Analysing the impact of nucleo-cytoplasmic shuttling of β-catenin and its antagonists APC, Axin and GSK3 on Wnt/β-catenin signalling

The canonical Wnt signalling pathway plays a critical role in development and disease. The key player of the pathway is β-catenin. Its activity is mainly regulated by the destruction complex consisting of APC, Axin and GSK3. In the nucleus, the complex formation of β-catenin and TCF initiates target gene expression. Our study provides a comprehensive analysis of the role of nucleo-cytoplasmic shuttling of APC, Axin, and GSK3 and the inactivation of β-catenin by the destruction complex in Wnt/. β-catenin signalling.We address the following questions: Can nucleo-cytoplasmic shuttling of APC, Axin and GSK3 increase the [. β-catenin/TCF] concentration? And, how is the [. β-catenin/TCF] concentration influenced by phosphorylation and subsequent degradation of nuclear β-catenin?Based on experimental findings, we develop a compartmental model and conduct several simulation experiments. Our analysis reveals the following key findings: 1) nucleo-cytoplasmic shuttling of β-catenin and its antagonists can yield a spatial separation between the said proteins, which results in a breakdown of β-catenin degradation, followed by an accumulation of β-catenin and hence leads to an increase of the [. β-catenin/TCF] concentration. Our results strongly suggest that Wnt signalling can benefit from nucleo-cytoplasmic shuttling of APC, Axin and GSK3, although they are in general β-catenin antagonising proteins. 2) The total robustness of the [. β-catenin/TCF] output is closely linked to its absolute concentration levels. We demonstrate that the compartmental separation of β-catenin and the destruction complex does not only lead to a maximization, but additionally to an increased robustness of [. β-catenin/TCF] signalling against perturbations in the cellular environment. 3) A nuclear accumulation of the destruction complex renders the pathway robust against fluctuations in Wnt signalling and against changes in the compartmental distribution of β-catenin. 4) Elucidating the impact of destruction complex inhibition, we show that the [. β-catenin/TCF] concentration is more effectively enhanced by inhibition of the kinase GSK3 rather than the binding of β-catenin to the destruction complex.