Poisson-Boltzmann theory of bionanosystems

The structure and function of BNS (bionanosystems) such as macromolecules, viruses and ribosomes are strongly affected by electrostatic interactions. Yet their supra-million atom size makes them difficult to simulate via a straightforward Poisson-Boltzmann (PB) approach. Here we explore a multiscale approach that results in a coarse-grained PB equation that follows rigorously from the all-atom PB equation. The derivation of the coarse-grained equation follows from an ansatz on the dependence of the electrical potential in two distinct ways, i.e.~one reflecting atomic-scale variations and the other capturing nanometer-scale features. With this ansatz and a series expansion of the potential in a length-scale ratio, the coarse-grained PB equation is obtained. This multiscale methodology and an efficient computational methodology provide a way to efficiently simulate BNS electrostatics with atomic-scale resolution for the first time, avoiding the need for excessive supercomputer resources. The coarse-grained PB equation contains a tensorial dielectric constant that mediates the channeling of the electric field along macromolecules in an aqueous medium. The multiscale approach and novel salinity connections to the PB equation presented here should enhance the accuracy and wider applicability of PB modeling