Mathematical modelling suggests a differential impact of β‐transducin repeat‐containing protein paralogues on Wnt/β‐catenin signalling dynamics

The Wnt/β‐catenin signalling pathway is involved in the regulation of a multitude of cellular processes by controlling the concentration of the transcriptional regulator β‐catenin. Proteasomal degradation of β‐catenin is mediated by two β‐transducin repeat‐containing protein paralogues, homologous to Slimb protein (HOS) and F‐box/WD repeat‐containing protein 1A (FWD1), which are functionally interchangeable and thereby considered to function redundantly in the pathway. HOS and FWD1 are both regulated by Wnt/β‐catenin signalling, albeit in opposite directions, thus establishing interlocked negative and positive feedback loops. The functional relevance of the opposite regulation of HOS and FWD1 by Wnt/β‐catenin signalling in conjunction with their redundant activities in proteasomal degradation of β‐catenin remains unresolved. Using a detailed ordinary differential equation model, we investigated the specific influence of each individual feedback mechanism and their combination on Wnt/β‐catenin signal transduction under wild‐type and cancerous conditions. We found that, under wild‐type conditions, the signalling dynamics are predominantly affected by the HOS feedback as a result of a higher concentration of HOS than FWD1. Transcriptional up‐regulation of FWD1 by other signalling pathways reduced the impact of the HOS feedback. The opposite regulation of HOS and FWD1 expression by Wnt/β‐catenin signalling allows the FWD1 feedback to be employed as a compensation mechanism against aberrant pathway activation as a result of a reduced HOS concentration. By contrast, the FWD1 feedback provides no protection against aberrant activation in adenomatous polyposis coli protein mutant cancer cells.

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