IMA Postdoc Seminar (May 6, 2008)

Speaker: Peter Hinow (IMA)

Title: A model for transfer phenomena in structured populations

Abstract: P-glycoprotein (P-gp) is known to cause resistance to cancer chemotherapy as it is able to remove toxic substances from the cytoplasm of a cell. Recent experimental work by Levchenko et al. shows that cells rich in P-gp are able to transfer part of their P-gp to other cells and thereby may confer resistance. We propose a mathematical model for the transfer of a scalar quantity in a structured population. It is shown that the solutions of this 'pure transfer' model converge to a Radon measure. We add to this model production of P-gp and random fluctuations in P-gp content. For the amended model we show the existence of a globally asymptotically stable steady state, provided that the rate of P-gp transfer is sufficiently small.

This is joint work with Pierre Magal (University of Le Havre, France) and Glenn F. Webb (Vanderbilt University).