Journal of Theoretical Medicine
Volume 3 (2001), Issue 2, Pages 101-123

A Mathematical Model for Cellular Locomotion Exhibiting Chemotaxis

School of Mathematics, Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK

Received 3 February 2000; Revised 23 May 2000; Accepted 12 June 2000

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A fundamental problem of cellular biology is to understand the mechanisms underlying cellular locomotion. Bacterial organisms may use appendages such as flagellae or cilia to facilitate motion. Amoeboid motion [6], exhibited by eucaryotic cells are seen to flatten onto surfaces and extend thin sheets of cytosol called lamellipodia. These in turn make attachments to the surface and by the initiation of internal contractions within the cell, a forward motion is achieved. The processes which govern this behaviour are extremely complex, however, key ingredients have been identified which may provide a sufficient basis for persistent cellular motion. These factors are osmotichydrostatic expansion and cellular contraction mediated by intracellular calcium ca2+. In this paper, we develop a simple two dimensional model for a non-muscle motile cell based on these two key factors. We show it is capable of producing persistent cellular motion and chemotactic behaviour.