Extending the horizon: towards the efficient modeling of large biomolecular complexes in atomic detail

The application of evaluation of implicit solvent methods for the simulation of biomolecules is described. Detailed comparisons with explicit solvent are described for the modeling of peptide and proteins in continuum aqueous solvent. In addition, we are presenting new data on the simulation of DNA with implicit solvent and describe the development of a heterogeneous dielectric model for the simulation of integral membranes. The performance of implicit solvent simulations based on the GBMV generalized Born method is compared with explicit solvent simulations, and implications for the simulation of very large biomolecular complexes is discussed. We are anticipating that the work described herein will lead to new, efficient modeling tools that will allow the simulation of longer timescales and larger system sizes in order to meet current and future challenges by the experimental community.     

Surveying implicit solvent models for estimating small molecule absolute hydration free energies

Implicit solvent models are powerful tools in accounting for the aqueous environment at a fraction of the computational expense of explicit solvent representations. Here, we compare the ability of common implicit solvent models (TC, OBC, OBC2, GBMV, GBMV2, GBSW, GBSW/MS, GBSW/MS2 and FACTS) to reproduce experimental absolute hydration free energies for a series of 499 small neutral molecules that are modeled using AMBER/GAFF parameters and AM1-BCC charges. Given optimized surface tension coefficients for scaling the surface area term in the nonpolar contribution, most implicit solvent models demonstrate reasonable agreement with extensive explicit solvent simulations (average difference 1.0-1.7 kcal/mol and R(2)=0.81-0.91) and with experimental hydration free energies (average unsigned errors=1.1-1.4 kcal/mol and R(2)=0.66-0.81). Chemical classes of compounds are identified that need further optimization of their ligand force field parameters and others that require improvement in the physical parameters of the implicit solvent models themselves. More sophisticated nonpolar models are also likely necessary to more effectively represent the underlying physics of solvation and take the quality of hydration free energies estimated from implicit solvent models to the next level.     

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     

Molecular dynamics simulations of large integral membrane proteins with an implicit membrane model

The heterogeneous dielectric generalized Born (HDGB) methodology is an the extension of the GBMV model for the simulation of integral membrane proteins with an implicit membrane environment. Three large integral membrane proteins, the bacteriorhodopsin monomer and trimer and the BtuCD protein, were simulated with the HDGB model in order to evaluate how well thermodynamic and dynamic properties are reproduced. Effects of the truncation of electrostatic interactions were examined. For all proteins, the HDGB model was able to generate stable trajectories that remained close to the starting experimental structures, in excellent agreement with explicit membrane simulations. Dynamic properties evaluated through a comparison of B-factors are also in good agreement with experiment and explicit membrane simulations. However, overall flexibility was slightly underestimated with the HDGB model unless a very large electrostatic cutoff is employed. Results with the HDGB model are further compared with equivalent simulations in implicit aqueous solvent, demonstrating that the membrane environment leads to more realistic simulations.     

Efficient implementation of constant pH molecular dynamics on modern graphics processors

The treatment of pH sensitive ionization states for titratable residues in proteins is often omitted from molecular dynamics (MD) simulations. While static charge models can answer many questions regarding protein conformational equilibrium and protein–ligand interactions, pH‐sensitive phenomena such as acid‐activated chaperones and amyloidogenic protein aggregation are inaccessible to such models. Constant pH molecular dynamics (CPHMD) coupled with the Generalized Born with a Simple sWitching function (GBSW) implicit solvent model provide an accurate framework for simulating pH sensitive processes in biological systems. Although this combination has demonstrated success in predicting pK_a values of protein structures, and in exploring dynamics of ionizable side‐chains, its speed has been an impediment to routine application. The recent availability of low‐cost graphics processing unit (GPU) chipsets with thousands of processing cores, together with the implementation of the accurate GBSW implicit solvent model on those chipsets (Arthur and Brooks, J. Comput. Chem. 2016, 37, 927), provide an opportunity to improve the speed of CPHMD and ionization modeling greatly. Here, we present a first implementation of GPU‐enabled CPHMD within the CHARMM‐OpenMM simulation package interface. Depending on the system size and nonbonded force cutoff parameters, we find speed increases of between one and three orders of magnitude. Additionally, the algorithm scales better with system size than the CPU‐based algorithm, thus allowing for larger systems to be modeled in a cost effective manner. We anticipate that the improved performance of this methodology will open the door for broad‐spread application of CPHMD in its modeling pH‐mediated biological processes. © 2016 Wiley Periodicals, Inc.     

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.     

Comparison of solvation-effect methods for the simulation of peptide interactions with a hydrophobic surface

In this study we investigated the interaction behavior between thirteen different small peptides and a hydrophobic surface using three progressively more complex methods of representing solvation effects: a united-atom implicit solvation method [CHARMM 19 force field (C19) with Analytical Continuum Electrostatics (ACE)], an all-atom implicit solvation method (C22 with GBMV), and an all-atom explicit solvation method (C22 with TIP3P). The adsorption behavior of each peptide was characterized by the calculation of the potential of mean force as a function of peptide-surface separation distance. The results from the C22/TIP3P model suggest that hydrophobic peptides exhibit relatively strong adsorption behavior, polar and positively-charged peptides exhibit negligible to relatively weak favorable interactions with the surface, and negatively-charged peptides strongly resist adsorption. Compared to the TIP3P model, the ACE and GBMV implicit solvent models predict much stronger attractions for the hydrophobic peptides as well as stronger repulsions for the negatively-charged peptides on the CH(3)-SAM surface. These comparisons provide a basis from which each of these implicit solvation methods may be reparameterized to provide closer agreement with explicitly represented solvation in simulations of peptide and protein adsorption to functionalized surfaces.     

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.     

Solvent viscosity dependence of the folding rate of a small protein: distributed computing study

By using distributed computing techniques and a supercluster of more than 20,000 processors we simulated folding of a 20-residue Trp Cage miniprotein in atomistic detail with implicit GB/SA solvent at a variety of solvent viscosities (gamma). This allowed us to analyze the dependence of folding rates on viscosity. In particular, we focused on the low-viscosity regime (values below the viscosity of water). In accordance with Kramers' theory, we observe approximately linear dependence of the folding rate on 1/gamma for values from 1-10(-1)x that of water viscosity. However, for the regime between 10(-4)-10(-1)x that of water viscosity we observe power-law dependence of the form k approximately gamma(-1/5). These results suggest that estimating folding rates from molecular simulations run at low viscosity under the assumption of linear dependence of rate on inverse viscosity may lead to erroneous results.     

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     

Assessing the quality of absolute hydration free energies among CHARMM‐compatible ligand parameterization schemes

Multipurpose atom‐typer for CHARMM (MATCH), an atom‐typing toolset for molecular mechanics force fields, was recently developed in our laboratory. Here, we assess the ability of MATCH‐generated parameters and partial atomic charges to reproduce experimental absolute hydration free energies for a series of 457 small neutral molecules in GBMV2, Generalized Born with a smooth SWitching (GBSW), and fast analytical continuum treatment of solvation (FACTS) implicit solvent models. The quality of hydration free energies associated with small molecule parameters obtained from ParamChem, SwissParam, and Antechamber are compared. Given optimized surface tension coefficients for scaling the surface area term in the nonpolar contribution, these automated parameterization schemes with GBMV2 and GBSW demonstrate reasonable agreement with experimental hydration free energies (average unsigned errors of 0.9–1.5 kcal/mol and R² of 0.63–0.87). GBMV2 and GBSW consistently provide slightly more accurate estimates than FACTS, whereas Antechamber parameters yield marginally more accurate estimates than the current generation of MATCH, ParamChem, and SwissParam parameterization strategies. Modeling with MATCH libraries that are derived from different CHARMM topology and parameter files highlights the importance of having sufficient coverage of chemical space within the underlying databases of these automated schemes and the benefit of targeting specific functional groups for parameterization efforts to maximize both the breadth and the depth of the parameterized space. © 2013 Wiley Periodicals, Inc.     

Solvent effects and dynamic averaging of 195Pt NMR shielding in cisplatin derivatives

The influences of solvent effects and dynamic averaging on the (195)Pt NMR shielding and chemical shifts of cisplatin and three cisplatin derivatives in aqueous solution were computed using explicit and implicit solvation models. Within the density functional theory framework, these simulations were carried out by combining ab initio molecular dynamics (aiMD) simulations for the phase space sampling with all-electron relativistic NMR shielding tensor calculations using the zeroth-order regular approximation. Structural analyses support the presence of a solvent-assisted "inverse" or "anionic" hydration previously observed in similar square-planar transition-metal complexes. Comparisons with computationally less demanding implicit solvent models show that error cancellation is ubiquitous when dealing with liquid-state NMR simulations. After aiMD averaging, the calculated chemical shifts for the four complexes are in good agreement with experiment, with relative deviations between theory and experiment of about 5% on average (1% of the Pt(II) chemical shift range).     

Solvent models for protein–ligand binding: Comparison of implicit solvent poisson and surface generalized born models with explicit solvent simulations

Solvent effects play a crucial role in mediating the interactions between proteins and their ligands. Implicit solvent models offer some advantages for modeling these interactions, but they have not been parameterized on such complex problems, and therefore, it is not clear how reliable they are. We have studied the binding of an octapeptide ligand to the murine MHC class I protein using both explicit solvent and implicit solvent models. The solvation free energy calculations are more than 10³ faster using the Surface Generalized Born implicit solvent model compared to FEP simulations with explicit solvent. For some of the electrostatic calculations needed to estimate the binding free energy, there is near quantitative agreement between the explicit and implicit solvent model results; overall, the qualitative trends in the binding predicted by the explicit solvent FEP simulations are reproduced by the implicit solvent model. With an appropriate choice of reference system based on the binding of the discharged ligand, electrostatic interactions are found to enhance the binding affinity because the favorable Coulomb interaction energy between the ligand and protein more than compensates for the unfavorable free energy cost of partially desolvating the ligand upon binding. Some of the effects of protein flexibility and thermal motions on charging the peptide in the solvated complex are also considered. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 591–607, 2001     

Solvent effects on electronic structures and chain conformations of alpha-oligothiophenes in polar and apolar solutions

Solvent effects on electronic structures and chain conformations of alpha-oligothiophenes nTs (n = 1 to 10) are investigated in solvents of n-hexane, 1,4-dioxane, carbon tetrachloride, chloroform, and water by using density functional theory (DFT) and molecular dynamics (MD) simulations. Both implicit and explicit solvent models are employed. The polarized continuum model (PCM) calculations and MD simulations demonstrate the weak solvent effects on the electronic structures of alpha-oligothiophenes. The lowest dipole-allowed vertical excitation energies of nTs, obtained from time-dependent DFT/PCM calculations at the B3LYP/6-31G(d) level, exhibit a red shift as the solvent polarity increases, in agreement with experiments. The studied solvents have little impact on the state order of the low-lying excited states provided that the nTs are kept in C2h or C2v symmetry. The MD simulations demonstrate that the chain conformations are distorted to some extent in polar and nonpolar solvents. A qualitative picture of the distribution of solvent molecules around the solvated nTs is drawn by means of radial and spatial distribution functions. The S...H-O and pi...H-O solute-solvent interactions are insignificant in aqueous solution.     

Implementation and testing of stable, fast implicit solvation in molecular dynamics using the smooth-permittivity finite difference Poisson-Boltzmann method

A fast stable finite difference Poisson-Boltzmann (FDPB) model for implicit solvation in molecular dynamics simulations was developed using the smooth permittivity FDPB method implemented in the OpenEye ZAP libraries. This was interfaced with two widely used molecular dynamics packages, AMBER and CHARMM. Using the CHARMM-ZAP software combination, the implicit solvent model was tested on eight proteins differing in size, structure, and cofactors: calmodulin, horseradish peroxidase (with and without substrate analogue bound), lipid carrier protein, flavodoxin, ubiquitin, cytochrome c, and a de novo designed 3-helix bundle. The stability and accuracy of the implicit solvent simulations was assessed by examining root-mean-squared deviations from crystal structure. This measure was compared with that of a standard explicit water solvent model. In addition we compared experimental and calculated NMR order parameters to obtain a residue level assessment of the accuracy of MD-ZAP for simulating dynamic quantities. Overall, the agreement of the implicit solvent model with experiment was as good as that of explicit water simulations. The implicit solvent method was up to eight times faster than the explicit water simulations, and approximately four times slower than a vacuum simulation (i.e., with no solvent treatment).     

Balancing an accurate representation of the molecular surface in generalized born formalisms with integrator stability in molecular dynamics simulations

Different integrator time steps in NVT and NVE simulations of protein and nucleic acid systems are tested with the GBMV (Generalized Born using Molecular Volume) and GBSW (Generalized Born with simple SWitching) methods. The simulation stability and energy conservation is investigated in relation to the agreement with the Poisson theory. It is found that very close agreement between generalized Born methods and the Poisson theory based on the commonly used sharp molecular surface definition results in energy drift and simulation artifacts in molecular dynamics simulation protocols with standard 2-fs time steps. New parameters are proposed for the GBMV method, which maintains very good agreement with the Poisson theory while providing energy conservation and stable simulations at time steps of 1 to 1.5 fs.     

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.     

Accelerating molecular modeling applications with graphics processors

Molecular mechanics simulations offer a computational approach to study the behavior of biomolecules at atomic detail, but such simulations are limited in size and timescale by the available computing resources. State-of-the-art graphics processing units (GPUs) can perform over 500 billion arithmetic operations per second, a tremendous computational resource that can now be utilized for general purpose computing as a result of recent advances in GPU hardware and software architecture. In this article, an overview of recent advances in programmable GPUs is presented, with an emphasis on their application to molecular mechanics simulations and the programming techniques required to obtain optimal performance in these cases. We demonstrate the use of GPUs for the calculation of long-range electrostatics and nonbonded forces for molecular dynamics simulations, where GPU-based calculations are typically 10-100 times faster than heavily optimized CPU-based implementations. The application of GPU acceleration to biomolecular simulation is also demonstrated through the use of GPU-accelerated Coulomb-based ion placement and calculation of time-averaged potentials from molecular dynamics trajectories. A novel approximation to Coulomb potential calculation, the multilevel summation method, is introduced and compared with direct Coulomb summation. In light of the performance obtained for this set of calculations, future applications of graphics processors to molecular dynamics simulations are discussed.