There is a connection between β-catenin and the expression of p62 (also known as SQSTM1). Several studies have shown that the Wnt/β-catenin signaling pathway negatively regulates p62 expression:

• β-catenin knockdown in HT29 cells increased p62 mRNA levels, while overexpression of β-catenin in HCT116 cells decreased p62 mRNA, suggesting that β-catenin represses p62 transcription.(R1)
• The increase in p62 protein levels following β-catenin knockdown was attenuated by translation inhibition using cycloheximide, indicating that the elevated p62 protein is due, at least in part, to increased p62 mRNA.(R1)
• Chromatin immunoprecipitation (ChIP) and qPCR experiments revealed that β-catenin and TCF4 associate with the p62 promoter region under normal nutrient-rich conditions, suggesting that p62 is a transcriptional target of β-catenin/TCF4.(R1)
• During nutrient deprivation, when increased p62 is required for autophagy, the association of β-catenin with the p62 promoter decreased, accompanied by an increase in acetylated histone H3 at the promoter, consistent with increased transcriptional permissivity.(R1)

These findings support the notion that the Wnt/β-catenin pathway, through the actions of β-catenin and TCF4, represses p62 transcription under normal conditions.

Conversely, a decrease in β-catenin signaling, such as during nutrient starvation or upon β-catenin knockdown, leads to derepression of p62 and increased p62 expression.

Interestingly, while β-catenin negatively regulates p62 expression, p62 has been shown to promote tumor growth in hepatocellular carcinoma (HCC) and downregulate β-catenin expression in vivo, suggesting a potential feedback loop between these two proteins.(R2)

Summary

1. the Wnt/β-catenin signaling pathway, particularly through the actions of β-catenin and TCF4, acts as a negative regulator of p62 expression.
2. Decreased β-catenin signaling or increased demand for p62, such as during autophagy, can lead to derepression and increased expression of p62.