Macroscopic and microscopic simulation methods as applied to biological macromolecules

This thesis concerns the development of theoretical models and methods for understanding the relationship between structure and the resulting function of proteins, and for enzymes in particular. The diffusional timescale will permit certain degrees of freedom (the solvent for example) to be represented implicitly in the stochastic equations of motion for the explicitly represented enzyme and substrate molecules. However, a systematic force is still present in the Brownian equation of motion, which, due to the spatial separation of the particles, is long-ranged. We have explored several electrostatic models to represent this systematic force for the enzyme-ligand Superoxide Dismutase/superoxide. For microscopic models, we have developed a method which addresses the problem of computational efficiency, accuracy, and suitability of current simulation implementations (such as molecular dynamics and SBMD) for molecular level descriptions of polypeptide and protein systems. The approach we have developed involves a reduced representation of the system in terms of electrostatic multipole expansions, excluded volumes, virtual connectivity degrees of freedom, and rigid body motion of individual amino acids in terms of either minimization or dynamical equations of motion. The computational efficiency and accuracy of the virtual rigid body (VRB) method will permit applications to the probing of structure, dynamics, and energetic properties of proteins with ligand binding sites, and the simulation of larger protein systems and longer timescales than has been reasonably possible in the past.