Elasticity of peptide omega bonds

Prahlada Rao V, K. Nagappa L, Balasubramanian S, Balaram H. Slow ligand-induced conformational switch increases the catalytic rate in Plasmodium falciparum hypoxanthine guanine xanthine phosphoribosyltransferase

Coupled events of ligand-induced isomerization and oligomerization in catalysis by PfHGXPRT.

Protecting High Energy Barriers: A New Equation to Regulate Boost Energy in Accelerated Molecular Dynamics Simulations

Molecular dynamics (MD) is one of the most common tools in computational chemistry. Recently, our group has employed accelerated molecular dynamics (aMD) to improve the conformational sampling over conventional molecular dynamics techniques. In the original aMD implementation, sampling is greatly improved by raising energy wells below a predefined energy level. Recently, our group presented an alternative aMD implementation where simulations are accelerated by lowering energy barriers of the potential energy surface. When coupled with thermodynamic integration simulations, this implementation showed very promising results. However, when applied to large systems, such as proteins, the simulation tends to be biased to high energy regions of the potential landscape. The reason for this behavior lies in the boost equation used since the highest energy barriers are dramatically more affected than the lower ones. To address this issue, in this work, we present a new boost equation that prevents oversampling of unfavorable high energy conformational states. The new boost potential provides not only better recovery of statistics throughout the simulation but also enhanced sampling of statistically relevant regions in explicit solvent MD simulations.

Examining the limits of time reweighting and Kramers' rate theory to obtain correct kinetics from accelerated molecular dynamics

Accelerated molecular dynamics simulations are routinely being used to recover the correct canonical probability distributions corresponding to the original potential energy landscape of biomolecular systems. However, the limits of time reweighting, based on transition state theory, in obtaining true kinetic rates from accelerated molecular dynamics for biomolecular systems are less obvious. Here, we investigate this issue by studying the kinetics of cis-trans isomerization of peptidic omega bond by accelerated molecular dynamics. We find that time reweighting is valid for obtaining true kinetics when the original potential is not altered at the transition state regions, as expected. When the original potential landscape is modified such that the applied boost potential alters the transition state regions, time reweighting fails to reproduce correct kinetics and the reweighted rate is much slower than the true rate. By adopting the overdamped limit of Kramers' rate theory, we are successful in recovering correct kinetics irrespective of whether or not the transition state regions are modified. Furthermore, we tested the validity of the acceleration weight factor from the path integral formalism for obtaining the correct kinetics of cis-trans isomerization. It was found that this formulation of the weight factor is not suitable for long time scale processes such as cis-trans isomerization with high energy barriers.

Thermodynamics and folding pathways of trpzip2: an accelerated molecular dynamics simulation study

In this paper, we apply an enhanced sampling method introduced earlier to study the folding mechanism of a beta-hairpin, trpzip2, using an all-atom potential for the protein and an implicit model for the solvent. The enhanced sampling method allows us to obtain multiple protein folding and unfolding trajectories in relatively short simulations. The sufficient sampling of folding and unfolding events of trpzip2 makes possible a more detailed investigation of its folding landscape and thermodynamics, leading to the identification of folding pathways. The analysis of the thermodynamics involved in the folding of trpzip2 showed that this polypeptide folds by two stages: a downhill hydrophobic collapse followed by formation of native hydrogen bonds. During the hydrogen bond formation, a transition state can be identified with only one native hydrogen bond being formed, which is more consistent with a 'zip-out' mechanism. To address the dynamics in a more reliable way, explicit solvent was used for the estimation of the diffusion constant, which was used in the Kramer's theory, together with the free energy profile calculated using the enhanced sampling and the implicit solvent, to calculate the folding rate. The calculated folding time agrees well with the experimental value of 2.5 micros.

A statistical analysis of the precision of reweighting-based simulations

Various advanced simulation techniques, which are used to sample the statistical ensemble of systems with complex Hamiltonians, such as those displayed in condensed matters and biomolecular systems, rely heavily on successfully reweighting the sampled configurations. The sampled points of a system from an elevated thermal environment or on a modified Hamiltonian are reused with different statistical weights to evaluate its properties at the initial desired temperature or of the original Hamiltonian. Often, the decrease of accuracy induced by this procedure is ignored and the final results can be far from what is expected. We have addressed the reasons behind such a phenomenon and have provided a quantitative method to estimate the number of sampled points required in the crucial step of reweighting of these advanced simulation methods. We also provided examples from temperature histogram reweighting and accelerated molecular dynamics reweighting to illustrate this idea, which can be generalized to the dynamic reweighting as well. The study shows that this analysis may provide a priori guidance for the strategy of setting up the parameters of advanced simulations before a lengthy one is carried out. The method can therefore provide insights for optimizing the parameters for high accuracy simulations with finite amount of computational resources.

Estimating kinetic rates from accelerated molecular dynamics simulations: alanine dipeptide in explicit solvent as a case study

Molecular dynamics (MD) simulation is the standard computational technique used to obtain information on the time evolution of the conformations of proteins and many other molecular systems. However, for most biological systems of interest, the time scale for slow conformational transitions is still inaccessible to standard MD simulations. Several sampling methods have been proposed to address this issue, including the accelerated molecular dynamics method. In this work, we study the extent of sampling of the phi/psi space of alanine dipeptide in explicit water using accelerated molecular dynamics and present a framework to recover the correct kinetic rate constant for the helix to beta-strand transition. We show that the accelerated MD can drastically enhance the sampling of the phi/psi conformational phase space when compared to normal MD. In addition, the free energy density plots of the phi/psi space show that all minima regions are accurately sampled and the canonical distribution is recovered. Moreover, the kinetic rate constant for the helix to beta-strand transition is accurately estimated from these simulations by relating the diffusion coefficient to the local energetic roughness of the energy landscape. Surprisingly, even for such a low barrier transition, it is difficult to obtain enough transitions to accurately estimate the rate constant when one uses normal MD.

Sampling of slow diffusive conformational transitions with accelerated molecular dynamics

Slow diffusive conformational transitions play key functional roles in biomolecular systems. Our ability to sample these motions with molecular dynamics simulation in explicit solvent is limited by the slow diffusion of the solvent molecules around the biomolecules. Previously, we proposed an accelerated molecular dynamics method that has been shown to efficiently sample the torsional degrees of freedom of biomolecules beyond the millisecond timescale. However, in our previous approach, large-amplitude displacements of biomolecules are still slowed by the diffusion of the solvent. Here we present a unified approach of efficiently sampling both the torsional degrees of freedom and the diffusive motions concurrently. We show that this approach samples the configuration space more efficiently than normal molecular dynamics and that ensemble averages converge faster to the correct values.

Application of the accelerated molecular dynamics simulations to the folding of a small protein

In this paper, we further explore the applicability of the accelerated molecular dynamics simulation method using a bias potential. The method is applied to both simple model systems and real multidimensional systems. The method is also compared to replica exchange simulations in folding a small protein, Trp cage, using an all atom potential for the protein and an implicit model for the solvent. We show that the bias potential method allows quick searches of folding pathways. We also show that the choice of the bias potential has significant influence on the efficiency of the bias potential method.