Comparison of two simulation methods to compute solvation free energies and partition coefficients

The thermodynamic integration (TI) and expanded ensemble (EE) methods are used here to calculate the hydration free energy in water, the solvation free energy in 1‐octanol, and the octanol‐water partition coefficient for a six compounds of varying functionality using the optimized potentials for liquid simulations (OPLS) all‐atom (AA) force field parameters and atomic charges. Both methods use the molecular dynamics algorithm as a primary component of the simulation protocol, and both have found wide applications in fields such as the calculation of activity coefficients, phase behavior, and partition coefficients. Both methods result in solvation free energies and 1‐octanol/water partition coefficients with average absolute deviations (AAD) from experimental data to within 4 kJ/mol and 0.5 log units, respectively. Here, we find that in simulations the OPLS‐AA force field parameters (with fixed charges) can reproduce solvation free energies of solutes in 1‐octanol with AAD of about half that for the solute hydration free energies using a extended simple point charge (SPC/E) model of water. The computational efficiency of the two simulation methods are compared based on the time (in nanoseconds) required to obtain similar standard deviations in the solvation free energies and 1‐octanol/water partition coefficients. By this analysis, the EE method is found to be a factor of nine more efficient than the TI algorithm. For both methods, solvation free energy calculations in 1‐octanol consume roughly an order of magnitude more CPU hours than the hydration free energy calculations. © 2012 Wiley Periodicals, Inc.     

Computer simulations of ligand–protein binding with ensembles of protein conformations: A Monte Carlo study of HIV‐1 protease binding energy landscapes

We present the results of molecular docking simulations with HIV‐1 protease for the sb203386 and skf107457 inhibitors by Monte Carlo simulated annealing. A simplified piecewise linear energy function, the standard AMBER force field, and the AMBER force field with solvation and a soft‐core smoothing component are employed in simulations with a single‐protein conformation to determine the relationship between docking simulations with a simple energy function and more realistic force fields. The temperature‐dependent binding free energy profiles of the inhibitors interacting with a single protein conformation provide a detailed picture of relative thermodynamic stability and a distribution of ligand binding modes in agreement with experimental crystallographic data. Using the simplified piecewise linear energy function, we also performed Monte Carlo docking simulations with an ensemble of protein conformations employing preferential biased sampling of low‐energy protein conformations, and the results are analyzed in connection with the free energy profiles. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 73–84, 1999     

Testing the semi-explicit assembly solvation model in the SAMPL3 community blind test

We report here a test of the Semi-Explicit Assembly (SEA) model in the solvation free energy category of the SAMPL3 blind prediction event (summer 2011). We tested how dependent the SEA results are on the chosen force field by performing calculations with both the General Amber and OPLS force fields. We compared our SEA results with full molecular dynamics simulations in explicit solvent. Of the 20 submissions, our SEA/OPLS results gave the second smallest RMS errors in free energies compared to experiments. SEA gives results that are very similar to those of its underlying force field and explicit solvent model. Hence, while the SEA water modeling approach is much faster than explicit solvent simulations, its predictions appear to be just as accurate.     

Simulation of multiphase systems utilizing independent force fields to control intraphase and interphase behavior

Fixed‐charge empirical force fields have been developed and widely used over the past three decades for all‐atom molecular simulations. Most simulation programs providing these methods enable only one set of force field parameters to be used for the entire system. Whereas this is generally suitable for single‐phase systems, the molecular environment at the interface between two phases may be sufficiently different from the individual phases to require a different set of parameters to be used to accurately represent the system. Recently published simulations of peptide adsorption to material surfaces using the CHARMM force field have clearly demonstrated this issue by revealing that calculated values of adsorption free energy substantially differ from experimental results. Whereas nonbonded parameters could be adjusted to correct this problem, this cannot be done without also altering the conformational behavior of the peptide in solution, for which CHARMM has been carefully tuned. We have developed a dual‐force‐field approach (Dual‐FF) to address this problem and implemented it in the CHARMM simulation package. This Dual‐FF method provides the capability to use two separate sets of nonbonded force field parameters within the same simulation: one set to represent intraphase interactions and a separate set to represent interphase interactions. Using this approach, we show that interfacial parameters can be adjusted to correct errors in peptide adsorption free energy without altering peptide conformational behavior in solution. This program thus provides the capability to enable both intraphase and interphase molecular behavior to be accurately and efficiently modeled in the same simulation. © 2012 Wiley Periodicals, Inc.     

Force field parameters for the simulation of modified histone tails

We describe the development of force field parameters for methylated lysines and arginines, and acetylated lysine for the CHARMM all‐atom force field. We also describe a CHARMM united‐atom force field for modified sidechains suitable for use with fragment‐based docking methods. The development of these parameters is based on results of ab initio quantum mechanics calculations of model compounds with subsequent refinement and validation by molecular mechanics and molecular dynamics simulations. The united‐atom parameters are tested by fragment docking to target proteins using the MCSS procedure. The all‐atom force field is validated by molecular dynamics simulations of multiple experimental structures. In both sets of calculations, the computational predictions using the force field were compared to the corresponding experimental structures. We show that the parameters yield an accurate reproduction of experimental structures. Together with the existing CHARMM force field, these parameters will enable the general modeling of post‐translational modifications of histone tails. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Computer simulation of trifluoromethane properties with ab initio force field

Intermolecular interaction potentials of the trifluoromethane dimer in 15 orientations have been calculated using the Hartree‐Fock (HF) self‐consistent theory and the second‐order Møller‐Plesset (MP2) perturbation theory. Single point energies at important geometries were also calibrated by the coupled cluster with single and double and perturbative triple excitation [CCSD(T)] calculations. We have employed Pople's medium size basis sets [up to 6‐311++G(3df,3pd)] and Dunning's correlation consistent basis sets (up to aug‐cc‐pVQZ). Basis set limit potential values were obtained through well‐studied extrapolation methods. The calculated MP2 potential data were employed to parameterize a 5‐site force field for molecular simulations. We performed molecular dynamics simulations using the constructed ab initio force field and compared the simulation results with experiments. Quantitative agreements for the atom‐wise radial distribution functions and the self‐diffusion coefficients over a wide range of experimental conditions can be obtained, thus validating the ab initio force field without using experimental data a priori. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

A molecular mechanics model for imatinib and imatinib:kinase binding

Imatinib is an important anticancer drug, which binds specifically to the Abl kinase and blocks its signalling activity. To model imatinib:protein interactions, we have developed a molecular mechanics force field for imatinib and four close analogues, which is consistent with the CHARMM force field for proteins and nucleic acids. Atomic charges and Lennard‐Jones parameters were derived from a supermolecule ab initio approach. We considered the ab initio energies and geometries of a probe water molecule interacting with imatinib fragments at 32 different positions. We considered both a neutral and a protonated imatinib. The final RMS deviation between the ab initio and force field energies, averaged over both forms, was 0.2 kcal/mol. The model also reproduces the ab initio geometry and flexibility of imatinib. To apply the force field to imatinib:Abl simulations, it is also necessary to determine the most likely imatinib protonation state when it binds to Abl. This was done using molecular dynamics free energy simulations, where imatinib is reversibly protonated during a series of MD simulations, both in solution and in complex with Abl. The simulations indicate that imatinib binds to Abl in its protonated, positively‐charged form. To help test the force field and the protonation prediction, we did MD free energy simulations that compare the Abl binding affinities of two imatinib analogs, obtaining good agreement with experiment. Finally, two new imatinib variants were considered, one of which is predicted to have improved Abl binding. This variant could be of interest as a potential drug. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Molecular dynamics simulations of peptide-surface interactions

Proteins, which are bioactive molecules, adsorb on implants placed in the body through complex and poorly understood mechanisms and directly influence biocompatibility. Molecular dynamics modeling using empirical force fields provides one of the most direct methods of theoretically analyzing the behavior of complex molecular systems and is well-suited for the simulation of protein adsorption behavior. To accurately simulate protein adsorption behavior, a force field must correctly represent the thermodynamic driving forces that govern peptide residue-surface interactions. However, since existing force fields were developed without specific consideration of protein-surface interactions, they may not accurately represent this type of molecular behavior. To address this concern, we developed a host-guest peptide adsorption model in the form of a G(4)-X-G(4) peptide (G is glycine, X is a variable residue) to enable determination of the contributions to adsorption free energy of different X residues when adsorbed to functionalized Au-alkanethiol self-assembled monolayers (SAMs). We have previously reported experimental results using surface plasmon resonance (SPR) spectroscopy to measure the free energy of peptide adsorption for this peptide model with X = G and K (lysine) on OH and COOH functionalized SAMs. The objectives of the present research were the development and assessment of methods to calculate adsorption free energy using molecular dynamics simulations with the GROMACS force field for these same peptide adsorption systems, with an oligoethylene oxide (OEG) functionalized SAM surface also being considered. By comparing simulation results to the experimental results, the accuracy of the selected force field to represent the behavior of these molecular systems can be evaluated. From our simulations, the G(4)-G-G(4) and G(4)-K-G(4) peptides showed minimal to no adsorption to the OH SAM surfaces and the G(4)-K-G(4) showed strong adsorption to the COOH SAM surface, which is in agreement with our SPR experiments. Contrary to our experimental results, however, the simulations predicted a relatively strong adsorption of G(4)-G-G(4) peptide to the COOH SAM surface. In addition, both peptides were unexpectedly predicted to adsorb to the OEG surface. These findings demonstrate the need for GROMACS force field parameters to be rebalanced for the simulation of peptide adsorption behavior on SAM surfaces. The developed methods provide a direct means of assessing, modifying, and validating force field performance for the simulation of peptide and protein adsorption to surfaces, without which little confidence can be placed in the simulation results that are generated with these types of systems.     

Partition coefficients of methylated DNA bases obtained from free energy calculations with molecular electron density derived atomic charges

Partition coefficients serve in various areas as pharmacology and environmental sciences to predict the hydrophobicity of different substances. Recently, they have also been used to address the accuracy of force fields for various organic compounds and specifically the methylated DNA bases. In this study, atomic charges were derived by different partitioning methods (Hirshfeld and Minimal Basis Iterative Stockholder) directly from the electron density obtained by electronic structure calculations in a vacuum, with an implicit solvation model or with explicit solvation taking the dynamics of the solute and the solvent into account. To test the ability of these charges to describe electrostatic interactions in force fields for condensed phases, the original atomic charges of the AMBER99 force field were replaced with the new atomic charges and combined with different solvent models to obtain the hydration and chloroform solvation free energies by molecular dynamics simulations. Chloroform–water partition coefficients derived from the obtained free energies were compared to experimental and previously reported values obtained with the GAFF or the AMBER‐99 force field. The results show that good agreement with experimental data is obtained when the polarization of the electron density by the solvent has been taken into account, and when the energy needed to polarize the electron density of the solute has been considered in the transfer free energy. These results were further confirmed by hydration free energies of polar and aromatic amino acid side chain analogs. Comparison of the two partitioning methods, Hirshfeld‐I and Minimal Basis Iterative Stockholder (MBIS), revealed some deficiencies in the Hirshfeld‐I method related to the unstable isolated anionic nitrogen pro‐atom used in the method. Hydration free energies and partitioning coefficients obtained with atomic charges from the MBIS partitioning method accounting for polarization by the implicit solvation model are in good agreement with the experimental values. © 2018 Wiley Periodicals, Inc.     

Comparison between self-guided Langevin dynamics and molecular dynamics simulations for structure refinement of protein loop conformations

This article presents a comparative analysis of two replica‐exchange simulation methods for the structure refinement of protein loop conformations, starting from low‐resolution predictions. The methods are self‐guided Langevin dynamics (SGLD) and molecular dynamics (MD) with a Nosé–Hoover thermostat. We investigated a small dataset of 8‐ and 12‐residue loops, with the shorter loops placed initially from a coarse‐grained lattice model and the longer loops from an enumeration assembly method (the Loopy program). The CHARMM22 + CMAP force field with a generalized Born implicit solvent model (molecular‐surface parameterized GBSW2) was used to explore conformational space. We also assessed two empirical scoring methods to detect nativelike conformations from decoys: the all‐atom distance‐scaled ideal‐gas reference state (DFIRE‐AA) statistical potential and the Rosetta energy function. Among the eight‐residue loop targets, SGLD out performed MD in all cases, with a median of 0.48 Å reduction in global root‐mean‐square deviation (RMSD) of the loop backbone coordinates from the native structure. Among the more challenging 12‐residue loop targets, SGLD improved the prediction accuracy over MD by a median of 1.31 Å, representing a substantial improvement. The overall median RMSD for SGLD simulations of 12‐residue loops was 0.91 Å, yielding refinement of a median 2.70 Å from initial loop placement. Results from DFIRE‐AA and the Rosetta model applied to rescoring conformations failed to improve the overall detection calculated from the CHARMM force field. We illustrate the advantage of SGLD over the MD simulation model by presenting potential‐energy landscapes for several loop predictions. Our results demonstrate that SGLD significantly outperforms traditional MD in the generation and populating of nativelike loop conformations and that the CHARMM force field performs comparably to other empirical force fields in identifying these conformations from the resulting ensembles. Published 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Combining the polarizable Drude force field with a continuum electrostatic Poisson–Boltzmann implicit solvation model

In this work, we have combined the polarizable force field based on the classical Drude oscillator with a continuum Poisson–Boltzmann/solvent‐accessible surface area (PB/SASA) model. In practice, the positions of the Drude particles experiencing the solvent reaction field arising from the fixed charges and induced polarization of the solute must be optimized in a self‐consistent manner. Here, we parameterized the model to reproduce experimental solvation free energies of a set of small molecules. The model reproduces well‐experimental solvation free energies of 70 molecules, yielding a root mean square difference of 0.8 kcal/mol versus 2.5 kcal/mol for the CHARMM36 additive force field. The polarization work associated with the solute transfer from the gas‐phase to the polar solvent, a term neglected in the framework of additive force fields, was found to make a large contribution to the total solvation free energy, comparable to the polar solute–solvent solvation contribution. The Drude PB/SASA also reproduces well the electronic polarization from the explicit solvent simulations of a small protein, BPTI. Model validation was based on comparisons with the experimental relative binding free energies of 371 single alanine mutations. With the Drude PB/SASA model the root mean square deviation between the predicted and experimental relative binding free energies is 3.35 kcal/mol, lower than 5.11 kcal/mol computed with the CHARMM36 additive force field. Overall, the results indicate that the main limitation of the Drude PB/SASA model is the inability of the SASA term to accurately capture non‐polar solvation effects. © 2018 Wiley Periodicals, Inc.     

Calculations of the free energy of interaction of the c-Fos-c-Jun coiled coil: effects of the solvation model and the inclusion of polarization effects

The leucine zipper region of activator protein-1 (AP-1) comprises the c-Jun and c-Fos proteins and constitutes a well-known coiled coil protein-protein interaction motif. We have used molecular dynamics (MD) simulations in conjunction with the molecular mechanics/Poisson-Boltzmann generalized-Born surface area [MM/PB(GB)SA] methods to predict the free energy of interaction of these proteins. In particular, the influence of the choice of solvation model, protein force field, and water potential on the stability and dynamic properties of the c-Fos-c-Jun complex were investigated. Use of the AMBER polarizable force field ff02 in combination with the polarizable POL3 water potential was found to result in increased stability of the c-Fos-c-Jun complex. MM/PB(GB)SA calculations revealed that MD simulations using the POL3 water potential give the lowest predicted free energies of interaction compared to other nonpolarizable water potentials. In addition, the calculated absolute free energy of binding was predicted to be closest to the experimental value using the MM/GBSA method with independent MD simulation trajectories using the POL3 water potential and the polarizable ff02 force field, while all other binding affinities were overestimated.     

Coulomb replica‐exchange method: Handling electrostatic attractive and repulsive forces for biomolecules

We propose a new type of the Hamiltonian replica‐exchange method (REM) for molecular dynamics (MD) and Monte Carlo simulations, which we refer to as the Coulomb REM (CREM). In this method, electrostatic charge parameters in the Coulomb interactions are exchanged among replicas while temperatures are exchanged in the usual REM. By varying the atom charges, the CREM overcomes free‐energy barriers and realizes more efficient sampling in the conformational space than the REM. Furthermore, this method requires only a smaller number of replicas because only the atom charges of solute molecules are used as exchanged parameters. We performed Coulomb replica‐exchange MD simulations of an alanine dipeptide in explicit water solvent and compared the results with those of the conventional canonical, replica exchange, and van der Waals REMs. Two force fields of AMBER parm99 and AMBER parm99SB were used. As a result, the CREM sampled all local‐minimum free‐energy states more frequently than the other methods for both force fields. Moreover, the Coulomb, van der Waals, and usual REMs were applied to a fragment of an amyloid‐β peptide (Aβ) in explicit water solvent to compare the sampling efficiency of these methods for a larger system. The CREM sampled structures of the Aβ fragment more efficiently than the other methods. We obtained β‐helix, α‐helix, 3₁₀‐helix, β‐hairpin, and β‐sheet structures as stable structures and deduced pathways of conformational transitions among these structures from a free‐energy landscape. © 2012 Wiley Periodicals, Inc.     

Efficient estimation of binding free energies between peptides and an MHC class II molecule using coarse‐grained molecular dynamics simulations with a weighted histogram analysis method

We estimate the binding free energy between peptides and an MHC class II molecule using molecular dynamics (MD) simulations with the weighted histogram analysis method (WHAM). We show that, owing to its more thorough sampling in the available computational time, the binding free energy obtained by pulling the whole peptide using a coarse‐grained (CG) force field (MARTINI) is less prone to significant error induced by inadequate‐sampling than using an atomistic force field (AMBER). We further demonstrate that using CG MD to pull 3–4 residue peptide segments while leaving the remaining peptide segments in the binding groove and adding up the binding free energies of all peptide segments gives robust binding free energy estimations, which are in good agreement with the experimentally measured binding affinities for the peptide sequences studied. Our approach thus provides a promising and computationally efficient way to rapidly and reliably estimate the binding free energy between an arbitrary peptide and an MHC class II molecule. © 2017 Wiley Periodicals, Inc.     

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.     

A semiempirical free energy force field with charge-based desolvation

The authors describe the development and testing of a semiempirical free energy force field for use in AutoDock4 and similar grid-based docking methods. The force field is based on a comprehensive thermodynamic model that allows incorporation of intramolecular energies into the predicted free energy of binding. It also incorporates a charge-based method for evaluation of desolvation designed to use a typical set of atom types. The method has been calibrated on a set of 188 diverse protein-ligand complexes of known structure and binding energy, and tested on a set of 100 complexes of ligands with retroviral proteases. The force field shows improvement in redocking simulations over the previous AutoDock3 force field.     

Accurate and Rigorous Prediction of the Changes in Protein Free Energies in a Large‐Scale Mutation Scan

The prediction of mutation‐induced free‐energy changes in protein thermostability or protein–protein binding is of particular interest in the fields of protein design, biotechnology, and bioengineering. Herein, we achieve remarkable accuracy in a scan of 762 mutations estimating changes in protein thermostability based on the first principles of statistical mechanics. The remaining error in the free‐energy estimates appears to be due to three sources in approximately equal parts, namely sampling, force‐field inaccuracies, and experimental uncertainty. We propose a consensus force‐field approach, which, together with an increased sampling time, leads to a free‐energy prediction accuracy that matches those reached in experiments. This versatile approach enables accurate free‐energy estimates for diverse proteins, including the prediction of changes in the melting temperature of the membrane protein neurotensin receptor 1.     

Comparing Dimerization Free Energies and Binding Modes of Small Aromatic Molecules with Different Force Fields

Dimerization free energies are fundamental quantities that describe the strength of interaction of different molecules. Obtaining accurate experimental values for small molecules and disentangling the conformations that contribute most to the binding can be extremely difficult, due to the size of the systems and the small energy differences. In many cases, one has to resort to computational methods to calculate such properties. In this work, we used molecular dynamics simulations in conjunction with metadynamics to calculate the free energy of dimerization of small aromatic rings, and compared three models from popular online servers for atomistic force fields, namely G54a7, CHARMM36 and OPLS. We show that, regardless of the force field, the profiles for the dimerization free energy of these compounds are very similar. However, significant care needs to be taken when studying larger molecules, since the deviations from the trends increase with the size of the molecules, resulting in force field dependent preferred stacking modes; for example, in the cases of pyrene and tetracene. Our results provide a useful background study for using topology builders to model systems which rely on stacking of aromatic moieties, and are relevant in areas ranging from drug design to supramolecular assembly.     

Simulating the Physiological Phase of Hydrated DPPC Bilayers: The Ester Moiety

Abstract

The charge on the ester oxygen of the sn2 group of the dipalmitoylphosphatidylcholine (DPPC) has a remarkable effect on the square area per lipid in simulations of a hydrated bilayer. This is in contrast to simulations of nonpolar, neutral lipids, where it has been found to have little effect. The charges associated with the GROMOS96 45A3 and 45A4 biomolecular force fields have been previously shown to cause significant membrane shrinkage. We find that the use of larger charges at the ester groups alone (as opposed to on all the polar moieties in the head group) remedies the shrinkage. The source of this effect in DPPC lies in the fact that the charge distribution of this polar group profoundly influences its free energy of hydration and, correspondingly, the water distribution around it. In an attempt to rationally tune the ester parameters, the repulsive Lennard–Jones parameters that represent the van der Waals interaction have been refined to reproduce the experimental density and heat of vaporization, and the charges of the ester groups have been tuned to reproduce the experimental free energies of hydration of a series of alkane esters. The new parameters form part of the GROMOS96 53A5 and 53A6 force fields. However, with the new force‐field parameters, the area per lipid in simulations of hydrated DPPC bilayers lies below that of the physiological liquid‐crystalline phase, the implications of which are discussed.