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From Individual to Collective Behaviour in Biological Systems

Participation in INI programmes is by invitation only. Anyone wishing to apply to participate in the associated workshop(s) should use the relevant workshop application form.

10th September 2001 to 19th December 2001

Organisers: Professor PK Maini (Oxford), Professor H Othmer (Minnesota), Professor TJ Pedley (Cambridge), Professor BD Sleeman (Leeds)

Programme Theme

In recent years there has been an explosive growth in our knowledge of biological processes, especially at the molecular and cellular level. However, understanding the behaviour of an individual chemical reaction or cell (or organism) in isolation is only a first step in understanding the collective behaviour of a population of such individuals. The situation is complicated by the fact that the individual behaviour is in many cases stochastic, and even if it were intrinsically deterministic, the environment is not. Therefore probabilistic methods are essential in deriving a population-level description from models of individual behaviour, though it is unlikely that the same mathematical approach will be applicable in all systems.

Biology is too broad for one programme to cover all systems susceptible to mathematical analysis. Therefore this programme will concentrate on four biological topics: (1) Physiology. The emphasis will be on bringing together those who have established detailed descriptions of individual cells and then put them together into a whole organ on a parallel computer, one cell per processor, and those who try to establish average or continuum models, based on the same microscopic data, in advance of computation. (2) Development biology. This topic covers all aspects of pattern-formation in populations of cells. Given that we know more and more about what chemical and other processes are switched on or off by which genes, it is increasingly desirable to understand how the cells act and interact to produce observed structures. (3) Stochastic spatial ecology. In this time of unprecedented environmental change it is crucial for scientists to formulate a mechanistic (stochastic) description of the change based on underlying ecological processes: examples include the spatial spread of introduced pests; the shift of species ranges as a result of environmental change (climatic or directly man-made), etc. (4) Theoretical immunology. New techniques have led to an increasing stream of kinetic data on the populations of various types of immune cells. However, proper understanding of the dynamics of these populations will come only in the framework of a formal theoretical model.

The specific program in each of the four major areas is formulated with the advice and assistance of a leading biologist:

  • Physiology - Dennis Noble (Oxford)
  • Developmental biology - Michael Akam (Cambridge)
  • Stochastic spatial ecology - Charles Godfray (Imperial)
  • Theoretical immunology - Martin Nowak (Princeton)

Each month of the programme will be devoted to one of the topics, beginning with a workshop on both the biological problems and those mathematical approaches which might be expected to be fruitful. While most biological participants will probably wish to stay for only one of the topics, it is hoped that key mathematical scientists will stay for the whole four-month period.

Final Scientific Report: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons