Introduction to the special issue
Jamie Davies
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Michael Grinfeld
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Steven D. Webb
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M. Grinfeld S. D. Webb (&) Department of Mathematics and Statistics, University of Strathclyde
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Glasgow, Scotland
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J. Davies Centre for Integrative Physiology, University of Edinburgh
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Edinburgh, Scotland
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This special issue of Theory of Biosciences is the response
to call for papers we circulated during and following the
International Centre for Mathematical Sciences (ICMS)
workshop on Emerging Modelling Methodologies in
Medicine and Biology, held in Edinburgh July 20thJuly
24th, 2009.
The aim of the meeting was to bring together modellers
(mathematicians, physicists, computer-scientists, or
engineers) attracted by the challenges and opportunities
provided by twenty-first century life sciences, biologists with a
synoptic view of their disciplines looking for over-arching
explanatory schemes, and philosophers of science
interested in the nature of biological systems, explanation, and
understanding in biology.
We thought that organising such a meeting was timely
and important, because from the point of view of biology,
we live in exciting times. New techniques for the
investigation of life at the subcellular level appear all the time,
and new data on the organisation and function of
macromolecules are continuously collected. In the resulting
increasingly and recursively involved picture, we need to
uncover principles that govern this complexity. In many
areas of science, notably in physics, mathematics has been
successfully used to deal with complexity. The overarching
aim of the meeting was to discuss foundational
methodologies of the mathematisation of biology (Israel 1996).
There is limited methodological work on modelling in
biology; see for example (Fox-Keller 2000; Lander 2004),
or the cautionary work in Buiatti (1998) and Rosen (1985).
In biology, unlike physics, there are no discernible
natural laws to anchor modeling to. In addition, biological
systems are distinguished by being the product of
evolutionary forces, and they persist in time while recycling and
renewing their components. In biology it is very rare to
have a system of a few interacting parts on the same scale:
biological systems are complex, multi-scale systems by
definition. Hence modelling a biological system is a highly
nontrivial task. At the same time, mathematical formalism
seems to be the only approach for dealing with the
complexity of biological systems.
There is a real need to confront this complexity, since in
therapy, in principled drug design, or in ecosystem
management it is often necessary to predict what the system as
a whole would do in particular circumstances. The
piecemeal methodology of experimental biology has no tools of
its own to address this need.
Complex systems, that is systems comprised of many
tightly coupled heterogeneous (by nature and scale)
components, can be approached in a number of ways. The
reductionist way of an engineer is to decompose the system
into simpler subsystems, analyse the workings of each
subsystem separately, understand the coupling of the
subsystems, and reconstruct in this way the function of the
entire mechanism. This approach does not work in
biology as it is not clear how, even in principle, to define a
(reasonably closed) subsystem. So far, reductionist
approaches in biology always leave open an explanatory
gap between what the system does and what can with
confidence be said about its parts.
From the above remarks, the usefulness of a
multidisciplinary approach to modelling in the life sciences should
be clear. In the event, we had a very enthusiastic response
from the modelling community and a strong showing from
biologists in areas where some form of holistic approach is
seen as necessary (ageing, cancer, developmental biology,
structure of the nervous system). Unfortunately, for
administrative reasons, we were not able to recruit as many
philosophers of science as we would have wanted, and
furthermore, all accepted papers in this special issue come
from the modelling community.
It seems to us that the set of fundamental questions we
have identified (see http://www.icms.org.uk/workshops/
modellingmethodologies) is acutely relevant for
developing successful applications of mathematical modelling in
biology and medicine, and we hope that future meetings
will realise our vision of a philosophically and biologically
informed modelling activity.
This special issue thus covers a variety of modelling
approaches, encompassing both traditional techniques and
a range of emerging methodologies. Differential equations
form the main theme but these are approached, derived,
and indeed used from a number of different angles.
Examples include their application to a problem of energy
metabolism at the whole organismal scale, their rigorous
derivation using process algebra techniques, their coupling
to bioinformatic data to provide a multifactorial network
approach to model proteinprotein interactions and their
applicat (...truncated)