Synergistic and antagonistic effects of deterministic and stochastic cell-cell variations

By diversifying, cells in a clonal population can together overcome the limits of individuals. Diversity in single-cell growth rates allows the population to survive environmental stresses, such as antibiotics, and grow faster than the undiversified population. These functional cell-cell variations can arise stochastically, from noise in biochemical reactions, or deterministically, by asymmetrically distributing damaged components. While each of the mechanisms is well understood, the effect of the combined mechanisms is unclear. To evaluate the contribution of the deterministic component we developed a mathematical model by mapping the growing population to the Ising model. To analyze the combined effects of stochastic and deterministic contributions we introduced the analytical results of the Ising-mapping into an Euler-Lotka framework. Model results, confirmed by simulations and experimental data, show that deterministic cell-cell variations increase near-linearly with stress. As a consequence, we predict that the gain in population doubling time from cell-cell variations is primarily stochastic at low stress but may cross over to deterministic at higher stresses. Furthermore, we find that while the deterministic component minimizes population damage, stochastic variations antagonize this effect. Together our results may help identifying stress-tolerant pathogenic cells and thus inspire novel antibiotic strategies.