Dynamic processes of fate decision in inducible bistable systems

The process of biological fate decision regulated by gene regulatory networks (GRNs) involves numerous complex dynamical interactions among many components. Mathematical modeling typically employed ordinary differential equations (ODEs) and steady-state analysis, which has yielded valuable quantitative insights. However, stable states predicted by theoretical models often fail to capture transient or metastable phenomena that occur during most observation periods in experimental or real biological systems. We attribute this discrepancy to the omission of dynamic processes of various complex interactions. Here, we demonstrate the influence of delays in gene regulatory steps and the time scales of the external induction on the dynamic processes of the fate decision in inducible bistable systems. We propose that steady-state parameters determine the landscape of fate decision. However, during the dynamic evolution along the landscape, the unequal delays of biochemical interactions as well as time scale of external induction cause deviations in the differentiation trajectories, leading to the formation of new transient distributions that persist long-term. Our findings emphasize the importance of considering dynamic processes in fate decision, instead of relying solely on steady-state analysis. We provide insights into the interpretation of experimental phenomena, and offer valuable guidance for future efforts in dynamical modeling and synthetic biology design.