David Kinderlehrer
Carnegie Mellon University
Department of Mathematical Sciences

Diffusion mediated transport: can we understand the motion of small systems

Diffusion mediated transport is implicated in the operation of many molecular level systems. These include some liquid crystal and lipid bilayer systems, and, especially, the motor proteins responsible for eukaryotic cellular traffic. All of these systems are extremely complex and involve subtle interactions on varying scales. Our plan is to take advantage of Monge-Kanotorovich mass transfer methods to study the motion of these small molecules in a highly viscous and random environment.

What properties are necessary for transport? What is the role of diffusion? What is the role of other elements of the system and how can dissipation be exploited to understand this? How successful are we? Our special focus is the analysis of a simple model for conventional kinesin and to explore the relationship between the interaction potentials and the kinetic pathway which lead to transport. The opportunity to discover the interplay between chemistry and mechanics could not offer a more exciting venue.