Citation
E. C. Cyr, Numerical Methods for Computing the FreeEnergy of
CoarseGrained Molecular Systems, PhD Thesis, Department
of Computer Science, University of Illinois at UrbanaChampaign,
November 2008.
Abstract
Coarsegrained 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 coarsegrained 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 ABFWRM, which combines the flexibility of the WRM framework with the
enhanced sampling of the adaptive biasing force (ABF) method.
The second coarsegrained system reduces a fully explicit
solventsolute 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 PoissonBoltzmann equation. We
develop algorithms that accurately compute the solvation free
energy by using goaloriented mesh refinement. Results indicating
the benefits of goaloriented refinement are presented.
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