Generalized solvent boundary potential for computer simulations

Abstract

A general approach has been developed to allow accurate simulations of a small region part of a large macromolecular system while incorporating the influence of the remaining distant atoms with an effective boundary potential. The method is called the Generalized Solvent Boundary Potential (GSBP). By representing the surrounding solvent as a continuum dielectric, both the solvent-shielded static field from the distant atoms of the macromolecule and the reaction field from the dielectric solvent acting on the atoms in the region of interest are included. The static field is calculated once, using the finite-difference Poisson–Boltzmann (PB) equation, and the result is stored on a discrete grid for efficient simulations. The solvent reaction field is developed using a basis-set expansion whose coefficients correspond to generalized electrostatic multipoles. A matrix representing the reaction field Green’s function between those generalized multipoles is calculated only once using the PB equation and stored for efficient simulations. In the present work, the formalism is applied to both spherical and orthorhombic simulation regions for which orthonormal basis-sets exist based on spherical harmonics or cartesian Legendre polynomials. The GSBP method is also tested and illustrated with simple model systems and two detailed atomic systems: the active site region of aspartyl-tRNA synthetase (spherical region) and the interior of the KcsA potassium channel (orthorhombic region). Comparison with numerical finite-difference PB calculations shows that GSBP can accurately describe all long-range electrostatic interactions and remain computationally inexpensive.