Markov state models of biomolecular conformational dynamics

N-Terminal-Driven Binding Mechanism of an Antigen Peptide to Human Leukocyte Antigen-A*2402 Elucidated by Multicanonical Molecular Dynamic-Based Dynamic Docking and Path Sampling Simulations

We have applied our advanced multicanonical molecular dynamics (McMD)-based dynamic docking methodology to investigate the binding mechanism of an HIV-1 Nef protein epitope to the Asian-dominant allele human leukocyte antigen (HLA)-A*2402. Even though pMHC complex formation [between a Major histocompatibility complex (MHC) class I molecule, which is encoded by an HLA allele, and an antigen peptide] is one of the fundamental processes of the adaptive human immune response, its binding mechanism has not yet been well studied, partially due to the high allelic variation of HLAs in the population. We have used our developed McMD-based dynamic docking method and have successfully reproduced the native complex structure, which is located near the free energy global minimum. Subsequent path sampling MD simulations elucidated the atomic details of the binding process and indicated that the peptide binding is initially driven by the highly positively charged N-terminus of the peptide that is attracted to the various negatively charged residues on the MHC molecule's surface. Upon nearing the pocket, the second tyrosine residue of the peptide anchors the peptide by strongly binding to the B-site of the MHC molecule via hydrophobic driven interactions, resulting in a very strong bound complex structure. Our methodology can be effectively used to predict the bound complex structures between MHC molecules and their antigens to study their binding mechanism in close detail, which would help with the development of new vaccines against cancers, as well as viral infections such as HIV and COVID-19.

Worldwide Protein Data Bank (wwPDB): A virtual treasure for research in biotechnology

The Research Collaboratory for Structural Bioinformatics Protein Data Bank (RSCB PDB) provides a wide range of digital data regarding biology and biomedicine. This huge internet resource involves a wide range of important biological data, obtained from experiments around the globe by different scientists. The Worldwide Protein Data Bank (wwPDB) represents a brilliant collection of 3D structure data associated with important and vital biomolecules including nucleic acids (RNAs and DNAs) and proteins. Moreover, this database accumulates knowledge regarding function and evolution of biomacromolecules which supports different disciplines such as biotechnology. 3D structure, functional characteristics and phylogenetic properties of biomacromolecules give a deep understanding of the biomolecules' characteristics. An important advantage of the wwPDB database is the data updating time, which is done every week. This updating process helps users to have the newest data and information for their projects. The data and information in wwPDB can be a great support to have an accurate imagination and illustrations of the biomacromolecules in biotechnology. As demonstrated by the SARS-CoV-2 pandemic, rapidly reliable and accessible biological data for microbiology, immunology, vaccinology, and drug development are critical to address many healthcare-related challenges that are facing humanity. The aim of this paper is to introduce the readers to wwPDB, and to highlight the importance of this database in biotechnology, with the expectation that the number of scientists interested in the utilization of Protein Data Bank's resources will increase substantially in the coming years.

Critical role of backbone coordination in the mRNA recognition by RNA induced silencing complex

Despite its functional importance, the molecular mechanism underlying target mRNA recognition by Argonaute (Ago) remains largely elusive. Based on extensive all-atom molecular dynamics simulations, we constructed quasi-Markov State Model (qMSM) to reveal the dynamics during recognition at position 6-7 in the seed region of human Argonaute 2 (hAgo2). Interestingly, we found that the slowest mode of motion therein is not the gRNA-target base-pairing, but the coordination of the target phosphate groups with a set of positively charged residues of hAgo2. Moreover, the ability of Helix-7 to approach the PIWI and MID domains was found to reduce the effective volume accessible to the target mRNA and therefore facilitate both the backbone coordination and base-pair formation. Further mutant simulations revealed that alanine mutation of the D358 residue on Helix-7 enhanced a trap state to slow down the loading of target mRNA. Similar trap state was also observed when wobble pairs were introduced in g6 and g7, indicating the role of Helix-7 in suppressing non-canonical base-paring. Our study pointed to a general mechanism for mRNA recognition by eukaryotic Agos and demonstrated the promise of qMSM in investigating complex conformational changes of biomolecular systems.

Paratope states in solution improve structure prediction and docking

Structure-based antibody design and accurate predictions of antibody-antigen interactions remain major challenges in computational biology. By using molecular dynamics simulations, we show that a single static X-ray structure is not sufficient to identify determinants of antibody-antigen recognition. Here, we investigate antibodies that undergo substantial conformational changes upon antigen binding and have been classified as difficult cases in an extensive benchmark for antibody-antigen docking. We present thermodynamics and transition kinetics of these conformational rearrangements and show that paratope states can be used to improve antibody-antigen docking. By using the unbound antibody X-ray structure as starting structure for molecular dynamics simulations, we retain a binding competent conformation substantially different to the unbound antibody X-ray structure. We also observe that the kinetically dominant antibody paratope conformations are chosen by the bound antigen conformation with the highest probability. Thus, we show that paratope states in solution can improve antibody-antigen docking and structure prediction.

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.

FSATOOL 2.0: An integrated molecular dynamics simulation and trajectory data analysis program

Molecular dynamics simulation is important in the computational study of the biomolecules. In this paper, we upgrade our previous FSATOOL to version 2.0. It is no longer a plugin as before. Besides the existed enhanced sampling and Markov state model analysis module, FSATOOL 2.0 has three new features now. First, it contains a molecular dynamics simulation engine on both CPU and GPU device. The engine works with an embedded enhanced sampling module. Second, it can do the free energy calculation by various practical methods, including the weighted histogram analysis method and Gaussian mixture model. Third, it has many subroutines to process the trajectory data, such as principal component analysis, time-structure based independent component analysis, contact analysis, and Φ-value analysis. Most importantly, all these calculations are integrated into one package. The trajectory data format is compatible with all the modules. With a proper input parameter file, users can do the molecular dynamics simulation and data analysis work by only a few simplified commands. The capabilities and theoretical backgrounds of FSATOOL 2.0 are introduced in the paper.

Multiscale Approach for Computing Gated Ligand Binding from Molecular Dynamics and Brownian Dynamics Simulations

We develop an approach to characterize the effects of gating by a multiconformation protein consisting of macrostate conformations that are either accessible or inaccessible to ligand binding. We first construct a Markov state model of the apo-protein from atomistic molecular dynamics simulations from which we identify macrostates and their conformations, compute their relative macrostate populations and interchange kinetics, and structurally characterize them in terms of ligand accessibility. We insert the calculated first-order rate constants for conformational transitions into a multistate gating theory from which we derive a gating factor γ that quantifies the degree of conformational gating. Applied to HIV-1 protease, our approach yields a kinetic network of three accessible (semi-open, open, and wide-open) and two inaccessible (closed and a newly identified, "parted") macrostate conformations. The parted conformation sterically partitions the active site, suggesting a possible role in product release. We find that the binding kinetics of drugs and drug-like inhibitors to HIV-1 protease falls in the slow gating regime. However, because γ = 0.75, conformational gating only modestly slows ligand binding. Brownian dynamics simulations of the diffusional association of eight inhibitors to the protease─having a wide range of experimental association constants (∼10⁴-10¹⁰ M^-1 s^-1)─yields gated rate constants in the range of ∼0.5-5.7 × 10⁸ M^-1 s^-1. This indicates that, whereas the association rate of some inhibitors could be described by the model, for many inhibitors either subsequent conformational transitions or alternate binding mechanisms may be rate-limiting. For systems known to be modulated by conformational gating, the approach could be scaled computationally efficiently to screen association kinetics for a large number of ligands.

Molecular dynamics simulations elucidate oligosaccharide recognition pathways by galectin-3 at atomic resolution

The recognition of carbohydrates by lectins plays key roles in diverse cellular processes such as cellular adhesion, proliferation, and apoptosis, which makes it a therapeutic target of significance against cancers. One of the most functionally active lectins, galectin-3 is distinctively known for its specific binding affinity toward β-galactoside. However, despite the prevalence of high-resolution crystallographic structures, the mechanistic basis and more significantly, the dynamic process underlying carbohydrate recognition by galectin-3 are currently elusive. To this end, we employed extensive Molecular Dynamics simulations to unravel the complete binding event of human galectin-3 with its native natural ligand N-acetyllactosamine (LacNAc) at atomic precision. The simulation trajectory demonstrates that the oligosaccharide diffuses around the protein and eventually identifies and binds to the biologically designated binding site of galectin-3 in real time. The simulated bound pose correlates with the crystallographic pose with atomic-level accuracy and recapitulates the signature stabilizing galectin-3/oligosaccharide interactions. The recognition pathway also reveals a set of transient non-native ligand poses in its course to the receptor. Interestingly, kinetic analysis in combination with a residue-level picture revealed that the key to the efficacy of a more active structural variant of the LacNAc lay in the ligand's resilience against disassociation from galectin-3. By catching the ligand in the act of finding its target, our investigations elucidate the detailed recognition mechanism of the carbohydrate-binding domain of galectin-3 and underscore the importance of ligand-target binary complex residence time in understanding the structure-activity relationship of cognate ligands.

Determining Sequence-Dependent DNA Oligonucleotide Hybridization and Dehybridization Mechanisms Using Coarse-Grained Molecular Simulation, Markov State Models, and Infrared Spectroscopy

A robust understanding of the sequence-dependent thermodynamics of DNA hybridization has enabled rapid advances in DNA nanotechnology. A fundamental understanding of the sequence-dependent kinetics and mechanisms of hybridization and dehybridization remains comparatively underdeveloped. In this work, we establish new understanding of the sequence-dependent hybridization/dehybridization kinetics and mechanism within a family of self-complementary pairs of 10-mer DNA oligomers by integrating coarse-grained molecular simulation, machine learning of the slow dynamical modes, data-driven inference of long-time kinetic models, and experimental temperature-jump infrared spectroscopy. For a repetitive ATATATATAT sequence, we resolve a rugged dynamical landscape comprising multiple metastable states, numerous competing hybridization/dehybridization pathways, and a spectrum of dynamical relaxations. Introduction of a G:C pair at the terminus (GATATATATC) or center (ATATGCATAT) of the sequence reduces the ruggedness of the dynamics landscape by eliminating a number of metastable states and reducing the number of competing dynamical pathways. Only by introducing a G:C pair midway between the terminus and the center to maximally disrupt the repetitive nature of the sequence (ATGATATCAT) do we recover a canonical "all-or-nothing" two-state model of hybridization/dehybridization with no intermediate metastable states. Our results establish new understanding of the dynamical richness of sequence-dependent kinetics and mechanisms of DNA hybridization/dehybridization by furnishing quantitative and predictive kinetic models of the dynamical transition network between metastable states, present a molecular basis with which to understand experimental temperature jump data, and furnish foundational design rules by which to rationally engineer the kinetics and pathways of DNA association and dissociation for DNA nanotechnology applications.

Collective variable-based enhanced sampling and machine learning

ABSTRACT

Collective variable-based enhanced sampling methods have been widely used to study thermodynamic properties of complex systems. Efficiency and accuracy of these enhanced sampling methods are affected by two factors: constructing appropriate collective variables for enhanced sampling and generating accurate free energy surfaces. Recently, many machine learning techniques have been developed to improve the quality of collective variables and the accuracy of free energy surfaces. Although machine learning has achieved great successes in improving enhanced sampling methods, there are still many challenges and open questions. In this perspective, we shall review recent developments on integrating machine learning techniques and collective variable-based enhanced sampling approaches. We also discuss challenges and future research directions including generating kinetic information, exploring high-dimensional free energy surfaces, and efficiently sampling all-atom configurations.

GRAPHIC ABSTRACT

Spontaneous transmembrane pore formation by short-chain synthetic peptide

Amphiphilic β-peptides, which are synthetically designed short-chain helical foldamers of β-amino acids, are established potent biomimetic alternatives of natural antimicrobial peptides. An intriguing question is how the distinct molecular architecture of these short-chain and rigid synthetic peptides translates to its potent membrane-disruption ability. Here, we address this question via a combination of all-atom and coarse-grained molecular dynamics simulations of the interaction of mixed phospholipid bilayer with an antimicrobial 10-residue globally amphiphilic helical β-peptide at a wide range of concentrations. The simulation demonstrates that multiple copies of this synthetic peptide, initially placed in aqueous solution, readily self-assemble and adsorb at membrane interface. Subsequently, beyond a threshold peptide/lipid ratio, the surface-adsorbed oligomeric aggregate moves inside the membrane and spontaneously forms stable water-filled transmembrane pores via a cooperative mechanism. The defects induced by these pores lead to the dislocation of interfacial lipid headgroups, membrane thinning, and substantial water leakage inside the hydrophobic core of the membrane. A molecular analysis reveals that despite having a short architecture, these synthetic peptides, once inside the membrane, would stretch themselves toward the distal leaflet in favor of potential contact with polar headgroups and interfacial water layer. The pore formed in coarse-grained simulation was found to be resilient upon structural refinement. Interestingly, the pore-inducing ability was found to be elusive in a non-globally amphiphilic sequence isomer of the same β-peptide, indicating strong sequence dependence. Taken together, this work puts forward key perspectives of membrane activity of minimally designed synthetic biomimetic oligomers relative to the natural antimicrobial peptides.

Nearly reducible finite Markov chains: Theory and algorithms

Finite Markov chains, memoryless random walks on complex networks, appear commonly as models for stochastic dynamics in condensed matter physics, biophysics, ecology, epidemiology, economics, and elsewhere. Here, we review exact numerical methods for the analysis of arbitrary discrete- and continuous-time Markovian networks. We focus on numerically stable methods that are required to treat nearly reducible Markov chains, which exhibit a separation of characteristic timescales and are therefore ill-conditioned. In this metastable regime, dense linear algebra methods are afflicted by propagation of error in the finite precision arithmetic, and the kinetic Monte Carlo algorithm to simulate paths is unfeasibly inefficient. Furthermore, iterative eigendecomposition methods fail to converge without the use of nontrivial and system-specific preconditioning techniques. An alternative approach is provided by state reduction procedures, which do not require additional a priori knowledge of the Markov chain. Macroscopic dynamical quantities, such as moments of the first passage time distribution for a transition to an absorbing state, and microscopic properties, such as the stationary, committor, and visitation probabilities for nodes, can be computed robustly using state reduction algorithms. The related kinetic path sampling algorithm allows for efficient sampling of trajectories on a nearly reducible Markov chain. Thus, all of the information required to determine the kinetically relevant transition mechanisms, and to identify the states that have a dominant effect on the global dynamics, can be computed reliably even for computationally challenging models. Rare events are a ubiquitous feature of realistic dynamical systems, and so the methods described herein are valuable in many practical applications.

Naturally Occurring Genetic Variants in the Oxytocin Receptor Alter Receptor Signaling Profiles

The hormone oxytocin is commonly administered during childbirth to initiate and strengthen uterine contractions and prevent postpartum hemorrhage. However, patients have wide variation in the oxytocin dose required for a clinical response. To begin to uncover the mechanisms underlying this variability, we screened the 11 most prevalent missense genetic variants in the oxytocin receptor (OXTR) gene. We found that five variants, V45L, P108A, L206V, V281M, and E339K, significantly altered oxytocin-induced Ca²⁺ signaling or β-arrestin recruitment and proceeded to assess the effects of these variants on OXTR trafficking to the cell membrane, desensitization, and internalization. The variants P108A and L206V increased OXTR localization to the cell membrane, whereas V281M and E339K caused OXTR to be retained inside the cell. We examined how the variants altered the balance between OXTR activation and desensitization, which is critical for appropriate oxytocin dosing. The E339K variant impaired OXTR activation, internalization, and desensitization to roughly equal extents. In contrast, V281M decreased OXTR activation but had no effect on internalization and desensitization. V45L and P108A did not alter OXTR activation but did impair β-arrestin recruitment, internalization, and desensitization. Molecular dynamics simulations predicted that V45L and P108A prevent extension of the first intracellular loop of OXTR, thus inhibiting β-arrestin binding. Overall, our data suggest mechanisms by which OXTR genetic variants could alter clinical response to oxytocin.

Natural Polyphenols Inhibit the Dimerization of the SARS-CoV-2 Main Protease: The Case of Fortunellin and Its Structural Analogs

3CL-Pro is the SARS-CoV-2 main protease (MPro). It acts as a homodimer to cleave the large polyprotein 1ab transcript into proteins that are necessary for viral growth and replication. 3CL-Pro has been one of the most studied SARS-CoV-2 proteins and a main target of therapeutics. A number of drug candidates have been reported, including natural products. Here, we employ elaborate computational methods to explore the dimerization of the 3CL-Pro protein, and we formulate a computational context to identify potential inhibitors of this process. We report that fortunellin (acacetin 7-O-neohesperidoside), a natural flavonoid O-glycoside, and its structural analogs are potent inhibitors of 3CL-Pro dimerization, inhibiting viral plaque formation in vitro. We thus propose a novel basis for the search of pharmaceuticals as well as dietary supplements in the fight against SARS-CoV-2 and COVID-19.

AI-driven prediction of SARS-CoV-2 variant binding trends from atomistic simulations

We present a novel technique to predict binding affinity trends between two molecules from atomistic molecular dynamics simulations. The technique uses a neural network algorithm applied to a series of images encoding the distance between two molecules in time. We demonstrate that our algorithm is capable of separating with high accuracy non-hydrophobic mutations with low binding affinity from those with high binding affinity. Moreover, we show high accuracy in prediction using a small subset of the simulation, therefore requiring a much shorter simulation time. We apply our algorithm to the binding between several variants of the SARS-CoV-2 spike protein and the human receptor ACE2.

Multiscale molecular kinetics by coupling Markov state models and reaction-diffusion dynamics

A novel approach to simulate simple protein-ligand systems at large time and length scales is to couple Markov state models (MSMs) of molecular kinetics with particle-based reaction-diffusion (RD) simulations, MSM/RD. Currently, MSM/RD lacks a mathematical framework to derive coupling schemes, is limited to isotropic ligands in a single conformational state, and lacks multiparticle extensions. In this work, we address these needs by developing a general MSM/RD framework by coarse-graining molecular dynamics into hybrid switching diffusion processes. Given enough data to parameterize the model, it is capable of modeling protein-protein interactions over large time and length scales, and it can be extended to handle multiple molecules. We derive the MSM/RD framework, and we implement and verify it for two protein-protein benchmark systems and one multiparticle implementation to model the formation of pentameric ring molecules. To enable reproducibility, we have published our code in the MSM/RD software package.

Markov State Models to Study the Functional Dynamics of Proteins in the Wake of Machine Learning

Markov state models (MSMs) based on molecular dynamics (MD) simulations are routinely employed to study protein folding, however, their application to functional conformational changes of biomolecules is still limited. In the past few years, the field of computational chemistry has experienced a surge of advancements stemming from machine learning algorithms, and MSMs have not been left out. Unlike global processes, such as protein folding, the application of MSMs to functional conformational changes is challenging because they mostly consist of localized structural transitions. Therefore, it is critical to properly select a subset of structural features that can describe the slowest dynamics of these functional conformational changes. To address this challenge, we recommend several automatic feature selection methods such as Spectral-OASIS. To identify states in MSMs, the chosen features can be subject to dimensionality reduction methods such as TICA or deep learning based VAMPNets to project MD conformations onto a few collective variables for subsequent clustering. Another challenge for the application of MSMs to the study of functional conformational changes is the ability to comprehend their biophysical mechanisms, as MSMs built for these processes often require a large number of states. We recommend the recently developed quasi-MSMs (qMSMs) to address this issue. Compared to MSMs, qMSMs encode the non-Markovian dynamics via the generalized master equation and can significantly reduce the number of states. As a result, qMSMs can be built with a handful of states to facilitate the interpretation of functional conformational changes. In the wake of machine learning, we believe that the rapid advancement in the MSM methodology will lead to their wider application in studying functional conformational changes of biomolecules.

Nonparametric Analysis of Nonequilibrium Simulations

We extend the nonparametric framework of reaction coordinate optimization to nonequilibrium ensembles of (short) trajectories. For example, we show how, starting from such an ensemble, one can obtain an equilibrium free-energy profile along the committor, which can be used to determine important properties of the dynamics exactly. A new adaptive sampling approach, the transition-state ensemble enrichment, is suggested, which samples the configuration space by "growing" committor segments toward each other starting from the boundary states. This framework is suggested as a general tool, alternative to the Markov state models, for a rigorous and accurate analysis of simulations of large biomolecular systems, as it has the following attractive properties. It is immune to the curse of dimensionality, does not require system-specific information, can approximate arbitrary reaction coordinates with high accuracy, and has sensitive and rigorous criteria to test optimality and convergence. The approaches are illustrated on a 50-dimensional model system and a realistic protein folding trajectory.

CORE-MD II: A fast, adaptive, and accurate enhanced sampling method

In this paper, we present a fast and adaptive correlation guided enhanced sampling method (CORE-MD II). The CORE-MD II technique relies, in part, on partitioning of the entire pathway into short trajectories that we refer to as instances. The sampling within each instance is accelerated by adaptive path-dependent metadynamics simulations. The second part of this approach involves kinetic Monte Carlo (kMC) sampling between the different states that have been accessed during each instance. Through the combination of the partition of the total simulation into short non-equilibrium simulations and the kMC sampling, the CORE-MD II method is capable of sampling protein folding without any a priori definitions of reaction pathways and additional parameters. In the validation simulations, we applied the CORE-MD II on the dialanine peptide and the folding of two peptides: TrpCage and TrpZip2. In a comparison with long time equilibrium Molecular Dynamics (MD), 1 µs replica exchange MD (REMD), and CORE-MD I simulations, we find that the level of convergence of the CORE-MD II method is improved by a factor of 8.8, while the CORE-MD II method reaches acceleration factors of ∼120. In the CORE-MD II simulation of TrpZip2, we observe the formation of the native state in contrast to the REMD and the CORE-MD I simulations. The method is broadly applicable for MD simulations and is not restricted to simulations of protein folding or even biomolecules but also applicable to simulations of protein aggregation, protein signaling, or even materials science simulations.

Energy penalties enhance flexible receptor docking in a model cavity

Protein flexibility remains a major challenge in library docking because of difficulties in sampling conformational ensembles with accurate probabilities. Here, we use the model cavity site of T4 lysozyme L99A to test flexible receptor docking with energy penalties from molecular dynamics (MD) simulations. Crystallography with larger and smaller ligands indicates that this cavity can adopt three major conformations: open, intermediate, and closed. Since smaller ligands typically bind better to the cavity site, we anticipate an energy penalty for the cavity opening. To estimate its magnitude, we calculate conformational preferences from MD simulations. We find that including a penalty term is essential for retrospective ligand enrichment; otherwise, high-energy states dominate the docking. We then prospectively docked a library of over 900,000 compounds for new molecules binding to each conformational state. Absent a penalty term, the open conformation dominated the docking results; inclusion of this term led to a balanced sampling of ligands against each state. High ranked molecules were experimentally tested by Tm upshift and X-ray crystallography. From 33 selected molecules, we identified 18 ligands and determined 13 crystal structures. Most interesting were those bound to the open cavity, where the buried site opens to bulk solvent. Here, highly unusual ligands for this cavity had been predicted, including large ligands with polar tails; these were confirmed both by binding and by crystallography. In docking, incorporating protein flexibility with thermodynamic weightings may thus access new ligand chemotypes. The MD approach to accessing and, crucially, weighting such alternative states may find general applicability.

Drug repurposing studies targeting SARS-CoV-2: an ensemble docking approach on drug target 3C-like protease (3CLpro)

The COVID-19 pandemic has been responsible for several deaths worldwide. The causative agent behind this disease is the Severe Acute Respiratory Syndrome - novel Coronavirus 2 (SARS-CoV-2). SARS-CoV-2 belongs to the category of RNA viruses. The main protease, responsible for the cleavage of the viral polyprotein is considered as one of the hot targets for treating COVID-19. Earlier reports suggest the use of HIV anti-viral drugs for targeting the main protease of SARS-CoV, which caused SARS in the year 2002-2003. Hence, drug repurposing approach may prove to be useful in targeting the main protease of SARS-CoV-2. The high-resolution crystal structure of the main protease of SARS-CoV-2 (PDB ID: 6LU7) was used as the target. The Food and Drug Administration approved and SWEETLEAD database of drug molecules were screened. The apo form of the main protease was simulated for a cumulative of 150 ns and 10 μs open-source simulation data was used, to obtain conformations for ensemble docking. The representative structures for docking were selected using RMSD-based clustering and Markov State Modeling analysis. This ensemble docking approach for the main protease helped in exploring the conformational variation in the drug-binding site of the main protease leading to the efficient binding of more relevant drug molecules. The drugs obtained as top hits from the ensemble docking possessed anti-bacterial and anti-viral properties. This in silico ensemble docking approach would support the identification of potential candidates for repurposing against COVID-19.Communicated by Ramaswamy H. Sarma.

Germline-Dependent Antibody Paratope States and Pairing Specific VH-VL Interface Dynamics

Antibodies have emerged as one of the fastest growing classes of biotherapeutic proteins. To improve the rational design of antibodies, we investigate the conformational diversity of 16 different germline combinations, which are composed of 4 different kappa light chains paired with 4 different heavy chains. In this study, we systematically show that different heavy and light chain pairings strongly influence the paratope, interdomain interaction patterns and the relative VH-VL interface orientations. We observe changes in conformational diversity and substantial population shifts of the complementarity determining region (CDR) loops, resulting in distinct dominant solution structures and differently favored canonical structures. Additionally, we identify conformational changes in the structural diversity of the CDR-H3 loop upon different heavy and light chain pairings, as well as upon changes in sequence and structure of the neighboring CDR loops, despite having an identical CDR-H3 loop amino acid sequence. These results can also be transferred to all CDR loops and to the relative VH-VL orientation, as certain paratope states favor distinct interface angle distributions. Furthermore, we directly compare the timescales of sidechain rearrangements with the well-described transition kinetics of conformational changes in the backbone of the CDR loops. We show that sidechain flexibilities are strongly affected by distinct heavy and light chain pairings and decipher germline-specific structural features co-determining stability. These findings reveal that all CDR loops are strongly correlated and that distinct heavy and light chain pairings can result in different paratope states in solution, defined by a characteristic combination of CDR loop conformations and VH-VL interface orientations. Thus, these results have broad implications in the field of antibody engineering, as they clearly show the importance of considering paired heavy and light chains to understand the antibody binding site, which is one of the key aspects in the design of therapeutics.

Independent Markov decomposition: Toward modeling kinetics of biomolecular complexes

To advance the mission of in silico cell biology, modeling the interactions of large and complex biological systems becomes increasingly relevant. The combination of molecular dynamics (MD) simulations and Markov state models (MSMs) has enabled the construction of simplified models of molecular kinetics on long timescales. Despite its success, this approach is inherently limited by the size of the molecular system. With increasing size of macromolecular complexes, the number of independent or weakly coupled subsystems increases, and the number of global system states increases exponentially, making the sampling of all distinct global states unfeasible. In this work, we present a technique called independent Markov decomposition (IMD) that leverages weak coupling between subsystems to compute a global kinetic model without requiring the sampling of all combinatorial states of subsystems. We give a theoretical basis for IMD and propose an approach for finding and validating such a decomposition. Using empirical few-state MSMs of ion channel models that are well established in electrophysiology, we demonstrate that IMD models can reproduce experimental conductance measurements with a major reduction in sampling compared with a standard MSM approach. We further show how to find the optimal partition of all-atom protein simulations into weakly coupled subunits.

p-cymene impairs SARS-CoV-2 and Influenza A (H1N1) viral replication: In silico predicted interaction with SARS-CoV-2 nucleocapsid protein and H1N1 nucleoprotein

Therapeutic regimens for the COVID-19 pandemics remain unmet. In this line, repurposing of existing drugs against known or predicted SARS-CoV-2 protein actions have been advanced, while natural products have also been tested. Here, we propose that p-cymene, a natural monoterpene, can act as a potential novel agent for the treatment of SARS-CoV-2-induced COVID-19 and other RNA-virus-induced diseases (influenza, rabies, Ebola). We show by extensive molecular simulations that SARS-CoV-2 C-terminal structured domain contains a nuclear localization signal (NLS), like SARS-CoV, on which p-cymene binds with low micromolar affinity, impairing nuclear translocation of this protein and inhibiting viral replication, as verified by preliminary in vitro experiments. A similar mechanism may occur in other RNA-viruses (influenza, rabies and Ebola), also verified in vitro for influenza, by interaction of p-cymene with viral nucleoproteins, and structural modification of their NLS site, weakening its interaction with importin A. This common mechanism of action renders therefore p-cymene as a possible antiviral, alone, or in combination with other agents, in a broad spectrum of RNA viruses, from SARS-CoV-2 to influenza A infections.

SARS-CoV-2 Nsp16 activation mechanism and a cryptic pocket with pan-coronavirus antiviral potential

Coronaviruses have caused multiple epidemics in the past two decades, in addition to the current COVID-19 pandemic that is severely damaging global health and the economy. Coronaviruses employ between 20 and 30 proteins to carry out their viral replication cycle, including infection, immune evasion, and replication. Among these, nonstructural protein 16 (Nsp16), a 2'-O-methyltransferase, plays an essential role in immune evasion. Nsp16 achieves this by mimicking its human homolog, CMTr1, which methylates mRNA to enhance translation efficiency and distinguish self from other. Unlike human CMTr1, Nsp16 requires a binding partner, Nsp10, to activate its enzymatic activity. The requirement of this binding partner presents two questions that we investigate in this manuscript. First, how does Nsp10 activate Nsp16? Although experimentally derived structures of the active Nsp16/Nsp10 complex exist, structures of inactive, monomeric Nsp16 have yet to be solved. Therefore, it is unclear how Nsp10 activates Nsp16. Using over 1 ms of molecular dynamics simulations of both Nsp16 and its complex with Nsp10, we investigate how the presence of Nsp10 shifts Nsp16's conformational ensemble to activate it. Second, guided by this activation mechanism and Markov state models, we investigate whether Nsp16 adopts inactive structures with cryptic pockets that, if targeted with a small molecule, could inhibit Nsp16 by stabilizing its inactive state. After identifying such a pocket in SARS-CoV2 Nsp16, we show that this cryptic pocket also opens in SARS-CoV1 and MERS but not in human CMTr1. Therefore, it may be possible to develop pan-coronavirus antivirals that target this cryptic pocket.

Enhanced sampling protocol to elucidate fusion peptide opening of SARS-CoV-2 spike protein

Large-scale conformational transitions in the spike protein S2 domain are required during host-cell infection of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus. Although conventional molecular dynamics simulations have been extensively used to study therapeutic targets of SARS-CoV-2, it is still challenging to gain molecular insight into the key conformational changes because of the size of the spike protein and the long timescale required to capture these transitions. In this work, we have developed an efficient simulation protocol that leverages many short simulations, a dynamic selection algorithm, and Markov state models to interrogate the structural changes of the S2 domain. We discovered that the conformational flexibility of the dynamic region upstream of the fusion peptide in S2 is coupled to the proteolytic cleavage state of the spike protein. These results suggest that opening of the fusion peptide likely occurs on a submicrosecond timescale after cleavage at the S2' site. Building on the structural and dynamical information gained to date about S2 domain dynamics, we provide proof of principle that a small molecule bound to a seam neighboring the fusion peptide can slow the opening of the fusion peptide, leading to a new inhibition strategy for experiments to confirm. In aggregate, these results will aid the development of drug cocktails to inhibit infections caused by SARS-CoV-2 and other coronaviruses.

Estradiol induces allosteric coupling and partitioning of sex-hormone-binding globulin monomers among conformational states

Sex-hormone-binding globulin (SHBG) regulates the transport and bioavailability of estradiol. The dynamics of estradiol's binding to SHBG are incompletely understood, although it is believed that estradiol binds to each monomer of SHBG dimer with identical affinity (Kd ∼2 nM). Contrary to the prevalent view, we show that estradiol's binding to SHBG is nonlinear, and the "apparent" Kd changes with varying estradiol and SHBG concentrations. Estradiol's binding to each SHBG monomer influences residues in the ligand-binding pocket of both monomers and differentially alters the conformational and energy landscapes of both monomers. Monomers are not energetically or conformationally equivalent even in fully bound state. Estradiol's binding to SHBG involves bidirectional, inter-monomeric allostery that changes the distribution of both monomers among various energy and conformational states. Inter-monomeric allostery offers a mechanism to extend the binding range of SHBG and regulate hormone bioavailability as estradiol concentrations vary widely during life.

Transition pathway of hydrogen bond switching in supercooled water analyzed by the Markov state model

In this work, we examine hydrogen-bond (H-bond) switching by employing the Markov State Model (MSM). During the H-bond switching, a water hydrogen initially H-bonded with water oxygen becomes H-bonded to a different water oxygen. MSM analysis was applied to trajectories generated from molecular dynamics simulations of the TIP4P/2005 model from a room-temperature state to a supercooled state. We defined four basis states to characterize the configuration between two water molecules: H-bonded ("H"), unbound ("U"), weakly H-bonded ("w"), and alternative H-bonded ("a") states. A 16 × 16 MSM matrix was constructed, describing the transition probability between states composed of three water molecules. The mean first-passage time of the H-bond switching was estimated by calculating the total flux from the HU to UH states. It is demonstrated that the temperature dependence of the mean first-passage time is in accordance with that of the H-bond lifetime determined from the H-bond correlation function. Furthermore, the flux for the H-bond switching is decomposed into individual pathways that are characterized by different forms of H-bond configurations of trimers. The dominant pathway of the H-bond switching is found to be a direct one without passing through such intermediate states as "w" and "a," the existence of which becomes evident in supercooled water. The pathway through "w" indicates a large reorientation of the donor molecule. In contrast, the pathway through "a" utilizes the tetrahedral H-bond network, which is revealed by the further decomposition based on the H-bond number of the acceptor molecule.

The Two-Step Clustering Approach for Metastable States Learning

Understanding the energy landscape and the conformational dynamics is crucial for studying many biological or chemical processes, such as protein-protein interaction and RNA folding. Molecular Dynamics (MD) simulations have been a major source of dynamic structure. Although many methods were proposed for learning metastable states from MD data, some key problems are still in need of further investigation. Here, we give a brief review on recent progresses in this field, with an emphasis on some popular methods belonging to a two-step clustering framework, and hope to draw more researchers to contribute to this area.

Diffusive search and trajectories on tubular networks: a propagator approach

Several organelles in eukaryotic cells, including mitochondria and the endoplasmic reticulum, form interconnected tubule networks extending throughout the cell. These tubular networks host many biochemical pathways that rely on proteins diffusively searching through the network to encounter binding partners or localized target regions. Predicting the behavior of such pathways requires a quantitative understanding of how confinement to a reticulated structure modulates reaction kinetics. In this work, we develop both exact analytical methods to compute mean first passage times and efficient kinetic Monte Carlo algorithms to simulate trajectories of particles diffusing in a tubular network. Our approach leverages exact propagator functions for the distribution of transition times between network nodes and allows large simulation time steps determined by the network structure. The methodology is applied to both synthetic planar networks and organelle network structures, demonstrating key general features such as the heterogeneity of search times in different network regions and the functional advantage of broadly distributing target sites throughout the network. The proposed algorithms pave the way for future exploration of the interrelationship between tubular network structure and biomolecular reaction kinetics.

Pushing Camera-Based Single-Molecule Kinetic Measurements to the Frame Acquisition Limit with Stroboscopic smFRET

Single-molecule fluorescence resonance energy transfer (smFRET) experiments permit detailed examination of microscopic dynamics. However, kinetic rate constants determined by smFRET are susceptible to systematic underestimation when the rate constants are comparable to the data acquisition rate. We demonstrate how such systematic errors in camera-based total internal reflection fluorescence microscopy experiments can be greatly reduced by using stroboscopic illumination/detection, allowing accurate rate constant determination up to the data sampling rate and yielding an order of magnitude increase in the dynamic range. Implementation of these stroboscopic smFRET ideas is straightforward, and the stroboscopically obtained data are compatible with multiple trajectory analysis methods, including dwell-time analysis and hidden Markov modeling. Such stroboscopic methods therefore offer a remarkably simple yet valuable addition to the smFRET toolkit, requiring only relatively modest modification to the normal data collection and analysis procedures.

From System Modeling to System Analysis: The Impact of Resolution Level and Resolution Distribution in the Computer-Aided Investigation of Biomolecules

The ever increasing computer power, together with the improved accuracy of atomistic force fields, enables researchers to investigate biological systems at the molecular level with remarkable detail. However, the relevant length and time scales of many processes of interest are still hardly within reach even for state-of-the-art hardware, thus leaving important questions often unanswered. The computer-aided investigation of many biological physics problems thus largely benefits from the usage of coarse-grained models, that is, simplified representations of a molecule at a level of resolution that is lower than atomistic. A plethora of coarse-grained models have been developed, which differ most notably in their granularity; this latter aspect determines one of the crucial open issues in the field, i.e. the identification of an optimal degree of coarsening, which enables the greatest simplification at the expenses of the smallest information loss. In this review, we present the problem of coarse-grained modeling in biophysics from the viewpoint of system representation and information content. In particular, we discuss two distinct yet complementary aspects of protein modeling: on the one hand, the relationship between the resolution of a model and its capacity of accurately reproducing the properties of interest; on the other hand, the possibility of employing a lower resolution description of a detailed model to extract simple, useful, and intelligible information from the latter.

Artificial intelligence in drug design: algorithms, applications, challenges and ethics

The discovery paradigm of drugs is rapidly growing due to advances in machine learning (ML) and artificial intelligence (AI). This review covers myriad faces of AI and ML in drug design. There is a plethora of AI algorithms, the most common of which are summarized in this review. In addition, AI is fraught with challenges that are highlighted along with plausible solutions to them. Examples are provided to illustrate the use of AI and ML in drug discovery and in predicting drug properties such as binding affinities and interactions, solubility, toxicology, blood–brain barrier permeability and chemical properties. The review also includes examples depicting the implementation of AI and ML in tackling intractable diseases such as COVID-19, cancer and Alzheimer’s disease. Ethical considerations and future perspectives of AI are also covered in this review.

Computational methods for exploring protein conformations

Proteins are dynamic molecules that can transition between a potentially wide range of structures comprising their conformational ensemble. The nature of these conformations and their relative probabilities are described by a high-dimensional free energy landscape. While computer simulation techniques such as molecular dynamics simulations allow characterisation of the metastable conformational states and the transitions between them, and thus free energy landscapes, to be characterised, the barriers between states can be high, precluding efficient sampling without substantial computational resources. Over the past decades, a dizzying array of methods have emerged for enhancing conformational sampling, and for projecting the free energy landscape onto a reduced set of dimensions that allow conformational states to be distinguished, known as collective variables (CVs), along which sampling may be directed. Here, a brief description of what biomolecular simulation entails is followed by a more detailed exposition of the nature of CVs and methods for determining these, and, lastly, an overview of the myriad different approaches for enhancing conformational sampling, most of which rely upon CVs, including new advances in both CV determination and conformational sampling due to machine learning.

A comprehensive mechanism for 5-carboxylcytosine-induced transcriptional pausing revealed by Markov state models

RNA polymerase II (Pol II) surveils the genome, pausing as it encounters DNA lesions and base modifications and initiating signals for DNA repair among other important regulatory events. Recent work suggests that Pol II pauses at 5-carboxycytosine (5caC), an epigenetic modification of cytosine, because of a specific hydrogen bond between the carboxyl group of 5caC and a specific residue in fork loop 3 of Pol II. This hydrogen bond compromises productive NTP binding and slows down elongation. Apart from this specific interaction, the carboxyl group of 5caC can potentially interact with numerous charged residues in the cleft of Pol II. However, it is not clear how other interactions between Pol II and 5caC contribute to pausing. In this study, we use Markov state models (a type of kinetic network models) built from extensive molecular dynamics simulations to comprehensively study the impact of 5caC on Pol II translocation. We describe two translocation intermediates with specific interactions that prevent the template base from loading into the Pol II active site. In addition to the previously observed state with 5caC constrained by fork loop 3, we discovered a new intermediate state with a hydrogen bond between 5caC and fork loop 2. Surprisingly, we find that 5caC may curb translocation by suppressing kinking of the helix bordering the active site (the bridge helix) because its high flexibility is critical to translocation. Our work provides new insights into how epigenetic modifications of genomic DNA can modulate Pol II translocation, inducing pauses in transcription.

What Markov State Models Can and Cannot Do: Correlation versus Path-Based Observables in Protein-Folding Models

Markov state models (MSMs) have been widely applied to study the kinetics and pathways of protein conformational dynamics based on statistical analysis of molecular dynamics (MD) simulations. These MSMs coarse-grain both configuration space and time in ways that limit what kinds of observables they can reproduce with high fidelity over different spatial and temporal resolutions. Despite their popularity, there is still limited understanding of which biophysical observables can be computed from these MSMs in a robust and unbiased manner, and which suffer from the space-time coarse-graining intrinsic in the MSM model. Most theoretical arguments and practical validity tests for MSMs rely on long-time equilibrium kinetics, such as the slowest relaxation time scales and experimentally observable time-correlation functions. Here, we perform an extensive assessment of the ability of well-validated protein folding MSMs to accurately reproduce path-based observable such as mean first-passage times (MFPTs) and transition path mechanisms compared to a direct trajectory analysis. We also assess a recently proposed class of history-augmented MSMs (haMSMs) that exploit additional information not accounted for in standard MSMs. We conclude with some practical guidance on the use of MSMs to study various problems in conformational dynamics of biomolecules. In brief, MSMs can accurately reproduce correlation functions slower than the lag time, but path-based observables can only be reliably reproduced if the lifetimes of states exceed the lag time, which is a much stricter requirement. Even in the presence of short-lived states, we find that haMSMs reproduce path-based observables more reliably.

"Dividing and Conquering" and "Caching" in Molecular Modeling

Molecular modeling is widely utilized in subjects including but not limited to physics, chemistry, biology, materials science and engineering. Impressive progress has been made in development of theories, algorithms and software packages. To divide and conquer, and to cache intermediate results have been long standing principles in development of algorithms. Not surprisingly, most important methodological advancements in more than half century of molecular modeling are various implementations of these two fundamental principles. In the mainstream classical computational molecular science, tremendous efforts have been invested on two lines of algorithm development. The first is coarse graining, which is to represent multiple basic particles in higher resolution modeling as a single larger and softer particle in lower resolution counterpart, with resulting force fields of partial transferability at the expense of some information loss. The second is enhanced sampling, which realizes "dividing and conquering" and/or "caching" in configurational space with focus either on reaction coordinates and collective variables as in metadynamics and related algorithms, or on the transition matrix and state discretization as in Markov state models. For this line of algorithms, spatial resolution is maintained but results are not transferable. Deep learning has been utilized to realize more efficient and accurate ways of "dividing and conquering" and "caching" along these two lines of algorithmic research. We proposed and demonstrated the local free energy landscape approach, a new framework for classical computational molecular science. This framework is based on a third class of algorithm that facilitates molecular modeling through partially transferable in resolution "caching" of distributions for local clusters of molecular degrees of freedom. Differences, connections and potential interactions among these three algorithmic directions are discussed, with the hope to stimulate development of more elegant, efficient and reliable formulations and algorithms for "dividing and conquering" and "caching" in complex molecular systems.

Reconciling conformational heterogeneity and substrate recognition in cytochrome P450

Cytochrome P450, the ubiquitous metalloenzyme involved in detoxification of foreign components, has remained one of the most popular systems for substrate-recognition process. However, despite being known for its high substrate specificity, the mechanistic basis of substrate-binding by archetypal system cytochrome P450cam has remained at odds with the contrasting reports of multiple diverse crystallographic structures of its substrate-free form. Here, we address this issue by elucidating the probability of mutual dynamical transition to the other crystallographic pose of cytochrome P450cam and vice versa via unbiased all-atom computer simulation. A robust Markov state model, constructed using adaptively sampled 84-μs-long molecular dynamics simulation trajectories, maps the broad and heterogenous P450cam conformational landscape into five key substates. In particular, the Markov state model identifies an intermediate-assisted dynamic equilibrium between a pair of conformations of P450cam, in which the substrate-recognition sites remain "closed" and "open," respectively. However, the estimate of a significantly higher stationary population of closed conformation, coupled with faster rate of open → closed transition than its reverse process, dictates that the net conformational equilibrium would be swayed in favor of "closed" conformation. Together, the investigation quantitatively infers that although a potential substrate of cytochrome P450cam would, in principle, explore a diverse array of conformations of substrate-free protein, it would mostly encounter a "closed" or solvent-occluded conformation and hence would follow an induced-fit-based recognition process. Overall, the work reconciles multiple precedent crystallographic, spectroscopic investigations and establishes how a statistical elucidation of conformational heterogeneity in protein would provide crucial insights in the mechanism of potential substrate-recognition process.

X-Entropy: A Parallelized Kernel Density Estimator with Automated Bandwidth Selection to Calculate Entropy

X-Entropy is a Python package used to calculate the entropy of a given distribution, in this case, based on the distribution of dihedral angles. The dihedral entropy facilitates an alignment-independent measure of local protein flexibility. The key feature of our approach is a Gaussian kernel density estimation (KDE) using a plug-in bandwidth selection, which is fully implemented in a C++ backend and parallelized with OpenMP. We further provide a Python frontend, with predefined wrapper functions for classical coordinate-based dihedral entropy calculations, using a 1D approximation. This makes the package very straightforward to include in any Python-based analysis workflow. Furthermore, the frontend allows full access to the C++ backend, so that the KDE can be used on any binnable one-dimensional input data. In this application note, we discuss implementation and usage details and illustrate potential applications. In particular, we benchmark the performance of our module in calculating the entropy of samples drawn from a Gaussian distribution and the analytical solution thereof. Further, we analyze the computational performance of this module compared to well-established python libraries that perform KDE analyses. X-Entropy is available free of charge on GitHub (https://github.com/liedllab/X-Entropy).

Role of bacterial RNA polymerase gate opening dynamics in DNA loading and antibiotics inhibition elucidated by quasi-Markov State Model

To initiate transcription, the holoenzyme (RNA polymerase [RNAP] in complex with σ factor) loads the promoter DNA via the flexible loading gate created by the clamp and β-lobe, yet their roles in DNA loading have not been characterized. We used a quasi-Markov State Model (qMSM) built from extensive molecular dynamics simulations to elucidate the dynamics of Thermus aquaticus holoenzyme's gate opening. We showed that during gate opening, β-lobe oscillates four orders of magnitude faster than the clamp, whose opening depends on the Switch 2's structure. Myxopyronin, an antibiotic that binds to Switch 2, was shown to undergo a conformational selection mechanism to inhibit clamp opening. Importantly, we reveal a critical but undiscovered role of β-lobe, whose opening is sufficient for DNA loading even when the clamp is partially closed. These findings open the opportunity for the development of antibiotics targeting β-lobe of RNAP. Finally, we have shown that our qMSMs, which encode non-Markovian dynamics based on the generalized master equation formalism, hold great potential to be widely applied to study biomolecular dynamics.

Shark Antibody Variable Domains Rigidify Upon Affinity Maturation-Understanding the Potential of Shark Immunoglobulins as Therapeutics

Sharks and other cartilaginous fish are the phylogenetically oldest living organisms that have antibodies as part of their adaptive immune system. As part of their humoral adaptive immune response, they produce an immunoglobulin, the so-called immunoglobulin new antigen receptor (IgNAR), a heavy-chain only antibody. The variable domain of an IgNAR, also known as V NAR , binds the antigen as an independent soluble domain. In this study, we structurally and dynamically characterized the affinity maturation mechanism of the germline and somatically matured (PBLA8) V NAR to better understand their function and their applicability as therapeutics. We observed a substantial rigidification upon affinity maturation, which is accompanied by a higher number of contacts, thereby contributing to the decrease in flexibility. Considering the static x-ray structures, the observed rigidification is not obvious, as especially the mutated residues undergo conformational changes during the simulation, resulting in an even stronger network of stabilizing interactions. Additionally, the simulations of the V NAR in complex with the hen egg-white lysozyme show that the V NAR antibodies evidently follow the concept of conformational selection, as the binding-competent state already preexisted even without the presence of the antigen. To have a more detailed description of antibody-antigen recognition, we also present here the binding/unbinding mechanism between the hen egg-white lysozyme and both the germline and matured V NAR s. Upon maturation, we observed a substantial increase in the resulting dissociation-free energy barrier. Furthermore, we were able to kinetically and thermodynamically describe the binding process and did not only identify a two-step binding mechanism, but we also found a strong population shift upon affinity maturation toward the native binding pose.

How do antiporters exchange substrates across the cell membrane? An atomic-level description of the complete exchange cycle in NarK

Major facilitator superfamily (MFS) proteins operate via three different mechanisms: uniport, symport, and antiport. Despite extensive investigations, the molecular understanding of antiporters is less advanced than that of other transporters due to the complex coupling between two substrates and the lack of distinct structures. We employ extensive all-atom molecular dynamics simulations to dissect the complete substrate exchange cycle of the bacterial NO₃^-/NO₂^- antiporter, NarK. We show that paired basic residues in the binding site prevent the closure of unbound protein and ensure the exchange of two substrates. Conformational transition occurs only in the presence of substrate, which weakens the electrostatic repulsion and stabilizes the transporter. Furthermore, we propose a state-dependent substrate exchange model, in which the relative spacing between the paired basic residues determines whether NO₃^- and NO₂^- bind simultaneously or sequentially. Overall, this work presents a general working model for the antiport mechanism within the MFS.

Effect of the Hydration Shell on the Carbonyl Vibration in the Ala-Leu-Ala-Leu Peptide

The vibrational spectrum of the Ala-Leu-Ala-Leu peptide in solution, computed from first-principles simulations, shows a prominent band in the amide I region that is assigned to stretching of carbonyl groups. Close inspection reveals combined but slightly different contributions by the three carbonyl groups of the peptide. The shift in their exact vibrational signature is in agreement with the different probabilities of these groups to form hydrogen bonds with the solvent. The central carbonyl group has a hydrogen bond probability intermediate to the other two groups due to interchanges between different hydrogen-bonded states. Analysis of the interaction energies of individual water molecules with that group shows that shifts in its frequency are directly related to the interactions with the water molecules in the first hydration shell. The interaction strength is well correlated with the hydrogen bond distance and hydrogen bond angle, though there is no perfect match, allowing geometrical criteria for hydrogen bonds to be used as long as the sampling is sufficient to consider averages. The hydrogen bond state of a carbonyl group can therefore serve as an indicator of the solvent's effect on the vibrational frequency.

Microsecond timescale MD simulations at the transition state of PmHMGR predict remote allosteric residues

Understanding the mechanisms of enzymatic catalysis requires a detailed understanding of the complex interplay of structure and dynamics of large systems that is a challenge for both experimental and computational approaches. More importantly, the computational demands of QM/MM simulations mean that the dynamics of the reaction can only be considered on a timescale of nanoseconds even though the conformational changes needed to reach the catalytically active state happen on a much slower timescale. Here we demonstrate an alternative approach that uses transition state force fields (TSFFs) derived by the quantum-guided molecular mechanics (Q2MM) method that provides a consistent treatment of the entire system at the classical molecular mechanics level and allows simulations at the microsecond timescale. Application of this approach to the second hydride transfer transition state of HMG-CoA reductase from Pseudomonas mevalonii (PmHMGR) identified three remote residues, R396, E399 and L407, (15-27 Å away from the active site) that have a remote dynamic effect on enzyme activity. The predictions were subsequently validated experimentally via site-directed mutagenesis. These results show that microsecond timescale MD simulations of transition states are possible and can predict rather than just rationalize remote allosteric residues.

Structural determinants of voltage-gating properties in calcium channels

Voltage-gated calcium channels control key functions of excitable cells, like synaptic transmission in neurons and the contraction of heart and skeletal muscles. To accomplish such diverse functions, different calcium channels activate at different voltages and with distinct kinetics. To identify the molecular mechanisms governing specific voltage sensing properties, we combined structure modeling, mutagenesis, and electrophysiology to analyze the structures, free energy, and transition kinetics of the activated and resting states of two functionally distinct voltage sensing domains (VSDs) of the eukaryotic calcium channel CaV1.1. Both VSDs displayed the typical features of the sliding helix model; however, they greatly differed in ion-pair formation of the outer gating charges. Specifically, stabilization of the activated state enhanced the voltage dependence of activation, while stabilization of resting states slowed the kinetics. This mechanism provides a mechanistic model explaining how specific ion-pair formation in separate VSDs can realize the characteristic gating properties of voltage-gated cation channels.

The RED scheme: Rate-constant estimation from pre-steady state weighted ensemble simulations

We present the Rate from Event Durations (RED) scheme, a new scheme that more efficiently calculates rate constants using the weighted ensemble path sampling strategy. This scheme enables rate-constant estimation from shorter trajectories by incorporating the probability distribution of event durations, or barrier-crossing times, from a simulation. We have applied the RED scheme to weighted ensemble simulations of a variety of rare-event processes that range in complexity: residue-level simulations of protein conformational switching, atomistic simulations of Na+/Cl- association in explicit solvent, and atomistic simulations of protein-protein association in explicit solvent. Rate constants were estimated with up to 50% greater efficiency than the original weighted ensemble scheme. Importantly, our scheme accounts for the systematic error that results from statistical bias toward the observation of events with short durations and reweights the event duration distribution accordingly. The RED scheme is relevant to any simulation strategy that involves unbiased trajectories of similar length to the most probable event duration, including weighted ensemble, milestoning, and standard simulations as well as the construction of Markov state models.

Analyzing the Long Time-Scale Dynamics of Uremic Toxins Bound to Sudlow Site II in Human Serum Albumin

Protein bound uremic toxins (PBUTs), a series of chemicals that remain a challenge for removal strategies used on patients suffering with chronic kidney disease, could be strong candidates for MD study in order to better understand the interactions and time scales associated with binding mode transitions. Currently, traditional dialysis methods cannot satisfactorily remove PBUTs from the bloodstream. This is at least partly due to these toxin's high level of affinity for protein binding sites, particularly the prominent human serum albumin (HSA) and two of its drug binding sites (Sudlow site I and II). We investigate the dynamics of binding site transitions and interactions by MD simulations targeting four well-known toxins: indoxyl sulfate (IS), p-cresyl sulfate (PCS), indole-3-acetic acid (IAA), and hippurate acid (HIP). Long-time scale dynamics are obtained by the use of time-structure independent component analysis (tICA) for dimensionality reduction followed by spectral analysis of a Markov state model (MSM) scored using the generalized matrix Rayleigh quotient (GMRQ). Our results add new insights to prior findings related to the key role of charge-pairing in governing toxin-protein interactions. We find that IAA, the bulkiest hydrophobic toxin studied, observes the slowest process of at least 3 times slower than the smaller, less hydrophobic toxins. In general, we find that the processes slower than 15 ns are correlated with a transition from dominantly hydrophobic interactions deep in the binding pocket to a gain in hydrogen bonding partners near the mouth of the pocket. Our results indicate that aromatic residues such as PHE play a part in a type of toxin stabilization akin to π-stacking. In conclusion, this work presents mechanistic descriptions of interactions/transitions for a set of important PBUTs that bind Sudlow site II on time scales relevant to the underlying binding kinetics of most interest.

1'-Ribose cyano substitution allows Remdesivir to effectively inhibit nucleotide addition and proofreading during SARS-CoV-2 viral RNA replication

COVID-19 has recently caused a global health crisis and an effective interventional therapy is urgently needed. Remdesivir is one effective inhibitor for SARS-CoV-2 viral RNA replication. It supersedes other NTP analogues because it not only terminates the polymerization activity of RNA-dependent RNA polymerase (RdRp), but also inhibits the proofreading activity of intrinsic exoribonuclease (ExoN). Even though the static structure of Remdesivir binding to RdRp has been solved and biochemical experiments have suggested it to be a "delayed chain terminator", the underlying molecular mechanisms is not fully understood. Here, we performed all-atom molecular dynamics (MD) simulations with an accumulated simulation time of 24 microseconds to elucidate the inhibitory mechanism of Remdesivir on nucleotide addition and proofreading. We found that when Remdesivir locates at an upstream site in RdRp, the 1'-cyano group experiences electrostatic interactions with a salt bridge (Asp865-Lys593), which subsequently halts translocation. Our findings can supplement the current understanding of the delayed chain termination exerted by Remdesivir and provide an alternative molecular explanation about Remdesivir's inhibitory mechanism. Such inhibition also reduces the likelihood of Remdesivir to be cleaved by ExoN acting on 3'-terminal nucleotides. Furthermore, our study also suggests that Remdesivir's 1'-cyano group can disrupt the cleavage site of ExoN via steric interactions, leading to a further reduction in the cleavage efficiency. Our work provides plausible and novel mechanisms at the molecular level of how Remdesivir inhibits viral RNA replication, and our findings may guide rational design for new treatments of COVID-19 targeting viral replication.

Structural insight into the binding interactions of NTPs and nucleotide analogues to RNA dependent RNA polymerase of SARS-CoV-2

RNA dependent RNA polymerase (RdRP) from positive-stranded RNA viruses has always been a hot target for designing of new drugs. Major class of drugs that are targeted against RdRP are nucleotide analogues. Extensive docking and molecular dynamics study describing the binding of natural nucleotides (NTPs) and its analogues leading to significant structural variation in the RdRP has been presented here. RdRP simulations in its apo, NTP-bound, and analogue-bound form have been performed. Nucleotide analogues included in this study were, favipiravir, galidesivir, lamivudine, ribavirin, remdesivir and sofosbuvir. The conformational flexibility of the RdRP molecule has been explored using principal component (PCA) and Markov state modeling (MSM) analysis. PCA inferred the presence of correlated motions among the conserved motifs of RdRP. Inter-domain distances between the finger and thumb subdomain flanking the nascent RNA template entry site sampled open and closed conformations. The ligand and template binding motifs F and G showed negatively correlated motions. K551, R553, and R555, a part of motif F appear to form strong interactions with the ligand molecules. R836, a primer binding residue was observed to strongly bind to the analogues. MSM analysis helped to extract statistically distinct conformations explored by the RdRP. Ensemble docking of the ligands on the Markov states also suggested the involvement of the above residues in ligand interactions. Markov states obtained clearly demarcated the open/closed conformations of the template entry site. These observations on residues from the conserved motifs involved in binding to the ligands may provide an insight into designing new inhibitors.Communicated by Ramaswamy H. Sarma.