Multipole electrostatics in hydration free energy calculations

Modeling Structural Coordination and Ligand Binding in Zinc Proteins with a Polarizable Potential

As the second most abundant cation in human body, zinc is vital for the structures and functions of many proteins. Zinc-containing matrix metalloproteinases (MMPs) have been widely investigated as potential drug targets in a range of diseases ranging from cardiovascular disorders to cancers. However, it remains a challenge in theoretical studies to treat zinc in proteins with classical mechanics. In this study, we examined Zn(2+) coordination with organic compounds and protein side chains using a polarizable atomic multipole based electrostatic model. We find that polarization effect plays a determining role in Zn(2+) coordination geometry in both matrix metalloproteinase (MMP) complexes and in zinc-finger proteins. In addition, the relative binding free energies of selected inhibitors binding with MMP13 have been estimated and compared with experimental results. While not directly interacting with the small molecule inhibitors, the permanent and polarizing field of Zn(2+) exerts a strong influence on the relative affinities of the ligands. The simulation results also reveal the polarization effect on binding is ligand dependent and thus difficult to be incorporated into fixed-charge models implicitly.

Automation of AMOEBA polarizable force field parameterization for small molecules

A protocol to generate parameters for the AMOEBA polarizable force field for small organic molecules has been established, and polarizable atomic typing utility, Poltype, which fully automates this process, has been implemented. For validation, we have compared with quantum mechanical calculations of molecular dipole moments, optimized geometry, electrostatic potential, and conformational energy for a variety of neutral and charged organic molecules, as well as dimer interaction energies of a set of amino acid side chain model compounds. Furthermore, parameters obtained in gas phase are substantiated in liquid-phase simulations. The hydration free energy (HFE) of neutral and charged molecules have been calculated and compared with experimental values. The RMS error for the HFE of neutral molecules is less than 1 kcal/mol. Meanwhile, the relative error in the predicted HFE of salts (cations and anions) is less than 3% with a correlation coefficient of 0.95. Overall, the performance of Poltype is satisfactory and provides a convenient utility for applications such as drug discovery. Further improvement can be achieved by the systematic study of various organic compounds, particularly ionic molecules, and refinement and expansion of the parameter database.

Probing the effect of conformational constraint on phosphorylated ligand binding to an SH2 domain using polarizable force field simulations

Preorganizing a ligand in the conformation it adopts upon binding to a protein has long been considered to be an effective way to improve affinity by making the binding entropy more favorable. However, recent thermodynamic studies of a series of complexes of the Grb2 SH2 domain with peptide analogues having constrained and flexible replacements for a phosphotyrosine residue revealed that less favorable binding entropies may result from constraining ligands in their biologically active conformations. Toward probing the origin of this unexpected finding, we examined the complexes of four phosphotyrosine-derived analogues with the Grb2 SH2 domain using molecular dynamics simulations with a polarizable force field. Significantly, the computed values for the relative binding free energies, entropies, and enthalpies of two pairs of constrained and unconstrained ligands reproduced the trends that were determined experimentally, although the relative differences were overestimated. These calculations also revealed that a large fraction of the ligands lacking the constraining element exist in solution as compact, macrocyclic-like structures that are stabilized by interactions between the phosphate groups and the amide moieties of the C-terminal pY+2 residues. In contrast, the three-membered ring in the constrained ligands prevents the formation of such macrocyclic structures, leading instead to globally extended, less ordered conformations. Quasiharmonic analysis of these conformational ensembles suggests that the unconstrained ligands possess significantly lower entropies in solution, a finding that is consistent with the experimental observation that the binding entropies for the unconstrained ligands are more favorable than for their constrained counterparts. This study suggests that introducing local constraints in flexible molecules may have unexpected consequences, and a detailed understanding of the conformational preferences of ligands in their unbound states is a critical prerequisite to correlating changes in their chemical structure with protein binding entropies and enthalpies.

Polarizable Atomic Multipole-based Molecular Mechanics for Organic Molecules

An empirical potential based on permanent atomic multipoles and atomic induced dipoles is reported for alkanes, alcohols, amines, sulfides, aldehydes, carboxylic acids, amides, aromatics and other small organic molecules. Permanent atomic multipole moments through quadrupole moments have been derived from gas phase ab initio molecular orbital calculations. The van der Waals parameters are obtained by fitting to gas phase homodimer QM energies and structures, as well as experimental densities and heats of vaporization of neat liquids. As a validation, the hydrogen bonding energies and structures of gas phase heterodimers with water are evaluated using the resulting potential. For 32 homo- and heterodimers, the association energy agrees with ab initio results to within 0.4 kcal/mol. The RMS deviation of hydrogen bond distance from QM optimized geometry is less than 0.06 Å. In addition, liquid self-diffusion and static dielectric constants computed from molecular dynamics simulation are consistent with experimental values. The force field is also used to compute the solvation free energy of 27 compounds not included in the parameterization process, with a RMS error of 0.69 kcal/mol. The results obtained in this study suggest the AMOEBA force field performs well across different environments and phases. The key algorithms involved in the electrostatic model and a protocol for developing parameters are detailed to facilitate extension to additional molecular systems.