Parameter sensitivity and critical transition anticipation in bistable toxin-antitoxin dynamics

Toxin-antitoxin systems are central to bacterial persistence, promoting drug tolerance and infection relapse, and therefore demand a clear mechanistic understanding of their regulation. It is thus intriguing to investigate the possible routes to persister cell formation through mathematical modelling and to assess whether their emergence can be anticipated using statistical measures. For this dual purpose, a mathematical model describing the fundamental biochemical interactions among the operon, mRNA, toxin, antitoxin, and two associated protein complexes is considered in this study. The uncertainty in the steady-state behaviour of the deterministic model outcomes is analysed using two complementary forms of global sensitivity analysis. Both these techniques identify six key parameters that substantially influence transcription, translation, and the turnover of antitoxins. Among these, the parameter controlling the quadratic repression of antitoxin through toxin binding has opposite effects on the two species, thereby driving hysteresis between alternate physiological states. Intrinsic noise is introduced into the deterministic model via the chemical master equation. Subsequent Gillespie simulations reveal a critical transition from normal to persister cells, which is then detected using twelve multivariate statistical indicators within moving- and expanding-window frameworks. Sensitivity analyses define hyperparameter ranges that ensure reliable predictions, and robustness tests across repeated simulations show consistent performance for most moving-window indicators, except for some variance-covariance and information-based measures. The expanding-window approach reveals different types of warnings-flickering, sustained, and spurious-quantified by true-positive rates, lead times, and total warning counts. Together, these results demonstrate that multivariate measures can reliably predict critical transitions and provide a solid framework for understanding the loss of resilience in complex biological systems.