Translational diffusion of macromolecules and nanoparticles modeled as non-overlapping bead arrays in an effective medium.

There are three objectives to the present work. First, starting from a boundary element (BE) formulation of low Reynolds number hydrodynamics, model the translational diffusion of macromolecules modeled as an array of non-overlapping beads, and show how this approach is equivalent to previous formulations of "bead hydrodynamics" and under what conditions. Second, show how this approach can be improved upon by accounting for the variation in forces over the surfaces of individual beads and also extending the approach to a gel modeled as an effective medium, EM. Third, develop a "combined obstruction and hydrodynamic effect" model of the translational diffusion of irregularly shaped macromolecules in a gel. In one of the cases studied, the BE approach is shown to be equivalent to previous "bead model" formulations in which intersubunit hydrodynamic interaction is modeled using the Rotne-Prager tensor. A bead model that accounts for the variation in hydrodynamic stress forces over the individual bead surfaces is shown to be in best agreement with exact results for simple bead arrays made up of 2-4 subunits. The translational diffusion of rods, modeled as strings of from 2 to 100 touching beads in dilute gels is examined. Interpolation formulas valid over a range of gel concentrations and rod lengths are derived for the parallel and perpendicular components of the diffusion tensor as well as the orientationally averaged diffusion tensor. The EM model accounts for the long-range hydrodynamic interaction exerted by the gel support matrix on the diffusing particle of interest but does not account for the reduction in diffusion caused by the direct obstruction of the gel, or steric effect. Both effects are accounted for by writing the translational diffusion in a gel as the product of two terms representing long-range hydrodynamic interaction and steric effects. Finally, the diffusion of a 564 base pair DNA in a 2% agarose gel is examined and model results are compared to experiment (Pluen, A.; Netti, P. A.; Jain, R. K.; Berk, D. A. Biophys. J. 1999, 77, 542-552). For reasonable choices of model parameters, fair agreement between theory and experiment is achieved.