Ermod: Fast and versatile computation software for solvation free energy with approximate theory of solutions

ERmod is a software package to efficiently and approximately compute the solvation free energy using the method of energy representation. Molecular simulation is to be conducted at two condensed‐phase systems of the solution of interest and the reference solvent with test‐particle insertion of the solute. The subprogram ermod in ERmod then provides a set of energy distribution functions from the simulation trajectories, and another subprogram slvfe determines the solvation free energy from the distribution functions through an approximate functional. This article describes the design and implementation of ERmod, and illustrates its performance in solvent water for two organic solutes and two protein solutes. Actually, the free‐energy computation with ERmod is not restricted to the solvation in homogeneous medium such as fluid and polymer and can treat the binding into weakly ordered system with nano‐inhomogeneity such as micelle and lipid membrane. ERmod is available on web at http://sourceforge.net/projects/ermod . © 2014 Wiley Periodicals, Inc.     

The performance of ANI-ML potentials for ligand-n(H2O) interaction energies and estimation of hydration free energies from end-point MD simulations

Here, we investigate the performance of “Accurate NeurAl networK engINe for Molecular Energies” (ANI), trained on small organic compounds, on bulk systems including non-covalent interactions and applicability to estimate solvation (hydration) free energies using the interaction between the ligand and explicit solvent (water) from single-step MD simulations. The method is adopted from ANI using the Atomic Simulation Environment (ASE) and predicts the non-covalent interaction energies at the accuracy of wb97x/6-31G(d) level by a simple linear scaling for the conformations sampled by molecular dynamics (MD) simulations of ligand-n(H₂O) systems. For the first time, we test ANI potentials' abilities to reproduce solvation free energies using linear interaction energy (LIE) formulism by modifying the original LIE equation. Our results on ~250 different complexes show that the method can be accurate and have a correlation of R² = 0.88–0.89 (MAE <1.0 kcal/mol) to the experimental solvation free energies, outperforming current end-state methods. Moreover, it is competitive to other conventional free energy methods such as FEP and BAR with 15-20 × fold reduced computational cost.     

Electrostatic solvation free energy of amino acid side chain analogs: implications for the validity of electrostatic linear response in water

Electrostatic free energies of solvation for 15 neutral amino acid side chain analogs are computed. We compare three methods of varying computational complexity and accuracy for three force fields: free energy simulations, Poisson-Boltzmann (PB), and linear response approximation (LRA) using AMBER, CHARMM, and OPLS-AA force fields. We find that deviations from simulation start at low charges for solutes. The approximate PB and LRA produce an overestimation of electrostatic solvation free energies for most of molecules studied here. These deviations are remarkably systematic. The variations among force fields are almost as large as the variations found among methods. Our study confirms that success of the approximate methods for electrostatic solvation free energies comes from their ability to evaluate free energy differences accurately.     

Parameterization of the Hamiltonian Dielectric Solvent (HADES) Reaction‐Field Method for the Solvation Free Energies of Amino Acid Side‐Chain Analogs

Optimization of the Hamiltonian dielectric solvent (HADES) method for biomolecular simulations in a dielectric continuum is presented with the goal of calculating accurate absolute solvation free energies while retaining the model’s accuracy in predicting conformational free‐energy differences. The solvation free energies of neutral and polar amino acid side‐chain analogs calculated by using HADES, which may optionally include nonpolar contributions, were optimized against experimental data to reach a chemical accuracy of about 0.5 kcal mol^?1. The new parameters were evaluated for charged side‐chain analogs. The HADES results were compared with explicit‐solvent, generalized Born, Poisson–Boltzmann, and QM‐based methods. The potentials of mean force (PMFs) between pairs of side‐chain analogs obtained by using HADES and explicit‐solvent simulations were used to evaluate the effects of the improved parameters optimized for solvation free energies on intermolecular potentials.     

Implicit solvation in the self-consistent mean field theory method: sidechain modelling and prediction of folding free energies of protein mutants

The Atomic Solvation Parameter (ASP) model is one of the simplest models of solvation, in which the solvation free energy of a molecule is proportional to the solvent accessible surface area (SAS) of its atoms. However, until now this model had not been incorporated into the Self-Consistent Mean Field Theory (SCMFT) method for modelling sidechain conformations in proteins. The reason for this is that SAS is a many-body quantity and, thus, it is not obvious how to define it within the Mean Field (MF) framework, where multiple copies of each sidechain exist simultaneously. Here, we present a method for incorporating an SAS-based potential, such as the ASP model, into SCMFT. The theory on which the method is based is exact within the MF framework, that is, it does not depend on a pairwise or any other approximation of SAS. Therefore, SAS can be calculated to arbitrary accuracy. The method is computationally very efficient: only 7.6% slower on average than the method without solvation. We applied the method to the prediction of sidechain conformation, using as a test set high-quality solution structures of 11 proteins. Solvation was found to substantially improve the prediction accuracy of well-defined surface sidechains. We also investigated whether the methodology can be applied to prediction of folding free energies of protein mutants, using a set of barnase mutants. For apolar mutants, the modest correlation observed between calculated and observed folding free energies without solvation improved substantially when solvation was included, allowing the prediction of trends in the folding free energies of this type of mutants. For polar mutants, correlation was not significant even with solvation. Several other factors also responsible for the correlation were identified and analysed. From this analysis, future directions for applying and improving the present methodology are discussed.     

Continuous medium theory for nonequilibrium solvation: IV. Solvent reorganization energy of electron transfer based on conductor-like screening model

In this work the authors present some evidences of defects in the popular continuous medium theories for nonequilibrium solvation. Particular attention has been paid to the incorrect reversible work approach. After convincing reasoning, the nonequilibrium free energy has been formulated to an expression different from the traditional ones. In a series of recent works by the authors, new formulations and some analytical application models for ultrafast processes were developed. Here, the authors extend the new theory to the cases of discrete bound charge distributions and present the correct form of the nonequilibrium solvation energy in such cases. A numerical solution method is applied to the evaluation of solvent reorganization energy of electron transfer. The test calculation for biphenyl-cyclohexane-naphthalene anion system achieves excellent agreement with the experimental fitting. The central importance presented in this work is the very simple and a consistent form of nonequilibrium free energy for both continuous and discrete charge distributions, based on which the new models can be established.     

New approach to free energy of solvation applying continuum models to molecular dynamics simulation

A new approach to the calculation of the free energy of solvation from trajectories obtained by molecular dynamics simulation is presented. The free energy of solvation is computed as the sum of three contributions originated at the cavitation of the solute by the solvent, the solute-solvent nonpolar (repulsion and dispersion) interactions, and the electrostatic solvation of the solute. The electrostatic term is calculated based on ideas developed for the broadly used continuum models, the cavitational contribution from the excluded volume by the Claverie-Pierotti model, and the Van der Waals term directly from the molecular dynamics simulation. The proposed model is tested for diluted aqueous solutions of simple molecules containing a variety of chemically important functions: methanol, methylamine, water, methanethiol, and dichloromethane. These solutions were treated by molecular dynamics simulations using SPC/E water and the OPLS force field for the organic molecules. Obtained free energies of solvation are in very good agreement with experimental data.     

自由能微扰法研究系列烷基芳基磺酸盐的胶束化焓-熵补偿现象

为了研究不同结构的表面活性剂分子在水溶液中的胶束化焓-熵补偿现象, 采用自由能微扰(FEP)法计算了系列烷基芳基磺酸盐的溶剂化自由能, 并根据胶团化过程的质量作用模型讨论了相关热力学性质. 结果表明: 自由能微扰法得到的溶剂化自由能大小与用传统热力学表面张力法测定的吉布斯自由能相近, 能够用于比较不同结构的烷基芳基磺酸盐间胶束化能力; 烷基芳基磺酸盐在水溶液中的胶束化过程是自发进行的, 且存在焓-熵补偿现象, 补偿温度范围均在(302±2) K; 随着分子结构中芳环向长烷基链中间位置移动, 胶束化能力和胶束的稳定性均下降; 而随着芳环上短烷基链或长烷基链碳数的增加, 形成胶束的能力与稳定性均提高.     

Semiglobal simplex optimization and its application to determining the preferred solvation sites of proteins

The classical simplex method is extended into the Semiglobal Simplex (SGS) algorithm. Although SGS does not guarantee finding the global minimum, it affords a much more thorough exploration of the local minima than any traditional minimization method. The basic idea of SGS is to perform a local minimization in each step of the simplex algorithm, and thus, similarly to the Convex Global Underestimator (CGU) method, the search is carried out on a surface spanned by local minima. The SGS and CGU methods are compared by minimizing a set of test functions of increasing complexity, each with a known global minimum and many local minima. Although CGU delivers substantially better success rates in simple problems, the two methods become comparable as the complexity of the problems increases. Because SGS is generally faster than CGU, it is the method of choice for solving optimization problems in which function evaluation is computationally inexpensive and the search region is large. The extreme simplicity of the method is also a factor. The SGS method is applied here to the problem of finding the most preferred (i.e., minimum free energy) solvation sites on a streptavidin monomer. It is shown that the SGS method locates the same lowest free energy positions as an exhaustive multistart Simplex search of the protein surface, with less than one-tenth the number of minizations. The combination of the two methods, i.e.. multistart simplex and SGS, provides a reliable procedure for predicting all potential solvation sites of a protein.     

Hybrid Solvation Model with First Solvation Shell for Calculation of Solvation Free Energy

We present a hybrid solvation model with first solvation shell to calculate solvation free energies. This hybrid model combines the quantum mechanics and molecular mechanics methods with the analytical expression based on the Born solvation model to calculate solvation free energies. Based on calculated free energies of solvation and reaction profiles in gas phase, we set up a unified scheme to predict reaction profiles in solution. The predicted solvation free energies and reaction barriers are compared with experimental results for twenty bimolecular nucleophilic substitution reactions. These comparisons show that our hybrid solvation model can predict reliable solvation free energies and reaction barriers for chemical reactions of small molecules in aqueous solution.     

Calculation of the water-cyclohexane transfer free energies of neutral amino acid side-chain analogs using the OPLS all-atom force field

We calculated the free energy of solvation of the neutral analogs of 18 amino acid side-chains (not including glycine and proline) using the OPLS all-atom force field in TIP4P water, SPC water, and cyclohexane by molecular dynamics simulation and thermodynamic integration. The average unsigned errors in the free energies of solvation in TIP4P, SPC, and cyclohexane are 4.4, 4.9, and 2.1 kJ/mol respectively. Most of the calculated hydration free energies are not favorable enough compared to experiment. The largest errors are found for tryptophan, histidine, glutamic acid, and glutamine. The average unsigned errors in the free energy of transfer from TIP4P to cyclohexane and from SPC to cyclohexane are 4.0 and 4.1 kJ/mol, respectively. The largest errors, of more than 7.5 kJ/mol, are found for histidine, glutamine, and glutamatic acid.     

Improper matching of solvation energy components in G-based mixing rules

The physical significance of terms in two excess Gibbs free energy (G^ex)-based mixing rules, the modified Huron–Vidal (MHV1) and Wong–Sandler (WS) mixing rule, are examined through the use of solvation free energy. It is found that these mixing rules are in fact matching the charging contributions of solvation in an equation of state (EOS) to the complete solvation free energy in a liquid activity coefficient model (LM). The cavity contributions in the EOS are canceled as a result of the constant liquid molar volume to molecular volume ratio. The underlying idea of G^ex-based mixing rules that the EOS should behave like a LM at some limiting condition breaks down due to such an improper matching of solvation free energy components.     

用离散-连续模型计算NH2-,NH3和NH4+的溶剂化自由能

通过理论计算推测NH2-,NH3和NH4+在水溶液第一溶剂化层中与之直接作用的水分子分别为2,4和4个,并采用离散-连续模型计算了NH2-,NH3,NH3和NH4+在水溶液中的溶剂化自由能.结果表明,由于离散-连续模型在从头算水平考虑了溶质分子与第一溶剂化层溶剂分子之间的作用,能更准确地描述溶剂化作用.此外,采用更加符合溶液中真实情况的溶剂化构型,能得到更准确的溶剂化性质.     

Breaking the polar‐nonpolar division in solvation free energy prediction

Implicit solvent models divide solvation free energies into polar and nonpolar additive contributions, whereas polar and nonpolar interactions are inseparable and nonadditive. We present a feature functional theory (FFT) framework to break this ad hoc division. The essential ideas of FFT are as follows: (i) representability assumption: there exists a microscopic feature vector that can uniquely characterize and distinguish one molecule from another; (ii) feature‐function relationship assumption: the macroscopic features, including solvation free energy, of a molecule is a functional of microscopic feature vectors; and (iii) similarity assumption: molecules with similar microscopic features have similar macroscopic properties, such as solvation free energies. Based on these assumptions, solvation free energy prediction is carried out in the following protocol. First, we construct a molecular microscopic feature vector that is efficient in characterizing the solvation process using quantum mechanics and Poisson–Boltzmann theory. Microscopic feature vectors are combined with macroscopic features, that is, physical observable, to form extended feature vectors. Additionally, we partition a solvation dataset into queries according to molecular compositions. Moreover, for each target molecule, we adopt a machine learning algorithm for its nearest neighbor search, based on the selected microscopic feature vectors. Finally, from the extended feature vectors of obtained nearest neighbors, we construct a functional of solvation free energy, which is employed to predict the solvation free energy of the target molecule. The proposed FFT model has been extensively validated via a large dataset of 668 molecules. The leave‐one‐out test gives an optimal root‐mean‐square error (RMSE) of 1.05 kcal/mol. FFT predictions of SAMPL0, SAMPL1, SAMPL2, SAMPL3, and SAMPL4 challenge sets deliver the RMSEs of 0.61, 1.86, 1.64, 0.86, and 1.14 kcal/mol, respectively. Using a test set of 94 molecules and its associated training set, the present approach was carefully compared with a classic solvation model based on weighted solvent accessible surface area. © 2017 Wiley Periodicals, Inc.     

The treatment of solvation by a generalized Born model and a self-consistent charge-density functional theory-based tight-binding method

We present a model to calculate the free energies of solvation of small organic compounds as well as large biomolecules. This model is based on a generalized Born (GB) model and a self-consistent charge-density functional theory-based tight-binding (SCC-DFTB) method with the nonelectrostatic contributions to the free energy of solvation modeled in terms of solvent-accessible surface areas (SA). The parametrization of the SCC-DFTB/GBSA model has been based on 60 neutral and six ionic molecules composed of H, C, N, O, and S, and spanning a wide range of chemical groups. Effective atomic radii as parameters have been obtained through Monte Carlo Simulated Annealing optimization in the parameter space to minimize the differences between the calculated and experimental free energies of solvation. The standard error in the free energies of solvation calculated by the final model is 1.11 kcal mol(-1). We also calculated the free energies of solvation for these molecules using a conductor-like screening model (COSMO) in combination with different levels of theory (AM1, SCC-DFTB, and B3LYP/6-31G*) and compared the results with SCC-DFTB/GBSA. To assess the efficiency of our model for large biomolecules, we calculated the free energy of solvation for a HIV protease-inhibitor complex containing 3,204 atoms using the SCC-DFTB/GBSA and the SCC-DFTB/COSMO models, separately. The computed relative free energies of solvation are comparable, while the SCC-DFTB/GBSA model is three to four times more efficient, in terms of computational cost.     

Comparison of implicit solvent models for the simulation of protein-surface interactions

Empirical force field-based molecular simulations can provide valuable atomistic-level insights into protein-surface interactions in aqueous solution. While the implicit treatment of solvation effects is desired as a means of improving simulation efficiency, existing implicit solvent models were primarily developed for the simulation of peptide or protein behavior in solution alone, and thus may not be appropriate for protein interactions with synthetic material surfaces. The objective of this research was to calculate the change in free energy as a function of surface-separation distance for peptide-surface interactions using different empirical force field-based implicit solvation models (ACE, ASP, EEF1, and RDIE with the CHARMM 19 force field), and to compare these results with the same calculations conducted using density functional theory (DFT) combined with the self-consistent reaction field (SCRF) implicit solvation model. These comparisons show that distinctly different types of behavior are predicted with each implicit solvation method, with ACE providing the best overall agreement with DFT/SCRF calculations. These results also identify areas where ACE is in need of improvement for this application and provide a basis for subsequent parameter refinement.     

烷基芳基磺酸盐的分子动力学模拟与自由能微扰计算

为研究不同结构的表面活性剂分子在溶液中胶束化能力的差异, 采用分子动力学方法模拟三种烷基芳基磺酸盐在真空和水溶液环境下的结构与相互作用. 利用自由能微扰(FEP)方法计算了水合自由能, 发现与用传统热力学表面张力法测定自制的烷基芳基磺酸盐结果一致. 研究表明: 烷基芳基磺酸盐在水溶液中的胶束化过程是自发进行的, 随着分子结构中芳环向长烷基链中间位置移动, 胶束化能力和胶束稳定性均下降; 疏水基周围水分子的“冰山结构”会影响胶束的稳定性, 而水分子中氢键的生存周期是反映冰山结构变化的重要指标; 同时, 亲水基与水分子间形成氢键的数目会增强或减弱分子脱离胶束体的趋势, 从而影响胶束结构的稳定性.     

Predicting relative binding affinities of non-peptide HIV protease inhibitors with free energy perturbation calculations

The relative binding free energies in HIV protease of haloperidol thioketal (THK) and three of its derivatives were examined with free energy calculations. THK is a weak inhibitor (IC50 = 15 M) for which two cocrystal structures with HIV type 1 proteases have been solved [Rutenber, E. et al., J. Biol. Chem., 268 (1993) 15343]. A THK derivative with a phenyl group on C2 of the piperidine ring was expected to be a poor inhibitor based on experiments with haloperidol ketal and its 2- phenyl derivative (Caldera, P., personal communication). Our calculations predict that a 5-phenyl THK derivative, suggested based on examination of the crystal structure, will bind significantly better than THK. Although there are large error bars as estimated from hysteresis, the calculations predict that the 5-phenyl substituent is clearly favored over the 2-phenyl derivative as well as the parent compound. The unfavorable free energies of solvation of both phenyl THK derivatives relative to the parent compound contributed to their predicted binding free energies. In a third simulation, the change in binding free energy for 5-benzyl THK relative to THK was calculated. Although this derivative has a lower free energy in the protein, its decreased free energy of solvation increases the predicted G(bind) to the same range as that of the 2-phenyl derivative.