Cell Fate by Design or Chance: Interplay of Nonlinearity and Stochasticity in Gene Regulatory Network motifs

Cell fate decisions emerge from the intricate tug-of-war between deterministic regulatory logic and stochastic molecular fluctuations. How stochasticity, inherent in intracellular Gene Regulatory Networks (the heart of determining cellular fates), shapes cellular regulatory dynamics is central to and essential for both interpreting natural cellular decision-making and designing robust synthetic circuits. In this work, we develop a general mathematical framework based on the linear noise approximation (LNA) to quantify intrinsic fluctuations around the mean expression levels in a single-cell GRN motif with nonlinear cooperative regulatory couplings. The genetic toggle switch (TS) and TS coupled with positive autoregulation, as illustrative examples, exhibit both continuous and discontinuous transitions (bifurcation) between low- and high-expression states driven by nonlinear regulation. We demonstrate that LNA captures both deterministic and stochastic dynamics. We find that the LNA performs well in capturing the inherent stochasticity in both monostable and bistable regimes. Still, deviations arise near bifurcation points: fluctuations are enhanced near criticality in continuous transitions, while finite-size effects dominate discontinuous transitions, analogous to critical phenomena in statistical physics. Finally, we discuss the implications of our framework for designing synthetic gene circuits.