Intergenerational scaling law determines the precision kinematics of stochastic individual-cell-size homeostasis

Individual bacterial cells grow and divide stochastically. Yet they maintain their characteristic sizes across generations within a tightly controlled range. What rules ensure intergenerational stochastic homeostasis of individual cell sizes? Valuable clues have emerged from high-precision longterm tracking of individual statistically-identicalCaulobacter crescentuscells as reported in [1]: Intergenerational cell size homeostasis is an inherently stochastic phenomenon, follows Markovian or memory-free dynamics, and cells obey an intergenerational scaling law, which governs the stochastic map characterizing generational sequences of characteristic cell sizes. These observed emergent simplicities serve as essential building blocks of the first-principles-based theoretical framework we develop here. Our exact analytic fitting-parameter-free results for the predicted intergenerational stochastic map governing the precision kinematics of cell size homeostasis are remarkably well borne out by experimental data, including extant published data on other microorganisms,Escherichia coliandBacillus subtilis. Furthermore, our framework naturally yields the general exact and analytic condition, necessary and sufficient, which ensures that stochastic homeostasis can be achieved and maintained. Significantly, this condition is more stringent than the known heuristic result for the popular quasi-deterministic adder-sizer-timer frameworks. In turn the fully stochastic treat-ment we present here extends and updates extant frameworks, and challenges the notion that the mythical “average cell” can serve as a reasonable proxy for the inherently stochastic behaviors of actual individual cells.