Citation:

E. C. Cyr, Numerical Methods for Computing the Free-Energy of Coarse-Grained Molecular Systems, PhD Thesis, Department of Computer Science, University of Illinois at Urbana-Champaign, November 2008.

Abstract:

Coarse-grained models reduce the number of degrees of freedom in a molecular system. Key to these models is accounting for the mean effect of the fine degrees of freedom decoupled from the coarse system. The mean effect is expressed as a thermodynamic quantity known as the free energy. In this thesis, we develop numerical methods for computing the free energy of two distinct coarse-grained systems.

We first consider computing the potential of mean force (PMF) along a single degree of freedom. Our approach is to develop algorithms based on the method of weighted residuals (WRM) and maximum likelihood estimation (MLE). We show that traditional methods, like thermodynamic integration and the direct histogram method, are specific instances of the WRM and MLE. The efficacy of the WRM and MLE is demonstrated using two sample systems. Results indicate that methods based on WRM are more robust with respect to the size of the solution space, while those based on MLE, are more accurate. We also show how both the MLE and WRM can be used to perform adaptive sampling. This leads to the development of the ABF-WRM, which combines the flexibility of the WRM framework with the enhanced sampling of the adaptive biasing force (ABF) method.

The second coarse-grained system reduces a fully explicit solvent-solute system to an explicit solute in an implicitly represented solvent environment. The critical step in this reduction is to solve a partial differential equation known as the Poisson-Boltzmann equation. We develop algorithms that accurately compute the solvation free energy by using goal-oriented mesh refinement. Results indicating the benefits of goal-oriented refinement are presented.

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Last updated November 26, 2008