Hidden variables and divergent time-scales: Non-bistable mechanisms for phenotypic diversification under stress

Single-cell experiments reveal that genetically identical bacteria can follow divergent growth and survival trajectories after antibiotic exposure. The mechanism underlying this divergence is unclear and cannot be explained by existing models based on bistability. We propose a class of models linking proteome allocation, gene expression, and growth rate during antibiotic stress. In our framework, transcriptional and translational resources for resistance genes behave like generalized momenta whose initial allocation predicts cell fate. This model reproduces key experimental observations and suggests that preexisting extrinsic variability drives growth rate variation following antibiotic exposure.