Diffusion Mediated Transport with a Look at Motor Proteins

Stuart Hastings Department of Mathematics University of Pittsburgh Pittsburgh, PA 15260 email: sph+@pitt.edu

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

Bryce McLeod Department of Mathematics University of Pittsburgh Pittsburgh, PA 15260 mcleod@pitt.edu

Abstract: In this note we discuss transport properties of weakly coupled parabolic systems of evolution equations. These arise in the study of molecular motors, like conventional kinesin, which are re sponsible for eukaryotic intracellular transport. It falls under the rubric of what we call diffusion mediated transport. Diffusion mediated transport generally concrns directed transport or oriented fluctuations of a system with a high degree of randomness and requires special collaboration among its various elements to achieve. We discuss how this plays out in multiple state systems.