We reconceptualize homeostasis from an inherently stochastic, intergenerational perspective. Here we use our SChemostat technology to directly record high-precision multigenerational trains of sizes of statistically identical non-interacting individual cells of Caulobacter crescentus in precisely controlled environmental conditions. We first show that individual cells indeed maintain stochastic intergenerational homeostasis of their characteristic sizes, then extract organizational principles in the form of an intergenerational scaling law and other "emergent simplicities", which facilitate a principled route to dimensional reduction of the problem. We use these emergent simplicities to formulate the precise theoretical framework for stochastic homeostasis, which not only captures the exact kinematics of stochastic intergenerational cell size homeostasis (providing spectacular theory-data matches with no fitting parameters), but also determines the necessary and sufficient condition for stochastic intergenerational homeostasis. Compellingly, our reanalysis of existing data published by other groups using different single-cell technologies demonstrates that this intergenerational framework is applicable to other microorganisms (Escherichia coli and Bacillus subtilis) in a variety of growth conditions. Finally, we establish that in balanced growth conditions stochastic intergenerational cell size homeostasis is achieved through elastic adaptation, thus precluding the possibility that cell size can act as a repository of intergenerational memory.

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-identical Caulobacter crescentus cells 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 coli and Bacillus 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 treatment 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.

In isolation from their peers, Photinus carolinus fireflies flash with no intrinsic period between successive bursts. Yet, when congregating into large mating swarms, these fireflies transition into predictability, synchronizing with their neighbors with a rhythmic periodicity. Here we propose a mechanism for emergence of synchrony and periodicity, and formulate the principle in a mathematical framework. Remarkably, with no fitting parameters, analytic predictions from this simple principle and framework agree strikingly well with data. Next, we add further sophistication to the framework using a computational approach featuring groups of random oscillators via integrate-and-fire interactions controlled by a tunable parameter. This agent-based framework of P. carolinus fireflies interacting in swarms of increasing density also shows quantitatively similar phenomenology and reduces to the analytic framework in the appropriate limit of the tunable coupling strength. We discuss our findings and note that the resulting dynamics follow the style of a decentralized follow-the-leader synchronization, where any of the randomly flashing individuals may take the role of the leader of any subsequent synchronized flash burst.

Building on the known scaling law that a single timescale, a cellular unit of time, governs stochastic growth and division of individual bacterial cells under constant growth conditions, here we articulate an analogous ansatz for time-varying growth conditions. We propose that a dynamic rescaling of the cellular unit of time captures the predominant effect of external variations in conditions. Using this temporal scaling ansatz, we derive exact analytic results for how the time-dependent cell age distribution adapts to changing conditions. Our results reveal the natural representation for these time-dependent dynamics. When recast in terms of the new representation, the cell age distribution evolves under time-invarant rules even as growth conditions remain dynamic! This result corresponds to the generalization of the scaling law for constant growth condition. Finally, we provide a prescription for convenient experimental tests of the temporal scaling ansatz.

Our understanding of the bacterial cell cycle is framed largely by population-based experiments that focus on the behavior of idealized average cells. Most famously, the contributions of Cooper and Helmstetter help to contextualize the phenomenon of overlapping replication cycles observed in rapidly growing bacteria. Despite the undeniable value of these approaches, their necessary reliance on the behavior of idealized average cells masks the stochasticity inherent in single-cell growth and physiology and limits their mechanistic value. To bridge this gap, we propose an updated and agnostic framework, informed by extant single-cell data, that quantitatively accounts for stochastic variations in single-cell dynamics and the impact of medium composition on cell growth and cell cycle progression. In this framework, stochastic timers sensitive to medium composition impact the relationship between cell cycle events, accounting for observed differences in the relationship between cell cycle events in slow- and fast-growing cells. We conclude with a roadmap for potential application of this framework to longstanding open questions in the bacterial cell cycle field.