Let there be multifunctionality: Uncovering the criticality zoo of the AC-DC genetic circuit

Gene regulatory networks (GRNs) govern processes such as cell fate, patterning, and adaptation. While multistability and oscillations are both common GRN dynamics in cell biology, they are typically studied and engineered in isolation. Here, we challenge this separation using the AC-DC circuit, a minimal three-gene network that merges the classical toggle switch and repressilator. Using a thermodynamic formalism and Bayesian inference, we show that even a single-inducer version of the circuit can display diverse multifunctional dynamics, including the coexistence of oscillations and multistability. In addition we explore robustness, classify emergent behaviours, and analyse critical slowing down and regime transitions. Remarkably, the AC-DC circuit can produce more than 30 topologically distinct bifurcation diagrams, challenging the classical view that network topology rigidly constrains dynamical outcomes. This flexibility enables synthetic capabilities that couple hysteresis with oscillations, critical slowing down, and reversibility. By uncovering the hidden potential of minimal genetic circuits and outlining design principles for their implementation, this work opens new directions for harnessing emergent complexity using the basic building blocks of life.