Size-Modified Poisson-Boltzmann Electrostatics for Realistic Biomolecular Systems

Abstract

Calculating the electrostatic potential (EP) around a biomolecule is essential for many types of biomolecular modeling. When a biomolecule is solvated by an ionic solution, the EP of the system is typically approximated by the solution of the Poisson-Boltzmann equation (PBE). This is a good approximation when the biomolecule is not highly charged. However, the concentrations of counterions can exceed their maximum packing densities near the highly charged regions of the biomolecule as PBE neglects the finite ion radii. A size-modified Poisson-Boltzmann equation (SMPBE) has previously been formulated to integrate ion sizes into PBE to calculate more accurate EP and ion distributions around biomolecules. Here, we extend the implementation of SMPBE to realistic biomolecular systems that contain an arbitrary number of ion species with non-uniform sizes. Specifically, we apply our method to study the Ca++ adsorption to the negatively charged cytoplasmic side of the sarcolemma by electrostatic forces. We use an atomic representation of the sarcolemma for the EP calculation and the solution surrounding the sarcolemma contains Ca++, Na+, K+ and Cl- ions. Our calculations indicate that, out of all the counterions, Ca++ is the most energetically favorable to be adsorbed to the negatively charged lipid head groups. Our results support the so-called Ca++ buffering effect by the sarcolemma and explain, from an electrostatics perspective, how the sarcolemma acts as one of the regulating agents of the free Ca++ level in the cardiac myocyte cytosol.