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Isaac Newton Institute for Mathematical Sciences

From Individual to Collective Behaviour in Biological Systems
September to December, 2001 - Cambridge University

Organisers: HG Othmer (Utah), PK Maini (Oxford), TJ Pedley (Cambridge), BD Sleeman (Leeds)

Description of the programme:
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 individual enzymes, cells or organisms in isolation is only a first step in understanding the collective behaviour of a population of such individuals. Incorporating individual aspects of behaviour into macroscopic descriptions of population behaviour is a challenging problem, even if only deterministic aspects are considered. In addition, stochastic effects are often important, whether at the level of switching on genes or at the level of spatial variability in ecology. However, random noise can produce undesirable effects, and one may expect to find mechanisms for buffering the effects of noise in development and ecology. Therefore probabilistic methods play an important role in deriving a population-level description from models of individual behaviour, though it is unlikely that the same mathematical approach will be applicable at all levels of organization.

Four major biological areas in which these mathematical questions are central and in which the biological questions can guide the mathematical developments have been chosen for this programme:

  1. Physiology. Here the emphasis will be on bringing together those who have established detailed descriptions of individual cells and study their interactions in a computational framework, and those who try to establish average or continuum models, based on the same microscopic data, in advance of computation.
  2. Developmental biology. This topic covers all aspects of pattern-formation in populations of cells. The interaction between signalling, gene expression, genetic regulatory networks, cell movement and differentiation at the single-cell and population level will be stressed.
  3. Stochastic spatial ecology. In this time of unprecedented environmental change it is crucial for scientists to formulate and analyze stochastic mechanistic descriptions of the change based on underlying ecological processes: examples include, the evolution and maintenance of biodiversity, extinction thresholds, 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. Mathematical approaches are required to integrate this data to gain insights into the dynamics of the immune cell response, the homeostatic regulation of immune cells and immune memory, and mechanisms of cytopathicity and resistance.
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.

Description of the Newton Institute:
The purpose of Newton Institute programmes is to bring together mathematicians and scientists who are interested in a particular area of science or mathematics but do not commonly join forces to attack research problems simultaneously from their different points of view. It is hoped that, by means of conferences, workshops, seminars and, especially, intense and prolonged interaction among small numbers of key people, significant new advances can be promoted. Normally, there are up to 20 long-term participants staying at the Institute at any one time during a programme, though it is expected that only a few of those 20 will remain for the whole programme.

Thus, in the context of the present programme, we expect that a few participants from (different areas in) the mathematical sciences will be present throughout, but that the principal long-term biologists will normally stay only for their particular subject, though overlapping a bit with the neighbouring ones, we hope. We will welcome young scientists (recent PhDs) as long-term participants as much as more senior figures. Larger numbers of participants will of course be invited to the associated workshops and conferences.

The Newton Institute is able to offer financial support to those of the longer-term participants who need it. This will be in the form of a contribution to travel and subsistence costs (maximum: 335 pounds per day) rather than salary. The Institute will arrange accommodation, desk space, and computer access for long-term participants. By September 2001, a substantial part of the University‘s two mathematics departments (Department of Pure Mathematics and Mathematical Statistics and Department of Applied Mathematics and Theoretical Physics) will be installed in the new Centre for Mathematical Sciences in nearby buildings. The University‘s new Mathematical and Physical Sciences Library should also be open by then, on a neighbouring site, and the Institute has a small library of its own.

At the same time as our programme, there will be a parallel programme at the Institute, on Integrable Systems.

Frequently updated information on the programme, including details of how to apply to participate, can be found on the web-site: