Donghong Min

Essential energy space random walk via energy space metadynamics method to accelerate molecular dynamics simulations

To overcome the possible pseudoergodicity problem, molecular dynamic simulation can be accelerated via the realization of an energy space random walk. To achieve this, a biased free energy function (BFEF) needs to be priori obtained. Although the quality of BFEF is essential for sampling efficiency, its generation is usually tedious and nontrivial. In this work, we present an energy space metadynamics algorithm to efficiently and robustly obtain BFEFs. Moreover, in order to deal with the associated diffusion sampling problem caused by the random walk in the total energy space, the idea in the original umbrella sampling method is generalized to be the random walk in the essential energy space, which only includes the energy terms determining the conformation of a region of interest. This essential energy space generalization allows the realization of efficient localized enhanced sampling and also offers the possibility of further sampling efficiency improvement when high frequency energy terms irrelevant to the target events are free of activation. The energy space metadynamics method and its generalization in the essential energy space for the molecular dynamics acceleration are demonstrated in the simulation of a pentanelike system, the blocked alanine dipeptide model, and the leucine model.

On the convergence improvement in the metadynamics simulations: A Wang-Landau recursion approach

As a popular tool in exploring free energy landscapes, the metadynamics method has been widely applied to elucidate various chemical or biochemical processes. As deeply discussed by Laio et al. [J. Phys. Chem. B 109, 6714 (2005)], the size of the updating Gaussian function is pivotal to the free energy convergence toward the target free energy surface. For instance, a greater Gaussian height can facilitate the quick visit of a conformation region of interest; however, it may lead to a larger error of the calculated free energy surface. In contrast, a lower Gaussian height can guarantee a better resolution of the calculated free energy surface; however, it will take longer time for such a simulation to navigate through the defined conformational region. In order to reconcile such confliction, the authors present a method by implementing the Wang-Landau recursion scheme in the metadynamics simulations to adaptively update the height of the unit Gaussian function. As demonstrated in their model studies on both a toy system, and a realistic molecular system treated with the hybrid quantum mechanical and molecular mechanical (QMMM) potential, the present approach can quickly result in more decently converged free energy surfaces, compared with the classical metadynamics simulations employing the fixed Gaussian heights.

Practically Efficient QM/MM Alchemical Free Energy Simulations: The Orthogonal Space Random Walk Strategy

The difference between free energy changes occurring at two chemical states can be rigorously estimated via alchemical free energy (AFE) simulations. Traditionally, most AFE simulations are carried out under the classical energy potential treatment; then, accuracy and applicability of AFE simulations are limited. In the present work, we integrate a recent second-order generalized ensemble strategy, the orthogonal space random walk (OSRW) method, into the combined quantum mechanical/molecular mechanical (QM/MM) potential based AFE simulation scheme. Thereby, within a commonly affordable simulation length, accurate QM/MM alchemical free energy simulations can be achieved. As revealed by the model study on the equilibrium of a tautomerization process of hydrated 3-hydroxypyrazole and by the model calculations of the redox potentials of two flavin derivatives, lumichrome (LC) and riboflavin (RF) in aqueous solution, the present OSRW-based scheme could be a viable path toward the realization of practically efficient QM/MM AFE simulations.

Enhancing QM/MM molecular dynamics sampling in explicit environments via an orthogonal-space-random-walk-based strategy.

Accurate prediction of molecular conformations in explicit environments, such as aqueous solution and protein interiors, can facilitate our understanding of various molecular recognition processes. Most computational approaches are limited as a result of their compromised choices between the underlying energy model and the sampling length. Taking advantage of a recent second-order generalized ensemble scheme [e.g., the orthogonal space random walk (OSRW) strategy], which can synergistically accelerate the motion of a focused region and its coupled environmental response, we are presenting a QM/MM (combined quantum mechanical/molecular mechanical)-based molecular dynamics sampling technique to explore molecular conformational landscapes in explicit environments. The present QM/MM potential scaling-based OSRW sampling scheme is employed to study the binding of DMSO to the FKBP12 protein, the conformation distribution of a novel mercaptosulfonamide inhibitor in aqueous solution, and its binding poses in zinc-containing matrix metalloproteinase-9 (MMP-9). As demonstrated, the present QM/MM second-order generalized ensemble sampling technique enables feasible usage of the QM/MM model to sample molecular conformations in condensed environments.

‘In-line attack’ conformational effect plays a modest role in an enzyme-catalyzed RNA cleavage: a free energy simulation study

Since the proposal of ‘in-line attack’ conformation as a possibly important intermediate in RNA cleavage, its structure has been captured in various protein and RNA enzymes; these structures strengthen the belief that this conformation plays an essential role in the catalysis of RNA cleavage. As generally discussed, this intermediate structure can be involved in energy barrier reduction in two possible ways, e.g. through either conformational effect or electrostatic effect. In order to quantitatively elucidate the contribution of conformational effect in this type of enzyme catalysis, free energy simulations were performed on the RNA structures both in a splicing endonuclease complex and in the aqueous solution. Our free energy simulation results revealed that the ‘in-line attack’ conformational effect plays a modest role in facilitating the reaction rate enhancement (∼12-fold) compared with the overall 1012-fold rate increase. The close agreement between the present computational estimation and an experimental measurement on the spontaneous RNA cleavage in an in vitro evolved ATP aptamer motives us to realize that the conformation distribution of an enzyme substrate prior to rather than after its binding determines the upper bound of the rate enhancement ability through the conformational strategy.

An Enzymatic Atavist Revealed in Dual Pathways for Water Activation

Inosine monophosphate dehydrogenase (IMPDH) catalyzes an essential step in the biosynthesis of guanine nucleotides. This reaction involves two different chemical transformations, an NAD-linked redox reaction and a hydrolase reaction, that utilize mutually exclusive protein conformations with distinct catalytic residues. How did Nature construct such a complicated catalyst? Here we employ a “Wang-Landau” metadynamics algorithm in hybrid quantum mechanical/molecular mechanical (QM/MM) simulations to investigate the mechanism of the hydrolase reaction. These simulations show that the lowest energy pathway utilizes Arg418 as the base that activates water, in remarkable agreement with previous experiments. Surprisingly, the simulations also reveal a second pathway for water activation involving a proton relay from Thr321 to Glu431. The energy barrier for the Thr321 pathway is similar to the barrier observed experimentally when Arg418 is removed by mutation. The Thr321 pathway dominates at low pH when Arg418 is protonated, which predicts that the substitution of Glu431 with Gln will shift the pH-rate profile to the right. This prediction is confirmed in subsequent experiments. Phylogenetic analysis suggests that the Thr321 pathway was present in the ancestral enzyme, but was lost when the eukaryotic lineage diverged. We propose that the primordial IMPDH utilized the Thr321 pathway exclusively, and that this mechanism became obsolete when the more sophisticated catalytic machinery of the Arg418 pathway was installed. Thus, our simulations provide an unanticipated window into the evolution of a complex enzyme.

Allosteric activation via kinetic control: Potassium accelerates a conformational change in IMP dehydrogenase

Allosteric activators are generally believed to shift the equilibrium distribution of enzyme conformations to favor a catalytically productive structure; the kinetics of conformational exchange is seldom addressed. Several observations suggested that the usual allosteric mechanism might not apply to the activation of IMP dehydrogenase (IMPDH) by monovalent cations. Therefore, we investigated the mechanism of K(+) activation in IMPDH by delineating the kinetic mechanism in the absence of monovalent cations. Surprisingly, the K(+) dependence of k(cat) derives from the rate of flap closure, which increases by ≥65-fold in the presence of K(+). We performed both alchemical free energy simulations and potential of mean force calculations using the orthogonal space random walk strategy to computationally analyze how K(+) accelerates this conformational change. The simulations recapitulate the preference of IMPDH for K(+), validating the computational models. When K(+) is replaced with a dummy ion, the residues of the K(+) binding site relax into ordered secondary structure, creating a barrier to conformational exchange. K(+) mobilizes these residues by providing alternate interactions for the main chain carbonyls. Potential of mean force calculations indicate that K(+) changes the shape of the energy well, shrinking the reaction coordinate by shifting the closed conformation toward the open state. This work suggests that allosteric regulation can be under kinetic as well as thermodynamic control.

QM/MM Alchemical Free Energy Simulations: Challenges and Recent Developments

Abstract The difference between free energy changes occurring at two chemical states can be rigorously estimated via alchemical free energy (AFE) simulations. Traditionally, most AFE simulations are carried out under the classical energy potential treatment; then, accuracy and applicability of AFE simulations are limited. Following the natural evolution, employing the quantum mechanical (QM)-based potentials, particularly the combined QM and molecular mechanical (QM/MM) potentials, in AFE simulations is a natural next step. To make such QM/MM AFE simulations routinely applicable and reliable to complex systems, several major challenges have to be met: (1) to ensure structural integrities for robust electronic structural calculations when unphysical states are simulated; (2) to accurately describe long-range electrostatic interactions; and (3) to efficiently sample the configuration space to guarantee free energy convergence when costly QM/MM potentials are applied. This review summarizes recent developments related to these challenges.

Energy difference space random walk to achieve fast free energy calculations

A method is proposed to efficiently obtain free energy differences. In the present algorithm, free energy calculations proceed by the realization of an energy difference space random walk. Thereby, this algorithm can greatly improve the sampling of the regions in phase space where target states overlap.