A Phase-Gated AR(2) Framework for Colonic Crypt Renewal — Reproducible Analysis

This archive contains the complete code and input data for the Phase-Gated Autoregressive of Order 2 (PAR(2)) time-series analysis of gene expression in colorectal cancer organoids. The study investigates the dynamic stability of key cancer and circadian rhythm genes under genetic variations of the tumor suppressor APC and the clock gene BMAL1. Summary of Analysis: The analysis models time-series gene expression data (GSE157357) using a PAR(2) model to quantify the stability (kernel dynamics) and oscillatory capacity of six critical genes (Lgr5, Myc, Per2, Ascl2, Olfm4, and Axin2) across four distinct genetic conditions: APC-WT / BMAL1-WT (Healthy + Clock) APC-WT / BMAL1-Mut (Healthy – Clock KO) APC-Mut / BMAL1-WT (Cancer + Clock) APC-Mut / BMAL1-Mut (Cancer – Clock KO) Key findings relate to the explosive instability of the Myc kernel upon Bmal1 knockout in cancer cells, revealing a mechanistically linked chronopathology.