order-of-magnitude improvement in speed while retaining the same accuracy as explicit-solvent simulations.
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    32. 32
      Jurtz, V. I.; Johansen, A. R.; Nielsen, M.; Almagro Armenteros, J. J.; Nielsen, H.; Sønderby, C. K.; Winther, O.; Sønderby, S. K. An introduction to deep learning on biological sequence data: examples and solutions. Bioinformatics 2017, 33, 3685– 3690,  DOI: 10.1093/bioinformatics/btx531
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      An introduction to deep learning on biological sequence data: Examples and solutions
      Jurtz, Vanessa Isabell; Johansen, Alexander Rosenberg; Nielsen, Morten; Armenteros, Jose Juan Almagro; Nielsen, Henrik; Soenderby, Casper Kaae; Winther, Ole; Soenderby, Soeren Kaae
      Bioinformatics (2017), 33 (22), 3685-3690CODEN: BOINFP; ISSN:1367-4811. (Oxford University Press)
      Motivation: Deep neural network architectures such as convolutional and long short-term memory networks have become increasingly popular as machine learning tools during the recent years. The availability of greater computational resources, more data, new algorithms for training deep models and easy to use libraries for implementation and training of neural networks are the drivers of this development. The use of deep learning has been esp. successful in image recognition; and the development of tools, applications and code examples are in most cases centered within this field rather than within biol. Results: Here, we aim to further the development of deep learning methods within biol. by providing application examples and ready to apply and adapt code templates. Given such examples, we illustrate how architectures consisting of convolutional and long short-term memory neural networks can relatively easily be designed and trained to state-of-the-art performance on three biol. sequence problems: prediction of subcellular localization, protein secondary structure and the binding of peptides to MHC Class II mols.
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      Hou, J.; Adhikari, B.; Cheng, J. DeepSF: deep convolutional neural network for mapping protein sequences to folds. Bioinformatics 2018, 34, 1295– 1303,  DOI: 10.1093/bioinformatics/btx780
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      DeepSF: deep convolutional neural network for mapping protein sequences to folds
      Hou, Jie; Adhikari, Badri; Cheng, Jianlin
      Bioinformatics (2018), 34 (8), 1295-1303CODEN: BOINFP; ISSN:1367-4811. (Oxford University Press)
      Motivation: Protein fold recognition is an important problem in structural bioinformatics. Almost all traditional fold recognition methods use sequence (homol.) comparison to indirectly predict the fold of a target protein based on the fold of a template protein with known structure, which cannot explain the relationship between sequence and fold. Only a few methods had been developed to classify protein sequences into a small no. of folds due to methodol. limitations, which are not generally useful in practice. Results: We develop a deep 1D-convolution neural network (DeepSF) to directly classify any protein sequence into one of 1195 known folds, which is useful for both fold recognition and the study of sequence-structure relationship. Different from traditional sequence alignment (comparison) based methods, our method automatically exts. fold-related features from a protein sequence of any length and maps it to the fold space. We train and test our method on the datasets curated from SCOP1.75, yielding an av. classification accuracy of 75.3%. On the independent testing dataset curated from SCOP2.06, the classification accuracy is 73.0%. We compare our method with a top profile-profile alignment method-HHSearch on hard template-based and template-free modeling targets of CASP9-12 in terms of fold recognition accuracy. The accuracy of our method is 12.63-26.32% higher than HHSearch on template-free modeling targets and 3.39-17.09% higher on hard template-based modeling targets for top 1, 5 and 10 predicted folds. The hidden features extd. from sequence by our method is robust against sequence mutation, insertion, deletion and truncation, and can be used for other protein pattern recognition problems such as protein clustering, comparison and ranking.
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    34. 34
      Cheng, J.; Liu, Y.; Ma, Y. Protein secondary structure prediction based on integration of CNN and LSTM model. J. Vis. Commun. Image Representation. 2020, 71, 102844,  DOI: 10.1016/j.jvcir.2020.102844
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      Chen, Z.; Min, M. R.; Ning, X. Ranking-Based Convolutional Neural Network Models for Peptide-MHC Class I Binding Prediction. Front. Mol. Biosci. 2021, 8, 634836,  DOI: 10.3389/fmolb.2021.634836
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      Ranking-based convolutional neural network models for peptide-MHC class I binding prediction
      Chen, Ziqi; Min, Martin Renqiang; Ning, Xia
      Frontiers in Molecular Biosciences (2021), 8 (), 634836CODEN: FMBRBS; ISSN:2296-889X. (Frontiers Media S.A.)
      T-cell receptors can recognize foreign peptides bound to major histocompatibility complex (MHC) class-I proteins, and thus trigger the adaptive immune response. Therefore, identifying peptides that can bind to MHC class-I mols. plays a vital role in the design of peptide vaccines. Many computational methods, for example, the state-of-the-art allele-specific method mhcflurry, have been developed to predict the binding affinities between peptides and MHC mols. In this manuscript, we develop two allele-specific Convolutional Neural Network-based methods named convm and spconvm to tackle the binding prediction problem. Specifically, we formulate the problem as to optimize the rankings of peptide-MHC bindings via ranking-based learning objectives. Such optimization is more robust and tolerant to the measurement inaccuracy of binding affinities, and therefore enables more accurate prioritization of binding peptides. In addn., we develop a new position encoding method in convm and spconvm to better identify the most important amino acids for the binding events. We conduct a comprehensive set of expts. using the latest Immune Epitope Database (IEDB) datasets. Our exptl. results demonstrate that our models significantly outperform the state-of-the-art methods including mhcflurry with an av. percentage improvement of 6.70% on AUC and 17.10% on ROC5 across 128 alleles.
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    36. 36
      Gelman, S.; Fahlberg, S. A.; Heinzelman, P.; Romero, P. A.; Gitter, A. Neural networks to learn protein sequence─function relationships from deep mutational scanning data. Proc. Natl. Acad. Sci. U.S.A. 2021, 118, e2104878118  DOI: 10.1073/pnas.2104878118
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      Neural networks to learn protein sequence-function relationships from deep mutational scanning data
      Gelman, Sam; Fahlberg, Sarah A.; Heinzelman, Pete; Romero, Philip A.; Gitter, Anthony
      Proceedings of the National Academy of Sciences of the United States of America (2021), 118 (48), e2104878118CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
      The mapping from protein sequence to function is highly complex, making it challenging to predict how sequence changes will affect a protein's behavior and properties. We present a supervised deep learning framework to learn the sequence-function mapping from deep mutational scanning data and make predictions for new, uncharacterized sequence variants. We test multiple neural network architectures, including a graph convolutional network that incorporates protein structure, to explore how a network's internal representation affects its ability to learn the sequence-function mapping. Our supervised learning approach displays superior performance over physics-based and unsupervised prediction methods. We find that networks that capture nonlinear interactions and share parameters across sequence positions are important for learning the relationship between sequence and function. Further anal. of the trained models reveals the networks' ability to learn biol. meaningful information about protein structure and mechanism. Finally, we demonstrate the models' ability to navigate sequence space and design new proteins beyond the training set. We applied the protein G B1 domain (GB1) models to design a sequence that binds to IgG with substantially higher affinity than wild-type GB1.
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    37. 37
      Hosseinzadeh, P.; Bhardwaj, G.; Mulligan, V. K.; Shortridge, M. D.; Craven, T. W.; Pardo-Avila, F.; Rettie, S. A.; Kim, D. E.; Silva, D.-A.; Ibrahim, Y. M.; Webb, I. K.; Cort, J. R.; Adkins, J. N.; Varani, G.; Baker, D. Comprehensive computational design of ordered peptide macrocycles. Science 2017, 358, 1461– 1466,  DOI: 10.1126/science.aap7577
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      Comprehensive computational design of ordered peptide macrocycles
      Hosseinzadeh, Parisa; Bhardwaj, Gaurav; Mulligan, Vikram Khipple; Shortridge, Matthew D.; Craven, Timothy W.; Pardo-Avila, Fatima; Rettie, Stephen A.; Kim, David E.; Silva, Daniel-Adriano; Ibrahim, Yehia M.; Webb, Ian K.; Cort, John R.; Adkins, Joshua N.; Varani, Gabriele; Baker, David
      Science (Washington, DC, United States) (2017), 358 (6369), 1461-1466CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
      Mixed-chirality peptide macrocycles such as cyclosporine are among the most potent therapeutics identified to date, but there is currently no way to systematically search the structural space spanned by such compds. Natural proteins do not provide a useful guide: Peptide macrocycles lack regular secondary structures and hydrophobic cores, and can contain local structures not accessible with L-amino acids. Here, we enumerate the stable structures that can be adopted by macrocyclic peptides composed of L- and D-amino acids by near-exhaustive backbone sampling followed by sequence design and energy landscape calcns. We identify more than 200 designs predicted to fold into single stable structures, many times more than the no. of currently available unbound peptide macrocycle structures. NMR structures of 9 of 12 designed 7- to 10-residue macrocycles, and three 11- to 14-residue bicyclic designs, are close to the computational models. Our results provide a nearly complete coverage of the rich space of structures possible for short peptide macrocycles and vastly increase the available starting scaffolds for both rational drug design and library selection methods.
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      Li, X.; Du, X.; Li, J.; Gao, Y.; Pan, Y.; Shi, J.; Zhou, N.; Xu, B. Introducing d-Amino Acid or Simple Glycoside into Small Peptides to Enable Supramolecular Hydrogelators to Resist Proteolysis. Langmuir 2012, 28, 13512– 13517,  DOI: 10.1021/la302583a
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      Introducing d-Amino Acid or Simple Glycoside into Small Peptides to Enable Supramolecular Hydrogelators to Resist Proteolysis
      Li, Xinming; Du, Xuewen; Li, Jiayang; Gao, Yuan; Pan, Yue; Shi, Junfeng; Zhou, Ning; Xu, Bing
      Langmuir (2012), 28 (37), 13512-13517CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      Here we report the examn. of two convenient strategies, the use of a d-amino acid residue or a glycoside segment, for increasing the proteolytic resistance of supramol. hydrogelators based on small peptides. Our results show that the introduction of d-amino acid or glycoside to the peptides significantly increases the resistance of the hydrogelators against proteinase K, a powerful endopeptidase. The insertion of d-amino acid in the peptide backbone, however, results relatively low storage moduli of the hydrogels, likely due to the disruption of the superstructures of the mol. assembly. In contrast, the introduction of a glycoside to the C-terminal of peptide enhances the biostability of the hydrogelators without the significant decrease of the storage moduli of the hydrogels. This work suggests that the inclusion of a simple glycogen in hydrogelators is a useful approach to increase their biostability, and the gained understanding from the work may ultimately lead to development of hydrogels of functional peptides for biomedical applications that require long-term biostability.
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    39. 39
      Liu, J.; Liu, J.; Chu, L.; Zhang, Y.; Xu, H.; Kong, D.; Yang, Z.; Yang, C.; Ding, D. Self-Assembling Peptide of d-Amino Acids Boosts Selectivity and Antitumor Efficacy of 10-Hydroxycamptothecin. ACS Appl. Mater. Interfaces 2014, 6, 5558– 5565,  DOI: 10.1021/am406007g
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      37
      Self-Assembling Peptide of d-Amino Acids Boosts Selectivity and Antitumor Efficacy of 10-Hydroxycamptothecin
      Liu, Jianfeng; Liu, Jinjian; Chu, Liping; Zhang, Yumin; Xu, Hongyan; Kong, Deling; Yang, Zhimou; Yang, Cuihong; Ding, Dan
      ACS Applied Materials & Interfaces (2014), 6 (8), 5558-5565CODEN: AAMICK; ISSN:1944-8244. (American Chemical Society)
      D-Peptides, which consist of D-amino acids and can resist the hydrolysis catalyzed by endogenous peptidases, are one of the promising candidates for construction of peptide materials with enhanced biostability in vivo. In this paper, we report on a self-assembling supramol. nanostructure of D-amino acid-based peptide Nap-GDFDFDYGRGD (D-fiber, DF meant D-phenylalanine, DY meant D-tyrosine), which were used as carriers for 10-hydroxycamptothecin (HCPT). Transmission electron microscopy observations demonstrated the filamentous morphol. of the HCPT-loaded peptides (D-fiber-HCPT). The better selectivity and antitumor activity of D-fiber-HCPT than L-fiber-HCPT were found in the in vitro and in vivo antitumor studies. These results highlight that this model D-fiber system holds great promise as vehicles of hydrophobic drugs for cancer therapy.
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      Piana, S.; Laio, A. A bias-exchange approach to protein folding. J. Phys. Chem. B 2007, 111, 4553– 4559,  DOI: 10.1021/jp067873l
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      A Bias-Exchange Approach to Protein Folding
      Piana, Stefano; Laio, Alessandro
      Journal of Physical Chemistry B (2007), 111 (17), 4553-4559CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
      By suitably extending a recent approach [Bussi, G., et al., 2006] the authors introduce a powerful methodol. that allows the parallel reconstruction of the free energy of a system in a virtually unlimited no. of variables. Multiple metadynamics simulations of the same system at the same temp. are performed, biasing each replica with a time-dependent potential constructed in a different set of collective variables. Exchanges between the bias potentials in the different variables are periodically allowed according to a replica exchange scheme. Due to the efficaciously multidimensional nature of the bias the method allows exploring complex free energy landscapes with high efficiency. The usefulness of the method is demonstrated by performing an atomistic simulation in explicit solvent of the folding of a Triptophane cage miniprotein. It is shown that the folding free energy landscape can be fully characterized starting from an extended conformation with use of only 40 ns of simulation on 8 replicas.
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    41. 41
      Laio, A.; Parrinello, M. Escaping free-energy minima. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 12562– 12566,  DOI: 10.1073/pnas.202427399
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      Escaping free-energy minima
      Laio, Alessandro; Parrinello, Michele
      Proceedings of the National Academy of Sciences of the United States of America (2002), 99 (20), 12562-12566CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
      We introduce a powerful method for exploring the properties of the multidimensional free energy surfaces (FESs) of complex many-body systems by means of coarse-grained non-Markovian dynamics in the space defined by a few collective coordinates. A characteristic feature of these dynamics is the presence of a history-dependent potential term that, in time, fills the min. in the FES, allowing the efficient exploration and accurate detn. of the FES as a function of the collective coordinates. We demonstrate the usefulness of this approach in the case of the dissocn. of a NaCl mol. in water and in the study of the conformational changes of a dialanine in soln.
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      McHugh, S. M.; Rogers, J. R.; Yu, H.; Lin, Y.-S. Insights into How Cyclic Peptides Switch Conformations. J. Chem. Theory Comput. 2016, 12, 2480– 2488,  DOI: 10.1021/acs.jctc.6b00193
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      40
      Insights into How Cyclic Peptides Switch Conformations
      McHugh, Sean M.; Rogers, Julia R.; Yu, Hongtao; Lin, Yu-Shan
      Journal of Chemical Theory and Computation (2016), 12 (5), 2480-2488CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      Cyclic peptides have recently emerged as promising modulators of protein-protein interactions. However, it is currently highly difficult to predict the structures of cyclic peptides owing to their rugged conformational free energy landscape, which prevents sampling of all thermodynamically relevant conformations. In this article, we first investigate how a relatively flexible cyclic hexapeptide switches conformations. It is found that, although the circular geometry of small cyclic peptides of size 6-8 may require rare, coherent dihedral changes to sample a new conformation, the changes are rather local, involving simultaneous changes of .vphi.i and ψi or ψi and .vphi.i+1. The understanding of how these cyclic peptides switch conformations enables the use of metadynamics simulations with reaction coordinates specifically targeting such coupled two-dihedral changes to effectively sample cyclic peptide conformational space.
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      Sugita, Y.; Kitao, A.; Okamoto, Y. Multidimensional replica-exchange method for free-energy calculations. J. Chem. Phys. 2000, 113, 6042– 6051,  DOI: 10.1063/1.1308516
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      Multidimensional replica-exchange method for free-energy calculations
      Sugita, Yuji; Kitao, Akio; Okamoto, Yuko
      Journal of Chemical Physics (2000), 113 (15), 6042-6051CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      We have developed a new simulation algorithm for free-energy calcns. The method is a multidimensional extension of the replica-exchange method. While pairs of replicas with different temps. are exchanged during the simulation in the original replica-exchange method, pairs of replicas with different temps. and/or different parameters of the potential energy are exchanged in the new algorithm. This greatly enhances the sampling of the conformational space and allows accurate calcns. of free energy in a wide temp. range from a single simulation run, using the weighted histogram anal. method.
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      Pettersen, E. F.; Goddard, T. D.; Huang, C. C.; Couch, G. S.; Greenblatt, D. M.; Meng, E. C.; Ferrin, T. E. UCSF Chimera-a visualization system for exploratory research and analysis. J. Comput. Chem. 2004, 25, 1605– 1612,  DOI: 10.1002/jcc.20084
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      UCSF Chimera-A visualization system for exploratory research and analysis
      Pettersen, Eric F.; Goddard, Thomas D.; Huang, Conrad C.; Couch, Gregory S.; Greenblatt, Daniel M.; Meng, Elaine C.; Ferrin, Thomas E.
      Journal of Computational Chemistry (2004), 25 (13), 1605-1612CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
      The design, implementation, and capabilities of an extensible visualization system, UCSF Chimera, are discussed. Chimera is segmented into a core that provides basic services and visualization, and extensions that provide most higher level functionality. This architecture ensures that the extension mechanism satisfies the demands of outside developers who wish to incorporate new features. Two unusual extensions are presented: Multiscale, which adds the ability to visualize large-scale mol. assemblies such as viral coats, and Collab., which allows researchers to share a Chimera session interactively despite being at sep. locales. Other extensions include Multalign Viewer, for showing multiple sequence alignments and assocd. structures; ViewDock, for screening docked ligand orientations; Movie, for replaying mol. dynamics trajectories; and Vol. Viewer, for display and anal. of volumetric data. A discussion of the usage of Chimera in real-world situations is given, along with anticipated future directions. Chimera includes full user documentation, is free to academic and nonprofit users, and is available for Microsoft Windows, Linux, Apple Mac OS X, SGI IRIX, and HP Tru64 Unix from http://www.cgl.ucsf.edu/chimera/.
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    45. 45
      Abraham, M. J.; Murtola, T.; Schulz, R.; Páll, S.; Smith, J. C.; Hess, B.; Lindahl, E. GROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputers. SoftwareX 2015, 1–2, 19– 25,  DOI: 10.1016/j.softx.2015.06.001
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      Zhou, C.-Y.; Jiang, F.; Wu, Y.-D. Residue-Specific Force Field Based on Protein Coil Library. RSFF2: Modification of AMBER ff99SB. J. Phys. Chem. B 2015, 119, 1035– 1047,  DOI: 10.1021/jp5064676
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      Residue-Specific Force Field Based on Protein Coil Library. RSFF2: Modification of AMBER ff99SB
      Zhou, Chen-Yang; Jiang, Fan; Wu, Yun-Dong
      Journal of Physical Chemistry B (2015), 119 (3), 1035-1047CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
      Recently, we developed a residue-specific force field (RSFF1) based on conformational free-energy distributions of the 20 amino acid residues from a protein coil library. Most parameters in RSFF1 were adopted from the OPLS-AA/L force field, but some van der Waals and torsional parameters that effectively affect local conformational preferences were introduced specifically for individual residues to fit the coil library distributions. Here a similar strategy has been applied to modify the Amber ff99SB force field, and a new force field named RSFF2 is developed. It can successfully fold α-helical structures such as polyalanine peptides, Trp-cage miniprotein, and villin headpiece subdomain and β-sheet structures such as Trpzip-2, GB1 β-hairpins, and the WW domain, simultaneously. The properties of various popular force fields in balancing between α-helix and β-sheet are analyzed based on their descriptions of local conformational features of various residues, and the anal. reveals the importance of accurate local free-energy distributions. Unlike the RSFF1, which overestimates the stability of both α-helix and β-sheet, RSFF2 gives melting curves of α-helical peptides and Trp-cage in good agreement with exptl. data. Fitting to the two-state model, RSFF2 gives folding enthalpies and entropies in reasonably good agreement with available exptl. results.
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    47. 47
      Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. Comparison of simple potential functions for simulating liquid water. J. Chem. Phys. 1983, 79, 926– 935,  DOI: 10.1063/1.445869
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      Comparison of simple potential functions for simulating liquid water
      Jorgensen, William L.; Chandrasekhar, Jayaraman; Madura, Jeffry D.; Impey, Roger W.; Klein, Michael L.
      Journal of Chemical Physics (1983), 79 (2), 926-35CODEN: JCPSA6; ISSN:0021-9606.
      Classical Monte Carlo simulations were carried out for liq. H2O in the NPT ensemble at 25° and 1 atm using 6 of the simpler intermol. potential functions for the dimer. Comparisons were made with exptl. thermodn. and structural data including the neutron diffraction results of Thiessen and Narten (1982). The computed densities and potential energies agree with expt. except for the original Bernal-Fowler model, which yields an 18% overest. of the d. and poor structural results. The discrepancy may be due to the correction terms needed in processing the neutron data or to an effect uniformly neglected in the computations. Comparisons were made for the self-diffusion coeffs. obtained from mol. dynamics simulations.
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    48. 48
      Jiang, F.; Zhou, C.-Y.; Wu, Y.-D. Residue-Specific Force Field Based on the Protein Coil Library. RSFF1: Modification of OPLS-AA/L. J. Phys. Chem. B 2014, 118, 6983– 6998,  DOI: 10.1021/jp5017449
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      46
      Residue-Specific Force Field Based on the Protein Coil Library. RSFF1: Modification of OPLS-AA/L
      Jiang, Fan; Zhou, Chen-Yang; Wu, Yun-Dong
      Journal of Physical Chemistry B (2014), 118 (25), 6983-6998CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
      Traditional protein force fields use one set of parameters for most of the 20 amino acids (AAs), allowing transferability of the parameters. However, a significant shortcoming is the difficulty to fit the Ramachandran plots of all AA residues simultaneously, affecting the accuracy of the force field. In this Feature Article, the authors report a new strategy for protein force field parametrization. Backbone and side-chain conformational distributions of all 20 AA residues obtained from protein coil library were used as the target data. The dihedral angle (torsion) potentials and some local nonbonded (1-4/1-5/1-6) interactions in OPLS-AA/L force field were modified such that the target data can be excellently reproduced by mol. dynamics simulations of dipeptides (blocked AAs) in explicit water, resulting in a new force field with AA-specific parameters, RSFF1. An efficient free energy decompn. approach was developed to sep. the corrections on φ and ψ from the two-dimensional Ramachandran plots. RSFF1 is shown to reproduce the exptl. NMR 3J-coupling consts. of AA dipeptides better than other force fields. It has a good balance between α-helical and β-sheet secondary structures. It can successfully fold a set of α-helix proteins (Trp-cage and Homeodomain) and β-hairpins (Trpzip-2, GB1 hairpin), which cannot be consistently stabilized by other state-of-the-art force fields. The RSFF1 force field systematically overestimates the melting temp. (and the stability of native state) of these peptides/proteins. It has a potential application in the simulation of protein folding and protein structure refinement.
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    49. 49
      Lindorff-Larsen, K.; Piana, S.; Palmo, K.; Maragakis, P.; Klepeis, J. L.; Dror, R. O.; Shaw, D. E. Improved side-chain torsion potentials for the Amber ff99SB protein force field. Proteins: Struct., Funct., Bioinf. 2010, 78, 1950– 1958,  DOI: 10.1002/prot.22711
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      Improved side-chain torsion potentials for the Amber ff99SB protein force field
      Lindorff-Larsen, Kresten; Piana, Stefano; Palmo, Kim; Maragakis, Paul; Klepeis, John L.; Dror, Ron O.; Shaw, David E.
      Proteins: Structure, Function, and Bioinformatics (2010), 78 (8), 1950-1958CODEN: PSFBAF ISSN:. (Wiley-Liss, Inc.)
      Recent advances in hardware and software have enabled increasingly long mol. dynamics (MD) simulations of biomols., exposing certain limitations in the accuracy of the force fields used for such simulations and spurring efforts to refine these force fields. Recent modifications to the Amber and CHARMM protein force fields, for example, have improved the backbone torsion potentials, remedying deficiencies in earlier versions. Here, the authors further advance simulation accuracy by improving the amino acid side-chain torsion potentials of the Amber ff99SB force field. First, the authors used simulations of model alpha-helical systems to identify the four residue types whose rotamer distribution differed the most from expectations based on Protein Data Bank statistics. Second, the authors optimized the side-chain torsion potentials of these residues to match new, high-level quantum-mech. calcns. Finally, the authors used microsecond-timescale MD simulations in explicit solvent to validate the resulting force field against a large set of exptl. NMR measurements that directly probe side-chain conformations. The new force field, which the authors have termed Amber ff99SB-ILDN, exhibits considerably better agreement with the NMR data. Proteins 2010. © 2010 Wiley-Liss, Inc.
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      Geng, H.; Jiang, F.; Wu, Y.-D. Accurate Structure Prediction and Conformational Analysis of Cyclic Peptides with Residue-Specific Force Fields. J. Phys. Chem. Lett. 2016, 7, 1805– 1810,  DOI: 10.1021/acs.jpclett.6b00452
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      48
      Accurate Structure Prediction and Conformational Analysis of Cyclic Peptides with Residue-Specific Force Fields
      Geng, Hao; Jiang, Fan; Wu, Yun-Dong
      Journal of Physical Chemistry Letters (2016), 7 (10), 1805-1810CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
      Cyclic peptides (CPs) are promising candidates for drugs, chem. biol. tools, and self-assembling nanomaterials. However, the development of reliable and accurate computational methods for their structure prediction has been challenging. Here, 20 all-trans CPs of 5-12 residues selected from Cambridge Structure Database have been simulated using replica-exchange mol. dynamics with four different force fields. The authors' recently developed residue-specific force fields RSFF1 and RSFF2 can correctly identify the crystal-like conformations of more than half CPs as the most populated conformation. The RSFF2 performs the best, which consistently predicts the crystal structures of 17 out of 20 CPs with RMSD < 1.1 Å. The authors also compared the backbone (φ,ψ) sampling of residues in CPs which those in short linear peptides and in globular proteins. In general, unlike linear peptides, CPs have local conformational free energies and entropies quite similar to globular proteins.
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      Kaminski, G. A.; Friesner, R. A.; Tirado-Rives, J.; Jorgensen, W. L. Evaluation and Reparametrization of the OPLS-AA Force Field for Proteins via Comparison with Accurate Quantum Chemical Calculations on Peptides. J. Phys. Chem. B 2001, 105, 6474– 6487,  DOI: 10.1021/jp003919d
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      Evaluation and Reparametrization of the OPLS-AA Force Field for Proteins via Comparison with Accurate Quantum Chemical Calculations on Peptides
      Kaminski, George A.; Friesner, Richard A.; Tirado-Rives, Julian; Jorgensen, William L.
      Journal of Physical Chemistry B (2001), 105 (28), 6474-6487CODEN: JPCBFK; ISSN:1089-5647. (American Chemical Society)
      We present results of improving the OPLS-AA force field for peptides by means of refitting the key Fourier torsional coeffs. The fitting technique combines using accurate ab initio data as the target, choosing an efficient fitting subspace of the whole potential-energy surface, and detg. wts. for each of the fitting points based on magnitudes of the potential-energy gradient. The av. energy RMS deviation from the LMP2/cc-pVTZ(-f)//HF/6-31G** data is reduced by ∼40% from 0.81 to 0.47 kcal/mol as a result of the fitting for the electrostatically uncharged dipeptides. Transferability of the parameters is demonstrated by using the same alanine dipeptide-fitted backbone torsional parameters for all of the other dipeptides (with the appropriate side-chain refitting) and the alanine tetrapeptide. Parameters of nonbonded interactions have also been refitted for the sulfur-contg. dipeptides (cysteine and methionine), and the validity of the new Coulombic charges and the van der Waals σ's and ε's is proved through reproducing gas-phase energies of complex formation heats of vaporization and densities of pure model liqs. Moreover, a novel approach to fitting torsional parameters for electrostatically charged mol. systems has been presented and successfully tested on five dipeptides with charged side chains.
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      Essmann, U.; Perera, L.; Berkowitz, M. L.; Darden, T.; Lee, H.; Pedersen, L. G. A smooth particle mesh Ewald method. J. Chem. Phys. 1995, 103, 8577– 8593,  DOI: 10.1063/1.470117
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      A smooth particle mesh Ewald method
      Essmann, Ulrich; Perera, Lalith; Berkowitz, Max L.; Darden, Tom; Lee, Hsing; Pedersen, Lee G.
      Journal of Chemical Physics (1995), 103 (19), 8577-93CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      The previously developed particle mesh Ewald method is reformulated in terms of efficient B-spline interpolation of the structure factors. This reformulation allows a natural extension of the method to potentials of the form 1/rp with p ≥ 1. Furthermore, efficient calcn. of the virial tensor follows. Use of B-splines in the place of Lagrange interpolation leads to analytic gradients as well as a significant improvement in the accuracy. The authors demonstrate that arbitrary accuracy can be achieved, independent of system size N, at a cost that scales as N log(N). For biomol. systems with many thousands of atoms and this method permits the use of Ewald summation at a computational cost comparable to that of a simple truncation method of 10 Å or less.
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      Tribello, G. A.; Bonomi, M.; Branduardi, D.; Camilloni, C.; Bussi, G. PLUMED 2: New feathers for an old bird. Comput. Phys. Commun. 2014, 185, 604– 613,  DOI: 10.1016/j.cpc.2013.09.018
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      PLUMED 2: New feathers for an old bird
      Tribello, Gareth A.; Bonomi, Massimiliano; Branduardi, Davide; Camilloni, Carlo; Bussi, Giovanni
      Computer Physics Communications (2014), 185 (2), 604-613CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
      Enhancing sampling and analyzing simulations are central issues in mol. simulation. Recently, we introduced PLUMED, an open-source plug-in that provides some of the most popular mol. dynamics (MD) codes with implementations of a variety of different enhanced sampling algorithms and collective variables (CVs). The rapid changes in this field, in particular new directions in enhanced sampling and dimensionality redn. together with new hardware, require a code that is more flexible and more efficient. We therefore present PLUMED 2 here-a complete rewrite of the code in an object-oriented programming language (C++). This new version introduces greater flexibility and greater modularity, which both extends its core capabilities and makes it far easier to add new methods and CVs. It also has a simpler interface with the MD engines and provides a single software library contg. both tools and core facilities. Ultimately, the new code better serves the ever-growing community of users and contributors in coping with the new challenges arising in the field.
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      Mu, Y.; Nguyen, P. H.; Stock, G. Energy landscape of a small peptide revealed by dihedral angle principal component analysis. Proteins 2005, 58, 45– 52,  DOI: 10.1002/prot.20310
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      Energy landscape of a small peptide revealed by dihedral angle principal component analysis
      Mu Yuguang; Nguyen Phuong H; Stock Gerhard
      Proteins (2005), 58 (1), 45-52 ISSN:.
      A 100 ns molecular dynamics simulation of penta-alanine in explicit water is performed to study the reversible folding and unfolding of the peptide. Employing a standard principal component analysis (PCA) using Cartesian coordinates, the resulting free-energy landscape is found to have a single minimum, thus suggesting a simple, relatively smooth free-energy landscape. Introducing a novel PCA based on a transformation of the peptide dihedral angles, it is found, however, that there are numerous free energy minima of comparable energy (less than or approximately 1 kcal/mol), which correspond to well-defined structures with characteristic hydrogen-bonding patterns. That is, the true free-energy landscape is actually quite rugged and its smooth appearance in the Cartesian PCA represents an artifact of the mixing of internal and overall motion. Well-separated minima corresponding to specific conformational structures are also found in the unfolded part of the free energy landscape, revealing that the unfolded state of penta-alanine is structured rather than random. Performing a connectivity analysis, it is shown that neighboring states are connected by low barriers of similar height and that each state typically makes transitions to three or four neighbor states. Several principal pathways for helix nucleation are identified and discussed in some detail.
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      Damas, J. M.; Filipe, L. C.; Campos, S. R.; Lousa, D.; Victor, B. L.; Baptista, A. M.; Soares, C. M. Predicting the Thermodynamics and Kinetics of Helix Formation in a Cyclic Peptide Model. J. Chem. Theory Comput. 2013, 9, 5148– 5157,  DOI: 10.1021/ct400529k
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      Predicting the thermodynamics and kinetics of helix formation in a cyclic peptide model
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    • Lists of sequences in the training and test datasets; structural binning maps 2 and 3; hyperparameter tuning schemes; neural network model performances on the training datasets for cyclic pentapeptides and cyclic hexapeptides; performances of linear regression and neural network models including only (1,2) or only (1,3) interactions on training and test datasets for cyclic pentapeptides; performances of linear regression and neural network models including only (1,2), only (1,3), or only (1,4) interactions on training and test datasets for cyclic hexapeptides; comparison of model performances using different binning maps (PDF)


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