Potential of mean force of water–proton bath and molecular dynamic simulation of proteins at constant pH

An advanced implicit solvent model of water–proton bath for protein simulations at constant pH is presented. The implicit water–proton bath model approximates the potential of mean force of a protein in water solvent in a presence of hydrogen ions. Accurate and fast computational implementation of the implicit water–proton bath model is developed using the continuum electrostatic Poisson equation model for calculation of ionization equilibrium and the corrected MSR6 generalized Born model for calculation of the electrostatic atom–atom interactions and forces. Molecular dynamics (MD) method for protein simulation in the potential of mean force of water–proton bath is developed and tested on three proteins. The model allows to run MD simulations of proteins at constant pH, to calculate pH‐dependent properties and free energies of protein conformations. The obtained results indicate that the developed implicit model of water–proton bath provides an efficient way to study thermodynamics of biomolecular systems as a function of pH, pH‐dependent ionization‐conformation coupling, and proton transfer events. © 2012 Wiley Periodicals, Inc.     

Implicit and explicit solvent models for modeling a bifunctional arene ruthenium hydrogen‐storage catalyst: A classical and ab initio molecular simulation study

Classical and ab initio, density functional theory‐ and semiempirical‐based molecular simulation, including molecular dynamics, have been carried out to compare and contrast the effect of explicit and implicit solvation representation of tetrahydrofuran (THF) solvent on the structural, energetic, and dynamical properties of a novel bifunctional arene ruthenium catalyst embedded therein. Particular scrutiny was afforded to hydrogen‐bonding and energetic interactions with the THF liquid. It was found that the presence of explicit THF solvent molecules is required to capture an accurate picture of the catalyst's structural properties, particularly in view of the importance of hydrogen bonding with the surrounding THF molecules. This has implications for accurate modeling of the reactivity of the catalyst. © 2014 Wiley Periodicals, Inc.     

Parallelization and improvements of the generalized born model with a simple sWitching function for modern graphics processors

Two fundamental challenges of simulating biologically relevant systems are the rapid calculation of the energy of solvation and the trajectory length of a given simulation. The Generalized Born model with a Simple sWitching function (GBSW) addresses these issues by using an efficient approximation of Poisson–Boltzmann (PB) theory to calculate each solute atom's free energy of solvation, the gradient of this potential, and the subsequent forces of solvation without the need for explicit solvent molecules. This study presents a parallel refactoring of the original GBSW algorithm and its implementation on newly available, low cost graphics chips with thousands of processing cores. Depending on the system size and nonbonded force cutoffs, the new GBSW algorithm offers speed increases of between one and two orders of magnitude over previous implementations while maintaining similar levels of accuracy. We find that much of the algorithm scales linearly with an increase of system size, which makes this water model cost effective for solvating large systems. Additionally, we utilize our GPU‐accelerated GBSW model to fold the model system chignolin, and in doing so we demonstrate that these speed enhancements now make accessible folding studies of peptides and potentially small proteins. © 2016 Wiley Periodicals, Inc.     

Accelerating molecular dynamic simulation on graphics processing units

We describe a complete implementation of all‐atom protein molecular dynamics running entirely on a graphics processing unit (GPU), including all standard force field terms, integration, constraints, and implicit solvent. We discuss the design of our algorithms and important optimizations needed to fully take advantage of a GPU. We evaluate its performance, and show that it can be more than 700 times faster than a conventional implementation running on a single CPU core. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Efficient gaussian density formulation of volume and surface areas of macromolecules on graphical processing units

We present an algorithm to efficiently compute accurate volumes and surface areas of macromolecules on graphical processing unit (GPU) devices using an analytic model which represents atomic volumes by continuous Gaussian densities. The volume of the molecule is expressed by means of the inclusion–exclusion formula, which is based on the summation of overlap integrals among multiple atomic densities. The surface area of the molecule is obtained by differentiation of the molecular volume with respect to atomic radii. The many‐body nature of the model makes a port to GPU devices challenging. To our knowledge, this is the first reported full implementation of this model on GPU hardware. To accomplish this, we have used recursive strategies to construct the tree of overlaps and to accumulate volumes and their gradients on the tree data structures so as to minimize memory contention. The algorithm is used in the formulation of a surface area‐based non‐polar implicit solvent model implemented as an open source plug‐in (named GaussVol) for the popular OpenMM library for molecular mechanics modeling. GaussVol is 50 to 100 times faster than our best optimized implementation for the CPUs, achieving speeds in excess of 100 ns/day with 1 fs time‐step for protein‐sized systems on commodity GPUs. © 2017 Wiley Periodicals, Inc.     

A GPU solvent–solvent interaction calculation accelerator for biomolecular simulations using the GROMOS software

During the past few years, graphics processing units (GPUs) have become extremely popular in the high performance computing community. In this study, we present an implementation of an acceleration engine for the solvent–solvent interaction evaluation of molecular dynamics simulations. By careful optimization of the algorithm speed‐ups up to a factor of 54 (single‐precision GPU vs. double‐precision CPU) could be achieved. The accuracy of the single‐precision GPU implementation is carefully investigated and does not influence structural, thermodynamic, and dynamic quantities. Therefore, the implementation enables users of the GROMOS software for biomolecular simulation to run the solvent–solvent interaction evaluation on a GPU, and thus, to speed‐up their simulations by a factor 6–9. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Ab-initio molecular dynamics and hybrid explicit-implicit solvation model for aqueous and nonaqueous solvents: GFP chromophore in water and methanol solution as case study

Solute–solvent interactions are proxies for understanding how the electronic density of a chromophore interacts with the environment in a more exhaustive way. The subtle balance between polarization, electrostatic, and non-bonded interactions need to be accurately described to obtain good agreement between simulations and experiments. First principles approaches providing accurate configurational sampling through molecular dynamics may be a suitable choice to describe solvent effects on solute chemical–physical properties and spectroscopic features, such as optical absorption of dyes. In this context, accurate energy potentials, obtained by hybrid implicit/explicit solvation methods along with employing nonperiodic boundary conditions, are required to represent bulk solvent around a large solute–solvent cluster. In this work, a novel strategy to simulate methanol solutions is proposed combining ab initio molecular dynamics, a hybrid implicit/explicit flexible solvent model, nonperiodic boundary conditions, and time dependent density functional theory. As case study, the robustness of the proposed protocol has been gauged by investigating the microsolvation and electronic absorption of the anionic green fluorescent protein chromophore in methanol and aqueous solution. Satisfactory results are obtained, reproducing the microsolvation layout of the chromophore and, as a consequence, the experimental trends shown by the optical absorption in different solvents.     

Molecular dynamics with the united-residue model of polypeptide chains. II. Langevin and Berendsen-bath dynamics and tests on model alpha-helical systems

The implementation of molecular dynamics (MD) with our physics-based protein united-residue (UNRES) force field, described in the accompanying paper, was extended to Langevin dynamics. The equations of motion are integrated by using a simplified stochastic velocity Verlet algorithm. To compare the results to those with all-atom simulations with implicit solvent in which no explicit stochastic and friction forces are present, we alternatively introduced the Berendsen thermostat. Test simulations on the Ala(10) polypeptide demonstrated that the average kinetic energy is stable with about a 5 fs time step. To determine the correspondence between the UNRES time step and the time step of all-atom molecular dynamics, all-atom simulations with the AMBER 99 force field and explicit solvent and also with implicit solvent taken into account within the framework of the generalized Born/surface area (GBSA) model were carried out on the unblocked Ala(10) polypeptide. We found that the UNRES time scale is 4 times longer than that of all-atom MD simulations because the degrees of freedom corresponding to the fastest motions in UNRES are averaged out. When the reduction of the computational cost for evaluation of the UNRES energy function is also taken into account, UNRES (with hydration included implicitly in the side chain-side chain interaction potential) offers about at least a 4000-fold speed up of computations relative to all-atom simulations with explicit solvent and at least a 65-fold speed up relative to all-atom simulations with implicit solvent. To carry out an initial full-blown test of the UNRES/MD approach, we ran Berendsen-bath and Langevin dynamics simulations of the 46-residue B-domain of staphylococcal protein A. We were able to determine the folding temperature at which all trajectories converged to nativelike structures with both approaches. For comparison, we carried out ab initio folding simulations of this protein at the AMBER 99/GBSA level. The average CPU time for folding protein A by UNRES molecular dynamics was 30 min with a single Alpha processor, compared to about 152 h for all-atom simulations with implicit solvent. It can be concluded that the UNRES/MD approach will enable us to carry out microsecond and, possibly, millisecond simulations of protein folding and, consequently, of the folding process of proteins in real time.     

Probing pH-dependent dissociation of HdeA dimers

HdeA protein is a small, ATP-independent, acid stress chaperone that undergoes a dimer-to-monomer transition in acidic environments. The HdeA monomer binds a broad range of proteins to prevent their acid-induced aggregation. To understand better HdeA's function and mechanism, we perform constant-pH molecular dynamics simulations (CPHMD) to elucidate the details of the HdeA dimer dissociation process. First the pK(a) values of all the acidic titratable groups in HdeA are obtained and reveal a large pK(a) shift only for Glu(37). However, the pH-dependent monomer charge exhibits a large shift from -4 at pH > 6 to +6 at pH = 2.5, suggesting that the dramatic change in charge on each monomer may drive dissociation. By combining the CPHMD approach with umbrella sampling, we demonstrate a significant stability decrease of the HdeA dimer when the environmental pH changes from 4.0 to 3.5 and identify the key acidic residue-lysine interactions responsible for the observed pH sensing in HdeA chaperon activity function.     

A perspective on MALDI alternatives—total solvent‐free analysis and electron transfer dissociation of highly charged ions by laserspray ionization

Progress in research is hindered by analytical limitations, especially in biological areas in which sensitivity and dynamic range are critical to success. Inherent difficulties of characterization associated with complexity arising from heterogeneity of various materials including topologies (isomeric composition) and insolubility also limit progress. For this reason, we are developing methods for total solvent‐free analysis by mass spectrometry consisting of solvent‐free ionization followed by solvent‐free gas‐phase separation. We also recently constructed a novel matrix‐assisted laser desorption ionization (MALDI) source that provides a simple, practical and sensitive way of producing highly charged ions by laserspray ionization (LSI) or singly charged ions commonly observed with MALDI by choice of matrix or matrix preparation. This is the first ionization source with such freedom—an extremely powerful analytical ‘switch’. Multiply charged LSI ions allow molecules exceeding the mass‐to‐charge range of the instrument to be observed and permit for the first time electron transfer dissociation fragment ion analysis. Copyright © 2010 John Wiley & Sons, Ltd.     

Benchmarking the thermodynamic analysis of water molecules around a model beta sheet

Water molecules play a vital role in biological and engineered systems by controlling intermolecular interactions in the aqueous phase. Inhomogeneous fluid solvation theory provides a method to quantify solvent thermodynamics from molecular dynamics or Monte Carlo simulations and provides an insight into intermolecular interactions. In this study, simulations of TIP4P‐2005 and TIP5P‐Ewald water molecules around a model beta sheet are used to investigate the orientational correlations and predicted thermodynamic properties of water molecules at a protein surface. This allows the method to be benchmarked and provides information about the effect of a protein on the thermodynamics of nearby water molecules. The results show that the enthalpy converges with relatively little sampling, but the entropy and thus the free energy require considerably more sampling to converge. The two water models yield a very similar pattern of hydration sites, and these hydration sites have very similar thermodynamic properties, despite notable differences in their orientational preferences. The results also predict that a protein surface affects the free energy of water molecules to a distance of approximately 4.0 Å, which is in line with previous work. In addition, all hydration sites have a favorable free energy with respect to bulk water, but only when the water–water entropy term is included. A new technique for calculating this term is presented and its use is expected to be very important in accurately calculating solvent thermodynamics for quantitative application. © 2012 Wiley Periodicals, Inc.     

On the nonpolar hydration free energy of proteins: surface area and continuum solvent models for the solute-solvent interaction energy

Implicit solvent hydration free energy models are an important component of most modern computational methods aimed at protein structure prediction, binding affinity prediction, and modeling of conformational equilibria. The nonpolar component of the hydration free energy, consisting of a repulsive cavity term and an attractive van der Waals solute-solvent interaction term, is often modeled using estimators based on the solvent exposed solute surface area. In this paper, we analyze the accuracy of linear surface area models for predicting the van der Waals solute-solvent interaction energies of native and non-native protein conformations, peptides and small molecules, and the desolvation penalty of protein-protein and protein-ligand binding complexes. The target values are obtained from explicit solvent simulations and from a continuum solvent van der Waals interaction energy model. The results indicate that the standard surface area model, while useful on a coarse-grained scale, may not be accurate or transferable enough for high resolution modeling studies of protein folding and binding. The continuum model constructed in the course of this study provides one path for the development of a computationally efficient implicit solvent nonpolar hydration free energy estimator suitable for high-resolution structural and thermodynamic modeling of biological macromolecules.     

CAST: A new program package for the accurate characterization of large and flexible molecular systems

The presented program package, Conformational Analysis and Search Tool (CAST) allows the accurate treatment of large and flexible (macro) molecular systems. For the determination of thermally accessible minima CAST offers the newly developed TabuSearch algorithm, but algorithms such as Monte Carlo (MC), MC with minimization, and molecular dynamics are implemented as well. For the determination of reaction paths, CAST provides the PathOpt, the Nudge Elastic band, and the umbrella sampling approach. Access to free energies is possible through the free energy perturbation approach. Along with a number of standard force fields, a newly developed symmetry‐adapted perturbation theory‐based force field is included. Semiempirical computations are possible through DFTB+ and MOPAC interfaces. For calculations based on density functional theory, a Message Passing Interface (MPI) interface to the Graphics Processing Unit (GPU)‐accelerated TeraChem program is available. The program is available on request. © 2014 Wiley Periodicals, Inc.     

A simple method for faster nonbonded force evaluations

Accurate approximations are introduced for the evaluation of inverse interparticle distances such that square root or division operations are not required in the computation of interparticle interactions and forces. These generally applicable approximations are illustrated by incorporation into the protein simulation package TINKER along with several other speed enhancement strategies. With these modifications, implicit solvent Langevin dynamics simulations of proteins are performed factors of 4.6 times faster than the modified open source distributed program. Programming speedups are obtained by extensive vectorization, simplification of the inner loop to avoid IF statements, and by using lookup tables for the distance dependent "dielectric constant" in implicit solvent models. Benchmarks are provided for the all-atom, implicit solvent dynamics of Met-enkephalin, the villin headpiece, the B1 domain of protein-G, and barnase. We also discuss the more general applicability of the approximation methods to explicit solvent simulations and of look-up tables for other implicit solvent models such as the generalized Born models.