Multivariate measures of critical transitions in a bistable gene regulatory network.

Developing concise gene regulatory networks that accurately encode cellular decision-making processes remains a key area of research across biological dynamics. Here, this challenge is addressed by investigating the behavior of a minimal gene regulatory network comprising three transcription factors within deterministic and stochastic frameworks. The components of the network interact through self-activation of a single transcription factor, mutual inhibition between a pair, and additional cross-inhibition exerted by the third. Following a brief mathematical analysis of the deterministic model, the influence of parameter variations on the steady-state concentrations of the transcription factors is quantified using Sobol's sensitivity method. The subsequent bifurcation analysis, conducted by varying the most sensitive parameter, reveals three distinct bistable configurations: isola, mushroom, and canonical toggle. Thereafter, basin stability quantifies the resilience of coexisting attractors, demonstrating that inhibitory strength can shift stability in favor of one state. In addition, 12 multivariate statistical indicators are computed using different strategies to anticipate emergent critical transitions within the mushroom architecture. Their predictive efficacy is systematically evaluated across four different criteria. First, sensitivity analysis reveals that the predictive performance of principal component-based indicators, along with the mutual interdependence-based measure, remains less affected by variations in the hyperparameter configurations. Statistical significance testing further demonstrates the superior efficacy of multivariate indicators in capturing the transition from the upper to the lower branch of the mushroom, compared with the reverse case. These results are further justified by a detailed robustness assessment and false-positive detection test. Taken together, this work bridges contemporary gene regulatory dynamics with the prediction of critical transitions, introducing methodologies that have not been previously applied in this context.