Decoding cancer dynamics: The role of miRNA in E2F/Myc networks and bifurcation points

Cancer development is driven by critical state transitions in gene regulatory networks, particularly the miRNA-E2F/Myc pathway, yet the nonlinear dynamics underlying this process remain relatively scarce. Here, we construct a dynamic model incorporating parameters, time delays, and diffusion to elucidate how bifurcations and spatiotemporal oscillations drive carcinogenesis. The model reveals that regulatory variations can induce saddle-node, Hopf, Bogdanov-Takens, and Cusp bifurcations, with key events-such as extracellular matrix protein levels exceeding a threshold-triggering irreversible oncogenic switches. Time delays and diffusion further generate gene oscillations and spatial heterogeneity through Hopf and Turing-Hopf bifurcations; these dynamic signatures can serve as early warning indicators, and our multiscale modeling enables quantitative prediction of critical transitions, providing a theoretical basis for optimizing targeted therapy timing.