The aim of mathematical immunology is to aid understanding of the complexities
of the immune system through mathematical modelling. Control and regulation
is fundamental to the proper functioning of the imune systems, ie delivering
an appropriate response to a stimulous. Much of the research in the mathematical
immunology group in this area involves an analysis of mechanisms of control,
selection and activation, often extrapolating between scales, i.e. molecular
to cellular, or cellular to repertoire; simulating and predicting effects
of mechanisms at the lower level on the upper. We work hard at the following
research projects -
Related grant: Modelling stochastic
activation of T cells, EPSRC.
- Stochastic models of T cell activation.
A fundamental issue in immunology is the specificity of T-cells for specific
peptides given that the process of T-cell recognition is based on low affinity
receptors. These peptides are a minority species within the excess of presented
self, and therefore the system is very noisy. Through the use of large
deviation theory to signalling in cell-cell contacts we show .that working
repertoires based on current theories of single T cell activation lead
to robust responses with good reactivity properties and low autoimmunity.
Our theory illustrates the importance of rapid sampling of presented peptides
to enhance the signal to noise ratio, understood in the immunological community
as the serial triggering hypothesis. See our recent paper for details:
A reliable and safe T cell repertoire based on low-affinity T cell receptors.
J. Theor. Bio. 209; (2001) 465-486. H. van den Berg, D.A.
Rand and NJ Burroughs. PDF
- Cytokine driven selection. Control of the
immune system involves soluble mediators called cytokines. Cells respond
to these cytokines through specific receptors. The predominant growth cytokine
of T-cells is IL2. A model of IL2 induced growth based on physiologically
structured models (integro-differential equations) structured with respect
to the receptor density has been developed and is currently being analysed.
- Related grant: Life and death
of T-lymphocytes, BBSRC.
- Immunological memory. Memory has been a
phenomena invoking long standing debate and hypothesis. By analysis of
the population dependence of the processes of down-sizing at the end of
an immune response (cytokine deprivation induced death) and competition
for memory differentiation signals (survival signals) we have shown that
control of the number of cells entering memory can be rigidly controlled,
and can overcome the variability in immune system strength and numbers
of activated T cells during an immune response. Thus these regulatory effects
are vital in giving good vaccination properties and safety from unrelated
memory wipe-out under a strong immune response.
- The immunological synapse and
differential enrichment. T cell conjugation with an antigen
presenting cell involves a redistribution and segregation of important
signalling and adhesion molecules in the contact interface. A model based
on reaction diffusion equations incorporating thermodynamic effects of
membranes is being investigated through simulations and analysis. We have
found criteria for segregation involving a balance of thermodynamic effects,
and reproduce realistic segregation patterns. This project is being extended
into an associated analysis of fluorescent images (3+1D).
Simulation of a T cell APC contact interface: MHC green, ICAM1
Segregation through free energy minimisation occurs within a
Membrane adjusts locally to optimise binding of short and long
bonds. Domains do not coalesce without another mechanism, eg cytoskeletal