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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 populationlevel 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:
 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.
 Developmental biology. This topic covers all aspects of
patternformation in populations of cells. The interaction between
signalling, gene expression, genetic regulatory networks, cell
movement and differentiation at the singlecell and population
level will be stressed.
 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 manmade), etc.
 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 fourmonth 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 longterm 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 longterm
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 longterm 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 longerterm 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 longterm
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 website:
http://www.newton.cam.ac.uk/programs/icb.html
