Spatiotemporal behaviour of stochastic and continuum models for biological signalling on stationary and growing domains - Woolley, T; Thomas Woolley (2012)
One of the main challenges in developmental biology is elucidating the mechanisms underlying the formation and maintenance of complex spatial and temporal structures. This thesis aims to explore two different and yet complementary approaches to address this challenge. Firstly, we investigate a number of specific developmental systems in order to suggest mechanisms underlying their observed biological behaviour. Critically, we show that, without modifications, standard mathematical formulations are unable to capture certain details. In particular, it is demonstrated that accurate descriptions of domain growth need to be included in order to construct mathematical models that compare favourably with experimental systems. In conjunction with understanding biological development better, we also analytically investigate the existence of spot patterns in a paradigm patterning model, resulting in the use of numerical methods to compare theory with simulation. The second approach used to investigate spatial-temporal complexity is more theoretical; we aim to characterise the effects of stochastic perturbations and growth on pattern generation. To achieve this we derive a stochastic description of biochemical reactions, diffusion and domain growth that is consistent with the deterministic description in the thermodynamic limit. This is then used to determine conditions under which robust patterns form. By exploring developmental complexity through these two different approaches of creating broad analytical methods and investigating specific biological models, we not only gain a deeper insight into the creation of complexity in specific cases but also a wider appreciation of how noise can affect such systems.