Concurrent processes set E. coli cell division

Determining the rate-limiting processes for cell division in Escherichia coli

A critical cell cycle checkpoint for most bacteria is the onset of constriction when the septal peptidoglycan synthesis starts. According to the current understanding, the arrival of FtsN to midcell triggers this checkpoint in Escherichia coli. Recent structural and in vitro data suggests that recruitment of FtsN to the Z-ring leads to a conformational switch in actin-like FtsA, which links FtsZ protofilaments to the cell membrane and acts as a hub for the late divisome proteins. Here, we investigate this putative pathway using in vivo measurements and stochastic cell cycle modeling at moderately fast growth rates. Quantitatively upregulating protein concentrations and determining the resulting division timings shows that FtsN and FtsA numbers are not rate-limiting for the division in E. coli. However, at higher overexpression levels, they affect divisions: FtsN by accelerating and FtsA by inhibiting them. At the same time, we find that the FtsZ numbers in the cell are one of the rate-limiting factors for cell divisions in E. coli. Altogether, these findings suggest that instead of FtsN, accumulation of FtsZ in the Z-ring is one of the main drivers of the onset of constriction in E. coli at faster growth rates.

Direct single-cell observation of a key Escherichia coli cell-cycle oscillator

Initiation of DNA replication in Escherichia coli is coupled to cell size via the DnaA protein, whose activity is dependent on its nucleotide-bound state. However, the oscillations in DnaA activity have never been observed at the single-cell level. By measuring the volume-specific production rate of a reporter protein under control of a DnaA-regulated promoter, we could distinguish two distinct cell-cycle oscillators. The first, driven by both DnaA activity and SeqA repression, shows a causal relationship with cell size and divisions, similarly to initiation events. The second one, a reporter of DnaA activity alone, loses the synchrony and causality properties. Our results show that transient inhibition of gene expression by SeqA keeps the oscillation of volume-sensing DnaA activity in phase with the subsequent division event and suggest that DnaA activity peaks do not correspond directly to initiation events.

Deciphering the Relationship between Cell Growth and Cell Cycle in Individual Escherichia coli Cells by Flow Cytometry

Accurate coordination of chromosome replication and cell division is essential for cellular processes, yet the regulatory mechanisms governing the bacterial cell cycle remain contentious. The lack of quantitative data connecting key cell cycle players at the single-cell level across large samples hinders consensus. Employing high-throughput flow cytometry, we quantitatively correlated the expression levels of key cell cycle proteins (FtsZ, MreB, and DnaA) with DNA content in individual bacteria. Our findings reveal distinct correlations depending on the chromosome number (CN), specifically whether CN ≤2 or ≥4, unveiling a mixed regulatory scenario in populations where CN of 2 or 4 coexist. We observed function-dependent regulations for these key proteins across nonoverlapping division cycles and various nutrient conditions. Notably, a logarithmic relationship between total protein content and replication origin number across nutrient conditions suggests a unified mechanism governing cell cycle progression, confirming the applicability of Schaechter's growth law to cells with CN ≥4. For the first time, we established a proportional relationship between the synthesis rates of key cell cycle proteins and chromosome dynamics in cells with CN ≥4. Drug experiments highlighted CN 2 and 4 as pivotal turning points influencing cellular resource allocation. This high-throughput, single-cell analysis provides interconnected quantitative insights into key molecular events, facilitating a predictive understanding of the relationship between cell growth and cell cycle.

Mechanisms of cell size regulation in slow-growing Escherichia coli cells: discriminating models beyond the adder

Under ideal conditions, Escherichia coli cells divide after adding a fixed cell size, a strategy known as the adder. This concept applies to various microbes and is often explained as the division that occurs after a certain number of stages, associated with the accumulation of precursor proteins at a rate proportional to cell size. However, under poor media conditions, E. coli cells exhibit a different size regulation. They are smaller and follow a sizer-like division strategy where the added size is inversely proportional to the size at birth. We explore three potential causes for this deviation: degradation of the precursor protein and two models where the propensity for accumulation depends on the cell size: a nonlinear accumulation rate, and accumulation starting at a threshold size termed the commitment size. These models fit the mean trends but predict different distributions given the birth size. To quantify the precision of the models to explain the data, we used the Akaike information criterion and compared them to open datasets of slow-growing E. coli cells in different media. We found that none of the models alone can consistently explain the data. However, the degradation model better explains the division strategy when cells are larger, whereas size-related models (power-law and commitment size) account for smaller cells. Our methodology proposes a data-based method in which different mechanisms can be tested systematically.

Accurate Prediction of Antimicrobial Susceptibility for Point-of-Care Testing of Urine in Less than 90 Minutes via iPRISM Cassettes

The extensive and improper use of antibiotics has led to a dramatic increase in the frequency of antibiotic resistance among human pathogens, complicating infectious disease treatments. In this work, a method for rapid antimicrobial susceptibility testing (AST) is presented using microstructured silicon diffraction gratings integrated into prototype devices, which enhance bacteria-surface interactions and promote bacterial colonization. The silicon microstructures act also as optical sensors for monitoring bacterial growth upon exposure to antibiotics in a real-time and label-free manner via intensity-based phase-shift reflectometric interference spectroscopic measurements (iPRISM). Rapid AST using clinical isolates of Escherichia coli (E. coli) from urine is established and the assay is applied directly on unprocessed urine samples from urinary tract infection patients. When coupled with a machine learning algorithm trained on clinical samples, the iPRISM AST is able to predict the resistance or susceptibility of a new clinical sample with an Area Under the Receiver Operating Characteristic curve (AUC) of ∼ 0.85 in 1 h, and AUC > 0.9 in 90 min, when compared to state-of-the-art automated AST methods used in the clinic while being an order of magnitude faster.

Bacterial cell-size changes resulting from altering the relative expression of Min proteins

The timing of cell division, and thus cell size in bacteria, is determined in part by the accumulation dynamics of the protein FtsZ, which forms the septal ring. FtsZ localization depends on membrane-associated Min proteins, which inhibit FtsZ binding to the cell pole membrane. Changes in the relative concentrations of Min proteins can disrupt FtsZ binding to the membrane, which in turn can delay cell division until a certain cell size is reached, in which the dynamics of Min proteins frees the cell membrane long enough to allow FtsZ ring formation. Here, we study the effect of Min proteins relative expression on the dynamics of FtsZ ring formation and cell size in individual Escherichia coli bacteria. Upon inducing overexpression of minE, cell size increases gradually to a new steady-state value. Concurrently, the time required to initiate FtsZ ring formation grows as the size approaches the new steady-state, at which point the ring formation initiates as early as before induction. These results highlight the contribution of Min proteins to cell size control, which may be partially responsible for the size fluctuations observed in bacterial populations, and may clarify how the size difference acquired during asymmetric cell division is offset.

Mechanisms of Cell Size Regulation in Slow-Growing Escherichia coli Cells: Discriminating Models Beyond the Adder

Under ideal conditions, Escherichia coli cells divide after adding a fixed cell size, a strategy known as the adder. This concept applies to various microbes and is often explained as the division that occurs after a certain number of stages, associated with the accumulation of precursor proteins at a rate proportional to cell size. However, under poor media conditions, E. coli cells exhibit a different size regulation. They are smaller and follow a sizer-like division strategy where the added size is inversely proportional to the size at birth. We explore three potential causes for this deviation: precursor protein degradation, nonlinear accumulation rate, and a threshold size termed the commitment size. These models fit mean trends but predict different distributions given the birth size. To validate these models, we used the Akaike information criterion and compared them to open datasets of slow-growing E. coli cells in different media. the degradation model could explain the division strategy for media where cells are larger, while the commitment size model could account for smaller cells. The power-law model, finally, better fits the data at intermediate regimes.

Out-of-equilibrium gene expression fluctuations in the presence of extrinsic noise

Cell-to-cell variability in protein concentrations is strongly affected by extrinsic noise, especially for highly expressed genes. Extrinsic noise can be due to fluctuations of several possible cellular factors connected to cell physiology and to the level of key enzymes in the expression process. However, how to identify the predominant sources of extrinsic noise in a biological system is still an open question. This work considers a general stochastic model of gene expression with extrinsic noise represented as fluctuations of the different model rates, and focuses on the out-of-equilibrium expression dynamics. Combining analytical calculations with stochastic simulations, we characterize how extrinsic noise shapes the protein variability during gene activation or inactivation, depending on the prevailing source of extrinsic variability, on its intensity and timescale. In particular, we show that qualitatively different noise profiles can be identified depending on which are the fluctuating parameters. This indicates an experimentally accessible way to pinpoint the dominant sources of extrinsic noise using time-coarse experiments.

Implications of differential size-scaling of cell-cycle regulators on cell size homeostasis

Accurate timing of division and size homeostasis is crucial for cells. A potential mechanism for cells to decide the timing of division is the differential scaling of regulatory protein copy numbers with cell size. However, it remains unclear whether such a mechanism can lead to robust growth and division, and how the scaling behaviors of regulatory proteins influence the cell size distribution. Here we study a mathematical model combining gene expression and cell growth, in which the cell-cycle activators scale superlinearly with cell size while the inhibitors scale sublinearly. The cell divides once the ratio of their concentrations reaches a threshold value. We find that the cell can robustly grow and divide within a finite range of the threshold value with the cell size proportional to the ploidy. In a stochastic version of the model, the cell size at division is uncorrelated with that at birth. Also, the more differential the cell-size scaling of the cell-cycle regulators is, the narrower the cell-size distribution is. Intriguingly, our model with multiple regulators rationalizes the observation that after the deletion of a single regulator, the coefficient of variation of cell size remains roughly the same though the average cell size changes significantly. Our work reveals that the differential scaling of cell-cycle regulators provides a robust mechanism of cell size control.

Regulatory elements coordinating initiation of chromosome replication to the Escherichia coli cell cycle

Escherichia coli coordinates replication and division cycles by initiating replication at a narrow range of cell sizes. By tracking replisomes in individual cells through thousands of division cycles in wild-type and mutant strains, we were able to compare the relative importance of previously described control systems. We found that accurate triggering of initiation does not require synthesis of new DnaA. The initiation size increased only marginally as DnaA was diluted by growth after dnaA expression had been turned off. This suggests that the conversion of DnaA between its active ATP- and inactive ADP-bound states is more important for initiation size control than the total free concentration of DnaA. In addition, we found that the known ATP/ADP converters DARS and datA compensate for each other, although the removal of them makes the initiation size more sensitive to the concentration of DnaA. Only disruption of the regulatory inactivation of DnaA mechanism had a radical impact on replication initiation. This result was corroborated by the finding that termination of one round of replication correlates with the next initiation at intermediate growth rates, as would be the case if RIDA-mediated conversion from DnaA-ATP to DnaA-ADP abruptly stops at termination and DnaA-ATP starts accumulating.

Advancing synthetic biology through cell-free protein synthesis

The rapid development of synthetic biology has enabled the production of compounds with revolutionary improvements in biotechnology. DNA manipulation tools have expedited the engineering of cellular systems for this purpose. Nonetheless, the inherent constraints of cellular systems persist, imposing an upper limit on mass and energy conversion efficiencies. Cell-free protein synthesis (CFPS) has demonstrated its potential to overcome these inherent constraints and has been instrumental in the further advancement of synthetic biology. Via the removal of the cell membranes and redundant parts of cells, CFPS has provided flexibility in directly dissecting and manipulating the Central Dogma with rapid feedback. This mini-review summarizes recent achievements of the CFPS technique and its application to a wide range of synthetic biology projects, such as minimal cell assembly, metabolic engineering, and recombinant protein production for therapeutics, as well as biosensor development for in vitro diagnostics. In addition, current challenges and future perspectives in developing a generalized cell-free synthetic biology are outlined.

Using conditional independence tests to elucidate causal links in cell cycle regulation in Escherichia coli

How cells regulate their cell cycles is a central question for cell biology. Models of cell size homeostasis have been proposed for bacteria, archaea, yeast, plant, and mammalian cells. New experiments bring forth high volumes of data suitable for testing existing models of cell size regulation and proposing new mechanisms. In this paper, we use conditional independence tests in conjunction with data of cell size at key cell cycle events (birth, initiation of DNA replication, and constriction) in the model bacterium Escherichia coli to select between the competing cell cycle models. We find that in all growth conditions that we study, the division event is controlled by the onset of constriction at midcell. In slow growth, we corroborate a model where replication-related processes control the onset of constriction at midcell. In faster growth, we find that the onset of constriction is affected by additional cues beyond DNA replication. Finally, we also find evidence for the presence of additional cues triggering initiations of DNA replication apart from the conventional notion where the mother cells solely determine the initiation event in the daughter cells via an adder per origin model. The use of conditional independence tests is a different approach in the context of understanding cell cycle regulation and it can be used in future studies to further explore the causal links between cell events.

Bacterial filaments recover by successive and accelerated asymmetric divisions that allow rapid post-stress cell proliferation

Filamentation is a reversible morphological change triggered in response to various stresses that bacteria might encounter in the environment, during host infection or antibiotic treatments. Here we re-visit the dynamics of filament formation and recovery using a consistent framework based on live-cells microscopy. We compare the fate of filamentous Escherichia coli induced by cephalexin that inhibits cell division or by UV-induced DNA-damage that additionally perturbs chromosome segregation. We show that both filament types recover by successive and accelerated rounds of divisions that preferentially occur at the filaments' tip, thus resulting in the rapid production of multiple daughter cells with tightly regulated size. The DNA content, viability and further division of the daughter cells essentially depends on the coordination between chromosome segregation and division within the mother filament. Septum positioning at the filaments' tip depends on the Min system, while the nucleoid occlusion protein SlmA regulates the timing of division to prevent septum closure on unsegregated chromosomes. Our results not only recapitulate earlier conclusions but provide a higher level of detail regarding filaments division and the fate of the daughter cells. Together with previous reports, this work uncovers how filamentation recovery allows for a rapid cell proliferation after stress treatment.

Beyond the average: An updated framework for understanding the relationship between cell growth, DNA replication, and division in a bacterial system

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.

Cellular resource allocation strategies for cell size and shape control in bacteria

Bacteria are highly adaptive microorganisms that thrive in a wide range of growth conditions via changes in cell morphologies and macromolecular composition. How bacterial morphologies are regulated in diverse environmental conditions is a long-standing question. Regulation of cell size and shape implies control mechanisms that couple the growth and division of bacteria to their cellular environment and macromolecular composition. In the past decade, simple quantitative laws have emerged that connect cell growth to proteomic composition and the nutrient availability. However, the relationships between cell size, shape, and growth physiology remain challenging to disentangle and unifying models are lacking. In this review, we focus on regulatory models of cell size control that reveal the connections between bacterial cell morphology and growth physiology. In particular, we discuss how changes in nutrient conditions and translational perturbations regulate the cell size, growth rate, and proteome composition. Integrating quantitative models with experimental data, we identify the physiological principles of bacterial size regulation, and discuss the optimization strategies of cellular resource allocation for size control.

Robust replication initiation from coupled homeostatic mechanisms

The bacterium Escherichia coli initiates replication once per cell cycle at a precise volume per origin and adds an on average constant volume between successive initiation events, independent of the initiation size. Yet, a molecular model that can explain these observations has been lacking. Experiments indicate that E. coli controls replication initiation via titration and activation of the initiator protein DnaA. Here, we study by mathematical modelling how these two mechanisms interact to generate robust replication-initiation cycles. We first show that a mechanism solely based on titration generates stable replication cycles at low growth rates, but inevitably causes premature reinitiation events at higher growth rates. In this regime, the DnaA activation switch becomes essential for stable replication initiation. Conversely, while the activation switch alone yields robust rhythms at high growth rates, titration can strongly enhance the stability of the switch at low growth rates. Our analysis thus predicts that both mechanisms together drive robust replication cycles at all growth rates. In addition, it reveals how an origin-density sensor yields adder correlations.

Microfluidics for long-term single-cell time-lapse microscopy: Advances and applications

Cells are inherently dynamic, whether they are responding to environmental conditions or simply at equilibrium, with biomolecules constantly being made and destroyed. Due to their small volumes, the chemical reactions inside cells are stochastic, such that genetically identical cells display heterogeneous behaviors and gene expression profiles. Studying these dynamic processes is challenging, but the development of microfluidic methods enabling the tracking of individual prokaryotic cells with microscopy over long time periods under controlled growth conditions has led to many discoveries. This review focuses on the recent developments of one such microfluidic device nicknamed the mother machine. We overview the original device design, experimental setup, and challenges associated with this platform. We then describe recent methods for analyzing experiments using automated image segmentation and tracking. We further discuss modifications to the experimental setup that allow for time-varying environmental control, replicating batch culture conditions, cell screening based on their dynamic behaviors, and to accommodate a variety of microbial species. Finally, this review highlights the discoveries enabled by this technology in diverse fields, such as cell-size control, genetic mutations, cellular aging, and synthetic biology.

Scaling of biosynthesis and metabolism with cell size

Cells adopt a size that is optimal for their function, and pushing them beyond this limit can cause cell aging and death by senescence or reduce proliferative potential. However, by increasing their genome copy number (ploidy), cells can increase their size dramatically and homeostatically maintain physiological properties such as biosynthesis rate. Recent studies investigating the relationship between cell size and rates of biosynthesis and metabolism under normal, polyploid, and pathological conditions are revealing new insights into how cells attain the best function or fitness for their size by tuning processes including transcription, translation, and mitochondrial respiration. A new frontier is to connect single-cell scaling relationships with tissue and whole-organism physiology, which promises to reveal molecular and evolutionary principles underlying the astonishing diversity of size observed across the tree of life.

Density fluctuations, homeostasis, and reproduction effects in bacteria

Single-cells grow by increasing their biomass and size. Here, we report that while mass and size accumulation rates of single Escherichia coli cells are exponential, their density and, thus, the levels of macromolecular crowding fluctuate during growth. As such, the average rates of mass and size accumulation of a single cell are generally not the same, but rather cells differentiate into increasing one rate with respect to the other. This differentiation yields a density homeostasis mechanism that we support mathematically. Further, we observe that density fluctuations can affect the reproduction rates of single cells, suggesting a link between the levels of macromolecular crowding with metabolism and overall population fitness. We detail our experimental approach and the “invisible” microfluidic arrays that enabled increased precision and throughput. Infections and natural communities start from a few cells, thus, emphasizing the significance of density-fluctuations when taking non-genetic variability into consideration.

Quantitative imaging, invisible microfluidics, and mathematical models demonstrate how the density of single E. coli cells fluctuates during the cell cycle, unmasking key homeostasis and population fitness effects.

Coupling between DNA replication, segregation, and the onset of constriction in Escherichia coli

Escherichia coli cell cycle features two critical cell-cycle checkpoints: initiation of replication and the onset of constriction. While the initiation of DNA replication has been extensively studied, it is less clear what triggers the onset of constriction and when exactly it occurs during the cell cycle. Here, using high-throughput fluorescence microscopy in microfluidic devices, we determine the timing for the onset of constriction relative to the replication cycle in different growth rates. Our single-cell data and modeling indicate that the initiation of constriction is coupled to replication-related processes in slow growth conditions. Furthermore, our data suggest that this coupling involves the mid-cell chromosome blocking the onset of constriction via some form of nucleoid occlusion occurring independently of SlmA and the Ter linkage proteins. This work highlights the coupling between replication and division cycles and brings up a new nucleoid mediated control mechanism in E. coli.

Using high-throughput microscopy, Tiruvadi-Krishnan et al. determine timings for critical cell-cycle checkpoints related to division and replication in Escherichia coli. The data, combined with cell-cycle modeling, show that the onset of constriction is blocked by the mid-cell nucleoid. In slow-growth conditions, the blockage is limiting for cell division.

Distinguishing different modes of growth using single-cell data

Collection of high-throughput data has become prevalent in biology. Large datasets allow the use of statistical constructs such as binning and linear regression to quantify relationships between variables and hypothesize underlying biological mechanisms based on it. We discuss several such examples in relation to single-cell data and cellular growth. In particular, we show instances where what appears to be ordinary use of these statistical methods leads to incorrect conclusions such as growth being non-exponential as opposed to exponential and vice versa. We propose that the data analysis and its interpretation should be done in the context of a generative model, if possible. In this way, the statistical methods can be validated either analytically or against synthetic data generated via the use of the model, leading to a consistent method for inferring biological mechanisms from data. On applying the validated methods of data analysis to infer cellular growth on our experimental data, we find the growth of length in E. coli to be non-exponential. Our analysis shows that in the later stages of the cell cycle the growth rate is faster than exponential.

Quantitative Examination of Five Stochastic Cell-Cycle and Cell-Size Control Models for Escherichia coli and Bacillus subtilis

We examine five quantitative models of the cell-cycle and cell-size control in Escherichia coli and Bacillus subtilis that have been proposed over the last decade to explain single-cell experimental data generated with high-throughput methods. After presenting the statistical properties of these models, we test their predictions against experimental data. Based on simple calculations of the defining correlations in each model, we first dismiss the stochastic Helmstetter-Cooper model and the Initiation Adder model, and show that both the Replication Double Adder (RDA) and the Independent Double Adder (IDA) model are more consistent with the data than the other models. We then apply a recently proposed statistical analysis method and obtain that the IDA model is the most likely model of the cell cycle. By showing that the RDA model is fundamentally inconsistent with size convergence by the adder principle, we conclude that the IDA model is most consistent with the data and the biology of bacterial cell-cycle and cell-size control. Mechanistically, the Independent Adder Model is equivalent to two biological principles: (i) balanced biosynthesis of the cell-cycle proteins, and (ii) their accumulation to a respective threshold number to trigger initiation and division.

Two different cell-cycle processes determine the timing of cell division in Escherichia coli

Cells must control the cell cycle to ensure that key processes are brought to completion. In Escherichia coli, it is controversial whether cell division is tied to chromosome replication or to a replication-independent inter-division process. A recent model suggests instead that both processes may limit cell division with comparable odds in single cells. Here, we tested this possibility experimentally by monitoring single-cell division and replication over multiple generations at slow growth. We then perturbed cell width, causing an increase of the time between replication termination and division. As a consequence, replication became decreasingly limiting for cell division, while correlations between birth and division and between subsequent replication-initiation events were maintained. Our experiments support the hypothesis that both chromosome replication and a replication-independent inter-division process can limit cell division: the two processes have balanced contributions in non-perturbed cells, while our width perturbations increase the odds of the replication-independent process being limiting.

Cell Growth Model with Stochastic Gene Expression Helps Understand the Growth Advantage of Metabolic Exchange and Auxotrophy

During cooperative growth, microbes often experience higher fitness by sharing resources via metabolite exchange. How competitive species evolve to cooperate is, however, not known. Moreover, existing models (based on optimization of steady-state resources or fluxes) are often unable to explain the growth advantage for the cooperating species, even for simple reciprocally cross-feeding auxotrophic pairs. We present here an abstract model of cell growth that considers the stochastic burst-like gene expression of biosynthetic pathways of limiting biomass precursor metabolites and directly connect the amount of metabolite produced to cell growth and division, using a "metabolic sizer/adder" rule. Our model recapitulates Monod's law and yields the experimentally observed right-skewed long-tailed distribution of cell doubling times. The model further predicts the growth effect of secretion and uptake of metabolites by linking it to changes in the internal metabolite levels. The model also explains why auxotrophs may grow faster when supplied with the metabolite they cannot produce and why two reciprocally cross-feeding auxotrophs can grow faster than prototrophs. Overall, our framework allows us to predict the growth effect of metabolic interactions in independent microbes and microbial communities, setting up the stage to study the evolution of these interactions. IMPORTANCE Cooperative behaviors are highly prevalent in the wild, but their evolution is not understood. Metabolic flux models can demonstrate the viability of metabolic exchange as cooperative interactions, but steady-state growth models cannot explain why cooperators grow faster. We present a stochastic model that connects growth to the cell's internal metabolite levels and quantifies the growth effect of metabolite exchange and auxotrophy. We show that a reduction in gene expression noise can explain why cells that import metabolites or become auxotrophs can grow faster and why reciprocal cross-feeding of metabolites between complementary auxotrophs allows them to grow faster. Furthermore, our framework can simulate the growth of interacting cells, which will enable us to understand the possible trajectories of the evolution of cooperation in silico.

Robust surface-to-mass coupling and turgor-dependent cell width determine bacterial dry-mass density

Intracellular biomass density is an important variable for cellular physiology. It defines the crowded state of the cytoplasm and thus influences macromolecular interactions and transport. To control density during growth, bacteria must expand their cell volumes in synchrony with biomass. The regulation of volume growth and biomass density remain fundamentally not understood—in bacteria or any other organism. Using advanced microscopy, we demonstrate that cells control dry-mass density indirectly through two independent processes. First, cells expand surface area, rather than volume, in proportion with biomass growth. Second, cell width is controlled independently, with an important influence of turgor pressure. Our findings overturn a long-standing paradigm of mass-density constancy in bacteria and reveal fundamental determinants of dry-mass density and shape.

During growth, cells must expand their cell volumes in coordination with biomass to control the level of cytoplasmic macromolecular crowding. Dry-mass density, the average ratio of dry mass to volume, is roughly constant between different nutrient conditions in bacteria, but it remains unknown whether cells maintain dry-mass density constant at the single-cell level and during nonsteady conditions. Furthermore, the regulation of dry-mass density is fundamentally not understood in any organism. Using quantitative phase microscopy and an advanced image-analysis pipeline, we measured absolute single-cell mass and shape of the model organisms Escherichia coli and Caulobacter crescentus with improved precision and accuracy. We found that cells control dry-mass density indirectly by expanding their surface, rather than volume, in direct proportion to biomass growth—according to an empirical surface growth law. At the same time, cell width is controlled independently. Therefore, cellular dry-mass density varies systematically with cell shape, both during the cell cycle or after nutrient shifts, while the surface-to-mass ratio remains nearly constant on the generation time scale. Transient deviations from constancy during nutrient shifts can be reconciled with turgor-pressure variations and the resulting elastic changes in surface area. Finally, we find that plastic changes of cell width after nutrient shifts are likely driven by turgor variations, demonstrating an important regulatory role of mechanical forces for width regulation. In conclusion, turgor-dependent cell width and a slowly varying surface-to-mass coupling constant are the independent variables that determine dry-mass density.

Limits and Constraints on Mechanisms of Cell-Cycle Regulation Imposed by Cell Size-Homeostasis Measurements

High-throughput imaging has led to an explosion of observations about cell-size homeostasis across the kingdoms of life. Among bacteria, "adder" behavior-in which a constant size increment appears to be added during each cell cycle-is ubiquitous, while various eukaryotes show other size-homeostasis behaviors. Since interactions between cell-cycle progression and growth ultimately determine such behaviors, we developed a general model of cell-cycle regulation. Our analyses reveal a range of scenarios that are plausible but fail to regulate cell size, indicating that mechanisms of cell-cycle regulation are stringently limited by size-control requirements, and possibly why certain cell-cycle features are strongly conserved. Cell-cycle features can play unintuitive roles in altering size-homeostasis behaviors: noisy regulator production can enhance adder behavior, while Whi5-like inhibitor dilutors respond sensitively to perturbations to G2/M control and noisy G1/S checkpoints. Our model thus provides holistic insights into the mechanistic implications of size-homeostasis experimental measurements.

Threshold accumulation of a constitutive protein explains E. coli cell-division behavior in nutrient upshifts

Despite a boost of recent progress in dynamic single-cell measurements and analyses in Escherichia coli, we still lack a mechanistic understanding of the determinants of the decision to divide. Specifically, the debate is open regarding the processes linking growth and chromosome replication to division and on the molecular origin of the observed "adder correlations," whereby cells divide, adding roughly a constant volume independent of their initial volume. In order to gain insight into these questions, we interrogate dynamic size-growth behavior of single cells across nutrient upshifts with a high-precision microfluidic device. We find that the division rate changes quickly after nutrients change, much before growth rate goes to a steady state, and in a way that adder correlations are robustly conserved. Comparison of these data to simple mathematical models falsifies proposed mechanisms, where replication-segregation or septum completions are the limiting step for cell division. Instead, we show that the accumulation of a putative constitutively expressed "P-sector divisor" protein explains the behavior during the shift.

Bacterial cell proliferation: from molecules to cells

Bacterial cell proliferation is highly efficient, both because bacteria grow fast and multiply with a low failure rate. This efficiency is underpinned by the robustness of the cell cycle and its synchronization with cell growth and cytokinesis. Recent advances in bacterial cell biology brought about by single-cell physiology in microfluidic chambers suggest a series of simple phenomenological models at the cellular scale, coupling cell size and growth with the cell cycle. We contrast the apparent simplicity of these mechanisms based on the addition of a constant size between cell cycle events (e.g. two consecutive initiation of DNA replication or cell division) with the complexity of the underlying regulatory networks. Beyond the paradigm of cell cycle checkpoints, the coordination between the DNA and division cycles and cell growth is largely mediated by a wealth of other mechanisms. We propose our perspective on these mechanisms, through the prism of the known crosstalk between DNA replication and segregation, cell division and cell growth or size. We argue that the precise knowledge of these molecular mechanisms is critical to integrate the diverse layers of controls at different time and space scales into synthetic and verifiable models.

Asymmetric chromosome segregation and cell division in DNA damage-induced bacterial filaments

Faithful propagation of life requires coordination of DNA replication and segregation with cell growth and division. In bacteria, this results in cell size homeostasis and periodicity in replication and division. The situation is perturbed under stress such as DNA damage, which induces filamentation as cell cycle progression is blocked to allow for repair. Mechanisms that release this morphological state for reentry into wild-type growth are unclear. Here we show that damage-induced Escherichia coli filaments divide asymmetrically, producing short daughter cells that tend to be devoid of damage and have wild-type size and growth dynamics. The Min-system primarily determines division site location in the filament, with additional regulation of division completion by chromosome segregation. Collectively, we propose that coordination between chromosome (and specifically terminus) segregation and cell division may result in asymmetric division in damage-induced filaments and facilitate recovery from a stressed state.

Artificial modulation of cell width significantly affects the division time of Escherichia coli

Bacterial cells have characteristic spatial and temporal scales. For instance, Escherichia coli, the typical rod-shaped bacteria, always maintains a relatively constant cell width and cell division time. However, whether the external physical perturbation of cell width has an impact on cell division time remains largely unexplored. In this work, we developed two microchannel chips, namely straight channels and ‘necked’ channels, to precisely regulate the width of E. coli cells and to investigate the correlation between cell width and division time of the cells. Our results show that, in the straight channels, the wide cells divide much slower than narrow cells. In the ‘necked’ channels, the cell division is remarkably promoted compared to that in straight channels with the same width. Besides, fluorescence time-lapse microscopy imaging of FtsZ dynamics shows that the cell pre-constriction time is more sensitive to cell width perturbation than cell constriction time. Finally, we revealed a significant anticorrelation between the death rate and the division rate of cell populations with different widths. Our work provides new insights into the correlation between the geometrical property and division time of E. coli cells and sheds new light on the future study of spatial–temporal correlation in cell physiology.

A bacterial size law revealed by a coarse-grained model of cell physiology

Universal observations in Biology are sometimes described as “laws”. In E. coli, experimental studies performed over the past six decades have revealed major growth laws relating ribosomal mass fraction and cell size to the growth rate. Because they formalize complex emerging principles in biology, growth laws have been instrumental in shaping our understanding of bacterial physiology. Here, we discovered a novel size law that connects cell size to the inverse of the metabolic proteome mass fraction and the active fraction of ribosomes. We used a simple whole-cell coarse-grained model of cell physiology that combines the proteome allocation theory and the structural model of cell division. This integrated model captures all available experimental data connecting the cell proteome composition, ribosome activity, division size and growth rate in response to nutrient quality, antibiotic treatment and increased protein burden. Finally, a stochastic extension of the model explains non-trivial correlations observed in single cell experiments including the adder principle. This work provides a simple and robust theoretical framework for studying the fundamental principles of cell size determination in unicellular organisms.

Bacteria respond to environmental changes by adjusting their molecular composition, cell size and growth rate. This plasticity is thought to result from years of evolution and to be at least in part optimal for bacterial physiology. Over the past decades, quantitative studies of bacterial growth have revealed simple phenomenological relationships, called “growth laws”, which link cell size and cell composition to the growth rate. Simplified mathematical models of cell physiology are useful tools to gain quantitative understanding of the molecular mechanisms that underlie growth laws. For instance, these models helped explaining how optimal allocation of cellular resource to physiological processes and pathways governs the cell molecular composition in response to specific environmental conditions. In this study, we have extended and integrated existing mathematical models and used experimental data from several recent studies to understand the co-regulation of cell composition, cell size and the cellular growth rate. The model predictions uncovered a novel “size law” that links cell size to the levels of metabolic proteins and the fraction of active ribosomes present in the cell. This work provides a useful theoretical tool and a quantitative basis for understanding mechanistically bacterial physiology as a function of external conditions.

General quantitative relations linking cell growth and the cell cycle in Escherichia coli

Growth laws emerging from studies of cell populations provide essential constraints on the global mechanisms that coordinate cell growth^1-3. The foundation of bacterial cell cycle studies relies on two interconnected dogmas that were proposed more than 50 years ago-the Schaechter-Maaloe-Kjeldgaard growth law that relates cell mass to growth rate¹ and Donachie's hypothesis of a growth-rate-independent initiation mass⁴. These dogmas spurred many efforts to understand their molecular bases and physiological consequences^5-14. Although they are generally accepted in the fast-growth regime, that is, for doubling times below 1 h, extension of these dogmas to the slow-growth regime has not been consistently achieved. Here, through a quantitative physiological study of Escherichia coli cell cycles over an extensive range of growth rates, we report that neither dogma holds in either the slow- or fast-growth regime. In their stead, linear relations between the cell mass and the rate of chromosome replication-segregation were found across the range of growth rates. These relations led us to propose an integral-threshold model in which the cell cycle is controlled by a licensing process, the rate of which is related in a simple way to chromosomal dynamics. These results provide a quantitative basis for predictive understanding of cell growth-cell cycle relationships.

Hidden long-range memories of growth and cycle speed correlate cell cycles in lineage trees

Cell heterogeneity may be caused by stochastic or deterministic effects. The inheritance of regulators through cell division is a key deterministic force, but identifying inheritance effects in a systematic manner has been challenging. Here, we measure and analyze cell cycles in deep lineage trees of human cancer cells and mouse embryonic stem cells and develop a statistical framework to infer underlying rules of inheritance. The observed long-range intra-generational correlations in cell-cycle duration, up to second cousins, seem paradoxical because ancestral correlations decay rapidly. However, this correlation pattern is naturally explained by the inheritance of both cell size and cell-cycle speed over several generations, provided that cell growth and division are coupled through a minimum-size checkpoint. This model correctly predicts the effects of inhibiting cell growth or cycle progression. In sum, we show how fluctuations of cell cycles across lineage trees help in understanding the coordination of cell growth and division.

Initiation of chromosome replication controls both division and replication cycles in E. coli through a double-adder mechanism

Living cells proliferate by completing and coordinating two cycles, a division cycle controlling cell size and a DNA replication cycle controlling the number of chromosomal copies. It remains unclear how bacteria such as Escherichia coli tightly coordinate those two cycles across a wide range of growth conditions. Here, we used time-lapse microscopy in combination with microfluidics to measure growth, division and replication in single E. coli cells in both slow and fast growth conditions. To compare different phenomenological cell cycle models, we introduce a statistical framework assessing their ability to capture the correlation structure observed in the data. In combination with stochastic simulations, our data indicate that the cell cycle is driven from one initiation event to the next rather than from birth to division and is controlled by two adder mechanisms: the added volume since the last initiation event determines the timing of both the next division and replication initiation events.

Mechanistic Origin of Cell-Size Control and Homeostasis in Bacteria

Evolutionarily divergent bacteria share a common phenomenological strategy for cell-size homeostasis under steady-state conditions. In the presence of inherent physiological stochasticity, cells following this "adder" principle gradually return to their steady-state size by adding a constant volume between birth and division, regardless of their size at birth. However, the mechanism of the adder has been unknown despite intense efforts. In this work, we show that the adder is a direct consequence of two general processes in biology: (1) threshold-accumulation of initiators and precursors required for cell division to a respective fixed number-and (2) balanced biosynthesis-maintenance of their production proportional to volume growth. This mechanism is naturally robust to static growth inhibition but also allows us to "reprogram" cell-size homeostasis in a quantitatively predictive manner in both Gram-negative Escherichia coli and Gram-positive Bacillus subtilis. By generating dynamic oscillations in the concentration of the division protein FtsZ, we were able to oscillate cell size at division and systematically break the adder. In contrast, periodic induction of replication initiator protein DnaA caused oscillations in cell size at initiation but did not alter division size or the adder. Finally, we were able to restore the adder phenotype in slow-growing E. coli, the only known steady-state growth condition wherein E. coli significantly deviates from the adder, by repressing active degradation of division proteins. Together, these results show that cell division and replication initiation are independently controlled at the gene-expression level and that division processes exclusively drive cell-size homeostasis in bacteria. VIDEO ABSTRACT.

Coordination of Growth, Chromosome Replication/Segregation, and Cell Division in E. coli

Bacterial cells growing in steady state maintain a 1:1:1 relationship between an appropriate mass increase, a round of DNA replication plus sister chromosome segregation, and cell division. This is accomplished without the cell cycle engine found in eukaryotic cells. We propose here a formal logic, and an accompanying mechanism, for how such coordination could be provided in E. coli. Completion of chromosomal and divisome-related events would lead, interactively, to a “progression control complex” (PCC) which provides integrated physical coupling between sister terminus regions and the nascent septum. When a cell has both (i) achieved a sufficient mass increase, and (ii) the PCC has developed, a conformational change in the PCC occurs. This change results in “progression permission,” which triggers both onset of cell division and release of terminus regions. Release of the terminus region, in turn, directly enables a next round of replication initiation via physical changes transmitted through the nucleoid. Division and initiation are then implemented, each at its own rate and timing, according to conditions present. Importantly: (i) the limiting step for progression permission may be either completion of the growth requirement or the chromosome/divisome processes required for assembly of the PCC; and, (ii) the outcome of the proposed process is granting of permission to progress, not determination of the absolute or relative timings of downstream events. This basic logic, and the accompanying mechanism, can explain coordination of events in both slow and fast growth conditions; can accommodate diverse variations and perturbations of cellular events; and is compatible with existing mathematical descriptions of the E. coli cell cycle. Also, while our proposition is specifically designed to provide 1:1:1 coordination among basic events on a “per-cell cycle” basis, it is a small step to further envision permission progression is also the target of basic growth rate control. In such a case, the rate of mass accumulation (or its equivalent) would determine the length of the interval between successive permission events and, thus, successive cell divisions and successive replication initiations.