Implicit solvent models: Combining an analytical formulation of continuum electrostatics with simple models of the hydrophobic effect

The recent development of approximate analytical formulations of continuum electrostatics opens the possibility of efficient and accurate implicit solvent models for biomolecular simulations. One such formulation (ACE, Schaefer & Karplus, J. Phys. Chem., 1996, 100:1578) is used to compute the electrostatic contribution to solvation and conformational free energies of a set of small solutes and three proteins. Results are compared to finite-difference solutions of the Poisson equation (FDPB) and explicit solvent simulations and experimental data where available. Small molecule solvation free energies agree with FDPB within 1–1.5 kcal/mol, which is comparable to differences in FDPB due to different surface treatments or different force field parameterizations. Side chain conformation free energies of aspartate and asparagine are in qualitative agreement with explicit solvent simulations, while 74 conformations of a surface loop in the protein Ras are accurately ranked compared to FDPB. Preliminary results for solvation free energies of small alkane and polar solutes suggest that a recent Gaussian model could be used in combination with analytical continuum electrostatics to treat nonpolar interactions. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 322–335, 1999     

Comparison of various implicit solvent models in molecular dynamics simulations of immunoglobulin G light chain dimer

The present study tests performance of different solvation models applied to molecular dynamics simulation of a large, dimeric protein molecule. Analytical Continuum Electrostatics (ACE) with two different parameter sets, older V98 and new V01, and Effective Energy Function (EEF) are employed in molecular dynamics simulation of immunoglobulin G (IgG) light chain dimer and variable domain of IgG light chain. Results are compared with explicit solvent and distance dependent dielectric constant (DDE) calculations. The overall analysis shows that the EEF method yields results comparable to explicit solvent simulations; however, the stability of simulations is lower. On the other hand, the ACE_V98 model does not seem to achieve the accuracy or stability expected in nanosecond timescale MD simulation for the studied systems. The ACE_V01 model greatly improves stability of the calculation; nonetheless, changes in radius of gyration and solvent accessible surface of the studied systems may indicate that the parameter set still needs to be improved if the method is supposed to be used for simulations of large, polymeric proteins. Additionally, electrostatic contribution to the solvation free energy calculated in the ACE model is compared with a numerical treatment of the dielectric continuum model. Wall clock time of all simulations is compared. It shows that EEF calculation is six times faster than corresponding ACE and 50 times faster than explicit solvent simulations.     

Molecular mechanics and dynamics of biomolecules using a solvent continuum model

An easy implementation of molecular mechanics and molecular dynamics simulation using a continuum solvent model is presented that is particularly suitable for biomolecular simulations. The computation of solvation forces is made using the linear Poisson-Boltzmann equation (polar contribution) and the solvent-accessible surface area approach (nonpolar contribution). The feasibility of the methodology is demonstrated on a small protein and a small DNA hairpin. Although the parameters employed in this model must be refined to gain reliability, the performance of the method, with a standard choice of parameters, is comparable with results obtained by explicit water simulations. Copyright 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1830-1842, 2001     

Stability of ion triplets in ionic liquid/lithium salt solutions: Insights from implicit and explicit solvent models and molecular dynamics simulations

Binding energies of ion triplets formed in ionic liquids by Li⁺ with two anions have been studied using quantum‐chemical calculations with implicit and explicit solvent supplemented by molecular dynamics (MD) simulations. Explicit solvent approach confirms variation of solute‐ionic liquid interactions at distances up to 2 nm, resulting from structure of solvation shells induced by electric field of the solute. Binding energies computed in explicit solvent and from the polarizable continuum model approach differ largely, even in sign, but relative values generally agree between these two models. Stabilities of ion triplets obtained in quantum‐chemical calculations for some systems disagree with MD results; the discrepancy is attributed to the difference between static optimized geometries used in quantum chemical modeling and dynamic structures of triplets in MD simulations. © 2015 Wiley Periodicals, Inc.     

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.     

Optimized parameters for continuum solvation calculations with carbohydrates

Continuum solvent models have been shown to be an efficient method for the calculation of the energetics of biomolecules in solution. However, for these methods to produce accurate results, an appropriate set of atomic radii or volumes is needed. While these have been developed for proteins and nucleic acids, the same is not true of carbohydrates. Here, a set of optimized parameters for continuum solvation calculations of carbohydrates in conjunction with the Carbohydrate Solution Force Field are presented. Explicit solvent free-energy perturbation simulations were performed on a set of hexapyranose sugars and used to fit atomic radii for Poisson-Boltzmann and generalized-Born calculations, and to fit atomic volumes for use with the analytical continuum electrostatics model. The solvation energetics computed with the optimized radii and a Poisson-Boltzmann model show remarkable agreement with explicit solvent simulation, with a root-mean-square error of 1.19 kcal/mol over a large test set of sugars in many conformations. The generalized-Born model gives slightly poorer agreement, but still correlates very strongly, with an error of 1.69 kcal/mol. The analytical continuum electrostatics model correlates well with the explicit solvent results, but gives a larger error of 4.71 kcal/mol. The remarkable agreement between the solvation free energies computed in explicit and implicit solvent provides strong motivation for the use of implicit solvent models in the simulation of carbohydrate-containing systems.     

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).     

Implicit solvent simulations of DNA and DNA-protein complexes: agreement with explicit solvent vs experiment

Molecular dynamics simulations of biomolecules with implicit solvent reduce the computational cost and complexity of such simulations so that longer time scales and larger system sizes can be reached. While implicit solvent simulations of proteins have become well established, the success of implicit solvent in the simulation of nucleic acids has not been fully established to date. Results obtained in this study demonstrate that stable and efficient simulations of DNA and a protein-DNA complex can be achieved with an implicit solvent model based on continuum dielectric electrostatics. Differences in conformational sampling of DNA with two sets of atomic radii that are used to define the dielectric interface between the solute and the continuum dielectric model of the solvent are investigated. Results suggest that depending on the choice of atomic radii agreement is either closer to experimental data or to explicit solvent simulations. Furthermore, partial conformational transitions toward A-DNA conformations when salt is added within the implicit solvent framework are observed.     

Predicting hydration free energies of polychlorinated aromatic compounds from the SAMPL-3 data set with FiSH and LIE models

Next-generation solvation models are devised to mimic the accuracy and generality of explicit solvation models at the speed of current popular implicit solvation models. One such method is the first-shell of hydration (FiSH) continuum model that was trained on hydration energetics from LIE calculations and molecular dynamics simulations in explicit solvent. Here we tested prospectively the FiSH model on the SAMPL-3 hydration data set that zooms in the effect of chlorination on solvation. We compare these FiSH predictions with those from retrospective LIE calculations. We find that neither FiSH nor LIE can reproduce well the absolute values and the trend of hydration free energies in the biphenyl and dioxin aromatic chlorination series. Some of the hypotheses behind this performance are discussed and tested. The LIE explicit-solvent model shows some improvement relative to the FiSH continuum model, and we correct a systematic deviation in the continuum van der Waals term of FiSH associated with aromatic Cl atom type.     

Insight into the role of hydration on protein dynamics

The potential energy surface of a protein is rough. This intrinsic energetic roughness affects diffusion, and hence the kinetics. The dynamics of a system undergoing Brownian motion on this surface in an implicit continuum solvent simulation can be tuned via the frictional drag or collision frequency to be comparable to that of experiments or explicit solvent simulations. We show that the kinetic rate constant for a local rotational isomerization in stochastic simulations with continuum solvent and a collision frequency of 2 ps(-1) is about 10(4) times faster than that in explicit water and experiments. A further increase in the collision frequency to 60 ps(-1) slows down the dynamics, but does not fully compensate for the lack of explicit water. We also show that the addition of explicit water does not only slow down the dynamics by increasing the frictional drag, but also increases the local energetic roughness of the energy landscape by as much as 1.0 kcal/mol.     

XH-NH3(X=F,Cl,Br)质子传递的溶剂效应:簇模型,连续介质模型和离散-连续组合模型的比较

分别采用分子簇模型、连续介质模型和离散-连续组合模型研究了XH-NH3(X=F,Cl,Br)分子内质子传递的溶剂效应．结果表明,对于弱酸性化合物FH-NH3,其溶剂效应主要为短程作用,3个H2O分子即可使其发生质子传递,而简单的连续介质模型得到的仍为分子化合物形式,需进一步包含溶剂效应短程作用．对于强酸性化合物ClH-NH3和BrH-NH3,较弱的溶剂效应即可促使其发生质子传递,分子簇模型和连续介质模型均可合理描述,且与离散-连续组合模型的结果相近．离散-连续组合模型既在从头算水平考虑了溶质分子和第一溶剂化层中溶剂分子间的短程作用,又包含了溶剂效应的长程静电作用,能更准确地描述溶剂化作用,且对弱酸性化合物和强酸性化合物体系均适用．     

Free energies of solvation in the context of protein folding: Implications for implicit and explicit solvent models

Implicit solvent models for biomolecular simulations have been developed to use in place of more expensive explicit models; however, these models make many assumptions and approximations that are likely to affect accuracy. Here, the changes in free energies of solvation upon folding of several fast folding proteins are calculated from previously run μs–ms simulations with a number of implicit solvent models and compared to the values needed to be consistent with the explicit solvent model used in the simulations. In the majority of cases, there is a significant and substantial difference between the values calculated from the two approaches that is robust to the details of the calculations. These differences could only be remedied by selecting values for the model parameters—the internal dielectric constant for the polar term and the surface tension coefficient for the nonpolar term—that were system‐specific or physically unrealistic. We discuss the potential implications of our findings for both implicit and explicit solvent simulations. © 2015 Wiley Periodicals, Inc.     

Impact of the solvent on the conformational isomerism of calix[4]arenes: a study based on continuum solvation models

The influence of solvation on the conformational isomerism of calix[4]arene and p-tert-butylcalix[4]arene has been investigated by using the continuum model reported by Miertus, Scrocco, and Tomasi (MST). The quantum mechanical (QM) and semiclassical (SC) formalisms of the MST model have been considered for two different solvents (chloroform and water). The suitability of the QM-MST and SC-MST methods has been examined by comparison with previous results derived from classical molecular dynamics (MD) simulations with explicit solvent molecules. The application of the continuum model to the solute configurations generated by using in vacuo classical MD simulations provides a fast strategy to evaluate the effects of the solvent on the conformational preferences of calixarenes. These encouraging results allow us to propose the use of continuum models to solutes with complex molecular structures, which are traditionally studied by MD simulations.     

Proton binding to proteins: pK(a) calculations with explicit and implicit solvent models

Ionizable residues play important roles in protein structure and activity, and proton binding is a valuable reporter of electrostatic interactions in these systems. We use molecular dynamics free energy simulations (MDFE) to compute proton pKa shifts, relative to a model compound in solution, for three aspartate side chains in two proteins. Simulations with explicit solvent and with an implicit, dielectric continuum solvent are reported. The implicit solvent simulations use the generalized Born (GB) model, which provides an approximate, analytical solution to Poisson's equation. With explicit solvent, the direction of the pKa shifts is correct in all three cases with one force field (AMBER) and in two out of three cases with another (CHARMM). For two aspartates, the dielectric response to ionization is found to be linear, even though the separate protein and solvent responses can be nonlinear. For thioredoxin Asp26, nonlinearity arises from the presence of two substates that correspond to the two possible orientations of the protonated carboxylate. For this side chain, which is partly buried and has a large pKa upshift, very long simulations are needed to correctly sample several slow degrees of freedom that reorganize in response to the ionization. Thus, nearby Lys57 rotates to form a salt bridge and becomes buried, while three waters intercalate along the opposite edge of Asp26. Such strong and anisotropic reorganization is very difficult to predict with Poisson-Boltzmann methods that only consider electrostatic interactions and employ a single protein structure. In contrast, MDFE with a GB dielectric continuum solvent, used for the first time for pKa calculations, can describe protein reorganization accurately and gives encouraging agreement with experiment and with the explicit solvent simulations.     

An efficient hybrid explicit/implicit solvent method for biomolecular simulations

We present a new hybrid explicit/implicit solvent method for dynamics simulations of macromolecular systems. The method models explicitly the hydration of the solute by either a layer or sphere of water molecules, and the generalized Born (GB) theory is used to treat the bulk continuum solvent outside the explicit simulation volume. To reduce the computational cost, we implemented a multigrid method for evaluating the pairwise electrostatic and GB terms. It is shown that for typical ion and protein simulations our method achieves similar equilibrium and dynamical observables as the conventional particle mesh Ewald (PME) method. Simulation timings are reported, which indicate that the hybrid method is much faster than PME, primarily due to a significant reduction in the number of explicit water molecules required to model hydration effects.