Abstract
Physiological states of bacterial cells exhibit a wide spectrum of timescale. Under the nutrient-rich conditions, most of the cells in an isogenic bacterial population grow at certain rates, while a small subpopulation sometimes stays in a dormant state where the growth rates slow down by orders of magnitude. What is the origin of such heterogeneity of timescales? Here we addressed this question by studying the kinetic model of Escherichia coli central carbon metabolism including the dynamics of the energy currency molecules, which have often been ignored. We found that the model robustly exhibits both the growing-and the dormant state. In order to unveil the mechanism of distinct behaviours, we developed a recursive method to simplify the model without changing the qualitative feature of the dynamics. Analytical and numerical studies of the 2-variable minimal model revealed the necessary conditions for the distinct behaviour, namely, the depletion of energy due to the futile cycle and its non-uniform impact to the kinetics because of the co-existence of the energy currency-coupled and uncoupled reactions as well as branching of the network. The result is consistent with the experimental evidences of the appearance of the futile cycle in mutants and provides a possible explanation for the appearance of dormant cells that causes antibiotic persistence.
Significance Statement Bacterial cells can exhibit extremely slow growth or dormancy, even when the environment allows fast growth. It is a challenging question how the cellular metabolism can show such a long timescale even though it operates in much shorter timescales to grow quickly under favorable conditions. By simulating the kinetic model of Escherichia coli metabolism including the energy currency molecules, we found that the system robustly exhibits distinctively fast and slow dynamics. Through a systematic reduction of the original model, we derived a minimal model that exhibits both slow and fast dynamics. The analysis demonstrated that it is the robust feature of the network structure that includes the futile cycle, energy currency-coupled and uncoupled reactions, and branching.
Competing Interest Statement
The authors have declared no competing interest.
Footnotes
The authors declare no competing interest.
