A Conservation Model for Density of Actin-Polymers in the Crawling Cell

In collaboration with Alex Mogilner, University of California at Davis

In progress to present to International Conference on Mathematical and Theoretical Biology July 15-29, 2001 Hilo, Hawaii USA

Migration of animal cells is the most striking process underlying the phenomena of wound healing, morphogenesis and carcinogenesis. The front part of the migrating cell, a lamellipod, is a broad, flat cytoskeletal protrusion devoid of organelles. Behind the lamellipod is a roundish cell body containing the nucleus and organelles. It is now widely accepted that the lamellipod contains the basic engine pulling the cell body forward.

Despite recent radical advances in cell biology and the biophysics of the motile cell, we still do not have a complete picture of how animal cells move across surfaces. One reason for this is that a huge variety of molecular mechanisms are involved in locomotion, which leads to a

multiplicity and redundancy in force generation machineries and regulatory pathways. Roughly speaking, the current research is aimed at dissecting the complex processes of motility into simpler phenomena that can be more easily analyzed. Phenomenological models of cellular mechanics based on conservation laws and plausible constitutive relations have been formulated. We aim at incorporating a description

of processes on molecular biological level into a comprehensive

realistic model of migrating cells. We will derive and solve numerically and analytically 1-D partial differential equations describing the cytoskeletal dynamics to develop an intuition of how biological behavior depends on essential mechanical and chemical parameters. Then, in order to make quantitative predictions of biological interest, we will develop realistic 2-D models of the moving cell. Our goals are to understand quantitatively the molecular origins of cytoskeletal mechanics and to model the motility related signal transduction processes. Such model will have a predictive value in important biomedical and biotechnological situations.

This activity is part of millenial changes in applied mathematics and biology. Namely, the problem of cell motility is a prototypical problem in higher order biological complexity. We are just starting to develop the methods to understand such complexity and formulate the intellectual strategies to attack this problem. It is a formidable challenge that will be interdisciplinary in nature.