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ArticleJanuary 6, 2025

Quantitative Prediction of Protein–Polyelectrolyte Binding Thermodynamics: Adsorption of Heparin-Analog Polysulfates to the SARS-CoV-2 Spike Protein RBD
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Lenard Neander
Lenard Neander
Department of Physics, Freie Universität Berlin, Arnimallee 14, Berlin 14195, Germany
Institute of Chemistry and Biochemistry, Freie Universität Berlin, Takustraße 3, Berlin 14195, Germany
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Cedric Hannemann
Cedric Hannemann
Department of Physics, Freie Universität Berlin, Arnimallee 14, Berlin 14195, Germany
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https://orcid.org/0009-0005-2467-168X
Roland R. Netz*
Roland R. Netz
Department of Physics, Freie Universität Berlin, Arnimallee 14, Berlin 14195, Germany
*Email: [email protected]
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https://orcid.org/0000-0003-0147-0162
Anil Kumar Sahoo*
Anil Kumar Sahoo
Department of Physics, Freie Universität Berlin, Arnimallee 14, Berlin 14195, Germany
*Email: [email protected]
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https://orcid.org/0000-0001-7769-4774

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JACS Au

Cite this: JACS Au 2025, XXXX, XXX, XXX-XXX

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https://doi.org/10.1021/jacsau.4c00886

Published January 6, 2025

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Abstract

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Interactions of polyelectrolytes (PEs) with proteins play a crucial role in numerous biological processes, such as the internalization of virus particles into host cells. Although docking, machine learning methods, and molecular dynamics (MD) simulations are utilized to estimate binding poses and binding free energies of small-molecule drugs to proteins, quantitative prediction of the binding thermodynamics of PE-based drugs presents a significant obstacle in computer-aided drug design. This is due to the sluggish dynamics of PEs caused by their size and strong charge–charge correlations. In this paper, we introduce advanced sampling methods based on a force-spectroscopy setup and theoretical modeling to overcome this barrier. We exemplify our method with explicit solvent all-atom MD simulations of the interactions between anionic PEs that show antiviral properties, namely heparin and linear polyglycerol sulfate (LPGS), and the SARS-CoV-2 spike protein receptor binding domain (RBD). Our prediction for the binding free-energy of LPGS to the wild-type RBD matches experimentally measured dissociation constants within thermal energy, k_BT, and correctly reproduces the experimental PE-length dependence. We find that LPGS binds to the Delta-variant RBD with an additional free-energy gain of 2.4 k_BT, compared to the wild-type RBD, due to the additional presence of two mutated cationic residues contributing to the electrostatic energy gain. We show that the LPGS–RBD binding is solvent dominated and enthalpy driven, though with a large entropy–enthalpy compensation. Our method is applicable to general polymer adsorption phenomena and predicts precise binding free energies and reconfigurational friction as needed for drug and drug-delivery design.

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Introduction

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Understanding the interaction of polyelectrolytes (PEs) with proteins is important for interpreting structure formation in biology, e.g., in nucleosomes, (1−3) intracellular condensates, (4) and the brain, (5,6) as well as elucidating different biological processes including viral infections or inhibitions. (7−9) The cell entry of many viruses is mediated by the interaction of anionic heparan sulfate proteoglycans (HSPGs) present on the extracellular matrix of the host cell with positively charged viral surface glycoproteins. (10) Due to this nonspecific electrostatic attraction, the concentration of virions at the cell surface is increased, making it more likely for them to bind to the host cell receptor proteins, which often includes multivalent interactions (11) and eventually leads to viral invasion. (12) This mechanism has been observed for different viruses such as Hepatitis B and C, herpes simplex virus, etc. (10) and more recently for the SARS-CoV-2 virus, responsible for the COVID-19 pandemic. (13,14) In the case of SARS-CoV-2, a cationic patch present on the spike protein receptor binding domain (RBD) binds to HSPGs, (15) which makes it more feasible for the RBD to specifically interact with the host cell receptor, the angiotensin-converting enzyme 2 (ACE2). (16)

The study of PE–protein interaction is also of major importance for the development of new drugs. Heparin, a naturally occurring anionic PE for which the chemical structure is shown in Figure 1a has been the subject of intense research in the last few decades due to its ability to adsorb at positively charged surfaces and thereby modulate biological processes. (17−19)

Figure 1. Simulation details. Chemical structures of (a) heparin and (b) linear polyglycerol sulfate (LPGS). (c) Structure of the spike protein trimer in the secondary structure representation (PDB ID: 7DK3). (32) Monomers are shown in purple, cyan, and yellow. The receptor binding domain (RBD) of one monomer (cyan) is present in the up conformation and is shown in red. (d) Zoomed-in view of the RBD. (e) Simulation unit cell (blue box) for equilibrium adsorption of a polymer to the RBD (red). An LPGS undecamer is shown in the space-filling representation with color coding for the different atom types: hydrogen in white, carbon in cyan, oxygen in red, and sulfur in yellow. Water and ions are present but not shown for clarity. The x, y, and z axes are indicated with red, green, and blue arrows, respectively. (f) Simulation snapshot after 1000 ns of equilibration representing adsorption of the LPGS (shown in orange) to the Delta-variant RBD surface (shown in gray). Protein cationic residues are pointed out in blue, whereas mutated residues R452 and L478 are in red. (g) Dynamic pulling simulation protocol in which a spring connected to one of the terminal atoms of the polymer is pulled away from the protein surface with a constant velocity ν along the z-axis. The spring is free to move along the lateral direction. (h) Static pulling simulation protocol in which one of the terminal atoms of the polymer is allowed to freely move in a plane at constant z-separation (distance projected along the normal to the plane) from the protein center-of-mass (red circle).

More recently it has been used to treat patients with SARS CoV-2 infections. (15,16,20,21) By binding to the cationic patch of the RBD, heparin can compete with HSPGs and block the first step of the cell-entry process. However, heparin-based drugs come with anticoagulatory side effects, which can be a disadvantage for the treatment of specific diseases. (20,22) Therefore, there is great interest in developing heparin analogs that share the same characteristic for adsorbing to cationic surfaces but with fewer side effects. Linear polyglycerol sulfate (LPGS), the chemical structure of which is shown in Figure 1b, has recently been tested to show excellent inhibitory activity against SARS-CoV-2, with significantly reduced cytotoxicity. (15) LPGS, compared to heparin, shows larger binding affinities to the RBD of wild-type SARS-CoV-2 and its different variants, (15,23) though having a lower linear charge density than heparin, details are provided in Figure S4 in the Supporting Information.

Computational methods developed in the last few decades have been quite successful in predicting binding poses and binding free-energies of small-molecule drugs with proteins. (24−28) However, quantitative prediction of polymer–protein binding thermodynamics remains challenging because of the limited length scales and time scales accessible by atomistic simulations using present-day computational power. (29,30) Specifically, PE-based viral inhibitors tested in experiments typically are 100–1000mers long with molecular weights of 10–100 kDa (15,31) and the binding–unbinding equilibrium relaxation time for interactions between a charged monomeric unit and an oppositely charged protein residue can be a few microseconds.

In this article, we combine advanced sampling techniques and theoretical modeling to investigate the interaction of LPGS and heparin with the SARS-CoV-2 spike protein RBD using explicit solvent all-atom molecular dynamics (MD) simulations. Adapting a simulation setup that mimics atomic force microscopy experiments, (33,34) we determine the PE–protein adsorption free energy from measuring the force to pull one terminus of the adsorbed PE away from the protein surface. By pulling this way, the intermolecular contacts are broken sequentially, overcoming a small free-energy barrier for each breakage, which leads to rather fast equilibration. The adsorption free energy thus obtained is compared with that computed using umbrella sampling simulations for validation. To obtain the standard binding free-energy of PEs, we add two correction terms: the PE stretching free energy due to the applied force and an entropic term accounting for its binding volume. For comparing the simulation results with experiments where longer PEs have been considered, we add the polymer translational entropy contribution in the bound state, which scales logarithmically in the degree of polymerization N, and find good agreement for the interaction of LPGS with the wild-type RBD compared with recent experimental measurements. (15,35) Moreover, we decompose the free energy into enthalpic and entropic contributions arising from solute–solute and solute–solvent interactions and determine the PE–protein relative friction in the bound state, for a deeper understanding of the PE–protein binding thermodynamics and relaxation dynamics.

Results and Discussion

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Due to the large size of the trimeric SARS-CoV-2 spike protein, we consider in simulations only one monomer’s RBD (Figure 1c,d). The RBD binds to not only the HSPGs on the cell surfaces but also to the cell receptor protein ACE2. Thus, it plays a central role in the cell entry process of the virion and constitutes a suitable target for new drugs. Moreover, dissociation constants for PEs binding to a monomeric RBD have been reported from microscale thermophoresis experiments, (15,35) making a meaningful comparison with the simulations possible. It should be noted that in vivo, there are glycans attached to the RBD, (36,37) but far away from the cationic patch (the putative sulfate binding sites on the RBD), (15,23) and hence these are not expected to affect the binding of anionic PEs to the RBD. We test this in a simulation (see Methods section for details) by attaching a glycan on top of the cationic patch and find LPGS to readily bind to the RBD, as shown in Figure S5 in the Supporting Information. This demonstrates that the entropic cost of replacing surface glycans is small compared to other interactions. Thus, we have excluded any glycan in our simulations for the results presented in the main text.

We perform simulations of LPGS interacting with both the wild-type RBD and the Delta-variant RBD with L452R and T478 K mutations. We take an LPGS undecamer in the simulations, much shorter than that used in experiments, to ensure fast equilibration. Additionally, we conduct simulations of a heparin pentamer interaction with the wild-type RBD, for which we observe a very long equilibration time, as will be discussed in Figure 6b,d. Therefore, we primarily focus in this study on simulation results involving LPGS binding and their quantitative comparison with experiments.

We start with unrestrained simulations (the setup shown in Figure 1e), where a polymer can move freely in the simulation box and interact with the protein surface. We observe that LPGS binds to the cationic patch of both the wild-type and Delta-variant RBD (shown in Figure 1f in blue). To validate that the adsorption to the cationic patch corresponds to the optimal binding position and is not an artifact of the starting position, we conduct six independent simulations, where we place LPGS at different starting positions as shown in Figure S6a in the Supporting Information. We find that within 400 ns LPGS binds to the same cationic patch in all six simulations, as shown in Figures S6b and S7 in the Supporting Information. Moreover, we calculate pairwise root-mean-square deviations (see eq 10 for the definition) of the RBD-bound LPGS conformations sampled in the different simulations and find significant overlaps among the corresponding distributions as shown in Figure S8. Therefore, the observed binding conformations are expected to be the minimum free-energy configurations and are suitable as starting structures for subsequent pulling simulations.

Polymer Desorption Free Energy

To obtain the LPGS desorption free-energy profile as a function of the reaction coordinate ξ, defined as the distance of the pulled polymer terminus from the protein surface (see Figure 1h), we use three different sampling techniques: dynamic pulling, static pulling, and umbrella sampling (see simulation details in Methods section). In the dynamic pulling simulations, a harmonic spring attached to one of the polymer’s terminal atoms is moved away from the protein surface along ξ at speed ν (see Figure 1g) and the force f acting on the spring is measured. Starting with the system configuration of LPGS adsorbed to the wild-type RBD, simulations are conducted with six different speeds ranging ν = 0.006 to 1.2 m/s. To make sampling comparable for different ν, we perform multiple simulations such that a total simulation time of at least 1 μs is reached for each ν. Mean desorption force profiles f(ξ) for different ν are shown in Figure 2a. We find that the most distinct force peaks are situated at ξ in the range of 2–4 nm and the desorption forces are higher for faster pulling speeds. The latter observation can be rationalized by friction effects originating from the force-induced breaking of hydrogen bonds and salt bridges. (38−40) Free energy profiles F(ξ), obtained by integrating over the force profile as

F (ξ) = \int_{0}^{ξ} f (ξ^{'}) d ξ^{'}

(1)

are shown for different pulling speeds in Figure 2b. We find that apart from the higher free energy values for faster ν, the profiles for higher ν (= 1.2 and 0.6 m/s) do not reach plateau values, even after the complete desorption of the polymer. This shows that simulations are far from equilibrium for higher ν. As the friction contribution to the desorption force f in the viscous (i.e., low-velocity) regime is linear in v, the free-energy difference between the desorbed and adsorbed state, ΔF = F(ξ → ∞), increases linearly with ν according to ΔF(ν) = ΔF(ν = 0) + γνL₀, where L₀ = 4.03 nm (see Methods section) is the unstretched contour length of the polymer. (38) We use this linear relationship to determine the equilibrium free energy of polymer desorption, ΔF(ν = 0), and the friction coefficient γ. Linear regression, using ΔF data for only the three lowest ν, leads to an excellent fit (Figure 2c), resulting in ΔF(ν = 0) = 9.7 ± 1.6 k_BT and γ = 4.05 × 10^–10 Ns/m (for results from fitting the whole data set, see Figure S9 in the Supporting Information). This is equivalent to a diffusion constant of D = k_BT/γ = 10.23 nm²/μs, from which we obtain the diffusion time τ_D = L₀²/2D = 0.8 μs. We see that the bound polymer diffuses over its contour length in about a microsecond, allowing for rather quick equilibration of the bound state.

Figure 2. Simulation results for the desorption of an LPGS undecamer from the wild-type (WT) and, only if mentioned, Delta-variant RBD surface. (a) Force f and (b) free energy F profiles from dynamic pulling simulations, results for only four out of the six pulling velocities are displayed for visual clarity. Error bars are displayed as shaded colored areas in panel b. (c) Free-energy difference ΔF between the desorbed and adsorbed states as a function of the pulling velocity ν. The equilibrium free-energy difference ΔF (ν = 0) is obtained from linear extrapolation of the data for the three slowest pulling rates to zero velocity. (d) Force and (e) free-energy profiles from static pulling simulations. (f) Comparison of free energy profiles obtained from umbrella sampling and static pulling simulations with the dynamic pulling simulation result using the slowest pulling velocity ν = 0.006 m/s.

For the static pulling simulations, we select initial configurations from the dynamic pulling simulation at nine different ξ values with a spacing of 0.4 nm. At each ξ value, the polymer terminal atom is allowed only to freely move on a plane, maintaining a constant z-separation (distance projected along the normal to the plane) from the protein surface, see Figure 1h. The average force needed to keep the LPGS terminal atom at different ξ values is shown in Figure 2d for the wild-type and Delta-variant RBD. Compared to dynamic pulling results shown in Figure 2a, the peak force here is significantly lower. Also, the ξ value corresponding to the complete desorption of the polymer, represented by the force dropping to zero, is smaller than that observed in the dynamic pulling simulations. This is because the polymer is stretched more due to the larger pulling forces in the latter case. These deviations illustrate that even for the slowest pulling rate, the dynamic pulling simulation is far from equilibrium. Moreover, it is observed that forces for the Delta variant are significantly higher than the wild-type RBD at ξ = 0.8 nm. To understand this, we investigate the interaction of LPGS with individual protein residues as shown in Figure S10 in the Supporting Information, noting that conformational dynamics of wild-type and Delta-variant RBDs, whether free in solution or bound to LPGS, are very similar (see Figure S11 in the Supporting Information). For both RBD types, we find that LPGS forms a higher number of contacts with cationic residues such as R346 and R466. For the Delta variant, there is however an extra charged residue on the cationic patch (R452), which makes additional, electrostatically favorable contacts with LPGS simultaneously possible (Figure S10d in the Supporting Information), giving rise to the increased force. Free energy profiles show that the complete desorption of LPGS from the Delta-variant RBD, compared to the wild-type, requires an extra free energy of 2 k_BT (Figure 2e). This demonstrates that cationic mutations in proteins lead to an increase in their binding affinities to anionic polymers, which supports the hypothesis of Nie et al. (23) that the increased infectivities of Delta and Omicron variants are caused by additional cationic residues of the RBD that interact strongly with cellular HSPGs.

We also calculate the free energy profile of LPGS desorption from the wild-type RBD using umbrella sampling simulations with the weighted histogram analysis method (for details, see Methods section). (41,42) Free energy profiles F(ξ) obtained from all three methods are compared in Figure 2f. F(ξ) from the dynamic pulling simulation using even the slowest pulling velocity, ν = 0.006 m/s, deviates significantly from the other two methods, while the extrapolated free-energy difference ΔF(ν = 0) to zero velocity exhibits less deviation from the umbrella sampling result, ΔF = 5.8 ± 0.5 k_BT, and the static pulling result, ΔF = 5.6 ± 0.6 k_BT.

Dissociation Constant and Standard Binding Free Energy

The dissociation constant K_D for a complexation reaction between protein P and polymeric ligand L,

P + L ⇌ PL

determines the ratio of concentrations of free, [P], [L], and bound, [PL], species in solution and is related to the free-energy change upon binding, ΔF_b, and the ligand-binding volume V_b according to (43)

K_{D} = \frac{[P] [L]}{[P L]} = \frac{1}{V_{b}} e^{Δ F_{b} / k_{B} T} = \frac{1}{V_{0}} e^{Δ F_{b}^{0} / k_{B} T}

(2)

Here, V_b represents the limited volume available for the polymer to move in the protein-bound state (for the procedure to obtain V_b from simulations, see the Supporting Information text and Figures S2 and S3). V₀ = 1.661 nm³ is the standard-state volume corresponding to the concentration of 1 M and the standard free-energy of binding is given by ΔF_b⁰ = ΔF_b – k_BT ln (V_b/ V₀). ΔF_b is obtained from the polymer desorption free-energy ΔF by removing the polymer stretching free-energy due to the applied force, resulting in

Δ F_{b} = - Δ F - Δ F_{stretch}

(3)

ΔF_stretch, in eq 3, describes the change in free energy to stretch the polymer from its relaxed state and is not present in the experiments and hence its contribution is subtracted from the simulated free energy. ΔF_stretch is obtained from constant-force stretching simulations of the polymer in free solution (details given in Methods section), by measuring the average end-to-end distances, z_ete, projected along the direction of external force at different stretching forces, f_stretch, applied to each end of the polymer. We fit the force–extension relation of the inhomogeneous partially freely rotating chain (iPFRC) model (44) (for details, see Methods section) to the simulation values and find an excellent fitting as shown in Figure 3a. By integrating the force–extension relation from the relaxed end-to-end distance z_ete⁰ = 0 to a stretched end-to-end distance z_ete^stretch,

Δ F_{stretch} = \int_{z_{ete}^{0}}^{z_{ete}^{stretch}} f_{stretch} (z_{ete}) d z_{ete}

(4)

we obtain the stretching free energy profile as a function of f_stretch, shown in Figure 3b. To obtain ΔF_stretch, we compute the average force experienced by a strained LPGS bound to the RBD (see the force plateau in Figure 2d from 1.2 to 2.4 nm) and take the stretching free energy at the average forces of f_stretch = 11.7 pN and 13.5 pN for the wild-type and Delta RBD, respectively (see Figure 3b, green points). Note that the resulting polymer stretching free-energy contribution, ΔF_stretch ≃ 2–2.5 k_BT, is sizable.

Figure 3. (a) Stretching force f_stretch versus the average end-to-end distance z_ete of an LPGS undecamer along the direction of applied force. Data points are fitted to the iPFRC model force–extension relation eq 8. (b) Stretching free-energy profile F_stretch as a function of f_stretch, obtained by integrating the fitted curve in panel a.

Finally, the standard binding free-energy ΔF_b⁰ as a function of the degree of polymerization, N, for longer polymers used in the experiments, (15,35) compared to the simulations, N > N_sim, can be extrapolated from simulations data as (for a derivation, see Section S1 in the Supporting Information)

Δ F_{b}^{0} (N) = - Δ F (N_{sim}) - Δ F_{stretch} (N_{sim}) - k_{B} T \ln (\frac{V_{b} (N_{sim})}{V_{0}}) - k_{B} T \ln (\frac{N}{N_{sim}})

(5)

Here, the last term represents the avidity entropy contribution, −TΔS_avidity, to the binding, as explained in the following. (31,45,46) The direct polymer–protein interaction energy contribution to the binding free energy is limited to the number of binding sites n_b ≃ 5 on the protein, estimated to be the number of charged residues on the cationic patch of the RBD. Thus, LPGS longer than a critical length, equivalent to the size of the cationic patch, do not contribute to this direct interaction. There is, however, a combinatorial entropy contribution for a longer polymer with N > n_b, because of the different ways the polymer can bind to the protein, given by S_avidity = k_B ln (N – n_b + 1). As this entropy contribution, S_avidity^sim = k_B ln (N_sim – n_b + 1), is already accounted for in our simulations, we obtain in the limit of N > N_sim ≫ n_b, ΔS_avidity = k_B ln (N/N_sim).

For the binding of the simulated LPGS undecamer to the wild-type and Delta-variant RBD, values of ΔF_b⁰ (N_sim) = −ΔF – ΔF_stretch – k_BT ln (V_b/V₀), noting that the avidity entropy term in eq 5 vanishes for N = N_sim, and its different contributions are provided in Table 1 based on the static pulling results. The LPGS undecamer binds to the Delta RBD more strongly than the wild-type with an additional free-energy gain of around 2.4 k_BT, as expected from the favorable electrostatic interaction discussed before.

Table 1. Values for the Standard Free-Energy of Binding ΔF_b⁰ of an LPGS undecamer, N_sim = 11, to the Wild-Type and Delta-Variant RBD Based on the Static Pulling Simulation Results, Along with the Contributions in eq 5 to Calculate ΔF_b⁰

contributions	WT	Delta
ΔF	5.59 ± 0.63 k_BT	7.46 ± 1.17 k_BT
ΔF_stretch	2.06 ± 0.29 k_BT	2.51 ± 0.41 k_BT
V_b	11.32 ± 2.02 nm³	11.89 ± 4.91 nm³
k_BT ln (V_b/ V₀)	1.92 ± 0.11 k_BT	1.97 ± 0.25 k_BT
ΔF_b⁰	–9.57 ± 0.72 k_BT	–11.94 ± 1.30 k_BT

The standard binding free energy ΔF_b⁰ and dissociation constant K_D for different polymer lengths predicted according to eqs 5 and 2 match nicely with the corresponding experimental values, as shown in Figure 4 and Table 2. The theoretical and experimental ΔF_b⁰ values differ only within 1 k_BT (the thermal energy), consequently K_D differ by a factor of roughly two.

Figure 4. Theoretical prediction for (a) the standard binding free-energy ΔF_b⁰ and (b) dissociation constant K_D for the complexation reaction of the wild-type RBD and LPGS as a function of its degree of polymerization N. Experimental values are reproduced from publications by Nie et al. (15) (Available under a CC BY-NC 4.0 license. Copyright 2021 The Authors.) and Page et al. (35) (Available under a CC BY-NC 4.0 license. Copyright 2023 The Authors.). Shaded regions in panels a and b represent simulation errors of propagation coming from the first three terms in eq 5 and from ΔF_b⁰, respectively.

Table 2. Comparison of ΔF_b⁰ and K_D Values from Experiments and Theoretical Predictions for the Wild-Type RBD and LPGS Binding for Different Experimental Degrees of Polymerization N_exp^a

N_exp	ΔF_b⁰ (exp.)^b	ΔF_b⁰ (theory)^b	K_D (exp.)^c	K_D (theory)^c
110 (Page et al.)	–11.11 ± 0.37	–11.87 ± 0.72	15.0 ± 5.5	7.0 ± 5.0
274 (Nie et al.)	–12.17 ± 0.69	–12.78 ± 0.72	5.2 ± 3.6	2.8 ± 2.0

^{^a}

Experimental values are reproduced from publications by Nie et al., ref. (15) (Available under a CC BY-NC 4.0 license. Copyright 2021 The Authors.) and Page et al., ref. (35) (Available under a CC BY-NC 4.0 license. Copyright 2023 The Authors).

^{^b}

Standard binding free-energy, ΔF_b⁰ in k_BT.

^{^c}

Dissociation constant, K_D in μM.

Enthalpy–Entropy Decomposition

To understand the underlying contributions to the binding free energy ΔF_b = ΔU_b – TΔS_b, we decompose it into its enthalpic ΔU_b and entropic TΔS_b parts, see Figure 5a,b. From the simulation trajectories (see Methods section), we calculate the net change in interaction energy, ΔU_b = ΔU_PP + ΔU_PL + ΔU_PW + ΔU_LL + ΔU_LW + ΔU_WW, for the transition of the polymer from the desorbed to the adsorbed state from interactions among different components of the system: protein P, polymeric ligand L, and solvent (water molecules and ions) W. In the polymer adsorption process, we find favorable intersolute direct interaction (ΔU_PL < 0) and solvent reorganization energy (ΔU_WW < 0) and unfavorable solute–solvent interactions (ΔU_PW > 0 and ΔU_LW > 0). ΔU_b is quite small compared to the different contributions. Thus, there are huge cancellations among the different interaction energy contributions, as seen for other receptor–ligand systems, (33) calling for highly accurate calculations of the solvent contribution. (47)

Figure 5. (a) Snapshots from the static pulling simulations for the desorbed state (at the pulling distance ξ = 3.6 nm) and the adsorbed state (ξ = 0 nm). (b) Enthalpic, ΔU_b, and entropic, TΔS_b, contributions to the binding free-energy ΔF_b of the wild-type RBD–LPGS complex, along with the different internal energy contributions to ΔU_b (see text). The average number of (c) water molecules and (d) ions, Na⁺ and Cl^–, bound to the RBD or LPGS as a function of ξ.

We obtain the entropy contribution to the binding using the thermodynamic relation ΔS_b = (ΔU_b – ΔF_b)/T. By observing that ΔU_b < TΔS_b < 0, we conclude that the adsorption process is entropically unfavorable and enthalpy driven. In the adsorption process, we find that 50–60 water molecules and only one ion are released as shown in Figure 5c,d (for the definition of bound water and ions, see Methods section). Thus, water release is expected to contribute significantly to the entropy as gain, while the contribution due to counterion release is minimal. The latter is not surprising though, as the linear charge density of LPGS is just above the counterion condensation limit by Manning, (48) the length of the simulated LPGS is short, thus leading to end effects, (49) and the simulated salt concentration of 150 mM is high. (50) However, the net change in the binding entropy is negative (Figure 5b), which has to arise from the restricted conformational, translational, and rotational degrees of freedom of the polymer and protein in the bound state, overcompensating the entropy gain due to water and ion release. (50−53) As the release of a single water molecule from a typical protein surface leads to an entropy gain of ∼1 k_BT, (54) the entropic loss due to conformational transformations of the protein and polymer is suggested to be greater than 60 k_BT.

Relaxation Time for Binding of Charged Groups

The validity of the binding free energy obtained from the static pulling simulations depends on whether the binding–unbinding equilibrium for interactions between the charged groups of the protein and polymer has been reached within the simulation time. The time-series data shows that anionic sulfate groups of LPGS bind intermittently to various cationic residues of the RBD (see Figure 6a). To quantify the time required to attain binding–unbinding equilibrium, we calculate the intermittent survival probability (SP) defined as (55)

SP (t) = {⟨ \frac{\sum_{ij} s_{ij} (t^{'}) s_{ij} (t^{'} + t)}{\sum_{ij} s_{ij} (t^{'})} ⟩}_{t'}

(6)

where

s_{ij} (t) = {\begin{array}{l} 0 & if N_{C}^{ij} (t) = 0 \\ 1 & if N_{C}^{ij} (t) > 0, \end{array}

(7)

with N_C^ij(t) being the number of close contacts (defined by an interatomic distance cutoff of 3.5 Å) between a polymer charge group i and a protein residue j at time t. SP(t) represents the probability of finding a polymer group that is bound to a protein residue at time t′ to be bound to the same residue at time t′ + t and is shown for LPGS interactions with the wild-type and Delta-variant RBD in Figures 6c and S12, respectively. The relaxation time τ refers to the largest time scale involved and is obtained by fitting a biexponential function (= ae^–t/τ₀ + be^–t/τ + c) to the SP data. τ values for LPGS bound to the wild-type and Delta-variant RBD are similar, around 250 ns, which is an order of magnitude smaller than the total simulation time of 5 μs at each ξ, ensuring sufficient sampling. Moreover, we check the convergence of the free-energy profile F(ξ) by splitting the simulation into five blocks, each of duration 1 μs, and calculating F(ξ) for each block, for LPGS binding to the wild-type or Delta-variant RBD (see Figure S13 in the Supporting Information).

Figure 6. Time series for the binding of (a) LPGS’s and (b) heparin’s anionic groups (highlighted in red in Figure 1a,b) to cationic residues of the wild-type RBD that exhibit a significant number of close contacts with the polymers. Binding for LPGS (heparin) to the residues R346 (R346), K444 (R356) and R466 (R357) are visualized in red, green, and orange, respectively. The survival probability (defined in eq 6), averaging over all binding–unbinding time series data, is shown for (c) LPGS and (d) heparin. The dashed line in panel c or d represents the double exponential fit to the data, with the value of the largest decay time τ provided in the legend.

For heparin, the time-series data in Figure 6b shows that charged groups of heparin stay bound to a single protein residue for almost the whole simulation time. From the SP function in Figure 6d we estimate a relaxation time of 7.1 μs, which suggests that an order of magnitude-longer simulation (∼50 μs) would be required to achieve heparin binding–unbinding equilibrium. The significantly slower relaxation dynamics of heparin bound to the RBD surface, despite having a lower binding affinity than LPGS in experiments, is reflected by the slower conformational dynamics of heparin free in solution (see Figure S14 in the Supporting Information). Besides, heparin is significantly stiffer than LPGS and has a persistence length of about 1.4 nm that is roughly three times longer than the one of LPGS, as we have shown in our recent paper. (15) Thus, any reconfiguration of a protein-bound conformation of heparin involves large-scale rigid body rotations compared to the small-scale bending available to LPGS, which additionally is expected to slow down the relaxation of the RBD-bound heparin. Furthermore, to study the binding mechanism of heparin to the RBD we calculate contact maps of sulfate, carboxyl, and hydroxyl groups with the RBD residues. We find that heparin primarily interacts with the same set of cationic residues of the RBD, as the sulfates of LPGS, as shown in Figure S15a–d in the Supporting Information. Carboxyl groups form a greater number of close contacts with the RBD, primarily to its cationic residues, as shown in Figure S15e, whereas hydroxyl groups form hydrogen bonds with both cationic and polar residues, as shown in Figure S15f.

Protein Conformational Transitions

When LPGS is present near the wild-type RBD surface, we observe transitions between different protein conformations, which adds further complexity to the quantitative prediction of the binding thermodynamics. The RBD has a loop region (residues 470–490) that exhibits higher root-mean-square positional fluctuations (see eq 11 for the definition) and is highly flexible (see Figure 7a). Due to this, the loop region can switch between multiple states and thus modify the overall protein structure significantly, as seen from the time-series plot of the distance between the center-of-mass of the loop region and the remaining part of the protein in Figure 7b. From the autocorrelation function (defined in eq 12) of this center-of-mass distance, we find for the RBD conformational dynamics a relaxation time of 590 ns as shown in Figure 7c (for further details, see Methods section). As our simulation time is an order of magnitude larger than the relaxation time, sufficient sampling of different protein configurations is ensured. However, the error in the desorption force for the Delta-variant RBD is large (see Figure 2d, e.g., at ξ = 0.4 nm) since the bound polymer attracts the flexible loop of the protein toward it (see snapshots in Figure S16 in the Supporting Information).

Figure 7. Conformational fluctuations of the wild-type RBD and dynamics of its loop region (residues 470 to 490) from the static simulation at ξ = 1.6 nm. (a) Root-mean-square fluctuation (RMSF) of the protein backbone atoms for different residues. The shaded region represents residues corresponding to the RBD’s loop region. (b) Time series of the distance between the center-of-mass of the loop region and the remaining part of the RBD. Snapshots for two different states at the start and after 2700 ns of the simulation are displayed above. The RBD surface is shown in gray except for its loop region in red, whereas LPGS is shown in the ball–stick representation in orange. (c) The center-of-mass distance autocorrelation function. The dashed line represents a double exponential fit to the data, with the value of the largest decay time τ given in the legend.

Due to these protein structural transitions, also the error in the hydration number is large (Figure 5c, e.g., at ξ = 2.8 nm). Because the loop region occasionally adsorbs on the protein surface itself, multiple water molecules are released during this process (see Figure S17 in the Supporting Information). This accounts for large fluctuations in the number of bound water within a single simulation window, making a quantitative estimate of the entropic contribution due to water release difficult. Note that as the loop region is part of the receptor binding motif that forms direct contact with the host cell receptor protein ACE2, its flexibility might help in adapting the viral spike protein structure for binding to other cell receptors and thus improve viral infectivity.

Conclusions

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We demonstrate a method to obtain the binding free energy of long polymers (10–100 kDa) typically considered in experiments, from the simulated free-energy profile of shorter polymer desorption from a protein. This requires correctly accounting for (i) the binding volume of the polymer, (ii) the polymer stretching free energy, and (iii) the avidity entropy due to the different possible ways the polymer can bind to the protein (cf. eq 5). We validate our method by favorable comparison with the experimental free-energy of binding between LPGS and the wild-type SARS-CoV-2 spike protein RBD and reproducing accurately the polymer-length dependence. We find that anionic LPGS binds more strongly to the Delta-variant RBD (with extra 2 mutated cationic residues) than the wild-type RBD, underlining the role of electrostatic interactions. The LPGS–RBD binding at T = 300 K is found to be enthalpy driven with a large enthalpy–entropy compensation. Decomposing the enthalpy of binding, we find significant cancellation between the polymer–protein, the solute–solvent, and the solvent–solvent interaction energy contributions. These observations signify the importance of solvent and entropic effects in molecular binding. (33,54,56)

We identify a highly flexible loop region of the RBD, which transitions between different states with a relaxation time of 600 ns. Thus, slow protein conformation transitions can add complications in predicting the binding thermodynamics accurately. Moreover, we show that modeling the adsorption of a highly charged polymer, e.g., the drug heparin to RBD, requires a high computational effort as the relaxation time for the charged-group binding equilibrium is ∼7 μs.

Comparing three different simulation protocols (see additional discussion in Section S2 in the Supporting Information) for obtaining the polymer adsorption free-energy difference, we find that the extrapolation method using the dynamic pulling data, as shown in Figure 2, gives larger values than umbrella sampling and static pulling results. This hints at the relevance of dissipative chain reconfiguration effects when pulling a polymer from an absorbing surface, as is relevant in force spectroscopy experiments (57) and biological nonequilibrium scenarios. Thus, the dynamic pulling method is not only useful in generating initial configurations for the static pulling method but also for understanding friction and diffusion in the bound protein–polymer complex, which is important for the kinetics of the binding process.

We have developed a theoretical method to predict the dissociation constant for a multivalent linear polymer binding to a monovalent receptor, i.e., a single RBD in solution, mimicking recent experiments where the binding of polymers to monomeric RBDs in solution was studied. (15,35) A long polymer, however, can simultaneously bind to three RBDs (either in the up or down configuration) of a single trimeric spike protein or can bridge between multiple trivalent spike-protein receptors on the virion. Predicting multivalent dissociation constants in these two scenarios is possible with our recently developed multiscale modeling approach, (11,58) for which the monovalent dissociation constant calculated in this paper is the essential input parameter.

Methods

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MD Simulations

Models, Parameters, and Simulation Set-Up

The coordinates for the wild-type RBD of the SARS-CoV-2 spike protein are obtained from the deposited crystal structure (PDB ID: 6M0J). (21) The Delta-variant RBD with L452R and T478 K mutations is built using PyMOL. The structure of the heparin pentamer is built using CHARMM-GUI Glycan Reader & Modeler. (59−62) The structure of the LPGS undecamer is built using Avogadro software. (63) CHARMM36m (64) and CHARMM Carbohydrates (65,66) force field parameters are used to model the protein and heparin, respectively. Parameters and partial atomic charges for LPGS are modeled with the CHARMM General force field (67,68) and obtained using the CGenFF program. (69,70) CHARMM-compatible TIP3P water (71,72) and ion parameters (73) are used. RBD/LPGS and RBD/heparin are arranged and solvated in boxes of sizes 7 × 7 × 9.5 and 7 × 7 × 10 nm³, respectively. Enough Na⁺ ions are added to charge neutralize each system, then Na⁺/Cl^– ion pairs are added to obtain a 150 mm NaCl solution estimated from the mole fraction of ion pairs and water.

Before starting pulling simulations, unconstrained simulations are performed for at least 1 μs in the NpT ensemble at T = 300 K and p = 1 bar with periodic boundary conditions in xyz directions, using the GROMACS 2020.6 package. (74) During the simulations, backbone atoms of three residues of the RBD are fixed to stop its center-of-mass translation and its rotation around the principal axes. The stochastic velocity rescaling thermostat (75) with a time constant of τ = 0.1 ps is used to control the temperature, while for the pressure control an isotropic Parrinello–Rahman barostat (76) is used with a time constant of τ = 2 ps and a compressibility of κ = 4.5 × 10^–5/bar. The LINCS algorithm (77) is used to constrain the bonds involving H-atoms, allowing a time step of Δt = 2 fs. Electrostatic interactions are computed using the particle mesh Ewald method (78) with a real-space cutoff distance of 1.2 nm, while van der Waals interactions are modeled using Lennard-Jones potentials with a cutoff distance of 1.2 nm where the resulting forces smoothly switch to zero between of 1 and 1.2 nm. A data saving frequency of 100 ps is used.

Glycan-Conjugated RBD

A glycan (chemical details in Figure S5a in the Supporting Information) conjugated to the residue N354 of the wild-type RBD is built using the CHARMM-GUI Glycan Reader & Modeler. (60−62) Parameters for the glycan are taken from the CHARMM Carbohydrates (65,66) force field.

Dynamic and Static Pulling Simulations

For performing pulling simulations, the z-distance between the center-of-mass of the protein and one terminal atom of the polymer is chosen as a reaction coordinate ξ, which is shifted such that ξ = 0 when the terminal atom is bound to the surface. Constant velocity pulling simulations (which we refer to as dynamic pulling) are conducted in the NVT ensemble. Here, a spring with spring constant k = 1660 pN/nm is attached to a terminal polymer atom and pulled with a constant velocity v, and the pulling force f is obtained from the extension of the spring from its equilibrium position. The used pulling speed v ranges from 0.006 to 1.2 m/s. To ensure that the whole polymer is desorbed from the protein surface, a simulation time in the range of 5 to 1000 ns is used so that at the end, a pulling distance of roughly 6 nm is reached. For each pulling speed, simulations are repeated until the combined simulation time reaches 1000 ns or more. The coordinates of the system are saved every 100 ps and pulling forces are recorded every 100 fs.

For the static simulations, the starting configurations are generated from multiple configurations from the dynamic pulling simulations with a 0.4 nm spacing of the reaction coordinate. The time for each static simulation window is set to 5 μs, summing up to a total simulation time of 45 μs. The free-energy profile from the static simulations is calculated by first computing the average force for each simulation window using the last 4.5 μs data and then integrating over the average force profile, see eq 1.

Umbrella Sampling Simulations

Taking configurations from the dynamic pulling simulations for the wild-type RBD–LPGS system, we have conducted 30 simulations for 100 ns each where umbrella or harmonic potentials are applied to restrain the system at different values of the reaction coordinate ξ (the same as defined before), from 0.1 to 3.0 nm with a window spacing of 0.1 nm. The same spring constant as in the dynamic pulling is used for each umbrella window. The weighted histogram analysis method, (41) implemented in the GROMACS module wham, (74) is used to obtain the free-energy landscape F(ξ) for LPGS desorption from the RBD surface, shown in Figure 2f. The first 20 ns data for each umbrella window is discarded in the calculation of F(ξ). The overlapping of histograms for consecutive umbrella windows needed for the accurate computation of F(ξ) and its convergence check by taking different lengths of the simulation data are shown in Figure S18 in the Supporting Information. Note that the simulation time for each umbrella window is shorter than the RBD loop relaxation time reported in Figure 7c. However, the good comparison with the free-energy profile obtained from the static pulling simulations, each of a much longer duration of 5 μs, demonstrates that the umbrella simulations are converged (see Figure 2f).

Constant-Force Stretching of LPGS

An LPGS undecamer, placed in a rectangular simulation box of size 5 × 5 × 9 nm³, charge-neutralized by adding counterions (Na⁺) and solvated with water in a 150 mM NaCl solution, is taken for the simulations. The simulation-related parameters coincide with the ones of the unconstrained RBD/LPGS simulation in the NpT ensemble except, that the GROMACS 2021.3 package (74) and ion parameters of Loche et al. (79) are used. Additionally, we have chosen a higher trajectory saving frequency of 10 ps. The equilibration process starts with employing the steepest descent algorithm for the initial energy minimization. This is followed by two stages of simulation: a 500 ps NVT simulation and a 2 ns NpT simulation, during which the polymer atom positions are restrained.

To determine the stretching free-energy ΔF_stretch of LPGS, we have performed in the NpT ensemble several production simulations in each of which a constant force between 1 and 1000 pN is applied to the polymer ends in opposite directions along the z-axis. The anchor points for the constant force are the first (C1) and last (C22) carbon atoms of the LPGS undecamer along its backbone, as depicted in Figure 8. The average extension ⟨z_ete⟩ for ten monomers, defined as the distance between the carbon atoms C1 and C21 in the pulling direction, is measured. This ensures the inclusion of all relevant monomers under strain. We have performed NpT production simulations for different durations from 200 ns (at higher forces) to 2000 ns (at lower forces), depending on the relaxation time of the ion distribution around the polymer and the polymer end-to-end distance at different applied forces. For data analysis, the initial part (20–50 ns depending on the applied force) of a production run is discarded for the equilibration which accounts for initial stretching or shortening of LPGS.

Figure 8. Stretching protocol showing the LPGS undecamer at an applied force f = 800 pN. Color coding for the different atom types: hydrogen in white, carbon in cyan, oxygen in red, and sulfur in yellow.

Simulation Data Analysis

Simulation data are visualized and analyzed with VMD (80) and the software package MDAnalysis, (81,82) respectively.

iPFRC Model and Stretching Free Energy of LPGS

The force f versus extension z_ete profile obtained from constant-force stretching of LPGS is depicted in Figure 3a (for the complete range of forces used in this study, the profile is shown in Figure S19 in the Supporting Information). To interpolate the data points, we use the heuristic force–extension relation of the iPFRC model (44)

f = \frac{k_{B} T z_{ete}}{L} (\frac{3}{a_{Kuhn}} + \frac{1}{c a_{0}} \frac{z_{ete} / L}{1 - z_{ete} / L})

(8)

Here, L is the contour length of the polymer, and a₀ is the equilibrium monomer length. The Kuhn length a_Kuhn is defined by the linear stretching response at low applied forces and c is a free parameter, whose choice accounts for restricted backbone dihedral rotation and side chain interactions. The iPFRC model has been shown to describe the force–extension relation of various polypeptides quite well, (83) when a force-dependent contour length L(f) is introduced additionally

L (f) = L_{0} (1 + \frac{\sqrt{γ_{1}^{2} + 4 γ_{2} f} - γ_{1}}{2 γ_{2}})

(9)

In eq 9, L₀ denotes the unstretched contour length of the polymer. The linear stretching modulus γ₁ and the nonlinear coefficient γ₂ describe the force-dependent extension of a monomer at zero temperature in vacuum. The variables a₀, a_Kuhn, c, γ₁, and γ₂ have been used as free fitting parameters and their values corresponding to the shown line in Figure 3a are reported in Table 3. The stretching free energy ΔF_stretch follows by integrating the fitted force–extension curve eq 4 and is shown in Figure 3b. The choice of setting the lower bound of the integral in eq 4 to zero is grounded on the premise that, in the absence of an applied force, the expected value of the average extension is zero.

Table 3. Fitting Parameters of the iPFRC Model

parameter	value
a₀	366.82 ± 0.67 pm
a_Kuhn	0.873 ± 0.033 nm
c	0.793 ± 0.018
γ₁	96 ± 36 nN
γ₂	500 ± 2000 nN

Internal Energy Decomposition

Interaction energy calculations are done using the GROMACS module energy. (74) The average energy is calculated for the adsorbed state, ξ = 0 nm, and the desorbed state, ξ = 3.6 nm, for interactions between different components of the system: protein, polymer, and solvent (water and ions), and the energy differences are computed. Only the short-range part of the Coulomb interaction with a cutoff distance 1.2 nm is included in these calculations, as the full, long-range electrostatic energy of a subsystem with a nonzero net charge with periodic boundary conditions diverges. However, calculation of the net change in interaction energy, ΔU_b, for the whole system includes also the long-range electrostatic contribution. Simulation data of 2.5 μs (25,000 frames) and 5 μs (50,000 frames) are used for calculating the interaction energies for adsorbed and desorbed states, respectively.

Distance Criteria for Close Contacts and Bound Water and Ions

For calculating the number of close contacts, we define a contact by an atom of LPGS falling within 3.5 Å of any atom of a protein residue. The same cutoff distance (of 3.5 Å) criterion is used to calculate the protein-bound water molecules and ions.

Root-Mean-Square Deviation

The root-mean-square deviation (RMSD) of a molecular conformation is calculated using the GROMACS module rmsd (74) and is defined as

RMSD (t) = \sqrt{\frac{1}{N} \sum_{i = 1}^{N} {(r_{j} (t) - r_{j}^{ref})}^{2}}

(10)

where N is the total number of atoms, r_j(t) is the position of atom j at time t, and r_j^ref is the position the same atom in the reference state.

Root-Mean-Square Fluctuation of the RBD Structure

The root-mean-square fluctuation (RMSF) of the backbone atom positions for each RBD residue is calculated using the GROMACS module rmsf (74) and is defined as

RMSF (i) = \sqrt{\frac{1}{N_{t}} \sum_{t = 1}^{N_{t}} {(r_{i} (t) - r_{i}^{ref})}^{2}}

(11)

where N_t is the total number of frames in a trajectory, r_i(t) is the position of residue i at time t, and r_i^ref is the position the same residue in the reference state (the native state of RBD).

Relaxation Time for the RBD’s Loop Region Movement

The movement of the flexible loop region (residues 470–490) of the RBD is tracked by calculating the center-of-mass (COM) distance between the loop region and the rest of the protein. To get an estimate of the relaxation time, we calculate the COM distance autocorrelation function C(t) defined as

C (t) = \frac{{⟨ (A (t^{'}) - \bar{A}) (A (t^{'} + t) - \bar{A}) ⟩}_{t'}}{{⟨ {(A (t^{'}) - \bar{A})}^{2} ⟩}_{t'}}

(12)

where A(t′) is an observable at an initial time t′, A is the time average of observable A, ⟨·⟩_t′ represents the time-origin averaging. The relaxation time is estimated by fitting a biexponential function (= ae^–t/τ₀ + be^–t/τ) to the COM distance autocorrelation C(t) and refers to the longest time scale involved τ.

Error Estimations

Errors for the static pulling, the average extension of LPGS, internal energy calculations, and the number of protein-bound water molecules and ions are estimated by using the block averaging method by Flyvbjerg and Petersen. (84) The number of blocks is changed until the standard error of the different blocks converges to a constant value. In case the standard error does not converge, the maximum standard error is used as an error estimate. For the dynamic pulling, the error is estimated by calculating the standard error of ΔF for each pulling rate.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacsau.4c00886.

Derivation of the standard free-energy of binding from a polymer desorption free-energy profile; additional figures (PDF)

au4c00886_si_001.pdf (7.76 MB)

Terms & Conditions

Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.

Author Information

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Corresponding Authors
- Roland R. Netz - Department of Physics, Freie Universität Berlin, Arnimallee 14, Berlin 14195, Germany; https://orcid.org/0000-0003-0147-0162; Email: [email protected]
- Anil Kumar Sahoo - Department of Physics, Freie Universität Berlin, Arnimallee 14, Berlin 14195, Germany; https://orcid.org/0000-0001-7769-4774; Email: [email protected]
Authors
- Lenard Neander - Department of Physics, Freie Universität Berlin, Arnimallee 14, Berlin 14195, Germany; Institute of Chemistry and Biochemistry, Freie Universität Berlin, Takustraße 3, Berlin 14195, Germany
- Cedric Hannemann - Department of Physics, Freie Universität Berlin, Arnimallee 14, Berlin 14195, Germany; https://orcid.org/0009-0005-2467-168X
Author Contributions
A.K.S. and R.R.N.: Designed research. L.N., C.H., and A.K.S.: Performed research. L.N., C.H., and A.K.S.: Analyzed data. A.K.S. and R.R.N.: Wrote the paper with inputs from all authors.
Notes
The authors declare no competing financial interest.

Acknowledgments

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We acknowledge support provided by Deutsche Forschungsgemeinschaft Grant No. IRTG-2662 Project No. 434130070 “Charging into the future,” and by the European Research Council under the European Union’s Horizon 2020 research and innovation program Grant Agreement No. 835117. We gratefully acknowledge computing time on the HPC clusters at the Physics department, Freie Universität Berlin.

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A review. The counterions neutralizing the charges on polyelectrolytes such as DNA or heparin may dissoc. in water and greatly influence the interaction of such polyelectrolytes with biomols., particularly proteins. In this Review the authors give an overview of studies on the interaction of proteins with polyelectrolytes and how this knowledge can be used for medical applications. Counterion release was identified as the main driving force for the binding of proteins to polyelectrolytes: Patches of pos. charge become multivalent counterions of the polyelectrolyte and lead to the release of counterions from the polyelectrolyte and a concomitant increase in entropy. This is shown from studies on the interaction of proteins with natural and synthetic polyelectrolytes. Special emphasis is paid to sulfated dendritic polyglycerols (dPGS). The Review demonstrates that the authors are moving to a better understanding of charge-charge interactions in systems of biol. relevance. Research along these lines will aid and promote the design of synthetic polyelectrolytes for medical applications.
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Kayitmazer, A. B.; Seeman, D.; Minsky, B. B.; Dubin, P. L.; Xu, Y. Protein–polyelectrolyte interactions. Soft Matter 2013, 9, 2553– 2583, DOI: 10.1039/c2sm27002a
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Protein-polyelectrolyte interactions
Kayitmazer, A. Basak; Seeman, Daniel; Minsky, Burcu Baykal; Dubin, Paul L.; Xu, Yisheng
Soft Matter (2013), 9 (9), 2553-2583CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)
A review. The interactions of proteins and polyelectrolytes lead to diverse applications in sepns., delivery and wound repair, and are thus of interest to scientists in e.g. (a) glycobiol., (b) tissue engineering, (c) biosensing, and (d) pharmacol. This breadth is accompanied by an assortment of contexts and models in which polyelectrolytes are seen as (a) protein cognates assisting in complex cellular roles, (b) surrogates for the extracellular matrix, mimicking its hydration, mech. and sequestering properties, (c) benign hosts that gently entrap, deposit and tether protein substrate specificity, and (d) selective but non-specific agents that modify protein soly. Unsurprisingly, this literature is somewhat segregated by objectives and paradigms. We hope this review, which emphasizes publications over the last 8 years, represents and also counterbalances that divergence. An ongoing theme is the role of electrostatics, and we show how this leads to the variety of phys. forms taken by protein-polyelectrolyte complexes. We present approaches towards anal. and characterization, motivated by the goal of structure-property elucidation. Such understanding should guide in applications, our third topic. We present recent developments in modeling and simulations of protein-polyelectrolyte systems. We close with a prospective on future developments in this field.
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Nandy, B.; Saurabh, S.; Sahoo, A. K.; Dixit, N. M.; Maiti, P. K. The SPL7013 dendrimer destabilizes the HIV-1 gp120-CD4 complex. Nanoscale 2015, 7, 18628– 18641, DOI: 10.1039/C5NR04632G
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The SPL7013 dendrimer destabilizes the HIV-1 gp120-CD4 complex
Nandy, Bidisha; Saurabh, Suman; Sahoo, Anil Kumar; Dixit, Narendra M.; Maiti, Prabal K.
Nanoscale (2015), 7 (44), 18628-18641CODEN: NANOHL; ISSN:2040-3372. (Royal Society of Chemistry)
The poly (l-lysine)-based SPL7013 dendrimer with naphthalene disulfonate surface groups blocks the entry of HIV-1 into target cells and is in clin. trials for development as a topical microbicide. Its mechanism of action against R5 HIV-1, the HIV-1 variant implicated in transmission across individuals, remains poorly understood. Using docking and fully atomistic MD simulations, we find that SPL7013 binds tightly to R5 gp120 in the gp120-CD4 complex but weakly to gp120 alone. Further, the binding, although to multiple regions of gp120, does not occlude the CD4 binding site on gp120, suggesting that SPL7013 does not prevent the binding of R5 gp120 to CD4. Using MD simulations to compute binding energies of several docked structures, we find that SPL7013 binding to gp120 significantly weakens the gp120-CD4 complex. Finally, we use steered mol. dynamics (SMD) to study the kinetics of the dissocn. of the gp120-CD4 complex in the absence of the dendrimer and with the dendrimer bound in each of the several stable configurations to gp120. We find that SPL7013 significantly lowers the force required to rupture the gp120-CD4 complex and accelerates its dissocn. Taken together, our findings suggest that SPL7013 compromises the stability of the R5 gp120-CD4 complex, potentially preventing the accrual of the requisite no. of gp120-CD4 complexes across the virus-cell interface, thereby blocking virus entry.
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Cagno, V.; Tseligka, E. D.; Jones, S. T.; Tapparel, C. Heparan sulfate proteoglycans and viral attachment: true receptors or adaptation bias?. Viruses 2019, 11, 596 DOI: 10.3390/v11070596
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Heparan sulfate proteoglycans and viral attachment: true receptors or adaptation bias?
Cagno, Valeria; Tseligka, Eirini D.; Jones, Samuel T.; Tapparel, Caroline
Viruses (2019), 11 (7), 596CODEN: VIRUBR; ISSN:1999-4915. (MDPI AG)
A review. Heparan sulfate proteoglycans (HSPG) are composed of unbranched, neg. charged heparan sulfate (HS) polysaccharides attached to a variety of cell surface or extracellular matrix proteins. Widely expressed, they mediate many biol. activities, including angiogenesis, blood coagulation, developmental processes, and cell homeostasis. HSPG are highly sulfated and broadly used by a range of pathogens, esp. viruses, to attach to the cell surface. In this review, we summarize the current knowledge on HSPG-virus interactions and distinguish viruses with established HS binding, viruses that bind HS only after intra-host or cell culture adaptation, and finally, viruses whose dependence on HS for infection is debated. We also provide an overview of the antiviral compds. designed to interfere with HS binding. Many questions remain about the true importance of these receptors in vivo, knowledge that is crit. for the design of future antiviral therapies.
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Liese, S.; Netz, R. R. Quantitative prediction of multivalent ligand-receptor binding affinities for influenza, cholera, and anthrax inhibition. ACS Nano 2018, 12, 4140– 4147, DOI: 10.1021/acsnano.7b08479
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Quantitative Prediction of Multivalent Ligand-Receptor Binding Affinities for Influenza, Cholera, and Anthrax Inhibition
Liese, Susanne; Netz, Roland R.
ACS Nano (2018), 12 (5), 4140-4147CODEN: ANCAC3; ISSN:1936-0851. (American Chemical Society)
Multivalency achieves strong, yet reversible binding by the simultaneous formation of multiple weak bonds. It is a key interaction principle in biol. and promising for the synthesis of high-affinity inhibitors of pathogens. We present a mol. model for the binding affinity of synthetic multivalent ligands onto multivalent receptors consisting of n receptor units arranged on a regular polygon. Ligands consist of a geometrically matching rigid polygonal core to which monovalent ligand units are attached via flexible linker polymers, closely mimicking existing exptl. designs. The calcd. binding affinities quant. agree with exptl. studies for cholera toxin (n = 5) and anthrax receptor (n = 7) and allow to predict optimal core size and optimal linker length. Maximal binding affinity is achieved for a core that matches the receptor size and for linkers that have an equil. end-to-end distance that is slightly longer than the geometric sepn. between ligand core and receptor sites. Linkers that are longer than optimal are greatly preferable compared to shorter linkers. The angular steric restriction between ligand unit and linker polymer is shown to be a key parameter. We construct an enhancement diagram that quantifies the multivalent binding affinity compared to monovalent ligands. We conclude that multivalent ligands against influenza viral hemagglutinin (n = 3), cholera toxin (n = 5), and anthrax receptor (n = 7) can outperform monovalent ligands only for a monovalent ligand affinity that exceeds a core-size dependent threshold value. Thus, multivalent drug design needs to balance core size, linker length, as well as monovalent ligand unit affinity.
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Lauster, D.; Osterrieder, K.; Haag, R.; Ballauff, M.; Herrmann, A. Respiratory viruses interacting with cells: The importance of electrostatics. Front. Microbiol. 2023, 14, 1169547 DOI: 10.3389/fmicb.2023.1169547
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Chu, H.; Hu, B.; Huang, X.; Chai, Y.; Zhou, D.; Wang, Y.; Shuai, H.; Yang, D.; Hou, Y.; Zhang, X. Host and viral determinants for efficient SARS-CoV-2 infection of the human lung. Nat. Commun. 2021, 12, 134 DOI: 10.1038/s41467-020-20457-w
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Host and viral determinants for efficient SARS-CoV-2 infection of the human lung
Chu, Hin; Hu, Bingjie; Huang, Xiner; Chai, Yue; Zhou, Dongyan; Wang, Yixin; Shuai, Huiping; Yang, Dong; Hou, Yuxin; Zhang, Xi; Yuen, Terrence Tsz-Tai; Cai, Jian-Piao; Zhang, Anna Jinxia; Zhou, Jie; Yuan, Shuofeng; To, Kelvin Kai-Wang; Chan, Ivy Hau-Yee; Sit, Ko-Yung; Foo, Dominic Chi-Chung; Wong, Ian Yu-Hong; Ng, Ada Tsui-Lin; Cheung, Tan To; Law, Simon Ying-Kit; Au, Wing-Kuk; Brindley, Melinda A.; Chen, Zhiwei; Kok, Kin-Hang; Chan, Jasper Fuk-Woo; Yuen, Kwok-Yung
Nature Communications (2021), 12 (1), 134CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)
Abstr.: Understanding the factors that contribute to efficient SARS-CoV-2 infection of human cells may provide insights on SARS-CoV-2 transmissibility and pathogenesis, and reveal targets of intervention. Here, we analyze host and viral determinants essential for efficient SARS-CoV-2 infection in both human lung epithelial cells and ex vivo human lung tissues. We identify heparan sulfate as an important attachment factor for SARS-CoV-2 infection. Next, we show that sialic acids present on ACE2 prevent efficient spike/ACE2-interaction. While SARS-CoV infection is substantially limited by the sialic acid-mediated restriction in both human lung epithelial cells and ex vivo human lung tissues, infection by SARS-CoV-2 is limited to a lesser extent. We further demonstrate that the furin-like cleavage site in SARS-CoV-2 spike is required for efficient virus replication in human lung but not intestinal tissues. These findings provide insights on the efficient SARS-CoV-2 infection of human lungs.
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Kim, S. H.; Kearns, F. L.; Rosenfeld, M. A.; Votapka, L.; Casalino, L.; Papanikolas, M.; Amaro, R. E.; Freeman, R. SARS-CoV-2 evolved variants optimize binding to cellular glycocalyx. Cell Rep. Phys. Sci. 2023, 4, 101346 DOI: 10.1016/j.xcrp.2023.101346
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Nie, C.; Pouyan, P.; Lauster, D.; Trimpert, J.; Kerkhoff, Y.; Szekeres, G. P.; Wallert, M.; Block, S.; Sahoo, A. K.; Dernedde, J.; Pagel, K.; Kaufer, B. B.; Netz, R. R.; Ballauff, M.; Haag, R. Polysulfates block SARS-CoV-2 uptake via electrostatic interactions. Angew. Chem., Int. Ed. 2021, 60, 15870– 15878, DOI: 10.1002/anie.202102717
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Polysulfates Block SARS-CoV-2 Uptake through Electrostatic Interactions
Nie, Chuanxiong; Pouyan, Paria; Lauster, Daniel; Trimpert, Jakob; Kerkhoff, Yannic; Szekeres, Gergo Peter; Wallert, Matthias; Block, Stephan; Sahoo, Anil Kumar; Dernedde, Jens; Pagel, Kevin; Kaufer, Benedikt B.; Netz, Roland R.; Ballauff, Matthias; Haag, Rainer
Angewandte Chemie, International Edition (2021), 60 (29), 15870-15878CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
Here we report that neg. charged polysulfates can bind to the spike protein of SARS-CoV-2 via electrostatic interactions. Using a plaque redn. assay, we compare inhibition of SARS-CoV-2 by heparin, pentosan sulfate, linear polyglycerol sulfate (LPGS) and hyperbranched polyglycerol sulfate (HPGS). Highly sulfated LPGS is the optimal inhibitor, with an IC50 of 67μg mL-1 (approx. 1.6μM). This synthetic polysulfate exhibits more than 60-fold higher virus inhibitory activity than heparin (IC50: 4084μg mL-1), along with much lower anticoagulant activity. Furthermore, in mol. dynamics simulations, we verified that LPGS can bind more strongly to the spike protein than heparin, and that LPGS can interact even more with the spike protein of the new N501Y and E484K variants. Our study demonstrates that the entry of SARS-CoV-2 into host cells can be blocked via electrostatic interactions, therefore LPGS can serve as a blueprint for the design of novel viral inhibitors of SARS-CoV-2.
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Clausen, T. M.; Sandoval, D. R.; Spliid, C. B.; Pihl, J.; Perrett, H. R.; Painter, C. D.; Narayanan, A.; Majowicz, S. A.; Kwong, E. M.; McVicar, R. N. SARS-CoV-2 infection depends on cellular heparan sulfate and ACE2. Cell 2020, 183, 1043– 1057, DOI: 10.1016/j.cell.2020.09.033
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SARS-CoV-2 Infection Depends on Cellular Heparan Sulfate and ACE2
Clausen, Thomas Mandel; Sandoval, Daniel R.; Spliid, Charlotte B.; Pihl, Jessica; Perrett, Hailee R.; Painter, Chelsea D.; Narayanan, Anoop; Majowicz, Sydney A.; Kwong, Elizabeth M.; McVicar, Rachael N.; Thacker, Bryan E.; Glass, Charles A.; Yang, Zhang; Torres, Jonathan L.; Golden, Gregory J.; Bartels, Phillip L.; Porell, Ryan N.; Garretson, Aaron F.; Laubach, Logan; Feldman, Jared; Yin, Xin; Pu, Yuan; Hauser, Blake M.; Caradonna, Timothy M.; Kellman, Benjamin P.; Martino, Cameron; Gordts, Philip L. S. M.; Chanda, Sumit K.; Schmidt, Aaron G.; Godula, Kamil; Leibel, Sandra L.; Jose, Joyce; Corbett, Kevin D.; Ward, Andrew B.; Carlin, Aaron F.; Esko, Jeffrey D.
Cell (Cambridge, MA, United States) (2020), 183 (4), 1043-1057.e15CODEN: CELLB5; ISSN:0092-8674. (Cell Press)
We show that SARS-CoV-2 spike protein interacts with both cellular heparan sulfate and angiotensin-converting enzyme 2 (ACE2) through its receptor-binding domain (RBD). Docking studies suggest a heparin/heparan sulfate-binding site adjacent to the ACE2-binding site. Both ACE2 and heparin can bind independently to spike protein in vitro, and a ternary complex can be generated using heparin as a scaffold. Electron micrographs of spike protein suggests that heparin enhances the open conformation of the RBD that binds ACE2. On cells, spike protein binding depends on both heparan sulfate and ACE2. Unfractionated heparin, non-anticoagulant heparin, heparin lyases, and lung heparan sulfate potently block spike protein binding and/or infection by pseudotyped virus and authentic SARS-CoV-2 virus. We suggest a model in which viral attachment and infection involves heparan sulfate-dependent enhancement of binding to ACE2. Manipulation of heparan sulfate or inhibition of viral adhesion by exogenous heparin presents new therapeutic opportunities.
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Lever, R.; Page, C. P. Non-Anticoagulant Effects of Heparin: An Overview. In Heparin - A Century of Progress; Lever, R.; Mulloy, B.; Page, C. P., Eds.; Springer: Berlin, Heidelberg, 2012; pp 281– 305.
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Page, C. Heparin and related drugs: beyond anticoagulant activity. ISRN Pharmacol. 2013, 1, 910743 DOI: 10.1155/2013/910743
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Oates, J. A.; Wood, A. J. J.; Hirsh, J. Heparin. N. Engl. J. Med. 1991, 324, 1565– 1574, DOI: 10.1056/NEJM199105303242206
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There is no corresponding record for this reference.
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Cate, H. T. Surviving Covid-19 with Heparin?. N. Engl. J. Med. 2021, 385, 845– 846, DOI: 10.1056/NEJMe2111151
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Lan, J.; Ge, J.; Yu, J.; Shan, S.; Zhou, H.; Fan, S.; Zhang, Q.; Shi, X.; Wang, Q.; Zhang, L.; Wang, X. Structure of the SARS-CoV-2 spike receptor-binding domain bound to the ACE2 receptor. Nature 2020, 581, 215– 220, DOI: 10.1038/s41586-020-2180-5
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Structure of the SARS-CoV-2 spike receptor-binding domain bound to the ACE2 receptor
Lan, Jun; Ge, Jiwan; Yu, Jinfang; Shan, Sisi; Zhou, Huan; Fan, Shilong; Zhang, Qi; Shi, Xuanling; Wang, Qisheng; Zhang, Linqi; Wang, Xinquan
Nature (London, United Kingdom) (2020), 581 (7807), 215-220CODEN: NATUAS; ISSN:0028-0836. (Nature Research)
Abstr.: A new and highly pathogenic coronavirus (severe acute respiratory syndrome coronavirus-2, SARS-CoV-2) caused an outbreak in Wuhan city, Hubei province, China, starting from Dec. 2019 that quickly spread nationwide and to other countries around the world1-3. Here, to better understand the initial step of infection at an at. level, we detd. the crystal structure of the receptor-binding domain (RBD) of the spike protein of SARS-CoV-2 bound to the cell receptor ACE2. The overall ACE2-binding mode of the SARS-CoV-2 RBD is nearly identical to that of the SARS-CoV RBD, which also uses ACE2 as the cell receptor4. Structural anal. identified residues in the SARS-CoV-2 RBD that are essential for ACE2 binding, the majority of which either are highly conserved or share similar side chain properties with those in the SARS-CoV RBD. Such similarity in structure and sequence strongly indicate convergent evolution between the SARS-CoV-2 and SARS-CoV RBDs for improved binding to ACE2, although SARS-CoV-2 does not cluster within SARS and SARS-related coronaviruses1-3,5. The epitopes of two SARS-CoV antibodies that target the RBD are also analyzed for binding to the SARS-CoV-2 RBD, providing insights into the future identification of cross-reactive antibodies.
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Pishko, A. M.; Lefler, D. S.; Gimotty, P.; Paydary, K.; Fardin, S.; Arepally, G. M.; Crowther, M.; Rice, L.; Vega, R.; Cines, D. B. The risk of major bleeding in patients with suspected heparin-induced thrombocytopenia. J. Thromb. Haemostasis 2019, 17, 1956– 1965, DOI: 10.1111/jth.14587
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Nie, C.; Sahoo, A. K.; Netz, R. R.; Herrmann, A.; Ballauff, M.; Haag, R. Charge matters: Mutations in omicron variant favor binding to cells. ChemBioChem 2022, 23, e202100681 DOI: 10.1002/cbic.202100681
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Charge Matters: Mutations in Omicron Variant Favor Binding to Cells
Nie, Chuanxiong; Sahoo, Anil Kumar; Netz, Roland R.; Herrmann, Andreas; Ballauff, Matthias; Haag, Rainer
ChemBioChem (2022), 23 (6), e202100681CODEN: CBCHFX; ISSN:1439-4227. (Wiley-VCH Verlag GmbH & Co. KGaA)
A review. Evidence is strengthening to suggest that the novel SARS-CoV-2 mutant Omicron, with its more than 60 mutations, will spread and dominate worldwide. Although the mutations in the spike protein are known, the mol. basis for why the addnl. mutations in the spike protein that have not previously occurred account for Omicron's higher infection potential, is not understood. We propose, based on chem. rational and mol. dynamics simulations, that the elevated occurrence of pos. charged amino acids in certain domains of the spike protein (Delta: +4; Omicron: +5 vs. wild type) increases binding to cellular polyanionic receptors, such as heparan sulfate due to multivalent charge-charge interactions. This observation is a starting point for targeted drug development.
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Wang, L.; Wu, Y.; Deng, Y.; Kim, B.; Pierce, L.; Krilov, G.; Lupyan, D.; Robinson, S.; Dahlgren, M. K.; Greenwood, J. Accurate and reliable prediction of relative ligand binding potency in prospective drug discovery by way of a modern free-energy calculation protocol and force field. J. Am. Chem. Soc. 2015, 137, 2695– 2703, DOI: 10.1021/ja512751q
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Accurate and Reliable Prediction of Relative Ligand Binding Potency in Prospective Drug Discovery by Way of a Modern Free-Energy Calculation Protocol and Force Field
Wang, Lingle; Wu, Yujie; Deng, Yuqing; Kim, Byungchan; Pierce, Levi; Krilov, Goran; Lupyan, Dmitry; Robinson, Shaughnessy; Dahlgren, Markus K.; Greenwood, Jeremy; Romero, Donna L.; Masse, Craig; Knight, Jennifer L.; Steinbrecher, Thomas; Beuming, Thijs; Damm, Wolfgang; Harder, Ed; Sherman, Woody; Brewer, Mark; Wester, Ron; Murcko, Mark; Frye, Leah; Farid, Ramy; Lin, Teng; Mobley, David L.; Jorgensen, William L.; Berne, Bruce J.; Friesner, Richard A.; Abel, Robert
Journal of the American Chemical Society (2015), 137 (7), 2695-2703CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
Designing tight-binding ligands is a primary objective of small-mol. drug discovery. Over the past few decades, free-energy calcns. have benefited from improved force fields and sampling algorithms, as well as the advent of low-cost parallel computing. However, it has proven to be challenging to reliably achieve the level of accuracy that would be needed to guide lead optimization (∼5× in binding affinity) for a wide range of ligands and protein targets. Not surprisingly, widespread com. application of free-energy simulations has been limited due to the lack of large-scale validation coupled with the tech. challenges traditionally assocd. with running these types of calcns. Here, we report an approach that achieves an unprecedented level of accuracy across a broad range of target classes and ligands, with retrospective results encompassing 200 ligands and a wide variety of chem. perturbations, many of which involve significant changes in ligand chem. structures. In addn., we have applied the method in prospective drug discovery projects and found a significant improvement in the quality of the compds. synthesized that have been predicted to be potent. Compds. predicted to be potent by this approach have a substantial redn. in false positives relative to compds. synthesized on the basis of other computational or medicinal chem. approaches. Furthermore, the results are consistent with those obtained from our retrospective studies, demonstrating the robustness and broad range of applicability of this approach, which can be used to drive decisions in lead optimization.
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Cournia, Z.; Allen, B.; Sherman, W. Relative binding free energy calculations in drug discovery: recent advances and practical considerations. J. Chem. Inf. Model. 2017, 57, 2911– 2937, DOI: 10.1021/acs.jcim.7b00564
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Relative Binding Free Energy Calculations in Drug Discovery: Recent Advances and Practical Considerations
Cournia, Zoe; Allen, Bryce; Sherman, Woody
Journal of Chemical Information and Modeling (2017), 57 (12), 2911-2937CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
A review. Accurate in silico prediction of protein-ligand binding affinities has been a primary objective of structure-based drug design for decades due to the putative value it would bring to the drug discovery process. However, computational methods have historically failed to deliver value in real-world drug discovery applications due to a variety of scientific, tech., and practical challenges. Recently, a family of approaches commonly referred to as relative binding free energy (RBFE) calcns., which rely on physics-based mol. simulations and statistical mechanics, have shown promise in reliably generating accurate predictions in the context of drug discovery projects. This advance arises from accumulating developments in the underlying scientific methods (decades of research on force fields and sampling algorithms) coupled with vast increases in computational resources (graphics processing units and cloud infrastructures). Mounting evidence from retrospective validation studies, blind challenge predictions, and prospective applications suggests that RBFE simulations can now predict the affinity differences for congeneric ligands with sufficient accuracy and throughput to deliver considerable value in hit-to-lead and lead optimization efforts. Here, the authors present an overview of current RBFE implementations, highlighting recent advances and remaining challenges, along with examples that emphasize practical considerations for obtaining reliable RBFE results. The authors focus specifically on relative binding free energies because the calcns. are less computationally intensive than abs. binding free energy (ABFE) calcns. and map directly onto the hit-to-lead and lead optimization processes, where the prediction of relative binding energies between a ref. mol. and new ideas (virtual mols.) can be used to prioritize mols. for synthesis. The authors describe the crit. aspects of running RBFE calcns., from both theor. and applied perspectives, using a combination of retrospective literature examples and prospective studies from drug discovery projects. This work is intended to provide a contemporary overview of the scientific, tech., and practical issues assocd. with running relative binding free energy simulations, with a focus on real-world drug discovery applications. The authors offer guidelines for improving the accuracy of RBFE simulations, esp. for challenging cases, and emphasize unresolved issues that could be improved by further research in the field.
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Mobley, D. L.; Gilson, M. K. Predicting binding free energies: frontiers and benchmarks. Annu. Rev. Biophys. 2017, 46, 531– 558, DOI: 10.1146/annurev-biophys-070816-033654
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Predicting Binding Free Energies: Frontiers and Benchmarks
Mobley, David L.; Gilson, Michael K.
Annual Review of Biophysics (2017), 46 (), 531-558CODEN: ARBNCV; ISSN:1936-122X. (Annual Reviews)
Binding free energy calcns. based on mol. simulations provide predicted affinities for biomol. complexes. These calcns. begin with a detailed description of a system, including its chem. compn. and the interactions among its components. Simulations of the system are then used to compute thermodn. information, such as binding affinities. Because of their promise for guiding mol. design, these calcns. have recently begun to see widespread applications in early-stage drug discovery. However, many hurdles remain in making them a robust and reliable tool. In this review, we highlight key challenges of these calcns., discuss some examples of these challenges, and call for the designation of std. community benchmark test systems that will help the research community generate and evaluate progress. In our view, progress will require careful assessment and evaluation of new methods, force fields, and modeling innovations on well-characterized benchmark systems, and we lay out our vision for how this can be achieved.
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Zhao, J.; Cao, Y.; Zhang, L. Exploring the computational methods for protein-ligand binding site prediction. Comput. Struct. Biotechnol. J. 2020, 18, 417– 426, DOI: 10.1016/j.csbj.2020.02.008
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Exploring the computational methods for protein-ligand binding site prediction
Zhao, Jingtian; Cao, Yang; Zhang, Le
Computational and Structural Biotechnology Journal (2020), 18 (), 417-426CODEN: CSBJAC; ISSN:2001-0370. (Elsevier B.V.)
A review. Proteins participate in various essential processes in vivo via interactions with other mols. Identifying the residues participating in these interactions not only provides biol. insights for protein function studies but also has great significance for drug discoveries. Therefore, predicting protein-ligand binding sites has long been under intense research in the fields of bioinformatics and computer aided drug discovery. In this review, we first introduce the research background of predicting protein-ligand binding sites and then classify the methods into four categories, namely, 3D structure-based, template similarity-based, traditional machine learning-based and deep learning-based methods. We describe representative algorithms in each category and elaborate on machine learning and deep learning-based prediction methods in more detail. Finally, we discuss the trends and challenges of the current research such as mol. dynamics simulation based cryptic binding sites prediction, and highlight prospective directions for the near future.
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Gapsys, V.; Yildirim, A.; Aldeghi, M.; Khalak, Y.; Van der Spoel, D.; de Groot, B. L. Accurate absolute free energies for ligand–protein binding based on non-equilibrium approaches. Commun. Chem. 2021, 4, 61 DOI: 10.1038/s42004-021-00498-y
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Accurate absolute free energies for ligand-protein binding based on non-equilibrium approaches
Gapsys, Vytautas; Yildirim, Ahmet; Aldeghi, Matteo; Khalak, Yuriy; van der Spoel, David; de Groot, Bert L.
Communications Chemistry (2021), 4 (1), 61CODEN: CCOHCT; ISSN:2399-3669. (Nature Research)
Abstr.: The accurate calcn. of the binding free energy for arbitrary ligand-protein pairs is a considerable challenge in computer-aided drug discovery. Recently, it has been demonstrated that current state-of-the-art mol. dynamics (MD) based methods are capable of making highly accurate predictions. Conventional MD-based approaches rely on the first principles of statistical mechanics and assume equil. sampling of the phase space. In the current work we demonstrate that accurate abs. binding free energies (ABFE) can also be obtained via theor. rigorous non-equil. approaches. Our investigation of ligands binding to bromodomains and T4 lysozyme reveals that both equil. and non-equil. approaches converge to the same results. The non-equil. approach achieves the same level of accuracy and convergence as an equil. free energy perturbation (FEP) method enhanced by Hamiltonian replica exchange. We also compare uni- and bi-directional non-equil. approaches and demonstrate that considering the work distributions from both forward and reverse directions provides substantial accuracy gains. In summary, non-equil. ABFE calcns. are shown to yield reliable and well-converged ests. of protein-ligand binding affinity.
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Xu, X.; Angioletti-Uberti, S.; Lu, Y.; Dzubiella, J.; Ballauff, M. Interaction of proteins with polyelectrolytes: Comparison of theory to experiment. Langmuir 2019, 35, 5373– 5391, DOI: 10.1021/acs.langmuir.8b01802
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Interaction of Proteins with Polyelectrolytes: Comparison of Theory to Experiment
Xu, Xiao; Angioletti-Uberti, Stefano; Lu, Yan; Dzubiella, Joachim; Ballauff, Matthias
Langmuir (2019), 35 (16), 5373-5391CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
A review on the authors' recent studies on the interaction of simple proteins such as human serum albumin (HSA) and lysozyme with linear polyelectrolytes, charged dendrimers, charged networks, and polyelectrolyte brushes, based on exptl. works combined with mol. dynamics (MD) simulations and mean-field theories.
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Paiardi, G.; Ferraz, M.; Rusnati, M.; Wade, R. C. The accomplices: Heparan sulfates and N-glycans foster SARS-CoV-2 spike: ACE2 receptor binding and virus priming. Proc. Natl. Acad. Sci. U.S.A. 2024, 121, e2404892121 DOI: 10.1073/pnas.2404892121
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Bhatia, S.; Lauster, D.; Bardua, M.; Ludwig, K.; Angioletti-Uberti, S.; Popp, N.; Hoffmann, U.; Paulus, F.; Budt, M.; Stadtmüller, M. Linear polysialoside outperforms dendritic analogs for inhibition of influenza virus infection in vitro and in vivo. Biomaterials 2017, 138, 22– 34, DOI: 10.1016/j.biomaterials.2017.05.028
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Linear polysialoside outperforms dendritic analogs for inhibition of influenza virus infection in vitro and in vivo
Bhatia, Sumati; Lauster, Daniel; Bardua, Markus; Ludwig, Kai; Angioletti-Uberti, Stefano; Popp, Nicole; Hoffmann, Ute; Paulus, Florian; Budt, Matthias; Stadtmueller, Marlena; Wolff, Thorsten; Hamann, Alf; Boettcher, Christoph; Herrmann, Andreas; Haag, Rainer
Biomaterials (2017), 138 (), 22-34CODEN: BIMADU; ISSN:0142-9612. (Elsevier Ltd.)
Inhibition of influenza A virus infection by multivalent sialic acid inhibitors preventing viral hemagglutinin binding to host cells of the respiratory tract is a promising strategy. However, optimal geometry and optimal ligand presentation on multivalent scaffolds for efficient inhibition both in vitro and in vivo application are still unclear. Here, by comparing linear and dendritic polyglycerol sialosides (LPGSA and dPGSA) we identified architectural requirements and optimal ligand densities for an efficient multivalent inhibitor of influenza virus A/X31/1 (H3N2). Due to its large vol., the LPGSA at optimal ligand d. sterically shielded the virus significantly better than the dendritic analog. A statistical mechanics model rationalizes the relevance of ligand d., morphol., and the size of multivalent scaffolds for the potential to inhibit virus-cell binding. Optimized LPGSA inhibited virus infection at IC50 in the low nanomolar nanoparticle concn. range and also showed potent antiviral activity against two avian influenza strains A/Mallard/439/2004 (H3N2) and A/turkey/Italy/472/1999 (H7N1) post infection. In vivo application of inhibitors clearly confirmed the higher inhibition potential of linear multivalent scaffolds to prevent infection. The optimized LPGSA did not show any acute toxicity, and was much more potent than the neuraminidase inhibitor oseltamivir carboxylate in vivo. Combined application of the LPGSA and oseltamivir carboxylate revealed a synergistic inhibitory effect and successfully prevented influenza virus infection in mice.
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Xu, C.; Wang, Y.; Liu, C.; Zhang, C.; Han, W.; Hong, X.; Wang, Y.; Hong, Q.; Wang, S.; Zhao, Q. Conformational dynamics of SARS-CoV-2 trimeric spike glycoprotein in complex with receptor ACE2 revealed by cryo-EM. Sci. Adv. 2021, 7, eabe5575 DOI: 10.1126/sciadv.abe5575
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Horinek, D.; Serr, A.; Geisler, M.; Pirzer, T.; Slotta, U.; Lud, S. Q.; Garrido, J.; Scheibel, T.; Hugel, T.; Netz, R. R. Peptide adsorption on a hydrophobic surface results from an interplay of solvation, surface, and intrapeptide forces. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 2842– 2847, DOI: 10.1073/pnas.0707879105
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Peptide adsorption on a hydrophobic surface results from an interplay of solvation, surface, and intrapeptide forces
Horinek, D.; Serr, A.; Geisler, M.; Pirzer, T.; Slotta, U.; Lud, S. Q.; Garrido, J. A.; Scheibel, T.; Hugel, T.; Netz, R. R.
Proceedings of the National Academy of Sciences of the United States of America (2008), 105 (8), 2842-2847CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
The hydrophobic effect, i.e., the poor solvation of nonpolar parts of mols., plays a key role in protein folding and more generally for mol. self-assembly and aggregation in aq. media. The perturbation of the water structure accounts for many aspects of protein hydrophobicity. However, to what extent the dispersion interaction between mol. entities themselves contributes has remained unclear. This is so because in peptide folding interactions and structural changes occur on all length scales and make disentangling various contributions impossible. The authors address this issue both exptl. and theor. by looking at the force necessary to peel a mildly hydrophobic single peptide mol. from a flat hydrophobic diamond surface in the presence of water. This setup avoids problems caused by bubble adsorption, cavitation, and slow equilibration that complicate the much-studied geometry with two macroscopic surfaces. Using at.-force spectroscopy, the authors det. the mean desorption force of a single spider-silk peptide chain as F = 58 ± 8 pN, which corresponds to a desorption free energy of ≈5 k8T per amino acid. The authors' all-atomistic mol. dynamics simulation including explicit water correspondingly yields the desorption force F = 54 ± 15 pN. This observation demonstrates that std. nonpolarizable force fields used in classical simulations are capable of resolving the fine details of the hydrophobic attraction of peptides. The anal. of the involved energetics shows that water-structure effects and dispersive interactions give contributions of comparable magnitude that largely cancel out. It follows that the correct modeling of peptide hydrophobicity must take the intimate coupling of solvation and dispersive effects into account.
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Schwierz, N.; Horinek, D.; Liese, S.; Pirzer, T.; Balzer, B. N.; Hugel, T.; Netz, R. R. On the relationship between peptide adsorption resistance and surface contact angle: a combined experimental and simulation single-molecule study. J. Am. Chem. Soc. 2012, 134, 19628– 19638, DOI: 10.1021/ja304462u
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On the Relationship between Peptide Adsorption Resistance and Surface Contact Angle: A Combined Experimental and Simulation Single-Molecule Study
Schwierz, Nadine; Horinek, Dominik; Liese, Susanne; Pirzer, Tobias; Balzer, Bizan N.; Hugel, Thorsten; Netz, Roland R.
Journal of the American Chemical Society (2012), 134 (48), 19628-19638CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
The force-induced desorption of single peptide chains from mixed OH/CH3-terminated self-assembled monolayers was studied in closely matched mol. dynamics simulations and at. force microscopy expts. with the goal to gain microscopic understanding of the transition between peptide adsorption and adsorption resistance as the surface contact angle is varied. In both simulations and expts., the surfaces become adsorption resistant against hydrophilic as well as hydrophobic peptides when their contact angle decreases below θ ≈ 50°-60°, thus confirming the so-called Berg limit established in the context of protein and cell adsorption. Entropy/enthalpy decompn. of the simulation results reveals that the key discriminator between the adsorption of different residues on a hydrophobic monolayer is of entropic nature and thus probably is linked to the hydrophobic effect. By pushing a polyalanine peptide onto a polar surface, simulations reveal that the peptide adsorption resistance is caused by the strongly bound water hydration layer and characterized by the simultaneous gain of both total entropy in the system and total no. of hydrogen bonds between water, peptide, and surface. This mechanistic insight into peptide adsorption resistance might help to refine design principles for anti-fouling surfaces.
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Page, T. M.; Nie, C.; Neander, L.; Povolotsky, T. L.; Sahoo, A. K.; Nickl, P.; Adler, J. M.; Bawadkji, O.; Radnik, J.; Achazi, K. Functionalized Fullerene for Inhibition of SARS-CoV-2 Variants. Small 2023, 19, 2206154 DOI: 10.1002/smll.202206154
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Functionalized Fullerene for Inhibition of SARS-CoV-2 Variants
Page, Taylor M.; Nie, Chuanxiong; Neander, Lenard; Povolotsky, Tatyana L.; Sahoo, Anil Kumar; Nickl, Philip; Adler, Julia M.; Bawadkji, Obida; Radnik, Jorg; Achazi, Katharina; Ludwig, Kai; Lauster, Daniel; Netz, Roland R.; Trimpert, Jakob; Kaufer, Benedikt; Haag, Rainer; Donskyi, Ievgen S.
Small (2023), 19 (15), 2206154CODEN: SMALBC; ISSN:1613-6810. (Wiley-VCH Verlag GmbH & Co. KGaA)
As virus outbreaks continue to pose a challenge, a nonspecific viral inhibitor can provide significant benefits, esp. against respiratory viruses. Polyglycerol sulfates recently emerge as promising agents that mediate interactions between cells and viruses through electrostatics, leading to virus inhibition. Similarly, hydrophobic C60 fullerene can prevent virus infection via interactions with hydrophobic cavities of surface proteins. Here, two strategies are combined to inhibit infection of SARS-CoV-2 variants in vitro. Effective inhibitory concns. in the millimolar range highlight the significance of bare fullerene's hydrophobic moiety and electrostatic interactions of polysulfates with surface proteins of SARS-CoV-2. Furthermore, microscale thermophoresis measurements support that fullerene linear polyglycerol sulfates interact with the SARS-CoV-2 virus via its spike protein, and highlight importance of electrostatic interactions within it. All-atom mol. dynamics simulations reveal that the fullerene binding site is situated close to the receptor binding domain, within 4 nm of polyglycerol sulfate binding sites, feasibly allowing both portions of the material to interact simultaneously.
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Woo, H.; Park, S.-J.; Choi, Y. K.; Park, T.; Tanveer, M.; Cao, Y.; Kern, N. R.; Lee, J.; Yeom, M. S.; Croll, T. I. Developing a fully glycosylated full-length SARS-CoV-2 spike protein model in a viral membrane. J. Phys. Chem. B 2020, 124, 7128– 7137, DOI: 10.1021/acs.jpcb.0c04553
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Developing a fully glycosylated full-length SARS-CoV-2 spike protein model in a viral membrane
Woo, Hyeonuk; Park, Sang-Jun; Choi, Yeol Kyo; Park, Taeyong; Tanveer, Maham; Cao, Yiwei; Kern, Nathan R.; Lee, Jumin; Yeom, Min Sun; Croll, Tristan I.; Seok, Chaok; Im, Wonpil
Journal of Physical Chemistry B (2020), 124 (33), 7128-7137CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
This tech. study describes all-atom modeling and simulation of a fully glycosylated full-length SARS-CoV-2 spike (S) protein in a viral membrane. First, starting from PDB: 6VSB and 6VXX, full-length S protein structures were modeled using template-based modeling, de-novo protein structure prediction, and loop modeling techniques in GALAXY modeling suite. Then, using the recently detd. most occupied glycoforms, 22 N-glycans and 1 O-glycan of each monomer were modeled using Glycan Reader & Modeler in CHARMM-GUI. These fully glycosylated full-length S protein model structures were assessed and further refined against the low-resoln. data in their resp. exptl. maps using ISOLDE. The authors then used CHARMM-GUI Membrane Builder to place the S proteins in a viral membrane and performed all-atom mol. dynamics simulations. All structures are available in CHARMM-GUI COVID-19 Archive so that researchers can use these models to carry out innovative and novel modeling and simulation research for the prevention and treatment of COVID-19.
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Casalino, L.; Gaieb, Z.; Goldsmith, J. A.; Hjorth, C. K.; Dommer, A. C.; Harbison, A. M.; Fogarty, C. A.; Barros, E. P.; Taylor, B. C.; McLellan, J. S. Beyond shielding: the roles of glycans in the SARS-CoV-2 spike protein. ACS Cent. Sci. 2020, 6, 1722– 1734, DOI: 10.1021/acscentsci.0c01056
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Beyond Shielding: The Roles of Glycans in the SARS-CoV-2 Spike Protein
Casalino, Lorenzo; Gaieb, Zied; Goldsmith, Jory A.; Hjorth, Christy K.; Dommer, Abigail C.; Harbison, Aoife M.; Fogarty, Carl A.; Barros, Emilia P.; Taylor, Bryn C.; McLellan, Jason S.; Fadda, Elisa; Amaro, Rommie E.
ACS Central Science (2020), 6 (10), 1722-1734CODEN: ACSCII; ISSN:2374-7951. (American Chemical Society)
The ongoing COVID-19 pandemic caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has resulted in more than 28,000,000 infections and 900,000 deaths worldwide to date. Antibody development efforts mainly revolve around the extensively glycosylated SARS-CoV-2 spike (S) protein, which mediates host cell entry by binding to the angiotensin-converting enzyme 2 (ACE2). Similar to many other viral fusion proteins, the SARS-CoV-2 spike utilizes a glycan shield to thwart the host immune response. Here, we built a full-length model of the glycosylated SARS-CoV-2 S protein, both in the open and closed states, augmenting the available structural and biol. data. Multiple microsecond-long, all-atom mol. dynamics simulations were used to provide an atomistic perspective on the roles of glycans and on the protein structure and dynamics. We reveal an essential structural role of N-glycans at sites N165 and N234 in modulating the conformational dynamics of the spike's receptor binding domain (RBD), which is responsible for ACE2 recognition. This finding is corroborated by biolayer interferometry expts., which show that deletion of these glycans through N165A and N234A mutations significantly reduces binding to ACE2 as a result of the RBD conformational shift toward the "down" state. Addnl., end-to-end accessibility analyses outline a complete overview of the vulnerabilities of the glycan shield of the SARS-CoV-2 S protein, which may be exploited in the therapeutic efforts targeting this mol. machine. Overall, this work presents hitherto unseen functional and structural insights into the SARS-CoV-2 S protein and its glycan coat, providing a strategy to control the conformational plasticity of the RBD that could be harnessed for vaccine development. The glycan shield is a sugary barrier that helps the viral SARS-CoV-2 spikes to evade the immune system. Beyond shielding, two of the spike's glycans are discovered to prime the virus for infection.
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Erbaş, A.; Netz, R. R. Confinement-dependent friction in peptide bundles. Biophys. J. 2013, 104, 1285– 1295, DOI: 10.1016/j.bpj.2013.02.008
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Confinement-Dependent Friction in Peptide Bundles
Erbas, Aykut; Netz, Roland R.
Biophysical Journal (2013), 104 (6), 1285-1295CODEN: BIOJAU; ISSN:0006-3495. (Cell Press)
Friction within globular proteins or between adhering macromols. crucially dets. the kinetics of protein folding, the formation, and the relaxation of self-assembled mol. systems. One fundamental question is how these friction effects depend on the local environment and in particular on the presence of water. In this model study, we use fully atomistic MD simulations with explicit water to obtain friction forces as a single polyglycine peptide chain is pulled out of a bundle of k adhering parallel polyglycine peptide chains. The whole system is periodically replicated along the peptide axes, so a stationary state at prescribed mean sliding velocity V is achieved. The aggregation no. is varied between k = 2 (two peptide chains adhering to each other with plenty of water present at the adhesion sites) and k = 7 (one peptide chain pulled out from a close-packed cylindrical array of six neighboring peptide chains with no water inside the bundle). The friction coeff. per hydrogen bond, extrapolated to the viscous limit of vanishing pulling velocity V → 0, exhibits an increase by five orders of magnitude when going from k = 2 to k = 7. This dramatic confinement-induced friction enhancement we argue to be due to a combination of water depletion and increased hydrogen-bond cooperativity.
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Erbaş, A.; Horinek, D.; Netz, R. R. Viscous friction of hydrogen-bonded matter. J. Am. Chem. Soc. 2012, 134, 623– 630, DOI: 10.1021/ja209454a
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Viscous Friction of Hydrogen-Bonded Matter
Erbas, Aykut; Horinek, Dominik; Netz, Roland R.
Journal of the American Chemical Society (2012), 134 (1), 623-630CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
Amontons' law successfully describes friction between macroscopic solid bodies for a wide range of velocities and normal forces. For the diffusion and forced sliding of adhering or entangled macromols., proteins, and biol. complexes, temp. effects are invariably important, and a similarly successful friction law at biol. length and velocity scales is missing. Hydrogen bonds (HBs) are key to the specific binding of biomatter. Here we show that friction between hydrogen-bonded matter in the biol. relevant low-velocity viscous regime obeys a simple law: the friction force is proportional to the no. of HBs, the sliding velocity, and a friction coeff. γHB. This law is deduced from atomistic mol. dynamics simulations for short peptide chains that are laterally pulled over planar hydroxylated substrates in the presence of water and holds for widely different peptides, surface polarities, and applied normal forces. The value of γHB is extrapolated from simulations at sliding velocities in the range from V = 10-2 to 100 m/s by mapping on a simple stochastic model and turns out to be of the order of γHB ≃ 10-8 kg/s. The friction of a single HB thus amts. to the Stokes friction of a sphere with an equiv. radius of roughly 1 μm moving in water. Cooperativity is pronounced; roughly three HBs act collectively.
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Patil, S. P.; Xiao, S.; Gkagkas, K.; Markert, B.; Gräter, F. Viscous friction between crystalline and amorphous phase of dragline silk. PLoS One 2014, 9, e104832 DOI: 10.1371/journal.pone.0104832
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Kumar, S.; Rosenberg, J. M.; Bouzida, D.; Swendsen, R. H.; Kollman, P. A. The weighted histogram analysis method for free-energy calculations on biomolecules. I. The method. J. Comput. Chem. 1992, 13, 1011– 1021, DOI: 10.1002/jcc.540130812
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The weighted histogram analysis method for free-energy calculations on biomolecules. I. The method
Kumar, Shankar; Bouzida, Djamal; Swendsen, Robert H.; Kollman, Peter A.; Rosenberg, John M.
Journal of Computational Chemistry (1992), 13 (8), 1011-21CODEN: JCCHDD; ISSN:0192-8651.
The Weighted Histogram Anal. Method (WHAM), an extension of Ferrenberg and Swendsen's Multiple Histogram Technique, has been applied for the first time on complex biomol. Hamiltonians. The method is presented here as an extension of the Umbrella Sampling method for free-energy and Potential of Mean Force calcns. This algorithm possesses the following advantages over methods that are currently employed: (1) it provides a built-in est. of sampling errors thereby yielding objective ests. of the optimal location and length of addnl. simulations needed to achieve a desired level of precision; (2) it yields the "best" value of free energies by taking into account all the simulations so as to minimize the statistical errors; (3) in addn. to optimizing the links between simulations, it also allows multiple overlaps of probability distributions for obtaining better ests. of the free-energy differences. By recasting the Ferrenberg-Swendsen Multiple Histogram equations in a form suitable for mol. mechanics type Hamiltonians, we have demonstrated the feasibility and robustness of this method by applying it to a test problem of the generation of the Potential of Mean Force profile of the pseudorotation phase angle of the sugar ring in deoxyadenosine.
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Torrie, G. M.; Valleau, J. P. Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling. J. Comput. Phys. 1977, 23, 187– 199, DOI: 10.1016/0021-9991(77)90121-8
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Phillips, R.; Kondev, J.; Theriot, J.; Garcia, H. Physical Biology of the Cell, 2nd ed.; Garland Science: New York, 2012; p 1088.
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Hanke, F.; Serr, A.; Kreuzer, H. J.; Netz, R. R. Stretching single polypeptides: The effect of rotational constraints in the backbone. Europhys. Lett. 2010, 92, 53001 DOI: 10.1209/0295-5075/92/53001
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Kitov, P. I.; Bundle, D. R. On the nature of the multivalency effect: a thermodynamic model. J. Am. Chem. Soc. 2003, 125, 16271– 16284, DOI: 10.1021/ja038223n
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On the Nature of the Multivalency Effect: A Thermodynamic Model
Kitov, Pavel I.; Bundle, David R.
Journal of the American Chemical Society (2003), 125 (52), 16271-16284CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
A quant. model is proposed for the anal. of the thermodn. parameters of multivalent interactions in dil. solns. or with immobilized multimeric receptor. The model takes into account all bound species and describes multivalent binding via two microscopic binding energies corresponding to inter- and intramol. interactions (ΔG°inter and ΔG°intra), the relative contributions of which depend on the distribution of complexes with different nos. of occupied binding sites. The third component of the overall free energy, which we call the "avidity entropy" term, is a function of the degeneracy of bound states, Ωi, which is calcd. on the basis of the topol. of interaction and the distribution of all bound species. This term grows rapidly with the no. of receptor sites and ligand multivalency, it always favors binding, and explains why multivalency can overcome the loss of conformational entropy when ligands displayed at the ends of long tethers are bound. The microscopic parameters ΔG°inter and ΔG°intra may be detd. from the obsd. binding energies for a set of oligovalent ligands by nonlinear fitting with the theor. model. Here binding data obtained from two series of oligovalent carbohydrate inhibitors for Shiga-like toxins were used to verify the theory. The decavalent and octavalent inhibitors exhibit subnanomolar activity and are the most active sol. inhibitors yet seen that block Shiga-like toxin binding to its native receptor. The theory developed here in conjunction with our protocol for the optimization of tether length provides a predictive approach to design and maximize the avidity of multivalent ligands.
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Zumbro, E.; Witten, J.; Alexander-Katz, A. Computational insights into avidity of polymeric multivalent binders. Biophys. J. 2019, 117, 892– 902, DOI: 10.1016/j.bpj.2019.07.026
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Computational Insights into Avidity of Polymeric Multivalent Binders
Zumbro, Emiko; Witten, Jacob; Alexander-Katz, Alfredo
Biophysical Journal (2019), 117 (5), 892-902CODEN: BIOJAU; ISSN:0006-3495. (Cell Press)
Multivalent binding interactions are commonly found throughout biol. to enhance weak monovalent binding such as between glycoligands and protein receptors. Designing multivalent polymers to bind to viruses and toxic proteins is a promising avenue for inhibiting their attachment and subsequent infection of cells. Several studies have focused on oligomeric multivalent inhibitors and how changing parameters such as ligand shape, size, linker length, and flexibility affect binding. However, exptl. studies of how larger structural parameters of multivalent polymers, such as d.p., affect binding avidity to targets have mixed results, with some finding an improvement with longer polymers and some finding no effect. Here, we use Brownian dynamics simulations to provide a theor. understanding of how the d.p. affects the binding avidity of multivalent polymers. We show that longer polymers increase binding avidity to multivalent targets but reach a limit in binding avidity at high ds.p. We also show that when interacting with multiple targets simultaneously, longer polymers are able to use intertarget interactions to promote clustering and improve binding efficiency. We expect our results to narrow the design space for optimizing the structure and effectiveness of multivalent inhibitors as well as be useful to understand biol. design strategies for multivalent binding.
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Qiao, B.; Jiménez-Ángeles, F.; Nguyen, T. D.; Olvera de la Cruz, M. Water follows polar and nonpolar protein surface domains. Proc. Natl. Acad. Sci. U.S.A. 2019, 116, 19274– 19281, DOI: 10.1073/pnas.1910225116
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Water follows polar and nonpolar protein surface domains
Qiao, Baofu; Jimenez-Angeles, Felipe; Nguyen, Trung Dac; de la Cruz, Monica Olvera
Proceedings of the National Academy of Sciences of the United States of America (2019), 116 (39), 19274-19281CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
The conformation of water around proteins is of paramount importance, as it dets. protein interactions. Although the av. water properties around the surface of proteins have been provided exptl. and computationally, protein surfaces are highly heterogeneous. Therefore, it is crucial to det. the correlations of water to the local distributions of polar and nonpolar protein surface domains to understand functions such as aggregation, mutations, and delivery. By using atomistic simulations, we investigate the orientation and dynamics of water mols. next to 4 types of protein surface domains: neg. charged, pos. charged, and charge-neutral polar and nonpolar amino acids. The neg. charged amino acids orient around 98% of the neighboring water dipoles toward the protein surface, and such correlation persists up to around 16 Å from the protein surface. The pos. charged amino acids orient around 94% of the nearest water dipoles against the protein surface, and the correlation persists up to around 12 Å. The charge-neutral polar and nonpolar amino acids are also orienting the water neighbors in a quant. weaker manner. A similar trend was obsd. in the residence time of the nearest water neighbors. These findings hold true for 3 tech. important enzymes (PETase, cytochrome P 450, and organophosphorus hydrolase). Our results demonstrate that the water-amino acid degree of correlation follows the same trend as the amino acid contribution in proteins soly., namely, the neg. charged amino acids are the most beneficial for protein soly., then the pos. charged amino acids, and finally the charge-neutral amino acids.
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Manning, G. S. Limiting laws and counterion condensation in polyelectrolyte solutions I. Colligative properties. J. Chem. Phys. 1969, 51, 924– 933, DOI: 10.1063/1.1672157
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Limiting laws and counterion condensation in polyelectroyte solutions. I. Colligative properties
Manning, Gerald S.
Journal of Chemical Physics (1969), 51 (3), 924-33CODEN: JCPSA6; ISSN:0021-9606.
Formulas are derived for the osmotic coeff., the Donnan salt-exclusion factor, and the mobile-ion activity coeffs. in a polyelectrolyte soln. with or without added sample salt. The formulas, which contain no adjustable parameters, are based on the (theoretical) observation by several workers that counterions will "condense" on the polyion until the charge d. on the polyion is reduced below a certain crit. value. The uncondensed mobile ions are treated in the Debye-Hueckel approxn. In a restricted sense, the formulas are "limiting laws," and this aspect is discussed at length. Detailed comparison with exptl. data in the literature is given; agreement of the theory with expt. is usually quant.
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Fenley, M. O.; Manning, G. S.; Olson, W. K. Approach to the limit of counterion condensation. Biopolymers 1990, 30, 1191– 1203, DOI: 10.1002/bip.360301305
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Approach to the limit of counterion condensation
Fenley, Marcia O.; Manning, Gerald S.; Olson, Wilma K.
Biopolymers (1990), 30 (13-14), 1191-203CODEN: BIPMAA; ISSN:0006-3525.
According to counterion condensation theory, one of the contributions to the polyelectrolyte free energy is a pairwise sum of Debye-Hueckel potentials between polymer charges that are reduced by condensed counterions. When the polyion model is taken as an infinitely long and uniformly spaced line of charges, a simple closed expression for the summation, combined with entropy-derived mixing contributions, leads to the central result of the theory, a condensed fraction of counterions dependent only on the linear charge d. of the polyion and the valence of the counterion, stable against increases of salt up to concns. in excess of 0.1M. Here the sum is numerically evaluated for B-DNA models other than the infinite line of B-DNA charges. For a finite-length line there are end effects at low salt. The condensation limit is reached as a flat plateau by increasing the salt concn. At a fixed salt concn. the condensation limit is reached by increasing the length of the line. At moderate salt even very short B-DNA line-model oligomers have condensed fractions not far from the infinite polymer limit. For a long double-helical array with charge coordinates at the phosphates of B-DNA, the limiting condensed fraction appears to be approached at low salt. In contrast to the results for the line of charges, however, the computed condensed fraction varies strongly with salt in the range of exptl. typical concns. Salt invariance is restored, in agreement with both the line model and exptl. data, when dielec. satn. is considered by means of a distance-dependent dielec. function. For sufficiently long B-DNA line and helical models, at typical salt concns., the counterion binding fraction approaches the polymer limit as a linear function of 1/P, where P is the no. of phosphate groups of B-DNA.
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Walkowiak, J. J.; Ballauff, M. Interaction of polyelectrolytes with proteins: quantifying the role of water. Adv. Sci. 2021, 8, 2100661 DOI: 10.1002/advs.202100661
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Interaction of Polyelectrolytes with Proteins: Quantifying the Role of Water
Walkowiak, Jacek J.; Ballauff, Matthias
Advanced Science (Weinheim, Germany) (2021), 8 (12), 2100661CODEN: ASDCCF; ISSN:2198-3844. (Wiley-VCH Verlag GmbH & Co. KGaA)
A theor. model is presented for the free energy ΔGb of complex formation between a highly charged polyelectrolyte and a protein. The model introduced here comprises both the effect of released counterions and the uptake or release of water mols. during complex formation. The resulting expression for ΔGb is hence capable of describing the dependence of ΔGb on temp. as well as on the concn. of salt in the system: An increase of the salt concn. in the soln. increases the activity of the ions and counterion release becomes less effective for binding. On the other hand, an increased salt concn. leads to the decrease of the activity of water in bulk. Hence, release of water mols. during complex formation will be more advantageous and lead to an increase of the magnitude of ΔGb and the binding const. It is furthermore demonstrated that the release or uptake of water mols. is the origin of the marked enthalpy-entropy cancellation obsd. during complex formation of polyelectrolytes with proteins. The comparison with exptl. data on complex formation between a synthetic (sulfated dendritic polyglycerol) and natural polyelectrolytes (DNA; heparin) with proteins shows full agreement with theory.
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Irudayam, S. J.; Henchman, R. H. Entropic cost of protein- ligand binding and its dependence on the entropy in solution. J. Phys. Chem. B 2009, 113, 5871– 5884, DOI: 10.1021/jp809968p
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Entropic Cost of Protein-Ligand Binding and Its Dependence on the Entropy in Solution
Irudayam, Sheeba Jem; Henchman, Richard H.
Journal of Physical Chemistry B (2009), 113 (17), 5871-5884CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
Two theor. formulations are proposed and compared for the loss of translational and rotational entropy upon protein-ligand binding in water. The two theories share the same approach to evaluate the translational and rotational entropy of the ligand when bound. The potential of the bound ligand is modeled by six harmonic oscillators that are parametrized from the force and torque magnitudes measured in a mol. dynamics simulation, yielding vibrational and librational entropies. In the aq. phase, the theories differ because there is no unique way to assign the total entropy to mols. in soln. In one approach, the ligand is allowed unrestricted access to the full soln. vol. at the std. concn. and is assigned the same translational and rotational entropy as if it were an ideal gas. We term this a "mol.-frame" (MF) theory because it considers configurational space in the ref. frame of the mol. of interest. The entropy of the solvent is penalized because it is excluded from the mol.'s vol. In the second theory, all mols. including the solvent are confined by their neighbors in mean-field configurational vols. This we term a "system-frame" (SF) theory because the configurational space available to all mols. is considered in the ref. frame of the whole system. Mols. have vibrational and librational entropy in the same way as they do when bound. In addn., the discrete size of the solvent mols. quantizes the configurational space into an effective no. of min. according to the solute mol.'s std. concn. and the mean vol. of a solvent mol. This leads to the cratic entropy expressed in terms of the solute mol.'s mole fraction. The equivalent no. of min. in rotational space depends on both the solute mol.'s vol. and the solvent mol.'s vol. This leads to an equation for the orientational entropy based on the proposed concept of "angle fraction". The MF and SF theories are applied to calc. the translational and rotational entropy losses involved in the formation of six different protein-ligand complexes, in two of which the ligand is water. The MF entropy losses range from -80 to -142 J K-1 mol-1 for ligands at the 1 M std.-state concn. and from -52 to -63 J K-1 mol-1 for water at the 55.6 M std.-state concn. They depend logarithmically on both the no. and strength of interactions between the ligand and protein through the forces and torques. This is obsd. to lead to moderate dependencies on the ligands' moments of inertia and masses. The SF entropy losses are smaller and range from -50 to -75 J K-1 mol-1 for ligands at the 1 M std.-state concn. and from 0 to -12 J K-1 mol-1 for water. They depend logarithmically on the ligand solvent's mol. vol. and weakly on the relative strengths of the ligand's interactions with the protein and water. The cratic entropy loss in water at the std. concn. is const. and is also demonstrated to be implicit in MF theories. Entropy losses from the two approaches are also compared with those from other computational approaches and with expt. The use of the force and torque magnitudes leads to smaller bound vols. than are obtained from ligand-displacement approaches. The general agreement of the SF entropy losses with those from expt. suggests that the SF theory is more consistent with the assumptions made in exptl. measurements than the MF solvation theories, which would require a compensating entropy gain in the solvent in order to agree.
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Xu, X.; Ran, Q.; Dey, P.; Nikam, R.; Haag, R.; Ballauff, M.; Dzubiella, J. Counterion-release entropy governs the inhibition of serum proteins by polyelectrolyte drugs. Biomacromolecules 2018, 19, 409– 416, DOI: 10.1021/acs.biomac.7b01499
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Counterion-Release Entropy Governs the Inhibition of Serum Proteins by Polyelectrolyte Drugs
Xu, Xiao; Ran, Qidi; Dey, Pradip; Nikam, Rohit; Haag, Rainer; Ballauff, Matthias; Dzubiella, Joachim
Biomacromolecules (2018), 19 (2), 409-416CODEN: BOMAF6; ISSN:1525-7797. (American Chemical Society)
Dendritic polyelectrolytes constitute high potential drugs and carrier systems for biomedical purposes. Still, their biomol. interaction modes, in particular those detg. the binding affinity to proteins, have not been rationalized. We study the interaction of the drug candidate dendritic polyglycerol sulfate (dPGS) with serum proteins using isothermal titrn. calorimetry (ITC) interpreted and complemented with mol. computer simulations. Lysozyme is first studied as a well-defined model protein to verify theor. concepts, which are then applied to the important cell adhesion protein family of selectins. We demonstrate that the driving force of the strong complexation, leading to a distinct protein corona, originates mainly from the release of only a few condensed counterions from the dPGS upon binding. The binding const. shows a surprisingly weak dependence on dPGS size (and bare charge) which can be understood by colloidal charge-renormalization effects and by the fact that the magnitude of the dominating counterion-release mechanism almost exclusively depends on the interfacial charge structure of the protein-specific binding patch. Our findings explain the high selectivity of P- and L-selectins over E-selectin for dPGS to act as a highly anti-inflammatory drug. The entire anal. demonstrates that the interaction of proteins with charged polymeric drugs can be predicted by simulations with unprecedented accuracy. Thus, our results open new perspectives for the rational design of charged polymeric drugs and carrier systems.
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Caro, J. A.; Harpole, K. W.; Kasinath, V.; Lim, J.; Granja, J.; Valentine, K. G.; Sharp, K. A.; Wand, A. J. Entropy in molecular recognition by proteins. Proc. Natl. Acad. Sci. U.S.A. 2017, 114, 6563– 6568, DOI: 10.1073/pnas.1621154114
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Entropy in molecular recognition by proteins
Caro, Jose A.; Harpole, Kyle W.; Kasinath, Vignesh; Lim, Jackwee; Granja, Jeffrey; Valentine, Kathleen G.; Sharp, Kim A.; Wand, A. Joshua
Proceedings of the National Academy of Sciences of the United States of America (2017), 114 (25), 6563-6568CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
Mol. recognition by proteins is fundamental to mol. biol. Dissection of the thermodn. energy terms governing protein-ligand interactions has proven difficult, with detn. of entropic contributions being particularly elusive. NMR relaxation measurements have suggested that changes in protein conformational entropy can be quant. obtained through a dynamical proxy, but the generality of this relationship has not been shown. Twenty-eight protein-ligand complexes are used to show a quant. relationship between measures of fast side-chain motion and the underlying conformational entropy. We find that the contribution of conformational entropy can range from favorable to unfavorable, which demonstrates the potential of this thermodn. variable to modulate protein-ligand interactions. For about one-quarter of these complexes, the absence of conformational entropy would render the resulting affinity biol. meaningless. The dynamical proxy for conformational entropy or "entropy meter" also allows for refinement of the contributions of solvent entropy and the loss in rotational-translational entropy accompanying formation of high-affinity complexes. Furthermore, structure-based application of the approach can also provide insight into long-lived specific water-protein interactions that escape the generic treatments of solvent entropy based simply on changes in accessible surface area. These results provide a comprehensive and unified view of the general role of entropy in high-affinity mol. recognition by proteins.
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Sahoo, A. K.; Schreiber, F.; Netz, R. R.; Maiti, P. K. Role of entropy in determining the phase behavior of protein solutions induced by multivalent ions. Soft Matter 2022, 18, 592– 601, DOI: 10.1039/D1SM00730K
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Rapaport, D. Hydrogen bonds in water: Network organization and lifetimes. Mol. Phys. 1983, 50, 1151– 1162, DOI: 10.1080/00268978300102931
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Hydrogen bonds in water. Network organization and lifetimes
Rapaport, D. C.
Molecular Physics (1983), 50 (5), 1151-62CODEN: MOPHAM; ISSN:0026-8976.
Equil. and dynamical properties of H bonds in liq. H2O are analyzed using the results of mol. dynamics simulations of the MCY-CI model. Properties of the H bond clusters as functions of temp. are described. The connectivity of the clusters is analyzed in terms of the bridgeless polygons which are formed by the bonds. The problem of obtaining a meaningful definition of bond lifetime is discussed, and the results of lifetime measurements based on alternative definitions are shown.
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Malicka, W.; Haag, R.; Ballauff, M. Interaction of heparin with proteins: hydration effects. J. Phys. Chem. B 2022, 126, 6250– 6260, DOI: 10.1021/acs.jpcb.2c04928
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Geisler, M.; Xiao, S.; Puchner, E. M.; Gräter, F.; Hugel, T. Controlling the structure of proteins at surfaces. J. Am. Chem. Soc. 2010, 132, 17277– 17281, DOI: 10.1021/ja107212z
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Controlling the Structure of Proteins at Surfaces
Geisler, Michael; Xiao, Sen-Bo; Puchner, Elias M.; Graeter, Frauke; Hugel, Thorsten
Journal of the American Chemical Society (2010), 132 (48), 17277-17281CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
With the help of single mol. force spectroscopy and mol. dynamics simulations, we det. the surface-induced structure of a single engineered spider silk protein. An amyloid like structure is induced in the vicinity of a surface with high surface energy and can be prohibited in the presence of a hydrophobic surface. The derived mol. energy landscapes highlight the role of single silk protein structure for the macroscopic toughness of spider silk.
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Liese, S.; Netz, R. R. Influence of length and flexibility of spacers on the binding affinity of divalent ligands. Beilstein J. Org. Chem. 2015, 11, 804– 816, DOI: 10.3762/bjoc.11.90
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Influence of length and flexibility of spacers on the binding affinity of divalent ligands
Liese, Susanne; Netz, Roland R.
Beilstein Journal of Organic Chemistry (2015), 11 (), 804-816CODEN: BJOCBH; ISSN:1860-5397. (Beilstein-Institut zur Foerderung der Chemischen Wissenschaften)
We present a quant. model for the binding of divalent ligand-receptor systems. We study the influence of length and flexibility of the spacers on the overall binding affinity and derive general rules for the optimal ligand design. To this end, we first compare different polymeric models and det. the probability to simultaneously bind to two neighboring receptor binding pockets. In a second step the binding affinity of divalent ligands in terms of the IC50 value is derived. We find that a divalent ligand has the potential to bind more efficiently than its monovalent counterpart only, if the monovalent dissocn. const. is lower than a crit. value. This crit. monovalent dissocn. const. depends on the ligand-spacer length and flexibility as well as on the size of the receptor. Regarding the optimal ligand-spacer length and flexibility, we find that the av. spacer length should be equal or slightly smaller than the distance between the receptor binding pockets and that the end-to-end spacer length fluctuations should be in the same range as the size of a receptor binding pocket.
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Jo, S.; Kim, T.; Iyer, V. G.; Im, W. CHARMM-GUI: a web-based graphical user interface for CHARMM. J. Comput. Chem. 2008, 29, 1859– 1865, DOI: 10.1002/jcc.20945
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CHARMM-GUI: a web-based graphical user interface for CHARMM
Jo, Sunhwan; Kim, Taehoon; Iyer, Vidyashankara G.; Im, Wonpil
Journal of Computational Chemistry (2008), 29 (11), 1859-1865CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
CHARMM is an academic research program used widely for macromol. mechanics and dynamics with versatile anal. and manipulation tools of at. coordinates and dynamics trajectories. CHARMM-GUI, http://www.charmm-gui.org, has been developed to provide a web-based graphical user interface to generate various input files and mol. systems to facilitate and standardize the usage of common and advanced simulation techniques in CHARMM. The web environment provides an ideal platform to build and validate a mol. model system in an interactive fashion such that, if a problem is found through visual inspection, one can go back to the previous setup and regenerate the whole system again. In this article, we describe the currently available functional modules of CHARMM-GUI Input Generator that form a basis for the advanced simulation techniques. Future directions of the CHARMM-GUI development project are also discussed briefly together with other features in the CHARMM-GUI website, such as Archive and Movie Gallery.
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Park, S.-J.; Lee, J.; Qi, Y.; Kern, N. R.; Lee, H. S.; Jo, S.; Joung, I.; Joo, K.; Lee, J.; Im, W. CHARMM-GUI Glycan Modeler for modeling and simulation of carbohydrates and glycoconjugates. Glycobiology 2019, 29, 320– 331, DOI: 10.1093/glycob/cwz003
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CHARMM-GUI Glycan Modeler for modeling and simulation of carbohydrates and glycoconjugates
Park, Sang-Jun; Lee, Jumin; Qi, Yifei; Kern, Nathan R.; Lee, Hui Sun; Jo, Sunhwan; Joung, Insuk; Joo, Keehyung; Lee, Jooyoung; Im, Wonpil
Glycobiology (2019), 29 (4), 320-331CODEN: GLYCE3; ISSN:1460-2423. (Oxford University Press)
Characterizing glycans and glycoconjugates in context of three-dimensional structures is important in understanding their biol. roles and developing efficient therapeutic agents. Computational modeling and mol. simulation have become essential tool complementary to exptl. methods. Here, we present computational tool, Glycan Modeler for in silico N-/O-glycosylation of target protein and generation of carbohydrate-only systems. In our previous study, we developed Glycan Reader, web-based tool for detecting carbohydrate mols. from PDB structure and generation of simulation system and input files. As integrated into Glycan Reader in CHARMM-GUI, Glycan Modeler enables to generate structures of glycans and glycoconjugates for given glycan sequences and glycosylation sites using PDB glycan template structures from Glycan Fragment Database (http://glycanstructure.org/ fragment-db). Our benchmark tests demonstrate universal applicability of Glycan Reader & Modeler to various glycan sequences and target proteins. We also investigated structural properties of modeled glycan structures by running 2-μs mol. dynamics simulations of HIV envelope protein. Simulations show that modeled glycan structures built by Glycan Reader & Modeler have similar structural features compared to ones solved by X-ray crystallog. We also describe representative examples of glycoconjugate modeling with video demos to illustrate practical applications of Glycan Reader & Modeler.
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Jo, S.; Song, K. C.; Desaire, H.; MacKerell, A. D., Jr; Im, W. Glycan Reader: automated sugar identification and simulation preparation for carbohydrates and glycoproteins. J. Comput. Chem. 2011, 32, 3135– 3141, DOI: 10.1002/jcc.21886
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Glycan Reader: Automated sugar identification and simulation preparation for carbohydrates and glycoproteins
Jo, Sunhwan; Song, Kevin C.; Desaire, Heather; MacKerell, Alexander D.; Im, Wonpil
Journal of Computational Chemistry (2011), 32 (14), 3135-3141CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
Understanding how glycosylation affects protein structure, dynamics, and function is an emerging and challenging problem in biol. As a first step toward glycan modeling in the context of structural glycobiol., the authors have developed Glycan Reader and integrated it into the CHARMM-GUI,. Glycan Reader greatly simplifies the reading of PDB structure files contg. glycans through (i) detection of carbohydrate mols., (ii) automatic annotation of carbohydrates based on their three-dimensional structures, (iii) recognition of glycosidic linkages between carbohydrates as well as N-/O-glycosidic linkages to proteins, and (iv) generation of inputs for the biomol. simulation program CHARMM with the proper glycosidic linkage setup. In addn., Glycan Reader is linked to other functional modules in CHARMM-GUI, allowing users to easily generate carbohydrate or glycoprotein mol. simulation systems in soln. or membrane environments and visualize the electrostatic potential on glycoprotein surfaces. These tools are useful for studying the impact of glycosylation on protein structure and dynamics. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011.
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Park, S.-J.; Lee, J.; Patel, D. S.; Ma, H.; Lee, H. S.; Jo, S.; Im, W. Glycan Reader is improved to recognize most sugar types and chemical modifications in the Protein Data Bank. Bioinformatics 2017, 33, 3051– 3057, DOI: 10.1093/bioinformatics/btx358
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Glycan Reader is improved to recognize most sugar types and chemical modifications in the Protein Data Bank
Park, Sang-Jun; Lee, Jumin; Patel, Dhilon S.; Ma, Hongjing; Lee, Hui Sun; Jo, Sunhwan; Im, Wonpil
Bioinformatics (2017), 33 (19), 3051-3057CODEN: BOINFP; ISSN:1367-4811. (Oxford University Press)
Motivation: Glycans play a central role in many essential biol. processes. Glycan Reader was originally developed to simplify the reading of Protein Data Bank (PDB) files contg. glycans through the automatic detection and annotation of sugars and glycosidic linkages between sugar units and to proteins, all based on at. coordinates and connectivity information. Carbohydrates can have various chem. modifications at different positions, making their chem. space much diverse. Unfortunately, current PDB files do not provide exact annotations for most carbohydrate derivs. and more than 50% of PDB glycan chains have at least one carbohydrate deriv. that could not be correctly recognized by the original Glycan Reader. Results: Glycan Reader has been improved and now identifies most sugar types and chem. modifications (including various glycolipids) in the PDB, and both PDB and PDBx/mmCIF formats are supported. CHARMM-GUI Glycan Reader is updated to generate the simulation system and input of various glycoconjugates with most sugar types and chem. modifications. It also offers a new functionality to edit the glycan structures through addn./deletion/modification of glycosylation types, sugar types, chem. modifications, glycosidic linkages, and anomeric states. The simulation system and input files can be used for CHARMM, NAMD, GROMACS, AMBER, GENESIS, LAMMPS, Desmond, OpenMM, and CHARMM/OpenMM. Glycan Fragment Database in GlycanStructure.Org is also updated to provide an intuitive glycan sequence search tool for complex glycan structures with various chem. modifications in the PDB.
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Hanwell, M. D.; Curtis, D. E.; Lonie, D. C.; Vandermeersch, T.; Zurek, E.; Hutchison, G. R. Avogadro: an advanced semantic chemical editor, visualization, and analysis platform. J. Cheminf. 2012, 4, 1– 17, DOI: 10.1186/1758-2946-4-17
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Huang, J.; Rauscher, S.; Nawrocki, G.; Ran, T.; Feig, M.; De Groot, B. L.; Grubmüller, H.; MacKerell, A. D. CHARMM36m: an improved force field for folded and intrinsically disordered proteins. Nat. Methods 2017, 14, 71– 73, DOI: 10.1038/nmeth.4067
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CHARMM36m: an improved force field for folded and intrinsically disordered proteins
Huang, Jing; Rauscher, Sarah; Nawrocki, Grzegorz; Ran, Ting; Feig, Michael; de Groot, Bert L.; Grubmuller, Helmut; MacKerell, Alexander D. Jr
Nature Methods (2017), 14 (1), 71-73CODEN: NMAEA3; ISSN:1548-7091. (Nature Publishing Group)
The all-atom additive CHARMM36 protein force field is widely used in mol. modeling and simulations. We present its refinement, CHARMM36m (http://mackerell.umaryland.edu/charmm_ff.shtml), with improved accuracy in generating polypeptide backbone conformational ensembles for intrinsically disordered peptides and proteins.
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Guvench, O.; Mallajosyula, S. S.; Raman, E. P.; Hatcher, E.; Vanommeslaeghe, K.; Foster, T. J.; Jamison, F. W.; MacKerell, A. D., Jr CHARMM additive all-atom force field for carbohydrate derivatives and its utility in polysaccharide and carbohydrate-protein modeling. J. Chem. Theory Comput. 2011, 7, 3162– 3180, DOI: 10.1021/ct200328p
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CHARMM Additive All-Atom Force Field for Carbohydrate Derivatives and Its Utility in Polysaccharide and Carbohydrate-Protein Modeling
Guvench, Olgun; Mallajosyula, Sairam S.; Raman, E. Prabhu; Hatcher, Elizabeth; Vanommeslaeghe, Kenno; Foster, Theresa J.; Jamison, Francis W.; MacKerell, Alexander D.
Journal of Chemical Theory and Computation (2011), 7 (10), 3162-3180CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
Monosaccharide derivs. such as xylose, fucose, N-acetylglucosamine (GlcNAc), N-acetylgalactosamine (GlaNAc), glucuronic acid, iduronic acid, and N-acetylneuraminic acid (Neu5Ac) are important components of eukaryotic glycans. The present work details the development of force-field parameters for these monosaccharides and their covalent connections to proteins via O linkages to serine or threonine side chains and via N linkages to asparagine side chains. The force field development protocol was designed to explicitly yield parameters that are compatible with the existing CHARMM additive force field for proteins, nucleic acids, lipids, carbohydrates, and small mols. Therefore, when combined with previously developed parameters for pyranose and furanose monosaccharides, for glycosidic linkages between monosaccharides, and for proteins, the present set of parameters enables the mol. simulation of a wide variety of biol. important mols. such as complex carbohydrates and glycoproteins. Parametrization included fitting to quantum mech. (QM) geometries and conformational energies of model compds., as well as to QM pair interaction energies and distances of model compds. with water. Parameters were validated in the context of crystals of relevant monosaccharides, as well NMR and/or x-ray crystallog. data on larger systems including oligomeric hyaluronan, sialyl Lewis X, O- and N-linked glycopeptides, and a lectin:sucrose complex. As the validated parameters are an extension of the CHARMM all-atom additive biomol. force field, they further broaden the types of heterogeneous systems accessible with a consistently developed force-field model.
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Mallajosyula, S. S.; Guvench, O.; Hatcher, E.; MacKerell, A. D., Jr CHARMM additive all-atom force field for phosphate and sulfate linked to carbohydrates. J. Chem. Theory Comput. 2012, 8, 759– 776, DOI: 10.1021/ct200792v
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CHARMM Additive All-Atom Force Field for Phosphate and Sulfate Linked to Carbohydrates
Mallajosyula, Sairam S.; Guvench, Olgun; Hatcher, Elizabeth; MacKerell, Alexander D.
Journal of Chemical Theory and Computation (2012), 8 (2), 759-776CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
Presented is an extension of the CHARMM additive all-atom carbohydrate force field to enable the modeling of phosphate and sulfate linked to carbohydrates. The parameters are developed in a hierarchical fashion using model compds. contg. the key atoms in the full carbohydrates. Target data for parameter optimization included full two-dimensional energy surfaces defined by the glycosidic dihedral angle pairs in the phosphate/sulfate model compd. analogs of hexopyranose monosaccharide phosphates and sulfates, as detd. by quantum mech. (QM) MP2/cc-pVTZ single point energies on MP2/6-31+G(d) optimized structures. To achieve balanced, transferable dihedral parameters for the dihedral angles, surfaces for all possible anomeric and conformational states were included during the parametrization process. To model physiol. relevant systems, both the mono- and dianionic charged states were studied for the phosphates. This resulted in over 7000 MP2/cc-pVTZ//MP2/6-31G+(d) model compd. conformational energies which, supplemented with QM geometries, were the main target data for the parametrization. Parameters were validated against crystals of relevant monosaccharide derivs. obtained from the Cambridge Structural Database (CSD) and larger systems, inositol-(tri/tetra/penta) phosphates noncovalently bound to the pleckstrin homol. (PH) domain and oligomeric chondroitin sulfate in soln. and in complex with cathepsin K protein.
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Vanommeslaeghe, K.; Hatcher, E.; Acharya, C.; Kundu, S.; Zhong, S.; Shim, J.; Darian, E.; Guvench, O.; Lopes, P.; Vorobyov, I.; Mackerell, A. D. CHARMM general force field: A force field for drug-like molecules compatible with the CHARMM all-atom additive biological force fields. J. Comput. Chem. 2010, 31, 671– 690, DOI: 10.1002/jcc.21367
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CHARMM general force field: A force field for drug-like molecules compatible with the CHARMM all-atom additive biological force fields
Vanommeslaeghe, K.; Hatcher, E.; Acharya, C.; Kundu, S.; Zhong, S.; Shim, J.; Darian, E.; Guvench, O.; Lopes, P.; Vorobyov, I.; Mackerell, A. D., Jr.
Journal of Computational Chemistry (2010), 31 (4), 671-690CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
The widely used CHARMM additive all-atom force field includes parameters for proteins, nucleic acids, lipids, and carbohydrates. In the present article, an extension of the CHARMM force field to drug-like mols. is presented. The resulting CHARMM General Force Field (CGenFF) covers a wide range of chem. groups present in biomols. and drug-like mols., including a large no. of heterocyclic scaffolds. The parametrization philosophy behind the force field focuses on quality at the expense of transferability, with the implementation concg. on an extensible force field. Statistics related to the quality of the parametrization with a focus on exptl. validation are presented. Addnl., the parametrization procedure, described fully in the present article in the context of the model systems, pyrrolidine, and 3-phenoxymethyl-pyrrolidine will allow users to readily extend the force field to chem. groups that are not explicitly covered in the force field as well as add functional groups to and link together mols. already available in the force field. CGenFF thus makes it possible to perform "all-CHARMM" simulations on drug-target interactions thereby extending the utility of CHARMM force fields to medicinally relevant systems. © 2009 Wiley Periodicals, Inc.J Comput Chem, 2010.
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Yu, W.; He, X.; Vanommeslaeghe, K.; MacKerell, A. D., Jr Extension of the CHARMM general force field to sulfonyl-containing compounds and its utility in biomolecular simulations. J. Comput. Chem. 2012, 33, 2451– 2468, DOI: 10.1002/jcc.23067
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Extension of the CHARMM general force field to sulfonyl-containing compounds and its utility in biomolecular simulations
Yu, Wenbo; He, Xibing; Vanommeslaeghe, Kenno; MacKerell, Alexander D.
Journal of Computational Chemistry (2012), 33 (31), 2451-2468CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
Presented is an extension of the CHARMM General Force Field (CGenFF) to enable the modeling of sulfonyl-contg. compds. Model compds. contg. chem. moieties such as sulfone, sulfonamide, sulfonate, and sulfamate were used as the basis for the parameter optimization. Targeting high-level quantum mech. and exptl. crystal data, the new parameters were optimized in a hierarchical fashion designed to maintain compatibility with the remainder of the CHARMM additive force field. The optimized parameters satisfactorily reproduced equil. geometries, vibrational frequencies, interactions with water, gas phase dipole moments, and dihedral potential energy scans. Validation involved both cryst. and liq. phase calcns. showing the newly developed parameters to satisfactorily reproduce exptl. unit cell geometries, crystal intramol. geometries, and pure solvent densities. The force field was subsequently applied to study conformational preference of a sulfonamide-based peptide system. Good agreement with exptl. IR/NMR data further validated the newly developed CGenFF parameters as a tool to investigate the dynamic behavior of sulfonyl groups in a biol. environment. CGenFF now covers sulfonyl group contg. moieties allowing for modeling and simulation of sulfonyl-contg. compds. in the context of biomol. systems including compds. of medicinal interest.
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Vanommeslaeghe, K.; MacKerell, A. D., Jr Automation of the CHARMM General Force Field (CGenFF) I: bond perception and atom typing. J. Chem. Inf. Model. 2012, 52, 3144– 3154, DOI: 10.1021/ci300363c
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Automation of the CHARMM General Force Field (CGenFF) I: Bond Perception and Atom Typing
Vanommeslaeghe, K.; MacKerell, A. D.
Journal of Chemical Information and Modeling (2012), 52 (12), 3144-3154CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
Mol. mechanics force fields are widely used in computer-aided drug design for the study of drug-like mols. alone or interacting with biol. systems. In simulations involving biol. macromols., the biol. part is typically represented by a specialized biomol. force field, while the drug is represented by a matching general (org.) force field. In order to apply these general force fields to an arbitrary drug-like mol., functionality for assignment of atom types, parameters, and charges is required. In the present article, which is part I of a series of two, we present the algorithms for bond perception and atom typing for the CHARMM General Force Field (CGenFF). The CGenFF atom typer first assocs. attributes to the atoms and bonds in a mol., such as valence, bond order, and ring membership among others. Of note are a no. of features that are specifically required for CGenFF. This information is then used by the atom typing routine to assign CGenFF atom types based on a programmable decision tree. This allows for straight-forward implementation of CGenFF's complicated atom typing rules and for equally straight-forward updating of the atom typing scheme as the force field grows. The presented atom typer was validated by assigning correct atom types on 477 model compds. including in the training set as well as 126 test-set mols. that were constructed to specifically verify its different components. The program may be utilized via an online implementation at https://www.paramchem.org/.
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Vanommeslaeghe, K.; Raman, E. P.; MacKerell, A. D., Jr Automation of the CHARMM General Force Field (CGenFF) II: assignment of bonded parameters and partial atomic charges. J. Chem. Inf. Model. 2012, 52, 3155– 3168, DOI: 10.1021/ci3003649
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Automation of the CHARMM General Force Field (CGenFF) II: Assignment of Bonded Parameters and Partial Atomic Charges
Vanommeslaeghe, K.; Raman, E. Prabhu; MacKerell, A. D.
Journal of Chemical Information and Modeling (2012), 52 (12), 3155-3168CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
Mol. mechanics force fields are widely used in computer-aided drug design for the study of drug candidates interacting with biol. systems. In these simulations, the biol. part is typically represented by a specialized biomol. force field, while the drug is represented by a matching general (org.) force field. In order to apply these general force fields to an arbitrary drug-like mol., functionality for assignment of atom types, parameters, and partial at. charges is required. In the present article, algorithms for the assignment of parameters and charges for the CHARMM General Force Field (CGenFF) are presented. These algorithms rely on the existing parameters and charges that were detd. as part of the parametrization of the force field. Bonded parameters are assigned based on the similarity between the atom types that define said parameters, while charges are detd. using an extended bond-charge increment scheme. Charge increments were optimized to reproduce the charges on model compds. that were part of the parametrization of the force field. Case studies are presented to clarify the functioning of the algorithms and the significance of their output data.
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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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MacKerell, A. D., Jr; Bashford, D.; Bellott, M.; Dunbrack, R. L., Jr; Evanseck, J. D.; Field, M. J.; Fischer, S.; Gao, J.; Guo, H.; Ha, S. All-atom empirical potential for molecular modeling and dynamics studies of proteins. J. Phys. Chem. B 1998, 102, 3586– 3616, DOI: 10.1021/jp973084f
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All-Atom Empirical Potential for Molecular Modeling and Dynamics Studies of Proteins
MacKerell, A. D., Jr.; Bashford, D.; Bellott, M.; Dunbrack, R. L.; Evanseck, J. D.; Field, M. J.; Fischer, S.; Gao, J.; Guo, H.; Ha, S.; Joseph-McCarthy, D.; Kuchnir, L.; Kuczera, K.; Lau, F. T. K.; Mattos, C.; Michnick, S.; Ngo, T.; Nguyen, D. T.; Prodhom, B.; Reiher, W. E., III; Roux, B.; Schlenkrich, M.; Smith, J. C.; Stote, R.; Straub, J.; Watanabe, M.; Wiorkiewicz-Kuczera, J.; Yin, D.; Karplus, M.
Journal of Physical Chemistry B (1998), 102 (18), 3586-3616CODEN: JPCBFK; ISSN:1089-5647. (American Chemical Society)
New protein parameters are reported for the all-atom empirical energy function in the CHARMM program. The parameter evaluation was based on a self-consistent approach designed to achieve a balance between the internal (bonding) and interaction (nonbonding) terms of the force field and among the solvent-solvent, solvent-solute, and solute-solute interactions. Optimization of the internal parameters used exptl. gas-phase geometries, vibrational spectra, and torsional energy surfaces supplemented with ab initio results. The peptide backbone bonding parameters were optimized with respect to data for N-methylacetamide and the alanine dipeptide. The interaction parameters, particularly the at. charges, were detd. by fitting ab initio interaction energies and geometries of complexes between water and model compds. that represented the backbone and the various side chains. In addn., dipole moments, exptl. heats and free energies of vaporization, solvation and sublimation, mol. vols., and crystal pressures and structures were used in the optimization. The resulting protein parameters were tested by applying them to noncyclic tripeptide crystals, cyclic peptide crystals, and the proteins crambin, bovine pancreatic trypsin inhibitor, and carbonmonoxy myoglobin in vacuo and in a crystal. A detailed anal. of the relationship between the alanine dipeptide potential energy surface and calcd. protein φ, χ angles was made and used in optimizing the peptide group torsional parameters. The results demonstrate that use of ab initio structural and energetic data by themselves are not sufficient to obtain an adequate backbone representation for peptides and proteins in soln. and in crystals. Extensive comparisons between mol. dynamics simulation and exptl. data for polypeptides and proteins were performed for both structural and dynamic properties. Calcd. data from energy minimization and dynamics simulations for crystals demonstrate that the latter are needed to obtain meaningful comparisons with exptl. crystal structures. The presented parameters, in combination with the previously published CHARMM all-atom parameters for nucleic acids and lipids, provide a consistent set for condensed-phase simulations of a wide variety of mols. of biol. interest.
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Venable, R. M.; Luo, Y.; Gawrisch, K.; Roux, B.; Pastor, R. W. Simulations of anionic lipid membranes: development of interaction-specific ion parameters and validation using NMR data. J. Phys. Chem. B 2013, 117, 10183– 10192, DOI: 10.1021/jp401512z
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Simulations of Anionic Lipid Membranes: Development of Interaction-Specific Ion Parameters and Validation Using NMR Data
Venable, Richard M.; Luo, Yun; Gawrisch, Klaus; Roux, Benoit; Pastor, Richard W.
Journal of Physical Chemistry B (2013), 117 (35), 10183-10192CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
Overbinding of ions to lipid head groups is a potentially serious artifact in simulations of charged lipid bilayers. In this study, the Lennard-Jones radii in the CHARMM force field for interactions of Na+ and lipid oxygen atoms of carboxyl, phosphate, and ester groups were revised to match osmotic pressure data on sodium acetate and electrophoresis data on palmitoyloleoyl phosphatidylcholine (POPC) vesicles. The new parameters were then validated by successfully reproducing previously published exptl. NMR deuterium order parameters for dimyristoyl phosphatidylglycerol (DMPG) and newly obtained values for palmitoyloleoyl phosphatidylserine (POPS). Although the increases in Lennard-Jones diams. are only 0.02-0.12 Å, they are sufficient to reduce Na+ binding, and thereby increase surface areas per lipid by 5-10% compared with the unmodified parameters.
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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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Bussi, G.; Donadio, D.; Parrinello, M. Canonical sampling through velocity rescaling. J. Chem. Phys. 2007, 126, 014101 DOI: 10.1063/1.2408420
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Canonical sampling through velocity rescaling
Bussi, Giovanni; Donadio, Davide; Parrinello, Michele
Journal of Chemical Physics (2007), 126 (1), 014101/1-014101/7CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
The authors present a new mol. dynamics algorithm for sampling the canonical distribution. In this approach the velocities of all the particles are rescaled by a properly chosen random factor. The algorithm is formally justified and it is shown that, in spite of its stochastic nature, a quantity can still be defined that remains const. during the evolution. In numerical applications this quantity can be used to measure the accuracy of the sampling. The authors illustrate the properties of this new method on Lennard-Jones and TIP4P water models in the solid and liq. phases. Its performance is excellent and largely independent of the thermostat parameter also with regard to the dynamic properties.
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Parrinello, M.; Rahman, A. Polymorphic transitions in single crystals: A new molecular dynamics method. J. Appl. Phys. 1981, 52, 7182– 7190, DOI: 10.1063/1.328693
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Polymorphic transitions in single crystals: A new molecular dynamics method
Parrinello, M.; Rahman, A.
Journal of Applied Physics (1981), 52 (12), 7182-90CODEN: JAPIAU; ISSN:0021-8979.
A Lagrangian formulation is introduced; it can be used to make mol. dynamics (MD) calcns. on systems under the most general, externally applied, conditions of stress. In this formulation the MD cell shape and size can change according to dynamic equations given by this Lagrangian. This MD technique was used to the study of structural transitions of a Ni single crystal under uniform uniaxial compressive and tensile loads. Some results regarding the stress-strain relation obtained by static calcns. are invalid at finite temp. Under compressive loading, the model of Ni shows a bifurcation in its stress-strain relation; this bifurcation provides a link in configuration space between cubic and hexagonal close packing. Such a transition could perhaps be obsd. exptl. under extreme conditions of shock.
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Hess, B. P-LINCS: A A parallel linear constraint solver for molecular simulation. J. Chem. Theory Comput. 2008, 4, 116– 122, DOI: 10.1021/ct700200b
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P-LINCS: A Parallel Linear Constraint Solver for Molecular Simulation
Hess, Berk
Journal of Chemical Theory and Computation (2008), 4 (1), 116-122CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
By removing the fastest degrees of freedom, constraints allow for an increase of the time step in mol. simulations. In the last decade parallel simulations have become commonplace. However, up till now efficient parallel constraint algorithms have not been used with domain decompn. In this paper the parallel linear constraint solver (P-LINCS) is presented, which allows the constraining of all bonds in macromols. Addnl. the energy conservation properties of (P-)LINCS are assessed in view of improvements in the accuracy of uncoupled angle constraints and integration in single precision.
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Darden, T.; York, D.; Pedersen, L. Particle mesh Ewald: An N · log(N) method for Ewald sums in large systems. J. Chem. Phys. 1993, 98, 10089– 10092, DOI: 10.1063/1.464397
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Particle mesh Ewald: an N·log(N) method for Ewald sums in large systems
Darden, Tom; York, Darrin; Pedersen, Lee
Journal of Chemical Physics (1993), 98 (12), 10089-92CODEN: JCPSA6; ISSN:0021-9606.
An N·log(N) method for evaluating electrostatic energies and forces of large periodic systems is presented. The method is based on interpolation of the reciprocal space Ewald sums and evaluation of the resulting convolution using fast Fourier transforms. Timings and accuracies are presented for three large cryst. ionic systems.
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Loche, P.; Steinbrunner, P.; Friedowitz, S.; Netz, R. R.; Bonthuis, D. J. Transferable Ion Force Fields in Water from a Simultaneous Optimization of Ion Solvation and Ion–Ion Interaction. J. Phys. Chem. B 2021, 125, 8581– 8587, DOI: 10.1021/acs.jpcb.1c05303
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Transferable Ion Force Fields in Water from a Simultaneous Optimization of Ion Solvation and Ion-Ion Interaction
Loche, Philip; Steinbrunner, Patrick; Friedowitz, Sean; Netz, Roland R.; Bonthuis, Douwe Jan
Journal of Physical Chemistry B (2021), 125 (30), 8581-8587CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
The poor performance of many existing nonpolarizable ion force fields is typically blamed on either the lack of explicit polarizability, the absence of charge transfer, or the use of unreduced Coulomb interactions. However, this anal. disregards the large and mostly unexplored parameter range offered by the Lennard-Jones potential. We use a global optimization procedure to develop water-model-transferable force fields for the ions K+, Na+, Cl-, and Br- in the complete parameter space of all Lennard-Jones interactions using std. mixing rules. No extra-thermodn. assumption is necessary for the simultaneous optimization of the four ion pairs. After optimization with respect to the exptl. solvation free energy and activity, the force fields reproduce the concn. dependent d., ionic cond. and dielec. const. with high accuracy. The force field is fully transferable between SPC/E, TIP3P, and TIP4P/ε water models. Our results show that a thermodynamically consistent force field for these ions needs only Lennard-Jones and std. Coulomb interactions.
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Humphrey, W.; Dalke, A.; Schulten, K. VMD: visual molecular dynamics. J. Mol. Graphics 1996, 14, 33– 38, DOI: 10.1016/0263-7855(96)00018-5
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VDM: visual molecular dynamics
Humphrey, William; Dalke, Andrew; Schulten, Klaus
Journal of Molecular Graphics (1996), 14 (1), 33-8, plates, 27-28CODEN: JMGRDV; ISSN:0263-7855. (Elsevier)
VMD is a mol. graphics program designed for the display and anal. of mol. assemblies, in particular, biopolymers such as proteins and nucleic acids. VMD can simultaneously display any no. of structures using a wide variety of rendering styles and coloring methods. Mols. are displayed as one or more "representations," in which each representation embodies a particular rendering method and coloring scheme for a selected subset of atoms. The atoms displayed in each representation are chosen using an extensive atom selection syntax, which includes Boolean operators and regular expressions. VMD provides a complete graphical user interface for program control, as well as a text interface using the Tcl embeddable parser to allow for complex scripts with variable substitution, control loops, and function calls. Full session logging is supported, which produces a VMD command script for later playback. High-resoln. raster images of displayed mols. may be produced by generating input scripts for use by a no. of photorealistic image-rendering applications. VMD has also been expressly designed with the ability to animate mol. dynamics (MD) simulation trajectories, imported either from files or from a direct connection to a running MD simulation. VMD is the visualization component of MDScope, a set of tools for interactive problem solving in structural biol., which also includes the parallel MD program NAMD, and the MDCOMM software used to connect the visualization and simulation programs, VMD is written in C++, using an object-oriented design; the program, including source code and extensive documentation, is freely available via anonymous ftp and through the World Wide Web.
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Abstract
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Figure 1
Figure 1. Simulation details. Chemical structures of (a) heparin and (b) linear polyglycerol sulfate (LPGS). (c) Structure of the spike protein trimer in the secondary structure representation (PDB ID: 7DK3). (32) Monomers are shown in purple, cyan, and yellow. The receptor binding domain (RBD) of one monomer (cyan) is present in the up conformation and is shown in red. (d) Zoomed-in view of the RBD. (e) Simulation unit cell (blue box) for equilibrium adsorption of a polymer to the RBD (red). An LPGS undecamer is shown in the space-filling representation with color coding for the different atom types: hydrogen in white, carbon in cyan, oxygen in red, and sulfur in yellow. Water and ions are present but not shown for clarity. The x, y, and z axes are indicated with red, green, and blue arrows, respectively. (f) Simulation snapshot after 1000 ns of equilibration representing adsorption of the LPGS (shown in orange) to the Delta-variant RBD surface (shown in gray). Protein cationic residues are pointed out in blue, whereas mutated residues R452 and L478 are in red. (g) Dynamic pulling simulation protocol in which a spring connected to one of the terminal atoms of the polymer is pulled away from the protein surface with a constant velocity ν along the z-axis. The spring is free to move along the lateral direction. (h) Static pulling simulation protocol in which one of the terminal atoms of the polymer is allowed to freely move in a plane at constant z-separation (distance projected along the normal to the plane) from the protein center-of-mass (red circle).
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Figure 2
Figure 2. Simulation results for the desorption of an LPGS undecamer from the wild-type (WT) and, only if mentioned, Delta-variant RBD surface. (a) Force f and (b) free energy F profiles from dynamic pulling simulations, results for only four out of the six pulling velocities are displayed for visual clarity. Error bars are displayed as shaded colored areas in panel b. (c) Free-energy difference ΔF between the desorbed and adsorbed states as a function of the pulling velocity ν. The equilibrium free-energy difference ΔF (ν = 0) is obtained from linear extrapolation of the data for the three slowest pulling rates to zero velocity. (d) Force and (e) free-energy profiles from static pulling simulations. (f) Comparison of free energy profiles obtained from umbrella sampling and static pulling simulations with the dynamic pulling simulation result using the slowest pulling velocity ν = 0.006 m/s.
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Figure 3
Figure 3. (a) Stretching force f_stretch versus the average end-to-end distance z_ete of an LPGS undecamer along the direction of applied force. Data points are fitted to the iPFRC model force–extension relation eq 8. (b) Stretching free-energy profile F_stretch as a function of f_stretch, obtained by integrating the fitted curve in panel a.
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Figure 4
Figure 4. Theoretical prediction for (a) the standard binding free-energy ΔF_b⁰ and (b) dissociation constant K_D for the complexation reaction of the wild-type RBD and LPGS as a function of its degree of polymerization N. Experimental values are reproduced from publications by Nie et al. (15) (Available under a CC BY-NC 4.0 license. Copyright 2021 The Authors.) and Page et al. (35) (Available under a CC BY-NC 4.0 license. Copyright 2023 The Authors.). Shaded regions in panels a and b represent simulation errors of propagation coming from the first three terms in eq 5 and from ΔF_b⁰, respectively.
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Figure 5
Figure 5. (a) Snapshots from the static pulling simulations for the desorbed state (at the pulling distance ξ = 3.6 nm) and the adsorbed state (ξ = 0 nm). (b) Enthalpic, ΔU_b, and entropic, TΔS_b, contributions to the binding free-energy ΔF_b of the wild-type RBD–LPGS complex, along with the different internal energy contributions to ΔU_b (see text). The average number of (c) water molecules and (d) ions, Na⁺ and Cl^–, bound to the RBD or LPGS as a function of ξ.
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Figure 6
Figure 6. Time series for the binding of (a) LPGS’s and (b) heparin’s anionic groups (highlighted in red in Figure 1a,b) to cationic residues of the wild-type RBD that exhibit a significant number of close contacts with the polymers. Binding for LPGS (heparin) to the residues R346 (R346), K444 (R356) and R466 (R357) are visualized in red, green, and orange, respectively. The survival probability (defined in eq 6), averaging over all binding–unbinding time series data, is shown for (c) LPGS and (d) heparin. The dashed line in panel c or d represents the double exponential fit to the data, with the value of the largest decay time τ provided in the legend.
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Figure 7
Figure 7. Conformational fluctuations of the wild-type RBD and dynamics of its loop region (residues 470 to 490) from the static simulation at ξ = 1.6 nm. (a) Root-mean-square fluctuation (RMSF) of the protein backbone atoms for different residues. The shaded region represents residues corresponding to the RBD’s loop region. (b) Time series of the distance between the center-of-mass of the loop region and the remaining part of the RBD. Snapshots for two different states at the start and after 2700 ns of the simulation are displayed above. The RBD surface is shown in gray except for its loop region in red, whereas LPGS is shown in the ball–stick representation in orange. (c) The center-of-mass distance autocorrelation function. The dashed line represents a double exponential fit to the data, with the value of the largest decay time τ given in the legend.
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Figure 8
Figure 8. Stretching protocol showing the LPGS undecamer at an applied force f = 800 pN. Color coding for the different atom types: hydrogen in white, carbon in cyan, oxygen in red, and sulfur in yellow.
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  There is no corresponding record for this reference.
13. 13
  Chu, H.; Hu, B.; Huang, X.; Chai, Y.; Zhou, D.; Wang, Y.; Shuai, H.; Yang, D.; Hou, Y.; Zhang, X. Host and viral determinants for efficient SARS-CoV-2 infection of the human lung. Nat. Commun. 2021, 12, 134 DOI: 10.1038/s41467-020-20457-w
  13
  Host and viral determinants for efficient SARS-CoV-2 infection of the human lung
  Chu, Hin; Hu, Bingjie; Huang, Xiner; Chai, Yue; Zhou, Dongyan; Wang, Yixin; Shuai, Huiping; Yang, Dong; Hou, Yuxin; Zhang, Xi; Yuen, Terrence Tsz-Tai; Cai, Jian-Piao; Zhang, Anna Jinxia; Zhou, Jie; Yuan, Shuofeng; To, Kelvin Kai-Wang; Chan, Ivy Hau-Yee; Sit, Ko-Yung; Foo, Dominic Chi-Chung; Wong, Ian Yu-Hong; Ng, Ada Tsui-Lin; Cheung, Tan To; Law, Simon Ying-Kit; Au, Wing-Kuk; Brindley, Melinda A.; Chen, Zhiwei; Kok, Kin-Hang; Chan, Jasper Fuk-Woo; Yuen, Kwok-Yung
  Nature Communications (2021), 12 (1), 134CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)
  Abstr.: Understanding the factors that contribute to efficient SARS-CoV-2 infection of human cells may provide insights on SARS-CoV-2 transmissibility and pathogenesis, and reveal targets of intervention. Here, we analyze host and viral determinants essential for efficient SARS-CoV-2 infection in both human lung epithelial cells and ex vivo human lung tissues. We identify heparan sulfate as an important attachment factor for SARS-CoV-2 infection. Next, we show that sialic acids present on ACE2 prevent efficient spike/ACE2-interaction. While SARS-CoV infection is substantially limited by the sialic acid-mediated restriction in both human lung epithelial cells and ex vivo human lung tissues, infection by SARS-CoV-2 is limited to a lesser extent. We further demonstrate that the furin-like cleavage site in SARS-CoV-2 spike is required for efficient virus replication in human lung but not intestinal tissues. These findings provide insights on the efficient SARS-CoV-2 infection of human lungs.
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14. 14
  Kim, S. H.; Kearns, F. L.; Rosenfeld, M. A.; Votapka, L.; Casalino, L.; Papanikolas, M.; Amaro, R. E.; Freeman, R. SARS-CoV-2 evolved variants optimize binding to cellular glycocalyx. Cell Rep. Phys. Sci. 2023, 4, 101346 DOI: 10.1016/j.xcrp.2023.101346
  There is no corresponding record for this reference.
15. 15
  Nie, C.; Pouyan, P.; Lauster, D.; Trimpert, J.; Kerkhoff, Y.; Szekeres, G. P.; Wallert, M.; Block, S.; Sahoo, A. K.; Dernedde, J.; Pagel, K.; Kaufer, B. B.; Netz, R. R.; Ballauff, M.; Haag, R. Polysulfates block SARS-CoV-2 uptake via electrostatic interactions. Angew. Chem., Int. Ed. 2021, 60, 15870– 15878, DOI: 10.1002/anie.202102717
  15
  Polysulfates Block SARS-CoV-2 Uptake through Electrostatic Interactions
  Nie, Chuanxiong; Pouyan, Paria; Lauster, Daniel; Trimpert, Jakob; Kerkhoff, Yannic; Szekeres, Gergo Peter; Wallert, Matthias; Block, Stephan; Sahoo, Anil Kumar; Dernedde, Jens; Pagel, Kevin; Kaufer, Benedikt B.; Netz, Roland R.; Ballauff, Matthias; Haag, Rainer
  Angewandte Chemie, International Edition (2021), 60 (29), 15870-15878CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
  Here we report that neg. charged polysulfates can bind to the spike protein of SARS-CoV-2 via electrostatic interactions. Using a plaque redn. assay, we compare inhibition of SARS-CoV-2 by heparin, pentosan sulfate, linear polyglycerol sulfate (LPGS) and hyperbranched polyglycerol sulfate (HPGS). Highly sulfated LPGS is the optimal inhibitor, with an IC50 of 67μg mL-1 (approx. 1.6μM). This synthetic polysulfate exhibits more than 60-fold higher virus inhibitory activity than heparin (IC50: 4084μg mL-1), along with much lower anticoagulant activity. Furthermore, in mol. dynamics simulations, we verified that LPGS can bind more strongly to the spike protein than heparin, and that LPGS can interact even more with the spike protein of the new N501Y and E484K variants. Our study demonstrates that the entry of SARS-CoV-2 into host cells can be blocked via electrostatic interactions, therefore LPGS can serve as a blueprint for the design of novel viral inhibitors of SARS-CoV-2.
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16. 16
  Clausen, T. M.; Sandoval, D. R.; Spliid, C. B.; Pihl, J.; Perrett, H. R.; Painter, C. D.; Narayanan, A.; Majowicz, S. A.; Kwong, E. M.; McVicar, R. N. SARS-CoV-2 infection depends on cellular heparan sulfate and ACE2. Cell 2020, 183, 1043– 1057, DOI: 10.1016/j.cell.2020.09.033
  16
  SARS-CoV-2 Infection Depends on Cellular Heparan Sulfate and ACE2
  Clausen, Thomas Mandel; Sandoval, Daniel R.; Spliid, Charlotte B.; Pihl, Jessica; Perrett, Hailee R.; Painter, Chelsea D.; Narayanan, Anoop; Majowicz, Sydney A.; Kwong, Elizabeth M.; McVicar, Rachael N.; Thacker, Bryan E.; Glass, Charles A.; Yang, Zhang; Torres, Jonathan L.; Golden, Gregory J.; Bartels, Phillip L.; Porell, Ryan N.; Garretson, Aaron F.; Laubach, Logan; Feldman, Jared; Yin, Xin; Pu, Yuan; Hauser, Blake M.; Caradonna, Timothy M.; Kellman, Benjamin P.; Martino, Cameron; Gordts, Philip L. S. M.; Chanda, Sumit K.; Schmidt, Aaron G.; Godula, Kamil; Leibel, Sandra L.; Jose, Joyce; Corbett, Kevin D.; Ward, Andrew B.; Carlin, Aaron F.; Esko, Jeffrey D.
  Cell (Cambridge, MA, United States) (2020), 183 (4), 1043-1057.e15CODEN: CELLB5; ISSN:0092-8674. (Cell Press)
  We show that SARS-CoV-2 spike protein interacts with both cellular heparan sulfate and angiotensin-converting enzyme 2 (ACE2) through its receptor-binding domain (RBD). Docking studies suggest a heparin/heparan sulfate-binding site adjacent to the ACE2-binding site. Both ACE2 and heparin can bind independently to spike protein in vitro, and a ternary complex can be generated using heparin as a scaffold. Electron micrographs of spike protein suggests that heparin enhances the open conformation of the RBD that binds ACE2. On cells, spike protein binding depends on both heparan sulfate and ACE2. Unfractionated heparin, non-anticoagulant heparin, heparin lyases, and lung heparan sulfate potently block spike protein binding and/or infection by pseudotyped virus and authentic SARS-CoV-2 virus. We suggest a model in which viral attachment and infection involves heparan sulfate-dependent enhancement of binding to ACE2. Manipulation of heparan sulfate or inhibition of viral adhesion by exogenous heparin presents new therapeutic opportunities.
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17. 17
  Lever, R.; Page, C. P. Non-Anticoagulant Effects of Heparin: An Overview. In Heparin - A Century of Progress; Lever, R.; Mulloy, B.; Page, C. P., Eds.; Springer: Berlin, Heidelberg, 2012; pp 281– 305.
  There is no corresponding record for this reference.
18. 18
  Page, C. Heparin and related drugs: beyond anticoagulant activity. ISRN Pharmacol. 2013, 1, 910743 DOI: 10.1155/2013/910743
  There is no corresponding record for this reference.
19. 19
  Oates, J. A.; Wood, A. J. J.; Hirsh, J. Heparin. N. Engl. J. Med. 1991, 324, 1565– 1574, DOI: 10.1056/NEJM199105303242206
  There is no corresponding record for this reference.
20. 20
  Cate, H. T. Surviving Covid-19 with Heparin?. N. Engl. J. Med. 2021, 385, 845– 846, DOI: 10.1056/NEJMe2111151
  There is no corresponding record for this reference.
21. 21
  Lan, J.; Ge, J.; Yu, J.; Shan, S.; Zhou, H.; Fan, S.; Zhang, Q.; Shi, X.; Wang, Q.; Zhang, L.; Wang, X. Structure of the SARS-CoV-2 spike receptor-binding domain bound to the ACE2 receptor. Nature 2020, 581, 215– 220, DOI: 10.1038/s41586-020-2180-5
  21
  Structure of the SARS-CoV-2 spike receptor-binding domain bound to the ACE2 receptor
  Lan, Jun; Ge, Jiwan; Yu, Jinfang; Shan, Sisi; Zhou, Huan; Fan, Shilong; Zhang, Qi; Shi, Xuanling; Wang, Qisheng; Zhang, Linqi; Wang, Xinquan
  Nature (London, United Kingdom) (2020), 581 (7807), 215-220CODEN: NATUAS; ISSN:0028-0836. (Nature Research)
  Abstr.: A new and highly pathogenic coronavirus (severe acute respiratory syndrome coronavirus-2, SARS-CoV-2) caused an outbreak in Wuhan city, Hubei province, China, starting from Dec. 2019 that quickly spread nationwide and to other countries around the world1-3. Here, to better understand the initial step of infection at an at. level, we detd. the crystal structure of the receptor-binding domain (RBD) of the spike protein of SARS-CoV-2 bound to the cell receptor ACE2. The overall ACE2-binding mode of the SARS-CoV-2 RBD is nearly identical to that of the SARS-CoV RBD, which also uses ACE2 as the cell receptor4. Structural anal. identified residues in the SARS-CoV-2 RBD that are essential for ACE2 binding, the majority of which either are highly conserved or share similar side chain properties with those in the SARS-CoV RBD. Such similarity in structure and sequence strongly indicate convergent evolution between the SARS-CoV-2 and SARS-CoV RBDs for improved binding to ACE2, although SARS-CoV-2 does not cluster within SARS and SARS-related coronaviruses1-3,5. The epitopes of two SARS-CoV antibodies that target the RBD are also analyzed for binding to the SARS-CoV-2 RBD, providing insights into the future identification of cross-reactive antibodies.
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22. 22
  Pishko, A. M.; Lefler, D. S.; Gimotty, P.; Paydary, K.; Fardin, S.; Arepally, G. M.; Crowther, M.; Rice, L.; Vega, R.; Cines, D. B. The risk of major bleeding in patients with suspected heparin-induced thrombocytopenia. J. Thromb. Haemostasis 2019, 17, 1956– 1965, DOI: 10.1111/jth.14587
  There is no corresponding record for this reference.
23. 23
  Nie, C.; Sahoo, A. K.; Netz, R. R.; Herrmann, A.; Ballauff, M.; Haag, R. Charge matters: Mutations in omicron variant favor binding to cells. ChemBioChem 2022, 23, e202100681 DOI: 10.1002/cbic.202100681
  23
  Charge Matters: Mutations in Omicron Variant Favor Binding to Cells
  Nie, Chuanxiong; Sahoo, Anil Kumar; Netz, Roland R.; Herrmann, Andreas; Ballauff, Matthias; Haag, Rainer
  ChemBioChem (2022), 23 (6), e202100681CODEN: CBCHFX; ISSN:1439-4227. (Wiley-VCH Verlag GmbH & Co. KGaA)
  A review. Evidence is strengthening to suggest that the novel SARS-CoV-2 mutant Omicron, with its more than 60 mutations, will spread and dominate worldwide. Although the mutations in the spike protein are known, the mol. basis for why the addnl. mutations in the spike protein that have not previously occurred account for Omicron's higher infection potential, is not understood. We propose, based on chem. rational and mol. dynamics simulations, that the elevated occurrence of pos. charged amino acids in certain domains of the spike protein (Delta: +4; Omicron: +5 vs. wild type) increases binding to cellular polyanionic receptors, such as heparan sulfate due to multivalent charge-charge interactions. This observation is a starting point for targeted drug development.
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24. 24
  Wang, L.; Wu, Y.; Deng, Y.; Kim, B.; Pierce, L.; Krilov, G.; Lupyan, D.; Robinson, S.; Dahlgren, M. K.; Greenwood, J. Accurate and reliable prediction of relative ligand binding potency in prospective drug discovery by way of a modern free-energy calculation protocol and force field. J. Am. Chem. Soc. 2015, 137, 2695– 2703, DOI: 10.1021/ja512751q
  24
  Accurate and Reliable Prediction of Relative Ligand Binding Potency in Prospective Drug Discovery by Way of a Modern Free-Energy Calculation Protocol and Force Field
  Wang, Lingle; Wu, Yujie; Deng, Yuqing; Kim, Byungchan; Pierce, Levi; Krilov, Goran; Lupyan, Dmitry; Robinson, Shaughnessy; Dahlgren, Markus K.; Greenwood, Jeremy; Romero, Donna L.; Masse, Craig; Knight, Jennifer L.; Steinbrecher, Thomas; Beuming, Thijs; Damm, Wolfgang; Harder, Ed; Sherman, Woody; Brewer, Mark; Wester, Ron; Murcko, Mark; Frye, Leah; Farid, Ramy; Lin, Teng; Mobley, David L.; Jorgensen, William L.; Berne, Bruce J.; Friesner, Richard A.; Abel, Robert
  Journal of the American Chemical Society (2015), 137 (7), 2695-2703CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
  Designing tight-binding ligands is a primary objective of small-mol. drug discovery. Over the past few decades, free-energy calcns. have benefited from improved force fields and sampling algorithms, as well as the advent of low-cost parallel computing. However, it has proven to be challenging to reliably achieve the level of accuracy that would be needed to guide lead optimization (∼5× in binding affinity) for a wide range of ligands and protein targets. Not surprisingly, widespread com. application of free-energy simulations has been limited due to the lack of large-scale validation coupled with the tech. challenges traditionally assocd. with running these types of calcns. Here, we report an approach that achieves an unprecedented level of accuracy across a broad range of target classes and ligands, with retrospective results encompassing 200 ligands and a wide variety of chem. perturbations, many of which involve significant changes in ligand chem. structures. In addn., we have applied the method in prospective drug discovery projects and found a significant improvement in the quality of the compds. synthesized that have been predicted to be potent. Compds. predicted to be potent by this approach have a substantial redn. in false positives relative to compds. synthesized on the basis of other computational or medicinal chem. approaches. Furthermore, the results are consistent with those obtained from our retrospective studies, demonstrating the robustness and broad range of applicability of this approach, which can be used to drive decisions in lead optimization.
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25. 25
  Cournia, Z.; Allen, B.; Sherman, W. Relative binding free energy calculations in drug discovery: recent advances and practical considerations. J. Chem. Inf. Model. 2017, 57, 2911– 2937, DOI: 10.1021/acs.jcim.7b00564
  25
  Relative Binding Free Energy Calculations in Drug Discovery: Recent Advances and Practical Considerations
  Cournia, Zoe; Allen, Bryce; Sherman, Woody
  Journal of Chemical Information and Modeling (2017), 57 (12), 2911-2937CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
  A review. Accurate in silico prediction of protein-ligand binding affinities has been a primary objective of structure-based drug design for decades due to the putative value it would bring to the drug discovery process. However, computational methods have historically failed to deliver value in real-world drug discovery applications due to a variety of scientific, tech., and practical challenges. Recently, a family of approaches commonly referred to as relative binding free energy (RBFE) calcns., which rely on physics-based mol. simulations and statistical mechanics, have shown promise in reliably generating accurate predictions in the context of drug discovery projects. This advance arises from accumulating developments in the underlying scientific methods (decades of research on force fields and sampling algorithms) coupled with vast increases in computational resources (graphics processing units and cloud infrastructures). Mounting evidence from retrospective validation studies, blind challenge predictions, and prospective applications suggests that RBFE simulations can now predict the affinity differences for congeneric ligands with sufficient accuracy and throughput to deliver considerable value in hit-to-lead and lead optimization efforts. Here, the authors present an overview of current RBFE implementations, highlighting recent advances and remaining challenges, along with examples that emphasize practical considerations for obtaining reliable RBFE results. The authors focus specifically on relative binding free energies because the calcns. are less computationally intensive than abs. binding free energy (ABFE) calcns. and map directly onto the hit-to-lead and lead optimization processes, where the prediction of relative binding energies between a ref. mol. and new ideas (virtual mols.) can be used to prioritize mols. for synthesis. The authors describe the crit. aspects of running RBFE calcns., from both theor. and applied perspectives, using a combination of retrospective literature examples and prospective studies from drug discovery projects. This work is intended to provide a contemporary overview of the scientific, tech., and practical issues assocd. with running relative binding free energy simulations, with a focus on real-world drug discovery applications. The authors offer guidelines for improving the accuracy of RBFE simulations, esp. for challenging cases, and emphasize unresolved issues that could be improved by further research in the field.
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26. 26
  Mobley, D. L.; Gilson, M. K. Predicting binding free energies: frontiers and benchmarks. Annu. Rev. Biophys. 2017, 46, 531– 558, DOI: 10.1146/annurev-biophys-070816-033654
  26
  Predicting Binding Free Energies: Frontiers and Benchmarks
  Mobley, David L.; Gilson, Michael K.
  Annual Review of Biophysics (2017), 46 (), 531-558CODEN: ARBNCV; ISSN:1936-122X. (Annual Reviews)
  Binding free energy calcns. based on mol. simulations provide predicted affinities for biomol. complexes. These calcns. begin with a detailed description of a system, including its chem. compn. and the interactions among its components. Simulations of the system are then used to compute thermodn. information, such as binding affinities. Because of their promise for guiding mol. design, these calcns. have recently begun to see widespread applications in early-stage drug discovery. However, many hurdles remain in making them a robust and reliable tool. In this review, we highlight key challenges of these calcns., discuss some examples of these challenges, and call for the designation of std. community benchmark test systems that will help the research community generate and evaluate progress. In our view, progress will require careful assessment and evaluation of new methods, force fields, and modeling innovations on well-characterized benchmark systems, and we lay out our vision for how this can be achieved.
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27. 27
  Zhao, J.; Cao, Y.; Zhang, L. Exploring the computational methods for protein-ligand binding site prediction. Comput. Struct. Biotechnol. J. 2020, 18, 417– 426, DOI: 10.1016/j.csbj.2020.02.008
  27
  Exploring the computational methods for protein-ligand binding site prediction
  Zhao, Jingtian; Cao, Yang; Zhang, Le
  Computational and Structural Biotechnology Journal (2020), 18 (), 417-426CODEN: CSBJAC; ISSN:2001-0370. (Elsevier B.V.)
  A review. Proteins participate in various essential processes in vivo via interactions with other mols. Identifying the residues participating in these interactions not only provides biol. insights for protein function studies but also has great significance for drug discoveries. Therefore, predicting protein-ligand binding sites has long been under intense research in the fields of bioinformatics and computer aided drug discovery. In this review, we first introduce the research background of predicting protein-ligand binding sites and then classify the methods into four categories, namely, 3D structure-based, template similarity-based, traditional machine learning-based and deep learning-based methods. We describe representative algorithms in each category and elaborate on machine learning and deep learning-based prediction methods in more detail. Finally, we discuss the trends and challenges of the current research such as mol. dynamics simulation based cryptic binding sites prediction, and highlight prospective directions for the near future.
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28. 28
  Gapsys, V.; Yildirim, A.; Aldeghi, M.; Khalak, Y.; Van der Spoel, D.; de Groot, B. L. Accurate absolute free energies for ligand–protein binding based on non-equilibrium approaches. Commun. Chem. 2021, 4, 61 DOI: 10.1038/s42004-021-00498-y
  28
  Accurate absolute free energies for ligand-protein binding based on non-equilibrium approaches
  Gapsys, Vytautas; Yildirim, Ahmet; Aldeghi, Matteo; Khalak, Yuriy; van der Spoel, David; de Groot, Bert L.
  Communications Chemistry (2021), 4 (1), 61CODEN: CCOHCT; ISSN:2399-3669. (Nature Research)
  Abstr.: The accurate calcn. of the binding free energy for arbitrary ligand-protein pairs is a considerable challenge in computer-aided drug discovery. Recently, it has been demonstrated that current state-of-the-art mol. dynamics (MD) based methods are capable of making highly accurate predictions. Conventional MD-based approaches rely on the first principles of statistical mechanics and assume equil. sampling of the phase space. In the current work we demonstrate that accurate abs. binding free energies (ABFE) can also be obtained via theor. rigorous non-equil. approaches. Our investigation of ligands binding to bromodomains and T4 lysozyme reveals that both equil. and non-equil. approaches converge to the same results. The non-equil. approach achieves the same level of accuracy and convergence as an equil. free energy perturbation (FEP) method enhanced by Hamiltonian replica exchange. We also compare uni- and bi-directional non-equil. approaches and demonstrate that considering the work distributions from both forward and reverse directions provides substantial accuracy gains. In summary, non-equil. ABFE calcns. are shown to yield reliable and well-converged ests. of protein-ligand binding affinity.
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29. 29
  Xu, X.; Angioletti-Uberti, S.; Lu, Y.; Dzubiella, J.; Ballauff, M. Interaction of proteins with polyelectrolytes: Comparison of theory to experiment. Langmuir 2019, 35, 5373– 5391, DOI: 10.1021/acs.langmuir.8b01802
  29
  Interaction of Proteins with Polyelectrolytes: Comparison of Theory to Experiment
  Xu, Xiao; Angioletti-Uberti, Stefano; Lu, Yan; Dzubiella, Joachim; Ballauff, Matthias
  Langmuir (2019), 35 (16), 5373-5391CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
  A review on the authors' recent studies on the interaction of simple proteins such as human serum albumin (HSA) and lysozyme with linear polyelectrolytes, charged dendrimers, charged networks, and polyelectrolyte brushes, based on exptl. works combined with mol. dynamics (MD) simulations and mean-field theories.
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30. 30
  Paiardi, G.; Ferraz, M.; Rusnati, M.; Wade, R. C. The accomplices: Heparan sulfates and N-glycans foster SARS-CoV-2 spike: ACE2 receptor binding and virus priming. Proc. Natl. Acad. Sci. U.S.A. 2024, 121, e2404892121 DOI: 10.1073/pnas.2404892121
  There is no corresponding record for this reference.
31. 31
  Bhatia, S.; Lauster, D.; Bardua, M.; Ludwig, K.; Angioletti-Uberti, S.; Popp, N.; Hoffmann, U.; Paulus, F.; Budt, M.; Stadtmüller, M. Linear polysialoside outperforms dendritic analogs for inhibition of influenza virus infection in vitro and in vivo. Biomaterials 2017, 138, 22– 34, DOI: 10.1016/j.biomaterials.2017.05.028
  31
  Linear polysialoside outperforms dendritic analogs for inhibition of influenza virus infection in vitro and in vivo
  Bhatia, Sumati; Lauster, Daniel; Bardua, Markus; Ludwig, Kai; Angioletti-Uberti, Stefano; Popp, Nicole; Hoffmann, Ute; Paulus, Florian; Budt, Matthias; Stadtmueller, Marlena; Wolff, Thorsten; Hamann, Alf; Boettcher, Christoph; Herrmann, Andreas; Haag, Rainer
  Biomaterials (2017), 138 (), 22-34CODEN: BIMADU; ISSN:0142-9612. (Elsevier Ltd.)
  Inhibition of influenza A virus infection by multivalent sialic acid inhibitors preventing viral hemagglutinin binding to host cells of the respiratory tract is a promising strategy. However, optimal geometry and optimal ligand presentation on multivalent scaffolds for efficient inhibition both in vitro and in vivo application are still unclear. Here, by comparing linear and dendritic polyglycerol sialosides (LPGSA and dPGSA) we identified architectural requirements and optimal ligand densities for an efficient multivalent inhibitor of influenza virus A/X31/1 (H3N2). Due to its large vol., the LPGSA at optimal ligand d. sterically shielded the virus significantly better than the dendritic analog. A statistical mechanics model rationalizes the relevance of ligand d., morphol., and the size of multivalent scaffolds for the potential to inhibit virus-cell binding. Optimized LPGSA inhibited virus infection at IC50 in the low nanomolar nanoparticle concn. range and also showed potent antiviral activity against two avian influenza strains A/Mallard/439/2004 (H3N2) and A/turkey/Italy/472/1999 (H7N1) post infection. In vivo application of inhibitors clearly confirmed the higher inhibition potential of linear multivalent scaffolds to prevent infection. The optimized LPGSA did not show any acute toxicity, and was much more potent than the neuraminidase inhibitor oseltamivir carboxylate in vivo. Combined application of the LPGSA and oseltamivir carboxylate revealed a synergistic inhibitory effect and successfully prevented influenza virus infection in mice.
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32. 32
  Xu, C.; Wang, Y.; Liu, C.; Zhang, C.; Han, W.; Hong, X.; Wang, Y.; Hong, Q.; Wang, S.; Zhao, Q. Conformational dynamics of SARS-CoV-2 trimeric spike glycoprotein in complex with receptor ACE2 revealed by cryo-EM. Sci. Adv. 2021, 7, eabe5575 DOI: 10.1126/sciadv.abe5575
  There is no corresponding record for this reference.
33. 33
  Horinek, D.; Serr, A.; Geisler, M.; Pirzer, T.; Slotta, U.; Lud, S. Q.; Garrido, J.; Scheibel, T.; Hugel, T.; Netz, R. R. Peptide adsorption on a hydrophobic surface results from an interplay of solvation, surface, and intrapeptide forces. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 2842– 2847, DOI: 10.1073/pnas.0707879105
  33
  Peptide adsorption on a hydrophobic surface results from an interplay of solvation, surface, and intrapeptide forces
  Horinek, D.; Serr, A.; Geisler, M.; Pirzer, T.; Slotta, U.; Lud, S. Q.; Garrido, J. A.; Scheibel, T.; Hugel, T.; Netz, R. R.
  Proceedings of the National Academy of Sciences of the United States of America (2008), 105 (8), 2842-2847CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
  The hydrophobic effect, i.e., the poor solvation of nonpolar parts of mols., plays a key role in protein folding and more generally for mol. self-assembly and aggregation in aq. media. The perturbation of the water structure accounts for many aspects of protein hydrophobicity. However, to what extent the dispersion interaction between mol. entities themselves contributes has remained unclear. This is so because in peptide folding interactions and structural changes occur on all length scales and make disentangling various contributions impossible. The authors address this issue both exptl. and theor. by looking at the force necessary to peel a mildly hydrophobic single peptide mol. from a flat hydrophobic diamond surface in the presence of water. This setup avoids problems caused by bubble adsorption, cavitation, and slow equilibration that complicate the much-studied geometry with two macroscopic surfaces. Using at.-force spectroscopy, the authors det. the mean desorption force of a single spider-silk peptide chain as F = 58 ± 8 pN, which corresponds to a desorption free energy of ≈5 k8T per amino acid. The authors' all-atomistic mol. dynamics simulation including explicit water correspondingly yields the desorption force F = 54 ± 15 pN. This observation demonstrates that std. nonpolarizable force fields used in classical simulations are capable of resolving the fine details of the hydrophobic attraction of peptides. The anal. of the involved energetics shows that water-structure effects and dispersive interactions give contributions of comparable magnitude that largely cancel out. It follows that the correct modeling of peptide hydrophobicity must take the intimate coupling of solvation and dispersive effects into account.
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34. 34
  Schwierz, N.; Horinek, D.; Liese, S.; Pirzer, T.; Balzer, B. N.; Hugel, T.; Netz, R. R. On the relationship between peptide adsorption resistance and surface contact angle: a combined experimental and simulation single-molecule study. J. Am. Chem. Soc. 2012, 134, 19628– 19638, DOI: 10.1021/ja304462u
  34
  On the Relationship between Peptide Adsorption Resistance and Surface Contact Angle: A Combined Experimental and Simulation Single-Molecule Study
  Schwierz, Nadine; Horinek, Dominik; Liese, Susanne; Pirzer, Tobias; Balzer, Bizan N.; Hugel, Thorsten; Netz, Roland R.
  Journal of the American Chemical Society (2012), 134 (48), 19628-19638CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
  The force-induced desorption of single peptide chains from mixed OH/CH3-terminated self-assembled monolayers was studied in closely matched mol. dynamics simulations and at. force microscopy expts. with the goal to gain microscopic understanding of the transition between peptide adsorption and adsorption resistance as the surface contact angle is varied. In both simulations and expts., the surfaces become adsorption resistant against hydrophilic as well as hydrophobic peptides when their contact angle decreases below θ ≈ 50°-60°, thus confirming the so-called Berg limit established in the context of protein and cell adsorption. Entropy/enthalpy decompn. of the simulation results reveals that the key discriminator between the adsorption of different residues on a hydrophobic monolayer is of entropic nature and thus probably is linked to the hydrophobic effect. By pushing a polyalanine peptide onto a polar surface, simulations reveal that the peptide adsorption resistance is caused by the strongly bound water hydration layer and characterized by the simultaneous gain of both total entropy in the system and total no. of hydrogen bonds between water, peptide, and surface. This mechanistic insight into peptide adsorption resistance might help to refine design principles for anti-fouling surfaces.
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35. 35
  Page, T. M.; Nie, C.; Neander, L.; Povolotsky, T. L.; Sahoo, A. K.; Nickl, P.; Adler, J. M.; Bawadkji, O.; Radnik, J.; Achazi, K. Functionalized Fullerene for Inhibition of SARS-CoV-2 Variants. Small 2023, 19, 2206154 DOI: 10.1002/smll.202206154
  35
  Functionalized Fullerene for Inhibition of SARS-CoV-2 Variants
  Page, Taylor M.; Nie, Chuanxiong; Neander, Lenard; Povolotsky, Tatyana L.; Sahoo, Anil Kumar; Nickl, Philip; Adler, Julia M.; Bawadkji, Obida; Radnik, Jorg; Achazi, Katharina; Ludwig, Kai; Lauster, Daniel; Netz, Roland R.; Trimpert, Jakob; Kaufer, Benedikt; Haag, Rainer; Donskyi, Ievgen S.
  Small (2023), 19 (15), 2206154CODEN: SMALBC; ISSN:1613-6810. (Wiley-VCH Verlag GmbH & Co. KGaA)
  As virus outbreaks continue to pose a challenge, a nonspecific viral inhibitor can provide significant benefits, esp. against respiratory viruses. Polyglycerol sulfates recently emerge as promising agents that mediate interactions between cells and viruses through electrostatics, leading to virus inhibition. Similarly, hydrophobic C60 fullerene can prevent virus infection via interactions with hydrophobic cavities of surface proteins. Here, two strategies are combined to inhibit infection of SARS-CoV-2 variants in vitro. Effective inhibitory concns. in the millimolar range highlight the significance of bare fullerene's hydrophobic moiety and electrostatic interactions of polysulfates with surface proteins of SARS-CoV-2. Furthermore, microscale thermophoresis measurements support that fullerene linear polyglycerol sulfates interact with the SARS-CoV-2 virus via its spike protein, and highlight importance of electrostatic interactions within it. All-atom mol. dynamics simulations reveal that the fullerene binding site is situated close to the receptor binding domain, within 4 nm of polyglycerol sulfate binding sites, feasibly allowing both portions of the material to interact simultaneously.
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36. 36
  Woo, H.; Park, S.-J.; Choi, Y. K.; Park, T.; Tanveer, M.; Cao, Y.; Kern, N. R.; Lee, J.; Yeom, M. S.; Croll, T. I. Developing a fully glycosylated full-length SARS-CoV-2 spike protein model in a viral membrane. J. Phys. Chem. B 2020, 124, 7128– 7137, DOI: 10.1021/acs.jpcb.0c04553
  36
  Developing a fully glycosylated full-length SARS-CoV-2 spike protein model in a viral membrane
  Woo, Hyeonuk; Park, Sang-Jun; Choi, Yeol Kyo; Park, Taeyong; Tanveer, Maham; Cao, Yiwei; Kern, Nathan R.; Lee, Jumin; Yeom, Min Sun; Croll, Tristan I.; Seok, Chaok; Im, Wonpil
  Journal of Physical Chemistry B (2020), 124 (33), 7128-7137CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
  This tech. study describes all-atom modeling and simulation of a fully glycosylated full-length SARS-CoV-2 spike (S) protein in a viral membrane. First, starting from PDB: 6VSB and 6VXX, full-length S protein structures were modeled using template-based modeling, de-novo protein structure prediction, and loop modeling techniques in GALAXY modeling suite. Then, using the recently detd. most occupied glycoforms, 22 N-glycans and 1 O-glycan of each monomer were modeled using Glycan Reader & Modeler in CHARMM-GUI. These fully glycosylated full-length S protein model structures were assessed and further refined against the low-resoln. data in their resp. exptl. maps using ISOLDE. The authors then used CHARMM-GUI Membrane Builder to place the S proteins in a viral membrane and performed all-atom mol. dynamics simulations. All structures are available in CHARMM-GUI COVID-19 Archive so that researchers can use these models to carry out innovative and novel modeling and simulation research for the prevention and treatment of COVID-19.
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37. 37
  Casalino, L.; Gaieb, Z.; Goldsmith, J. A.; Hjorth, C. K.; Dommer, A. C.; Harbison, A. M.; Fogarty, C. A.; Barros, E. P.; Taylor, B. C.; McLellan, J. S. Beyond shielding: the roles of glycans in the SARS-CoV-2 spike protein. ACS Cent. Sci. 2020, 6, 1722– 1734, DOI: 10.1021/acscentsci.0c01056
  37
  Beyond Shielding: The Roles of Glycans in the SARS-CoV-2 Spike Protein
  Casalino, Lorenzo; Gaieb, Zied; Goldsmith, Jory A.; Hjorth, Christy K.; Dommer, Abigail C.; Harbison, Aoife M.; Fogarty, Carl A.; Barros, Emilia P.; Taylor, Bryn C.; McLellan, Jason S.; Fadda, Elisa; Amaro, Rommie E.
  ACS Central Science (2020), 6 (10), 1722-1734CODEN: ACSCII; ISSN:2374-7951. (American Chemical Society)
  The ongoing COVID-19 pandemic caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has resulted in more than 28,000,000 infections and 900,000 deaths worldwide to date. Antibody development efforts mainly revolve around the extensively glycosylated SARS-CoV-2 spike (S) protein, which mediates host cell entry by binding to the angiotensin-converting enzyme 2 (ACE2). Similar to many other viral fusion proteins, the SARS-CoV-2 spike utilizes a glycan shield to thwart the host immune response. Here, we built a full-length model of the glycosylated SARS-CoV-2 S protein, both in the open and closed states, augmenting the available structural and biol. data. Multiple microsecond-long, all-atom mol. dynamics simulations were used to provide an atomistic perspective on the roles of glycans and on the protein structure and dynamics. We reveal an essential structural role of N-glycans at sites N165 and N234 in modulating the conformational dynamics of the spike's receptor binding domain (RBD), which is responsible for ACE2 recognition. This finding is corroborated by biolayer interferometry expts., which show that deletion of these glycans through N165A and N234A mutations significantly reduces binding to ACE2 as a result of the RBD conformational shift toward the "down" state. Addnl., end-to-end accessibility analyses outline a complete overview of the vulnerabilities of the glycan shield of the SARS-CoV-2 S protein, which may be exploited in the therapeutic efforts targeting this mol. machine. Overall, this work presents hitherto unseen functional and structural insights into the SARS-CoV-2 S protein and its glycan coat, providing a strategy to control the conformational plasticity of the RBD that could be harnessed for vaccine development. The glycan shield is a sugary barrier that helps the viral SARS-CoV-2 spikes to evade the immune system. Beyond shielding, two of the spike's glycans are discovered to prime the virus for infection.
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38. 38
  Erbaş, A.; Netz, R. R. Confinement-dependent friction in peptide bundles. Biophys. J. 2013, 104, 1285– 1295, DOI: 10.1016/j.bpj.2013.02.008
  38
  Confinement-Dependent Friction in Peptide Bundles
  Erbas, Aykut; Netz, Roland R.
  Biophysical Journal (2013), 104 (6), 1285-1295CODEN: BIOJAU; ISSN:0006-3495. (Cell Press)
  Friction within globular proteins or between adhering macromols. crucially dets. the kinetics of protein folding, the formation, and the relaxation of self-assembled mol. systems. One fundamental question is how these friction effects depend on the local environment and in particular on the presence of water. In this model study, we use fully atomistic MD simulations with explicit water to obtain friction forces as a single polyglycine peptide chain is pulled out of a bundle of k adhering parallel polyglycine peptide chains. The whole system is periodically replicated along the peptide axes, so a stationary state at prescribed mean sliding velocity V is achieved. The aggregation no. is varied between k = 2 (two peptide chains adhering to each other with plenty of water present at the adhesion sites) and k = 7 (one peptide chain pulled out from a close-packed cylindrical array of six neighboring peptide chains with no water inside the bundle). The friction coeff. per hydrogen bond, extrapolated to the viscous limit of vanishing pulling velocity V → 0, exhibits an increase by five orders of magnitude when going from k = 2 to k = 7. This dramatic confinement-induced friction enhancement we argue to be due to a combination of water depletion and increased hydrogen-bond cooperativity.
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39. 39
  Erbaş, A.; Horinek, D.; Netz, R. R. Viscous friction of hydrogen-bonded matter. J. Am. Chem. Soc. 2012, 134, 623– 630, DOI: 10.1021/ja209454a
  39
  Viscous Friction of Hydrogen-Bonded Matter
  Erbas, Aykut; Horinek, Dominik; Netz, Roland R.
  Journal of the American Chemical Society (2012), 134 (1), 623-630CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
  Amontons' law successfully describes friction between macroscopic solid bodies for a wide range of velocities and normal forces. For the diffusion and forced sliding of adhering or entangled macromols., proteins, and biol. complexes, temp. effects are invariably important, and a similarly successful friction law at biol. length and velocity scales is missing. Hydrogen bonds (HBs) are key to the specific binding of biomatter. Here we show that friction between hydrogen-bonded matter in the biol. relevant low-velocity viscous regime obeys a simple law: the friction force is proportional to the no. of HBs, the sliding velocity, and a friction coeff. γHB. This law is deduced from atomistic mol. dynamics simulations for short peptide chains that are laterally pulled over planar hydroxylated substrates in the presence of water and holds for widely different peptides, surface polarities, and applied normal forces. The value of γHB is extrapolated from simulations at sliding velocities in the range from V = 10-2 to 100 m/s by mapping on a simple stochastic model and turns out to be of the order of γHB ≃ 10-8 kg/s. The friction of a single HB thus amts. to the Stokes friction of a sphere with an equiv. radius of roughly 1 μm moving in water. Cooperativity is pronounced; roughly three HBs act collectively.
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40. 40
  Patil, S. P.; Xiao, S.; Gkagkas, K.; Markert, B.; Gräter, F. Viscous friction between crystalline and amorphous phase of dragline silk. PLoS One 2014, 9, e104832 DOI: 10.1371/journal.pone.0104832
  There is no corresponding record for this reference.
41. 41
  Kumar, S.; Rosenberg, J. M.; Bouzida, D.; Swendsen, R. H.; Kollman, P. A. The weighted histogram analysis method for free-energy calculations on biomolecules. I. The method. J. Comput. Chem. 1992, 13, 1011– 1021, DOI: 10.1002/jcc.540130812
  41
  The weighted histogram analysis method for free-energy calculations on biomolecules. I. The method
  Kumar, Shankar; Bouzida, Djamal; Swendsen, Robert H.; Kollman, Peter A.; Rosenberg, John M.
  Journal of Computational Chemistry (1992), 13 (8), 1011-21CODEN: JCCHDD; ISSN:0192-8651.
  The Weighted Histogram Anal. Method (WHAM), an extension of Ferrenberg and Swendsen's Multiple Histogram Technique, has been applied for the first time on complex biomol. Hamiltonians. The method is presented here as an extension of the Umbrella Sampling method for free-energy and Potential of Mean Force calcns. This algorithm possesses the following advantages over methods that are currently employed: (1) it provides a built-in est. of sampling errors thereby yielding objective ests. of the optimal location and length of addnl. simulations needed to achieve a desired level of precision; (2) it yields the "best" value of free energies by taking into account all the simulations so as to minimize the statistical errors; (3) in addn. to optimizing the links between simulations, it also allows multiple overlaps of probability distributions for obtaining better ests. of the free-energy differences. By recasting the Ferrenberg-Swendsen Multiple Histogram equations in a form suitable for mol. mechanics type Hamiltonians, we have demonstrated the feasibility and robustness of this method by applying it to a test problem of the generation of the Potential of Mean Force profile of the pseudorotation phase angle of the sugar ring in deoxyadenosine.
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42. 42
  Torrie, G. M.; Valleau, J. P. Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling. J. Comput. Phys. 1977, 23, 187– 199, DOI: 10.1016/0021-9991(77)90121-8
  There is no corresponding record for this reference.
43. 43
  Phillips, R.; Kondev, J.; Theriot, J.; Garcia, H. Physical Biology of the Cell, 2nd ed.; Garland Science: New York, 2012; p 1088.
  There is no corresponding record for this reference.
44. 44
  Hanke, F.; Serr, A.; Kreuzer, H. J.; Netz, R. R. Stretching single polypeptides: The effect of rotational constraints in the backbone. Europhys. Lett. 2010, 92, 53001 DOI: 10.1209/0295-5075/92/53001
  There is no corresponding record for this reference.
45. 45
  Kitov, P. I.; Bundle, D. R. On the nature of the multivalency effect: a thermodynamic model. J. Am. Chem. Soc. 2003, 125, 16271– 16284, DOI: 10.1021/ja038223n
  45
  On the Nature of the Multivalency Effect: A Thermodynamic Model
  Kitov, Pavel I.; Bundle, David R.
  Journal of the American Chemical Society (2003), 125 (52), 16271-16284CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
  A quant. model is proposed for the anal. of the thermodn. parameters of multivalent interactions in dil. solns. or with immobilized multimeric receptor. The model takes into account all bound species and describes multivalent binding via two microscopic binding energies corresponding to inter- and intramol. interactions (ΔG°inter and ΔG°intra), the relative contributions of which depend on the distribution of complexes with different nos. of occupied binding sites. The third component of the overall free energy, which we call the "avidity entropy" term, is a function of the degeneracy of bound states, Ωi, which is calcd. on the basis of the topol. of interaction and the distribution of all bound species. This term grows rapidly with the no. of receptor sites and ligand multivalency, it always favors binding, and explains why multivalency can overcome the loss of conformational entropy when ligands displayed at the ends of long tethers are bound. The microscopic parameters ΔG°inter and ΔG°intra may be detd. from the obsd. binding energies for a set of oligovalent ligands by nonlinear fitting with the theor. model. Here binding data obtained from two series of oligovalent carbohydrate inhibitors for Shiga-like toxins were used to verify the theory. The decavalent and octavalent inhibitors exhibit subnanomolar activity and are the most active sol. inhibitors yet seen that block Shiga-like toxin binding to its native receptor. The theory developed here in conjunction with our protocol for the optimization of tether length provides a predictive approach to design and maximize the avidity of multivalent ligands.
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46. 46
  Zumbro, E.; Witten, J.; Alexander-Katz, A. Computational insights into avidity of polymeric multivalent binders. Biophys. J. 2019, 117, 892– 902, DOI: 10.1016/j.bpj.2019.07.026
  46
  Computational Insights into Avidity of Polymeric Multivalent Binders
  Zumbro, Emiko; Witten, Jacob; Alexander-Katz, Alfredo
  Biophysical Journal (2019), 117 (5), 892-902CODEN: BIOJAU; ISSN:0006-3495. (Cell Press)
  Multivalent binding interactions are commonly found throughout biol. to enhance weak monovalent binding such as between glycoligands and protein receptors. Designing multivalent polymers to bind to viruses and toxic proteins is a promising avenue for inhibiting their attachment and subsequent infection of cells. Several studies have focused on oligomeric multivalent inhibitors and how changing parameters such as ligand shape, size, linker length, and flexibility affect binding. However, exptl. studies of how larger structural parameters of multivalent polymers, such as d.p., affect binding avidity to targets have mixed results, with some finding an improvement with longer polymers and some finding no effect. Here, we use Brownian dynamics simulations to provide a theor. understanding of how the d.p. affects the binding avidity of multivalent polymers. We show that longer polymers increase binding avidity to multivalent targets but reach a limit in binding avidity at high ds.p. We also show that when interacting with multiple targets simultaneously, longer polymers are able to use intertarget interactions to promote clustering and improve binding efficiency. We expect our results to narrow the design space for optimizing the structure and effectiveness of multivalent inhibitors as well as be useful to understand biol. design strategies for multivalent binding.
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47. 47
  Qiao, B.; Jiménez-Ángeles, F.; Nguyen, T. D.; Olvera de la Cruz, M. Water follows polar and nonpolar protein surface domains. Proc. Natl. Acad. Sci. U.S.A. 2019, 116, 19274– 19281, DOI: 10.1073/pnas.1910225116
  47
  Water follows polar and nonpolar protein surface domains
  Qiao, Baofu; Jimenez-Angeles, Felipe; Nguyen, Trung Dac; de la Cruz, Monica Olvera
  Proceedings of the National Academy of Sciences of the United States of America (2019), 116 (39), 19274-19281CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
  The conformation of water around proteins is of paramount importance, as it dets. protein interactions. Although the av. water properties around the surface of proteins have been provided exptl. and computationally, protein surfaces are highly heterogeneous. Therefore, it is crucial to det. the correlations of water to the local distributions of polar and nonpolar protein surface domains to understand functions such as aggregation, mutations, and delivery. By using atomistic simulations, we investigate the orientation and dynamics of water mols. next to 4 types of protein surface domains: neg. charged, pos. charged, and charge-neutral polar and nonpolar amino acids. The neg. charged amino acids orient around 98% of the neighboring water dipoles toward the protein surface, and such correlation persists up to around 16 Å from the protein surface. The pos. charged amino acids orient around 94% of the nearest water dipoles against the protein surface, and the correlation persists up to around 12 Å. The charge-neutral polar and nonpolar amino acids are also orienting the water neighbors in a quant. weaker manner. A similar trend was obsd. in the residence time of the nearest water neighbors. These findings hold true for 3 tech. important enzymes (PETase, cytochrome P 450, and organophosphorus hydrolase). Our results demonstrate that the water-amino acid degree of correlation follows the same trend as the amino acid contribution in proteins soly., namely, the neg. charged amino acids are the most beneficial for protein soly., then the pos. charged amino acids, and finally the charge-neutral amino acids.
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48. 48
  Manning, G. S. Limiting laws and counterion condensation in polyelectrolyte solutions I. Colligative properties. J. Chem. Phys. 1969, 51, 924– 933, DOI: 10.1063/1.1672157
  48
  Limiting laws and counterion condensation in polyelectroyte solutions. I. Colligative properties
  Manning, Gerald S.
  Journal of Chemical Physics (1969), 51 (3), 924-33CODEN: JCPSA6; ISSN:0021-9606.
  Formulas are derived for the osmotic coeff., the Donnan salt-exclusion factor, and the mobile-ion activity coeffs. in a polyelectrolyte soln. with or without added sample salt. The formulas, which contain no adjustable parameters, are based on the (theoretical) observation by several workers that counterions will "condense" on the polyion until the charge d. on the polyion is reduced below a certain crit. value. The uncondensed mobile ions are treated in the Debye-Hueckel approxn. In a restricted sense, the formulas are "limiting laws," and this aspect is discussed at length. Detailed comparison with exptl. data in the literature is given; agreement of the theory with expt. is usually quant.
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49. 49
  Fenley, M. O.; Manning, G. S.; Olson, W. K. Approach to the limit of counterion condensation. Biopolymers 1990, 30, 1191– 1203, DOI: 10.1002/bip.360301305
  49
  Approach to the limit of counterion condensation
  Fenley, Marcia O.; Manning, Gerald S.; Olson, Wilma K.
  Biopolymers (1990), 30 (13-14), 1191-203CODEN: BIPMAA; ISSN:0006-3525.
  According to counterion condensation theory, one of the contributions to the polyelectrolyte free energy is a pairwise sum of Debye-Hueckel potentials between polymer charges that are reduced by condensed counterions. When the polyion model is taken as an infinitely long and uniformly spaced line of charges, a simple closed expression for the summation, combined with entropy-derived mixing contributions, leads to the central result of the theory, a condensed fraction of counterions dependent only on the linear charge d. of the polyion and the valence of the counterion, stable against increases of salt up to concns. in excess of 0.1M. Here the sum is numerically evaluated for B-DNA models other than the infinite line of B-DNA charges. For a finite-length line there are end effects at low salt. The condensation limit is reached as a flat plateau by increasing the salt concn. At a fixed salt concn. the condensation limit is reached by increasing the length of the line. At moderate salt even very short B-DNA line-model oligomers have condensed fractions not far from the infinite polymer limit. For a long double-helical array with charge coordinates at the phosphates of B-DNA, the limiting condensed fraction appears to be approached at low salt. In contrast to the results for the line of charges, however, the computed condensed fraction varies strongly with salt in the range of exptl. typical concns. Salt invariance is restored, in agreement with both the line model and exptl. data, when dielec. satn. is considered by means of a distance-dependent dielec. function. For sufficiently long B-DNA line and helical models, at typical salt concns., the counterion binding fraction approaches the polymer limit as a linear function of 1/P, where P is the no. of phosphate groups of B-DNA.
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50. 50
  Walkowiak, J. J.; Ballauff, M. Interaction of polyelectrolytes with proteins: quantifying the role of water. Adv. Sci. 2021, 8, 2100661 DOI: 10.1002/advs.202100661
  50
  Interaction of Polyelectrolytes with Proteins: Quantifying the Role of Water
  Walkowiak, Jacek J.; Ballauff, Matthias
  Advanced Science (Weinheim, Germany) (2021), 8 (12), 2100661CODEN: ASDCCF; ISSN:2198-3844. (Wiley-VCH Verlag GmbH & Co. KGaA)
  A theor. model is presented for the free energy ΔGb of complex formation between a highly charged polyelectrolyte and a protein. The model introduced here comprises both the effect of released counterions and the uptake or release of water mols. during complex formation. The resulting expression for ΔGb is hence capable of describing the dependence of ΔGb on temp. as well as on the concn. of salt in the system: An increase of the salt concn. in the soln. increases the activity of the ions and counterion release becomes less effective for binding. On the other hand, an increased salt concn. leads to the decrease of the activity of water in bulk. Hence, release of water mols. during complex formation will be more advantageous and lead to an increase of the magnitude of ΔGb and the binding const. It is furthermore demonstrated that the release or uptake of water mols. is the origin of the marked enthalpy-entropy cancellation obsd. during complex formation of polyelectrolytes with proteins. The comparison with exptl. data on complex formation between a synthetic (sulfated dendritic polyglycerol) and natural polyelectrolytes (DNA; heparin) with proteins shows full agreement with theory.
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51. 51
  Irudayam, S. J.; Henchman, R. H. Entropic cost of protein- ligand binding and its dependence on the entropy in solution. J. Phys. Chem. B 2009, 113, 5871– 5884, DOI: 10.1021/jp809968p
  51
  Entropic Cost of Protein-Ligand Binding and Its Dependence on the Entropy in Solution
  Irudayam, Sheeba Jem; Henchman, Richard H.
  Journal of Physical Chemistry B (2009), 113 (17), 5871-5884CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
  Two theor. formulations are proposed and compared for the loss of translational and rotational entropy upon protein-ligand binding in water. The two theories share the same approach to evaluate the translational and rotational entropy of the ligand when bound. The potential of the bound ligand is modeled by six harmonic oscillators that are parametrized from the force and torque magnitudes measured in a mol. dynamics simulation, yielding vibrational and librational entropies. In the aq. phase, the theories differ because there is no unique way to assign the total entropy to mols. in soln. In one approach, the ligand is allowed unrestricted access to the full soln. vol. at the std. concn. and is assigned the same translational and rotational entropy as if it were an ideal gas. We term this a "mol.-frame" (MF) theory because it considers configurational space in the ref. frame of the mol. of interest. The entropy of the solvent is penalized because it is excluded from the mol.'s vol. In the second theory, all mols. including the solvent are confined by their neighbors in mean-field configurational vols. This we term a "system-frame" (SF) theory because the configurational space available to all mols. is considered in the ref. frame of the whole system. Mols. have vibrational and librational entropy in the same way as they do when bound. In addn., the discrete size of the solvent mols. quantizes the configurational space into an effective no. of min. according to the solute mol.'s std. concn. and the mean vol. of a solvent mol. This leads to the cratic entropy expressed in terms of the solute mol.'s mole fraction. The equivalent no. of min. in rotational space depends on both the solute mol.'s vol. and the solvent mol.'s vol. This leads to an equation for the orientational entropy based on the proposed concept of "angle fraction". The MF and SF theories are applied to calc. the translational and rotational entropy losses involved in the formation of six different protein-ligand complexes, in two of which the ligand is water. The MF entropy losses range from -80 to -142 J K-1 mol-1 for ligands at the 1 M std.-state concn. and from -52 to -63 J K-1 mol-1 for water at the 55.6 M std.-state concn. They depend logarithmically on both the no. and strength of interactions between the ligand and protein through the forces and torques. This is obsd. to lead to moderate dependencies on the ligands' moments of inertia and masses. The SF entropy losses are smaller and range from -50 to -75 J K-1 mol-1 for ligands at the 1 M std.-state concn. and from 0 to -12 J K-1 mol-1 for water. They depend logarithmically on the ligand solvent's mol. vol. and weakly on the relative strengths of the ligand's interactions with the protein and water. The cratic entropy loss in water at the std. concn. is const. and is also demonstrated to be implicit in MF theories. Entropy losses from the two approaches are also compared with those from other computational approaches and with expt. The use of the force and torque magnitudes leads to smaller bound vols. than are obtained from ligand-displacement approaches. The general agreement of the SF entropy losses with those from expt. suggests that the SF theory is more consistent with the assumptions made in exptl. measurements than the MF solvation theories, which would require a compensating entropy gain in the solvent in order to agree.
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52. 52
  Xu, X.; Ran, Q.; Dey, P.; Nikam, R.; Haag, R.; Ballauff, M.; Dzubiella, J. Counterion-release entropy governs the inhibition of serum proteins by polyelectrolyte drugs. Biomacromolecules 2018, 19, 409– 416, DOI: 10.1021/acs.biomac.7b01499
  52
  Counterion-Release Entropy Governs the Inhibition of Serum Proteins by Polyelectrolyte Drugs
  Xu, Xiao; Ran, Qidi; Dey, Pradip; Nikam, Rohit; Haag, Rainer; Ballauff, Matthias; Dzubiella, Joachim
  Biomacromolecules (2018), 19 (2), 409-416CODEN: BOMAF6; ISSN:1525-7797. (American Chemical Society)
  Dendritic polyelectrolytes constitute high potential drugs and carrier systems for biomedical purposes. Still, their biomol. interaction modes, in particular those detg. the binding affinity to proteins, have not been rationalized. We study the interaction of the drug candidate dendritic polyglycerol sulfate (dPGS) with serum proteins using isothermal titrn. calorimetry (ITC) interpreted and complemented with mol. computer simulations. Lysozyme is first studied as a well-defined model protein to verify theor. concepts, which are then applied to the important cell adhesion protein family of selectins. We demonstrate that the driving force of the strong complexation, leading to a distinct protein corona, originates mainly from the release of only a few condensed counterions from the dPGS upon binding. The binding const. shows a surprisingly weak dependence on dPGS size (and bare charge) which can be understood by colloidal charge-renormalization effects and by the fact that the magnitude of the dominating counterion-release mechanism almost exclusively depends on the interfacial charge structure of the protein-specific binding patch. Our findings explain the high selectivity of P- and L-selectins over E-selectin for dPGS to act as a highly anti-inflammatory drug. The entire anal. demonstrates that the interaction of proteins with charged polymeric drugs can be predicted by simulations with unprecedented accuracy. Thus, our results open new perspectives for the rational design of charged polymeric drugs and carrier systems.
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53. 53
  Caro, J. A.; Harpole, K. W.; Kasinath, V.; Lim, J.; Granja, J.; Valentine, K. G.; Sharp, K. A.; Wand, A. J. Entropy in molecular recognition by proteins. Proc. Natl. Acad. Sci. U.S.A. 2017, 114, 6563– 6568, DOI: 10.1073/pnas.1621154114
  53
  Entropy in molecular recognition by proteins
  Caro, Jose A.; Harpole, Kyle W.; Kasinath, Vignesh; Lim, Jackwee; Granja, Jeffrey; Valentine, Kathleen G.; Sharp, Kim A.; Wand, A. Joshua
  Proceedings of the National Academy of Sciences of the United States of America (2017), 114 (25), 6563-6568CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
  Mol. recognition by proteins is fundamental to mol. biol. Dissection of the thermodn. energy terms governing protein-ligand interactions has proven difficult, with detn. of entropic contributions being particularly elusive. NMR relaxation measurements have suggested that changes in protein conformational entropy can be quant. obtained through a dynamical proxy, but the generality of this relationship has not been shown. Twenty-eight protein-ligand complexes are used to show a quant. relationship between measures of fast side-chain motion and the underlying conformational entropy. We find that the contribution of conformational entropy can range from favorable to unfavorable, which demonstrates the potential of this thermodn. variable to modulate protein-ligand interactions. For about one-quarter of these complexes, the absence of conformational entropy would render the resulting affinity biol. meaningless. The dynamical proxy for conformational entropy or "entropy meter" also allows for refinement of the contributions of solvent entropy and the loss in rotational-translational entropy accompanying formation of high-affinity complexes. Furthermore, structure-based application of the approach can also provide insight into long-lived specific water-protein interactions that escape the generic treatments of solvent entropy based simply on changes in accessible surface area. These results provide a comprehensive and unified view of the general role of entropy in high-affinity mol. recognition by proteins.
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54. 54
  Sahoo, A. K.; Schreiber, F.; Netz, R. R.; Maiti, P. K. Role of entropy in determining the phase behavior of protein solutions induced by multivalent ions. Soft Matter 2022, 18, 592– 601, DOI: 10.1039/D1SM00730K
  There is no corresponding record for this reference.
55. 55
  Rapaport, D. Hydrogen bonds in water: Network organization and lifetimes. Mol. Phys. 1983, 50, 1151– 1162, DOI: 10.1080/00268978300102931
  55
  Hydrogen bonds in water. Network organization and lifetimes
  Rapaport, D. C.
  Molecular Physics (1983), 50 (5), 1151-62CODEN: MOPHAM; ISSN:0026-8976.
  Equil. and dynamical properties of H bonds in liq. H2O are analyzed using the results of mol. dynamics simulations of the MCY-CI model. Properties of the H bond clusters as functions of temp. are described. The connectivity of the clusters is analyzed in terms of the bridgeless polygons which are formed by the bonds. The problem of obtaining a meaningful definition of bond lifetime is discussed, and the results of lifetime measurements based on alternative definitions are shown.
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56. 56
  Malicka, W.; Haag, R.; Ballauff, M. Interaction of heparin with proteins: hydration effects. J. Phys. Chem. B 2022, 126, 6250– 6260, DOI: 10.1021/acs.jpcb.2c04928
  There is no corresponding record for this reference.
57. 57
  Geisler, M.; Xiao, S.; Puchner, E. M.; Gräter, F.; Hugel, T. Controlling the structure of proteins at surfaces. J. Am. Chem. Soc. 2010, 132, 17277– 17281, DOI: 10.1021/ja107212z
  57
  Controlling the Structure of Proteins at Surfaces
  Geisler, Michael; Xiao, Sen-Bo; Puchner, Elias M.; Graeter, Frauke; Hugel, Thorsten
  Journal of the American Chemical Society (2010), 132 (48), 17277-17281CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
  With the help of single mol. force spectroscopy and mol. dynamics simulations, we det. the surface-induced structure of a single engineered spider silk protein. An amyloid like structure is induced in the vicinity of a surface with high surface energy and can be prohibited in the presence of a hydrophobic surface. The derived mol. energy landscapes highlight the role of single silk protein structure for the macroscopic toughness of spider silk.
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58. 58
  Liese, S.; Netz, R. R. Influence of length and flexibility of spacers on the binding affinity of divalent ligands. Beilstein J. Org. Chem. 2015, 11, 804– 816, DOI: 10.3762/bjoc.11.90
  58
  Influence of length and flexibility of spacers on the binding affinity of divalent ligands
  Liese, Susanne; Netz, Roland R.
  Beilstein Journal of Organic Chemistry (2015), 11 (), 804-816CODEN: BJOCBH; ISSN:1860-5397. (Beilstein-Institut zur Foerderung der Chemischen Wissenschaften)
  We present a quant. model for the binding of divalent ligand-receptor systems. We study the influence of length and flexibility of the spacers on the overall binding affinity and derive general rules for the optimal ligand design. To this end, we first compare different polymeric models and det. the probability to simultaneously bind to two neighboring receptor binding pockets. In a second step the binding affinity of divalent ligands in terms of the IC50 value is derived. We find that a divalent ligand has the potential to bind more efficiently than its monovalent counterpart only, if the monovalent dissocn. const. is lower than a crit. value. This crit. monovalent dissocn. const. depends on the ligand-spacer length and flexibility as well as on the size of the receptor. Regarding the optimal ligand-spacer length and flexibility, we find that the av. spacer length should be equal or slightly smaller than the distance between the receptor binding pockets and that the end-to-end spacer length fluctuations should be in the same range as the size of a receptor binding pocket.
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59. 59
  Jo, S.; Kim, T.; Iyer, V. G.; Im, W. CHARMM-GUI: a web-based graphical user interface for CHARMM. J. Comput. Chem. 2008, 29, 1859– 1865, DOI: 10.1002/jcc.20945
  59
  CHARMM-GUI: a web-based graphical user interface for CHARMM
  Jo, Sunhwan; Kim, Taehoon; Iyer, Vidyashankara G.; Im, Wonpil
  Journal of Computational Chemistry (2008), 29 (11), 1859-1865CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
  CHARMM is an academic research program used widely for macromol. mechanics and dynamics with versatile anal. and manipulation tools of at. coordinates and dynamics trajectories. CHARMM-GUI, http://www.charmm-gui.org, has been developed to provide a web-based graphical user interface to generate various input files and mol. systems to facilitate and standardize the usage of common and advanced simulation techniques in CHARMM. The web environment provides an ideal platform to build and validate a mol. model system in an interactive fashion such that, if a problem is found through visual inspection, one can go back to the previous setup and regenerate the whole system again. In this article, we describe the currently available functional modules of CHARMM-GUI Input Generator that form a basis for the advanced simulation techniques. Future directions of the CHARMM-GUI development project are also discussed briefly together with other features in the CHARMM-GUI website, such as Archive and Movie Gallery.
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60. 60
  Park, S.-J.; Lee, J.; Qi, Y.; Kern, N. R.; Lee, H. S.; Jo, S.; Joung, I.; Joo, K.; Lee, J.; Im, W. CHARMM-GUI Glycan Modeler for modeling and simulation of carbohydrates and glycoconjugates. Glycobiology 2019, 29, 320– 331, DOI: 10.1093/glycob/cwz003
  60
  CHARMM-GUI Glycan Modeler for modeling and simulation of carbohydrates and glycoconjugates
  Park, Sang-Jun; Lee, Jumin; Qi, Yifei; Kern, Nathan R.; Lee, Hui Sun; Jo, Sunhwan; Joung, Insuk; Joo, Keehyung; Lee, Jooyoung; Im, Wonpil
  Glycobiology (2019), 29 (4), 320-331CODEN: GLYCE3; ISSN:1460-2423. (Oxford University Press)
  Characterizing glycans and glycoconjugates in context of three-dimensional structures is important in understanding their biol. roles and developing efficient therapeutic agents. Computational modeling and mol. simulation have become essential tool complementary to exptl. methods. Here, we present computational tool, Glycan Modeler for in silico N-/O-glycosylation of target protein and generation of carbohydrate-only systems. In our previous study, we developed Glycan Reader, web-based tool for detecting carbohydrate mols. from PDB structure and generation of simulation system and input files. As integrated into Glycan Reader in CHARMM-GUI, Glycan Modeler enables to generate structures of glycans and glycoconjugates for given glycan sequences and glycosylation sites using PDB glycan template structures from Glycan Fragment Database (http://glycanstructure.org/ fragment-db). Our benchmark tests demonstrate universal applicability of Glycan Reader & Modeler to various glycan sequences and target proteins. We also investigated structural properties of modeled glycan structures by running 2-μs mol. dynamics simulations of HIV envelope protein. Simulations show that modeled glycan structures built by Glycan Reader & Modeler have similar structural features compared to ones solved by X-ray crystallog. We also describe representative examples of glycoconjugate modeling with video demos to illustrate practical applications of Glycan Reader & Modeler.
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61. 61
  Jo, S.; Song, K. C.; Desaire, H.; MacKerell, A. D., Jr; Im, W. Glycan Reader: automated sugar identification and simulation preparation for carbohydrates and glycoproteins. J. Comput. Chem. 2011, 32, 3135– 3141, DOI: 10.1002/jcc.21886
  61
  Glycan Reader: Automated sugar identification and simulation preparation for carbohydrates and glycoproteins
  Jo, Sunhwan; Song, Kevin C.; Desaire, Heather; MacKerell, Alexander D.; Im, Wonpil
  Journal of Computational Chemistry (2011), 32 (14), 3135-3141CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
  Understanding how glycosylation affects protein structure, dynamics, and function is an emerging and challenging problem in biol. As a first step toward glycan modeling in the context of structural glycobiol., the authors have developed Glycan Reader and integrated it into the CHARMM-GUI,. Glycan Reader greatly simplifies the reading of PDB structure files contg. glycans through (i) detection of carbohydrate mols., (ii) automatic annotation of carbohydrates based on their three-dimensional structures, (iii) recognition of glycosidic linkages between carbohydrates as well as N-/O-glycosidic linkages to proteins, and (iv) generation of inputs for the biomol. simulation program CHARMM with the proper glycosidic linkage setup. In addn., Glycan Reader is linked to other functional modules in CHARMM-GUI, allowing users to easily generate carbohydrate or glycoprotein mol. simulation systems in soln. or membrane environments and visualize the electrostatic potential on glycoprotein surfaces. These tools are useful for studying the impact of glycosylation on protein structure and dynamics. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011.
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62. 62
  Park, S.-J.; Lee, J.; Patel, D. S.; Ma, H.; Lee, H. S.; Jo, S.; Im, W. Glycan Reader is improved to recognize most sugar types and chemical modifications in the Protein Data Bank. Bioinformatics 2017, 33, 3051– 3057, DOI: 10.1093/bioinformatics/btx358
  62
  Glycan Reader is improved to recognize most sugar types and chemical modifications in the Protein Data Bank
  Park, Sang-Jun; Lee, Jumin; Patel, Dhilon S.; Ma, Hongjing; Lee, Hui Sun; Jo, Sunhwan; Im, Wonpil
  Bioinformatics (2017), 33 (19), 3051-3057CODEN: BOINFP; ISSN:1367-4811. (Oxford University Press)
  Motivation: Glycans play a central role in many essential biol. processes. Glycan Reader was originally developed to simplify the reading of Protein Data Bank (PDB) files contg. glycans through the automatic detection and annotation of sugars and glycosidic linkages between sugar units and to proteins, all based on at. coordinates and connectivity information. Carbohydrates can have various chem. modifications at different positions, making their chem. space much diverse. Unfortunately, current PDB files do not provide exact annotations for most carbohydrate derivs. and more than 50% of PDB glycan chains have at least one carbohydrate deriv. that could not be correctly recognized by the original Glycan Reader. Results: Glycan Reader has been improved and now identifies most sugar types and chem. modifications (including various glycolipids) in the PDB, and both PDB and PDBx/mmCIF formats are supported. CHARMM-GUI Glycan Reader is updated to generate the simulation system and input of various glycoconjugates with most sugar types and chem. modifications. It also offers a new functionality to edit the glycan structures through addn./deletion/modification of glycosylation types, sugar types, chem. modifications, glycosidic linkages, and anomeric states. The simulation system and input files can be used for CHARMM, NAMD, GROMACS, AMBER, GENESIS, LAMMPS, Desmond, OpenMM, and CHARMM/OpenMM. Glycan Fragment Database in GlycanStructure.Org is also updated to provide an intuitive glycan sequence search tool for complex glycan structures with various chem. modifications in the PDB.
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63. 63
  Hanwell, M. D.; Curtis, D. E.; Lonie, D. C.; Vandermeersch, T.; Zurek, E.; Hutchison, G. R. Avogadro: an advanced semantic chemical editor, visualization, and analysis platform. J. Cheminf. 2012, 4, 1– 17, DOI: 10.1186/1758-2946-4-17
  There is no corresponding record for this reference.
64. 64
  Huang, J.; Rauscher, S.; Nawrocki, G.; Ran, T.; Feig, M.; De Groot, B. L.; Grubmüller, H.; MacKerell, A. D. CHARMM36m: an improved force field for folded and intrinsically disordered proteins. Nat. Methods 2017, 14, 71– 73, DOI: 10.1038/nmeth.4067
  64
  CHARMM36m: an improved force field for folded and intrinsically disordered proteins
  Huang, Jing; Rauscher, Sarah; Nawrocki, Grzegorz; Ran, Ting; Feig, Michael; de Groot, Bert L.; Grubmuller, Helmut; MacKerell, Alexander D. Jr
  Nature Methods (2017), 14 (1), 71-73CODEN: NMAEA3; ISSN:1548-7091. (Nature Publishing Group)
  The all-atom additive CHARMM36 protein force field is widely used in mol. modeling and simulations. We present its refinement, CHARMM36m (http://mackerell.umaryland.edu/charmm_ff.shtml), with improved accuracy in generating polypeptide backbone conformational ensembles for intrinsically disordered peptides and proteins.
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65. 65
  Guvench, O.; Mallajosyula, S. S.; Raman, E. P.; Hatcher, E.; Vanommeslaeghe, K.; Foster, T. J.; Jamison, F. W.; MacKerell, A. D., Jr CHARMM additive all-atom force field for carbohydrate derivatives and its utility in polysaccharide and carbohydrate-protein modeling. J. Chem. Theory Comput. 2011, 7, 3162– 3180, DOI: 10.1021/ct200328p
  65
  CHARMM Additive All-Atom Force Field for Carbohydrate Derivatives and Its Utility in Polysaccharide and Carbohydrate-Protein Modeling
  Guvench, Olgun; Mallajosyula, Sairam S.; Raman, E. Prabhu; Hatcher, Elizabeth; Vanommeslaeghe, Kenno; Foster, Theresa J.; Jamison, Francis W.; MacKerell, Alexander D.
  Journal of Chemical Theory and Computation (2011), 7 (10), 3162-3180CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  Monosaccharide derivs. such as xylose, fucose, N-acetylglucosamine (GlcNAc), N-acetylgalactosamine (GlaNAc), glucuronic acid, iduronic acid, and N-acetylneuraminic acid (Neu5Ac) are important components of eukaryotic glycans. The present work details the development of force-field parameters for these monosaccharides and their covalent connections to proteins via O linkages to serine or threonine side chains and via N linkages to asparagine side chains. The force field development protocol was designed to explicitly yield parameters that are compatible with the existing CHARMM additive force field for proteins, nucleic acids, lipids, carbohydrates, and small mols. Therefore, when combined with previously developed parameters for pyranose and furanose monosaccharides, for glycosidic linkages between monosaccharides, and for proteins, the present set of parameters enables the mol. simulation of a wide variety of biol. important mols. such as complex carbohydrates and glycoproteins. Parametrization included fitting to quantum mech. (QM) geometries and conformational energies of model compds., as well as to QM pair interaction energies and distances of model compds. with water. Parameters were validated in the context of crystals of relevant monosaccharides, as well NMR and/or x-ray crystallog. data on larger systems including oligomeric hyaluronan, sialyl Lewis X, O- and N-linked glycopeptides, and a lectin:sucrose complex. As the validated parameters are an extension of the CHARMM all-atom additive biomol. force field, they further broaden the types of heterogeneous systems accessible with a consistently developed force-field model.
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66. 66
  Mallajosyula, S. S.; Guvench, O.; Hatcher, E.; MacKerell, A. D., Jr CHARMM additive all-atom force field for phosphate and sulfate linked to carbohydrates. J. Chem. Theory Comput. 2012, 8, 759– 776, DOI: 10.1021/ct200792v
  66
  CHARMM Additive All-Atom Force Field for Phosphate and Sulfate Linked to Carbohydrates
  Mallajosyula, Sairam S.; Guvench, Olgun; Hatcher, Elizabeth; MacKerell, Alexander D.
  Journal of Chemical Theory and Computation (2012), 8 (2), 759-776CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  Presented is an extension of the CHARMM additive all-atom carbohydrate force field to enable the modeling of phosphate and sulfate linked to carbohydrates. The parameters are developed in a hierarchical fashion using model compds. contg. the key atoms in the full carbohydrates. Target data for parameter optimization included full two-dimensional energy surfaces defined by the glycosidic dihedral angle pairs in the phosphate/sulfate model compd. analogs of hexopyranose monosaccharide phosphates and sulfates, as detd. by quantum mech. (QM) MP2/cc-pVTZ single point energies on MP2/6-31+G(d) optimized structures. To achieve balanced, transferable dihedral parameters for the dihedral angles, surfaces for all possible anomeric and conformational states were included during the parametrization process. To model physiol. relevant systems, both the mono- and dianionic charged states were studied for the phosphates. This resulted in over 7000 MP2/cc-pVTZ//MP2/6-31G+(d) model compd. conformational energies which, supplemented with QM geometries, were the main target data for the parametrization. Parameters were validated against crystals of relevant monosaccharide derivs. obtained from the Cambridge Structural Database (CSD) and larger systems, inositol-(tri/tetra/penta) phosphates noncovalently bound to the pleckstrin homol. (PH) domain and oligomeric chondroitin sulfate in soln. and in complex with cathepsin K protein.
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67. 67
  Vanommeslaeghe, K.; Hatcher, E.; Acharya, C.; Kundu, S.; Zhong, S.; Shim, J.; Darian, E.; Guvench, O.; Lopes, P.; Vorobyov, I.; Mackerell, A. D. CHARMM general force field: A force field for drug-like molecules compatible with the CHARMM all-atom additive biological force fields. J. Comput. Chem. 2010, 31, 671– 690, DOI: 10.1002/jcc.21367
  67
  CHARMM general force field: A force field for drug-like molecules compatible with the CHARMM all-atom additive biological force fields
  Vanommeslaeghe, K.; Hatcher, E.; Acharya, C.; Kundu, S.; Zhong, S.; Shim, J.; Darian, E.; Guvench, O.; Lopes, P.; Vorobyov, I.; Mackerell, A. D., Jr.
  Journal of Computational Chemistry (2010), 31 (4), 671-690CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
  The widely used CHARMM additive all-atom force field includes parameters for proteins, nucleic acids, lipids, and carbohydrates. In the present article, an extension of the CHARMM force field to drug-like mols. is presented. The resulting CHARMM General Force Field (CGenFF) covers a wide range of chem. groups present in biomols. and drug-like mols., including a large no. of heterocyclic scaffolds. The parametrization philosophy behind the force field focuses on quality at the expense of transferability, with the implementation concg. on an extensible force field. Statistics related to the quality of the parametrization with a focus on exptl. validation are presented. Addnl., the parametrization procedure, described fully in the present article in the context of the model systems, pyrrolidine, and 3-phenoxymethyl-pyrrolidine will allow users to readily extend the force field to chem. groups that are not explicitly covered in the force field as well as add functional groups to and link together mols. already available in the force field. CGenFF thus makes it possible to perform "all-CHARMM" simulations on drug-target interactions thereby extending the utility of CHARMM force fields to medicinally relevant systems. © 2009 Wiley Periodicals, Inc.J Comput Chem, 2010.
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68. 68
  Yu, W.; He, X.; Vanommeslaeghe, K.; MacKerell, A. D., Jr Extension of the CHARMM general force field to sulfonyl-containing compounds and its utility in biomolecular simulations. J. Comput. Chem. 2012, 33, 2451– 2468, DOI: 10.1002/jcc.23067
  68
  Extension of the CHARMM general force field to sulfonyl-containing compounds and its utility in biomolecular simulations
  Yu, Wenbo; He, Xibing; Vanommeslaeghe, Kenno; MacKerell, Alexander D.
  Journal of Computational Chemistry (2012), 33 (31), 2451-2468CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
  Presented is an extension of the CHARMM General Force Field (CGenFF) to enable the modeling of sulfonyl-contg. compds. Model compds. contg. chem. moieties such as sulfone, sulfonamide, sulfonate, and sulfamate were used as the basis for the parameter optimization. Targeting high-level quantum mech. and exptl. crystal data, the new parameters were optimized in a hierarchical fashion designed to maintain compatibility with the remainder of the CHARMM additive force field. The optimized parameters satisfactorily reproduced equil. geometries, vibrational frequencies, interactions with water, gas phase dipole moments, and dihedral potential energy scans. Validation involved both cryst. and liq. phase calcns. showing the newly developed parameters to satisfactorily reproduce exptl. unit cell geometries, crystal intramol. geometries, and pure solvent densities. The force field was subsequently applied to study conformational preference of a sulfonamide-based peptide system. Good agreement with exptl. IR/NMR data further validated the newly developed CGenFF parameters as a tool to investigate the dynamic behavior of sulfonyl groups in a biol. environment. CGenFF now covers sulfonyl group contg. moieties allowing for modeling and simulation of sulfonyl-contg. compds. in the context of biomol. systems including compds. of medicinal interest.
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69. 69
  Vanommeslaeghe, K.; MacKerell, A. D., Jr Automation of the CHARMM General Force Field (CGenFF) I: bond perception and atom typing. J. Chem. Inf. Model. 2012, 52, 3144– 3154, DOI: 10.1021/ci300363c
  69
  Automation of the CHARMM General Force Field (CGenFF) I: Bond Perception and Atom Typing
  Vanommeslaeghe, K.; MacKerell, A. D.
  Journal of Chemical Information and Modeling (2012), 52 (12), 3144-3154CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
  Mol. mechanics force fields are widely used in computer-aided drug design for the study of drug-like mols. alone or interacting with biol. systems. In simulations involving biol. macromols., the biol. part is typically represented by a specialized biomol. force field, while the drug is represented by a matching general (org.) force field. In order to apply these general force fields to an arbitrary drug-like mol., functionality for assignment of atom types, parameters, and charges is required. In the present article, which is part I of a series of two, we present the algorithms for bond perception and atom typing for the CHARMM General Force Field (CGenFF). The CGenFF atom typer first assocs. attributes to the atoms and bonds in a mol., such as valence, bond order, and ring membership among others. Of note are a no. of features that are specifically required for CGenFF. This information is then used by the atom typing routine to assign CGenFF atom types based on a programmable decision tree. This allows for straight-forward implementation of CGenFF's complicated atom typing rules and for equally straight-forward updating of the atom typing scheme as the force field grows. The presented atom typer was validated by assigning correct atom types on 477 model compds. including in the training set as well as 126 test-set mols. that were constructed to specifically verify its different components. The program may be utilized via an online implementation at https://www.paramchem.org/.
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70. 70
  Vanommeslaeghe, K.; Raman, E. P.; MacKerell, A. D., Jr Automation of the CHARMM General Force Field (CGenFF) II: assignment of bonded parameters and partial atomic charges. J. Chem. Inf. Model. 2012, 52, 3155– 3168, DOI: 10.1021/ci3003649
  70
  Automation of the CHARMM General Force Field (CGenFF) II: Assignment of Bonded Parameters and Partial Atomic Charges
  Vanommeslaeghe, K.; Raman, E. Prabhu; MacKerell, A. D.
  Journal of Chemical Information and Modeling (2012), 52 (12), 3155-3168CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
  Mol. mechanics force fields are widely used in computer-aided drug design for the study of drug candidates interacting with biol. systems. In these simulations, the biol. part is typically represented by a specialized biomol. force field, while the drug is represented by a matching general (org.) force field. In order to apply these general force fields to an arbitrary drug-like mol., functionality for assignment of atom types, parameters, and partial at. charges is required. In the present article, algorithms for the assignment of parameters and charges for the CHARMM General Force Field (CGenFF) are presented. These algorithms rely on the existing parameters and charges that were detd. as part of the parametrization of the force field. Bonded parameters are assigned based on the similarity between the atom types that define said parameters, while charges are detd. using an extended bond-charge increment scheme. Charge increments were optimized to reproduce the charges on model compds. that were part of the parametrization of the force field. Case studies are presented to clarify the functioning of the algorithms and the significance of their output data.
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71. 71
  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
  71
  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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72. 72
  MacKerell, A. D., Jr; Bashford, D.; Bellott, M.; Dunbrack, R. L., Jr; Evanseck, J. D.; Field, M. J.; Fischer, S.; Gao, J.; Guo, H.; Ha, S. All-atom empirical potential for molecular modeling and dynamics studies of proteins. J. Phys. Chem. B 1998, 102, 3586– 3616, DOI: 10.1021/jp973084f
  72
  All-Atom Empirical Potential for Molecular Modeling and Dynamics Studies of Proteins
  MacKerell, A. D., Jr.; Bashford, D.; Bellott, M.; Dunbrack, R. L.; Evanseck, J. D.; Field, M. J.; Fischer, S.; Gao, J.; Guo, H.; Ha, S.; Joseph-McCarthy, D.; Kuchnir, L.; Kuczera, K.; Lau, F. T. K.; Mattos, C.; Michnick, S.; Ngo, T.; Nguyen, D. T.; Prodhom, B.; Reiher, W. E., III; Roux, B.; Schlenkrich, M.; Smith, J. C.; Stote, R.; Straub, J.; Watanabe, M.; Wiorkiewicz-Kuczera, J.; Yin, D.; Karplus, M.
  Journal of Physical Chemistry B (1998), 102 (18), 3586-3616CODEN: JPCBFK; ISSN:1089-5647. (American Chemical Society)
  New protein parameters are reported for the all-atom empirical energy function in the CHARMM program. The parameter evaluation was based on a self-consistent approach designed to achieve a balance between the internal (bonding) and interaction (nonbonding) terms of the force field and among the solvent-solvent, solvent-solute, and solute-solute interactions. Optimization of the internal parameters used exptl. gas-phase geometries, vibrational spectra, and torsional energy surfaces supplemented with ab initio results. The peptide backbone bonding parameters were optimized with respect to data for N-methylacetamide and the alanine dipeptide. The interaction parameters, particularly the at. charges, were detd. by fitting ab initio interaction energies and geometries of complexes between water and model compds. that represented the backbone and the various side chains. In addn., dipole moments, exptl. heats and free energies of vaporization, solvation and sublimation, mol. vols., and crystal pressures and structures were used in the optimization. The resulting protein parameters were tested by applying them to noncyclic tripeptide crystals, cyclic peptide crystals, and the proteins crambin, bovine pancreatic trypsin inhibitor, and carbonmonoxy myoglobin in vacuo and in a crystal. A detailed anal. of the relationship between the alanine dipeptide potential energy surface and calcd. protein φ, χ angles was made and used in optimizing the peptide group torsional parameters. The results demonstrate that use of ab initio structural and energetic data by themselves are not sufficient to obtain an adequate backbone representation for peptides and proteins in soln. and in crystals. Extensive comparisons between mol. dynamics simulation and exptl. data for polypeptides and proteins were performed for both structural and dynamic properties. Calcd. data from energy minimization and dynamics simulations for crystals demonstrate that the latter are needed to obtain meaningful comparisons with exptl. crystal structures. The presented parameters, in combination with the previously published CHARMM all-atom parameters for nucleic acids and lipids, provide a consistent set for condensed-phase simulations of a wide variety of mols. of biol. interest.
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73. 73
  Venable, R. M.; Luo, Y.; Gawrisch, K.; Roux, B.; Pastor, R. W. Simulations of anionic lipid membranes: development of interaction-specific ion parameters and validation using NMR data. J. Phys. Chem. B 2013, 117, 10183– 10192, DOI: 10.1021/jp401512z
  73
  Simulations of Anionic Lipid Membranes: Development of Interaction-Specific Ion Parameters and Validation Using NMR Data
  Venable, Richard M.; Luo, Yun; Gawrisch, Klaus; Roux, Benoit; Pastor, Richard W.
  Journal of Physical Chemistry B (2013), 117 (35), 10183-10192CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
  Overbinding of ions to lipid head groups is a potentially serious artifact in simulations of charged lipid bilayers. In this study, the Lennard-Jones radii in the CHARMM force field for interactions of Na+ and lipid oxygen atoms of carboxyl, phosphate, and ester groups were revised to match osmotic pressure data on sodium acetate and electrophoresis data on palmitoyloleoyl phosphatidylcholine (POPC) vesicles. The new parameters were then validated by successfully reproducing previously published exptl. NMR deuterium order parameters for dimyristoyl phosphatidylglycerol (DMPG) and newly obtained values for palmitoyloleoyl phosphatidylserine (POPS). Although the increases in Lennard-Jones diams. are only 0.02-0.12 Å, they are sufficient to reduce Na+ binding, and thereby increase surface areas per lipid by 5-10% compared with the unmodified parameters.
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74. 74
  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
  There is no corresponding record for this reference.
75. 75
  Bussi, G.; Donadio, D.; Parrinello, M. Canonical sampling through velocity rescaling. J. Chem. Phys. 2007, 126, 014101 DOI: 10.1063/1.2408420
  75
  Canonical sampling through velocity rescaling
  Bussi, Giovanni; Donadio, Davide; Parrinello, Michele
  Journal of Chemical Physics (2007), 126 (1), 014101/1-014101/7CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  The authors present a new mol. dynamics algorithm for sampling the canonical distribution. In this approach the velocities of all the particles are rescaled by a properly chosen random factor. The algorithm is formally justified and it is shown that, in spite of its stochastic nature, a quantity can still be defined that remains const. during the evolution. In numerical applications this quantity can be used to measure the accuracy of the sampling. The authors illustrate the properties of this new method on Lennard-Jones and TIP4P water models in the solid and liq. phases. Its performance is excellent and largely independent of the thermostat parameter also with regard to the dynamic properties.
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76. 76
  Parrinello, M.; Rahman, A. Polymorphic transitions in single crystals: A new molecular dynamics method. J. Appl. Phys. 1981, 52, 7182– 7190, DOI: 10.1063/1.328693
  76
  Polymorphic transitions in single crystals: A new molecular dynamics method
  Parrinello, M.; Rahman, A.
  Journal of Applied Physics (1981), 52 (12), 7182-90CODEN: JAPIAU; ISSN:0021-8979.
  A Lagrangian formulation is introduced; it can be used to make mol. dynamics (MD) calcns. on systems under the most general, externally applied, conditions of stress. In this formulation the MD cell shape and size can change according to dynamic equations given by this Lagrangian. This MD technique was used to the study of structural transitions of a Ni single crystal under uniform uniaxial compressive and tensile loads. Some results regarding the stress-strain relation obtained by static calcns. are invalid at finite temp. Under compressive loading, the model of Ni shows a bifurcation in its stress-strain relation; this bifurcation provides a link in configuration space between cubic and hexagonal close packing. Such a transition could perhaps be obsd. exptl. under extreme conditions of shock.
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77. 77
  Hess, B. P-LINCS: A A parallel linear constraint solver for molecular simulation. J. Chem. Theory Comput. 2008, 4, 116– 122, DOI: 10.1021/ct700200b
  77
  P-LINCS: A Parallel Linear Constraint Solver for Molecular Simulation
  Hess, Berk
  Journal of Chemical Theory and Computation (2008), 4 (1), 116-122CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  By removing the fastest degrees of freedom, constraints allow for an increase of the time step in mol. simulations. In the last decade parallel simulations have become commonplace. However, up till now efficient parallel constraint algorithms have not been used with domain decompn. In this paper the parallel linear constraint solver (P-LINCS) is presented, which allows the constraining of all bonds in macromols. Addnl. the energy conservation properties of (P-)LINCS are assessed in view of improvements in the accuracy of uncoupled angle constraints and integration in single precision.
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78. 78
  Darden, T.; York, D.; Pedersen, L. Particle mesh Ewald: An N · log(N) method for Ewald sums in large systems. J. Chem. Phys. 1993, 98, 10089– 10092, DOI: 10.1063/1.464397
  78
  Particle mesh Ewald: an N·log(N) method for Ewald sums in large systems
  Darden, Tom; York, Darrin; Pedersen, Lee
  Journal of Chemical Physics (1993), 98 (12), 10089-92CODEN: JCPSA6; ISSN:0021-9606.
  An N·log(N) method for evaluating electrostatic energies and forces of large periodic systems is presented. The method is based on interpolation of the reciprocal space Ewald sums and evaluation of the resulting convolution using fast Fourier transforms. Timings and accuracies are presented for three large cryst. ionic systems.
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79. 79
  Loche, P.; Steinbrunner, P.; Friedowitz, S.; Netz, R. R.; Bonthuis, D. J. Transferable Ion Force Fields in Water from a Simultaneous Optimization of Ion Solvation and Ion–Ion Interaction. J. Phys. Chem. B 2021, 125, 8581– 8587, DOI: 10.1021/acs.jpcb.1c05303
  79
  Transferable Ion Force Fields in Water from a Simultaneous Optimization of Ion Solvation and Ion-Ion Interaction
  Loche, Philip; Steinbrunner, Patrick; Friedowitz, Sean; Netz, Roland R.; Bonthuis, Douwe Jan
  Journal of Physical Chemistry B (2021), 125 (30), 8581-8587CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
  The poor performance of many existing nonpolarizable ion force fields is typically blamed on either the lack of explicit polarizability, the absence of charge transfer, or the use of unreduced Coulomb interactions. However, this anal. disregards the large and mostly unexplored parameter range offered by the Lennard-Jones potential. We use a global optimization procedure to develop water-model-transferable force fields for the ions K+, Na+, Cl-, and Br- in the complete parameter space of all Lennard-Jones interactions using std. mixing rules. No extra-thermodn. assumption is necessary for the simultaneous optimization of the four ion pairs. After optimization with respect to the exptl. solvation free energy and activity, the force fields reproduce the concn. dependent d., ionic cond. and dielec. const. with high accuracy. The force field is fully transferable between SPC/E, TIP3P, and TIP4P/ε water models. Our results show that a thermodynamically consistent force field for these ions needs only Lennard-Jones and std. Coulomb interactions.
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80. 80
  Humphrey, W.; Dalke, A.; Schulten, K. VMD: visual molecular dynamics. J. Mol. Graphics 1996, 14, 33– 38, DOI: 10.1016/0263-7855(96)00018-5
  80
  VDM: visual molecular dynamics
  Humphrey, William; Dalke, Andrew; Schulten, Klaus
  Journal of Molecular Graphics (1996), 14 (1), 33-8, plates, 27-28CODEN: JMGRDV; ISSN:0263-7855. (Elsevier)
  VMD is a mol. graphics program designed for the display and anal. of mol. assemblies, in particular, biopolymers such as proteins and nucleic acids. VMD can simultaneously display any no. of structures using a wide variety of rendering styles and coloring methods. Mols. are displayed as one or more "representations," in which each representation embodies a particular rendering method and coloring scheme for a selected subset of atoms. The atoms displayed in each representation are chosen using an extensive atom selection syntax, which includes Boolean operators and regular expressions. VMD provides a complete graphical user interface for program control, as well as a text interface using the Tcl embeddable parser to allow for complex scripts with variable substitution, control loops, and function calls. Full session logging is supported, which produces a VMD command script for later playback. High-resoln. raster images of displayed mols. may be produced by generating input scripts for use by a no. of photorealistic image-rendering applications. VMD has also been expressly designed with the ability to animate mol. dynamics (MD) simulation trajectories, imported either from files or from a direct connection to a running MD simulation. VMD is the visualization component of MDScope, a set of tools for interactive problem solving in structural biol., which also includes the parallel MD program NAMD, and the MDCOMM software used to connect the visualization and simulation programs, VMD is written in C++, using an object-oriented design; the program, including source code and extensive documentation, is freely available via anonymous ftp and through the World Wide Web.
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81. 81
  Gowers, R. J.; Linke, M.; Barnoud, J.; Reddy, T. J.; Melo, M. N.; Seyler, S. L.; Domanski, J.; Dotson, D. L.; Buchoux, S.; Kenney, I. M.; Beckstein, O. MDAnalysis: A Python Package for the Rapid Analysis of Molecular Dynamics Simulations; Proceedings of the 15th Python in Science Conference; Office of Scientific and Technical Information: Los Alamos, NM, 2016; p 105.
  There is no corresponding record for this reference.
82. 82
  Michaud-Agrawal, N.; Denning, E. J.; Woolf, T. B.; Beckstein, O. MDAnalysis: a toolkit for the analysis of molecular dynamics simulations. J. Comput. Chem. 2011, 32, 2319– 2327, DOI: 10.1002/jcc.21787
  82
  MDAnalysis: A toolkit for the analysis of molecular dynamics simulations
  Michaud-Agrawal, Naveen; Denning, Elizabeth J.; Woolf, Thomas B.; Beckstein, Oliver
  Journal of Computational Chemistry (2011), 32 (10), 2319-2327CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
  MDAnal. is an object-oriented library for structural and temporal anal. of mol. dynamics (MD) simulation trajectories and individual protein structures. It is written in the Python language with some performance-crit. code in C. It uses the powerful NumPy package to expose trajectory data as fast and efficient NumPy arrays. It has been tested on systems of millions of particles. Many common file formats of simulation packages including CHARMM, Gromacs, Amber, and NAMD and the Protein Data Bank format can be read and written. Atoms can be selected with a syntax similar to CHARMM's powerful selection commands. MDAnal. enables both novice and experienced programmers to rapidly write their own anal. tools and access data stored in trajectories in an easily accessible manner that facilitates interactive explorative anal. MDAnal. has been tested on and works for most Unix-based platforms such as Linux and Mac OS X. It is freely available under the GNU General Public License from http://mdanal.googlecode.com. © 2011 Wiley Periodicals, Inc. J Comput Chem 2011.
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83. 83
  Schwarzl, R.; Liese, S.; Brünig, F. N.; Laudisio, F.; Netz, R. R. Force Response of Polypeptide Chains from Water-Explicit MD Simulations. Macromolecules 2020, 53, 4618– 4629, DOI: 10.1021/acs.macromol.0c00138
  83
  Force Response of Polypeptide Chains from Water-Explicit MD Simulations
  Schwarzl, Richard; Liese, Susanne; Bruenig, Florian N.; Laudisio, Fabio; Netz, Roland R.
  Macromolecules (Washington, DC, United States) (2020), 53 (12), 4618-4629CODEN: MAMOBX; ISSN:0024-9297. (American Chemical Society)
  Using mol. dynamics simulations in explicit water, the force-extension relations for the five homopeptides polyglycine, polyalanine, polyasparagine, poly(glutamic acid), and polylysine are investigated. From simulations in the low-force regime the Kuhn length is detd., from simulations in the high-force regime the equil. contour length and the linear and nonlinear stretching moduli, which agree well with quantum-chem. d.-functional theory calcns., are detd. All these parameters vary considerably between the different polypeptides. The augmented inhomogeneous partially freely rotating chain (iPFRC) model, which accounts for side-chain interactions and restricted dihedral rotation, is demonstrated to describe the simulated force-extension relations very well. We present a quant. comparison between published exptl. single-mol. force-extension curves for different polypeptides with simulation and model predictions. The thermodn. stretching properties of polypeptides are investigated by decompn. of the stretching free energy into energetic and entropic contributions.
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84. 84
  Flyvbjerg, H.; Petersen, H. G. Error estimates on averages of correlated data. J. Chem. Phys. 1989, 91, 461– 466, DOI: 10.1063/1.457480
  84
  Error estimates on averages of correlated data
  Flyvbjerg, H.; Petersen, H. G.
  Journal of Chemical Physics (1989), 91 (1), 461-6CODEN: JCPSA6; ISSN:0021-9606.
  A description is given on how the true statistical error on an av. of correlated data can be obtained with ease and efficiency by a renormalization group method. The method is illustrated with numerical and anal. examples, having finite as well as infinite range correlations.
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- PDB: 7DK3
- PDB: 6M0J
Supporting Information
Supporting Information
The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacsau.4c00886.
- Derivation of the standard free-energy of binding from a polymer desorption free-energy profile; additional figures (PDF)
- au4c00886_si_001.pdf (7.76 MB)
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Quantitative Prediction of Protein–Polyelectrolyte Binding Thermodynamics: Adsorption of Heparin-Analog Polysulfates to the SARS-CoV-2 Spike Protein RBDClick to copy article linkArticle link copied!

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Polymer Desorption Free Energy

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Dissociation Constant and Standard Binding Free Energy

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Figure 5

Relaxation Time for Binding of Charged Groups

Figure 6

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Glycan-Conjugated RBD

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Constant-Force Stretching of LPGS

Figure 8

Simulation Data Analysis

iPFRC Model and Stretching Free Energy of LPGS

Internal Energy Decomposition

Distance Criteria for Close Contacts and Bound Water and Ions

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Root-Mean-Square Fluctuation of the RBD Structure

Relaxation Time for the RBD’s Loop Region Movement

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Quantitative Prediction of Protein–Polyelectrolyte Binding Thermodynamics: Adsorption of Heparin-Analog Polysulfates to the SARS-CoV-2 Spike Protein RBD
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