Branching process models of T cell selection
Cell division history can be examined with the fluorescent dye: 5- (and 6-) carboxyflourescein diacetate succinimidyl ester (CFSE). Modelling the data produced by flow cytometric analysis of CFSE has recently been an active area of research and promises to give new insight into the behaviour of dividing populations of cells. Initially, this thesis describes how CFSE data can be modelled with discrete time multi-type branching processes. This approach has not previously been used where CFSE data is concerned, although branching process models of cell division have an established history of producing simple tractable models that yield biologically relevant results. In particular, these models can be adapted to staged behaviour. We therefore use a multi-type model in an attempt to isolate the phenotypic stage at which negative selection occurs in the thymus. In doing so we re-examine published experimental data that analyses the fate of positively selected double positive (DP CD69+) thymocytes during and after their transition to single positive (SP) stage. We analyse the data with respect to two alternative hypotheses: 1. Death occurs at the DP CD69 f stage and not at t he SP stage and 2. Death occurs at the SP stage and not at the DP CD69f stage and it occurs concurrently with division. We conclude that the second model fits the data better than the first. Motivated to avoid the discrete time assumption that division behaviour is synchronous, the thesis shows how a continuous time branching process model of CFSE can be obtained. The results of a subsequent re-analysis of the published data conflict with our discrete time modelling. Upon further investigation, we conclude that the continuous time model is a poorer model of the data. Finally, the effect of negative selection in combination with division on the thymocyte repertoire is modelled with a discrete time branching process. The results of our analysis suggest that there may be an advantage to division and selection being a combined process.