Spatiotemporal dynamics and control of the E2F/Myc/miR-17-92 proliferation switch in breast cancer

The E2F/Myc/miR-17-92 regulatory module functions as a decision-making gate between cellular quiescence and proliferation, and its dysregulation is implicated in breast cancer; however, how time delay, spatial transport, and intercellular coupling jointly reshape its dynamical regimes remains insufficiently characterized. In this work, we extend the Aguda-type miR-E2F/Myc feedback model by introducing a saturating miR-dependent degradation mechanism and then embedding the circuit into delay-diffusion and network-coupled settings, including scale-free coupling and higher-order (simplicial) interactions. Using bifurcation analysis, we derive verifiable conditions for saddle-node and Hopf bifurcations and identify cusp, Bautin, and Bogdanov-Takens points that partition parameter space into quiescent, proliferative, and bistable regimes. Exploiting these bifurcation signatures, we formulate two dynamical intervention principles: a switch-like strategy to steer trajectories away from high-activity attractors and a rhythm-reconstruction strategy to restore physiological oscillations. The same bifurcation structure also provides a basis for anticipating critical transitions, as increased variance and lag-1 autocorrelation in the E2F/Myc time series near a saddle-node transition emerge as potential early-warning signals of declining dynamical resilience. Extending the analysis to spatiotemporal settings, we show that delay and diffusion jointly generate oscillatory dynamics and pattern-forming instabilities, with diffusion promoting Turing-type symmetry breaking and delay facilitating synchronization. At the population level, asymmetric diffusion promotes heterogeneity via E2F/Myc, whereas miR coupling homogenizes cellular activity. Higher-order interactions further lower the critical synchronization delay and narrow the stability region of homogeneous equilibria. TCGA-BRCA analyses using GEPIA, LinkedOmics, and TIMER reveal elevated E2F expression and consistent associations with miRNAs and immune infiltration, supporting the biological relevance of the modeled regulatory axis. Overall, these findings provide a bifurcation-based multiscale framework for predicting critical transitions and guiding dynamical interventions in aberrant proliferation.