Fast and accurate macromolecular solvation energy and force computations

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.