Mesoscopic modeling of macromolecules in condensed media: General theory and computational techniques

A model that predicts the behavior of macromolecules in solution is presented. The model is written in terms of the Cartesian coordinates of the atoms in the macromolecules of interest and the position-orientation number density of the medium in which they are immersed. Following the second law of thermodynarrnics, equilibrium structures are obtained by minimizing an intermediate free energy which accounts for both the energy and entropy of the solvent but only the energy of macromolecules.; The intermediate free energy consists of three terms. The first is the potential energy of interatomic interactions describing the macromolecule(s) of interest. The second is the Helmholtz free energy of the medium, currently restricted to pure water. The expression for its free energy is developed through a density functional formalism, where a truncated expansion about the isotropic state is employed. Retaining terms up to first order, water position-orientation number density is obtained in mesoscopic structures such as droplets and the liquid-vapor interface. The last terra in the intermediate free energy is the molecule-medium interaction, an expression for which is not developed here.; In order to facilitate the simulation of large scale macromoleculer conformational changes, a novel technique, the space warping method, is set forth. In the space warping method; the energy is minimized with respect to a set of global coordinates that account for the overall deformation of molecules. The method scales better than direct minimization with respect to atomic coordinates and is successful in finding low lying minima, especially when combined with a simulated annealing-type thermal force.; Given an expression for the intermediate free energy, its minima are sought by local minimization using the method of steepest descent. The numerical algorithms used to do this minimization are discussed. They include a combination of space discretization techniques, notably the finite element and finite difference methods, and time discretization techniques, particularly Runge-Kutta algorithms and implicit/explicit time stepping.