Dexuan Xie
Calculation of electrostatics for a biomolecule (or a complex of a protein with a drug molecule) in an ionic solvent is a fundamental task in the fields of structural biology, computational biochemistry, biophysics, and mathematical biology. The Poisson-Boltzmann equation (PBE) is one commonly used dielectric model for predicting electrostatics of ionic solvated biomolecules. It has played important roles in rational drug design and protein design as well as other bioengineering applications. However, it is known not to work properly near a highly charged biomolecular surface, since it does not reflect any polarization correlation among water molecules and ionic size effects.
To improve the quality of PBE in the calculation of electrostatic solvation and binding free energies, we made many progresses recently on the study of nonlocal dielectric models, and developed several fast nonlocal model solvers. Meanwhile, we developed new numerical algorithms for solving PBE and one size modified PBE by using finite element, finite difference, solution decomposition, domain decomposition, and multigrid methods.
In this talk, I will first review our nonlocal dielectric theory. I then will present a new nonlocal PBE and its finite element solver. I will also describe our new numerical algorithms for solving PBE and one size modified PBE. A collection of these new solvers has led to a new software tool, called SDPBS (Solution Decomposition Poisson-Boltzmann Solvers), which is available online for free through our web server. Finally, application examples for chemical molecules, proteins, protein-drug, and peptide-RNA will be given to demonstrate the high performance and numerical stability of SDPBE in the calculation of salvation and binding free energies. This project is a joined work with Prof. L. Ridgway Scott at the University of Chicago under the support by NSF grants (DMS-0921004, DMS-1226259, and DMS-1226019).
Dexuan XieIn this talk, I will introduce hybrid methods that we developed recently using solution and domain decompositions, finite element, and finite difference techniques to fast calculate the electrostatics of protein in ionic solvent. In particular, they have been applied to the numerical solutions of three dielectric continuum models – the Poisson-Boltzmann equation, a size modified Poisson-Boltzmann equation, and a nonlocal modified Poisson-Boltzmann equation. Their performance will be discussed and compared with the corresponding finite element solvers. These hybrid techniques can also be extended to solve a class of nonlinear interface boundary value problems. This project is a joined work with my student, Jinyong Ying, under the support by NSF award DMS-1226259.