Motile organisms sense their environment and can respond to it by either directed movement toward or away from a signal, or by changing their speed of movement and/or frequency of turning. Such responses to extracellular chemical signals are often called chemotaxis. The first strategy is used by cells that move by crawling through their environment, provided they have receptors in the cell membrane and are large enough to detect typical differences in the signal over their body length. Examples include leukocytes (part of our immune system) and the model organism Dictyostelium discoideum. Small cells such as bacteria cannot effectively make a "two-point in space" measurement over their body length, and therefore they adopt the second strategy, measuring temporal variation in the signal as they move through the field. We investigate the mechanisms underlying chemotaxis on different space scales and time scales, from biochemical intracellular signal transduction pathways to the behaviour of a single organism and the collective properties of cellular populations. Due to the coupling of many nonlinear processes, mathematics can offer unique insights into the chemotaxis processes and provide connections between different levels of description. We also investigate fundamental questions about mathematical models of chemotaxis, for example, the global existence and behaviour of solutions of the complex chemotaxis partial-differential equations. One of the most impressive effects of chemotaxis is the so-called "chemotactic collapse". This collapse happens when the cells aggregate into small regions of space, forming high density configurations. Classical chemotaxis equations model the balance between collective chemotactic drift and individual cell diffusion. Depending on the particular situation, the drift might "win", and an aggregate is formed, or diffusion wins and cells disperse. This problem can be generalised to the context in which the cells perform some sort of anomalous diffusion and this balance between dispersal and aggregation can be studied too.

Bacterial chemotaxis

One of the most widely studied processes in biology is bacterial chemotaxis - the process by which a bacterium senses and responds to chemical gradients. Problems include the upregulation of the signal sensed, the transfer of information from the signalling centres to the bacterial motor, the response of the motor, and the swimming motion of the flagellum. Many of these issues are presently being addressed in a multi-disciplinary research program involving colleagues from Biochemistry (Professor Judith Armitage and Dr George Wadhams, Oxford; Dr Steven Porter, Exeter); Engineering (Dr Antonis Papachristodoulou, Oxford), Physics (Dr Richard Berry, Oxford) and Mathematics (Dr Marcus Tindall, Reading; Dr Dan Nicolau, Jr, Oxford). 

Please contact Professor Philip K. Maini for more details.

Key references in this area

  • A. Hamadeh, M. A. J. Roberts, E. August, P. E. McSharry, P. K. Maini, J. P. Armitage and A. Papachristodoulou (2011). Feedback control architecture and the bacterial chemotaxis network. PLoS  Comput. Biol. 7. (eprints)
  • F. Bai, R. W. Branch, D. V. Nicolau Jr, T. Pilizota, B. C. Steele, P. K. Maini and R. M. Berry (2010). Conformational spread as a mechanism for cooperativity in the bacterial flagellar switch. Science 327:685-689. (eprints)
  • M. A. J. Roberts, E. August, A. Hamadeh, P. K. Maini, P. E. McSharry, J. P. Armitage and A. Papachristodoulou (2009) A model invalidation-based approach for elucidating biological signalling pathways, applied to the chemotaxis pathway in R. sphaeroides. BMC Syst. Biol. 3:105. (eprints)
  • C. Xue, H. Hwang, K. Painter and R. Erban (2011). Travelling waves in hyperbolic chemotaxis equations. B. Math. Biol. 73(8):1695-1733.