Relative Rates of Surface and Volume Synthesis Set Bacterial Cell Size

Metallosphaera sedula bifurcates into two sizes when it is cultured mixotrophically on soluble iron

Metallosphaera sedula is a thermoacidophilic archaeon that obtains all of its energy for growth from aerobic respiration and oxidative phosphorylation at the expense of selected organic and inorganic sources of electrons. Initial velocities for the oxidation of soluble ferrous ions by intact cells at 60 °C and pH 1.5 were determined using an integrating cavity absorption meter that permitted accurate absorbance measurements to quantify the increase in soluble ferric iron in the presence of turbid suspensions of the live organisms. M. sedula that was cultured on yeast extract either in the absence or the presence of 20 mM soluble ferrous iron exhibited turnover numbers for soluble iron oxidation of 304 ± 26 and 333 ± 31 attamoles/cell/min, respectively. These functional data were consistent with the transcriptomic evidence presented by others, that the proteins presumably responsible for aerobic respiration on soluble iron are expressed constitutively in M. sedula. Intact cells of M. sedula were characterized by electrical impedance, laser light diffraction, and transmission electron microscopic measurements. All three types of measurements were consistent with the surprising observation that cells cultured on yeast extract in the presence of soluble iron bifurcated into approximately equal numbers of coccoidal cells of two sizes, smaller cells with an average diameter of 0.6 μm and larger cells with an average diameter of 1.35 μm. Cells cultured on the same concentration of yeast extract but in the absence of soluble iron comprised a single cell size with an intermediate average diameter of 1.06 μm. This unexpected bifurcation of a clonal cell population into two demonstrably different sizes when the extracellular nutrient environment changes has not previously been reported for M. sedula, or any other single-celled archaeon or eubacterium.

Plasma membrane folding enables constant surface area-to-volume ratio in growing mammalian cells

All cells are subject to geometric constraints, including the surface area-to-volume (SA/V) ratio, which can limit nutrient uptake, maximum cell size, and cell shape changes. Like the SA/V ratio of a sphere, it is generally assumed that the SA/V ratio of cells decreases as cell size increases. However, the structural complexity of the plasma membrane makes studies of the surface area challenging in cells that lack a cell wall. Here, we investigate near-spherical mammalian cells using single-cell measurements of cell mass and plasma membrane proteins and lipids, which allow us to examine the cell size scaling of cell surface components as a proxy for the SA/V ratio. Surprisingly, in various proliferating cell lines, cell surface components scale proportionally with cell size, indicating a nearly constant SA/V ratio as cells grow larger. This behavior is largely independent of the cell-cycle stage and is also observed in quiescent cells, including primary human monocytes. Moreover, the constant SA/V ratio persists when cell size increases excessively during polyploidization. This is enabled by increased plasma membrane folding in larger cells, as verified by electron microscopy. We also observe that specific cell surface proteins and cholesterol can deviate from the proportional size scaling. Overall, maintaining a constant SA/V ratio ensures sufficient plasma membrane area for critical functions such as cell division, nutrient uptake, growth, and deformation across a wide range of cell sizes.

Mechanistic basis for non-exponential bacterial growth

Bacterial populations typically exhibit exponential growth under resource-rich conditions, yet individual cells often deviate from this pattern. Recent work has shown that the elongation rates of Escherichia coli and Caulobacter crescentus increase throughout the cell cycle (super-exponential growth), while Bacillus subtilis displays a mid-cycle minimum (convex growth), and Mycobacterium tuberculosis grows linearly. Here, we develop a single-cell model linking gene expression, proteome allocation, and mass growth to explain these diverse growth trajectories. By calibrating model parameters with experimental data, we show that DNA-proportional mRNA transcription produces near-exponential growth, whereas deviations from this proportionality yield the observed non-exponential growth patterns. Analysis of gene expression perturbations reveals that ribosome expression primarily controls dry mass growth rate, whereas envelope expression more strongly affects cell elongation rate. Fitting our model to single-cell experimental data reproduces convex, super-exponential, and linear modes of growth, demonstrating how envelope and ribosome expression schedules drive cell-cycle-specific behaviors. These findings provide a mechanistic basis for non-exponential single-cell growth and offer insights into how bacterial cells dynamically regulate elongation rates within each generation.

Exploitative stress within Bacillus subtilis biofilm determines the spatial distribution of pleomorphic cells

Bacteria commonly live in a spatially organized biofilm assemblage. The metabolic activity inside the biofilm leads to segmented physiological microenvironments. In nature, bacteria possess several pleomorphic forms to withstand certain ecological alterations. We hypothesized that pleomorphism also exists within the biofilm, which can be considered as the fundamental niche for bacteria. We report a distinct pattern of cell size variation throughout the biofilm of Bacillus subtilis. Cell size heterogeneity was observed in biofilm development, wherein the frequency of long cells is higher in outer regions, whereas lower in inner regions. Moreover, compared to planktonic cells, bacteria in the biofilm mode reduce their geometric ratio from 8.34 to 3.69 and 2.65 in the outer and inner regions, respectively. There were no significant differences observed in nutrient diffusion from the outer to the inner region, and more than 73 % of cells in the inner region were viable. However, the inner and middle regions were more acidic than the outer of the biofilm. Conclusively, growth rate-independent cell size reduction at low pH suggests that the resulting phenotype switching within biofilm was observed due to the pH gradient of neutral to acidic from the outer to the core of the biofilm. This gradient of H+ ions concentration may create exploitative stress within the biofilm, which could favor specific pleomorphic cells to thrive in their specialized niches. By understanding the cell size variation in response to the local environment, we propose a model of biofilm formation by pleomorphic cells.

Cell size regulation in bacteria: a tale of old regulators with new mechanisms

Proper function in a bacterial cell relies on intrinsic cell size regulation. The molecular mechanisms underlying how bacteria maintain their cell size remain unclear. The conserved regulator DnaA, the initiator of chromosome replication, is associated to size regulation by controlling the number of origins of replication ( oriC ) per cell. In this study, we identify and characterize a new mechanism in which DnaA modulates cell size independently of oriC -copy number. By altering the levels of DnaA without impacting chromosome replication, we demonstrate that DnaA's activity as a transcription factor can slow down cell elongation rate resulting in cells that are ∼20% smaller. We identify the peptidoglycan biosynthetic enzyme MurD as a key player of cell size regulation in Caulobacter crescentus and in the evolutionarily distant bacterium Escherichia coli . Collectively, our findings provide mechanistic insights to the complex regulation of cell size in bacteria.

Plasma membrane folding enables constant surface area-to-volume ratio in growing mammalian cells

All cells are subject to geometric constraints, including the surface area-to-volume (SA/V) ratio, which can limit nutrient uptake, maximum cell size, and cell shape changes. Like the SA/V ratio of a sphere, it is generally assumed that the SA/V ratio of cells decreases as cell size increases. However, the structural complexity of the plasma membrane makes studies of the surface area challenging in cells that lack a cell wall. Here, we investigate near-spherical mammalian cells using single-cell measurements of cell mass and plasma membrane proteins and lipids, which allows us to examine the cell size scaling of cell surface components as a proxy for the SA/V ratio. Surprisingly, in various proliferating cell lines, cell surface components scale proportionally with cell size, indicating a nearly constant SA/V ratio as cells grow larger. This behavior is largely independent of the cell cycle stage and is also observed in quiescent cells, including primary human monocytes. Moreover, the constant SA/V ratio persists when cell size increases excessively during polyploidization. This is enabled by increased plasma membrane folding in larger cells, as verified by electron microscopy. We also observe that specific cell surface proteins and cholesterol can deviate from the proportional size scaling. Overall, maintaining a constant SA/V ratio ensures sufficient plasma membrane area for critical functions such as cell division, nutrient uptake, growth, and deformation across a wide range of cell sizes.

The design of unit cells by combining the self-reproduction systems and metabolic cushioning loads

Recently, we published a comprehensive theoretical analysis of the self-reproduction processes in proto-cells (doubling of their components) composed of different combinations of cellular subsystems. In this paper, we extend the detailed analysis of structural and functional peculiarities of self-reproduction processes to unit cells of the Cooper-Helmstetter-Donachie cell cycle theory. We show that: 1. Our modelling framework allows to calculate physiological parameters (numbers of cell components, flux patterns, cellular composition, etc.) of unit cells, including also unit cell mass that determines the DNA replication initiation conditions. 2. Unit cells might have additional cell (cushioning) components that are responsible not only for carrying out various special functions, but also for regulating cell size and stabilizing the growth of cells. 3. The optimal productivity of the synthesis of cushioning components (useful cellular load) is observed at doubling time approximately two times longer than the minimal doubling time of the unit cells.

Disruption of biological membranes by hydrophobic molecules: a way to inhibit bacterial growth

With antibiotic resistance increasing in the global population every year, efforts to discover new strategies against microbial diseases are urgently needed. One of the new therapeutic targets is the bacterial cell membrane since, in the event of a drastic alteration, it can cause cell death. We propose the utilization of hydrophobic molecules, namely, propofol (PFL) and cannabidiol (CBD), dissolved in nanodroplets of oil, to effectively strike the membrane of two well-known pathogens: Escherichia coli and Staphylococcus aureus. First, we carried out calorimetric measurements to evaluate the effects of these drugs on model membranes formed by lipids from these bacteria. We found that the drugs modify their transition temperature, enthalpy of cohesion, and cooperativity, which indicates a strong alteration of the membranes. Then, inhibition of colony-forming units is studied in incubation experiments. Finally, we demonstrate, using atomic force and fluorescence microscopy, that the drugs, especially propofol, produce a visible disruption in real bacterial membranes, explaining the observed inhibition. These findings may have useful implications in the global effort to discover new ways to effectively combat the growing threat of drug-resistant pathogens, especially in skin infections.

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

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

Homeostasis of cytoplasmic crowding by cell wall fluidization and ribosomal counterions

In bacteria, algae, fungi, and plant cells, the wall must expand in concert with cytoplasmic biomass production, otherwise cells would experience toxic molecular crowding1,2or lyse. But how cells achieve expansion of this complex biomaterial in coordination with biosynthesis of macromolecules in the cytoplasm remains unexplained3, although recent works have revealed that these processes are indeed coupled4,5. Here, we report a striking increase of turgor pressure with growth rate in E. coli, suggesting that the speed of cell wall expansion is controlled via turgor. Remarkably, despite this increase in turgor pressure, cellular biomass density remains constant across a wide range of growth rates. By contrast, perturbations of turgor pressure that deviate from this scaling directly alter biomass density. A mathematical model based on cell wall fluidization by cell wall endopeptidases not only explains these apparently confounding observations but makes surprising quantitative predictions that we validated experimentally. The picture that emerges is that turgor pressure is directly controlled via counterions of ribosomal RNA. Elegantly, the coupling between rRNA and turgor pressure simultaneously coordinates cell wall expansion across a wide range of growth rates and exerts homeostatic feedback control on biomass density. This mechanism may regulate cell wall biosynthesis from microbes to plants and has important implications for the mechanism of action of antibiotics6.

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.

Architectural underpinnings of stochastic intergenerational homeostasis

Living systems are naturally complex and adaptive and offer unique insights into the strategies for achieving and sustaining stochastic homeostasis in different conditions. Here we focus on homeostasis in the context of stochastic growth and division of individual bacterial cells. We take advantage of high-precision long-term dynamical data that have recently been used to extract emergent simplicities and to articulate empirical intra- and intergenerational scaling laws governing these stochastic dynamics. From these data, we identify the core motif in the mechanistic coupling between division and growth, which naturally yields these precise rules, thus also bridging the intra- and intergenerational phenomenologies. By developing and utilizing techniques for solving a broad class of first-passage processes, we derive the exact analytic necessary and sufficient condition for sustaining stochastic intergenerational cell-size homeostasis within this framework. Furthermore, we provide predictions for the precision kinematics of cell-size homeostasis and the shape of the interdivision time distribution, which are compellingly borne out by the high-precision data. Taken together, these results provide insights into the functional architecture of control systems that yield robust yet flexible stochastic homeostasis.

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

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

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

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

Homeostasis of cytoplasmic crowding by cell wall fluidization and ribosomal counterions

In bacteria, algae, fungi, and plant cells, the wall must expand in concert with cytoplasmic biomass production, otherwise cells would experience toxic molecular crowding1,2 or lyse. But how cells achieve expansion of this complex biomaterial in coordination with biosynthesis of macromolecules in the cytoplasm remains unexplained3, although recent works have revealed that these processes are indeed coupled4,5. Here, we report a striking increase of turgor pressure with growth rate in E. coli, suggesting that the speed of cell wall expansion is controlled via turgor. Remarkably, despite this increase in turgor pressure, cellular biomass density remains constant across a wide range of growth rates. By contrast, perturbations of turgor pressure that deviate from this scaling directly alter biomass density. A mathematical model based on cell wall fluidization by cell wall endopeptidases not only explains these apparently confounding observations but makes surprising quantitative predictions that we validated experimentally. The picture that emerges is that turgor pressure is directly controlled via counterions of ribosomal RNA. Elegantly, the coupling between rRNA and turgor pressure simultaneously coordinates cell wall expansion across a wide range of growth rates and exerts homeostatic feedback control on biomass density. This mechanism may regulate cell wall biosynthesis from microbes to plants and has important implications for the mechanism of action of antibiotics6.

Capturing of extracellular vesicles derived from single cells of Escherichia coli

Bacteria secrete extracellular vesicles (EVs), also referred to as bacterial membrane vesicles, which carry, among other compounds, lipids, nucleic acids and virulence factors. Recent studies highlight the role of EVs in the emergence of antibiotic resistance, e.g. as carrier and absorbent particles of the drug to protect the cells, or as a pathway to disseminate resistance elements. In this study, we are interested in characterizing the secretion of EVs at the single bacterial level to ultimately understand how cells respond to antibiotic treatment. We introduce a microfluidic device that enables culture of single bacterial cells and capture of EVs secreted from these individuals. The device incorporates parallel, narrow winding channels to trap single rod-shaped E. coli cells at their entrances. The daughter cells are immediately removed by continuous flow on the open side of the trap, so that the trap contains always only a single cell. Cells grew in these traps over 24 h with a doubling time of 25 minutes. Under antibiotic treatment, the doubling time did not change, but we observed small changes in the cell length of the trapped cells (decrease from 4.0 μm to 3.6 μm for 0 and 250 ng mL-1 polymyxin B, respectively), and cells stopped growing within hours, depending on the drug concentration. Compared to bulk culture, the results indicate a higher susceptibility of on-chip-cultured cells (250 ng mL-1vs. >500 ng mL-1 in bulk), which may be caused, among other reasons, by the space limitation in the cell trap and shear forces. During the culture, EVs secreted by the trapped cells entered the winding channel. We developed a procedure to selectively coat these channels with poly-L-lysine resulting in a positively charged surface, which enabled electrostatic capture of negatively charged EVs. Subsequently, the immobilized EVs were stained with a lipophilic dye and detected by fluorescence microscopy. Our findings confirm large variations of EV secretion among individual bacteria and indicate a relative high rate of EV secretion under antibiotic treatment. The proposed method can be extended to the detection of other secreted substances of interest and may facilitate the elucidation of unknown heterogeneities in bacteria.

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.

Gene expression tradeoffs determine bacterial survival and adaptation to antibiotic stress

To optimize their fitness, cells face the crucial task of efficiently responding to various stresses. This necessitates striking a balance between conserving resources for survival and allocating resources for growth and division. The fundamental principles governing these tradeoffs is an outstanding challenge in the physics of living systems. In this study, we introduce a coarse-grained theoretical framework for bacterial physiology that establishes a connection between the physiological state of cells and their survival outcomes in dynamic environments, particularly in the context of antibiotic exposure. Predicting bacterial survival responses to varying antibiotic doses proves challenging due to the profound influence of the physiological state on critical parameters, such as the Minimum Inhibitory Concentration (MIC) and killing rates, even within an isogenic cell population. Our proposed theoretical model bridges the gap by linking extracellular antibiotic concentration and nutrient quality to intracellular damage accumulation and gene expression. This framework allows us to predict and explain the control of cellular growth rate, death rate, MIC and survival fraction in a wide range of time-varying environments. Surprisingly, our model reveals that cell death is rarely due to antibiotic levels being above the maximum physiological limit, but instead survival is limited by the inability to alter gene expression sufficiently quickly to transition to a less susceptible physiological state. Moreover, bacteria tend to overexpress stress response genes at the expense of reduced growth, conferring greater protection against further antibiotic exposure. This strategy is in contrast to those employed in different nutrient environments, in which bacteria allocate resources to maximize growth rate. This highlights an important tradeoff between the cellular capacity for growth and the ability to survive antibiotic exposure.

Gene Expression Tradeoffs Determine Bacterial Survival and Adaptation to Antibiotic Stress

To optimize their fitness, cells face the crucial task of efficiently responding to various stresses. This necessitates striking a balance between conserving resources for survival and allocating resources for growth and division. The fundamental principles governing these tradeoffs is an outstanding challenge in the physics of living systems. In this study, we introduce a coarse-grained theoretical framework for bacterial physiology that establishes a connection between the physiological state of cells and their survival outcomes in dynamic environments, particularly in the context of antibiotic exposure. Predicting bacterial survival responses to varying antibiotic doses proves challenging due to the profound influence of the physiological state on critical parameters, such as the minimum inhibitory concentration (MIC) and killing rates, even within an isogenic cell population. Our proposed theoretical model bridges the gap by linking extracellular antibiotic concentration and nutrient quality to intracellular damage accumulation and gene expression. This framework allows us to predict and explain the control of cellular growth rate, death rate, MIC, and survival fraction in a wide range of time-varying environments. Surprisingly, our model reveals that cell death is rarely due to antibiotic levels being above the maximum physiological limit, but instead survival is limited by the inability to alter gene expression sufficiently quickly to transition to a less susceptible physiological state. Moreover, bacteria tend to overexpress stress response genes at the expense of reduced growth, conferring greater protection against further antibiotic exposure. This strategy is in contrast to those employed in different nutrient environments, in which bacteria allocate resources to maximize growth rate. This highlights an important tradeoff between the cellular capacity for growth and the ability to survive antibiotic exposure.

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.

Sedimentation Field-Flow Fractionation: A Diagnostic Tool for Rapid Antimicrobial Susceptibility Testing

Conventional antimicrobial susceptibility testing (AST) methods require 24-48 h to provide results, creating the need for a probabilistic antibiotic therapy that increases the risk of antibiotic resistance emergence. Consequently, the development of rapid AST methods has become a priority. Over the past decades, sedimentation field-flow fractionation (SdFFF) has demonstrated high sensitivity in early monitoring of induced biological events in eukaryotic cell populations. This proof-of-concept study aimed at investigating SdFFF for the rapid assessment of bacterial susceptibility to antibiotics. Three bacterial species were included (Escherichia coli, Klebsiella pneumoniae, and Pseudomonas aeruginosa) with two panels of antibiotics tailored to each bacterial species. The results demonstrate that SdFFF, when used in "Hyperlayer" elution mode, enables monitoring of antibiotic-induced morphological changes. The percentage variation of the retention factor (PΔR) was used to quantify the biological effect of antibiotics on bacteria with the establishment of a threshold value of 16.8% to differentiate susceptible and resistant strains. The results obtained with SdFFF were compared to that of the AST reference method, and a categorical agreement of 100% was observed. Overall, this study demonstrates the potential of SdFFF as a rapid method for the determination of antibiotic susceptibility or resistance since it is able to provide results within a shorter time frame than that needed for conventional methods (3-4 h vs 16-24 h, respectively), enabling earlier targeted antibiotic therapy. Further research and validation are necessary to establish the effectiveness and reliability of SdFFF in clinical settings.

Gene expression in growing cells: A biophysical primer

Cell growth and gene expression, two essential elements of all living systems, have long been the focus of biophysical interrogation. Advances in experimental single-cell methods have invigorated theoretical studies into these processes. However, until recently, there was little dialog between the two areas of study. In particular, most theoretical models for gene regulation assumed gene activity to be oblivious to the progression of the cell cycle between birth and division. But, in fact, there are numerous ways in which the periodic character of all cellular observables can modulate gene expression. The molecular factors required for transcription and translation-RNA polymerase, transcription factors, ribosomes-increase in number during the cell cycle, but are also diluted due to the continuous increase in cell volume. The replication of the genome changes the dosage of those same cellular players but also provides competing targets for regulatory binding. Finally, cell division reduces their number again, and so forth. Stochasticity is inherent to all these biological processes, manifested in fluctuations in the synthesis and degradation of new cellular components as well as the random partitioning of molecules at each cell division event. The notion of gene expression as stationary is thus hard to justify. In this review, we survey the emerging paradigm of cell-cycle regulated gene expression, with an emphasis on the global expression patterns rather than gene-specific regulation. We discuss recent experimental reports where cell growth and gene expression were simultaneously measured in individual cells, providing first glimpses into the coupling between the two, and motivating several questions. How do the levels of gene expression products - mRNA and protein - scale with the cell volume and cell-cycle progression? What are the molecular origins of the observed scaling laws, and when do they break down to yield non-canonical behavior? What are the consequences of cell-cycle dependence for the heterogeneity ("noise") in gene expression within a cell population? While the experimental findings, not surprisingly, differ among genes, organisms, and environmental conditions, several theoretical models have emerged that attempt to reconcile these differences and form a unifying framework for understanding gene expression in growing cells.

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.

A coarse-grained resource allocation model of carbon and nitrogen metabolism in unicellular microbes

Coarse-grained resource allocation models (C-GRAMs) are simple mathematical models of cell physiology, where large components of the macromolecular composition are abstracted into single entities. The dynamics and steady-state behaviour of such models provides insights on optimal allocation of cellular resources and have explained experimentally observed cellular growth laws, but current models do not account for the uptake of compound sources of carbon and nitrogen. Here, we formulate a C-GRAM with nitrogen and carbon pathways converging on biomass production, with parametrizations accounting for respirofermentative and purely respiratory growth. The model describes the effects of the uptake of sugars, ammonium and/or compound nutrients such as amino acids on the translational resource allocation towards proteome sectors that maximized the growth rate. It robustly recovers cellular growth laws including the Monod law and the ribosomal growth law. Furthermore, we show how the growth-maximizing balance between carbon uptake, recycling, and excretion depends on the nutrient environment. Lastly, we find a robust linear correlation between the ribosome fraction and the abundance of amino acid equivalents in the optimal cell, which supports the view that simple regulation of translational gene expression can enable cells to achieve an approximately optimal growth state.

The fission yeast cell size control system integrates pathways measuring cell surface area, volume, and time

Eukaryotic cells tightly control their size, but the relevant aspect of size is unknown in most cases. Fission yeast divide at a threshold cell surface area (SA) due, in part, to the protein kinase Cdr2. We find that fission yeast cells only divide by SA under a size threshold. Mutants that divide at a larger size shift to volume-based divisions. Diploid cells divide at a larger size than haploid cells do, but they maintain SA-based divisions, and this indicates that the size threshold for changing from surface-area-based to volume-based control is set by ploidy. Within this size control system, we found that the mitotic activator Cdc25 accumulates like a volume-based sizer molecule, whereas the mitotic cyclin Cdc13 accumulates in the nucleus as a timer. We propose an integrated model for cell size control based on multiple signaling pathways that report on distinct aspects of cell size and growth, including cell SA (Cdr2), cell volume (Cdc25), and time (Cdc13). Combined modeling and experiments show how this system can generate both sizer- and adder-like properties.

Mechanisms of Listeria monocytogenes Disinfection with Benzalkonium Chloride: From Molecular Dynamics to Kinetics of Time-Kill Curves

Unravelling the mechanisms of action of disinfectants is essential to optimise dosing regimes and minimise the emergence of antimicrobial resistance. In this work, we examined the mechanisms of action of a commonly used disinfectant-benzalkonium chloride (BAC)-over a significant pathogen-L. monocytogenes-in the food industry. For that purpose, we used modelling at multiple scales, from the cell membrane to cell population inactivation. Molecular modelling revealed that the integration of the BAC into the membrane requires three phases: (1) the approaching of BAC to the cellular membrane, (2) the absorption of BAC to its surface, and (3) the integration of the compound into the lipid bilayer, where it remains at least for several nanoseconds, probably destabilising the membrane. We hypothesised that the equilibrium of adsorption, although fast, was limiting for sufficiently large BAC concentrations, and a kinetic model was derived to describe time-kill curves of a large population of cells. The model was tested and validated with time series data of free BAC decay and time-kill curves of L. monocytogenes at different inocula and BAC dose concentrations. The knowledge gained from the molecular simulation plus the proposed kinetic model offers the means to design novel disinfection processes rationally.

Triclocarban-contaminated wastewater treatment by innovative hybrid moving entrapped bead activated sludge reactor (HyMER): Continuous performance and computational dynamic simulation analysis

Triclocarban (TCC) has been used in consumer products and is a widespread contaminant in municipal wastewater treatment systems that ultimately accumulates in natural receiving water and soil. This work aims to apply an innovative hybrid moving entrapped bead activated sludge reactor (named "HyMER") that integrates entrapped TCC-degrading microbes and freely suspended activated sludge to treat TCC-contaminated wastewater. A previously isolated TCC-degrading bacterium (Pseudomonas fluorescens strain MC46, called MC46) and barium alginate entrapment were applied. The synthetic TCC-contaminated wastewater treatment (with TCC concentration of 10 mg/L) was performed using 20-cycle fed-batch reactor operation with feeding times of 12 and 24 h and cycle times of 13 and 25 h. The results indicated that the HyMER effectively reduced chemical oxygen demand by up to 80 and 95 % and TCC by up to 53 and 83 %, respectively, with feeding times of 12 and 24 h. Three TCC degradation intermediate products were found-3,4-dichloroaniline, 4-chloroaniline, and aniline. Scanning electron microscopic analysis revealed shorter cells and bacterial appendage development as cell adaptations against TCC and its intermediates. The live/dead assay indicated high survival of entrapped MC46 in toxic conditions, with up to 84 % viable cells. Based on computational fluid dynamic analysis, no entrapped cell agglomeration showed in the reactor, indicating the potential application of HyMER for real wastewater treatment. These results exhibit the feasibility of HyMER and its applicability for future toxic wastewater treatment.

Contact Area and Deformation of Escherichia coli Cells Adhered on a Cationic Surface

When bacteria adhere to surfaces, the chemical and mechanical character of the cell-substrate interface guides cell function and the development of microcolonies and biofilms. Alternately on bactericidal surfaces, intimate contact is critical to biofilm prevention. The direct study of the buried cell-substrate interfaces at the heart of these behaviors is hindered by the small bacterial cell size and inaccessibility of the contact region. Here, we present a total internal reflectance fluorescence depletion approach to measure the size of the cell-substrate contact region and quantify the gap separation and curvature near the contact zone, providing an assessment of the shapes of the near-surface undersides of adhered bacterial cells. Resolution of the gap height is about 10%, down to a few nanometers at contact. Using 1 and 2 μm silica spheres as calibration standards we report that, for flagella-free Escherichia coli (E. coli) adhering on a cationic poly-l-lysine layer, the cell-surface contact and apparent cell deformation vary with adsorbed cell configuration. Most cells adhere by their ends, achieving small contact areas of 0.15 μm2, corresponding to about 1-2% of the cell's surface. The altered Gaussian curvatures of end-adhered cells suggest the flattening of the envelope within the small contact region. When cells adhere by their sides, the contact area is larger, in the range 0.3-1.1 μm2 and comprising up to ∼12% of the cell's total surface. A region of sharper curvature, greater than that of the cells' original spherocylindrical shape, borders the flat contact region in cases of side-on or end-on cell adhesion, suggesting envelope stress. From the measured curvatures, precise stress distributions over the cell surface could be calculated in future studies that incorporate knowledge of envelope moduli. Overall the small contact areas of end-adhered cells may be a limiting factor for antimicrobial surfaces that kill on contact rather than releasing bactericide.

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.

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.

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.

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.

Characterization of proteome-size scaling by integrative omics reveals mechanisms of proliferation control in cancer

Almost all living cells maintain size uniformity through successive divisions. Proteins that over and underscale with size can act as rheostats, which regulate cell cycle progression. Using a multiomic strategy, we leveraged the heterogeneity of melanoma cell lines to identify peptides, transcripts, and phosphorylation events that differentially scale with cell size. Subscaling proteins are enriched in regulators of the DNA damage response and cell cycle progression, whereas super-scaling proteins included regulators of the cytoskeleton, extracellular matrix, and inflammatory response. Mathematical modeling suggested that decoupling growth and proliferative signaling may facilitate cell cycle entry over senescence in large cells when mitogenic signaling is decreased. Regression analysis reveals that up-regulation of TP53 or CDKN1A/p21CIP1 is characteristic of proliferative cancer cells with senescent-like sizes/proteomes. This study provides one of the first demonstrations of size-scaling phenomena in cancer and how morphology influences the chemistry of the cell.

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.

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.

Feedback linking cell envelope stiffness, curvature, and synthesis enables robust rod-shaped bacterial growth

Bacterial growth is remarkably robust to environmental fluctuations, yet the mechanisms of growth-rate homeostasis are poorly understood. Here, we combine theory and experiment to infer mechanisms by which Escherichia coli adapts its growth rate in response to changes in osmolarity, a fundamental physicochemical property of the environment. The central tenet of our theoretical model is that cell-envelope expansion is only sensitive to local information, such as enzyme concentrations, cell-envelope curvature, and mechanical strain in the envelope. We constrained this model with quantitative measurements of the dynamics of E. coli elongation rate and cell width after hyperosmotic shock. Our analysis demonstrated that adaptive cell-envelope softening is a key process underlying growth-rate homeostasis. Furthermore, our model correctly predicted that softening does not occur above a critical hyperosmotic shock magnitude and precisely recapitulated the elongation-rate dynamics in response to shocks with magnitude larger than this threshold. Finally, we found that, to coordinately achieve growth-rate and cell-width homeostasis, cells employ direct feedback between cell-envelope curvature and envelope expansion. In sum, our analysis points to cellular mechanisms of bacterial growth-rate homeostasis and provides a practical theoretical framework for understanding this process.

Filamentous morphology of bacterial pathogens: regulatory factors and control strategies

Several studies have demonstrated that when exposed to physical, chemical, and biological stresses in the environment, many bacteria (Gram-positive and Gram-negative) change their morphology from a normal cell to a filamentous shape. The formation of filamentous morphology is one of the survival strategies against environmental stress and protection against phagocytosis or protist predators. Numerous pathogenic bacteria have shown filamentous morphologies when examined in vivo or in vitro. During infection, certain pathogenic bacteria adopt a filamentous shape inside the cell to avoid phagocytosis by immune cells. Filamentous morphology has also been seen in biofilms formed on biotic or abiotic surfaces by certain bacteria. As a result, in addition to protecting against phagocytosis by immune cells or predators, the filamentous shape aids in biofilm adhesion or colonization to biotic or abiotic surfaces. Furthermore, these filamentous morphologies of bacterial pathogens lead to antimicrobial drug resistance. Clinically, filamentous morphology has become one of the most serious challenges in treating bacterial infection. The current review went into great detail about the various factors involved in the change of filamentous morphology and the underlying mechanisms. In addition, the review discussed a control strategy for suppressing filamentous morphology in order to combat bacterial infections. Understanding the mechanism underlying the filamentous morphology induced by various environmental conditions will aid in drug development and lessen the virulence of bacterial pathogens. KEY POINTS: • The bacterial filamentation morphology is one of the survival mechanisms against several environmental stress conditions and protection from phagocytosis by host cells and protist predators. • The filamentous morphologies in bacterial pathogens contribute to enhanced biofilm formation, which develops resistance properties against antimicrobial drugs. • Filamentous morphology has become one of the major hurdles in treating bacterial infection, hence controlling strategies employed for inhibiting the filamentation morphology from combating bacterial infections.

Scaling of biosynthesis and metabolism with cell size

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

Antibiotic Resistance via Bacterial Cell Shape-Shifting

Bacteria have evolved to develop multiple strategies for antibiotic resistance by effectively reducing intracellular antibiotic concentrations or antibiotic binding affinities, but the role of cell morphology in antibiotic resistance remains poorly understood. By analyzing cell morphological data for different bacterial species under antibiotic stress, we find that bacteria increase or decrease the cell surface-to-volume ratio depending on the antibiotic target. Using quantitative modeling, we show that by reducing the surface-to-volume ratio, bacteria can effectively reduce the intracellular antibiotic concentration by decreasing antibiotic influx. The model further predicts that bacteria can increase the surface-to-volume ratio to induce the dilution of membrane-targeting antibiotics, in agreement with experimental data. Using a whole-cell model for the regulation of cell shape and growth by antibiotics, we predict shape transformations that bacteria can utilize to increase their fitness in the presence of antibiotics. We conclude by discussing additional pathways for antibiotic resistance that may act in synergy with shape-induced resistance.

Gene regulation by a protein translation factor at the single-cell level

Gene expression is inherently stochastic and pervasively regulated. While substantial work combining theory and experiments has been carried out to study how noise propagates through transcriptional regulations, the stochastic behavior of genes regulated at the level of translation is poorly understood. Here, we engineered a synthetic genetic system in which a target gene is down-regulated by a protein translation factor, which in turn is regulated transcriptionally. By monitoring both the expression of the regulator and the regulated gene at the single-cell level, we quantified the stochasticity of the system. We found that with a protein translation factor a tight repression can be achieved in single cells, noise propagation from gene to gene is buffered, and the regulated gene is sensitive in a nonlinear way to global perturbations in translation. A suitable mathematical model was instrumental to predict the transfer functions of the system. We also showed that a Gamma distribution parameterized with mesoscopic parameters, such as the mean expression and coefficient of variation, provides a deep analytical explanation about the system, displaying enough versatility to capture the cell-to-cell variability in genes regulated both transcriptionally and translationally. Overall, these results contribute to enlarge our understanding on stochastic gene expression, at the same time they provide design principles for synthetic biology.

In the cell, proteins can bind to DNA to regulate transcription as well as to RNA to regulate translation. However, cells have mainly evolved to exploit transcription factors as specific gene regulators, while translation factors have remained as global modulators of expression. Consequently, transcription regulation has attracted much attention over the last years to unveil design principles of genetic organization and to engineer synthetic circuits for cell reprogramming. In this work, the phage MS2 coat protein was exploited to regulate the expression of a green fluorescent protein at the level of translation. This synthetic system was instrumental to gain fundamental knowledge on stochasticity and regulation at an overlooked level within the genetic information flow.

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.

Primordial mimicry induces morphological change in Escherichia coli

The morphology of primitive cells has been the subject of extensive research. A spherical form was commonly presumed in prebiotic studies but lacked experimental evidence in living cells. Whether and how the shape of living cells changed are unclear. Here we exposed the rod-shaped bacterium Escherichia coli to a resource utilization regime mimicking a primordial environment. Oleate was given as an easy-to-use model prebiotic nutrient, as fatty acid vesicles were likely present on the prebiotic Earth and might have been used as an energy resource. Six evolutionary lineages were generated under glucose-free but oleic acid vesicle (OAV)-rich conditions. Intriguingly, fitness increase was commonly associated with the morphological change from rod to sphere and the decreases in both the size and the area-to-volume ratio of the cell. The changed cell shape was conserved in either OAVs or glucose, regardless of the trade-offs in carbon utilization and protein abundance. Highly differentiated mutations present in the genome revealed two distinct strategies of adaption to OAV-rich conditions, i.e., either directly targeting the cell wall or not. The change in cell morphology of Escherichia coli for adapting to fatty acid availability supports the assumption of the primitive spherical form.

Lu et al. investigate the evolution of the shape of living cells by generating six experimental lineages of the rod-shaped E. coli under glucose-free conditions in the presence of oleic acid mimicking a primordial environment. The authors show that the morphological changes from rod to sphere accompanied fitness increases and adaptation amongst fatty acid availability supports the assumption of a primitive spherical form.

ppGpp is a bacterial cell size regulator

Growth and division are central to cell size. Bacteria achieve size homeostasis by dividing when growth has added a constant size since birth, termed the adder principle, by unknown mechanisms.^1,2 Growth is well known to be regulated by guanosine tetraphosphate (ppGpp), which controls diverse processes from ribosome production to metabolic enzyme activity and replication initiation and whose absence or excess can induce stress, filamentation, and small growth-arrested cells.^3-6 These observations raise unresolved questions about the relation between ppGpp and size homeostasis mechanisms during normal exponential growth. Here, to untangle effects of ppGpp and nutrients, we gained control of cellular ppGpp by inducing the synthesis and hydrolysis enzymes RelA and Mesh1. We found that ppGpp not only exerts control over the growth rate but also over cell division and thus the steady state cell size. In response to changes in ppGpp level, the added size already establishes its new constant value while the growth rate still adjusts, aided by accelerated or delayed divisions. Moreover, the magnitude of the added size and resulting steady-state birth size correlate consistently with the ppGpp level, rather than with the growth rate, which results in cells of different size that grow equally fast. Our findings suggest that ppGpp serves as a key regulator that coordinates cell size and growth control.

A High-Content Microscopy Screening Identifies New Genes Involved in Cell Width Control in Bacillus subtilis

How cells control their shape and size is a fundamental question of biology. In most bacteria, cell shape is imposed by the peptidoglycan (PG) polymeric meshwork that surrounds the cell. Thus, bacterial cell morphogenesis results from the coordinated action of the proteins assembling and degrading the PG shell. Remarkably, during steady-state growth, most bacteria maintain a defined shape along generations, suggesting that error-proof mechanisms tightly control the process. In the rod-shaped model for the Gram-positive bacterium Bacillus subtilis, the average cell length varies as a function of the growth rate, but the cell diameter remains constant throughout the cell cycle and across growth conditions. Here, in an attempt to shed light on the cellular circuits controlling bacterial cell width, we developed a screen to identify genetic determinants of cell width in B. subtilis. Using high-content screening (HCS) fluorescence microscopy and semiautomated measurement of single-cell dimensions, we screened a library of ∼4,000 single knockout mutants. We identified 13 mutations significantly altering cell diameter, in genes that belong to several functional groups. In particular, our results indicate that metabolism plays a major role in cell width control in B. subtilis.

IMPORTANCE Bacterial shape is primarily dictated by the external cell wall, a vital structure that, as such, is the target of countless antibiotics. Our understanding of how bacteria synthesize and maintain this structure is therefore a cardinal question for both basic and applied research. Bacteria usually multiply from generation to generation while maintaining their progenies with rigorously identical shapes. This implies that the bacterial cells constantly monitor and maintain a set of parameters to ensure this perpetuation. Here, our study uses a large-scale microscopy approach to identify at the whole-genome level, in a model bacterium, the genes involved in the control of one of the most tightly controlled cellular parameters, the cell width.

Computational modeling of unphosphorylated CtrA:Cori binding in the Caulobacter cell cycle

In the alphaproteobacterium, Caulobacter crescentus, phosphorylated CtrA (CtrA∼P), a master regulatory protein, binds directly to the chromosome origin (Cori) to inhibit DNA replication. Using a mathematical model of CtrA binding at Cori site [d], we provide computational evidence that CtrA_U can displace CtrA∼P from Cori at the G1-S transition. Investigation of this interaction within a detailed model of the C. crescentus cell cycle suggests that CckA phosphatase may clear Cori of CtrA∼P by altering the [CtrA_U]/[CtrA∼P] ratio rather than by completely depleting CtrA∼P. Model analysis reveals that the mechanism allows for a speedier transition into S phase, stabilizes the timing of chromosome replication under fluctuating rates of CtrA proteolysis, and may contribute to the viability of numerous mutant strains. Overall, these results suggest that CtrA_U enhances the robustness of chromosome replication. More generally, our proposed regulation of CtrA:Cori dynamics may represent a novel motif for molecular signaling in cell physiology.

Distinguishing different modes of growth using single-cell data

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

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

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

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

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

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

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

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