QM/MM Reweighting Free Energy SCF for Geometry Optimization on Extensive Free Energy Surface of Enzymatic Reaction

Abstract

We developed a quantum mechanical/molecular mechanical (QM/MM) free energy geometry optimization method by which the geometry of a quantum chemically treated (QM) molecule is optimized on a free energy surface defined with thermal distribution of the surrounding molecular environment obtained by molecular dynamics simulation with a molecular mechanics (MM) force field. The method called QM/MM reweighting free energy self-consistent field combines a mean field theory of QM/MM free energy geometry optimization developed by Yamamoto (Yamamoto, T. J. Chem. Phys.2008, 129, 244104) with a reweighting scheme for updating the MM distribution introduced by Hu et al. (Hu, H., et al. J. Chem. Phys.2008, 128, 034105) and features high computational efficiency suitable for exploring the reaction free energy surface of extensive protein conformational space. The computational efficiency with improved treatment of a long-range electrostatic (ES) interaction using the Ewald summation technique permits one to take into account global conformational relaxation of an entire protein of an enzyme in the free energy geometry optimization of its reaction center. We applied the method to an enzymatic reaction of a substrate complex of psychrophilic α-amylase from Antarctic bacterium Pseudoalteromonas haloplanktis and succeeded in geometry optimizations of the reactant and the product of the catalytic reaction that involve large conformational changes of protein loops adjacent to the reaction center on time scales reaching sub-microseconds. We found that the adjacent loops in the reactant and the product form in different conformations and produce catalytic ES potentials on the reaction center.

Molecular Mechanism of Wide Photoabsorption Spectral Shifts of Color Variants of Human Cellular Retinol Binding Protein II

“…The free energy geometry optimization was first performed for M4 color variant. The optimization required 50 cycles of the sequential sampling, 18 i.e., MD simulation for 500 ns in total ( Figure S3c). During the simulations of M4 variant, two water molecules occupied a cavity in the vicinity of PSB in 15-syn form and one of them formed a hydrogen-bond with PSB (Figures 3a, S3, and S4).…”

“…18 In the method, the electronic wave function and the molecular geometry of the QM part are optimized on a mean field free energy surface constructed with statistical samples of MM configurations obtained by classical MD simulations. Accordingly, the direct coupling of the quantum mechanically treated electronic and geometric changes of the chromophore with slow and/or large conformational changes of the protein upon mutations treated with MM force field can be taken into account.…”

A Blue-shifted Light-driven Proton Pump for Neural Silencing

“…The simulation systems of the native protein and the triple mutant (M118A/S141A/A215T, corresponding to M126A/ S149A/A223T of HwBR) with a manually rotated ␤-ionone ring were first equilibrated by molecular dynamics simulations with molecular mechanics force fields. Molecular structures of the active site including the RPSB and the polar groups in the vicinity of protonated Schiff base, Arg-82, Asp-85, Glu-121, and three water molecules (Wat-401, Wat-402, and Wat-406) were then refined by QM/MM reweighting free energy self-consistent field (RWFE-SCF) geometry optimizations (25). The QM/MM RWFE-SCF method optimized the molecular geometries of the active site at the QM level of theory (density functional theory with B3LYP functional) on a free energy surface constructed with MM conformational statistical samples of the surrounding protein environment obtained by the molecular dynamics simulations.…”

QM/MM free energy simulations: recent progress and challenges

“…We focus on problems in which a direct sampling of the QM/MM potential function is important, although we also discuss the elegant minimum free energy path method of Yang and co-workers 11 (also see Ref. 43,44 ), in which the QM and MM fluctuations are decoupled and therefore finite-temperature sampling is done mainly for the MM degrees of freedom. For direct sampling, it is crucial to develop a low-level QM/MM potential that provides a semi-quantitative description of the underlying potential energy surface.…”