An overview of numerical algorithms for the Poisson-Boltzmann equation in biomolecular electrostatics
When
February 1, 2019 | 2:30 - 3.30 p.m.
Where
Campbell Hall 443
Speaker
Dr. Shan Zhao, University of Alabama
Abstract
The Poisson-Boltzmann Equation (PBE) is a widely used implicit solvent model for the electrostatic analysis of solvated biomolecules. The numerical solution of the PBE is known to be challenging, due to the consideration of discontinuous coefficients, complex geometry of protein structures, singular source terms, and strong nonlinearity. In this talk, I will offer a brief overview of recent studies in the literature as well as new developments in our group for resolving the PB numerical difficulties.
- For treating dielectric interface and complex geometry, both finite element methods and Cartesian grid finite difference methods have been developed for delivering a second order accuracy in space.
- In the framework of pseudo-time integration, we have constructed an analytical treatment to suppress the nonlinear instability.
- For treating charge singularity in solvated biomolecules, we have introduced a new regularization approach, which combines the efficiency of two-component schemes with the accuracy of the three-component methods. Finally, numerical experiments of several benchmark examples and free energy calculations of protein systems are presented to demonstrate the stability, accuracy, and efficiency of the new algorithms.