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

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.