Simulating asymmetric membranes using P21 periodic boundary conditions.

Molecular dynamics (MD) simulations of symmetric lipid bilayers are now well established, while those of asymmetric ones are considerably less developed. This disjunction arises in part because the surface tensions of leaflets in asymmetric bilayers can differ (unlike those of symmetric ones), and there is no simple way to determine them without assumptions. This chapter describes the use of P21 periodic boundary conditions (PBC), which allow lipids to switch leaflets, to generate asymmetric bilayers under the assumption of equal chemical potentials of lipids in opposing leaflets. A series of examples, ranging from bilayers with one lipid type to those with peptides and proteins, provides a guide for the use of P21 PBC. Critical properties of asymmetric membranes, such as spontaneous curvature, are highly sensitive to differences in the leaflet surface tensions (or differential stress), and equilibration with P21 PBC substantially reduces differential stress of asymmetric bilayers assembled with surface area-based methods. Limitations of the method are discussed. Technically, the nonstandard unit cell is difficult to parallelize and to incorporate restraints. Inherently, the assumption of equal chemical potentials, and therefore the method itself, is not applicable to all target systems. Despite these limitations, it is argued that P21 simulations should be considered when designing equilibration protocols for MD studies of most asymmetric membranes.

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.

Mapping the Oxygens in the Oxygen-Evolving Complex of Photosystem II by Their Nucleophilicity Using Quantum Descriptors.

The oxygen-evolving complex (OEC) of Photosystem II catalyzes the water-splitting reaction using solar energy. Thus, understanding the reaction mechanism will inspire the design of biomimetic artificial catalysts that convert solar energy to chemical energy. Conceptual Density Functional Theory (CDFT) focuses on understanding the reactivity of molecules and the atomic contribution to the overall nucleophilicity and electrophilicity of the molecule using quantum descriptors. However, this method has not been applied to the OEC before. Here, we use Fukui functions and the dual descriptor to provide quantitative measures of the nucleophilicity and electrophilicity of oxygens in the OEC for different models in different S states. Our results show that the µ-oxo bridges connected to terminal Mn4 are nucleophilic, and those in the cube formed by Mn1, Mn2, and Mn3 are mostly electrophilic. The dual descriptors of the bridging oxygens in the OEC showed a similar reactivity to that of bridging oxygens in Mn model compounds. However, the terminal water W1, which is bound to Mn4, showed very strong reactivity in some of the S3 models. Thus, our calculations support the model that proposes the formation of the O2 molecule through nucleophilic attack by a terminal water.

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.

Conformational Fluctuations in ß2-Microglubulin Using Markov State Modeling and Molecular Dynamics.

Conformational dynamics in proteins can give rise to aggregation prone states during folding, and these kinetically stable states could form oligomers and aggregates. In this study, we investigate the intermediate states and near-folded states of ß2-microglobulin and their physico-chemical properties using molecular dynamics and Markov state modeling. Analysis of hundreds of microseconds simulation show the importance of the edge strands in the misfolded states that give rise to a high exposure of hydrophobic residues in the core of the protein that could initiate oligomerization and aggregate formation. Our study sheds light on the first step of aggregation of ß2m monomers and gave a better picture of the landscape of protein misfolding and aggregation.

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.

Turning up the heat mimics allosteric signaling in imidazole-glycerol phosphate synthase.

Allosteric drugs have the potential to revolutionize biomedicine due to their enhanced selectivity and protection against overdosage. However, we need to better understand allosteric mechanisms in order to fully harness their potential in drug discovery. In this study, molecular dynamics simulations and nuclear magnetic resonance spectroscopy are used to investigate how increases in temperature affect allostery in imidazole glycerol phosphate synthase. Results demonstrate that temperature increase triggers a cascade of local amino acid-to-amino acid dynamics that remarkably resembles the allosteric activation that takes place upon effector binding. The differences in the allosteric response elicited by temperature increase as opposed to effector binding are conditional to the alterations of collective motions induced by either mode of activation. This work provides an atomistic picture of temperature-dependent allostery, which could be harnessed to more precisely control enzyme function.

Quantifying the effects of lossy compression on energies calculated from molecular dynamics trajectories.

Molecular dynamics (MD) simulations are now able to routinely reach timescales of microseconds and beyond. This has led to a corresponding increase in the amount of MD trajectory data that needs to be stored, particularly when those trajectories contain explicit solvent molecules. As such, it is desirable to be able to compress trajectory data while still retaining as much of the original information as possible. In this work, we describe compressing MD trajectory data using the NetCDF4/HDF5 file format, making use of quantization of the original positions to achieve better compression ratios. We also analyze the affect this has on both the resulting positions and the energies calculated from post-processing these trajectories, and recommend an optimal level of quantization. Overall we find the NetCDF4/HDF5 format to be an excellent choice for storing MD trajectory data in terms of speed, compressibility, and versatility.

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.

Protein pKa Prediction by Tree-Based Machine Learning.

Protonation states of ionizable protein residues modulate many essential biological processes. For correct modeling and understanding of these processes, it is crucial to accurately determine their pKa values. Here, we present four tree-based machine learning models for protein pKa prediction. The four models, Random Forest, Extra Trees, eXtreme Gradient Boosting (XGBoost), and Light Gradient Boosting Machine (LightGBM), were trained on three experimental PDB and pKa datasets, two of which included a notable portion of internal residues. We observed similar performance among the four machine learning algorithms. The best model trained on the largest dataset performs 37% better than the widely used empirical pKa prediction tool PROPKA and 15% better than the published result from the pKa prediction method DelPhiPKa. The overall root-mean-square error (RMSE) for this model is 0.69, with surface and buried RMSE values being 0.56 and 0.78, respectively, considering six residue types (Asp, Glu, His, Lys, Cys, and Tyr), and 0.63 when considering Asp, Glu, His, and Lys only. We provide pKa predictions for proteins in human proteome from the AlphaFold Protein Structure Database and observed that 1% of Asp/Glu/Lys residues have highly shifted pKa values close to the physiological pH.

CHARMM-GUI Nanomaterial Modeler for Modeling and Simulation of Nanomaterial Systems.

Molecular modeling and simulation are invaluable tools for nanoscience that predict mechanical, physicochemical, and thermodynamic properties of nanomaterials and provide molecular-level insight into underlying mechanisms. However, building nanomaterial-containing systems remains challenging due to the lack of reliable and integrated cyberinfrastructures. Here we present Nanomaterial Modeler in CHARMM-GUI, a web-based cyberinfrastructure that provides an automated process to generate various nanomaterial models, associated topologies, and configuration files to perform state-of-the-art molecular dynamics simulations using most simulation packages. The nanomaterial models are based on the interface force field, one of the most reliable force fields (FFs). The transferability of nanomaterial models among the simulation programs was assessed by single-point energy calculations, which yielded 0.01% relative absolute energy differences for various surface models and equilibrium nanoparticle shapes. Three widely used Lennard-Jones (LJ) cutoff methods are employed to evaluate the compatibility of nanomaterial models with respect to conventional biomolecular FFs: simple truncation at r = 12 Å (12 cutoff), force-based switching over 10 to 12 Å (10-12 fsw), and LJ particle mesh Ewald with no cutoff (LJPME). The FF parameters with these LJ cutoff methods are extensively validated by reproducing structural, interfacial, and mechanical properties. We find that the computed density and surface energies are in good agreement with reported experimental results, although the simulation results increase in the following order: 10-12 fsw <12 cutoff < LJPME. Nanomaterials in which LJ interactions are a major component show relatively higher deviations (up to 4% in density and 8% in surface energy differences) compared with the experiment. Nanomaterial Modeler's capability is also demonstrated by generating complex systems of nanomaterial-biomolecule and nanomaterial-polymer interfaces with a combination of existing CHARMM-GUI modules. We hope that Nanomaterial Modeler can be used to carry out innovative nanomaterial modeling and simulations to acquire insight into the structure, dynamics, and underlying mechanisms of complex nanomaterial-containing systems.

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.

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.

Replica Exchange Molecular Dynamics of Diphenylalanine Amyloid Peptides in Electric Fields.

The self-assembling propensity of amyloid peptides such as diphenylalanine (FF) allows them to form ordered, nanoscale structures, with biocompatible properties important for biomedical applications. Moreover, piezoelectric properties allow FF molecules and their aggregates (e.g., FF nanotubes) to be aligned in a controlled way by the application of external electric fields. However, while the behavior of FF nanostructures emerges from the biophysical properties of the monomers, the detailed responses of individual peptides to both temperature and electric fields are not fully understood. Here, we study the temperature-dependent conformational dynamics of FF peptides solvated in explicit water molecules, an environment relevant to biomedical applications, by using an enhanced sampling method, replica exchange molecular dynamics (REMD), in conjunction with applied electric fields. Our simulations highlight and overcome possible artifacts that may occur during the setup of REMD simulations of explicitly solvated peptides in the presence of external electric fields, a problem particularly important in the case of short peptides such as FF. The presence of the external fields could overstabilize certain conformational states in one or more REMD replicas, leading to distortions of the underlying potential energy distributions observed at each temperature. This can be overcome by correcting the REMD initial conditions to include the lower-energy conformations induced by the external field. We show that the converged REMD data can be analyzed using a Markovian description of conformational states and show that a rather complex, 3-state, temperature-dependent conformational dynamics in the absence of electric fields collapses to only one of these states in the presence of the electric fields. These details on the temperature- and electric-field-dependent thermodynamic and kinetic properties of small FF amyloid peptides can be useful in understanding and devising new methods to control their aggregation-prone biophysical properties and, possibly, the structural and biophysical properties of FF molecular nanostructures.

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.

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.

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.

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.