Elucidating the interactions between the adhesive and transcriptioanl functions of beta-catenin in normal and cancerous cells

Wnt signalling is involved in a wide range of physiological and pathological processes. The presence of an extracellular Wnt stimulus induces cytoplasmic stabilisation and nuclear translocation of beta-catenin, a protein that also plays an essential role in cadherin-mediated adhesion. Two main hypotheses have been proposed concerning the balance between beta-catenin's adhesive and transcriptional functions: either beta-catenin's fate is determined by competition between its binding partners, or Wnt induces folding of beta-catenin into a conformation allocated preferentially to transcription. The experimental data supporting each hypotheses remain inconclusive. In this paper we present a new mathematical model of the Wnt pathway that incorporates beta-catenin's dual function. We use this model to carry out a series of in silico experiments and compare the behaviour of systems governed by each hypothesis. Our analytical results and model simulations provide further insight into the current understanding of Wnt signalling and, in particular, reveal differences in the response of the two modes of interaction between adhesion and signalling in certain in silico settings. We also exploit our model to investigate the impact of the mutations most commonly observed in human colorectal cancer. Simulations show that the amount of functional APC required to maintain a normal phenotype increases with increasing strength of the Wnt signal, a result which illustrates that the environment can substantially influence both tumour initiation and phenotype.

Modelling Immunological Memory

Accurate immunological models offer the possibility of performing highthroughput experiments in silico that can predict, or at least suggest, in vivo phenomena. In this chapter, we compare various models of immunological memory. We first validate an experimental immunological simulator, developed by the authors, by simulating several theories of immunological memory with known results. We then use the same system to evaluate the predicted effects of a theory of immunological memory. The resulting model has not been explored before in artificial immune systems research, and we compare the simulated in silico output with in vivo measurements. Although the theory appears valid, we suggest that there are a common set of reasons why immunological memory models are a useful support tool; not conclusive in themselves.