Mathematical Modeling Quantifies "Just-Right" APC Inactivation for Colorectal Cancer Initiation

Dysregulation of the tumor suppressor gene adenomatous polyposis coli (APC) is a canonical step in colorectal cancer development by promoting activation of the WNT/β-catenin pathway. Curiously, most colorectal tumors carry biallelic mutations that result in only partial loss of APC function, suggesting that a "just-right" level of APC inactivation, and hence WNT signaling, provides the optimal conditions for tumorigenesis. Mutational processes act variably across the APC gene, which could contribute to the bias against complete APC inactivation. In this study, we propose a mathematical model to quantify the tumorigenic effect of biallelic APC genotypes, controlling for somatic mutational processes. Analysis of sequence data from >2,500 colorectal cancers showed that APC genotypes resulting in partial protein function confer about 50 times higher probability of progressing to cancer compared with complete APC inactivation. The optimal inactivation level varied with anatomic location and additional mutations of WNT pathway regulators. Assessment of the regulatory effects of secondary alterations in WNT drivers in combination with APC in vivo provided evidence that AMER1 mutations increase WNT activity in tumors with suboptimal APC genotypes. The fitness landscape of APC inactivation was consistent across microsatellite unstable and polymerase epsilon-deficient colorectal cancers and tumors in patients with familial adenomatous polyposis. Together, these findings suggest a general "just-right" optimum for APC inactivation and WNT signaling, pointing to WNT hyperactivation as a potential vulnerability in cancer.

Mathematical modeling of tumor development with different APC genotypes substantiates the "just-right" APC inactivation model and suggests alterations in secondary WNT regulators enhance WNT activity in colorectal cancers with suboptimal APC genotypes. This article is part of a special series: Driving Cancer Discoveries with Computational Research, Data Science, and Machine Learning/AI .