Pengyu Ren

Current Status of the AMOEBA Polarizable Force Field

Molecular force fields have been approaching a generational transition over the past several years, moving away from well-established and well-tuned, but intrinsically limited, fixed point charge models toward more intricate and expensive polarizable models that should allow more accurate description of molecular properties. The recently introduced AMOEBA force field is a leading publicly available example of this next generation of theoretical model, but to date, it has only received relatively limited validation, which we address here. We show that the AMOEBA force field is in fact a significant improvement over fixed charge models for small molecule structural and thermodynamic observables in particular, although further fine-tuning is necessary to describe solvation free energies of drug-like small molecules, dynamical properties away from ambient conditions, and possible improvements in aromatic interactions. State of the art electronic structure calculations reveal generally very good agreement with AMOEBA for demanding problems such as relative conformational energies of the alanine tetrapeptide and isomers of water sulfate complexes. AMOEBA is shown to be especially successful on protein-ligand binding and computational X-ray crystallography where polarization and accurate electrostatics are critical.

The COMPASS force field: parameterization and validation for phosphazenes

A new, condensed-phase optimised ab-initio force field, COMPASS, has been developed recently. In this paper, the validation of COMPASS for phosphazenes is presented. The functional forms of this force field are of the consistent force field (CFF) type. Charges and bonded terms were derived from HF/6–31G∗ calculations, while the nonbonded parameters (L-J 9-6 vdW potential) were initially transferred from the polymer consistent force field, pcff, and optimised using MD simulations of condensed-phase properties. As a validation of COMPASS, molecular mechanics calculations and molecular dynamics simulations have been made on a number of isolated molecules, liquids, and crystals. The calculated molecular structure, vibration frequencies, conformational properties for isolated molecules, crystal cell parameters and density, liquid density, and heat of evaporation agreed favourably with most experimental data. The special conformational properties of the tetracyclophosphazenes, (NPCI2)4 and (NPF2)4, in the solid state are discussed based on molecular mechanics and CASTEP ab-initio calculations. The effect of nonbonded cutoff distance and different algorithms for pressure control in NPT simulation was also investigated. Finally, molecular dynamics using the COMPASS force field was used to predict properties of three isomers of high-molecular-weight amorphous poly(dibutoxyphosphazenes). In this case, excellent agreement was achieved between densities and glass transition temperatures obtained from dynamics and experimental data.

Tinker 8: Software Tools for Molecular Design

The Tinker software, currently released as version 8, is a modular molecular mechanics and dynamics package written primarily in a standard, easily portable dialect of Fortran 95 with OpenMP extensions. It supports a wide variety of force fields, including polarizable models such as the Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field. The package runs on Linux, macOS, and Windows systems. In addition to canonical Tinker, there are branches, Tinker-HP and Tinker-OpenMM, designed for use on message passing interface (MPI) parallel distributed memory supercomputers and state-of-the-art graphical processing units (GPUs), respectively. The Tinker suite also includes a tightly integrated Java-based graphical user interface called Force Field Explorer (FFE), which provides molecular visualization capabilities as well as the ability to launch and control Tinker calculations.

Consistent treatment of inter‐ and intramolecular polarization in molecular mechanics calculations

A protocol is described for the treatment of molecular polarization in force field calculations. The resulting model is consistent in that both inter‐ and intramolecular polarization are handled within a single scheme. An analytical formula for removing intramolecular polarization from a set of atomic multipoles for an arbitrary static structure or conformation is given. With the help of the intramolecular polarization, these permanent atomic multipoles can then be applied in modeling alternative conformations of a molecule. Equipped with this simple technique, one can derive transferable electrostatic parameters for peptides and proteins using flexible model compounds such as dipeptides. The proposed procedure is tested for its ability to describe the electrostatic potential around various configurations of the N‐methylacetamide dimer. The effect of different intramolecular polarization schemes on the accuracy of a force field model of the electrostatic potential of alanine dipeptide is investigated. A group‐based scheme for including direct intramolecular polarization is shown to be most successful in accounting for the conformational dependence of electrostatic potentials.

Calculation of protein–ligand binding free energy by using a polarizable potential

The binding of charged ligands benzamidine and diazamidine to trypsin was investigated by using a polarizable potential energy function and explicit-water molecular dynamics simulations. The binding free energies were computed from the difference between the free energies of decoupling the ligand from water and protein environments. Both the absolute and the relative free energies from the perturbation simulations agree with experimental measurements to within 0.5 kcal·mol−1. Comparison of free-energy components sampled from different thermodynamic paths indicates that electrostatics is the main driving force behind benzamidine recognition of trypsin. The contribution of electronic polarization to binding appears to be crucial. By computing the free-energy contribution caused by the polarization between the ligand and its surroundings, we found that polarization has the opposite effect in dissimilar environments. Although polarization favors ligand solvation in water, it weakens the protein–ligand attraction by screening the electrostatic interaction between trypsin and benzamidine. We also examined the relative binding free energies of a benzamidine analog diazamidine to trypsin. The changes in free energy on benzamidine-diazamidine substitution were tens of kilocalories in both water and trypsin environments; however, the change in the total binding free energy is <2 kcal·mol−1 because of cancellation, consistent with the experimental results. Overall, our results suggest that the use of a polarizable force field, given adequate sampling, is capable of achieving chemical accuracy in molecular simulations of protein–ligand recognition.

Towards accurate solvation dynamics of divalent cations in water using the polarizable amoeba force field: From energetics to structure

Molecular dynamics simulations were performed using a modified amoeba force field to determine hydration and dynamical properties of the divalent cations Ca2+ and Mg2+. The extension of amoeba to divalent cations required the introduction of a cation specific parametrization. To accomplish this, the Thole polarization damping model parametrization was modified based on the ab initio polarization energy computed by a constrained space orbital variation energy decomposition scheme. Excellent agreement has been found with condensed phase experimental results using parameters derived from gas phase ab initio calculations. Additionally, we have observed that the coordination of the calcium cation is influenced by the size of the periodic water box, a recurrent issue in first principles molecular dynamics studies.

Biomolecular electrostatics and solvation: a computational perspective

An understanding of molecular interactions is essential for insight into biological systems at the molecular scale. Among the various components of molecular interactions, electrostatics are of special importance because of their long-range nature and their influence on polar or charged molecules, including water, aqueous ions, proteins, nucleic acids, carbohydrates, and membrane lipids. In particular, robust models of electrostatic interactions are essential for understanding the solvation properties of biomolecules and the effects of solvation upon biomolecular folding, binding, enzyme catalysis, and dynamics. Electrostatics, therefore, are of central importance to understanding biomolecular structure and modeling interactions within and among biological molecules. This review discusses the solvation of biomolecules with a computational biophysics view toward describing the phenomenon. While our main focus lies on the computational aspect of the models, we provide an overview of the basic elements of biomolecular solvation (e.g. solvent structure, polarization, ion binding, and non-polar behavior) in order to provide a background to understand the different types of solvation models.

Virtual screening using molecular simulations

Effective virtual screening relies on our ability to make accurate prediction of protein‐ligand binding, which remains a great challenge. In this work, utilizing the molecular‐mechanics Poisson‐Boltzmann (or Generalized Born) surface area approach, we have evaluated the binding affinity of a set of 156 ligands to seven families of proteins, trypsin β, thrombin α, cyclin‐dependent kinase (CDK), cAMP‐dependent kinase (PKA), urokinase‐type plasminogen activator, β‐glucosidase A, and coagulation factor Xa. The effect of protein dielectric constant in the implicit‐solvent model on the binding free energy calculation is shown to be important. The statistical correlations between the binding energy calculated from the implicit‐solvent approach and experimental free energy are in the range of 0.56–0.79 across all the families. This performance is better than that of typical docking programs especially given that the latter is directly trained using known binding data whereas the molecular mechanics is based on general physical parameters. Estimation of entropic contribution remains the barrier to accurate free energy calculation. We show that the traditional rigid rotor harmonic oscillator approximation is unable to improve the binding free energy prediction. Inclusion of conformational restriction seems to be promising but requires further investigation. On the other hand, our preliminary study suggests that implicit‐solvent based alchemical perturbation, which offers explicit sampling of configuration entropy, can be a viable approach to significantly improve the prediction of binding free energy. Overall, the molecular mechanics approach has the potential for medium to high‐throughput computational drug discovery. Proteins 2011;

Trypsin-ligand binding free energies from explicit and implicit solvent simulations with polarizable potential.

We have calculated the binding free energies of a series of benzamidine‐like inhibitors to trypsin with a polarizable force field using both explicit and implicit solvent approaches. Free energy perturbation has been performed for the ligands in bulk water and in protein complex with molecular dynamics simulations. The binding free energies calculated from explicit solvent simulations are well within the accuracy of experimental measurement and the direction of change is predicted correctly in all cases. We analyzed the molecular dipole moments of the ligands in gas, water and protein environments. Neither binding affinity nor ligand solvation free energy in bulk water shows much dependence on the molecular dipole moments of the ligands. Substitution of the aromatic or the charged group in the ligand results in considerable change in the solvation energy in bulk water and protein whereas the binding affinity varies insignificantly due to cancellation. The effect of chemical modification on ligand charge distribution is mostly local. Replacing benzene with diazine has minimal impact on the atomic multipoles at the amidinium group. We have also utilized an implicit solvent based end‐state approach to evaluate the binding free energies of these inhibitors. In this approach, the polarizable multipole model combined with Poisson‐Boltzmann/surface area (PMPB/SA) provides the electrostatic interaction energy and the polar solvation free energy. Overall the relative binding free energies obtained from the MM‐PMPB/SA model are in good agreement with the experimental data.

Polarizable Atomic Multipole Solutes in a Poisson-Boltzmann Continuum

Modeling the change in the electrostatics of organic molecules upon moving from vacuum into solvent, due to polarization, has long been an interesting problem. In vacuum, experimental values for the dipole moments and polarizabilities of small, rigid molecules are known to high accuracy; however, it has generally been difficult to determine these quantities for a polar molecule in water. A theoretical approach introduced by Onsager [J. Am. Chem. Soc. 58, 1486 (1936)] used vacuum properties of small molecules, including polarizability, dipole moment, and size, to predict experimentally known permittivities of neat liquids via the Poisson equation. Since this important advance in understanding the condensed phase, a large number of computational methods have been developed to study solutes embedded in a continuum via numerical solutions to the Poisson-Boltzmann equation. Only recently have the classical force fields used for studying biomolecules begun to include explicit polarization in their functional forms. Here the authors describe the theory underlying a newly developed polarizable multipole Poisson-Boltzmann (PMPB) continuum electrostatics model, which builds on the atomic multipole optimized energetics for biomolecular applications (AMOEBA) force field. As an application of the PMPB methodology, results are presented for several small folded proteins studied by molecular dynamics in explicit water as well as embedded in the PMPB continuum. The dipole moment of each protein increased on average by a factor of 1.27 in explicit AMOEBA water and 1.26 in continuum solvent. The essentially identical electrostatic response in both models suggests that PMPB electrostatics offers an efficient alternative to sampling explicit solvent molecules for a variety of interesting applications, including binding energies, conformational analysis, and pK(a) prediction. Introduction of 150 mM salt lowered the electrostatic solvation energy between 2 and 13 kcalmole, depending on the formal charge of the protein, but had only a small influence on dipole moments.