Research in Mathematical Biology

The lack of real contact between mathematics and biology is either a tragedy, a scandal, or a challenge, it is hard to decide which.
Gian-Carlo Rota (1986)

Although the fundamental principles of physics and chemistry that govern the inanimate world also govern living things, a quantitative, mathematically-informed theory of biology has been very slow in coming, though not, perhaps, quite so slow as Rota's much-quoted remark suggests. Today there is a new wave of biologists—well represented in Manchester—who aim to turn biology into a fully quantitative discipline. The time is ripe, therefore, for the introduction of mathematical ideas to produce theories and models of biological systems.

The range of modelling problems is vast. At the very smallest scales one can study the molecular interactions that regulate of gene expression and cellular control metabolism: the models here are typically large systems of coupled nonlinear—and in some cases stochastic—ODEs and present both mathematical challenges and opportunities for biological insight:

• How does one investigate the dynamics of such large systems?
• Are there systematic ways of simplifying these networks so as to retain the biologically important details?
• What principles govern the evolution of regulatory networks and why do they appear to be so robust?
• How can one relate the sorts of data that biologists can measure to models?

One can also consider longer time scales and ask questions about molecular evolution. In collaboration with Dr. Bette Korber of the HIV Sequence Database at Los Alamos (U.S.A.) we have addressed such questions as:

• Can one model the evolution of HIV so as to decide when and where the virus first emerged?
• What does the evolution of the virus, both in an infected person and in the world as a whole, tell us about the design of potential vaccines?

On the macroscopic level biological tissues and fluids may be modelled as complex (i.e. inhomogeneous and highly anisotropic) materials using traditional continuum mechanical descriptions. There is much research activity in the School in this area of biomechanics. Current projects include:

• the development of computational techniques for the simulation of physiological fluid-structure interaction problems (such as blood flow in the veins and arteries, or the flow of air in the pulmonary airways);
• the modelling of mass-transfer into the artery walls;
• the analysis of pulse-wave propagation signals (in collaboration with Dr. Paul Dark from the University's Medical School and Hope Hospital);
• the development of mechanical models for the growth of avascular tumours;
• and studies of pulmonary airway closure and reopening.

At rather higher levels of abstraction one can model neurological processes and the mechanisms of perception. Two examples of recent work in Manchester are:

• The study of eye movement control: we collaborate with vision scientists in Manchester and the Institute of Child Health in London on modelling the neural control of eye movements. A lot can be learned about these mechanisms by observing how they can go wrong. We are developing models-based on experimental work by neurobiologists and psychophysicists that are able to account for certain pathologies involving involuntary oscillations of the eyes.
• The study of "stochastic resonance", a paradoxical phenomenon arising from the nonlinearity of the perceptual system in which adding a bit of noise to a faint signal - a soft murmur, say, or a scene viewed in very low light - makes it easier to perceive.

Members of staff involved

NAME		Title	EMAIL @manchester.ac.uk	PHONE	LOCATION
Broomhead	Dave	Prof.	David.Broomhead	0161 30 63680	Alan Turing Bldg	2.230
Glendinning	Paul	Prof.	P.A.Glendinning	0161 30 68972	Alan Turing Bldg	2.236
Hazel	Andrew	Dr	Andrew.Hazel	0161 27 55809	Alan Turing Bldg	2.213
Heil	Matthias	Prof	Matthias.Heil	0161 27 55808	Alan Turing Bldg	2.224
Huke	Jerry	Dr	J.P.Huke	0161 30 68979	Alan Turing Bldg	2.222
Muldoon	Mark	Dr	Mark.Muldoon	0161 30 63646	Alan Turing Bldg	2.130
Shardlow	Tony	Dr	Tony.Shardlow	0161 27 55821	Alan Turing Bldg	2.143
Smallbone	Kieran	Dr	Kieran.Smallbone	0161 30 65201	MIB	2.002