Mathematical and stochastic modelling of reaction-diffusion processes in the Wnt signalling pathway

Reaction-diffusion processes in biological systems have been studied using a range of mathematical- and simulation-based approaches. In this thesis, novel techniques and algorithms are developed for reaction-diffusion processes based on Smoluchowski kinetics to simulate reversible reactions of any order. Simulating such reactions sheds light on the dynamics of Wnt signalling, an important biological process which regulates embryonic development, tissue homoeostasis, and diseases such as cancer. A detailed analysis into the fundamental dynamical properties of Wnt signalling helps explore the relationship between signalling mechanisms, protein binding affinities and the end product of cell fate.