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Méthodes numériques pour la simulation d'évènements rares en dynamique moléculaire

Abstract : In stochastic dynamical systems, such as those encountered in molecular dynamics, rare events naturally appear as events due to some low probability stochastic fluctuations. Examples of rare events in our everyday life includes earthquakes and major floods. In chemistry, protein folding, ligandunbinding from a protein cavity and opening or closing of channels in cell membranes are examples of rare events. Simulation of rare events has been an important field of research in biophysics over the past thirty years.The events of interest in molecular dynamics generally involve transitions between metastable states, which are regions of the phase space where the system tends to stay trapped. These transitions are rare, making the use of a naive, direct Monte Carlo method computationally impracticable. To dealwith this difficulty, sampling methods have been developed to efficiently simulate rare events. Among them are splitting methods, that consists in dividing the rare event of interest into successive nested more likely events.Adaptive Multilevel Splitting (AMS) is a splitting method in which the positions of the intermediate interfaces, used to split reactive trajectories, are adapted on the fly. The surfaces are defined suchthat the probability of transition between them is constant, which minimizes the variance of the rare event probability estimator. AMS is a robust method that requires a small quantity of user defined parameters, and is therefore easy to use.This thesis focuses on the application of the adaptive multilevel splitting method to molecular dynamics. Two kinds of systems are studied. The first one contains simple models that allowed us to improve the way AMS is used. The second one contains more realistic and challenging systems, where AMS isused to get better understanding of the molecular mechanisms. Hence, the contributions of this thesis include both methodological and numerical results.We first validate the AMS method by applying it to the paradigmatic alanine dipeptide conformational change. We then propose a new technique combining AMS and importance sampling to efficiently sample the initial conditions ensemble when using AMS to obtain the transition time. This is validatedon a simple one dimensional problem, and our results show its potential for applications in complex multidimensional systems. A new way to identify reaction mechanisms is also proposed in this thesis.It consists in performing clustering techniques over the reactive trajectories ensemble generated by the AMS method.The implementation of the AMS method for NAMD has been improved during this thesis work. In particular, this manuscript includes a tutorial on how to use AMS on NAMD. The use of the AMS method allowed us to study two complex molecular systems. The first consists in the analysis of the influence of the water model (TIP3P and TIP4P/2005) on the β -cyclodextrin and ligand unbinding process. In the second, we apply the AMS method to sample unbinding trajectories of a ligand from the N-terminal domain of the Hsp90 protein.
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Submitted on : Friday, August 14, 2020 - 9:56:47 AM
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Laura Silva Lopes. Méthodes numériques pour la simulation d'évènements rares en dynamique moléculaire. Topologie générale [math.GN]. Université Paris-Est, 2019. Français. ⟨NNT : 2019PESC1045⟩. ⟨tel-02915306⟩



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