MACROMOLECULAR ELECTROSTATIC ENERGY WITHIN THE NONLINEAR POISSON-BOLTZMANN EQUATION

A fundamental problem in macromolecular electrostatics is the calculat ion of the electrostatic energy of a macromolecule solvated in an elec trolyte solvated in an electrolyte solution, i.e., the work required t o charge up the macromolecule in the presence of the electrolytic ions . Through numerical calculations with the nonlinear Poisson-Boltzmann (PB) equation, Sharp and and Honig [J. Phys. Chem. 94, 7684 (1990)] ob served that this energy can be obtained with equal accuracy from the c harging integral and from their energy-density integral. Here we give an elementary analytical proof of the exact equivalence of the two dif ferent formulations of the energy. In order to calculate the macromole cular electrostatic energy, a boundary element method [Biophys. J. 65, 954 (1993)] previously developed for the linearized PB equation is mo dified to solve the nonlinear PB equation. Illustrative calculations s how that for globular proteins under physiological ionic strengths, th e electrostatic energy calculated from the linearized PB equation diff ers very little from that calculated from the nonlinear equation.