Diffusion Mediated Transport in Multiple State Systems

David Kinderlehrer Department of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213 davidk@andrew.cmu.edu

Stuart Hastings sph@pitt.edu J. Bryce McLeod mcleod@pitt.edu Department of Mathematics University of Pittsburgh Pittsburgh, PA 15260

Abstract. Intracellular transport in eukarya is attributed to motor proteins that transduce chemical energy into directed mechanical motion. Nanoscale motors like kinesins tow organelles and other cargo on microtubules or filaments, have a role separating the mitotic spindle during the cell cycle, and perform many other functions. The simplest description gives rise to a weakly coupled system of evolution equations. The transport process to the mind’s eye, is analogous to a biased coin toss. We describe how this intuition may be confirmed by a careful analysis of the cooperative effect among the conformational changes and the potentials.