Probabilistic modelling of three phenomena in the Life Sciences

This thesis describes the development and analysis of three probabilistic models of phenomena in the life sciences. Model 1 addresses the phenomenon in breast cancer called ‘dormancy’, where patients relapse suddenly after many years or decades during which they were regarded as cured. Where and by what mechanism the dangerous residual cancer remains hidden for so long is largely a mystery, and this lack of knowledge makes it difficult to design effective preventive treatments. Analysis of our model leads to a number of predictions related to dormancy’s disease course. Models 2 and 3 simulate the formation of high-fidelity, patterned nanoscale ornamentations in the biosilica exoskeletons of diatoms, that today defy synthesis in vitro. Very little is known about this diatom biosilica assembly yet, if the mechanisms are simple or synthetically imitable, then they are potentially of great interest to industry and to the curious scientist. Model 3, which is still presently under study, may lead to predictions about the nature of these mechanisms of biosilica assembly. Notably, Model 3 is a new probabilistic model of a well established pattern formation process that we envisage to have broader application.