Multiscale Convergence Optimization in Constrained Molecular Dynamics Simulations

Abstract

The energy analysis is essential for studying chemical or biochemical reactions but also for characterizing interactions between two protagonists. Molecular Dynamics Simulations are well suited to sampling interaction structures but under minimum energy. To sample unstable or high energy structures, it is necessary to apply a bias-constraint in the simulation, in order to maintain the system in a stable energy state. In MD constrained simulations of ""Umbrella Sampling"" type, the phenomenon of ligand-receptor dissociation is divided into a series of windows (space sampling) in which the simulation time is fixed in advance. A step of de-biasing and statistical processing then allows accessing to the Potential Force Medium (PMF) of the studied process. In this context, we have developed an algorithm that optimizes the DM computation time regarding each reaction coordinate (distance between the ligand and the receptor); and thus can dynamically adjust the sampling time in each US-Window. The data processing consists in studying the convergence of the distributions of the coordinate constraint and its performance is tested on different ligand-receptor systems. Its originality lies in the used processing technique which combines wavelet thresholding with statistical-tests decision in relation to distribution convergence. In this paper, we briefly describe a Molecular Dynamic Simulation, then by assumption we consider that distribution data are series of random-variables vectors obeying to a normal probality law. These vectors are first analyzed by a wavelet technique, thresholded and in a second step, their law probability is computed for comparison in terms of convergence. In this context, we give the result of PMF and computation time according to statistic-tests convergence criteria, such as Kolmogorov Smirnov, Student tTest, and ANOVA Tests. We also compare these results with those obtained after a preprocessing with Gaussian low-pass filtering in order to follow the influence of thresholding. Finally, the results are discussed and analyzed regarding the contribution of the muli-scale processing and the more suited criteria for time optimization.