Continuum solvent models have been widely used in bio-molecular modeling applications. Recently, much attention has been given to inclusion of implicit membrane models into existing continuum solvent models. A numerical Poisson-Boltzmann continuum solvation model in the Amber package was recently extended to allow incorporation of implicit membrane models. Inclusion of an implicit membrane complicates numerical solutions due to inhomogeneity in the dielectric constant along the boundary of the computational grid. Since use of periodicity to alleviate artifacts arising as a result of edge effects is commonplace in electrostatic computations, we have adapted the existing conjugate gradient solver for use with periodic boundaries. Adaptation of the conjugate gradient method was relatively straightforward, but the convergence was quite slow. To accelerate convergence, the Incomplete Cholesky preconditioning method was also adapted. A re-derivation of the preconditing matrix was required in order to account for an expansion in band structure required to describe the periodic boundary.Although additional numerical expense is required under a periodic solver, it is offset by reduction in expense of the boundary setup phase. Examples of operator matrix band structure for a simple 3x4x5 Grid.Left: Periodic Band Structure, Right: Non-periodic Band Structure

Efficient numerical Poisson-Boltzmann methods for membrane systems

246th National Meeting (2013)

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