Numerical Methods that Solve the PBE for Biomolecular Electrostatics

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By combining several innovative numerical methods, solutions to the modified Poisson-Boltzmann equation (mPBE) will be computed an order of magnitude faster than currently possible. The effort builds upon a previously developed efficient Poisson-Boltzmann solver and extends it to tackle the computationally more demanding mPBE. In Phase I, a preliminary version of the mPBE solver will be developed and tested for biomolecular configurations where the Poisson-Boltzmann equation is known to break down, such as highly charged biomolecules in multivalent salt environments. In Phase II, this model will be further refined, incorporated into an electrostatics modeling software package and used to study biologically significant systems requiring the mPBE-based level of physics modeling. Distribution of this software will allow researchers and biotech business to simulate highly charged biomolecules upon readily available computers. Specific Aims. The Phase I specific aims are as follows. (1) Select the appropriate mPBE theory that both captures the important physical behavior of highly charged biomolecules (e.g., volume exclusion, finite ion size, image effects at the molecular surface) and achieves fast computational performance using advanced numerical methods, and formulate numerical solution strategies. (2) Implement the approach in Aim (1) and conduct preliminary testing of the resulting software. (3) Conduct preliminary studies using the fast mPBE solver to assess the salt-dependent behavior of complex-shape biopolymers in multivalent salt solutions. Research Design. The Phase I research plan addresses the high-risk elements of the overall Phase I and II endeavor by demonstrating efficient mPBE calculations for generally-shaped biomolecules using carefully tailored computational methods. Thus, Phase I is concerned with the formulation, software implementation and testing of the mPBE solver. Methods. Components from existing software will be reconfigured for mPBE-based calculations. The main component is an adaptive Cartesian grid, which combines a hierarchical, octree decomposition of the domain and a singularity-free representation of the potential solution to minimize grid point count and thus computational cost. A new, self-consistent outer boundary treatment is also used to reduce domain size. Various mesh and multigrid options will be explored to expedite evaluation of the fluctuation potentials. Long Term Objectives. The computational methods will be incorporated into a software package offering a suite of electrostatics models with diverse computational performance and modeling fidelity options. The software will be distributed through an established molecular modeling vendor. Interfaces with existing MD codes and visualization software will also allow alternate distribution paths. Health Relatedness and relevance to Mission of the NIGMS Institute. This effort addresses the growing need for fast and accurate computer simulation of biologically important processes.