Delay induced multistability and oscillations in a microRNA-mediated gene regulatory network

MicroRNAs (miRNAs) serve as pivotal post-transcriptional regulators in many essential cellular processes, including division, differentiation, and apoptosis. Recent studies highlight that miRNA-mediated transcriptional regulation is not instantaneous but involves finite interaction times. In this work, we introduce two distinct time delays, auto-feedback delay (τ1) and interaction delay (τ2), into a Myc/E2F/miR-17-92 cancer network model to investigate their effects on network dynamics. Our results demonstrate that both delays significantly reshape the system’s stability landscape. Depending on delay conditions, the network can transition between stable high-protein (“on”) and low-protein (“off”) states, exhibit periodic oscillations, or enter multistable regimes. Through codimension-one and codimension-two bifurcation analyses, we show that variations in τ1 and τ2 drive diverse bifurcation behaviors, enabling switches among distinct dynamical states. These findings imply that modulating time delays within gene regulatory networks could offer a potential dynamical strategy for intervening in tumor progression.