(377f) PB-[S]AM, a Novel Solution to the Poisson-Boltzmann Equation for Applications Ranging from Protein Simulations to Polymer Membrane Design

Authors: 
Felberg, L., UC Berkeley
Head-Gordon, T., Lawrence Berkeley National Laboratory
While molecular dynamics (MD) simulations routinely and beneficially address questions concerning detailed structure and kinetic rates of assembly over fast timescales, there is another set of problems on the mesoscale that surpass the limits of timescale and size for MD. Fortunately, coarse-graining (CG) the participating nanoscale structures and their environment, combined with simulations using stochastic dynamics, can be just as insightful as the all-atom dynamics.

Electrostatic forces often dominate interactions in applications ranging from recognition events for biomolecular complex formation to proton transport in membranes. For this reason, a realistic simulation must include an accurate treatment of bulk electrolytes for large-scale systems. This can be achieved using continuum mean-field theory with the Poisson-Boltzmann (PB) equation, which, under the low-field condition, may be simplified to the linearized Poisson-Boltzmann equation (LPBE). 

Our group has achieved a fundamental result in deriving the first completely general analytical solution to the LPBE for computing screened (salty) electrostatic interactions between arbitrary numbers of nanoscale spheres of arbitrarily complex charge distributions, separated by arbitrary distance. This analytical solution, PB-AM, serves as the foundation of a semi-analytical approach to solving the LPBE for any shape (PB-SAM). We have recently incorporated PB-SAM into a Brownian Dynamics approach to create a robust CG simulation tool to study a range of biological systems. 

Overall, PB­-SAM has many benefits when compared to other PB solvers including accuracy, flexibility and memory management. We are currently working to integrate this package into the distributed software package APBS, and are continually seeking methods to improve the software. Additionally, we are continually working to improve PB-SAM’s efficiency, leveraging additional parallelization through further OpenMP implementations and exploring the option of MPI parallelization. We are also introducing the 3- or 4-body approximation to speed-up the n-body polarization.

This program has been used to examine protein-protein interactions in a crowded environment, and will be used in the future to explore  fundamental issues in performance properties of polymer electrolyte membranes, particularly in regards to water flooding and insufficient ion transport, which have prevented the widespread commercialization of it as a replacement for the common battery.