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 the two β-transducin repeat-containing protein (β-TrCP) paralogues HOS and 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 is an unresolved issue. Using a detailed ordinary differential equation (ODE) 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 due to 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 employing the FWD1 feedback as a compensation mechanism against aberrant pathway activation due to reduced HOS concentration. In contrast, the FWD1 feedback provides no protection against aberrant activation in APC mutant cancer cells
