Calculation of Free Energy Landscape in Multi-Dimensions with Hamiltonian-Exchange Umbrella Sampling on Petascale Supercomputer

Computational Insights into the Adsorption of Ligands on Gold Nanosurfaces

We study the adsorption process of model peptides, nucleobases, and selected standard ligands on gold through the development of a computational protocol based on fully atomistic classical molecular dynamics (MD) simulations combined with umbrella sampling techniques. The specific features of the interface components, namely, the molecule, the metallic substrate, and the solvent, are taken into account through different combinations of force fields (FFs), which are found to strongly affect the results, especially changing absolute and relative adsorption free energies and trends. Overall, noncovalent interactions drive the process along the adsorption pathways. Our findings also show that a suitable choice of the FF combinations can shed light on the affinity, position, orientation, and dynamic fluctuations of the target molecule with respect to the surface. The proposed protocol may help the understanding of the adsorption process at the microscopic level and may drive the in-silico design of biosensors for detection purposes.

Converging PMF Calculations of Antibiotic Permeation across an Outer Membrane Porin with Subkilocalorie per Mole Accuracy

The emergence of multidrug-resistant pathogens led to a critical need for new antibiotics. A key property of effective antibiotics against Gram-negative bacteria is their ability to permeate through the bacterial outer membrane via transmembrane porin proteins. Molecular dynamics (MD) simulations are, in principle, capable of modeling antibiotic permeation across outer membrane porins (OMPs). However, owing to sampling problems, it has remained challenging to obtain converged potentials of mean force (PMFs) for antibiotic permeation across OMPs. Here, we investigated the convergence of PMFs along a single collective variable aimed at quantifying the permeation of the antibiotic fosmidomycin across the OprO porin. We compared standard umbrella sampling (US) with three advanced flavors of the US technique: (i) Hamiltonian replica exchange with solute tempering in combination with US, (ii) simulated tempering-enhanced US, and (iii) replica-exchange US. To quantify the PMF convergence and to reveal hysteresis problems, we computed several independent sets of US simulations starting from pulling simulations in the outward and inward permeation directions. We find that replica-exchange US in combination with well-chosen restraints is highly successful for obtaining converged PMFs of fosmidomycin permeation through OprO, reaching PMFs converged to subkilocalorie per mole accuracy.

Enhanced Configurational Sampling Approaches to Alchemical Ligand Binding Free Energy Simulations: Current Status and Challenges

Ligand binding free energy simulations (LB-FES) have been routine tasks in modern drug discovery campaign. A long-standing challenge for LB-FES is the difficulty in adequately sampling nontrivial environmental reorganizations in response to ligand binding. Therefore, various enhanced configurational sampling (ECS) approaches were devised to speed up fluctuations of relevant slow degrees of freedom (SDOF) and ensure simulation convergence. However, in contrast to the achievements in parametrization, software performance, and workflow automation, efficient ECS methodology suitable for high throughput screening remains in an early stage of development. Here, a review of ECS developments with LB-FES is presented, revisiting current approaches and underlining the major technical pitfalls and challenges. This Perspective focuses on alchemical LB-FES on account of their predominant role in high throughput drug screening as well as the established partnership with ECS. The critical aspects of designing ECS approaches, from both theoretical and applied perspectives, are described. This work is intended to provide a contemporary review of the scientific, technical, and practical issues associated with the accelerating convergence of alchemical LB-FES.

ACES: Optimized Alchemically Enhanced Sampling

We present an alchemical enhanced sampling (ACES) method implemented in the GPU-accelerated AMBER free energy MD engine. The methods hinges on the creation of an "enhanced sampling state" by reducing or eliminating selected potential energy terms and interactions that lead to kinetic traps and conformational barriers while maintaining those terms that curtail the need to otherwise sample large volumes of phase space. For example, the enhanced sampling state might involve transforming regions of a ligand and/or protein side chain into a noninteracting "dummy state" with internal electrostatics and torsion angle terms turned off. The enhanced sampling state is connected to a real-state end point through a Hamiltonian replica exchange (HREMD) framework that is facilitated by newly developed alchemical transformation pathways and smoothstep softcore potentials. This creates a counterdiffusion of real and enhanced-sampling states along the HREMD network. The effect of a differential response of the environment to the real and enhanced-sampling states is minimized by leveraging the dual topology framework in AMBER to construct a counterbalancing HREMD network in the opposite alchemical direction with the same (or similar) real and enhanced sampling states at inverted end points. The method has been demonstrated in a series of test cases of increasing complexity where traditional MD, and in several cases alternative REST2-like enhanced sampling methods, are shown to fail. The hydration free energy for acetic acid was shown to be independent of the starting conformation, and the values for four additional edge case molecules from the FreeSolv database were shown to have a significantly closer agreement with experiment using ACES. The method was further able to handle different rotamer states in a Cdk2 ligand identified as fractionally occupied in crystal structures. Finally, ACES was applied to T4-lysozyme and demonstrated that the side chain distribution of V111χ1 could be reliably reproduced for the apo state, bound to p-xylene, and in p-xylene→ benzene transformations. In these cases, the ACES method is shown to be highly robust and superior to a REST2-like enhanced sampling implementation alone.

Multidimensional minimum-work control of a 2D Ising model

A system's configurational state can be manipulated using dynamic variation of control parameters, such as temperature, pressure, or magnetic field; for finite-duration driving, excess work is required above the equilibrium free-energy change. Minimum-work protocols in multidimensional control-parameter space have potential to significantly reduce work relative to one-dimensional control. By numerically minimizing a linear-response approximation to the excess work, we design protocols in control-parameter spaces of a 2D Ising model that efficiently drive the system from the all-down to all-up configuration. We find that such designed multidimensional protocols take advantage of more flexible control to avoid control-parameter regions of high system resistance, heterogeneously input and extract work to make use of system relaxation, and flatten the energy landscape, making accessible many configurations that would otherwise have prohibitively high energy and thus decreasing spin correlations. Relative to one-dimensional protocols, this speeds up the rate-limiting spin-inversion reaction, thereby keeping the system significantly closer to equilibrium for a wide range of protocol durations, and significantly reducing resistance and hence work.

Structure of native HIV-1 cores and their interactions with IP6 and CypA

The viral capsid plays essential roles in HIV replication and is a major platform engaging host factors. To overcome challenges in study native capsid structure, we used the perfringolysin O to perforate the membrane of HIV-1 particles, thus allowing host proteins and small molecules to access the native capsid while improving cryo–electron microscopy image quality. Using cryo–electron tomography and subtomogram averaging, we determined the structures of native capsomers in the presence and absence of inositol hexakisphosphate (IP6) and cyclophilin A and constructed an all-atom model of a complete HIV-1 capsid. Our structures reveal two IP6 binding sites and modes of cyclophilin A interactions. Free energy calculations substantiate the two binding sites at R18 and K25 and further show a prohibitive energy barrier for IP6 to pass through the pentamer. Our results demonstrate that perfringolysin O perforation is a valuable tool for structural analyses of enveloped virus capsids and interactions with host cell factors.

TYROSINE KINASES: COMPLEX MOLECULAR SYSTEMS CHALLENGING COMPUTATIONAL METHODOLOGIES

Classical molecular dynamics (MD) simulations based on atomic models play an increasingly important role in a wide range of applications in physics, biology, and chemistry. Nonetheless, generating genuine knowledge about biological systems using MD simulations remains challenging. Protein tyrosine kinases are important cellular signaling enzymes that regulate cell growth, proliferation, metabolism, differentiation, and migration. Due to the large conformational changes and long timescales involved in their function, these kinases present particularly challenging problems to modern computational and theoretical frameworks aimed at elucidating the dynamics of complex biomolecular systems. Markov state models have achieved limited success in tackling the broader conformational ensemble and biased methods are often employed to examine specific long timescale events. Recent advances in machine learning continue to push the limitations of current methodologies and provide notable improvements when integrated with the existing frameworks. A broad perspective is drawn from a critical review of recent studies.

Computational study of non-conductive selectivity filter conformations and C-type inactivation in a voltage-dependent potassium channel

C-type inactivation is a time-dependent process of great physiological significance that is observed in a large class of K⁺ channels. Experimental and computational studies of the pH-activated KcsA channel show that the functional C-type inactivated state, for this channel, is associated with a structural constriction of the selectivity filter at the level of the central glycine residue in the signature sequence, TTV(G)YGD. The structural constriction is allosterically promoted by the wide opening of the intracellular activation gate. However, whether this is a universal mechanism for C-type inactivation has not been established with certainty because similar constricted structures have not been observed for other K⁺ channels. Seeking to ascertain the general plausibility of the constricted filter conformation, molecular dynamics simulations of a homology model of the pore domain of the voltage-gated potassium channel Shaker were performed. Simulations performed with an open intracellular gate spontaneously resulted in a stable constricted-like filter conformation, providing a plausible nonconductive state responsible for C-type inactivation in the Shaker channel. While there are broad similarities with the constricted structure of KcsA, the hypothetical constricted-like conformation of Shaker also displays some subtle differences. Interestingly, those are recapitulated by the Shaker-like E71V KcsA mutant, suggesting that the residue at this position along the pore helix plays a pivotal role in determining the C-type inactivation behavior. Free energy landscape calculations show that the conductive-to-constricted transition in Shaker is allosterically controlled by the degree of opening of the intracellular activation gate, as observed with the KcsA channel. The behavior of the classic inactivating W434F Shaker mutant is also characterized from a 10-μs MD simulation, revealing that the selectivity filter spontaneously adopts a nonconductive conformation that is constricted at the level of the second glycine in the signature sequence, TTVGY(G)D.

Structural Changes beyond the EF-Hand Contribute to Apparent Calcium Binding Affinities: Insights from Parvalbumins

Members of the parvalbumin (PV) family of calcium (Ca²⁺) binding proteins (CBPs) share a relatively high level of sequence similarity. However, their Ca²⁺ affinities and selectivities against competing ions like Mg²⁺ can widely vary. We conducted molecular dynamics simulations of several α-parvalbumin (αPV) constructs with micromolar to nanomolar Ca²⁺ affinities to identify structural and dynamic features that contribute to their binding of ions. Specifically, we examined a D94S/G98E construct with a lower Ca²⁺ affinity (≈-18 kcal/mol) relative to the wild type (WT) (≈-22 kcal/mol) and an S55D/E59D variant with enhanced affinity (≈-24 kcal/mol). Additionally, we also examined the binding of Mg²⁺ to these isoforms, which is much weaker than Ca²⁺. We used mean spherical approximation (MSA) theory to evaluate ion binding thermodynamics within the proteins' EF-hand domains to account for the impact of ions' finite sizes and the surrounding electrolyte composition. While the MSA scores differentiated Mg²⁺ from Ca²⁺, they did not indicate that Ca²⁺ binding affinities at the binding loop differed between the PV isoforms. Instead, molecular mechanics generalized Born surface area (MM/GBSA) approximation energies, which we used to quantify the thermodynamic cost of structural rearrangement of the proteins upon binding ions, indicated that S55D/E59D αPV favored Ca²⁺ binding by -20 kcal/mol relative to WT versus 30 kcal/mol for D94S/G98E αPV. Meanwhile, Mg²⁺ binding was favored for the S55D/E59D αPV and D94S/G98E αPV variants by -18.32 and -1.65 kcal/mol, respectively. These energies implicate significant contributions to ion binding beyond oxygen coordination at the binding loop, which stemmed from changes in α-helicity, β-sheet character, and hydrogen bonding. Hence, Ca²⁺ affinity and selectivity against Mg²⁺ are emergent properties stemming from both local effects within the proteins' ion binding sites as well as non-local contributions elsewhere. Our findings broaden our understanding of the molecular bases governing αPV ion binding that are likely shared by members of the broad family of CBPs.

Molecular determinants of pro-arrhythmia proclivity of d- and l-sotalol via a multi-scale modeling pipeline

Drug isomers may differ in their proarrhythmia risk. An interesting example is the drug sotalol, an antiarrhythmic drug comprising d- and l- enantiomers that both block the hERG cardiac potassium channel and confer differing degrees of proarrhythmic risk. We developed a multi-scale in silico pipeline focusing on hERG channel – drug interactions and used it to probe and predict the mechanisms of pro-arrhythmia risks of the two enantiomers of sotalol. Molecular dynamics (MD) simulations predicted comparable hERG channel binding affinities for d- and l-sotalol, which were validated with electrophysiology experiments. MD derived thermodynamic and kinetic parameters were used to build multi-scale functional computational models of cardiac electrophysiology at the cell and tissue scales. Functional models were used to predict inactivated state binding affinities to recapitulate electrocardiogram (ECG) QT interval prolongation observed in clinical data. Our study demonstrates how modeling and simulation can be applied to predict drug effects from the atom to the rhythm for dl-sotalol and also increased proarrhythmia proclivity of d- vs. l-sotalol when accounting for stereospecific beta-adrenergic receptor blocking.

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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{kcal}}/{\text{mol}}$$\end{document}kcal/mol 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2.65$$\end{document}2.65 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.72 {\text{kcal}}/{\text{mol}}$$\end{document}1.72kcal/mol, 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.

Polarization Effects in Water-Mediated Selective Cation Transport across a Narrow Transmembrane Channel

Despite the progress in modeling complex molecular systems of ever-increasing complexity, a quantitatively accurate computational treatment of ion permeation through narrow membrane channels remains challenging. An important factor to reach this goal is induced electronic polarization, which is likely to impact the permeation rate of small ions through narrow molecular pores. In this work, we extended the recently developed polarizable force field based on the classical Drude oscillators to assess the role of induced polarization effects on the energetics of sodium and potassium ion transport across the gramicidin A (gA) ion channel. The inclusion of induced polarization lowers barriers present in 1D potential of mean force (PMF) for cation permeation by ∼50% compared to those obtained with the additive force field. Conductance properties calculated with 1D PMFs from Drude simulations are in better agreement with experimental results. Polarization of single-file water molecules and protein atoms forming the narrow pore has a direct impact on the free-energy barriers and cation-specific solid-state NMR chemical shifts. Sensitivity analysis indicates that small changes to water-channel interactions can alter the free energy barrier for ion permeation. These results, illustrating polarization effects present in the complex electrostatic environment of the gA channel, have broad implications for revising proposed mechanisms of ion permeation and selectivity in a variety of ion channels.

Mechanism of C-type inactivation in the hERG potassium channel

The fast C-type inactivation displayed by the voltage-activated potassium channel hERG plays a critical role in the repolarization of cardiac cells, and malfunction caused by nonspecific binding of drugs or naturally occurring missense mutations affecting inactivation can lead to pathologies. Because of its impact on human health, understanding the molecular mechanism of C-type inactivation in hERG represents an advance of paramount importance. Here, long-time scale molecular dynamics simulations, free energy landscape calculations, and electrophysiological experiments are combined to address the structural and functional impacts of several disease-associated mutations. Results suggest that C-type inactivation in hERG is associated with an asymmetrical constricted-like conformation of the selectivity filter, identifying F627 side-chain rotation and the hydrogen bond between Y616 and N629 as key determinants. Comparison of hERG with other K⁺ channels suggests that C-type inactivation depends on the degree of opening of the intracellular gate via the filter-gate allosteric coupling.

Permeability of the HIV-1 capsid to metabolites modulates viral DNA synthesis

Reverse transcription, an essential event in the HIV-1 life cycle, requires deoxynucleotide triphosphates (dNTPs) to fuel DNA synthesis, thus requiring penetration of dNTPs into the viral capsid. The central cavity of the capsid protein (CA) hexamer reveals itself as a plausible channel that allows the passage of dNTPs into assembled capsids. Nevertheless, the molecular mechanism of nucleotide import into the capsid remains unknown. Employing all-atom molecular dynamics (MD) simulations, we established that cooperative binding between nucleotides inside a CA hexamer cavity results in energetically favorable conditions for passive translocation of dNTPs into the HIV-1 capsid. Furthermore, binding of the host cell metabolite inositol hexakisphosphate (IP₆) enhances dNTP import, while binding of synthesized molecules like benzenehexacarboxylic acid (BHC) inhibits it. The enhancing effect on reverse transcription by IP₆ and the consequences of interactions between CA and nucleotides were corroborated using atomic force microscopy, transmission electron microscopy, and virological assays. Collectively, our results provide an atomistic description of the permeability of the HIV-1 capsid to small molecules and reveal a novel mechanism for the involvement of metabolites in HIV-1 capsid stabilization, nucleotide import, and reverse transcription.

This study shows that the HIV-1 capsid protein, in addition to its structural role, regulates reverse transcription, an essential metabolic process of the virus, by mediating the import of nucleotides. In addition, host cell metabolites such as inositol phosphates are recruited by the capsid to regulate viral DNA synthesis.

myPresto/omegagene 2020: a molecular dynamics simulation engine for virtual-system coupled sampling

The molecular dynamics (MD) method is a promising approach for investigating the molecular mechanisms of microscopic phenomena. In particular, generalized ensemble MD methods can efficiently explore the conformational space with a rugged free-energy surface. However, the implementation and acquisition of technical knowledge for each generalized ensemble MD method are not straightforward for end-users. Here, we present a new version of the myPresto/omegagene software, which is an MD simulation engine tailored for a series of generalized ensemble methods, which are virtual-system coupled multicanonical MD (V-McMD), virtual-system coupled adaptive umbrella sampling (V-AUS), and virtual-system coupled canonical MD (VcMD). This program has been applied in several studies analyzing free-energy landscapes of a variety of molecular systems with all-atom simulations. The updated version provides new functionality for coarse-grained simulations powered by the hydrophobicity scale method. The software package includes a step-by-step tutorial document for enhanced conformational sampling of the poly-glutamine (poly-Q) oligomer expressed as a one-bead per residue model. The myPresto/omegagene software is freely available at the following URL: https://github.com/kotakasahara/omegagene under the Apache2 license.

Retrieving functional pathways of biomolecules from single-particle snapshots

A primary reason for the intense interest in structural biology is the fact that knowledge of structure can elucidate macromolecular functions in living organisms. Sustained effort has resulted in an impressive arsenal of tools for determining the static structures. But under physiological conditions, macromolecules undergo continuous conformational changes, a subset of which are functionally important. Techniques for capturing the continuous conformational changes underlying function are essential for further progress. Here, we present chemically-detailed conformational movies of biological function, extracted data-analytically from experimental single-particle cryo-electron microscopy (cryo-EM) snapshots of ryanodine receptor type 1 (RyR1), a calcium-activated calcium channel engaged in the binding of ligands. The functional motions differ substantially from those inferred from static structures in the nature of conformationally active structural domains, the sequence and extent of conformational motions, and the way allosteric signals are transduced within and between domains. Our approach highlights the importance of combining experiment, advanced data analysis, and molecular simulations.

Open and Closed Structures of a Barium-Blocked Potassium Channel

Barium (Ba²⁺) is a classic permeant blocker of potassium (K⁺) channels. The "external lock-in effect" in barium block experiments, whereby the binding of external K⁺ impedes the forward translocation of the blocker, provides a powerful avenue to investigate the selectivity of the binding sites along the pore of potassium channels. Barium block experiments show that the external lock-in site is highly selective for K⁺ over Na⁺. Wild-type KcsA was crystallized in low K⁺ conditions, and the crystals were soaked in solutions containing various concentrations of barium. Structural analysis reveals open and closed gate conformations of the KcsA channel. Anomalous diffraction experiments show that Ba²⁺ primarily binds to the innermost site S4 of the selectivity filter of the open-gate conformation and also the site S2, but no binding is detected with the closed-gate conformation. Alchemical free-energy perturbation calculations indicate that the presence of a Ba²⁺ ion in the selectivity filter boosts the specificity of K⁺ binding relative to Na⁺ in the external sites S0-S2.

Scalable molecular dynamics on CPU and GPU architectures with NAMD

NAMDis a molecular dynamics program designed for high-performance simulations of very large biological objects on CPU- and GPU-based architectures. NAMD offers scalable performance on petascale parallel supercomputers consisting of hundreds of thousands of cores, as well as on inexpensive commodity clusters commonly found in academic environments. It is written in C++ and leans on Charm++ parallel objects for optimal performance on low-latency architectures. NAMD is a versatile, multipurpose code that gathers state-of-the-art algorithms to carry out simulations in apt thermodynamic ensembles, using the widely popular CHARMM, AMBER, OPLS, and GROMOS biomolecular force fields. Here, we review the main features of NAMD that allow both equilibrium and enhanced-sampling molecular dynamics simulations with numerical efficiency. We describe the underlying concepts utilized by NAMD and their implementation, most notably for handling long-range electrostatics; controlling the temperature, pressure, and pH; applying external potentials on tailored grids; leveraging massively parallel resources in multiple-copy simulations; and hybrid quantum-mechanical/molecular-mechanical descriptions. We detail the variety of options offered by NAMD for enhanced-sampling simulations aimed at determining free-energy differences of either alchemical or geometrical transformations and outline their applicability to specific problems. Last, we discuss the roadmap for the development of NAMD and our current efforts toward achieving optimal performance on GPU-based architectures, for pushing back the limitations that have prevented biologically realistic billion-atom objects to be fruitfully simulated, and for making large-scale simulations less expensive and easier to set up, run, and analyze. NAMD is distributed free of charge with its source code at www.ks.uiuc.edu.

Molecular Dynamics Simulation of Small Molecules Interacting with Biological Membranes

Cell membranes protect and compartmentalise cells and their organelles. The semi-permeable nature of these membranes controls the exchange of solutes across their structure. Characterising the interaction of small molecules with biological membranes is critical to understanding of physiological processes, drug action and permeation, and many biotechnological applications. This review provides an overview of how molecular simulations are used to study the interaction of small molecules with biological membranes, with a particular focus on the interactions of water, organic compounds, drugs and short peptides with models of plasma cell membrane and stratum corneum lipid bilayers. This review will not delve on other types of membranes which might have different composition and arrangement, such as thylakoid or mitochondrial membranes. The application of unbiased molecular dynamics simulations and enhanced sampling methods such as umbrella sampling, metadynamics and replica exchange are described using key examples. This review demonstrates how state-of-the-art molecular simulations have been used successfully to describe the mechanism of binding and permeation of small molecules with biological membranes, as well as associated changes to the structure and dynamics of these membranes. The review concludes with an outlook on future directions in this field.

Exploration of Free Energy Surfaces Across a Membrane Channel Using Metadynamics and Umbrella Sampling

To reach their site of action, it is essential for antibiotic molecules to cross the bacterial outer membrane. The progress of enhanced sampling techniques in molecular dynamics simulations enables us to understand these translocations at an atomic level. To this end, calculations of free energy surfaces for these permeation processes are of key importance. Herein, we investigate the translocation of a variety of anionic solutes through the outer membrane pore OprO of the Gram-negative bacterium Pseudomonas aeruginosa using the metadynamics and umbrella sampling techniques at the all-atom level. Free energy calculations have been performed employing these two distinct methods in order to illustrate the difference in computed free energies, if any. The investigated solutes range from a single atomic chloride ion over a multiatomic monophosphate ion to a more bulky fosmidomycin antibiotic. The role of complexity of the permeating solutes in estimating accurate free energy profiles is demonstrated by performing extensive convergence analysis. For simple monatomic ions, good agreement between the well-tempered metadynamics and the umbrella sampling approaches is achieved, while for the permeation of the monophosphate ion differences start to appear. In the case of larger molecules such as fosmidomycin it is a tough challenge to achieve converged free energy profiles. This issue is mainly due to neglecting orthogonal degrees of freedom during the free energy calculations. Nevertheless, the freely driven metadynamics approach leads to clearly advantageous results. Additionally, atomistic insights of the translocation mechanisms of all three solutes are discussed.

The Mechanism of Cholesterol Modification of Hedgehog Ligand

Hedgehog (Hh) proteins are important components of signal transduction pathways involved in animal development, and their defects are implicated in carcinogenesis. Their N-terminal domain (HhN) acts as a signaling ligand, and their C-terminal domain (HhC) performs an autocatalytic function of cleaving itself away, while adding a cholesterol moiety to HhN. HhC has two sub-domains: a hedgehog/intein (hint) domain that primarily performs the autocatalytic activity, and a sterol-recognition region (SRR) that binds to cholesterol and properly positions it with respect to HhN. The three-dimensional details of this autocatalytic mechanism remain unknown, as does the structure of the precursor Hh protein. In this study, a complete cholesterol-bound precursor form of the drosophila Hh precursor is modeled using known crystal structures of HhN and the hint domain, and a hypothesized similarity of SRR to an unrelated but similar-sized cholesterol binding protein. The restrained geometries and topology switching (RGATS) strategy is then used to predict atomic-detail pathways for the full autocatalytic reaction starting from the precursor and ending in a cholesterol-linked HhN domain and a cleaved HhC domain. The RGATS explicit solvent simulations indicate the roles of individual HhC residues in facilitating the reaction, which can be confirmed through mutational experiments. These simulations also provide plausible structural models for the N/S acyl transfer intermediate and the product states of this reaction. This study thus provides a good framework for future computational and experimental studies to develop a full structural and dynamic understanding of Hh autoprocessing. © 2019 Wiley Periodicals, Inc.

Enhanced sampling and free energy calculations for protein simulations

Molecular dynamics simulation is a powerful computational technique to study biomolecular systems, which complements experiments by providing insights into the structural dynamics relevant to biological functions at atomic scale. It can also be used to calculate the free energy landscapes of the conformational transitions to better understand the functions of the biomolecules. However, the sampling of biomolecular configurations is limited by the free energy barriers that need to be overcome, leading to considerable gaps between the timescales reached by MD simulation and those governing biological processes. To address this issue, many enhanced sampling methodologies have been developed to increase the sampling efficiency of molecular dynamics simulations and free energy calculations. Usually, enhanced sampling algorithms can be classified into methods based on collective variables (CV-based) and approaches which do not require predefined CVs (CV-free). In this chapter, the theoretical basis of free energy estimation is briefly reviewed first, followed by the reviews of the most common CV-based and CV-free methods including the presentation of some examples and recent developments. Finally, the combination of different enhanced sampling methods is discussed.

Simulating ion channel activation mechanisms using swarms of trajectories

Atomic-level studies of protein activity represent a significant challenge as a result of the complexity of conformational changes occurring on wide-ranging timescales, often greatly exceeding that of even the longest simulations. A prime example is the elucidation of protein allosteric mechanisms, where localized perturbations transmit throughout a large macromolecule to generate a response signal. For example, the conversion of chemical to electrical signals during synaptic neurotransmission in the brain is achieved by specialized membrane proteins called pentameric ligand-gated ion channels. Here, the binding of a neurotransmitter results in a global conformational change to open an ion-conducting pore across the nerve cell membrane. X-ray crystallography has produced static structures of the open and closed states of the proton-gated GLIC pentameric ligand-gated ion channel protein, allowing for atomistic simulations that can uncover changes related to activation. We discuss a range of enhanced sampling approaches that could be used to explore activation mechanisms. In particular, we describe recent application of an atomistic string method, based on Roux's "swarms of trajectories" approach, to elucidate the sequence and interdependence of conformational changes during activation. We illustrate how this can be combined with transition analysis and Brownian dynamics to extract thermodynamic and kinetic information, leading to understanding of what controls ion channel function. © 2019 Wiley Periodicals, Inc.

On Restraints in End-Point Protein-Ligand Binding Free Energy Calculations

The impact of harmonic restraints on protein heavy atoms and ligand atoms on end-point free energy calculations is systematically characterized for 54 protein-ligand complexes. We observe that stronger restraints reduce the equilibration time and statistical inefficiency, suppress conformational sampling, influence correlation with experiment, and monotonically decrease the estimated loss of entropy upon binding, leading to stronger estimated binding free energies in most systems. A statistical estimator that reweights for the biasing potential and includes data prior to the estimated equilibration time has the highest correlation with experiment. A spring constant of 20 cal mol^-1 Å^-2 maintains a near-native energy landscape and suppresses artifactual energy minima while minimally limiting thermal fluctuations about the crystal structure. © 2019 Wiley Periodicals, Inc.

String Method for Protein-Protein Binding Free-Energy Calculations

A powerful computational strategy to determine the equilibrium association constant of two macromolecules with explicit-solvent molecular dynamics (MD) simulations is the "geometric route", which considers the reversible physical separation of the bound complex in solution. Nonetheless, multiple challenges remain to render this type of methodology reliable and computationally efficient in practice. In particular, in one, formulation of the geometric route relies on the potential of mean force (PMF) for physically separating the two binding partners restrained along a straight axis, which must be selected prior to the calculation. However, practical applications indicate that the calculation of the separation PMF along the predefined rectilinear pathway may be suboptimal and slowly convergent. Recognizing that a rectilinear straight separation pathway is generally not representative of how the protein complex physically separates in solution, we put forth a novel theoretical framework for binding free-energy calculations, leaning on the optimal curvilinear minimum free-energy path (MFEP) determined from the string method. The proposed formalism is validated by comparing the results obtained using both rectilinear and curvilinear pathways for a prototypical host-guest complex formed by cucurbit[7]uril (CB[7]) binding benzene, and for the barnase-barstar protein complex. On the basis of multi-microsecond MD calculations, we find that the calculations following the traditional rectilinear pathway and the string-based curvilinear pathway agree quantitatively, but convergence is faster with the latter.

Multidimensional virtual-system coupled canonical molecular dynamics to compute free-energy landscapes of peptide multimer assembly

An enhanced-sampling method termed multidimensional virtual-system coupled canonical molecular dynamics (mD-VcMD) method is developed. In many cases, generalized-ensemble methods realizing enhanced sampling, for example, adaptive umbrella sampling, apply an effective potential, which is derived from temporarily assumed canonical distribution as a function of one or more arbitrarily defined reaction coordinates. However, it is not straightforward to estimate the appropriate canonical distribution, especially for cases applying multiple reaction coordinates. The current method, mD-VcMD, does not rely on the form of the canonical distribution. Therefore, it is practically useful to explore a high-dimensional reaction-coordinate space. In this article, formulation of mD-VcMD and its evaluation with the simple molecular models consisting of three or four alanine peptides are presented. We confirmed that mD-VcMD efficiently searched 2D and 3D reaction-coordinate spaces defined as interpeptide distances. Direct comparisons with results of long-term canonical MD simulations revealed that mD-VcMD produces correct canonical ensembles. © 2019 Wiley Periodicals, Inc.

Bases of Bacterial Sodium Channel Selectivity Among Organic Cations

Hille’s (1971) seminal study of organic cation selectivity of eukaryotic voltage-gated sodium channels showed a sharp size cut-off for ion permeation, such that no ion possessing a methyl group was permeant. Using the prokaryotic channel, NaChBac, we found some similarity and two peculiar differences in the selectivity profiles for small polyatomic cations. First, we identified a diverse group of minimally permeant cations for wildtype NaChBac, ranging in sizes from ammonium to guanidinium and tetramethylammonium; and second, for both ammonium and hydrazinium, the charge-conserving selectivity filter mutation (E191D) yielded substantial increases in relative permeability (P_X/P_Na). The relative permeabilities varied inversely with relative K_d calculated from 1D Potential of Mean Force profiles (PMFs) for the single cations traversing the channel. Several of the cations bound more strongly than Na⁺, and hence appear to act as blockers, as well as charge carriers. Consistent with experimental observations, the E191D mutation had little impact on Na⁺ binding to the selectivity filter, but disrupted the binding of ammonium and hydrazinium, consequently facilitating ion permeation across the NaChBac-like filter. We concluded that for prokaryotic sodium channels, a fine balance among filter size, binding affinity, occupancy, and flexibility seems to contribute to observed functional differences.

Massive-Scale Binding Free Energy Simulations of HIV Integrase Complexes Using Asynchronous Replica Exchange Framework Implemented on the IBM WCG Distributed Network

To perform massive-scale replica exchange molecular dynamics (REMD) simulations for calculating binding free energies of protein-ligand complexes, we implemented the asynchronous replica exchange (AsyncRE) framework of the binding energy distribution analysis method (BEDAM) in implicit solvent on the IBM World Community Grid (WCG) and optimized the simulation parameters to reduce the overhead and improve the prediction power of the WCG AsyncRE simulations. We also performed the first massive-scale binding free energy calculations using the WCG distributed computing grid and 301 ligands from the SAMPL4 challenge for large-scale binding free energy predictions of HIV-1 integrase complexes. In total there are ∼10000 simulated complexes, ∼1 million replicas, and ∼2000 μs of aggregated MD simulations. Running AsyncRE MD simulations on the WCG requires accepting a trade-off between the number of replicas that can be run (breadth) and the number of full RE cycles that can be completed per replica (depth). As compared with synchronous Replica Exchange (SyncRE) running on tightly coupled clusters like XSEDE, on the WCG many more replicas can be launched simultaneously on heterogeneous distributed hardware, but each full RE cycle requires more overhead. We compared the WCG results with that from AutoDock and more advanced RE simulations including the use of flattening potentials to accelerate sampling of selected degrees of freedom of ligands and/or receptors related to slow dynamics due to high energy barriers. We propose a suitable strategy of RE simulations to refine high throughput docking results which can be matched to corresponding computing resources: from HPC clusters, to small or medium-size distributed campus grids, and finally to massive-scale computing networks including millions of CPUs like the resources available on the WCG.

Molecular Dynamics of Ion Conduction through the Selectivity Filter of the NaVAb Sodium Channel

The determination of the atomic structures of voltage-gated bacterial sodium channels using X-ray crystallography has provided a first view of this family of membrane proteins. Molecular dynamics simulations offer one approach to clarify the underlying mechanism of permeation and selectivity in these channels. However, it appears that the intracellular gate of the pore domain is either closed or only open partially in the available X-ray structures. The lack of structure with a fully open intracellular gate poses a special challenge to computational studies aimed at simulating ion conduction. To circumvent this problem, we simulated a model of the Na_VAb channel in which the transmembrane S5 and S6 helices of the pore domain have been truncated to provide direct open access to the intracellular entryway to the pore. Molecular dynamics simulations were carried out over a range of membrane potential and ion concentration of sodium and potassium. The simulations show that the Na_VAb selectivity filter is essentially a cationic pore supporting the conduction of ions at a rate comparable to aqueous diffusion with no significant selectivity for sodium. Conductance and selectivity vary as a function of ion concentration for both cations. Permeation occurs primarily via a knock-on mechanism for both sodium and potassium, although the ion ordering in single file along the pore is not strictly maintained. The character of the outward current appears quite different from the inward current, with a buildup on ions in the selectivity filter prior to escape toward the extracellular side, indicating the presence of a rectification effect that is overcome by nonphysiological applied voltages.

Rapid constriction of the selectivity filter underlies C-type inactivation in the KcsA potassium channel

C-type inactivation in K⁺ channels is thought to be a result of constriction of the selectivity filter. By using MD simulations, Li et al. show that rapid constriction occurs within 1–2 s when the intracellular activation gate is fully open, but not when the gate is closed or partially open.

C-type inactivation is a time-dependent process observed in many K⁺ channels whereby prolonged activation by an external stimulus leads to a reduction in ionic conduction. While C-type inactivation is thought to be a result of a constriction of the selectivity filter, the local dynamics of the process remain elusive. Here, we use molecular dynamics (MD) simulations of the KcsA channel to elucidate the nature of kinetically delayed activation/inactivation gating coupling. Microsecond-scale MD simulations based on the truncated form of the KcsA channel (C-terminal domain deleted) provide a first glimpse of the onset of C-type inactivation. We observe over multiple trajectories that the selectivity filter consistently undergoes a spontaneous and rapid (within 1–2 µs) transition to a constricted conformation when the intracellular activation gate is fully open, but remains in the conductive conformation when the activation gate is closed or partially open. Multidimensional umbrella sampling potential of mean force calculations and nonequilibrium voltage-driven simulations further confirm these observations. Electrophysiological measurements show that the truncated form of the KcsA channel inactivates faster and greater than full-length KcsA, which is consistent with truncated KcsA opening to a greater degree because of the absence of the C-terminal domain restraint. Together, these results imply that the observed kinetics underlying activation/inactivation gating reflect a rapid conductive-to-constricted transition of the selectivity filter that is allosterically controlled by the slow opening of the intracellular gate.

Improving Prediction Accuracy of Binding Free Energies and Poses of HIV Integrase Complexes Using the Binding Energy Distribution Analysis Method with Flattening Potentials

To accelerate conformation sampling of slow dynamics from receptor or ligand, we introduced flattening potentials on selected bonded and nonbonded intramolecular interactions to the binding energy distribution analysis method (BEDAM) for calculating absolute binding free energies of protein-ligand complexes using an implicit solvent model and implemented flattening BEDAM using the asynchronous replica exchange (AsyncRE) framework for performing large scale replica exchange molecular dynamics (REMD) simulations. The advantage of using the flattening feature to reduce high energy barriers was exhibited first by the p-xylene-T4 lysozyme complex, where the intramolecular interactions of a protein side chain on the binding site were flattened to accelerate the conformational transition of the side chain from the trans to the gauche state when the p-xylene ligand is present in the binding site. Much more extensive flattening BEDAM simulations were performed for 53 experimental binders and 248 nonbinders of HIV-1 integrase which formed the SAMPL4 challenge, with the total simulation time of 24.3 μs. We demonstrated that the flattening BEDAM simulations not only substantially increase the number of true positives (and reduce false negatives) but also improve the prediction accuracy of binding poses of experimental binders. Furthermore, the values of area under the curve (AUC) of receiver operating characteristic (ROC) and the enrichment factors at 20% cutoff calculated from the flattening BEDAM simulations were improved significantly in comparison with that of simulations without flattening as we previously reported for the whole SAMPL4 database. Detailed analysis found that the improved ability to discriminate the binding free energies between the binders and nonbinders is due to the fact that the flattening simulations reduce the reorganization free energy penalties of binders and decrease the overlap of binding free energy distributions of binders relative to that of nonbinders. This happens because the conformational ensemble distributions for both the ligand and protein in solution match those at the fully coupled (complex) state more closely when the systems are more fully sampled after the flattening potentials are applied to the intermediate states.

Multi-dimensional virtual system introduced to enhance canonical sampling

When an important process of a molecular system occurs via a combination of two or more rare events, which occur almost independently to one another, computational sampling for the important process is difficult. Here, to sample such a process effectively, we developed a new method, named the "multi-dimensional Virtual-system coupled Monte Carlo (multi-dimensional-VcMC)" method, where the system interacts with a virtual system expressed by two or more virtual coordinates. Each virtual coordinate controls sampling along a reaction coordinate. By setting multiple reaction coordinates to be related to the corresponding rare events, sampling of the important process can be enhanced. An advantage of multi-dimensional-VcMC is its simplicity: Namely, the conformation moves widely in the multi-dimensional reaction coordinate space without knowledge of canonical distribution functions of the system. To examine the effectiveness of the algorithm, we introduced a toy model where two molecules (receptor and its ligand) bind and unbind to each other. The receptor has a deep binding pocket, to which the ligand enters for binding. Furthermore, a gate is set at the entrance of the pocket, and the gate is usually closed. Thus, the molecular binding takes place via the two events: ligand approach to the pocket and gate opening. In two-dimensional (2D)-VcMC, the two molecules exhibited repeated binding and unbinding, and an equilibrated distribution was obtained as expected. A conventional canonical simulation, which was 200 times longer than 2D-VcMC, failed in sampling the binding/unbinding effectively. The current method is applicable to various biological systems.

Free-energy simulations reveal molecular mechanism for functional switch of a DNA helicase

Helicases play key roles in genome maintenance, yet it remains elusive how these enzymes change conformations and how transitions between different conformational states regulate nucleic acid reshaping. Here, we developed a computational technique combining structural bioinformatics approaches and atomic-level free-energy simulations to characterize how the Escherichia coli DNA repair enzyme UvrD changes its conformation at the fork junction to switch its function from unwinding to rezipping DNA. The lowest free-energy path shows that UvrD opens the interface between two domains, allowing the bound ssDNA to escape. The simulation results predict a key metastable 'tilted' state during ssDNA strand switching. By simulating FRET distributions with fluorophores attached to UvrD, we show that the new state is supported quantitatively by single-molecule measurements. The present study deciphers key elements for the 'hyper-helicase' behavior of a mutant and provides an effective framework to characterize directly structure-function relationships in molecular machines.

Molecular dynamics coupled with a virtual system for effective conformational sampling

An enhanced conformational sampling method is proposed: virtual-system coupled canonical molecular dynamics (VcMD). Although VcMD enhances sampling along a reaction coordinate, this method is free from estimation of a canonical distribution function along the reaction coordinate. This method introduces a virtual system that does not necessarily obey a physical law. To enhance sampling the virtual system couples with a molecular system to be studied. Resultant snapshots produce a canonical ensemble. This method was applied to a system consisting of two short peptides in an explicit solvent. Conventional molecular dynamics simulation, which is ten times longer than VcMD, was performed along with adaptive umbrella sampling. Free-energy landscapes computed from the three simulations mutually converged well. The VcMD provided quicker association/dissociation motions of peptides than the conventional molecular dynamics did. The VcMD method is applicable to various complicated systems because of its methodological simplicity. © 2018 Wiley Periodicals, Inc.

Conformational landscapes of membrane proteins delineated by enhanced sampling molecular dynamics simulations

The expansion of computational power, better parameterization of force fields, and the development of novel algorithms to enhance the sampling of the free energy landscapes of proteins have allowed molecular dynamics (MD) simulations to become an indispensable tool to understand the function of biomolecules. The temporal and spatial resolution of MD simulations allows for the study of a vast number of processes of interest. Here, we review the computational efforts to uncover the conformational free energy landscapes of a subset of membrane proteins: ion channels, transporters and G-protein coupled receptors. We focus on the various enhanced sampling techniques used to study these questions, how the conclusions come together to build a coherent picture, and the relationship between simulation outcomes and experimental observables.

Computational membrane biophysics: From ion channel interactions with drugs to cellular function

The rapid development of experimental and computational techniques has changed fundamentally our understanding of cellular-membrane transport. The advent of powerful computers and refined force-fields for proteins, ions, and lipids has expanded the applicability of Molecular Dynamics (MD) simulations. A myriad of cellular responses is modulated through the binding of endogenous and exogenous ligands (e.g. neurotransmitters and drugs, respectively) to ion channels. Deciphering the thermodynamics and kinetics of the ligand binding processes to these membrane proteins is at the heart of modern drug development. The ever-increasing computational power has already provided insightful data on the thermodynamics and kinetics of drug-target interactions, free energies of solvation, and partitioning into lipid bilayers for drugs. This review aims to provide a brief summary about modeling approaches to map out crucial binding pathways with intermediate conformations and free-energy surfaces for drug-ion channel binding mechanisms that are responsible for multiple effects on cellular functions. We will discuss post-processing analysis of simulation-generated data, which are then transformed to kinetic models to better understand the molecular underpinning of the experimental observables under the influence of drugs or mutations in ion channels. This review highlights crucial mathematical frameworks and perspectives on bridging different well-established computational techniques to connect the dynamics and timescales from all-atom MD and free energy simulations of ion channels to the physiology of action potentials in cellular models. This article is part of a Special Issue entitled: Biophysics in Canada, edited by Lewis Kay, John Baenziger, Albert Berghuis and Peter Tieleman.

Chemical substitutions in the selectivity filter of potassium channels do not rule out constricted-like conformations for C-type inactivation

In many K⁺ channels, prolonged activating stimuli lead to a time-dependent reduction in ion conduction, a phenomenon known as C-type inactivation. X-ray structures of the KcsA channel suggest that this inactivated state corresponds to a "constricted" conformation of the selectivity filter. However, the functional significance of the constricted conformation has become a matter of debate. Functional and structural studies based on chemically modified semisynthetic KcsA channels along the selectivity filter led to the conclusion that the constricted conformation does not correspond to the C-type inactivated state. The main results supporting this view include the observation that C-type inactivation is not suppressed by a substitution of D-alanine at Gly77, even though this modification is believed to lock the selectivity filter into its conductive conformation, whereas it is suppressed following amide-to-ester backbone substitutions at Gly77 and Tyr78, even though these structure-conserving modifications are not believed to prevent the selectivity filter from adopting the constricted conformation. However, several untested assumptions about the structural and functional impact of these chemical modifications underlie these arguments. To make progress, molecular dynamics simulations based on atomic models of the KcsA channel were performed. The computational results support the notion that the constricted conformation of the selectivity filter corresponds to the functional C-type inactivated state of the KcsA. Importantly, MD simulations reveal that the semisynthetic KcsA^D-ala77 channel can adopt an asymmetrical constricted-like nonconductive conformation and that the amide-to-ester backbone substitutions at Gly77 and Tyr78 perturb the hydrogen bonding involving the buried water molecules stabilizing the constricted conformation.

Polymodal allosteric regulation of Type 1 Serine/Threonine Kinase Receptors via a conserved electrostatic lock

Type 1 Serine/Threonine Kinase Receptors (STKR1) transduce a wide spectrum of biological signals mediated by TGF-β superfamily members. The STKR1 activity is tightly controlled by their regulatory glycine-serine rich (GS) domain adjacent to the kinase domain. Despite decades of studies, it remains unknown how physiological or pathological GS domain modifications are coupled to STKR1 kinase activity. Here, by performing molecular dynamics simulations and free energy calculation of Activin-Like Kinase 2 (ALK2), we found that GS domain phosphorylation, FKBP12 dissociation, and disease mutations all destabilize a D354-R375 salt-bridge, which normally acts as an electrostatic lock to prevent coordination of adenosine triphosphate (ATP) to the catalytic site. We developed a WAFEX-guided principal analysis and unraveled how phosphorylation destabilizes this highly conserved salt-bridge in temporal and physical space. Using current-flow betweenness scores, we identified an allosteric network of residue-residue contacts between the GS domain and the catalytic site that controls the formation and disruption of this salt bridge. Importantly, our novel network analysis approach revealed how certain disease-causing mutations bypass FKBP12-mediated kinase inhibition to produce leaky signaling. We further provide experimental evidence that this salt-bridge lock exists in other STKR1s, and acts as a general safety mechanism in STKR1 to prevent pathological leaky signaling. In summary, our study provides a compelling and unifying allosteric activation mechanism in STKR1 kinases that reconciles a large number of experimental studies and sheds light on a novel therapeutic avenue to target disease-related STKR1 mutants.

Kinases play central role in essential physiological process and are attractive therapeutic drug targets. One of the important kinase families is Type 1 Serine/Threonine Kinase Receptors (STKR1), which control gene expression in response to extracellular growth factors. The activities of STKR1 are tightly controlled by their regulatory domain, which is distant from the kinase catalytic site. The underlying molecular mechanism is elucidated here. We identified that formation or disruption of a highly conserved charge-charge interaction located near the ATP binding site, mediates the physiological inhibition or activation of STKR1. We find that the stability of this charge-charge interaction is remotely controlled by interactions propagated from the distant regulatory domain. Several disease-causing mutations are located at the regulatory domain. We demonstrate how those mutations bypass these endogenous STKR1 inhibition mechanisms to produce pathological phenotypes. This study provides a general activation mechanism in STKR1 kinases, thus may benefit understanding the molecular mechanism of diseases and drug development.

Mapping Ryanodine Binding Sites in the Pore Cavity of Ryanodine Receptors

Ryanodine (Ryd) irreversibly targets ryanodine receptors (RyRs), a family of intracellular calcium release channels essential for many cellular processes ranging from muscle contraction to learning and memory. Little is known of the atomistic details about how Ryd binds to RyRs. In this study, we used all-atom molecular dynamics simulations with both enhanced and bidirectional sampling to gain direct insights into how Ryd interacts with major residues in RyRs that were experimentally determined to be critical for its binding. We found that the pyrrolic ring of Ryd displays preference for the R⁴⁸⁹²AGGG-F⁴⁹²¹ residues in the cavity of RyR1, which explain the effects of the corresponding mutations in RyR2 in experiments. Particularly, the mutant Q4933A (or Q4863A in RyR2) critical for both the gating and Ryd binding not only has significantly less interaction with Ryd than the wild-type, but also yields more space for Ryd and water molecules in the cavity. These results describe clear binding modes of Ryd in the RyR cavity and offer structural mechanisms explaining functional data collected on RyR blockade.

Computational Studies of Molecular Permeation through Connexin26 Channels

A signal property of connexin channels is the ability to mediate selective diffusive movement of molecules through plasma membrane(s), but the energetics and determinants of molecular movement through these channels have yet to be understood. Different connexin channels have distinct molecular selectivities that cannot be explained simply on the basis of size or charge of the permeants. To gain insight into the forces and interactions that underlie selective molecular permeation, we investigated the energetics of two uncharged derivatized sugars, one permeable and one impermeable, through a validated connexin26 (Cx26) channel structural model, using molecular dynamics and associated analytic tools. The system is a Cx26 channel equilibrated in explicit membrane/solvent, shown by Brownian dynamics to reproduce key conductance characteristics of the native channel. The results are consistent with the known difference in permeability to each molecule. The energetic barriers extend through most of the pore length, rather than being highly localized as in ion-specific channels. There is little evidence for binding within the pore. Force decomposition reveals how, for each tested molecule, interactions with water and the Cx26 protein vary over the length of the pore and reveals a significant contribution from hydrogen bonding and interaction with K(+). The flexibility of the pore width varies along its length, and the tested molecules have differential effects on pore width as they pass through. Potential sites of interaction within the pore are defined for each molecule. The results suggest that for the tested molecules, differences in hydrogen bonding and entropic factors arising from permeant flexibility substantially contribute to the energetics of permeation. This work highlights factors involved in selective molecular permeation that differ from those that define selectivity among atomic ions.

Differential Membrane Binding Mechanics of Synaptotagmin Isoforms Observed in Atomic Detail

Synaptotagmin (Syt) is a membrane-associated protein involved in vesicle fusion through the SNARE complex that is found throughout the human body in 17 different isoforms. These isoforms have two membrane-binding C2 domains, which sense Ca²⁺ and thereby promote anionic membrane binding and lead to vesicle fusion. Through molecular dynamics simulations using the highly mobile membrane mimetic acclerated bilayer model, we have investigated how small protein sequence changes in the Ca²⁺-binding loops of the C2 domains may give rise to the experimentally determined difference in binding kinetics between Syt-1 and Syt-7 isoforms. Syt-7 C2 domains are found to form more close contacts with anionic phospholipid headgroups, particularly in loop 1, where an additional positive charge in Syt-7 draws the loop closer to the membrane and causes the anchoring residue F167 to insert deeper into the bilayer than the corresponding methionine in Syt-1 (M173). By performing additional replica exchange umbrella sampling calculations, we demonstrate that these additional contacts increase the energetic cost of unbinding the Syt-7 C2 domains from the bilayer, causing them to unbind more slowly than their counterparts in Syt-1.

Molecular Basis of S100A1 Activation at Saturating and Subsaturating Calcium Concentrations

The S100A1 protein mediates a wide variety of physiological processes through its binding of calcium (Ca(2+)) and endogenous target proteins. S100A1 presents two Ca(2+)-binding domains: a high-affinity "canonical" EF (cEF) hand and a low-affinity "pseudo" EF (pEF) hand. Accumulating evidence suggests that both Ca(2+)-binding sites must be saturated to stabilize an open state conducive to peptide recognition, yet the pEF hand's low affinity limits Ca(2+) binding at normal physiological concentrations. To understand the molecular basis of Ca(2+) binding and open-state stabilization, we performed 100 ns molecular dynamics simulations of S100A1 in the apo/holo (Ca(2+)-free/bound) states and a half-saturated state, for which only the cEF sites are Ca(2+)-bound. Our simulations indicate that the pattern of oxygen coordination about Ca(2+) in the cEF relative to the pEF site contributes to the former's higher affinity, whereas Ca(2+) binding strongly reshapes the protein's conformational dynamics by disrupting β-sheet coupling between EF hands. Moreover, modeling of the half-saturated configuration suggests that the open state is unstable and reverts toward a closed state in the absence of the pEF Ca(2+) ion. These findings indicate that Ca(2+) binding at the cEF site alone is insufficient to stabilize opening; thus, posttranslational modification of the protein may be required for target peptide binding at subsaturating intracellular Ca(2+) levels.

Locally weighted histogram analysis and stochastic solution for large-scale multi-state free energy estimation

The weighted histogram analysis method (WHAM) including its binless extension has been developed independently in several different contexts, and widely used in chemistry, physics, and statistics, for computing free energies and expectations from multiple ensembles. However, this method, while statistically efficient, is computationally costly or even infeasible when a large number, hundreds or more, of distributions are studied. We develop a locally WHAM (local WHAM) from the perspective of simulations of simulations (SOS), using generalized serial tempering (GST) to resample simulated data from multiple ensembles. The local WHAM equations based on one jump attempt per GST cycle can be solved by optimization algorithms orders of magnitude faster than standard implementations of global WHAM, but yield similarly accurate estimates of free energies to global WHAM estimates. Moreover, we propose an adaptive SOS procedure for solving local WHAM equations stochastically when multiple jump attempts are performed per GST cycle. Such a stochastic procedure can lead to more accurate estimates of equilibrium distributions than local WHAM with one jump attempt per cycle. The proposed methods are broadly applicable when the original data to be "WHAMMED" are obtained properly by any sampling algorithm including serial tempering and parallel tempering (replica exchange). To illustrate the methods, we estimated absolute binding free energies and binding energy distributions using the binding energy distribution analysis method from one and two dimensional replica exchange molecular dynamics simulations for the beta-cyclodextrin-heptanoate host-guest system. In addition to the computational advantage of handling large datasets, our two dimensional WHAM analysis also demonstrates that accurate results similar to those from well-converged data can be obtained from simulations for which sampling is limited and not fully equilibrated.

The cellular membrane as a mediator for small molecule interaction with membrane proteins

The cellular membrane constitutes the first element that encounters a wide variety of molecular species to which a cell might be exposed. Hosting a large number of structurally and functionally diverse proteins associated with this key metabolic compartment, the membrane not only directly controls the traffic of various molecules in and out of the cell, it also participates in such diverse and important processes as signal transduction and chemical processing of incoming molecular species. In this article, we present a number of cases where details of interaction of small molecular species such as drugs with the membrane, which are often experimentally inaccessible, have been studied using advanced molecular simulation techniques. We have selected systems in which partitioning of the small molecule with the membrane constitutes a key step for its final biological function, often binding to and interacting with a protein associated with the membrane. These examples demonstrate that membrane partitioning is not only important for the overall distribution of drugs and other small molecules into different compartments of the body, it may also play a key role in determining the efficiency and the mode of interaction of the drug with its target protein. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.