Mechanistic Origin of Cell-Size Control and Homeostasis in Bacteria

Differential growth regulates asymmetric size partitioning in Caulobacter crescentus

Cell size regulation has been extensively studied in symmetrically dividing cells, but the mechanisms underlying the control of size asymmetry in asymmetrically dividing bacteria remain elusive. Here, we examine the control of asymmetric division in Caulobacter crescentus, a bacterium that produces daughter cells with distinct fates and morphologies upon division. Through comprehensive analysis of multi-generational growth and shape data, we uncover a tightly regulated cell size partitioning mechanism. We find that errors in division site positioning are promptly corrected early in the division cycle through differential growth. Our analysis reveals a negative feedback between the size of daughter cell compartments and their growth rates, wherein the larger compartment grows slower to achieve a homeostatic size partitioning ratio at division. To explain these observations, we propose a mechanistic model of differential growth, in which equal amounts of growth regulators are partitioned into daughter cell compartments of unequal sizes and maintained over time via size-independent synthesis.

Scaling of stochastic growth and division dynamics: A comparative study of individual rod-shaped cells in the Mother Machine and SChemostat platforms

Microfluidic platforms enable long-term quantification of stochastic behaviors of individual bacterial cells under precisely controlled growth conditions. Yet, quantitative comparisons of physiological parameters and cell behaviors of different microorganisms in different experimental and device modalities is not available due to experiment-specific details affecting cell physiology. To rigorously assess the effects of mechanical confinement, we designed, engineered, and performed side-by-side experiments under otherwise identical conditions in the Mother Machine (with confinement) and the SChemostat (without confinement), using the latter as the ideal comparator. We established a protocol to cultivate a suitably engineered rod-shaped mutant of Caulobacter crescentus in the Mother Machine and benchmarked the differences in stochastic growth and division dynamics with respect to the SChemostat. While the single-cell growth rate distributions are remarkably similar, the mechanically confined cells in the Mother Machine experience a substantial increase in interdivision times. However, we find that the division ratio distribution precisely compensates for this increase, which in turn reflects identical emergent simplicities governing stochastic intergenerational homeostasis of cell sizes across device and experimental configurations, provided the cell sizes are appropriately mean-rescaled in each condition. Our results provide insights into the nature of the robustness of the bacterial growth and division machinery.

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.

Tools and methods for high-throughput single-cell imaging with the mother machine

Despite much progress, image processing remains a significant bottleneck for high-throughput analysis of microscopy data. One popular platform for single-cell time-lapse imaging is the mother machine, which enables long-term tracking of microbial cells under precisely controlled growth conditions. While several mother machine image analysis pipelines have been developed in the past several years, adoption by a non-expert audience remains a challenge. To fill this gap, we implemented our own software, MM3, as a plugin for the multidimensional image viewer napari. napari-MM3 is a complete and modular image analysis pipeline for mother machine data, which takes advantage of the high-level interactivity of napari. Here, we give an overview of napari-MM3 and test it against several well-designed and widely used image analysis pipelines, including BACMMAN and DeLTA. Researchers often analyze mother machine data with custom scripts using varied image analysis methods, but a quantitative comparison of the output of different pipelines has been lacking. To this end, we show that key single-cell physiological parameter correlations and distributions are robust to the choice of analysis method. However, we also find that small changes in thresholding parameters can systematically alter parameters extracted from single-cell imaging experiments. Moreover, we explicitly show that in deep learning-based segmentation, 'what you put is what you get' (WYPIWYG) - that is, pixel-level variation in training data for cell segmentation can propagate to the model output and bias spatial and temporal measurements. Finally, while the primary purpose of this work is to introduce the image analysis software that we have developed over the last decade in our lab, we also provide information for those who want to implement mother machine-based high-throughput imaging and analysis methods in their research.

Effects of Molecular Noise on Cell Size Control

Cells employ control strategies to maintain a stable size. Dividing at a target size (the "sizer" strategy) is thought to produce the tightest size distribution. However, this result follows from phenomenological models that ignore the molecular mechanisms required to implement the strategy. Here we investigate a simple mechanistic model for exponentially growing cells whose division is triggered at a molecular abundance threshold. We find that size noise inherits the molecular noise and is consequently minimized not by the sizer but by the "adder" strategy, where a cell divides after adding a target amount to its birth size. We derive a lower bound on size noise that agrees with publicly available data from six microfluidic studies on Escherichia coli bacteria.

Tools and methods for high-throughput single-cell imaging with the mother machine

Despite much progress, image processing remains a significant bottleneck for high-throughput analysis of microscopy data. One popular platform for single-cell time-lapse imaging is the mother machine, which enables long-term tracking of microbial cells under precisely controlled growth conditions. While several mother machine image analysis pipelines have been developed in the past several years, adoption by a non-expert audience remains a challenge. To fill this gap, we implemented our own software, MM3, as a plugin for the multidimensional image viewer napari. napari-MM3 is a complete and modular image analysis pipeline for mother machine data, which takes advantage of the high-level interactivity of napari. Here, we give an overview of napari-MM3 and test it against several well-designed and widely-used image analysis pipelines, including BACMMAN and DeLTA. Researchers often analyze mother machine data with custom scripts using varied image analysis methods, but a quantitative comparison of the output of different pipelines has been lacking. To this end, we show that key single-cell physiological parameter correlations and distributions are robust to the choice of analysis method. However, we also find that small changes in thresholding parameters can systematically alter parameters extracted from single-cell imaging experiments. Moreover, we explicitly show that in deep learning based segmentation, "what you put is what you get" (WYPIWYG) - i.e., pixel-level variation in training data for cell segmentation can propagate to the model output and bias spatial and temporal measurements. Finally, while the primary purpose of this work is to introduce the image analysis software that we have developed over the last decade in our lab, we also provide information for those who want to implement mother-machine-based high-throughput imaging and analysis methods in their research.

MicroRNAs-associated with FOXO3 in cellular senescence and other stress responses

FOXO3 is a member of the FOXO transcription factor family and is known for regulating cellular survival in response to stress caused by various external and biological stimuli. FOXO3 decides cell fate by modulating cellular senescence, apoptosis and autophagy by transcriptional regulation of genes involved in DNA damage response and oxidative stress resistance. These cellular processes are tightly regulated physiologically, with FOXO3 acting as the hub that integrates signalling networks controlling them. The activity of FOXO3 is influenced by post-translational modifications, altering its subcellular localisation. In addition, FOXO3 can also be regulated directly or indirectly by microRNAs (miRNAs) or vice versa. This review discusses the involvement of various miRNAs in FOXO3-driven cellular responses such as senescence, apoptosis, autophagy, redox and inflammation defence. Given that these responses are linked and influence cell fate, a thorough understanding of the complex regulation by miRNAs would provide key information for developing therapeutic strategy and avoid unintended consequences caused by off-site targeting of FOXO3.

Nutritional control of bacterial DNA replication

All cells must ensure precise regulation of DNA replication initiation in coordination with growth rate and in response to nutrient availability. According to a long-standing model, DNA replication initiation is tightly coupled to cell mass increase in bacteria. Despite controversies regarding this model, recent studies have provided additional support of this idea. The exact molecular mechanisms linking cell growth with DNA replication under different nutrient conditions remain elusive. However, recent studies in Caulobacter crescentus and Escherichia coli have provided insights into the regulation of DNA replication initiation in response to starvation. These mechanisms include the starvation-dependent regulation of DnaA abundance as well as mechanisms involving the small signaling molecule (p)ppGpp. In this review, we discuss these mechanisms in the context of previous findings. We highlight species-dependent similarities and differences and consider the precise growth conditions, in which the different mechanisms are active.

Apparent simplicity and emergent robustness in the control of the Escherichia coli cell cycle

To examine how bacteria achieve robust cell proliferation across diverse conditions, we developed a method that quantifies 77 cell morphological, cell cycle, and growth phenotypes of a fluorescently labeled Escherichia coli strain and >800 gene deletion derivatives under multiple nutrient conditions. This approach revealed extensive phenotypic plasticity and deviating mutant phenotypes were often nutrient dependent. From this broad phenotypic landscape emerged simple and robust unifying rules (laws) that connect DNA replication initiation, nucleoid segregation, FtsZ ring formation, and cell constriction to specific aspects of cell size (volume, length, or added length) at the population level. Furthermore, completion of cell division followed the initiation of cell constriction after a constant time delay across strains and nutrient conditions, identifying cell constriction as a key control point for cell size determination. Our work provides a population-level description of the governing principles by which E. coli integrates cell cycle processes and growth rate with cell size to achieve its robust proliferative capability. A record of this paper's transparent peer review process is included in the supplemental information.

Energy allocation theory for bacterial growth control in and out of steady state

Efficient allocation of energy resources to key physiological functions allows living organisms to grow and thrive in diverse environments and adapt to a wide range of perturbations. To quantitatively understand how unicellular organisms utilize their energy resources in response to changes in growth environment, we introduce a theory of dynamic energy allocation which describes cellular growth dynamics based on partitioning of metabolizable energy into key physiological functions: growth, division, cell shape regulation, energy storage and loss through dissipation. By optimizing the energy flux for growth, we develop the equations governing the time evolution of cell morphology and growth rate in diverse environments. The resulting model accurately captures experimentally observed dependencies of bacterial cell size on growth rate, superlinear scaling of metabolic rate with cell size, and predicts nutrient-dependent trade-offs between energy expended for growth, division, and shape maintenance. By calibrating model parameters with available experimental data for the model organism E. coli, our model is capable of describing bacterial growth control in dynamic conditions, particularly during nutrient shifts and osmotic shocks. The model captures these perturbations with minimal added complexity and our unified approach predicts the driving factors behind a wide range of observed morphological and growth phenomena.

Cell size homeostasis is tightly controlled throughout the cell cycle

To achieve a stable size distribution over multiple generations, proliferating cells require a means of counteracting stochastic noise in the rate of growth, the time spent in various phases of the cell cycle, and the imprecision in the placement of the plane of cell division. In the most widely accepted model, cell size is thought to be regulated at the G1/S transition, such that cells smaller than a critical size pause at the end of G1 phase until they have accumulated mass to a predetermined size threshold, at which point the cells proceed through the rest of the cell cycle. However, a model, based solely on a specific size checkpoint at G1/S, cannot readily explain why cells with deficient G1/S control mechanisms are still able to maintain a very stable cell size distribution. Furthermore, such a model would not easily account for stochastic variation in cell size during the subsequent phases of the cell cycle, which cannot be anticipated at G1/S. To address such questions, we applied computationally enhanced quantitative phase microscopy (ceQPM) to populations of cultured human cell lines, which enables highly accurate measurement of cell dry mass of individual cells throughout the cell cycle. From these measurements, we have evaluated the factors that contribute to maintaining cell mass homeostasis at any point in the cell cycle. Our findings reveal that cell mass homeostasis is accurately maintained, despite disruptions to the normal G1/S machinery or perturbations in the rate of cell growth. Control of cell mass is generally not confined to regulation of the G1 length. Instead mass homeostasis is imposed throughout the cell cycle. In the cell lines examined, we find that the coefficient of variation (CV) in dry mass of cells in the population begins to decline well before the G1/S transition and continues to decline throughout S and G2 phases. Among the different cell types tested, the detailed response of cell growth rate to cell mass differs. However, in general, when it falls below that for exponential growth, the natural increase in the CV of cell mass is effectively constrained. We find that both mass-dependent cell cycle regulation and mass-dependent growth rate modulation contribute to reducing cell mass variation within the population. Through the interplay and coordination of these 2 processes, accurate cell mass homeostasis emerges. Such findings reveal previously unappreciated and very general principles of cell size control in proliferating cells. These same regulatory processes might also be operative in terminally differentiated cells. Further quantitative dynamical studies should lead to a better understanding of the underlying molecular mechanisms of cell size control.

Genome replication in asynchronously growing microbial populations

Biological cells replicate their genomes in a well-planned manner. The DNA replication program of an organism determines the timing at which different genomic regions are replicated, with fundamental consequences for cell homeostasis and genome stability. In a growing cell culture, genomic regions that are replicated early should be more abundant than regions that are replicated late. This abundance pattern can be experimentally measured using deep sequencing. However, a general quantitative theory linking this pattern to the replication program is still lacking. In this paper, we predict the abundance of DNA fragments in asynchronously growing cultures from any given stochastic model of the DNA replication program. As key examples, we present stochastic models of the DNA replication programs in budding yeast and Escherichia coli. In both cases, our model results are in excellent agreement with experimental data and permit to infer key information about the replication program. In particular, our method is able to infer the locations of known replication origins in budding yeast with high accuracy. These examples demonstrate that our method can provide insight into a broad range of organisms, from bacteria to eukaryotes.

Coupling Cell Size Regulation and Proliferation Dynamics of C. glutamicum Reveals Cell Division Based on Surface Area

Single cells actively coordinate growth and division to regulate their size, yet how this size homeostasis at the single-cell level propagates over multiple generations to impact clonal expansion remains fundamentally unexplored. Classical timer models for cell proliferation (where the duration of the cell cycle is an independent variable) predict that the stochastic variation in colony size will increase monotonically over time. In stark contrast, implementing size control according to adder strategy (where on average a fixed size added from cell birth to division) leads to colony size variations that eventually decay to zero. While these results assume a fixed size of the colony-initiating progenitor cell, further analysis reveals that the magnitude of the intercolony variation in population number is sensitive to heterogeneity in the initial cell size. We validate these predictions by tracking the growth of isogenic microcolonies of Corynebacterium glutamicum in microfluidic chambers. Approximating their cell shape to a capsule, we observe that the degree of random variability in cell size is different depending on whether the cell size is quantified as per length, surface area, or volume, but size control remains an adder regardless of these size metrics. A comparison of the observed variability in the colony population with the predictions suggests that proliferation matches better with a cell division based on the cell surface. In summary, our integrated mathematical-experimental approach bridges the paradigms of single-cell size regulation and clonal expansion at the population levels. This innovative approach provides elucidation of the mechanisms of size homeostasis from the stochastic dynamics of colony size for rod-shaped microbes.

Protein aggregates act as a deterministic disruptor during bacterial cell size homeostasis

Mechanisms underlying deviant cell size fluctuations among clonal bacterial siblings are generally considered to be cryptic and stochastic in nature. However, by scrutinizing heat-stressed populations of the model bacterium Escherichia coli, we uncovered the existence of a deterministic asymmetry in cell division that is caused by the presence of intracellular protein aggregates (PAs). While these structures typically locate at the cell pole and segregate asymmetrically among daughter cells, we now show that the presence of a polar PA consistently causes a more distal off-center positioning of the FtsZ division septum. The resulting increased length of PA-inheriting siblings persists over multiple generations and could be observed in both E. coli and Bacillus subtilis populations. Closer investigation suggests that a PA can physically perturb the nucleoid structure, which subsequently leads to asymmetric septation.

Involvement of OxyR and Dps in the repression of replication initiation by DsrA small RNA in Escherichia coli

Regulation of the cell cycle process is an effective measure to ensure the stability and fidelity of genetic material during the reproduction of bacteria under different stresses. The small RNA DsrA helps bacteria adapt to environments by binding to multiple targets, but its association with the cell cycle remains unclear. Detection by flow cytometry, we first found that the knockout of dsrA promoted replication initiation, and corresponding overexpression of DsrA inhibited replication initiation in Escherichia coli. The absence of the chaperone protein Hfq, the DNA replication negative regulator protein Dps, or the transcription factor OxyR, was found to cause DsrA to no longer inhibit replication initiation. Excess DsrA promotes expression of the oxyR and dps gene, whereas β-galactosidase activity assay showed that deleting oxyR limited the enhancement of dps promoter transcriptional activity by DsrA. OxyR is a known positive regulator of Dps. Our data suggests that the effect of DsrA on replication initiation requires Hfq and that the upregulation of Dps expression by OxyR in response to DsrA levels may be a potential regulatory pathway for the negative regulation of DNA replication initiation.

Self-buckling and self-writhing of semi-flexible microorganisms

The twisting and writhing of a cell body and associated mechanical stresses is an underappreciated constraint on microbial self-propulsion. Multi-flagellated bacteria can even buckle and writhe under their own activity as they swim through a viscous fluid. New equilibrium configurations and steady-state dynamics then emerge which depend on the organism's mechanical properties and on the oriented distribution of flagella along its surface. Modeling the cell body as a semi-flexible Kirchhoff rod and coupling the mechanics to a flagellar orientation field, we derive the Euler-Poincaré equations governing the dynamics of the system, and rationalize experimental observations of buckling and writhing of elongated swarmer cells of the bacterium Proteus mirabilis. A sequence of bifurcations is identified as the body is made more compliant, due to both buckling and torsional instabilities. These studies highlight a practical requirement for the stiffness of bacteria below which self-buckling occurs and cell motility becomes ineffective.

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.

Multigenerational memory in bacterial size control

Cells maintain a stable size as they grow and divide. Inspired by the available experimental data, most proposed models for size homeostasis assume size-control mechanisms that act on a timescale of one generation. Such mechanisms lead to short-lived autocorrelations in size fluctuations that decay within less than two generations. However, recent evidence from comparing sister lineages suggests that correlations in size fluctuations can persist for many generations. Here we develop a minimal model that explains these seemingly contradictory results. Our model proposes that different environments result in different control parameters, leading to distinct inheritance patterns. Multigenerational memory is revealed in constant environments but obscured when averaging over many different environments. Inferring the parameters of our model from Escherichia coli size data in microfluidic experiments, we recapitulate the observed statistics. Our paper elucidates the impact of the environment on cell homeostasis and growth and division dynamics.

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.

Bacterial Replication Initiation as Precision Control by Protein Counting

Balanced biosynthesis is the hallmark of bacterial cell physiology, where the concentrations of stable proteins remain steady. However, this poses a conceptual challenge to modeling the cell-cycle and cell-size controls in bacteria, as prevailing concentration-based eukaryote models are not directly applicable. In this study, we revisit and significantly extend the initiator-titration model, proposed 30 years ago, and we explain how bacteria precisely and robustly control replication initiation based on the mechanism of protein copy-number sensing. Using a mean-field approach, we first derive an analytical expression of the cell size at initiation based on three biological mechanistic control parameters for an extended initiator-titration model. We also study the stability of our model analytically and show that initiation can become unstable in multifork replication conditions. Using simulations, we further show that the presence of the conversion between active and inactive initiator protein forms significantly represses initiation instability. Importantly, the two-step Poisson process set by the initiator titration step results in significantly improved initiation synchrony with C V ~ 1 / N scaling rather than the standard 1 / N scaling in the Poisson process, where N is the total number of initiators required for initiation. Our results answer two long-standing questions in replication initiation: (i) Why do bacteria produce almost two orders of magnitude more DnaA, the master initiator proteins, than required for initiation? (ii) Why does DnaA exist in active (DnaA-ATP) and inactive (DnaA-ADP) forms if only the active form is competent for initiation? The mechanism presented in this work provides a satisfying general solution to how the cell can achieve precision control without sensing protein concentrations, with broad implications from evolution to the design of synthetic cells.

Replication initiation in bacteria: precision control based on protein counting

Balanced biosynthesis is the hallmark of bacterial cell physiology, where the concentrations of stable proteins remain steady. However, this poses a conceptual challenge to modeling the cell-cycle and cell-size controls in bacteria, as prevailing concentration-based eukaryote models are not directly applicable. In this study, we revisit and significantly extend the initiator-titration model, proposed thirty years ago, and explain how bacteria precisely and robustly control replication initiation based on the mechanism of protein copy-number sensing. Using a mean-field approach, we first derive an analytical expression of the cell size at initiation based on three biological mechanistic control parameters for an extended initiator-titration model. We also study the stability of our model analytically and show that initiation can become unstable in multifork replication conditions. Using simulations, we further show that the presence of the conversion between active and inactive initiator protein forms significantly represses initiation instability. Importantly, the two-step Poisson process set by the initiator titration step results in significantly improved initiation synchrony with C V ~ 1 / N scaling rather than the standard 1 / N scaling in the Poisson process, where N is the total number of initiators required for initiation. Our results answer two long-standing questions in replication initiation: (1) Why do bacteria produce almost two orders of magnitude more DnaA, the master initiator proteins, than required for initiation? (2) Why does DnaA exist in active (DnaA-ATP) and inactive (DnaA-ADP) forms if only the active form is competent for initiation? The mechanism presented in this work provides a satisfying general solution to how the cell can achieve precision control without sensing protein concentrations, with broad implications from evolution to the design of synthetic cells.

PyEcoLib: a python library for simulating stochastic cell size dynamics

Recently, there has been an increasing need for tools to simulate cell size regulation due to important applications in cell proliferation and gene expression. However, implementing the simulation usually presents some difficulties, as the division has a cycle-dependent occurrence rate. In this article, we gather a recent theoretical framework inPyEcoLib, a python-based library to simulate the stochastic dynamics of the size of bacterial cells. This library can simulate cell size trajectories with an arbitrarily small sampling period. In addition, this simulator can include stochastic variables, such as the cell size at the beginning of the experiment, the cycle duration timing, the growth rate, and the splitting position. Furthermore, from a population perspective, the user can choose between tracking a single lineage or all cells in a colony. They can also simulate the most common division strategies (adder, timer, and sizer) using the division rate formalism and numerical methods. As an example of PyecoLib applications, we explain how to couple size dynamics with gene expression predicting, from simulations, how the noise in protein levels increases by increasing the noise in division timing, the noise in growth rate and the noise in cell splitting position. The simplicity of this library and its transparency about the underlying theoretical framework yield the inclusion of cell size stochasticity in complex models of gene expression.

The Quantification of Bacterial Cell Size: Discrepancies Arise from Varied Quantification Methods

The robust regulation of the cell cycle is critical for the survival and proliferation of bacteria. To gain a comprehensive understanding of the mechanisms regulating the bacterial cell cycle, it is essential to accurately quantify cell-cycle-related parameters and to uncover quantitative relationships. In this paper, we demonstrate that the quantification of cell size parameters using microscopic images can be influenced by software and by the parameter settings used. Remarkably, even if the consistent use of a particular software and specific parameter settings is maintained throughout a study, the type of software and the parameter settings can significantly impact the validation of quantitative relationships, such as the constant-initiation-mass hypothesis. Given these inherent characteristics of microscopic image-based quantification methods, it is recommended that conclusions be cross-validated using independent methods, especially when the conclusions are associated with cell size parameters that were obtained under different conditions. To this end, we presented a flexible workflow for simultaneously quantifying multiple bacterial cell-cycle-related parameters using microscope-independent methods.

Mycobacterium tuberculosis grows linearly at the single-cell level with larger variability than model organisms

The ability of bacterial pathogens to regulate growth is crucial to control homeostasis, virulence, and drug response. Yet, we do not understand the growth and cell cycle behaviors of Mycobacterium tuberculosis (Mtb), a slow-growing pathogen, at the single-cell level. Here, we use time-lapse imaging and mathematical modeling to characterize these fundamental properties of Mtb. Whereas most organisms grow exponentially at the single-cell level, we find that Mtb exhibits a unique linear growth mode. Mtb growth characteristics are highly variable from cell-to-cell, notably in their growth speeds, cell cycle timing, and cell sizes. Together, our study demonstrates that growth behavior of Mtb diverges from what we have learned from model bacteria. Instead, Mtb generates a heterogeneous population while growing slowly and linearly. Our study provides a new level of detail into how Mtb grows and creates heterogeneity, and motivates more studies of growth behaviors in bacterial pathogens.

Dynamic proteome trade-offs regulate bacterial cell size and growth in fluctuating nutrient environments

Bacteria dynamically regulate cell size and growth to thrive in changing environments. While previous studies have characterized bacterial growth physiology at steady-state, a quantitative understanding of bacterial physiology in time-varying environments is lacking. Here we develop a quantitative theory connecting bacterial growth and division rates to proteome allocation in time-varying nutrient environments. In such environments, cell size and growth are regulated by trade-offs between prioritization of biomass accumulation or division, resulting in decoupling of single-cell growth rate from population growth rate. Specifically, bacteria transiently prioritize biomass accumulation over production of division machinery during nutrient upshifts, while prioritizing division over growth during downshifts. When subjected to pulsatile nutrient concentration, we find that bacteria exhibit a transient memory of previous metabolic states due to the slow dynamics of proteome reallocation. This allows for faster adaptation to previously seen environments and results in division control which is dependent on the time-profile of fluctuations.

★Track: Inferred counting and tracking of replicating DNA loci

Fluorescent microscopy is the primary method to study DNA organization within cells. However, the variability and low signal/noise commonly associated with live-cell time-lapse imaging challenges quantitative measurements. In particular, obtaining quantitative or mechanistic insight often depends on the accurate tracking of fluorescent particles. Here, we present ★Track, an inference method that determines the most likely temporal tracking of replicating intracellular particles such DNA loci while accounting for missing, merged, and spurious detections. It allows the accurate prediction of particle copy numbers as well as the timing of replication events. We demonstrate ★Track's abilities and gain new insight into plasmid copy number control and the volume dependence of bacterial chromosome replication initiation. By enabling the accurate tracking of DNA loci, ★Track can help to uncover the mechanistic principles of chromosome organization and dynamics across a range of systems.

Shaping bacterial gene expression by physiological and proteome allocation constraints

Networks of molecular regulators are often the primary objects of focus in the study of gene regulation, with the machinery of protein synthesis tacitly relegated to the background. Shifting focus to the constraints imposed by the allocation of protein synthesis flux reveals surprising ways in which the actions of molecular regulators are shaped by physiological demands. Using carbon catabolite repression as a case study, we describe how physiological constraints are sensed through metabolic fluxes and how flux-controlled regulation gives rise to simple empirical relations between protein levels and the rate of cell growth.

Super-exponential growth and stochastic size dynamics in rod-like bacteria

Proliferating bacterial cells exhibit stochastic growth and size dynamics, but the regulation of noise in bacterial growth and morphogenesis remains poorly understood. A quantitative understanding of morphogenetic noise control, and how it changes under different growth conditions, would provide better insights into cell-to-cell variability and intergenerational fluctuations in cell physiology. Using multigenerational growth and width data of single Escherichia coli and Caulobacter crescentus cells, we deduce the equations governing growth and size dynamics of rod-like bacterial cells. Interestingly, we find that both E. coli and C. crescentus cells deviate from exponential growth within the cell cycle. In particular, the exponential growth rate increases during the cell cycle irrespective of nutrient or temperature conditions. We propose a mechanistic model that explains the emergence of super-exponential growth from autocatalytic production of ribosomes coupled to the rate of cell elongation and surface area synthesis. Using this new model and statistical inference on large datasets, we construct the Langevin equations governing cell growth and size dynamics of E. coli cells in different nutrient conditions. The single-cell level model predicts how noise in intragenerational and intergenerational processes regulate variability in cell morphology and generation times, revealing quantitative strategies for cellular resource allocation and morphogenetic noise control in different growth conditions.

The in vivo measurement of replication fork velocity and pausing by lag-time analysis

An important step towards understanding the mechanistic basis of the central dogma is the quantitative characterization of the dynamics of nucleic-acid-bound molecular motors in the context of the living cell. To capture these dynamics, we develop lag-time analysis, a method for measuring in vivo dynamics. Using this approach, we provide quantitative locus-specific measurements of fork velocity, in units of kilobases per second, as well as replisome pause durations, some with the precision of seconds. The measured fork velocity is observed to be both locus and time dependent, even in wild-type cells. In this work, we quantitatively characterize known phenomena, detect brief, locus-specific pauses at ribosomal DNA loci in wild-type cells, and observe temporal fork velocity oscillations in three highly-divergent bacterial species.

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.

Growth rate is modulated by monitoring cell wall precursors in Bacillus subtilis

How bacteria link their growth rate to external nutrient conditions is unknown. To investigate how Bacillus subtilis cells alter the rate at which they expand their cell walls as they grow, we compared single-cell growth rates of cells grown under agar pads with the density of moving MreB filaments under a variety of growth conditions. MreB filament density increases proportionally with growth rate. We show that both MreB filament density and growth rate depend on the abundance of Lipid II and murAA, the first gene in the biosynthetic pathway creating the cell wall precursor Lipid II. Lipid II is sensed by the serine/threonine kinase PrkC, which phosphorylates RodZ and other proteins. We show that phosphorylated RodZ increases MreB filament density, which in turn increases cell growth rate. We also show that increasing the activity of this pathway in nutrient-poor media results in cells that elongate faster than wild-type cells, which means that B. subtilis contains spare 'growth capacity'. We conclude that PrkC functions as a cellular rheostat, enabling fine-tuning of cell growth rates in response to Lipid II in different nutrient conditions.

Control of Cell Size by c-di-GMP Requires a Two-Component Signaling System in the Cyanobacterium Anabaena sp. Strain PCC 7120

Each bacterial species possesses a specific cell size and morphology, which constitute important and recognizable physical traits. How bacteria maintain their particular cell size and morphology remains an essential question in microbiology. Cyanobacteria are oxygen-evolving photosynthetic prokaryotes. Although monophyletic, these organisms are highly diverse in their cell morphology and cell size. How these physical traits of cyanobacteria are controlled is poorly understood. Here, we report the identification of a two-component signaling system, composed of a histidine kinase CdgK and a response regulator CdgS, involved in cell size regulation in the filamentous, heterocyst-forming cyanobacterium Anabaena sp. PCC 7120. Inactivation of cdgK or cdgS led to reduction of cell length and width with little effect on cell growth capacity. CdgS has a GGDEF domain responsible for the synthesis of the second messenger c-di-GMP. Based on genetic and biochemical studies, we proposed a signaling pathway initiated by CdgK, leading to the phosphorylation of CdgS, and thereby an enhanced enzymatic activity for c-di-GMP synthesis of the latter. The GGDEF domain of CdgS was essential in cell size control, and the reduction of cell size observed in various mutants could be rescued by the expression of a c-di-GMP synthetase from E. coli. These results provided evidence that a minimal threshold of c-di-GMP level was required for maintaining cell size in Anabaena. IMPORTANCE Cyanobacteria are considered the first organisms to produce oxygen on Earth, and their activities shaped the evolution of our ecosystems. Cell size is an important trait fixed early in evolution, with the diversification of micro- and macrocyanobacterial species during the Great Oxidation Event. However, the genetic basis underlying cell size control in cyanobacteria was not understood. Our studies demonstrated that the CdgK-CdgS signaling pathway participates in the control of cell size, and their absence did not affect cell growth. CdgK has multiple domains susceptible to signal input, which are necessary for cell size regulation. This observation suggests that cell size in Anabaena could respond to environmental signals. These studies paved the way for genetic dissection of cell size regulation in cyanobacteria.

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.

A study on the antibacterial activity and antimicrobial resistance of pyridinium cationic pillar[5]arene against Staphylococcus aureus and Escherichia coli

An increasing number of infections caused by multidrug-resistant (MDR) Staphylococcus aureus （S. aureus） and Escherichia coli （E. coli） have severely affected human society. Thus, it is essential to develop an alternative type of antibacterial agents that has a different bacterial resistance mechanism from that of traditional antibiotics. After the synthesis and structural characterization of a cationic pillar[5]arene with pyridinium groups (PP5), the antibacterial and antibiofilm activities as well as its microbial resistance were systematically investigated. In-depth evaluation of biological studies revealed that PP5 was an active antibacterial agent, with surprising antibiofilm formation ability against E. coli and S. aureus. From the results of differential scanning calorimetry and transmission electron microscopy, it was concluded that the microbicidal activity of PP5 was due to the physical disruption of the pathogen's membrane and the subsequent leakage of cytoplasmic components, which could greatly reduce the rapid generation of resistance. It was presented that the easily available PP5 has high activity to inhibit Gram-positive and Gram-negative bacteria and/or their biofilms with low cytotoxicity. This pillar[5]arene derivative can be used as a good candidate for controlling drug-resistant pathogenic bacterial infections and treating MDR bacteria.

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.

Molecular mechanisms underlying iron and phosphorus co-limitation responses in the nitrogen-fixing cyanobacterium Crocosphaera

In the nitrogen-limited subtropical gyres, diazotrophic cyanobacteria, including Crocosphaera, provide an essential ecosystem service by converting dinitrogen (N2) gas into ammonia to support primary production in these oligotrophic regimes. Natural gradients of phosphorus (P) and iron (Fe) availability in the low-latitude oceans constrain the biogeography and activity of diazotrophs with important implications for marine biogeochemical cycling. Much remains unknown regarding Crocosphaera's physiological and molecular responses to multiple nutrient limitations. We cultured C. watsonii under Fe, P, and Fe/P (co)-limiting scenarios to link cellular physiology with diel gene expression and observed unique physiological and transcriptional profiles for each treatment. Counterintuitively, reduced growth and N2 fixation resource use efficiencies (RUEs) for Fe or P under P limitation were alleviated under Fe/P co-limitation. Differential gene expression analyses show that Fe/P co-limited cells employ the same responses as single-nutrient limited cells that reduce cellular nutrient requirements and increase responsiveness to environmental change including smaller cell size, protein turnover (Fe-limited), and upregulation of environmental sense-and-respond systems (P-limited). Combined, these mechanisms enhance growth and RUEs in Fe/P co-limited cells. These findings are important to our understanding of nutrient controls on N2 fixation and the implications for primary productivity and microbial dynamics in a changing ocean.

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.

Cellular mechanics during division of a genomically minimal cell

Genomically minimal cells, such as JCVI-syn3.0 and JCVI-syn3A, offer an empowering framework to study relationships between genotype and phenotype. With a polygenic basis, the fundamental physiological process of cell division depends on multiple genes of known and unknown function in JCVI-syn3A. A physical description of cellular mechanics can further understanding of the contributions of genes to cell division in this genomically minimal context. We review current knowledge on genes in JCVI-syn3A contributing to two physical parameters relevant to cell division, namely, the surface-area-to-volume ratio and membrane curvature. This physical view of JCVI-syn3A may inform the attribution of gene functions and conserved processes in bacterial physiology, as well as whole-cell models and the engineering of synthetic cells.

Nutrient availability as an arbiter of cell size

Pioneering work carried out over 60 years ago discovered that bacterial cell size is proportional to the growth rate set by nutrient availability. This relationship is traditionally referred to as the 'growth law'. Subsequent studies revealed the growth law to hold across all orders of life, a remarkable degree of conservation. However, recent work suggests the relationship between growth rate, nutrients, and cell size is far more complicated and less deterministic than originally thought. Focusing on bacteria and yeast, here we review efforts to understand the molecular mechanisms underlying the relationship between growth rate and cell size.

Effects of antibiotics on bacterial cell morphology and their physiological origins

Characterizing the physiological response of bacterial cells to antibiotic treatment is crucial for the design of antibacterial therapies and for understanding the mechanisms of antibiotic resistance. While the effects of antibiotics are commonly characterized by their minimum inhibitory concentrations or the minimum bactericidal concentrations, the effects of antibiotics on cell morphology and physiology are less well characterized. Recent technological advances in single-cell studies of bacterial physiology have revealed how different antibiotic drugs affect the physiological state of the cell, including growth rate, cell size and shape, and macromolecular composition. Here, we review recent quantitative studies on bacterial physiology that characterize the effects of antibiotics on bacterial cell morphology and physiological parameters. In particular, we present quantitative data on how different antibiotic targets modulate cellular shape metrics including surface area, volume, surface-to-volume ratio, and the aspect ratio. Using recently developed quantitative models, we relate cell shape changes to alterations in the physiological state of the cell, characterized by changes in the rates of cell growth, protein synthesis and proteome composition. Our analysis suggests that antibiotics induce distinct morphological changes depending on their cellular targets, which may have important implications for the regulation of cellular fitness under stress.

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.

Influence of homeostatic mechanisms of bacterial growth and division on structural properties of microcolonies: A computer simulation study

Bacterial growth and division generally occur by the process known as binary fission, in which the cells grow polarly until they divide into two daughter cells. Although this process is affected by factors that introduce stochastic variability in both growth rate and daughter cell length, the fact is that the size distribution in growing bacteria remains stable over time. This suggests the existence of homeostatic mechanisms that contribute to maintaining a stable size distribution. Those known as sizer and adder stand out among these mechanisms whose relevance is not entirely determined. In this work, computer simulations using an agent-based model are used to study the effect of these homeostatic mechanisms on the geometrical and structural properties of the developing microcolonies, focusing on the early stages of its development. Also, we examine the effect of linear or exponential dependence with the time of cellular growth on these properties. From our study, we deduce that these mechanisms do not have a noticeable impact on the properties studied, which could be due to the importance that stochastic factors play in the cell division and growth process. In addition, we discuss how competition between cell growth and diffusion is a key aspect in explaining the structure and geometry of developing bacterial microcolonies. The results of the study will help to clarify which processes and parameters should be considered relevant when designing simulation models.

Cell size homeostasis under the circadian regulation of cell division in cyanobacteria

Bacterial cells maintain their characteristic cell size over many generations. Several rod-shaped bacteria, such as Escherichia coli and the cyanobacteria Synechococcus elongatus, divide after adding a constant length to their length at birth. Through this division control known as the adder mechanism, perturbation in cell length due to physiological fluctuation decays over generations at a rate of 2^-1 per cell division. However, previous experiments have shown that the circadian clock in cyanobacteria reduces cell division frequency at a specific time of day under constant light. This circadian gating should modulate the division control by the adder mechanism, but its significance remains unknown. Here we address how the circadian gating affects cell length, doubling time, and cell length stability in cyanobacteria by using mathematical models. We show that a cell subject to circadian gating grows for a long time, and gives birth to elongated daughter cells. These elongated daughter cells grow faster than the previous generation, as elongation speed is proportional to cell length and divide in a short time before the next gating. Hence, the distributions of doubling time and cell length become bimodal, as observed in experimental data. Interestingly, the average doubling time over the population of cells is independent of gating because the extension of doubling time by gating is compensated by its reduction in the subsequent generation. On the other hand, average cell length is increased by gating, suggesting that the circadian clock controls cell length. We then show that the decay rate of perturbation in cell length depends on the ratio of delay in division by the gating τ_G to the average doubling time τ₀ as [Formula: see text] . We estimated τ_G≈2.5, τ₀≈13.6 hours, and τ_G/τ₀≈0.18 from experimental data, indicating that a long doubling time in cyanobacteria maintains the decay rate similar to that of the adder mechanism. Thus, our analysis suggests that the acquisition of the circadian clock during evolution did not impose a constraint on cell size homeostasis in cyanobacteria.

Cell Cycle-Dependent Recruitment of FtsN to the Divisome in Escherichia coli

Cell division in Escherichia coli starts with the formation of an FtsZ protofilament network at midcell, the Z ring. However, only after a considerable lag period does the cell start to form a midcell constriction. The onset of constriction depends upon the arrival of so-called late divisome proteins, among which, FtsN is the last essential one. The timing and dependency of FtsN arrival to the divisome, along with genetic evidence, suggests it triggers cell division. In this study, we used high-throughput fluorescence microscopy to determine the arrival of FtsN and the early divisome protein ZapA to midcell at a single-cell level during the cell cycle. Our data show while the recruitment of ZapA/FtsZ is gradual in the cell cycle, recruitment of FtsN is rapid and begins at about the onset of constriction. At this time, the fraction of ZapA/FtsZ in the Z ring approaches its peak value. We also find a second increase in FtsN recruitment to the divisome, which begins once the amount of ZapA/FtsZ at midcell starts decreasing. Increasing hypermorphic FtsA* (FtsA R286W), but not FtsA, accelerates FtsN recruitment but not constriction. This finding is consistent with FtsA* recruiting FtsN with some other divisome component being rate-limiting for constriction under these conditions. Finally, our data support the recently proposed idea that ZapA/FtsZ and FtsN are part of physically separate complexes in midcell throughout the whole septation process. IMPORTANCE Cell division in most bacteria starts with the formation of an FtsZ protofilament network at midcell, the Z ring. However, cells only start to constrict after a considerable lag. A factor thought to trigger the onset of constriction in Escherichia coli is FtsN, which is the last essential protein to be recruited to the Z ring. Using a high-throughput quantitative fluorescence microscopy, we determine the cell cycle-dependent recruitment of FtsN to the Z ring. Our data show rapid accumulation of FtsN to the Z ring about a quarter of the cell cycle after the formation of the Z ring. This initial wave is followed by another increase in FtsN recruitment once the FtsZ protofilament network starts to disassemble. The presence of FtsA* accelerates FtsN recruitment to the Z ring but does not lead to earlier constrictions. Our data furthermore suggest FtsZ and FtsN are part of physically separate complexes throughout the division process.

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.

Optimization and Fabrication of Multi-Level Microchannels for Long-Term Imaging of Bacterial Growth and Expansion

Bacteria are unicellular organisms whose length is usually around a few micrometers. Advances in microfabrication techniques have enabled the design and implementation of microdevices to confine and observe bacterial colony growth. Microstructures hosting the bacteria and microchannels for nutrient perfusion usually require separate microfabrication procedures due to different feature size requirements. This fact increases the complexity of device integration and assembly process. Furthermore, long-term imaging of bacterial dynamics over tens of hours requires stability in the microscope focusing mechanism to ensure less than one-micron drift in the focal axis. In this work, we design and fabricate an integrated multi-level, hydrodynamically-optimized microfluidic chip to study long-term Escherichia coli population dynamics in confined microchannels. Reliable long-term microscopy imaging and analysis has been limited by focus drifting and ghost effect, probably caused by the shear viscosity changes of aging microscopy immersion oil. By selecting a microscopy immersion oil with the most stable viscosity, we demonstrate successful captures of focally stable time-lapse bacterial images for ≥72 h. Our fabrication and imaging methodology should be applicable to other single-cell studies requiring long-term imaging.

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.

A feedback control principle common to several biological and engineered systems

Feedback control is used by many distributed systems to optimize behaviour. Traditional feedback control algorithms spend significant resources to constantly sense and stabilize a continuous control variable of interest, such as vehicle speed for implementing cruise control, or body temperature for maintaining homeostasis. By contrast, discrete-event feedback (e.g. a server acknowledging when data are successfully transmitted, or a brief antennal interaction when an ant returns to the nest after successful foraging) can reduce costs associated with monitoring a continuous variable; however, optimizing behaviour in this setting requires alternative strategies. Here, we studied parallels between discrete-event feedback control strategies in biological and engineered systems. We found that two common engineering rules—additive-increase, upon positive feedback, and multiplicative-decrease, upon negative feedback, and multiplicative-increase multiplicative-decrease—are used by diverse biological systems, including for regulating foraging by harvester ant colonies, for maintaining cell-size homeostasis, and for synaptic learning and adaptation in neural circuits. These rules support several goals of these systems, including optimizing efficiency (i.e. using all available resources); splitting resources fairly among cooperating agents, or conversely, acquiring resources quickly among competing agents; and minimizing the latency of responses, especially when conditions change. We hypothesize that theoretical frameworks from distributed computing may offer new ways to analyse adaptation behaviour of biology systems, and in return, biological strategies may inspire new algorithms for discrete-event feedback control in engineering.