No abstract

A planar four-charge model for the water molecule, with a spherically symmetric Lennard-Jones potential and a point polarizability, is examined. The model parameters are determined by fitting gas-phase data for the one and two-molecule systems. A reasonable description of water clusters of up to five molecules is obtained. The model gives qualitatively accurate properties in liquid and solid phases, but not enough condensation for agreement with experiment. It is suggested that the use of a point polarizability only partially accounts for many-body effects. Alternatives to the above model are discussed.

The nonlinear Poisson-Boltzmann equation (NPBE) provides a continuum description of the electrostatic field in an ionic medium around a macromolecule. Here, a novel approach to the solution of the full NPBE is developed. This robust and efficient algorithm combines multilevel techniques with a damped inexact Newton's method. The CPU time required for solution of the full NPBE, which is less than that for standard single-grid approaches in solving the corresponding linearized equation, is proportional to the number of unknowns enabling applications to very large macromolecular systems. Convergence of the method is demonstrated for a variety of protein systems. Comparison of the solutions to the linearized Poisson-Boltzmann equation shows that the damping of the electrostatic field around the charge is increased and that the potential scales logarithmically with charge. The inclusion of the full nonlinearity thus reduces the impact of highly charged residues on protein surfaces and provides a more realistic representation of electrostatic effects. This is demonstrated through calculation of potential around the active site regions of the 1,266-residue tryptophan synthase dimer and in the computation of rate constants from Brownian dynamics calculations in the superoxide dismutase-superoxide and antibody-antigen systems.

Brownian dynamics simulations are performed to investigate the role of long-range electrostatic forces in the association of the monoclonal antibody HyHEL-5 with hen egg lysozyme. The electrostatic field of the antibody is obtained from a solution of the nonlinear Poisson-Boltzmann using the x-ray crystal coordinates of this protein. The lysozyme is represented as an asymmetric dumbell consisting of two spheres of unequal size, an arrangement that allows for the modeling of the orientational requirements for docking. Calculations are done with the wild-type antibody and several point mutants at different ionic strengths. Changes in the charge distribution of the lysozyme are also considered. Results are compared with experiment and a simpler model in which the lysozyme is approximately by a single charged sphere.