Enzymatic minimum free energy path calculations using swarms of trajectories

Accelerated computation of free energy profile at ab initio quantum mechanical/molecular mechanical accuracy via a semi-empirical reference potential. II. Recalibrating semi-empirical parameters with force matching

An efficient and accurate reference potential simulation protocol is proposed for producing ab initio quantum mechanical/molecular mechanical (AI-QM/MM) quality free energy profiles for chemical reactions in a solvent or macromolecular environment. This protocol involves three stages: (a) using force matching to recalibrate a semi-empirical quantum mechanical (SE-QM) Hamiltonian for the specific reaction under study; (b) employing the recalibrated SE-QM Hamiltonian (in combination with molecular mechanical force fields) as the reference potential to drive umbrella samplings along the reaction pathway; and (c) computing AI-QM/MM energy values for collected configurations from the sampling and performing weighted thermodynamic perturbation to acquire an AI-QM/MM corrected reaction free energy profile. For three model reactions (identity SN2 reaction, Menshutkin reaction, and glycine proton transfer reaction) in aqueous solution and one enzyme reaction (Claisen arrangement in chorismate mutase), our simulations using recalibrated PM3 SE-QM Hamiltonians well reproduced QM/MM free energy profiles at the B3LYP/6-31G* level of theory all within 1 kcal mol-1 with a 20 to 45 fold reduction in the computer time.

Mapping Free Energy Pathways for ATP Hydrolysis in the E. coli ABC Transporter HlyB by the String Method

HlyB functions as an adenosine triphosphate (ATP)-binding cassette (ABC) transporter that enables bacteria to secrete toxins at the expense of ATP hydrolysis. Our previous work, based on potential energy profiles from combined quantum mechanical and molecular mechanical (QM/MM) calculations, has suggested that the highly conserved H-loop His residue H662 in the nucleotide binding domain (NBD) of E. coli HlyB may catalyze the hydrolysis of ATP through proton relay. To further test this hypothesis when entropic contributions are taken into account, we obtained QM/MM minimum free energy paths (MFEPs) for the HlyB reaction, making use of the string method in collective variables. The free energy profiles along the MFEPs confirm the direct participation of H662 in catalysis. The MFEP simulations of HlyB also reveal an intimate coupling between the chemical steps and a local protein conformational change involving the signature-loop residue S607, which may serve a catalytic role similar to an Arg-finger motif in many ATPases and GTPases in stabilizing the phosphoryl-transfer transition state.

Measurement and Prediction of Chlorine Kinetic Isotope Effects in Enzymatic Systems

Approaches to determine chlorine kinetic isotope effects (Cl-KIEs) on enzymatic dehalogenations are discussed and illustrated by representative examples. Three aspects are considered. First methodology for experimental measurement of Cl-KIEs, with stress being on FAB-IRMS technique developed in our laboratory, is described. Subsequently, we concentrate our discussion on the consequences of reaction complexity in the interpretation of experimental values, a problem especially important in cases of polychlorinated reactants. The most fruitful studies of enzymatic dehalogenations by Cl-KIEs require their theoretical evaluation, hence the computational focus of the second part of this chapter.

QM/MM free energy simulations: recent progress and challenges

Due to the higher computational cost relative to pure molecular mechanical (MM) simulations, hybrid quantum mechanical/molecular mechanical (QM/MM) free energy simulations particularly require a careful consideration of balancing computational cost and accuracy. Here we review several recent developments in free energy methods most relevant to QM/MM simulations and discuss several topics motivated by these developments using simple but informative examples that involve processes in water. For chemical reactions, we highlight the value of invoking enhanced sampling technique (e.g., replica-exchange) in umbrella sampling calculations and the value of including collective environmental variables (e.g., hydration level) in metadynamics simulations; we also illustrate the sensitivity of string calculations, especially free energy along the path, to various parameters in the computation. Alchemical free energy simulations with a specific thermodynamic cycle are used to probe the effect of including the first solvation shell into the QM region when computing solvation free energies. For cases where high-level QM/MM potential functions are needed, we analyze two different approaches: the QM/MM-MFEP method of Yang and co-workers and perturbative correction to low-level QM/MM free energy results. For the examples analyzed here, both approaches seem productive although care needs to be exercised when analyzing the perturbative corrections.

Generalized Ensemble Sampling of Enzyme Reaction Free Energy Pathways

Free energy path sampling plays an essential role in computational understanding of chemical reactions, particularly those occurring in enzymatic environments. Among a variety of molecular dynamics simulation approaches, the generalized ensemble sampling strategy is uniquely attractive for the fact that it not only can enhance the sampling of rare chemical events but also can naturally ensure consistent exploration of environmental degrees of freedom. In this review, we plan to provide a tutorial-like tour on an emerging topic: generalized ensemble sampling of enzyme reaction free energy path. The discussion is largely focused on our own studies, particularly ones based on the metadynamics free energy sampling method and the on-the-path random walk path sampling method. We hope that this minipresentation will provide interested practitioners some meaningful guidance for future algorithm formulation and application study.