ELECTROPHORESIS OF TOPOLOGICALLY NONTRIVIAL MACROMOLECULES - MATHEMATICAL AND COMPUTATIONAL STUDIES

Mathematical and numerical models for studying the electrophoresis of topologically nontrivial molecules in two and three dimensions are pre sented. The molecules are modeled as polygons residing on a square lat tice and a cubic lattice whereas the electrophoretic media of obstacle network are simulated by removing vertices from the lattices at rando m. The dynamics of the polymeric molecules are modeled by configuratio nal readjustments of segments of the polygons. Configurational readjus tments arise from thermal fluctuations and they correspond to piecewis e reptation in the simulations. A Metropolis algorithm is introduced t o simulate these dynamics, and the algorithms are proven to be reversi ble and ergodic. Monte Carlo simulations of steady field random obstac le electrophoresis are performed and the results are presented.