Step by Step, Cell by Cell: Quantification of the Bacterial Cell Cycle

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.

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.

Engineering Shewanella oneidensis to efficiently harvest electricity power by co-utilizing glucose and lactate in thin stillage of liquor industry

Thin stillage, rich in glucose and lactate, can seriously pollute water resources when directly discharged into the natural environment. Microbial fuel cells (MFC), as a green and sustainable technology, could utilize exoelectrogens to break down organics in wastewater and harvest electricity. Nevertheless, Shewanella oneidensis MR-1, cannot utilize thin stillage for efficient power generation. Here, to enable S. oneidensis to co-utilize glucose and lactate from thin stillage, an engineered S. oneidensis G₇∆RSL₁ was first created by constructing glucose metabolism pathway, promoting glucose and lactate co-utilization, and enhancing biofilm formation. Then, to enhance biofilm conductivity, we constructed a 3D self-assembled G₇∆RSL₁-rGO/CNT biohybrid with maximum power density of 560.4 mW m^-2 and 373.7 mW m^-2 in artificial and actual thin stillage, respectively, the highest among the reported genetically engineered S. oneidensis with thin stillage as carbon source. This study provides a new strategy to facilitate practical applications of MFC in wastewater remediation and efficient power recovery.

Single-Cell Analysis of the Antimicrobial and Bactericidal Activities of the Antimicrobial Peptide Magainin 2

Antimicrobial peptides (AMPs) inhibit the proliferation of or kill bacterial cells. To measure these activities, several methods have been used, which provide only the average value of many cells. Here, we report the development of a method to examine the antimicrobial and bactericidal activities of AMPs at the single-cell level (i.e., single-cell analysis) and apply this strategy to examine the interaction of an AMP, magainin 2 (Mag), with Escherichia coli cells. Using this method, we monitored the proliferation of single cells on agar in a microchamber and measured the distribution of the number of cells in each microcolony using optical microscopy. For method A, we incubated cells in the presence of various concentrations of AMPs for 3 h. The fraction of microcolonies containing only a single cell, Psingle, increased with the Mag concentration and reached 1 at a specific concentration, which corresponded to the MIC. For method B, after the interaction of a cell suspension with an AMP for a specific time, an aliquot was diluted to stop the interaction, and the proliferation of single cells then was monitored after a 3-h incubation; this method permits the definition of Psingle(t), the fraction of dead cells after the interaction. For the interaction of Mag with E. coli cells, Psingle(t) increased with the interaction time, reaching ~1 at 10 and 20 min for 25 and 13 μM Mag, respectively. Thus, these results indicate that a short interaction time between Mag and E. coli cells is sufficient to induce bacterial cell death. IMPORTANCE To elucidate the activity of antimicrobial peptides (AMPs) against bacterial cells, it is important to estimate the interaction time that is sufficient to induce cell death. We have developed a method to examine the antimicrobial and bactericidal activities of AMPs at the single-cell level (i.e., single-cell analysis). Using this method, we monitored the proliferation of single cells on agar in a microchamber and measured the distribution of the number of cells in each microcolony using optical microscopy. We found that during the interaction of magainin 2 (Mag) with E. coli cells, the fraction of dead cells, Psingle(t), increased with the interaction time, rapidly reaching 1 (e.g., 10 min for 25 μM Mag). This result indicates that Mag induces cell death after a short time of interaction.

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.

Genome-Scale Reconstruction of Microbial Dynamic Phenotype: Successes and Challenges

This review is a part of the SI 'Genome-Scale Modeling of Microorganisms in the Real World'. The goal of GEM is the accurate prediction of the phenotype from its respective genotype under specified environmental conditions. This review focuses on the dynamic phenotype; prediction of the real-life behaviors of microorganisms, such as cell proliferation, dormancy, and mortality; balanced and unbalanced growth; steady-state and transient processes; primary and secondary metabolism; stress responses; etc. Constraint-based metabolic reconstructions were successfully started two decades ago as FBA, followed by more advanced models, but this review starts from the earlier nongenomic predecessors to show that some GEMs inherited the outdated biokinetic frameworks compromising their performances. The most essential deficiencies are: (i) an inadequate account of environmental conditions, such as various degrees of nutrients limitation and other factors shaping phenotypes; (ii) a failure to simulate the adaptive changes of MMCC (MacroMolecular Cell Composition) in response to the fluctuating environment; (iii) the misinterpretation of the SGR (Specific Growth Rate) as either a fixed constant parameter of the model or independent factor affecting the conditional expression of macromolecules; (iv) neglecting stress resistance as an important objective function; and (v) inefficient experimental verification of GEM against simple growth (constant MMCC and SGR) data. Finally, we propose several ways to improve GEMs, such as replacing the outdated Monod equation with the SCM (Synthetic Chemostat Model) that establishes the quantitative relationships between primary and secondary metabolism, growth rate and stress resistance, process kinetics, and cell composition.

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.

Exponential trajectories, cell size fluctuations, and the adder property in bacteria follow from simple chemical dynamics and division control

Experiments on steady-state bacterial cultures have uncovered several quantitative regularities at the system level. These include, first, the exponential growth of cell size with time and the balanced growth of intracellular chemicals between cell birth and division, which are puzzling given the nonlinear and decentralized chemical dynamics in the cell. We model a cell as a set of chemical populations undergoing nonlinear mass action kinetics in a container whose volume is a linear function of the chemical populations. This turns out to be a special class of dynamical systems that generically has attractors in which all populations grow exponentially with time at the same rate. This explains exponential balanced growth of bacterial cells without invoking any regulatory mechanisms and suggests that this could be a robust property of protocells as well. Second, we consider the hypothesis that cells commit themselves to division when a certain internal chemical population reaches a threshold of N molecules. We show that this hypothesis leads to a simple explanation of some of the variability observed across cells in a bacterial culture. In particular, it reproduces the adder property of cell size fluctuations observed recently in E. coli; the observed correlations among interdivision time, birth volume, and added volume in a generation; and the observed scale of the fluctuations (CV ≈ 10-30%) when N is between 10 and 100. Third, upon including a suitable regulatory mechanism that optimizes the growth rate of the cell, the model reproduces the observed bacterial growth laws including the dependence of the growth rate and ribosomal protein fraction on the medium. Thus, the models provide a framework for unifying diverse aspects of bacterial growth physiology under one roof. They also suggest new questions for experimental and theoretical enquiry.

Cell size homeostasis is maintained by CDK4-dependent activation of p38 MAPK

While molecules that promote the growth of animal cells have been identified, it remains unclear how such signals are orchestrated to determine a characteristic target size for different cell types. It is increasingly clear that cell size is determined by size checkpoints-mechanisms that restrict the cell cycle progression of cells that are smaller than their target size. Previously, we described a p38 MAPK-dependent cell size checkpoint mechanism whereby p38 is selectively activated and prevents cell cycle progression in cells that are smaller than a given target size. In this study, we show that the specific target size required for inactivation of p38 and transition through the cell cycle is determined by CDK4 activity. Our data suggest a model whereby p38 and CDK4 cooperate analogously to the function of a thermostat: while p38 senses irregularities in size, CDK4 corresponds to the thermostat dial that sets the target size.

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.

Cell Size Is Coordinated with Cell Cycle by Regulating Initiator Protein DnaA in E. coli

Sixty years ago, bacterial cell size was found to be an exponential function of growth rate. Fifty years ago, a more general relationship was proposed, in which cell mass was equal to the initiation mass multiplied by 2 to the power of the ratio of the total time of C and D periods to the doubling time. This relationship has recently been experimentally confirmed by perturbing doubling time, C period, D period, or initiation mass. However, the underlying molecular mechanism remains unclear. Here, we developed a theoretical model for initiator protein DnaA mediating DNA replication initiation in Escherichia coli. We introduced an initiation probability function for competitive binding of DnaA-ATP and DnaA-ADP at oriC. We established a kinetic description of regulatory processes (e.g., expression regulation, titration, inactivation, and reactivation) of DnaA. Cell size as a spatial constraint also participates in the regulation of DnaA. By simulating DnaA kinetics, we obtained a regular DnaA oscillation coordinated with cell cycle and a converged cell size that matches replication initiation frequency to the growth rate. The relationship between the simulated cell size and growth rate, C period, D period, or initiation mass reproduces experimental results. The model also predicts how DnaA number and initiation mass vary with perturbation parameters, comparable with experimental data. The results suggest that 1) when growth rate, C period, or D period changes, the regulation of DnaA determines the invariance of initiation mass; 2) ppGpp inhibition of replication initiation may be important for the growth rate independence of initiation mass because three possible mechanisms therein produce different DnaA dynamics, which is experimentally verifiable; and 3) perturbation of some DnaA regulatory process causes a changing initiation mass or even an abnormal cell cycle. This study may provide clues for concerted control of cell size and cell cycle in synthetic biology.

Factors That Affect the Enlargement of Bacterial Protoplasts and Spheroplasts

Cell enlargement is essential for the microinjection of various substances into bacterial cells. The cell wall (peptidoglycan) inhibits cell enlargement. Thus, bacterial protoplasts/spheroplasts are used for enlargement because they lack cell wall. Though bacterial species that are capable of gene manipulation are limited, procedure for bacterial cell enlargement does not involve any gene manipulation technique. In order to prevent cell wall resynthesis during enlargement of protoplasts/spheroplasts, incubation media are supplemented with inhibitors of peptidoglycan biosynthesis such as penicillin. Moreover, metal ion composition in the incubation medium affects the properties of the plasma membrane. Therefore, in order to generate enlarged cells that are suitable for microinjection, metal ion composition in the medium should be considered. Experiment of bacterial protoplast or spheroplast enlargement is useful for studies on bacterial plasma membrane biosynthesis. In this paper, we have summarized the factors that influence bacterial cell enlargement.

Modeling homeostasis mechanisms that set the target cell size

How organisms maintain cell size homeostasis is a long-standing problem that remains unresolved, especially in multicellular organisms. Recent experiments in diverse animal cell types demonstrate that within a cell population, cellular proliferation is low for small and large cells, but high at intermediate sizes. Here we use mathematical models to explore size-control strategies that drive such a non-monotonic profile resulting in the proliferation capacity being maximized at a target cell size. Our analysis reveals that most models of size control yield proliferation capacities that vary monotonically with cell size, and non-monotonicity requires two key mechanisms: (1) the growth rate decreases with increasing size for excessively large cells; and (2) cell division occurs as per the Adder model (division is triggered upon adding a fixed size from birth), or a Sizer-Adder combination. Consistent with theory, Jurkat T cell growth rates increase with size for small cells, but decrease with size for large cells. In summary, our models show that regulation of both growth and cell-division timing is necessary for size control in animal cells, and this joint mechanism leads to a target cell size where cellular proliferation capacity is maximized.

Cell-size regulation in budding yeast does not depend on linear accumulation of Whi5

Cells must couple cell-cycle progress to their growth rate to restrict the spread of cell sizes present throughout a population. Linear, rather than exponential, accumulation of Whi5, was proposed to provide this coordination by causing a higher Whi5 concentration in cells born at a smaller size. We tested this model using the inducible GAL1 promoter to make the Whi5 concentration independent of cell size. At an expression level that equalizes the mean cell size with that of wild-type cells, the size distributions of cells with galactose-induced Whi5 expression and wild-type cells are indistinguishable. Fluorescence microscopy confirms that the endogenous and GAL1 promoters produce different relationships between Whi5 concentration and cell volume without diminishing size control in the G1 phase. We also expressed Cln3 from the GAL1 promoter, finding that the spread in cell sizes for an asynchronous population is unaffected by this perturbation. Our findings indicate that size control in budding yeast does not fundamentally originate from the linear accumulation of Whi5, contradicting a previous claim and demonstrating the need for further models of cell-cycle regulation to explain how cell size controls passage through Start.

Constructing and deconstructing the bacterial cell wall

The history of modern medicine cannot be written apart from the history of the antibiotics. Antibiotics are cytotoxic secondary metabolites that are isolated from Nature. The antibacterial antibiotics disproportionately target bacterial protein structure that is distinct from eukaryotic protein structure, notably within the ribosome and within the pathways for bacterial cell-wall biosynthesis (for which there is not a eukaryotic counterpart). This review focuses on a pre-eminent class of antibiotics-the β-lactams, exemplified by the penicillins and cephalosporins-from the perspective of the evolving mechanisms for bacterial resistance. The mechanism of action of the β-lactams is bacterial cell-wall destruction. In the monoderm (single membrane, Gram-positive staining) pathogen Staphylococcus aureus the dominant resistance mechanism is expression of a β-lactam-unreactive transpeptidase enzyme that functions in cell-wall construction. In the diderm (dual membrane, Gram-negative staining) pathogen Pseudomonas aeruginosa a dominant resistance mechanism (among several) is expression of a hydrolytic enzyme that destroys the critical β-lactam ring of the antibiotic. The key sensing mechanism used by P. aeruginosa is monitoring the molecular difference between cell-wall construction and cell-wall deconstruction. In both bacteria, the resistance pathways are manifested only when the bacteria detect the presence of β-lactams. This review summarizes how the β-lactams are sensed and how the resistance mechanisms are manifested, with the expectation that preventing these processes will be critical to future chemotherapeutic control of multidrug resistant bacteria.

Membrane potential is vital for rapid permeabilization of plasma membranes and lipid bilayers by the antimicrobial peptide lactoferricin B

Lactoferricin B (LfcinB) is a cationic antimicrobial peptide, and its capacity to damage the bacterial plasma membrane is suggested to be a main factor in LfcinB's antimicrobial activity. However, the specific processes and mechanisms in LfcinB-induced membrane damage are unclear. In this report, using confocal laser-scanning microscopy, we examined the interaction of LfcinB with single Escherichia coli cells and spheroplasts containing the water-soluble fluorescent probe calcein in the cytoplasm. LfcinB induced rapid calcein leakage from single E. coli cells and from single spheroplasts, indicating that LfcinB interacts directly with the plasma membrane and induces its rapid permeabilization. The proton ionophore carbonyl cyanide m-chlorophenylhydrazone suppressed this leakage. Next, we used the single giant unilamellar vesicle (GUV) method to examine LfcinB's interaction with GUVs comprising polar lipid extracts of E. coli containing a water-soluble fluorescent probe, Alexa Fluor 647 hydrazide (AF647). We observed that LfcinB stochastically induces local rupture in single GUVs, causing rapid AF647 leakage; however, higher LfcinB concentrations were required for AF647 leakage from GUVs than from E. coli cells and spheroplasts. To identify the reason for this difference, we examined the effect of membrane potential on LfcinB-induced pore formation, finding that the rate of LfcinB-induced local rupture in GUVs increases greatly with increasing negative membrane potential. These results indicate that membrane potential plays an important role in LfcinB-induced local rupture of lipid bilayers and rapid permeabilization of E. coli plasma membranes. On the basis of these results, we discuss the mode of action of LfcinB's antimicrobial activity.

Biochemistry, genetics and biotechnology of glycerol utilization in Pseudomonas species

The use of renewable waste feedstocks is an environment‐friendly choice contributing to the reduction of waste treatment costs and increasing the economic value of industrial by‐products. Glycerol (1,2,3‐propanetriol), a simple polyol compound widely distributed in biological systems, constitutes a prime example of a relatively cheap and readily available substrate to be used in bioprocesses. Extensively exploited as an ingredient in the food and pharmaceutical industries, glycerol is also the main by‐product of biodiesel production, which has resulted in a progressive drop in substrate price over the years. Consequently, glycerol has become an attractive substrate in biotechnology, and several chemical commodities currently produced from petroleum have been shown to be obtained from this polyol using whole‐cell biocatalysts with both wild‐type and engineered bacterial strains. Pseudomonas species, endowed with a versatile and rich metabolism, have been adopted for the conversion of glycerol into value‐added products (ranging from simple molecules to structurally complex biopolymers, e.g. polyhydroxyalkanoates), and a number of metabolic engineering strategies have been deployed to increase the number of applications of glycerol as a cost‐effective substrate. The unique genetic and metabolic features of glycerol‐grown Pseudomonas are presented in this review, along with relevant examples of bioprocesses based on this substrate – and the synthetic biology and metabolic engineering strategies implemented in bacteria of this genus aimed at glycerol valorization.

Bacterial growth: a statistical physicist's guide

Bacterial growth presents many beautiful phenomena that pose new theoretical challenges to statistical physicists, and are also amenable to laboratory experimentation. This review provides some of the essential biological background, discusses recent applications of statistical physics in this field, and highlights the potential for future research.

Concurrent processes set E. coli cell division

A cell can divide only upon completion of chromosome segregation; otherwise, its daughters would lose genetic material. However, we do not know whether the partitioning of chromosomes is the key event for the decision to divide. We show how key trends in single-cell data reject the classic idea of replication-segregation as the rate-limiting process for cell division. Instead, the data agree with a model where two concurrent processes (setting replication initiation and interdivision time) set cell division on competing time scales. During each cell cycle, division is set by the slowest process (an "AND" gate). The concept of transitions between cell cycle stages as decisional processes integrating multiple inputs instead of cascading from orchestrated steps can affect the way we think of the cell cycle in general.

Size control in mammalian cells involves modulation of both growth rate and cell cycle duration

Despite decades of research, how mammalian cell size is controlled remains unclear because of the difficulty of directly measuring growth at the single-cell level. Here we report direct measurements of single-cell volumes over entire cell cycles on various mammalian cell lines and primary human cells. We find that, in a majority of cell types, the volume added across the cell cycle shows little or no correlation to cell birth size, a homeostatic behavior called "adder". This behavior involves modulation of G1 or S-G2 duration and modulation of growth rate. The precise combination of these mechanisms depends on the cell type and the growth condition. We have developed a mathematical framework to compare size homeostasis in datasets ranging from bacteria to mammalian cells. This reveals that a near-adder behavior is the most common type of size control and highlights the importance of growth rate modulation to size control in mammalian cells.

The Empirical Fluctuation Pattern of E. coli Division Control

In physics, it is customary to represent the fluctuations of a stochastic system at steady state in terms of linear response to small random perturbations. Previous work has shown that the same framework describes effectively the trade-off between cell-to-cell variability and correction in the control of cell division of single E. coli cells. However, previous analyses were motivated by specific models and limited to a subset of the measured variables. For example, most analyses neglected the role of growth rate variability. Here, we take a comprehensive approach and consider several sets of available data from both microcolonies and microfluidic devices in different growth conditions. We evaluate all the coupling coefficients between the three main measured variables (interdivision times, cell sizes and individual-cell growth rates). The linear-response framework correctly predicts consistency relations between a priori independent experimental measurements, which confirms its validity. Additionally, the couplings between the cell-specific growth rate and the other variables are typically non zero. Finally, we use the framework to detect signatures of mechanisms in experimental data involving growth rate fluctuations, finding that (1) noise-generating coupling between size and growth rate is a consequence of inter-generation growth rate correlations and (2) the correlation patterns agree with a near-adder model where the added size has a dependence on the single-cell growth rate. Our findings define relevant constraints that any theoretical description should reproduce, and will help future studies aiming to falsify some of the competing models of the cell cycle existing today in the literature.

Surface Area to Volume Ratio: A Natural Variable for Bacterial Morphogenesis

An immediately observable feature of bacteria is that cell size and shape are remarkably constant and characteristic for a given species in a particular condition, but vary quantitatively with physiological parameters such as growth rate, indicating both genetic and environmental regulation. However, despite decades of research, the molecular mechanisms underlying bacterial morphogenesis have remained incompletely characterized. We recently demonstrated that a wide range of bacterial species exhibit a robust surface area to volume ratio (SA/V) homeostasis. Because cell size, shape, and SA/V are mathematically interconnected, if SA/V is indeed the natural variable that cells actively monitor, this finding has critical implications for our understanding of bacterial morphogenesis, placing fundamental constraints on the sizes and shapes that cells can adopt. In this Opinion article we discuss the broad implications that this novel perspective has for the field of bacterial growth and morphogenesis.

Modeling Cell Size Regulation: From Single-Cell-Level Statistics to Molecular Mechanisms and Population-Level Effects

Most microorganisms regulate their cell size. In this article, we review some of the mathematical formulations of the problem of cell size regulation. We focus on coarse-grained stochastic models and the statistics that they generate. We review the biologically relevant insights obtained from these models. We then describe cell cycle regulation and its molecular implementations, protein number regulation, and population growth, all in relation to size regulation. Finally, we discuss several future directions for developing understanding beyond phenomenological models of cell size regulation.

Fundamental principles in bacterial physiology-history, recent progress, and the future with focus on cell size control: a review

Bacterial physiology is a branch of biology that aims to understand overarching principles of cellular reproduction. Many important issues in bacterial physiology are inherently quantitative, and major contributors to the field have often brought together tools and ways of thinking from multiple disciplines. This article presents a comprehensive overview of major ideas and approaches developed since the early 20th century for anyone who is interested in the fundamental problems in bacterial physiology. This article is divided into two parts. In the first part (sections 1-3), we review the first 'golden era' of bacterial physiology from the 1940s to early 1970s and provide a complete list of major references from that period. In the second part (sections 4-7), we explain how the pioneering work from the first golden era has influenced various rediscoveries of general quantitative principles and significant further development in modern bacterial physiology. Specifically, section 4 presents the history and current progress of the 'adder' principle of cell size homeostasis. Section 5 discusses the implications of coarse-graining the cellular protein composition, and how the coarse-grained proteome 'sectors' re-balance under different growth conditions. Section 6 focuses on physiological invariants, and explains how they are the key to understanding the coordination between growth and the cell cycle underlying cell size control in steady-state growth. Section 7 overviews how the temporal organization of all the internal processes enables balanced growth. In the final section 8, we conclude by discussing the remaining challenges for the future in the field.

Stable Regulation of Cell Cycle Events in Mycobacteria: Insights From Inherently Heterogeneous Bacterial Populations

Model bacteria, such as E. coli and B. subtilis, tightly regulate cell cycle progression to achieve consistent cell size distributions and replication dynamics. Many of the hallmark features of these model bacteria, including lateral cell wall elongation and symmetric growth and division, do not occur in mycobacteria. Instead, mycobacterial growth is characterized by asymmetric polar growth and division. This innate asymmetry creates unequal birth sizes and growth rates for daughter cells with each division, generating a phenotypically heterogeneous population. Although the asymmetric growth patterns of mycobacteria lead to a larger variation in birth size than typically seen in model bacterial populations, the cell size distribution is stable over time. Here, we review the cellular mechanisms of growth, division, and cell cycle progression in mycobacteria in the face of asymmetry and inherent heterogeneity. These processes coalesce to control cell size. Although Mycobacterium smegmatis and Mycobacterium bovis Bacillus Calmette-Guérin (BCG) utilize a novel model of cell size control, they are similar to previously studied bacteria in that initiation of DNA replication is a key checkpoint for cell division. We compare the regulation of DNA replication initiation and strategies used for cell size homeostasis in mycobacteria and model bacteria. Finally, we review the importance of cellular organization and chromosome segregation relating to the physiology of mycobacteria and consider how new frameworks could be applied across the wide spectrum of bacterial diversity.

Learning from Noise: How Observing Stochasticity May Aid Microbiology

For many decades, the wedding of quantitative data with mathematical modeling has been fruitful, leading to important biological insights. Here, we review some of the ongoing efforts to gain insights into problems in microbiology - and, in particular, cell-cycle progression and its regulation - through observation and quantitative analysis of the natural fluctuations in the system. We first illustrate this idea by reviewing a classic example in microbiology - the Luria-Delbrück experiment - and discussing how, in that case, useful information was obtained by looking beyond the mean outcome of the experiment, but instead paying attention to the variability between replicates of the experiment. We then switch gears to the contemporary problem of cell cycle progression and discuss in more detail how insights into cell size regulation and, when relevant, coupling between the cell cycle and the circadian clock, can be gained by studying the natural fluctuations in the system and their statistical properties. We end with a more general discussion of how (in this context) the correct level of phenomenological model should be chosen, as well as some of the pitfalls associated with this type of analysis. Throughout this review the emphasis is not on providing details of the experimental setups or technical details of the models used, but rather, in fleshing out the conceptual structure of this particular approach to the problem. For this reason, we choose to illustrate the framework on a rather broad range of problems, and on organisms from all domains of life, to emphasize the commonality of the ideas and analysis used (as well as their differences).

Recent advances in understanding how rod-like bacteria stably maintain their cell shapes

Cell shape and cell volume are important for many bacterial functions. In recent years, we have seen a range of experimental and theoretical work that led to a better understanding of the determinants of cell shape and size. The roles of different molecular machineries for cell-wall expansion have been detailed and partially redefined, mechanical forces have been shown to influence cell shape, and new connections between metabolism and cell shape have been proposed. Yet the fundamental determinants of the different cellular dimensions remain to be identified. Here, we highlight some of the recent developments and focus on the determinants of rod-like cell shape and size in the well-studied model organisms Escherichia coli and Bacillus subtilis.

Details Matter: Noise and Model Structure Set the Relationship between Cell Size and Cell Cycle Timing

Organisms across all domains of life regulate the size of their cells. However, the means by which this is done is poorly understood. We study two abstracted “molecular” models for size regulation: inhibitor dilution and initiator accumulation. We apply the models to two settings: bacteria like Escherichia coli, that grow fully before they set a division plane and divide into two equally sized cells, and cells that form a bud early in the cell division cycle, confine new growth to that bud, and divide at the connection between that bud and the mother cell, like the budding yeast Saccharomyces cerevisiae. In budding cells, delaying cell division until buds reach the same size as their mother leads to very weak size control, with average cell size and standard deviation of cell size increasing over time and saturating up to 100-fold higher than those values for cells that divide when the bud is still substantially smaller than its mother. In budding yeast, both inhibitor dilution or initiator accumulation models are consistent with the observation that the daughters of diploid cells add a constant volume before they divide. This “adder” behavior has also been observed in bacteria. We find that in bacteria an inhibitor dilution model produces adder correlations that are not robust to noise in the timing of DNA replication initiation or in the timing from initiation of DNA replication to cell division (the C+D period). In contrast, in bacteria an initiator accumulation model yields robust adder correlations in the regime where noise in the timing of DNA replication initiation is much greater than noise in the C + D period, as reported previously (Ho and Amir, 2015). In bacteria, division into two equally sized cells does not broaden the size distribution.

Analysis of Noise Mechanisms in Cell-Size Control

At the single-cell level, noise arises from multiple sources, such as inherent stochasticity of biomolecular processes, random partitioning of resources at division, and fluctuations in cellular growth rates. How these diverse noise mechanisms combine to drive variations in cell size within an isoclonal population is not well understood. Here, we investigate the contributions of different noise sources in well-known paradigms of cell-size control, such as adder (division occurs after adding a fixed size from birth), sizer (division occurs after reaching a size threshold), and timer (division occurs after a fixed time from birth). Analysis reveals that variation in cell size is most sensitive to errors in partitioning of volume among daughter cells, and not surprisingly, this process is well regulated among microbes. Moreover, depending on the dominant noise mechanism, different size-control strategies (or a combination of them) provide efficient buffering of size variations. We further explore mixer models of size control, where a timer phase precedes/follows an adder, as has been proposed in Caulobacter crescentus. Although mixing a timer and an adder can sometimes attenuate size variations, it invariably leads to higher-order moments growing unboundedly over time. This results in a power-law distribution for the cell size, with an exponent that depends inversely on the noise in the timer phase. Consistent with theory, we find evidence of power-law statistics in the tail of C. crescentus cell-size distribution, although there is a discrepancy between the observed power-law exponent and that predicted from the noise parameters. The discrepancy, however, is removed after data reveal that the size added by individual newborns in the adder phase itself exhibits power-law statistics. Taken together, this study provides key insights into the role of noise mechanisms in size homeostasis, and suggests an inextricable link between timer-based models of size control and heavy-tailed cell-size distributions.