A Mathematical Model for Cellular Locomotion Exhibiting Chemotaxis

Abstract

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.