Generalized Replica Exchange Research Articles

Acceleration of generalized replica exchange with solute tempering simulations of large biological systems on massively parallel supercomputer.

Generalized replica exchange with solute tempering (gREST) is one of the enhanced sampling algorithms for proteins or other systems with rugged energy landscapes. Unlike the replica-exchange molecular dynamics (REMD) method, solvent temperatures are the same in all replicas, while solute temperatures are different and are exchanged frequently between replicas for exploring various solute structures. Here, we apply the gREST scheme to large biological systems containing over one million atoms using a large number of processors in a supercomputer. First, communication time on a multi-dimensional torus network is reduced by matching each replica to MPI processors optimally. This is applicable not only to gREST but also to other multi-copy algorithms. Second, energy evaluations, which are necessary for the multistate bennet acceptance ratio (MBAR) method for free energy estimations, are performed on-the-fly during the gREST simulations. Using these two advanced schemes, we observed 57.72 ns/day performance in 128-replica gREST calculations with 1.5 million atoms system using 16,384 nodes in Fugaku. These schemes implemented in the latest version of GENESIS software could open new possibilities to answer unresolved questions on large biomolecular complex systems with slow conformational dynamics.

Machine Learning-Assisted Phase Transition Temperatures from Generalized Replica Exchange Simulations of Dry Martini Lipid Bilayers.

Accurate estimation of phase transition temperatures has been a longstanding challenge for molecular simulations. Recently, the generalized Replica Exchange technique for estimating phase transition temperatures has allowed for improved sampling of the phase transition; however, it requires a significant number of simultaneous replicas both inside and outside of the transition region leading to costly computational expense. In this work, the recently developed machine learning-assisted lipid phase analysis technique for learning the phase of individual lipids has been combined with generalized Replica Exchange Molecular Dynamics to reduce the overall computational expense of evaluating transition temperatures. This technique is then applied to eight different Dry Martini lipids to demonstrate its ability to describe transition temperatures as a function of chain length and tail saturation.

Practical Protocols for Efficient Sampling of Kinase-Inhibitor Binding Pathways Using Two-Dimensional Replica-Exchange Molecular Dynamics.

Molecular dynamics (MD) simulations are increasingly used to study various biological processes such as protein folding, conformational changes, and ligand binding. These processes generally involve slow dynamics that occur on the millisecond or longer timescale, which are difficult to simulate by conventional atomistic MD. Recently, we applied a two-dimensional (2D) replica-exchange MD (REMD) method, which combines the generalized replica exchange with solute tempering (gREST) with the replica-exchange umbrella sampling (REUS) in kinase-inhibitor binding simulations, and successfully observed multiple ligand binding/unbinding events. To efficiently apply the gREST/REUS method to other kinase-inhibitor systems, we establish modified, practical protocols with non-trivial simulation parameter tuning. The current gREST/REUS simulation protocols are tested for three kinase-inhibitor systems: c-Src kinase with PP1, c-Src kinase with Dasatinib, and c-Abl kinase with Imatinib. We optimized the definition of kinase-ligand distance as a collective variable (CV), the solute temperatures in gREST, and replica distributions and umbrella forces in the REUS simulations. Also, the initial structures of each replica in the 2D replica space were prepared carefully by pulling each ligand from and toward the protein binding sites for keeping stable kinase conformations. These optimizations were carried out individually in multiple short MD simulations. The current gREST/REUS simulation protocol ensures good random walks in 2D replica spaces, which are required for enhanced sampling of inhibitor dynamics around a target kinase.

Development of the force field for cyclosporine A.

Membrane permeability of cyclic peptides is an important factor in drug design. To investigate the membrane permeability of cyclic peptides using molecular dynamics (MD) simulations, the accurate force fields for unnatural amino acids present in the cyclic peptides are required. Therefore, we developed the CHARMM force fields of the unnatural amino acids present in cyclosporin A (CsA), a cyclic peptide used as an immune suppressor. Especially for N-methyl amino acids, which contribute to the membrane permeability of cyclic peptides, we developed a grid correction map (CMAP) of the energy surface using the φ and ψ dihedral angles in the main chain of CsA. To validate the developed force field, we performed MD simulations, including the generalized replica exchange with solute tempering method, of CsA in water and chloroform solvents. The conformations of CsA in water and chloroform sampled using the developed force field were consistent with those of the experimental results of the solution nuclear magnetic resonance spectroscopy.

Mechanism of Vitamin D Receptor Ligand-Binding Domain Regulation Studied by gREST Simulations.

The vitamin D receptor ligand-binding domain (VDR-LBD) undergoes conformational changes upon ligand binding. In this nuclear receptor family, agonistic or antagonistic activities are controlled by the conformation of the helix (H)12. However, all crystal structures of VDR-LBD reported to date correspond to the active H12 conformation, regardless of agonist/antagonist binding. To understand the mechanism of VDR-LBD regulation structurally, conformational samplings of agonist- and antagonist-bound rat VDR-LBD were performed using the generalized replica exchange with solute tempering (gREST) method. The gREST simulations demonstrated different structural responses of rat VDR-LBD to agonist or antagonist binding, whereas in conventional molecular dynamics simulations, the conformation was the same as that of the crystal structures, regardless of agonist/antagonist binding. In the gREST simulations, a spontaneous conformational change of H12 was observed only for the antagonist complex. The different responses to agonist/antagonist binding were attributed to hydrophobic core formation at the ligand-binding pocket and cooperative rearrangements of H11. The gREST method can be applied to the examination of structure-activity relationships for multiple VDR-LBD ligands.

Optimizing String Method's Reproducibility Using Generalized Solute Tempering Replica Exchange.

Obtaining accurate and reproducible free energies from molecular simulations is somewhat tricky due to incomplete knowledge of crucial slow degrees of freedom leading to hidden barriers that can stymie sampling. Employing a sufficiently large number of collective variables (CV) and ensuring ergodic sampling in orthogonal CV space, perhaps via tempering methods, can reduce these issues to some extent. For complex systems with high-dimensional free energy landscapes, both these approaches become computationally expensive. For high-dimensional landscapes, efficient exploration can be enabled by using temperature-accelerated MD (TAMD) and identification and characterization of minimum free energy pathways connecting minima can be found by using the string method (SM). Both TAMD and SM use mean-force estimates from finite MD simulations and are thus susceptible to sampling restrictions from hidden variables. A recent development in parallel tempering methods, "generalized replica exchange solute tempering" (gREST), can enhance sampling at a reasonable computational cost with its flexibility to target very specific "solutes" which can include arbitrary independent variables. Considering the advantages of both methods, we implement gREST-enabled TAMD and SM. By considering two different collective variable representations of the pentapeptide neurotransmitter met-enkephalin, we show that both gREST-enabled TAMD and SM yield more accurate and reproducible free energy predictions than TAMD and SM alone. Given the moderate computational cost of gREST compared with other replica-exchange methods, gREST-enabled SM represents a more attractive method for characterizing free energy minima and pathways among them for a large variety of systems.

Unraveling the Coupling between Conformational Changes and Ligand Binding in Ribose Binding Protein Using Multiscale Molecular Dynamics and Free-Energy Calculations.

Conformational changes of proteins upon ligand binding are usually explained in terms of several mechanisms including the induced fit, conformational selection, or their mixtures. Due to the slow time scales, conventional molecular dynamics (cMD) simulations based on the atomistic models cannot easily simulate the open-to-closed conformational transition in proteins. In our previous study, we have developed an enhanced sampling scheme (generalized replica exchange with solute tempering selected surface charged residues: gREST_SSCR) for multidomain proteins and applied it to ligand-mediated conformational changes in the G134R mutant of ribose-binding protein (RBPG134R) in solution. The free-energy landscape (FEL) of RBPG134R in the presence of a ribose at the binding site included the open and closed states and two intermediates, open-like and closed-like forms. Only the open and open-like forms existed in the FEL without a ribose. In the current study, the coupling between the conformational changes and ligand binding is further investigated using coarse-grained MD, multiple atomistic cMD, and free-energy calculations. The ribose is easily dissociated from the binding site of wild-type RBP and RBPG134R in the cMD simulations starting from the open and open-like forms. In contrast, it is stable at the binding site in the simulations from the closed and closed-like forms. The free-energy calculations provide the binding affinities of different structures, supporting the results of cMD simulations. Importantly, cMD simulations from the closed-like structures reveal transitions toward the closed one in the presence of a bound ribose. On the basis of the computational results, we propose a molecular mechanism in which conformational selection and induced fit happen in the first and second halves of the open-to-closed transition in RBP, respectively.

Mutations of N1 Riboswitch Affect its Dynamics and Recognition by Neomycin Through Conformational Selection.

Short, structured fragments of non-coding mRNA may act as molecular switches upon binding specific ligands, regulating the translation of proteins encoded downstream this mRNA sequence. One switch, called riboswitch N1, is regulated by aminoglycosides such as neomycin. Nucleobase mutations in the apical loop, although distant from the binding pocket, significantly affect neomycin affinity and riboswitch regulatory efficiency. To explain this influence, we conducted molecular dynamics simulations using generalized replica exchange with solute tempering (gREST). Translation assay of a reporter protein in a yeast system shows that mutating A17 to G in the riboswitch apical loop reduces 6-fold the translation regulation efficiency of the mutant. Indeed, simulations of the unbound riboswitch show that G17 frequently stacks with base 7, while base 8 is stabilized towards the binding site in a way that it may interfere with the conformational selection mechanism and decrease riboswitch regulatory activity. In the riboswitch complexes, this single-point A to G mutation disrupts a strong hydrogen bond between nucleotides 5 and 17 and, instead, a new hydrogen bond between residue 17 and neomycin is created. This change forces neomycin to occupy a slightly shifted position in the binding pocket, which increases neomycin flexibility. Our simulations of the U14C mutation suggest that the riboswitch complex with neomycin is more stable if cytosine 14 is protonated. A hydrogen bond between the RNA phosphate and protonated cytosine appears as the stabilizing factor. Also, based on the cell-free translation assay and isothermal titration calorimetry experiments, mutations of nucleotides 14 and 15 affect only slightly the riboswitch ability to bind the ligand and its activity. Indeed, the simulation of the unbound U15A mutant suggests conformations preformed for ligand binding, which may explain slightly higher regulatory activity of this mutant. Overall, our results corroborate the in vivo and in vitro experiments on the N1 riboswitch-neomycin system, detail the relationship between nucleobase mutations and RNA dynamics, and reveal the conformations playing the major role in the conformational selection mechanism.

Prediction of Protein-Ligand Binding Pose and Affinity Using the gREST+FEP Method.

The accurate prediction of protein-ligand binding affinity is a central challenge in computational chemistry and in-silico drug discovery. The free energy perturbation (FEP) method based on molecular dynamics (MD) simulation provides reasonably accurate results only if a reliable structure is available via high-resolution X-ray crystallography. To overcome the limitation, we propose a sequential prediction protocol using generalized replica exchange with solute tempering (gREST) and FEP. At first, ligand binding poses are predicted using gREST, which weakens protein-ligand interactions at high temperatures to sample multiple binding poses. To avoid ligand dissociation at high temperatures, a flat-bottom restraint potential centered on the binding site is applied in the simulation. The binding affinity of the most reliable pose is then calculated using FEP. The protocol is applied to the bindings of ten ligands to FK506 binding proteins (FKBP), showing the excellent agreement between the calculated and experimental binding affinities. The present protocol, which is referred to as the gREST+FEP method, would help to predict the binding affinities without high-resolution structural information on the ligand-bound state.

Role of the N-Terminal Transmembrane Helix Contacts in the Activation of FGFR3.

Fibroblast growth factor receptor 3 (FGFR3) is a member of receptor tyrosine kinases, which is involved in skeletal cell growth, differentiation, and migration. FGFR3 transduces biochemical signals from the extracellular ligand-binding domain to the intracellular kinase domain through the conformational changes of the transmembrane (TM) helix dimer. Here, we apply generalized replica exchange with solute tempering method to wild type (WT) and G380R mutant (G380R) of FGFR3. The dimer interface in G380R is different from WT and the simulation results are in good agreement with the solid-state nuclear magnetic resonance (NMR) spectroscopy. TM helices in G380R are extended more than WT, and thereby, G375 in G380R contacts near the N-termini of the TM helix dimer. Considering that both G380R and G375C show the constitutive activation, the formation of the N-terminal contacts of the TM helices can be generally important for the activation mechanism. © 2019 Wiley Periodicals, Inc.

Studying vapor-liquid transition using a generalized ensemble.

Homogeneous vapor-liquid nucleation is studied using the generalized Replica Exchange Method (gREM). The generalized ensemble allows the study of unstable states that cannot directly be studied in the canonical ensemble. Along with replica exchange, this allows for efficient sampling of the multiple states in a single simulation. Statistical Temperature Weighted Histogram Analysis Method is used for postprocessing to get a continuous free energy curve from bulk vapor to bulk liquid. gREM allows the study of planar, cylindrical, and spherical interfaces in a single simulation. The excess Gibbs free energy for the formation of a spherical liquid droplet in vapor for a Lennard-Jones system is calculated from the free energy curve and compared against the umbrella sampling results. The nucleation free energy barrier obtained from gREM is then used to calculate the nucleation rate without relying on any classification scheme for separating the vapor and liquid.

De Novo Prediction of Binders and Nonbinders for T4 Lysozyme by gREST Simulations.

Molecular recognition underpins all specific protein-ligand interactions and is essential for biomolecular functions. The prediction of canonical binding poses and distinguishing binders from nonbinders are much sought after goals. Here, we apply the generalized replica exchange with solute tempering method, gREST, combined with a flat-bottom potential to evaluate binder and nonbinder interactions with a T4 lysozyme Leu99Ala mutant. The buried hydrophobic cavity and possibility of coupled conformational changes in this protein make binding predictions difficult. The present gREST simulations, enabling enhanced flexibilities of the ligand and protein residues near the binding site, sample bindings in multiple poses, and correct portrayal of X-ray structures. The free-energy profiles of binders (benzene, ethylbenzene, and n-hexylbenzene) are distinct from those of nonbinders (phenol and benzaldehyde). Bindings of the two larger molecules seem to be associated with a structural change toward an excited conformation of the protein, which agrees with experimental findings. The protocol is generally applicable to various proteins having buried cavities with limited access for ligands with different shapes, sizes, and chemical properties.

Enhanced Sampling of Phase Transitions in Coarse-Grained Lipid Bilayers.

Freezing and melting of dipalmitoylphosphatidylcholine (DPPC) bilayers are simulated in both the explicit (Wet) and implicit solvent (Dry) coarse-grained MARTINI force fields with enhanced sampling, via the isobaric, molecular dynamics version of the generalized replica exchange method (gREM). Phase transitions are described with the entropic viewpoint, based upon the statistical temperature as a function of enthalpy, TS(H) = 1/(dS(H)/dH), where S is the configurational entropy. Bilayer thickness, area per lipid, and the second-rank order parameter (P2) are calculated vs temperature in the transition range. In a 32-lipid Wet MARTINI system, transitions in the lipid and water subsystems are strongly coupled, giving rise to considerable structure in TS(H) and the need to specify the state of the water when reporting a lipid transition temperature. For gel lipid + liquid water → fluid lipid + liquid water, we find 292.4 K. The small system is influenced by finite-size effects, but it is argued that the entropic approach is well suited to revealing them, which will be particularly relevant for studies of finite nanosystems where there is no thermodynamic limit. In a 390-lipid Dry MARTINI system, two-dimensional analogues of the topographies of coexisting states ("subphases") seen in pure fluids are found. They are not seen in the 32-lipid Wet or Dry system, but the Dry lipids show a new type of state with gel in one leaflet and tilted gel in the other. Dry bilayer transition temperatures are 333.3 K (390 lipids) and 338 K (32 lipids), indicating that the 32-lipid system is not too small for a qualitative study of the transition. Physical arguments are given for Dry lipid system size dependence and for the difference between Wet and Dry systems.

Freezing Transitions of Nanoconfined Coarse-Grained Water Show Subtle Dependence on Confining Environment.

The solid-to-liquid phase transition in water nanofilms confined between plates, with varying separations and water-plate interactions ranging from strongly hydrophobic to strongly hydrophilic, was simulated using a coarse-grained monatomic water model (mW) and the generalized replica exchange method (gREM). Extensive gREM simulations combined with the statistical temperature weighted histogram analysis method (ST-WHAM) provide a detailed description of the thermodynamic properties intrinsic to the phase transition, including the transition temperature, isobaric heat capacity, phase change enthalpy, entropy, and their dependence on the interplate distance and the plate-water interaction. The ice structure of water nanofilms was characterized at various conditions using the transverse density profile and the distribution of angles formed by hydrogen-bonded neighboring molecules. Flat bilayer ice was observed to be the dominant solid phase at close interplate distance, while puckered bilayer ice, similar to a slab of ice Ih, is the predominant structure at larger interplates. Stable puckered bilayer ice, previously observed to have a low melting point, is observed to have enhanced stability with high melting temperature when confined between hydrophilic plates. These results demonstrate the strong dependence of phase stability and coexistence in nanoconfined systems on the geometry and physical properties of the confining environment.

Pathways through Equilibrated States with Coexisting Phases for Gas Hydrate Formation

Under ambient conditions, water freezes to either hexagonal ice or a hexagonal/cubic composite ice. The presence of hydrophobic guest molecules introduces a competing pathway: gas hydrate formation, with the guests in clathrate cages. Here, the pathways of the phase transitions are sought as sequences of states with coexisting phases, using a generalized replica exchange algorithm designed to sample them in equilibrium, avoiding nonequilibrium processes. For a dilute solution of methane in water under 200 atm, initializing the simulation with the full set of replicas leads to methane trapped in hexagonal/cubic ice, while gradually adding replicas with decreasing enthalpy produces the initial steps of hydrate growth. Once a small amount of hydrate is formed, water rearranges to form empty cages, eventually transforming the remainder of the system to metastable β ice, a scaffolding for hydrates. It is suggested that configurations with empty cages are reaction intermediates in hydrate formation when more guest molecules are available. Free energy profiles show that methane acts as a catalyst reducing the barrier for β ice versus hexagonal/cubic ice formation.

Water Freezing and Ice Melting.

The generalized replica exchange method (gREM) is designed to sample states with coexisting phases and thereby to describe strong first order phase transitions. The isobaric MD version of the gREM is presented and applied to the freezing of liquid water and the melting of hexagonal and cubic ice. It is confirmed that coexisting states are well-sampled. The statistical temperature as a function of enthalpy, TS(H), is obtained. Hysteresis between freezing and melting is observed and discussed. The entropic analysis of phase transitions is applied and equilibrium transition temperatures, latent heats, and surface tensions are obtained for hexagonal ice ↔ liquid and cubic ice ↔ liquid with excellent agreement with published values. A new method is given to assign water molecules among various symmetry types. Pathways for water freezing, ultimately leading to hexagonal ice, are found to contain intermediate layered structures built from hexagonal and cubic ice.

Isobaric Molecular Dynamics Version of the Generalized Replica Exchange Method (gREM): Liquid–Vapor Equilibrium

A prescription for sampling isobaric generalized ensembles with molecular dynamics is presented and applied to the generalized replica exchange method (gREM), which was designed to simulate first-order phase transitions. The properties of the isobaric gREM ensemble are discussed, and a study is presented for the liquid-vapor equilibrium of the guest molecules given for gas hydrate formation with the mW water model. Phase diagrams, critical parameters, and a law of corresponding states are obtained.

Generalized ensemble method applied to study systems with strong first order transitions

At strong first-order phase transitions, the entropy versus energy or, at constant pressure, enthalpy, exhibits convex behavior, and the statistical temperature curve correspondingly exhibits an S-loop or back-bending. In the canonical and isothermal-isobaric ensembles, with temperature as the control variable, the probability density functions become bimodal with peaks localized outside of the S-loop region. Inside, states are unstable, and as a result simulation of equilibrium phase coexistence becomes impossible. To overcome this problem, a method was proposed by Kim, Keyes and Straub [1], where optimally designed generalized ensemble sampling was combined with replica exchange, and denoted generalized replica exchange method (gREM). This new technique uses parametrized effective sampling weights that lead to a unimodal energy distribution, transforming unstable states into stable ones. In the present study, the gREM, originally developed as a Monte Carlo algorithm, was implemented to work with molecular dynamics in an isobaric ensemble and coded into LAMMPS, a highly optimized open source molecular simulation package. The method is illustrated in a study of the very strong solid/liquid transition in water.

Investigating the solid-liquid phase transition of water nanofilms using the generalized replica exchange method.

The generalized Replica Exchange Method (gREM) was applied to study a solid-liquid phase transition in a nanoconfined bilayer water system using the monatomic water (mW) model. Exploiting optimally designed non-Boltzmann sampling weights with replica exchanges, gREM enables an effective sampling of configurations that are metastable or unstable in the canonical ensemble via successive unimodal energy distributions across phase transition regions, often characterized by S-loop or backbending in the statistical temperature. Extensive gREM simulations combined with Statistical Temperature Weighted Histogram Analysis Method (ST-WHAM) for nanoconfined mW water at various densities provide a comprehensive characterization of diverse thermodynamic and structural properties intrinsic to phase transitions. Graph representation of minimized structures of bilayer water systems determined by the basin-hopping global optimization revealed heterogeneous ice structures composed of pentagons, hexagons, and heptagons, consistent with an increasingly ordered solid phase with decreasing density. Apparent crossover from a first-order solid-liquid transition to a continuous one in nanoconfined mW water with increasing density of the system was observed in terms of a diminishing S-loop in the statistical temperature, smooth variation of internal energies and heat capacities, and a characteristic variation of lateral radial distribution functions, and transverse density profiles across transition regions.

Order parameter free enhanced sampling of the vapor-liquid transition using the generalized replica exchange method

The generalized Replica Exchange Method (gREM) is extended into the isobaric-isothermal ensemble, and applied to simulate a vapor-liquid phase transition in Lennard-Jones fluids. Merging an optimally designed generalized ensemble sampling with replica exchange, gREM is particularly well suited for the effective simulation of first-order phase transitions characterized by "backbending" in the statistical temperature. While the metastable and unstable states in the vicinity of the first-order phase transition are masked by the enthalpy gap in temperature replica exchange method simulations, they are transformed into stable states through the parameterized effective sampling weights in gREM simulations, and join vapor and liquid phases with a succession of unimodal enthalpy distributions. The enhanced sampling across metastable and unstable states is achieved without the need to identify a "good" order parameter for biased sampling. We performed gREM simulations at various pressures below and near the critical pressure to examine the change in behavior of the vapor-liquid phase transition at different pressures. We observed a crossover from the first-order phase transition at low pressure, characterized by the backbending in the statistical temperature and the "kink" in the Gibbs free energy, to a continuous second-order phase transition near the critical pressure. The controlling mechanisms of nucleation and continuous phase transition are evident and the coexistence properties and phase diagram are found in agreement with literature results.