A computational framework for understanding the dynamics of signalling pathways

Signalling pathways are subcellular networks that enable the cell to respond to its microenvironment. Abnormal function of a signalling pathway is a hallmark of carcinogenesis and developmental diseases. The signalling cascades in these pathways involve biochemical interactions that can lead to highly nonlinear cellular responses. Studies of signalling pathways often involve the proposal of models based on experimental data that are difficult to quantify and reproduce. Due to the nature of the experimental procedures, the experimental results can often be qualitative or at best semi-quantitative. As a result, the data and models proposed in different studies can often appear inconsistent.
The canonical Wnt pathway, overactive in 90% of colorectal cancer cases, is not immune to these problems. A review of the literature reveals many seemingly inconsistent experimental results and models regarding the pathway dynamics. This makes the Wnt pathway a natural candidate for investigation using a new model selection framework using qualitative experimental data.
The steps involved in our model selection framework are as follows. We propose a set of candidate mathematical models that may be consistent with experimental observations. Using a qualitative cost function, we explore the output of these models to investigate whether they can reproduce qualitatively similar outputs to the experimental observations. Any consistent candidate models are analysed further using sen- sitivity analysis and in silico experiments, before new in vitro experiments are proposed to discriminate between remaining models.
Our literature review of the Wnt pathway revealed that a major source of discrepancy is the way in which Wnt stimulation leads to the initial accumulation of the Wnt-target β-catenin. Before studying this problem, we introduce a set of candidate models to study the first steps in the Wnt signalling cascade involving the Axin scaffolding protein that degrades β-catenin and the LRP6 co-receptor, which facilitates deactivation of this process. Using our framework, we reduce the number of suitable candidate models from twelve to four and propose new in vitro experiments to discriminate between these models further. In a multi-disciplinary study, we carry out these experiments in the laboratory to discriminate between the remaining candidate models.
Our results suggest that Axin can interact with LRP6 independently of Wnt, and that Wnt stimulation leads to Axin-driven LRP6 phosphorylation. We build on our initial candidate models and introduce β-catenin and further details of the pathway in a new set of candidate mathematical models. We compare these models to experimental results from three different studies of the pathway, which have proposed different models for the pathway. We establish that one of our candidate models can qualitatively reproduce the results from all three studies. According to this model, the first steps that lead to accumulation of β-catenin upon Wnt stimulation is sequestration of Axin at the membrane. Beyond the first half hour, dephosphorylation of Axin allows levels of β-catenin to increase further.
The existence of seemingly inconsistent experimental results and models is not unique to the Wnt pathway. Thus we believe that the framework developed in this thesis could be adapted for use in other studies of signalling pathways to understand the underlying networks of individual pathways and their crosstalk.

Advisor: Fletcher, A
Pitt-Francis, J
Byrne, H
Gavaghan, D