Mathematical biology

Mathematical biology or biomathematics is an interdisciplinaryfield of academic study which aims at modelling natural, biologicalprocesses using mathematicaltechniques 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 genomicsrevolution, which are difficult to understand without the use of analytical tools,
• recent development of mathematical tools such as chaos theoryto help understand complex, nonlinear mechanisms in biology,
• an increase in computingpower which enables calculations and simulationsto be performed that were not previously possible, and
• an increasing interest in in silicoexperimentation 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 dynamicshas traditionally been the dominant field of mathematical biology. Work in this area dates back to the 19th century. The Lotka-Volterra predator-prey equationsare a famous example.

Modelling cell and molecular biology

This area has received a boost due to the growing importance of molecular biology.

• Modelling of neuronsand carcinogenesis[1]
• Mechanics of biological tissues [2]
• Theoretical enzymology and enzyme kinetics[3]
• Cancermodelling and simulation [4]
• Modelling the movement of interacting cell populations [5]
• Mathematical modelling of scar tissue formation [6]
• Mathematical modelling of intracellular dynamics [7]

Check out the Gillespie algorithm J. Comput. Phys. 22, 403-434. (or a tutorial here: [8]) to simulate low-number chemical systems (like 100 copies of an mRNA, protein, or ribosome). This algorithm exactly simulates samples from the solution of the chemical master equation. (see also van Kampen's classic Stochastic Processes in Physics and Chemistry)

Modelling physiological systems

• Modelling of arterialdisease [9]
• Multi-scale modelling of the heart[10]

Spatial modelling

One classic work in this area is Alan Turing's paper on morphogenesisentitled The Chemical Basis of Morphogenesis, published in 1952 in the Philosophical Transactions of the Royal Society.

• Travelling waves in a wound-healing assay [11]
• Swarmingbehaviour [12]
• The mechanochemical theory of morphogenesis[13]
• Biological pattern formation [14]

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.

See also

• Bioinformatics, biologically-inspired computing, biostatistics, cellular automata, excitable medium, Ewens's sampling formula, mathematical model, morphometrics, population genetics, theoretical biology, D'Arcy Thompson, Neighbour-Sensing model.

External links

• Society for Mathematical Biology
• European Society for Mathematical and Theoretical Biology
• Centre for Mathematical Biology at Oxford University
• Mathematical Biology at the National Institute for Medical Research
• Institute for Medical BioMathematics
• Mathematical Biology Systems of Differential Equations from EqWorld: The World of Mathematical Equations

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It uses material from the http://en.wikipedia.org/wiki/Mathematical+biology Wikipedia article Mathematical biology.