## Fast and accurate macromolecular solvation energy and force computations

##### Abstract

This thesis reports a comprehensive study of the electrostatic solvation
energy computation for macromolecules. In the molecular dynamics (MD)
simulations it is important to be able to compute the free energy of the system
accurately and efficiently. The solvation energy which is dominated by
the electrostatics plays a significant role in the dynamics of macromolecules
in solution. The standard way of computing the electrostatic solvation energy
is to solve the Poisson-Boltzmann (PB) equations. However, due to the
large size of the system, the computation cost of solving the PB equation becomes
a bottleneck even for the continuum implicit solvent. The alternative
method is the newly developed generalized Born (GB) method which gives
a good approximation to the PB calculation if the Born radii are properly
computed. The computation of the Born radii is the core computation in the
GB method and is laborious. In this thesis we present a novel error-bounded
fast surface GB approach which significantly improves the traditional surface GB approaches. An analytic algebraic spline model is built for the geometric
model of the molecular surfaces which allows one to do the accurate computation
on a coarse mesh. Based on the surface GB theory, we develop an
algorithm that computes the Born radii by using the fast summation algorithm
at a complexity nearly linear in terms of the number of atoms of the
molecule and the number of elements on the mesh of the molecular surface.
The algorithm is also extended to the electrostatic forces calculations. Finally
we propose a hierarchical coarse grained (CG) model aiming at reducing the
number of atoms in a macromolecule while still being able to reproduce the
geometry as well as the electrostatic interactions of the atomic model.

##### Description

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