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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.

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.

Biological systems are complex and hierarchical. Yet, key physiological “state” variables are effectively held in homeostasis despite the inherent stochasticity of constitutive molecular processes. To identify quantitative rules governing the control systems responsible for homeostasis, we reconceptualize homeostasis as a dynamical—albeit stochastic—process, rather than as an end state (i.e., a setpoint). We focus on cell size homeostasis as a valuable case study. Using our SChemostat technology, we obtain high-precision multigenerational trains of cell sizes of statistically identical, non-interacting individualCaulobacter crescentuscells in precisely controlled environments. Characterizing the typical generational size of a bacterium by the size immediately following a division event, we first establish that individual cells indeed maintain stochastic intergenerational size homeostasis. Through extensive data analysis from single-cell experiments under multiple growth conditions, we uncover hidden simplicities in these data, including an intergenerational scaling law governing fluctuations in cell sizes across different generations. These “emergent simplicities” comprehensively describe the dynamics—in turn they specify (without need for any fitting parameters) the precise stochastic map governing the intergenerational evolution of cell sizes. Importantly, we find that intergenerational cell size homeostasis is achieved through memory-free, reflexive elastic adaptation. Thus, under balanced growth conditions, cell size cannot serve as a repository of intergenerational memory.

Organisms are able to partition resources adaptively between growth and repair. The precise nature of optimal partitioning and how this emerges from cellular dynamics including insurmountable trade-offs remains an open question. We construct a mathematical framework to estimate optimal partitioning and the corresponding maximal growth rate constrained by empirical scaling laws. We model a biosynthesis tradeoff governing the partitioning of the ribosome economy between replicating functional proteins and replicating the ribosome pool, and also an energy tradeoff arising from the finite energy budget of the cell. Through exact analytic calculations we predict limits on the range of values partitioning ratios take while sustaining growth. We calculate how partitioning and cellular composition scale with protein and ribosome degradation rates and organism size. These results reveal different classes of optimizing strategies corresponding to phenotypically distinct bacterial lifestyles. We summarize these findings in a quadrant-based taxonomy including: a “greedy” strategy maximally prioritizing growth, a “prudent” strategy maximally prioritizing the management of damaged pools, and “strategically limited” intermediates.

Endosomal maturation is a critical and fundamental process for robust transport of cargo (such as activated receptors) to specific cellular compartments in a timely manner. The most prominent model of endosomal maturation involves a phosphoinositide-driven gain or loss of specific proteins at the level of individual endosomes, emphasising an autonomous and stochastic model of maturation. However, to date, direct whole cell-level measurements of absolute number of maturation events have not been performed, owing to limitations in fast, volumetric imaging. Here, we use lattice light-sheet imaging to track individual very early and early endosomes over the entire population. We demonstrate that direct inter-endosomal contact drives the maturation from very early (APPL1-positive) to early (EEA1-positive) endosomes. Using fluorescence lifetime, we show that this endosomal interaction is underpinned by the asymmetric binding of EEA1 to very early and early endosomes through the N- and C-termini, respectively. Thus, stochastic microtubule-mediated inter-endosomal interactions through EEA1 provide a mechanism to bring temporal and population-level control to the process of endosome maturation. Our findings indicate that APPL1- to EEA1-positive endosomal maturation is not a result of autonomous endosomal events but is driven by heterotypic EEA1-mediated endosomal interactions.

Our current 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 washes out the stochasticity inherent in single cell growth and physiology limiting 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.

In isolation from their peers,Photinus carolinusfireflies 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 ofP. carolinusfireflies 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.

In the present paper, the possibility of invoking stochastic resonance (SR, periodic and aperiodic) by regulating the operating value of an appropriate parameter is explored. The operating values of these parameters are defined as the set point of the system throughout the present paper. Brusselator, a mathematical model [I. Prigogine and R. Lefever, J. Chem. Phys. 48, 1695 (1968)JCPSA60021-960610.1063/1.1668896] of nonlinear chemical reactions, is used for this purpose. We consider the effect of intrinsic noise in the Brusselator due to the Markovian nature of the chemical reactions. The stochastic time evolution is studied using the Gillespie algorithm [D. T. Gillespie, J. Comput. Phys. 22, 403 (1976)JCTPAH0021-999110.1016/0021-9991(76)90041-3], which is an exact stochastic simulation algorithm. We analyze the dependence of the resonance point on both the strength of the intrinsic noise as well as the distance from the bifurcation point. Subsequently, the phenomena of SR is explored using both periodic and aperiodic stimulus. It was found that, for a given system size, in both cases, SR is achieved by variation of the set point. Set-point variation can be achieved by regulating either the source concentration or the rate constants. Resonance is observed in both cases. However, this resonance occurs at different values of the set point, even with a fixed system size. This is clearly seen in the set-point versus system-size plane, where the resonance line has different slopes for the two scenarios. Our semianalytic treatment points to the fact that for a given system size intrinsic noise is affected differently for different methods involving the variation of the set point. This is explained by writing the corresponding chemical Langevin equation and comparing the various intrinsic noise sources.