From Wikipedia,
the free encyclopedia.
Mathematical biology or
biomathematics is an
interdisciplinary field of
academic study which aims at
modelling natural,
biological processes using
mathematical techniques and
tools. It has both practical and
theoretical applications in
biological research.
Importance
Applying mathematics to biology
has a long history, but only
recently has there been an
explosion of interest in the
field. Some reasons for this
include:
- the explosion of data-rich
information sets, due to the
genomics revolution, which
are difficult to understand
without the use of analytical
tools,
- recent development of
mathematical tools such as
chaos theory to help
understand complex, nonlinear
mechanisms in biology,
- an increase in
computing power which
enables calculations and
simulations to be performed
that were not previously
possible, and
- an increasing interest in
in silico experimentation
due to the complications
involved in human and animal
research.
Research
Below is a list of some areas
of research in mathematical
biology and links to related
projects in various universities:
Population dynamics
Population dynamics has
traditionally been the dominant
field of mathematical biology.
Work in this area dates back to
the
19th century. The
Lotka-Volterra predator-prey
equations are a famous
example.
Modelling cell and molecular
biology
This area has received a boost
due to the growing importance of
molecular biology.
Modelling physiological
systems
Spatial modelling
One classic work in this area
is
Alan Turing's paper on
morphogenesis entitled The
Chemical Basis of Morphogenesis,
published in 1952 in the
Philosophical Transactions of the
Royal Society.
These examples are
characterised by complex,
nonlinear mechanisms and it is
being increasingly recognised that
the result of such interactions
may only be understood through
mathematical and computational
models. Due to the wide diversity
of specific knowledge involved,
biomathematical research is often
done in collaboration between
mathematicians, physicists,
biologists, physicians,
zoologists, chemists etc.
Bibliographical references
- J.D. Murray, Mathematical
Biology. Springer-Verlag,
3rd ed. in 2 vols.:
Mathematical Biology: I. An
Introduction, 2002
ISBN 0387952233;
Mathematical Biology: II.
Spatial Models and Biomedical
Applications, 2003
ISBN 0387952284.
- L. Edelstein-Keshet,
Mathematical Models in Biology.
SIAM, 2004.
ISBN 0075549506
- L.A. Segel, Modeling
dynamic phenomena in molecular
and cellular biology. C.U.P.,
1984.
ISBN 052127477X
- F. Hoppensteadt,
Mathematical theories of
populations: demographics,
genetics and epidemics.
SIAM, Philadelphia, 1975
(reprinted 1993).
ISBN 0898710170
- S.I. Rubinow,
Introduction to mathematical
biology. John Wiley, 1975.
ISBN 0471744468
- A. Goldbeter, Biochemical
oscillations and cellular
rhythms. C.U.P., 1996.
ISBN 0521599466
- E. Renshaw, Modelling
biological populations in space
and time. C.U.P., 1991.
ISBN 0521448557
- P.G. Drazin, Nonlinear
systems. C.U.P., 1992.
ISBN 0521406684
- D.W. Jordan and P. Smith,
Nonlinear ordinary differential
equations, 2nd ed. O.U.P.,
1987.
ISBN 0198565623
External references
- F. Hoppensteadt,
Getting Started in Mathematical
Biology. Notices of
American Mathematical Society,
Sept. 1995.
- M. C. Reed,
Why Is Mathematical Biology So
Hard? Notices of
American Mathematical Society,
March, 2004.
- R. M. May,
Uses and Abuses of Mathematics
in Biology. Science,
February 6, 2004.
- J. D. Murray,
How the leopard gets its spots?
Scientific American, 258(3):
80-87, 1988.
Internal links
-
Bioinformatics,
biologically-inspired computing,
biostatistics,
cellular automata,
excitable medium,
Ewens's sampling formula,
mathematical model,
morphometrics,
population genetics,
theoretical biology,
D'Arcy Thompson.
External links
