Systematic coarse-graining in molecular simulations using relative entropy and generalized ensembles

Tremblett, Aidan (2019) Systematic coarse-graining in molecular simulations using relative entropy and generalized ensembles. Masters thesis, Memorial University of Newfoundland.

[English] PDF - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. Download (5MB)

Abstract

Computer simulations have become a powerful tool for studying the structure, dynamics, or other characteristics of a wide variety of physical systems. The goal of coarse-grained (CG) models is to simplify the representation of the physical system while still maintaining enough information to capture the desired properties of the system. A main challenge in the development of CG models is determining the potential energy function, UCG, which often depends on a large number of unknown model parameters, λ. Different methods for determining these model parameters have been proposed, (potential of mean force, multi-scale coarse-graining), but they rely on determining quantities, such as free energies, that are computationally challenging to calculate. Here we develop a systematic method to determine the optimal parameters for coarse-grained models of molecular systems, using the relative entropy, Srel, as a metric to compare a target ensemble to an ensemble generated from a CG model. The relative entropy depends on the free energy, and a novel approach for determining the free energy was developed, which used a generalized ensemble approach to simulate the joint probability distribution, p(r, λ), where r is a chain conformation. The generalized ensemble Monte Carlo simulation allowed the model parameters to be dynamic, which means they are allowed to change during the simulation. These simulations allow for the free energies, FCG(λ), to be obtained directly from the marginal probability distribution, p(λ), during the simulation. The relative entropy, Srel(λ), was calculated and minimized with respect to the CG model parameters in order to obtain the optimal model parameters. The systematic method was applied to an existing CG model for protein folding that was modified to include a new potential energy term that contained either 13 or 91 unknown model parameters. The method was used to systematically determined the optimal model parameters that allowed a protein to fold to its native structure. The relative entropy was calculated for two target ensembles, the experimentally determined single native structure, and the set of configurations from an all-atom simulation. It was found that the potential energy function with 91 unknown parameters converged to the optimal parameter set faster than the potential energy function with 13 unknown parameters. The optimal parameter set for the 13 model parameters was not able to fully capture the folding of the protein, while the 91 model parameter set was able to capture the folding behaviour. Furthermore, the optimal CG model parameter set that was found using the experimentally determined native structure as a target for the relative entropy minimization gave better results than the all-atom target ensemble. This is likely due to the set of configurations for the all-atom target ensemble being dominated by the unfolded state instead of a folded state.

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