The Smoluchowski diffusion equation for structured macromolecules near structured surfaces

Beginning with the molecular-based Fokker–Planck equation obtained previously [M. H. Peters, J. Chem. Phys. 110, 528 (1999); J. Stat. Phys. 94, 557 (1999)], the Smoluchowski diffusion equation is derived here to describe the spatial and orientational dynamics of molecularly structured macromolecules near molecularly structured surfaces. The formal scaling and perturbation methods employed allow the establishment of definite limits on the use of the Smoluchowski equation when surfaces are present. It is shown that the Smoluchowski equation reduces to that given previously [D. W. Condiff and J. S. Dahler, J. Chem. Phys. 44, 3988 (1966)] in the absence of external surfaces. A specific example application is given involving a spherical macromolecule with electrostatic charge segments near a planar surface with an arbitrary charge distribution. Finally, we show that the short-time solution to the Smoluchowski equation obtained here yields a Brownian dynamics method consistent with that given previously [E. Dickinson, S. A. Allison, and J. A. McCammon, J. Chem. Soc. Faraday Trans. 2 81, 591 (1985)] for orientable, interacting Brownian particles. This study has applications to problems involving site-specific adsorption of orientable, structured Brownian particles, such as association or adsorption of biological macromolecules to cellular surfaces and enzyme–substrate docking kinetics, to name a few.