Institute of Immunity and Transplantation


Mathematical models of T cell homeostasis

Find out about the Institute's research on mathematical models of T cell homeostasis.

It is becoming easier to generate large volumes of complex data. How can we get the most information out of such datasets? We have been using mathematical models to help organise data, generate and test hypotheses.

The interplay of cell death, division and differentiation processes that mediate homeostasis within the T cell compartment can result in highly complex cellular behaviour. To better understand these processes at a System’s level, we work with Mathematicians to develop models that formalise and test our understanding.

T cells develop in1the thymus through a number of well defined developmental stages. CD4 CD8 double positive thymocytes undergo positive selection which matches TCR restriction to CD4 or CD8 lineage.

The different developmental stages of thymic selection can be captured by a five compartment mathematical model. Death within, and transit between compartments can be captured by rate parameters. Equations then use these rates to describe population dynamics with time.

To help identify model parameters, we take advantage of Zap70-/- mice in which T cell development is arrested. Switching on an antibiotic inducible Zap70 transgene in vivo restores selection. The kinetics with which different compartments are restored is rich in information that the mathematical model can unlock.

We identify values for the model parameters that give the best fit (in red) to experimentally observed data (black).

The model predicts 7 death rates in the different compartments (top). Measuring survival of different populations in vivo validates the findings of the model. Survival mirrors the predicted death rates, and reveals an unexpectedly high death rate in DP2 thymocytes.

Identifying rates of maturation and death provides unique insights into the dynamics of development. Although more CD8 lineage cells start selection, their development is very inefficient, which >80% cells dying at DP2 stage. Fewer CD4 lineage cells die during development. Understanding how apoptosis is regulated in developing thymocytes will be an important 9% question in the future.