Professor David Kinderlehrer
CENTER FOR NONLINEAR ANALYSIS AND DEPARTMENT OF MATHEMATICAL SCIENCES; CARNEGIE MELLON UNIVERSITY
Transport in Small Systems with a Look at Motor Proteins
Motion in small live systems has many challenges. Prominent environmental conditions are high viscosity and warmth. Not only is it difficult to move, but maintaining a course is rendered difficult by immersion in a highly fluctuating bath. This holds especially for the motor proteins responsible for much of eukaryotic cellular traffic. The situation falls under the rubric of diffusion mediated transport. We give some brief historical notes, including the original work of many distinguished scientists, and then turn to an approach based on the Monge transport problem (1787) and its modern version, Monge-Kantorovich Theory, which offers us a means of studying these systems with analysis. We arrive at a precipice: does this help? Can we say anything about the behavior of the cellular process? An exciting venue for math in the natural world!