Ion channel selectivity through ion-modulated changes of selectivity filter pKa values.

In bacterial voltage-gated sodium channels, the passage of ions through the pore is controlled by a selectivity filter (SF) composed of four glutamate residues. The mechanism of selectivity has been the subject of intense research, with suggested mechanisms based on steric effects, and ion-triggered conformational change. Here, we propose an alternative mechanism based on ion-triggered shifts in pKa values of SF glutamates. We study the NavMs channel for which the open channel structure is available. Our free-energy calculations based on molecular dynamics simulations suggest that pKa values of the four glutamates are higher in solution of K+ ions than in solution of Na+ ions. Higher pKa in the presence of K+ stems primarily from the higher population of dunked conformations of the protonated Glu sidechain, which exhibit a higher pKa shift. Since pKa values are close to the physiological pH, this results in predominant population of the fully deprotonated state of glutamates in Na+ solution, while protonated states are predominantly populated in K+ solution. Through molecular dynamics simulations we calculate that the deprotonated state is the most conductive, the singly protonated state is less conductive, and the doubly protonated state has significantly reduced conductance. Thus, we propose that a significant component of selectivity is achieved through ion-triggered shifts in the protonation state, which favors more conductive states for Na+ ions and less conductive states for K+ ions. This mechanism also suggests a strong pH dependence of selectivity, which has been experimentally observed in structurally similar NaChBac channels.

The oxidation of the [4Fe-4S] cluster of DNA primase alters the binding energies with DNA and RNA primers.

DNA primase is an iron sulfur enzyme in DNA replication responsible for synthesizing short RNA primers that serve as starting points for DNA synthesis. The role of the [4Fe-4S] cluster is not well determined. Here, we calculate the redox potential of the [4Fe-4S] with and without DNA/RNA using continuum electrostatics. In addition, we identify the structural changes coupled to the oxidation/reduction. Our calculations show that the DNA/RNA primer lowers the redox potential by 110 and 50 mV for the [4Fe-4S]+ and [4Fe-4S]2+ states, respectively. The oxidation of the cluster is coupled to structural changes that significantly reduce the binding energies between the DNA and the nearby residues. The negative charges accumulated by the DNA and the RNA primers induce the oxidation of the [4Fe-4S] cluster. This in turn stimulates structural changes on the DNA-protein interface that significantly reduce the binding energies.

MPI-parallelization of the grid inhomogeneous solvation theory calculation.

The grid inhomogeneous solvation theory (GIST) method requires the often time-consuming calculation of water-water and water-solute energy on a grid. Previous efforts to speed up this calculation include using OpenMP, GPUs, and particle mesh Ewald. This article details how the speed of this calculation can be increased by parallelizing it with MPI, where trajectory frames are divided among multiple processors. This requires very little communication between individual processes during trajectory processing, meaning the calculation scales well to large processor counts. This article also details how the entropy calculation, which must happen after trajectory processing since it requires information from all trajectory frames, is parallelized via MPI. This parallelized GIST method has been implemented in the freely-available CPPTRAJ analysis software.

Obtaining QM/MM binding free energies in the SAMPL8 drugs of abuse challenge: indirect approaches.

Accurately predicting free energy differences is essential in realizing the full potential of rational drug design. Unfortunately, high levels of accuracy often require computationally expensive QM/MM Hamiltonians. Fortuitously, the cost of employing QM/MM approaches in rigorous free energy simulation can be reduced through the use of the so-called "indirect" approach to QM/MM free energies, in which the need for QM/MM simulations is avoided via a QM/MM "correction" at the classical endpoints of interest. Herein, we focus on the computation of QM/MM binding free energies in the context of the SAMPL8 Drugs of Abuse host-guest challenge. Of the 5 QM/MM correction coupled with force-matching submissions, PM6-D3H4/MM ranked submission proved the best overall QM/MM entry, with an RMSE from experimental results of 2.43 kcal/mol (best in ranked submissions), a Pearson's correlation of 0.78 (second-best in ranked submissions), and a Kendall [Formula: see text] correlation of 0.52 (best in ranked submissions).

GraphVAMPNet, using graph neural networks and variational approach to Markov processes for dynamical modeling of biomolecules.

Finding a low dimensional representation of data from long-timescale trajectories of biomolecular processes, such as protein folding or ligand-receptor binding, is of fundamental importance, and kinetic models, such as Markov modeling, have proven useful in describing the kinetics of these systems. Recently, an unsupervised machine learning technique called VAMPNet was introduced to learn the low dimensional representation and the linear dynamical model in an end-to-end manner. VAMPNet is based on the variational approach for Markov processes and relies on neural networks to learn the coarse-grained dynamics. In this paper, we combine VAMPNet and graph neural networks to generate an end-to-end framework to efficiently learn high-level dynamics and metastable states from the long-timescale molecular dynamics trajectories. This method bears the advantages of graph representation learning and uses graph message passing operations to generate an embedding for each datapoint, which is used in the VAMPNet to generate a coarse-grained dynamical model. This type of molecular representation results in a higher resolution and a more interpretable Markov model than the standard VAMPNet, enabling a more detailed kinetic study of the biomolecular processes. Our GraphVAMPNet approach is also enhanced with an attention mechanism to find the important residues for classification into different metastable states.

Determinants of conductance of a bacterial voltage-gated sodium channel.

Through molecular dynamics (MD) and free energy simulations in electric fields, we examine the factors influencing conductance of bacterial voltage-gated sodium channel NavMs. The channel utilizes four glutamic acid residues in the selectivity filter (SF). Previously, we have shown, through constant pH and free energy calculations of pKa values, that fully deprotonated, singly protonated, and doubly protonated states are all feasible at physiological pH, depending on how many ions are bound in the SF. With 173 MD simulations of 450 or 500 ns and additional free energy simulations, we determine that the conductance is highest for the deprotonated state and decreases with each additional proton bound. We also determine that the pKa value of the four glutamic residues for the transition between deprotonated and singly protonated states is close to the physiological pH and that there is a small voltage dependence. The pKa value and conductance trends are in agreement with experimental work on bacterial Nav channels, which show a decrease in maximal conductance with lowering of pH, with pKa in the physiological range. We examine binding sites for Na+ in the SF, compare with previous work, and note a dependence on starting structures. We find that narrowing of the gate backbone to values lower than the crystal structure's backbone radius reduces the conductance, whereas increasing the gate radius further does not affect the conductance. Simulations with some amount of negatively charged lipids as opposed to purely neutral lipids increases the conductance, as do simulations at higher voltages.

Exploring dynamics and network analysis of spike glycoprotein of SARS-COV-2.

The ongoing pandemic caused by severe acute respiratory syndrome coronavirus 2 continues to rage with devastating consequences on human health and global economy. The spike glycoprotein on the surface of coronavirus mediates its entry into host cells and is the target of all current antibody design efforts to neutralize the virus. The glycan shield of the spike helps the virus to evade the human immune response by providing a thick sugar-coated barrier against any antibody. To study the dynamic motion of glycans in the spike protein, we performed microsecond-long molecular dynamics simulation in two different states that correspond to the receptor binding domain in open or closed conformations. Analysis of this microsecond-long simulation revealed a scissoring motion on the N-terminal domain of neighboring monomers in the spike trimer. The roles of multiple glycans in shielding of spike protein in different regions were uncovered by a network analysis, in which the high betweenness centrality of glycans at the apex revealed their importance and function in the glycan shield. Microdomains of glycans were identified featuring a high degree of intracommunication in these microdomains. An antibody overlap analysis revealed the glycan microdomains as well as individual glycans that inhibit access to the antibody epitopes on the spike protein. Overall, the results of this study provide detailed understanding of the spike glycan shield, which may be utilized for therapeutic efforts against this crisis.

The Extended Eighth-Shell method for periodic boundary conditions with rotational symmetry.

The Eighth-Shell method for parallelization of molecular dynamics simulations has previously been shown to be the most optimal for efficiency at large process counts. However, in its current formulation only the P1 space group is supported for periodic boundary conditions (PBC) and thus reflection and/or rotational crystal symmetries are not supported. In this work, we outline the development and implementation of the Extended Eighth-Shell (EES) method that allows rotational symmetry by using an extended import region compared to the ES method. It simulates only the asymmetric unit and communicates coordinates and forces with images that correspond to P21 PBC. The P21 PBC has application in lipid bilayer simulations as it can be used to allow lipids to switch leaftlets, thus rapidly balancing the chemical potential difference between the two layers. Our results show that the EES method scales efficiently over large number of processes and can be used for simulations with P21 symmetry in an orthorhombic crystal.

A replica exchange umbrella sampling (REUS) approach to predict host-guest binding free energies in SAMPL8 challenge.

In this study, we report binding free energy calculations of various drugs-of-abuse to Cucurbit-[8]-uril as part of the SAMPL8 blind challenge. Force-field parameters were obtained from force-matching with different quantum mechanical levels of theory. The Replica Exchange Umbrella Sampling (REUS) approach was used with a cylindrical restraint to enhance the sampling of host-guest binding. Binding free energy was calculated by pulling the guest molecule from one side of the symmetric and cylindrical host, then into and through the host, and out the other side (bidirectional) as compared to pulling only to the bound pose inside the cylindrical host (unidirectional). The initial results with force-matched MP2 parameter set led to RMSE of 4.68 [Formula: see text] from experimental values. However, the follow-up study with CHARMM generalized force field parameters and force-matched PM6-D3H4 parameters resulted in RMSEs from experiment of [Formula: see text] and [Formula: see text], respectively, which demonstrates the potential of REUS for accurate binding free energy calculation given a more suitable description of energetics. Moreover, we compared the free energies for the so called bidirectional and unidirectional free energy approach and found that the binding free energies were highly similar. However, one issue in the bidirectional approach is the asymmetry of profile on the two sides of the host. This is mainly due to the insufficient sampling for these larger systems and can be avoided by longer sampling simulations. Overall REUS shows great promise for binding free energy calculations.

Analytical Hessians for Ewald and particle mesh Ewald electrostatics.

The particle mesh Ewald (PME) method has become ubiquitous in the molecular simulation community due to its ability to deliver long range electrostatics accurately with ON ⁡log(N) complexity. Despite this widespread use, spanning more than two decades, second derivatives (Hessians) have not been available. In this work, we describe the theory and implementation of PME Hessians, which have applications in normal mode analysis, characterization of stationary points, phonon dispersion curve calculation, crystal structure prediction, and efficient geometry optimization. We outline an exact strategy that requires O(1) effort for each Hessian element; after discussing the excessive memory requirements of such an approach, we develop an accurate, efficient approximation that is far more tractable on commodity hardware.

A compression strategy for particle mesh Ewald theory.

Particle Mesh Ewald (PME) has become a standard method for treating long-range electrostatics in molecular simulations. Although the method has inferior asymptotic computational complexity to its linear scaling competitors, it remains enormously popular due to its high efficiency, which stems from the use of fast Fourier transforms (FFTs). This use of FFTs provides great challenges for scaling the method up to massively parallel systems, in large part because of the need to transfer large amounts of data. In this work, we demonstrate that this data transfer volume can be greatly reduced as a natural consequence of the structure of the PME equations. We also suggest an alternative algorithm that supplants the FFT with a linear algebra approach, which further decreases communication costs at the expense of increased asymptotic computational complexity. This linear algebra based approach is demonstrated to have great potential for latency hiding by interleaving communication and computation steps of the short- and long-range electrostatic terms.

Variational embedding of protein folding simulations using Gaussian mixture variational autoencoders.

Conformational sampling of biomolecules using molecular dynamics simulations often produces a large amount of high dimensional data that makes it difficult to interpret using conventional analysis techniques. Dimensionality reduction methods are thus required to extract useful and relevant information. Here, we devise a machine learning method, Gaussian mixture variational autoencoder (GMVAE), that can simultaneously perform dimensionality reduction and clustering of biomolecular conformations in an unsupervised way. We show that GMVAE can learn a reduced representation of the free energy landscape of protein folding with highly separated clusters that correspond to the metastable states during folding. Since GMVAE uses a mixture of Gaussians as its prior, it can directly acknowledge the multi-basin nature of the protein folding free energy landscape. To make the model end-to-end differentiable, we use a Gumbel-softmax distribution. We test the model on three long-timescale protein folding trajectories and show that GMVAE embedding resembles the folding funnel with folded states down the funnel and unfolded states outside the funnel path. Additionally, we show that the latent space of GMVAE can be used for kinetic analysis and Markov state models built on this embedding produce folding and unfolding timescales that are in close agreement with other rigorous dynamical embeddings such as time independent component analysis.

Protonation state of the selectivity filter of bacterial voltage-gated sodium channels is modulated by ions.

The selectivity filter (SF) of bacterial voltage-gated sodium channels consists of four glutamate residues arranged in a C4 symmetry. The protonation state population of this tetrad is unclear. To address this question, we simulate the pore domain of bacterial voltage-gated sodium channel of Magnetococcus sp. (Nav Ms) through constant pH methodology in explicit solvent and free energy perturbation calculations. We find that at physiological pH the fully deprotonated as well as singly and doubly protonated states of the SF appear feasible, and that the calculated pKa decreases with each additional bound ion, suggesting that a decrease in the number of ions in the pore can lead to protonation of the SF. Previous molecular dynamics simulations have suggested that protonation can lead to a decrease in the conductance, but no pKa calculations were performed. We confirm a decreased ionic population of the pore with protonation, and also observe structural symmetry breaking triggered by protonation; the SF of the deprotonated channel is closest to the C4 symmetry observed in crystal structures of the open state, while the SF of protonated states display greater levels of asymmetry which could lead to transition to the inactivated state which possesses a C2 symmetry in the crystal structure. We speculate that the decrease in the number of ions near the mouth of the channel, due to either random fluctuations or ion depletion due to conduction, could be a self-regulatory mechanism resulting in a nonconducting state that functionally resembles inactivated states.

A deep learning approach for the blind logP prediction in SAMPL6 challenge.

Water octanol partition coefficient serves as a measure for the lipophilicity of a molecule and is important in the field of drug discovery. A novel method for computational prediction of logarithm of partition coefficient (logP) has been developed using molecular fingerprints and a deep neural network. The machine learning model was trained on a dataset of 12,000 molecules and tested on 2000 molecules. In this article, we present our results for the blind prediction of logP for the SAMPL6 challenge. While the best submission achieved a RMSE of 0.41 logP units, our submission had a RMSE of 0.61 logP units. Overall, we ranked in the top quarter out of the 92 submissions that were made. Our results show that the deep learning model can be used as a fast, accurate and robust method for high throughput prediction of logP of small molecules.

Quantum chemical predictions of water-octanol partition coefficients applied to the SAMPL6 logP blind challenge.

Theoretical approaches for predicting physicochemical properties are valuable tools for accelerating the drug discovery process. In this work, quantum chemical methods are used to predict water-octanol partition coefficients as a part of the SAMPL6 blind challenge. The SMD continuum solvent model was employed with MP2 and eight DFT functionals in conjunction with correlation consistent basis sets to determine the water-octanol transfer free energy. Several tactics towards improving the predictions of the partition coefficient were examined, including increasing the quality of basis sets, considering tautomerization, and accounting for inhomogeneities in the water and n-octanol phases. Evaluation of these various schemes highlights the impact of modeling approaches across different methods. With the inclusion of tautomers and adjustments to the permittivity constants, the best predictions were obtained with smaller basis sets and the O3LYP functional, which yielded an RMSE of 0.79 logP units. The results presented correspond to the SAMPL6 logP submission IDs: DYXBT, O7DJK, and AHMTF.

Multi-phase Boltzmann weighting: accounting for local inhomogeneity in molecular simulations of water-octanol partition coefficients in the SAMPL6 challenge.

Accurately computing partition coefficients is a pivotal part of drug discovery. Specifically, octanol-water partition coefficients can provide information into hydrophobicity of drug-like molecules, as well as a de facto representation of membrane permeability. However, one challenge facing the computation of partition coefficients is the need to encapsulate various microscopic environments. These include areas of largely bulk solvent (i.e., either water or octanol) or regions where octanol is saturated with water or areas of higher salt concentration. Also, tautomeric effects require consideration. Thus, we present a Boltzmann weighting approach that incorporates transfer free energies across varying microscopic media, as well as varying tautomeric state, to compute partition coefficients in the SAMPL6 challenge.

SAMPL6 logP challenge: machine learning and quantum mechanical approaches.

Two different types of approaches: (a) approaches that combine quantitative structure activity relationships, quantum mechanical electronic structure methods, and machine-learning and, (b) electronic structure vertical solvation approaches, were used to predict the logP coefficients of 11 molecules as part of the SAMPL6 logP blind prediction challenge. Using electronic structures optimized with density functional theory (DFT), several molecular descriptors were calculated for each molecule, including van der Waals areas and volumes, HOMO/LUMO energies, dipole moments, polarizabilities, and electrophilic and nucleophilic superdelocalizabilities. A multilinear regression model and a partial least squares model were used to train a set of 97 molecules. As well, descriptors were generated using the molecular operating environment and used to create additional machine learning models. Electronic structure vertical solvation approaches considered include DFT and the domain-based local pair natural orbital methods combined with the solvated variant of the correlation consistent composite approach.

Reformulation of the self-guided molecular simulation method.

Self-guided molecular/Langevin dynamics (SGMD/SGLD) simulation methods were developed to enhance conformational sampling through promoting low frequency motion of molecular systems and have been successfully applied in many simulation studies. Quantitative understanding of conformational distribution in SGLD has been achieved by separating microscopic properties according to frequency. However, a missing link between the guiding factors and conformational distributions makes it highly empirical and system dependent when choosing the values of the guiding parameters. Based on the understanding that molecular interactions are the source of energy barriers and diffusion friction, this work reformulates the equation of the low frequency motion to resemble Langevin dynamics. This reformulation leads to new forms of guiding forces and establishes a relation between the guiding factors and conformational distributions. We call simulations with these new guiding forces the generalized self-guided molecular/Langevin dynamics (SGMDg/SGLDg). In addition, we present a new way to calculate low frequency properties and an efficient algorithm to implement SGMDg/SGLDg that minimizes memory usage and inter-processor communication. Through example simulations with a skewed double well system, an argon fluid, and a cryo-EM map flexible fitting case, we demonstrate the guiding effects on conformational distributions and conformational searching.

A protocol for preparing explicitly solvated systems for stable molecular dynamics simulations.

Before beginning the production phase of molecular dynamics simulations, i.e., the phase that produces the data to be analyzed, it is often necessary to first perform a series of one or more preparatory minimizations and/or molecular dynamics simulations in order to ensure that subsequent production simulations are stable. This is particularly important for simulations with explicit solvent molecules. Despite the preparatory minimizations and simulations being ubiquitous and essential for stable production simulations, there are currently no general recommended procedures to perform them and very few criteria to decide whether the system is capable of producing a stable simulation trajectory. Here, we propose a simple and well-defined ten step simulation preparation protocol for explicitly solvated biomolecules, which can be applied to a wide variety of system types, as well as a simple test based on the system density for determining whether the simulation is stabilized.

Membrane permeability of small molecules from unbiased molecular dynamics simulations.

Permeation of many small molecules through lipid bilayers can be directly observed in molecular dynamics simulations on the nano- and microsecond timescale. While unbiased simulations provide an unobstructed view of the permeation process, their feasibility for computing permeability coefficients depends on various factors that differ for each permeant. The present work studies three small molecules for which unbiased simulations of permeation are feasible within less than a microsecond, one hydrophobic (oxygen), one hydrophilic (water), and one amphiphilic (ethanol). Permeabilities are computed using two approaches: counting methods and a maximum-likelihood estimation for the inhomogeneous solubility diffusion (ISD) model. Counting methods yield nearly model-free estimates of the permeability for all three permeants. While the ISD-based approach is reasonable for oxygen, it lacks precision for water due to insufficient sampling and results in misleading estimates for ethanol due to invalid model assumptions. It is also demonstrated that simulations using a Langevin thermostat with collision frequencies of 1/ps and 5/ps yield oxygen permeabilities and diffusion constants that are lower than those using Nosé-Hoover by statistically significant margins. In contrast, permeabilities from trajectories generated with Nosé-Hoover and the microcanonical ensemble do not show statistically significant differences. As molecular simulations become more affordable and accurate, calculation of permeability for an expanding range of molecules will be feasible using unbiased simulations. The present work summarizes theoretical underpinnings, identifies pitfalls, and develops best practices for such simulations.