Archaeal cells share common size control with bacteria despite noisier growth and division

A generalized adder for cell size homeostasis: Effects on stochastic clonal proliferation

Measurements of cell size dynamics have revealed phenomenological principles by which individual cells control their size across diverse organisms. One of the emerging paradigms of cell size homeostasis is the adder, where the cell cycle duration is established such that the cell size increase from birth to division is independent of the newborn cell size. We provide a mechanistic formulation of the adder, considering that cell size follows any arbitrary nonexponential growth law. Our results show that the main requirement to obtain an adder regardless of the growth law (the time derivative of cell size) is that cell cycle regulators are produced at a rate proportional to the growth law, and cell division is triggered when these molecules reach a prescribed threshold level. Among the implications of this generalized adder, we investigate fluctuations in the proliferation of single-cell-derived colonies. Considering exponential cell size growth, random fluctuations in clonal size show a transient increase and then eventually decay to zero over time (i.e., clonal populations become asymptotically more similar). In contrast, several forms of nonexponential cell size dynamics (with adder-based cell size control) yield qualitatively different results: clonal size fluctuations monotonically increase over time, reaching a nonzero value. These results characterize the interplay between cell size homeostasis at the single-cell level and clonal proliferation at the population level, explaining the broad fluctuations in clonal sizes seen in barcoded human cell lines.

Tissue-like multicellular development triggered by mechanical compression in archaea

The advent of clonal multicellularity is a critical evolutionary milestone, seen often in eukaryotes, rarely in bacteria, and only once in archaea. We show that uniaxial compression induces clonal multicellularity in haloarchaea, forming tissue-like structures. These archaeal tissues are mechanically and molecularly distinct from their unicellular lifestyle, mimicking several eukaryotic features. Archaeal tissues undergo a multinucleate stage followed by tubulin-independent cellularization, orchestrated by active membrane tension at a critical cell size. After cellularization, tissue junction elasticity becomes akin to that of animal tissues, giving rise to two cell types-peripheral (Per) and central scutoid (Scu) cells-with distinct actin and protein glycosylation polarity patterns. Our findings highlight the potential convergent evolution of a biophysical mechanism in the emergence of multicellular systems across domains of life.

From noisy cell size control to population growth: When variability can be beneficial

Single-cell experiments revealed substantial variability in generation times, growth rates, but also in birth and division sizes between genetically identical cells. Understanding how these fluctuations determine the fitness of the population, i.e., its growth rate, is necessary in any quantitative theory of evolution. Here, we develop a biologically relevant model which accounts for the stochasticity in single-cell growth rates, birth sizes, and division sizes. We derive expressions for the population growth rate and mean birth size in the population in terms of single-cell fluctuations. Allowing division sizes to fluctuate reveals how the mechanism of cell size control (timer, sizer, and adder) influences population growth. Surprisingly, we find that fluctuations in single-cell growth rates can be beneficial for population growth when slow-growing cells tend to divide at smaller sizes than fast-growing cells. Our framework is not limited to exponentially growing cells like Escherichia coli, and we derive similar expressions for cells with linear and bilinear growth laws, such as Mycobacterium tuberculosis and fission yeast Schizosaccharomyces pombe, respectively.

Single-cell imaging of the Mycobacterium tuberculosis cell cycle reveals linear and heterogenous growth

Difficulties in antibiotic treatment of Mycobacterium tuberculosis (Mtb) are partly thought to be due to heterogeneity in growth. Although the ability of bacterial pathogens to regulate growth is crucial to control homeostasis, virulence and drug responses, single-cell growth and cell cycle behaviours of Mtb are poorly characterized. Here we use time-lapse, single-cell imaging of Mtb coupled with mathematical modelling to observe asymmetric growth and heterogeneity in cell size, interdivision time and elongation speed. We find that, contrary to Mycobacterium smegmatis, Mtb initiates cell growth not only from the old pole but also from new poles or both poles. Whereas most organisms grow exponentially at the single-cell level, Mtb has a linear growth mode. Our data show that the growth behaviour of Mtb diverges from that of model bacteria, provide details into how Mtb grows and creates heterogeneity and suggest that growth regulation may also diverge from that in other bacteria.

The biosynthesis mechanism of bacterioruberin in halophilic archaea revealed by genome and transcriptome analysis

Halophilic archaea are promising microbial cell factories for bacterioruberin (BR) production. BR is a natural product with multi-bioactivities, allowing potential application in many fields. In the previous work, a haloarchaeon Halorubrum sp. HRM-150 with a high proportion of BR (about 85%) was isolated, but the low yield impeded its large-scale production. This work figured out BR synthesis characteristics and mechanisms, and proposed strategies for yield improvement. First, glucose (10 g/L) and tryptone (15 g/L) were tested to be better sources for BR production. Besides, the combination of glucose and starch achieved the diauxic growth, and the biomass and BR productivity increased by 85% and 54% than using glucose. Additionally, this work first proposed the BR synthesis pattern, which differs from that of other carotenoids. As a structural component of cell membranes, the BR synthesis is highly coupled with growth, which was most active in the logarithm phase. Meanwhile, the osmotic down shock at the logarithm phase could increase the BR productivity without sacrificing the biomass. Moreover, the de-novo pathway for BR synthesis with a key gene of lyeJ, and its competitive pathways (notably tetraether lipids and retinal) were revealed through genome, transcriptome, and osmotic down shock. Therefore, the BR yield is expected to be improved through mutant construction, such as the overexpression of key gene lyeJ and the knockout of competitive genes, which need to be further explored. The findings will contribute to a better understanding of the metabolism mechanism in haloarchaea and the development of haloarchaea as microbial cell factories.

IMPORTANCE

Recent studies have revealed that halophilic microorganism is a promising microbial factory for the next-generation industrialization. Among them, halophilic archaea are advantageous as microbial factories due to their low contamination risk and low freshwater consumption. The halophilic archaea usually accumulate long chain C50 carotenoids, which are barely found in other organisms. Bacterioruberin (BR), the major C50 carotenoid, has multi-bioactivities, allowing potential application in food, cosmetic, and biomedical industries. However, the low yield impedes its large-scale application. This work figured out the BR synthesis characteristics and mechanism, and proposed several strategies for BR yield improvement, encouraging halophilic archaea to function as microbial factories for BR production. Meanwhile, the archaea have special evolutionary status and unique characteristics in taxonomy, the revelation of BR biosynthesis mechanism is beneficial for a better understanding of archaea.

"Influence of plasmids, selection markers and auxotrophic mutations on Haloferax volcanii cell shape plasticity"

Haloferax volcanii and other Haloarchaea can be pleomorphic, adopting different shapes, which vary with growth stages. Several studies have shown that H. volcanii cell shape is sensitive to various external factors including growth media and physical environment. In addition, several studies have noticed that the presence of a recombinant plasmid in the cells is also a factor impacting H. volcanii cell shape, notably by favoring the development of rods in early stages of growth. Here we investigated the reasons for this phenomenon by first studying the impact of auxotrophic mutations on cell shape in strains that are commonly used as genetic backgrounds for selection during strain engineering (namely: H26, H53, H77, H98, and H729) and secondly, by studying the effect of the presence of different plasmids containing selection markers on the cell shape of these strains. Our study showed that most of these auxotrophic strains have variation in cell shape parameters including length, aspect ratio, area and circularity and that the plasmid presence is impacting these parameters too. Our results indicated that ΔhdrB strains and hdrB selection markers have the most influence on H. volcanii cell shape, in addition to the sole presence of a plasmid. Finally, we discuss limitations in studying cell shape in H. volcanii and make recommendations based on our results for improving reproducibility of such studies.

Evolutionary dynamics in non-Markovian models of microbial populations

In the past decade, great strides have been made to quantify the dynamics of single-cell growth and division in microbes. In order to make sense of the evolutionary history of these organisms, we must understand how features of single-cell growth and division influence evolutionary dynamics. This requires us to connect processes on the single-cell scale to population dynamics. Here, we consider a model of microbial growth in finite populations which explicitly incorporates the single-cell dynamics. We study the behavior of a mutant population in such a model and ask: can the evolutionary dynamics be coarse-grained so that the forces of natural selection and genetic drift can be expressed in terms of the long-term fitness? We show that it is in fact not possible, as there is no way to define a single fitness parameter (or reproductive rate) that defines the fate of an organism even in a constant environment. This is due to fluctuations in the population averaged division rate. As a result, various details of the single-cell dynamics affect the fate of a new mutant independently from how they affect the long-term growth rate of the mutant population. In particular, we show that in the case of neutral mutations, variability in generation times increases the rate of genetic drift, and in the case of beneficial mutations, variability decreases its fixation probability. Furthermore, we explain the source of the persistent division rate fluctuations and provide analytic solutions for the fixation probability as a multispecies generalization of the Euler-Lotka equation.

Coupling gene expression dynamics to cell size dynamics and cell cycle events: Exact and approximate solutions of the extended telegraph model

The standard model describing the fluctuations of mRNA numbers in single cells is the telegraph model which includes synthesis and degradation of mRNA, and switching of the gene between active and inactive states. While commonly used, this model does not describe how fluctuations are influenced by the cell cycle phase, cellular growth and division, and other crucial aspects of cellular biology. Here, we derive the analytical time-dependent solution of an extended telegraph model that explicitly considers the doubling of gene copy numbers upon DNA replication, dependence of the mRNA synthesis rate on cellular volume, gene dosage compensation, partitioning of molecules during cell division, cell-cycle duration variability, and cell-size control strategies. Based on the time-dependent solution, we obtain the analytical distributions of transcript numbers for lineage and population measurements in steady-state growth and also find a linear relation between the Fano factor of mRNA fluctuations and cell volume fluctuations. We show that generally the lineage and population distributions in steady-state growth cannot be accurately approximated by the steady-state solution of extrinsic noise models, i.e. a telegraph model with parameters drawn from probability distributions. This is because the mRNA lifetime is often not small enough compared to the cell cycle duration to erase the memory of division and replication. Accurate approximations are possible when this memory is weak, e.g. for genes with bursty expression and for which there is sufficient gene dosage compensation when replication occurs.

Robust replication initiation from coupled homeostatic mechanisms

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

Concentration fluctuations in growing and dividing cells: Insights into the emergence of concentration homeostasis

Intracellular reaction rates depend on concentrations and hence their levels are often regulated. However classical models of stochastic gene expression lack a cell size description and cannot be used to predict noise in concentrations. Here, we construct a model of gene product dynamics that includes a description of cell growth, cell division, size-dependent gene expression, gene dosage compensation, and size control mechanisms that can vary with the cell cycle phase. We obtain expressions for the approximate distributions and power spectra of concentration fluctuations which lead to insight into the emergence of concentration homeostasis. We find that (i) the conditions necessary to suppress cell division-induced concentration oscillations are difficult to achieve; (ii) mRNA concentration and number distributions can have different number of modes; (iii) two-layer size control strategies such as sizer-timer or adder-timer are ideal because they maintain constant mean concentrations whilst minimising concentration noise; (iv) accurate concentration homeostasis requires a fine tuning of dosage compensation, replication timing, and size-dependent gene expression; (v) deviations from perfect concentration homeostasis show up as deviations of the concentration distribution from a gamma distribution. Some of these predictions are confirmed using data for E. coli, fission yeast, and budding yeast.

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.

Spotlight on FtsZ-based cell division in Archaea

Compared with the extensive knowledge on cell division in model eukaryotes and bacteria, little is known about how archaea divide. Interestingly, both endosomal sorting complex required for transport (ESCRT)-based and FtsZ-based cell division systems are found in members of the Archaea. In the past couple of years, several studies have started to shed light on FtsZ-based cell division processes in members of the Euryarchaeota. In this review we highlight recent findings in this emerging field of research. We present current knowledge of the cell division machinery of halophiles which relies on two FtsZ proteins, and we compare it with that of methanobacteria, which relies on only one FtsZ. Finally, we discuss how these differences relate to the distinct cell envelopes of these two archaeal model systems.

Multiple timescales in bacterial growth homeostasis

In balanced exponential growth, bacteria maintain many properties statistically stable for a long time: cell size, cell cycle time, and more. As these are strongly coupled variables, it is not a-priori obvious which are directly regulated and which are stabilized through interactions. Here, we address this problem by separating timescales in bacterial single-cell dynamics. Disentangling homeostatic set points from fluctuations around them reveals that some variables, such as growth-rate, cell size and cycle time, are "sloppy" with highly volatile set points. Quantifying the relative contribution of environmental and internal sources, we find that sloppiness is primarily driven by the environment. Other variables such as fold-change define "stiff" combinations of coupled variables with robust set points. These results are manifested geometrically as a control manifold in the space of variables: set points span a wide range of values within the manifold, whereas out-of-manifold deviations are constrained. Our work offers a generalizable data-driven approach for identifying control variables in a multidimensional system.

Combining microscopy assays of bacteria-surface interactions to better evaluate antimicrobial polymer coatings

Validation of the antimicrobial performance of contact-killing polymer surfaces through experimental determination of bacterial adhesion or viability is essential for their targeted development and application. However, there is not yet a consensus on a single most appropriate evaluation method or procedure. Combining and benchmarking previously reported assays could reduce the significant variation and misinterpretation of efficacy data obtained from different methods. In this work, we systematically investigated the response of bacteria cells to anti-adhesive and antiseptic polymer coatings by combining (i) bulk solution-based, (ii) thin-film spacer-based and (iii) direct contact assays. In addition, we evaluated the studied assays using a five-point scoring framework that highlights key areas for improvement. Our data suggest that combined microscopy assays provide a more comprehensive representation of antimicrobial performance, thereby helping to identify effective types of antibacterial polymer coatings. Importance We present and evaluate a combination of methods for validating the efficacy of antimicrobial surfaces. Antimicrobial surfaces/coatings based on contact-killing components can be instrumental to functionalise a wide range of products. However, there is not yet a consensus on a single, most appropriate method to evaluate their performance. By combining three microscopy methods, we were able to discern contact killing effects at the single cell level that were not detectable by conventional bulk microbiological analyses. The developed approach is considered advantageous for the future targeted development of robust and sustainable antimicrobial surfaces.

Characterizing non-exponential growth and bimodal cell size distributions in fission yeast: An analytical approach

Unlike many single-celled organisms, the growth of fission yeast cells within a cell cycle is not exponential. It is rather characterized by three distinct phases (elongation, septation, and reshaping), each with a different growth rate. Experiments also showed that the distribution of cell size in a lineage can be bimodal, unlike the unimodal distributions measured for the bacterium Escherichia coli. Here we construct a detailed stochastic model of cell size dynamics in fission yeast. The theory leads to analytic expressions for the cell size and the birth size distributions, and explains the origin of bimodality seen in experiments. In particular, our theory shows that the left peak in the bimodal distribution is associated with cells in the elongation phase, while the right peak is due to cells in the septation and reshaping phases. We show that the size control strategy, the variability in the added size during a cell cycle, and the fraction of time spent in each of the three cell growth phases have a strong bearing on the shape of the cell size distribution. Furthermore, we infer all the parameters of our model by matching the theoretical cell size and birth size distributions to those from experimental single-cell time-course data for seven different growth conditions. Our method provides a much more accurate means of determining the size control strategy (timer, adder or sizer) than the standard method based on the slope of the best linear fit between the birth and division sizes. We also show that the variability in added size and the strength of size control in fission yeast depend weakly on the temperature but strongly on the culture medium. More importantly, we find that stronger size homeostasis and larger added size variability are required for fission yeast to adapt to unfavorable environmental conditions.

Advances in microscopy enable us to follow single cells over long timescales from which we can understand how their size varies with time and the nature of innate strategies developed to control cell size. These data show that in many cell types, growth is exponential and the distribution of cell size has one peak, namely there is a single characteristic cell size. However data for fission yeast show remarkable differences: growth is non-exponential and the distribution of cell sizes has two peaks, corresponding to different growth phases. Here we construct a detailed stochastic mathematical model of this organism; by solving the model analytically, we show that it is able to predict the two peaked distributions of cell size seen in data and provide an explanation for each peak in terms of various growth phases of the single-celled organism. Furthermore, by fitting the model to the data, we infer values for the rates of all microscopic processes in our model. This method is shown to provide a much more reliable inference than current methods and shed light on how the strategy used by fission yeast cells to control their size varies with external conditions.

Progress and Challenges in Archaeal Cell Biology

Over the past decades there has been a growing interest in the domain of archaea. In this chapter we highlight the recent advances that have been made in studying the cell biology of archaea. We particularly focus on methods for genetic manipulation and imaging of different archaeal species and discuss the technical limitations at the often-extreme growth conditions. Several ongoing developments will help us overcoming these limitations, thereby facilitating future studies in the existing field of archaeal cell biology.

An archaeal histone-like protein regulates gene expression in response to salt stress

Histones, ubiquitous in eukaryotes as DNA-packing proteins, find their evolutionary origins in archaea. Unlike the characterized histone proteins of a number of methanogenic and themophilic archaea, previous research indicated that HpyA, the sole histone encoded in the model halophile Halobacterium salinarum, is not involved in DNA packaging. Instead, it was found to have widespread but subtle effects on gene expression and to maintain wild type cell morphology. However, the precise function of halophilic histone-like proteins remain unclear. Here we use quantitative phenotyping, genetics, and functional genomics to investigate HpyA function. These experiments revealed that HpyA is important for growth and rod-shaped morphology in reduced salinity. HpyA preferentially binds DNA at discrete genomic sites under low salt to regulate expression of ion uptake, particularly iron. HpyA also globally but indirectly activates other ion uptake and nucleotide biosynthesis pathways in a salt-dependent manner. Taken together, these results demonstrate an alternative function for an archaeal histone-like protein as a transcriptional regulator, with its function tuned to the physiological stressors of the hypersaline environment.

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.

High-Temperature Live-Cell Imaging of Cytokinesis, Cell Motility, and Cell-Cell Interactions in the Thermoacidophilic Crenarchaeon Sulfolobus acidocaldarius

Significant technical challenges have limited the study of extremophile cell biology. Here we describe a system for imaging samples at 75°C using high numerical aperture, oil-immersion lenses. With this system we observed and quantified the dynamics of cell division in the model thermoacidophilic crenarchaeon Sulfolobus acidocaldarius with unprecedented resolution. In addition, we observed previously undescribed dynamic cell shape changes, cell motility, and cell-cell interactions, shedding significant new light on the high-temperature lifestyle of this organism.

Modeling the impact of single-cell stochasticity and size control on the population growth rate in asymmetrically dividing cells

Microbial populations show striking diversity in cell growth morphology and lifecycle; however, our understanding of how these factors influence the growth rate of cell populations remains limited. We use theory and simulations to predict the impact of asymmetric cell division, cell size regulation and single-cell stochasticity on the population growth rate. Our model predicts that coarse-grained noise in the single-cell growth rate λ decreases the population growth rate, as previously seen for symmetrically dividing cells. However, for a given noise in λ we find that dividing asymmetrically can enhance the population growth rate for cells with strong size control (between a “sizer” and an “adder”). To reconcile this finding with the abundance of symmetrically dividing organisms in nature, we propose that additional constraints on cell growth and division must be present which are not included in our model, and we explore the effects of selected extensions thereof. Further, we find that within our model, epigenetically inherited generation times may arise due to size control in asymmetrically dividing cells, providing a possible explanation for recent experimental observations in budding yeast. Taken together, our findings provide insight into the complex effects generated by non-canonical growth morphologies.

How rapidly a population of single-celled organisms can grow will strongly impact their long-term success. Prior work has shown that many factors impact this population growth rate, including the rate at which single cells grow, random variability between cells, and whether cells regulate their own size. Here we show that cell division asymmetry can also have a strong impact on the population growth rate. We use theory and computer simulations to study the growth rate of cells that divide asymmetrically, producing one smaller cell and one larger cell with each cell division event. We show that variability in how fast single cells grow will still decrease the population growth rate, when asymmetry is moderate or size control is weak, but that cells with strong size control can diminish this decrease by dividing more asymmetrically. We also demonstrate that cell cycle lengths can be positively correlated for closely related cells when they both divide asymmetrically and regulate their size. This counter-intuitive result contrasts with previous findings based on cell size regulation in symmetrically dividing cells that if cells grow for “too long” in one cell cycle, this will be corrected for by reduced growth during a shorter, subsequent cell cycle.

Tracking bacterial lineages in complex and dynamic environments with applications for growth control and persistence

As bacteria transition from exponential to stationary phase, they change substantially in size, morphology, growth and expression profiles. These responses also vary between individual cells, but it has proved difficult to track cell lineages along the growth curve to determine the progression of events or correlations between how individual cells enter and exit dormancy. Here, we developed a platform for tracking more than 10⁵ parallel cell lineages in dense and changing cultures, independently validating that the imaged cells closely track batch populations. Initial applications show that for both Escherichia coli and Bacillus subtilis, growth changes from an 'adder' mode in exponential phase to mixed 'adder-timers' entering stationary phase, and then a near-perfect 'sizer' upon exit-creating broadly distributed cell sizes in stationary phase but rapidly returning to narrowly distributed sizes upon exit. Furthermore, cells that undergo more divisions when entering stationary phase suffer reduced survival after long periods of dormancy but are the only cells observed that persist following antibiotic treatment.

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

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

Are bacteria claustrophobic? The problem of micrometric spatial confinement for the culturing of micro-organisms

Culturing cells confined in microscale geometries has been reported in many studies this last decade, in particular following the development of microfluidic-based applications and lab-on-a-chip devices. Such studies usually examine growth of Escherichia coli. In this article, we show that E. coli may be a poor model and that spatial confinement can severely prevent the growth of many micro-organisms. By studying different bacteria and confinement geometries, we determine that the growth inhibition observed for some bacteria results from fast dioxygen depletion, inherent to spatial confinement, and not to any depletion of nutriments. This article unravels the physical origin of confinement problems in cell culture, highlighting the importance of oxygen depletion, and paves the way for the effective culturing of bacteria in confined geometries by demonstrating enhanced cell growth in confined geometries in the proximity of air bubbles.

Bacterial Growth Control Mechanisms Inferred from Multivariate Statistical Analysis of Single-Cell Measurements

Analysis of single-cell measurements of bacterial growth and division often relied on testing preconceived models of cell size control mechanisms. Such an approach could limit the scope of data analysis and prevent us from uncovering new information. Here, we take an "agnostic" approach by applying regression methods to multiple simultaneously measured cellular variables, which allow us to infer dependencies among those variables from their apparent correlations. Besides previously observed correlations attributed to particular cell size control mechanisms, we identify dependencies that point to potentially new mechanisms. In particular, cells born smaller than their sisters tend to grow faster and make up for the size difference acquired during division. We also find that sister cells are correlated beyond what single-cell, size-control models predict. These trends are consistently found in repeat experiments, although the dependencies vary quantitatively. Such variation highlights the sensitivity of cell growth to environmental variations and the limitation of currently used experimental setups.

From single-cell variability to population growth

Single-cell experiments have revealed cell-to-cell variability in generation times and growth rates for genetically identical cells. Theoretical models relating the fluctuating generation times of single cells to the population growth rate are usually based on the assumption that the generation times of mother and daughter cells are uncorrelated. This assumption, however, is inconsistent with the exponential growth of cell volume in time observed for many cell types. Here we develop a more general and biologically relevant model in which cells grow exponentially and generation times are correlated in a manner which controls cell size. In addition to the fluctuating generation times, we also allow the single-cell growth rates to fluctuate and account for their correlations across the lineage tree. Surprisingly, we find that the population growth rate only depends on the distribution of single-cell growth rates and their correlations.

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

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

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

The Ribbon-Helix-Helix Domain Protein CdrS Regulates the Tubulin Homolog ftsZ2 To Control Cell Division in Archaea

Precise control of the cell cycle is central to the physiology of all cells. In prior work we demonstrated that archaeal cells maintain a constant size; however, the regulatory mechanisms underlying the cell cycle remain unexplored in this domain of life. Here, we use genetics, functional genomics, and quantitative imaging to identify and characterize the novel CdrSL gene regulatory network in a model species of archaea. We demonstrate the central role of these ribbon-helix-helix family transcription factors in the regulation of cell division through specific transcriptional control of the gene encoding FtsZ2, a putative tubulin homolog. Using time-lapse fluorescence microscopy in live cells cultivated in microfluidics devices, we further demonstrate that FtsZ2 is required for cell division but not elongation. The cdrS-ftsZ2 locus is highly conserved throughout the archaeal domain, and the central function of CdrS in regulating cell division is conserved across hypersaline adapted archaea. We propose that the CdrSL-FtsZ2 transcriptional network coordinates cell division timing with cell growth in archaea.IMPORTANCE Healthy cell growth and division are critical for individual organism survival and species long-term viability. However, it remains unknown how cells of the domain Archaea maintain a healthy cell cycle. Understanding the archaeal cell cycle is of paramount evolutionary importance given that an archaeal cell was the host of the endosymbiotic event that gave rise to eukaryotes. Here, we identify and characterize novel molecular players needed for regulating cell division in archaea. These molecules dictate the timing of cell septation but are dispensable for growth between divisions. Timing is accomplished through transcriptional control of the cell division ring. Our results shed light on mechanisms underlying the archaeal cell cycle, which has thus far remained elusive.

Large Deviation Principle Linking Lineage Statistics to Fitness in Microbial Populations

In exponentially proliferating populations of microbes, the population doubles at a rate less than the average doubling time of a single-cell due to variability at the single-cell level. It is known that the distribution of generation times obtained from a single lineage is, in general, insufficient to determine a population's growth rate. Is there an explicit relationship between observables obtained from a single lineage and the population growth rate? We show that a population's growth rate can be represented in terms of averages over isolated lineages. This lineage representation is related to a large deviation principle that is a generic feature of exponentially proliferating populations. Due to the large deviation structure of growing populations, the number of lineages needed to obtain an accurate estimate of the growth rate depends exponentially on the duration of the lineages, leading to a nonmonotonic convergence of the estimate, which we verify in both synthetic and experimental data sets.

Live Imaging of a Hyperthermophilic Archaeon Reveals Distinct Roles for Two ESCRT-III Homologs in Ensuring a Robust and Symmetric Division

Live-cell imaging has revolutionized our understanding of dynamic cellular processes in bacteria and eukaryotes. Although similar techniques have been applied to the study of halophilic archaea [1-5], our ability to explore the cell biology of thermophilic archaea has been limited by the technical challenges of imaging at high temperatures. Sulfolobus are the most intensively studied members of TACK archaea and have well-established molecular genetics [6-9]. Additionally, studies using Sulfolobus were among the first to reveal striking similarities between the cell biology of eukaryotes and archaea [10-15]. However, to date, it has not been possible to image Sulfolobus cells as they grow and divide. Here, we report the construction of the Sulfoscope, a heated chamber on an inverted fluorescent microscope that enables live-cell imaging of thermophiles. By using thermostable fluorescent probes together with this system, we were able to image Sulfolobus acidocaldarius cells live to reveal tight coupling between changes in DNA condensation, segregation, and cell division. Furthermore, by imaging deletion mutants, we observed functional differences between the two ESCRT-III proteins implicated in cytokinesis, CdvB1 and CdvB2. The deletion of cdvB1 compromised cell division, causing occasional division failures, whereas the ΔcdvB2 exhibited a profound loss of division symmetry, generating daughter cells that vary widely in size and eventually generating ghost cells. These data indicate that DNA separation and cytokinesis are coordinated in Sulfolobus, as is the case in eukaryotes, and that two contractile ESCRT-III polymers perform distinct roles to ensure that Sulfolobus cells undergo a robust and symmetrical division.

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.

Bacterial Growth: Cell-Cycle Dependent Growth-Rate Homeostasis

In the study of bacterial growth, the prevailing conclusion is that cells grow exponentially at a constant rate throughout the cell cycle. Using a new approach, Nordholt et al. reveal that bacterial growth is biphasic; immediately after division, the cell grows linearly, transitioning to exponential growth towards the end of the cell cycle.

A Mechanistic Model of the Regulation of Division Timing by the Circadian Clock in Cyanobacteria

The cyanobacterium Synechococcus elongatus possesses a circadian clock in the form of a group of proteins whose concentrations and phosphorylation states oscillate with daily periodicity under constant conditions. The circadian clock regulates the cell cycle such that the timing of the cell divisions is biased toward certain times during the circadian period, but the mechanism underlying this phenomenon remains unclear. Here, we propose a mechanism in which a protein limiting for division accumulates at a rate proportional to the cell volume growth and is modulated by the clock. This "modulated rate" model, in which the clock signal is integrated over time to affect division timing, differs fundamentally from the previously proposed "gating" concept, in which the clock is assumed to suppress divisions during a specific time window. We found that although both models can capture the single-cell statistics of division timing in S. elongatus, only the modulated rate model robustly places divisions away from darkness during changes in the environment. Moreover, within the framework of the modulated rate model, existing experiments on S. elongatus are consistent with the simple mechanism that division timing is regulated by the accumulation of a division limiting protein in a phase with genes whose activity peaks at dusk.

Lipid Anchoring of Archaeosortase Substrates and Midcell Growth in Haloarchaea

The archaeal cytoplasmic membrane provides an anchor for many surface proteins. Recently, a novel membrane anchoring mechanism involving a peptidase, archaeosortase A (ArtA), and C-terminal lipid attachment of surface proteins was identified in the model archaeon Haloferax volcanii ArtA is required for optimal cell growth and morphogenesis, and the S-layer glycoprotein (SLG), the sole component of the H. volcanii cell wall, is one of the targets for this anchoring mechanism. However, how exactly ArtA function and regulation control cell growth and morphogenesis is still elusive. Here, we report that archaeal homologs to the bacterial phosphatidylserine synthase (PssA) and phosphatidylserine decarboxylase (PssD) are involved in ArtA-dependent protein maturation. Haloferax volcanii strains lacking either HvPssA or HvPssD exhibited motility, growth, and morphological phenotypes similar to those of an ΔartA mutant. Moreover, we showed a loss of covalent lipid attachment to SLG in the ΔhvpssA mutant and that proteolytic cleavage of the ArtA substrate HVO_0405 was blocked in the ΔhvpssA and ΔhvpssD mutant strains. Strikingly, ArtA, HvPssA, and HvPssD green fluorescent protein (GFP) fusions colocalized to the midcell position of H. volcanii cells, strongly supporting that they are involved in the same pathway. Finally, we have shown that the SLG is also recruited to the midcell before being secreted and lipid anchored at the cell outer surface. Collectively, our data suggest that haloarchaea use the midcell as the main surface processing hot spot for cell elongation, division, and shape determination.IMPORTANCE The subcellular organization of biochemical processes in space and time is still one of the most mysterious topics in archaeal cell biology. Despite the fact that haloarchaea largely rely on covalent lipid anchoring to coat the cell envelope, little is known about how cells coordinate de novo synthesis and about the insertion of this proteinaceous layer throughout the cell cycle. Here, we report the identification of two novel contributors to ArtA-dependent lipid-mediated protein anchoring to the cell surface, HvPssA and HvPssD. ArtA, HvPssA, and HvPssD, as well as SLG, showed midcell localization during growth and cytokinesis, indicating that haloarchaeal cells confine phospholipid processing in order to promote midcell elongation. Our findings have important implications for the biogenesis of the cell surface.

Unification of cell division control strategies through continuous rate models

Recent experiments support the adder model for E. coli division control. This model posits that bacteria grow, on average, a fixed size before division. It also predicts decorrelation between the noise in the added size and the size at birth. Here we develop a theory based on stochastic hybrid systems which could explain the main division strategies, including not only the adder strategy but the whole range from sizer to timer. We use experiments to explore the division control of E. coli growing with glycerol as carbon source. In this medium, the division strategy is sizerlike, which means that the added size decreases with the size at birth. We found, as our theory predicts, that in a sizerlike strategy the mean added size decreases with the size at birth while the noise in added size increases. We discuss possible molecular mechanisms underlying this strategy and propose a general model that encompasses the different division strategies.

Efficient computation of stochastic cell-size transient dynamics

BACKGROUND

How small, fast-growing bacteria ensure tight cell-size distributions remains elusive. High-throughput measurement techniques have propelled efforts to build modeling tools that help to shed light on the relationships between cell size, growth and cycle progression. Most proposed models describe cell division as a discrete map between size at birth and size at division with stochastic fluctuations assumed. However, such models underestimate the role of cell size transient dynamics by excluding them.

RESULTS

We propose an efficient approach for estimation of cell size transient dynamics. Our technique approximates the transient size distribution and statistical moment dynamics of exponential growing cells following an adder strategy with arbitrary precision.

CONCLUSIONS

We approximate, up to arbitrary precision, the distribution of division times and size across time for the adder strategy in rod-shaped bacteria cells. Our approach is able to compute statistical moments like mean size and its variance from such distributions efficiently, showing close match with numerical simulations. Additionally, we observed that these distributions have periodic properties. Our approach further might shed light on the mechanisms behind gene product homeostasis.

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

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

The E. coli MinCDE system in the regulation of protein patterns and gradients

Molecular self-organziation, also regarded as pattern formation, is crucial for the correct distribution of cellular content. The processes leading to spatiotemporal patterns often involve a multitude of molecules interacting in complex networks, so that only very few cellular pattern-forming systems can be regarded as well understood. Due to its compositional simplicity, the Escherichia coli MinCDE system has, thus, become a paradigm for protein pattern formation. This biological reaction diffusion system spatiotemporally positions the division machinery in E. coli and is closely related to ParA-type ATPases involved in most aspects of spatiotemporal organization in bacteria. The ATPase MinD and the ATPase-activating protein MinE self-organize on the membrane as a reaction matrix. In vivo, these two proteins typically oscillate from pole-to-pole, while in vitro they can form a variety of distinct patterns. MinC is a passenger protein supposedly operating as a downstream cue of the system, coupling it to the division machinery. The MinCDE system has helped to extract not only the principles underlying intracellular patterns, but also how they are shaped by cellular boundaries. Moreover, it serves as a model to investigate how patterns can confer information through specific and non-specific interactions with other molecules. Here, we review how the three Min proteins self-organize to form patterns, their response to geometric boundaries, and how these patterns can in turn induce patterns of other molecules, focusing primarily on experimental approaches and developments.

Reassessment of the Basis of Cell Size Control Based on Analysis of Cell-to-Cell Variability

Fundamental mechanisms governing cell size control and homeostasis are still poorly understood. The relationship between sizes at division and birth in single cells is used as a metric to categorize the basis of size homeostasis. Cells dividing at a fixed size regardless of birth size (sizer) are expected to show a division-birth slope of zero, whereas cells dividing after growing for a fixed size increment (adder) have an expected slope of +1. These two theoretical values are, however, rarely experimentally observed. For example, rod-shaped fission yeast Schizosaccharomyces pombe cells, which divide at a fixed surface area, exhibit a division-birth slope for cell lengths of 0.25 ± 0.02, significantly different from the expected sizer value of zero. Here, we investigate possible reasons for this discrepancy by developing a mathematical model of sizer control including the relevant sources of variation. Our results support pure sizer control and show that deviation from zero slope is exaggerated by measurement of an inappropriate geometrical quantity (e.g., length instead of area), combined with cell-to-cell radius variability. The model predicts that mutants with greater errors in size sensing or septum positioning paradoxically appear to behave as better sizers. Furthermore, accounting for cell width variability, we show that pure sizer control can in some circumstances reproduce the apparent adder behavior observed in Escherichia coli. These findings demonstrate that analysis of geometric variation can lead to new insights into cell size control.

Microfluidic time-lapse analysis and reevaluation of the Bacillus subtilis cell cycle

Recent studies taking advantage of automated single-cell time-lapse analysis have reignited interest in the bacterial cell cycle. Several studies have highlighted alternative models, such as Sizer and Adder, which differ essentially in relation to whether cells can measure their present size or their amount of growth since birth. Most of the recent work has been done with Escherichia coli. We set out to study the well-characterized Gram-positive bacterium, Bacillus subtilis, at the single-cell level, using an accurate fluorescent marker for division as well as a marker for completion of chromosome replication. Our results are consistent with the Adder model in both fast and slow growth conditions tested, and with Sizer but only at the slower growth rate. We also find that cell size variation arises not only from the expected variation in size at division but also that division site offset from mid-cell contributes to a significant degree. Finally, although traditional cell cycle models imply a strong connection between the termination of a round of replication and subsequent division, we find that at the single-cell level these events are largely disconnected.

Division plane placement in pleomorphic archaea is dynamically coupled to cell shape

One mechanism for achieving accurate placement of the cell division machinery is via Turing patterns, where nonlinear molecular interactions spontaneously produce spatiotemporal concentration gradients. The resulting patterns are dictated by cell shape. For example, the Min system of Escherichia coli shows spatiotemporal oscillation between cell poles, leaving a mid-cell zone for division. The universality of pattern-forming mechanisms in divisome placement is currently unclear. We examined the location of the division plane in two pleomorphic archaea, Haloferax volcanii and Haloarcula japonica, and showed that it correlates with the predictions of Turing patterning. Time-lapse analysis of H. volcanii shows that divisome locations after successive rounds of division are dynamically determined by daughter cell shape. For H. volcanii, we show that the location of DNA does not influence division plane location, ruling out nucleoid occlusion. Triangular cells provide a stringent test for Turing patterning, where there is a bifurcation in division plane orientation. For the two archaea examined, most triangular cells divide as predicted by a Turing mechanism; however, in some cases multiple division planes are observed resulting in cells dividing into three viable progeny. Our results suggest that the division site placement is consistent with a Turing patterning system in these archaea.

Cell size sensing-a one-dimensional solution for a three-dimensional problem?

Individual cell types have characteristic sizes, suggesting that size sensing mechanisms may coordinate transcription, translation, and metabolism with cell growth rates. Two types of size-sensing mechanisms have been proposed: spatial sensing of the location or dimensions of a signal, subcellular structure or organelle; or titration-based sensing of the intracellular concentrations of key regulators. Here we propose that size sensing in animal cells combines both titration and spatial sensing elements in a dynamic mechanism whereby microtubule motor-dependent localization of RNA encoding importin β1 and mTOR, coupled with regulated local protein synthesis, enable cytoskeleton length sensing for cell growth regulation.

Cell Size Regulation Induces Sustained Oscillations in the Population Growth Rate

We study the effect of correlations in generation times on the dynamics of population growth of microorganisms. We show that any nonzero correlation that is due to cell-size regulation, no matter how small, induces long-term oscillations in the population growth rate. The population only reaches its steady state when we include the often-neglected variability in the growth rates of individual cells. We discover that the relaxation timescale of the population to its steady state is determined by the distribution of single-cell growth rates and is surprisingly independent of details of the division process such as the noise in the timing of division and the mechanism of cell-size regulation. We validate the predictions of our model using existing experimental data and propose an experimental method to measure single-cell growth variability by observing how long it takes for the population to reach its steady state or balanced growth.

A size-invariant bud-duration timer enables robustness in yeast cell size control

Cell populations across nearly all forms of life generally maintain a characteristic cell type-dependent size, but how size control is achieved has been a long-standing question. The G1/S boundary of the cell cycle serves as a major point of size control, and mechanisms operating here restrict passage of cells to Start if they are too small. In contrast, it is less clear how size is regulated post-Start, during S/G2/M. To gain further insight into post-Start size control, we prepared budding yeast that can be reversibly blocked from bud initiation. While blocked, cells continue to grow isotropically, increasing their volume by more than an order of magnitude over unperturbed cells. Upon release from their block, giant mothers reenter the cell cycle and their progeny rapidly return to the original unperturbed size. We found this behavior to be consistent with a size-invariant 'timer' specifying the duration of S/G2/M. These results indicate that yeast use at least two distinct mechanisms at different cell cycle phases to ensure size homeostasis.

Engineering Bacterial Shape Using Soft Matter Microchambers

This article describes the design and fabrication of microchambers that are used for the study of bacterial cells. The design allows for the confinement and precise manipulation of bacterial cell shape. The application of fluorescent dyes and fluorescent proteins enables the precise analysis of the localization of biomolecules within confined bacterial cell. This article also outlines three methods to engineer cell shape from a filamentous cell type and from spheroplasts without a cell wall using soft lithography-based technologies. © 2018 by John Wiley & Sons, Inc.

Archaeal cell biology: diverse functions of tubulin-like cytoskeletal proteins at the cell envelope

The tubulin superfamily of cytoskeletal proteins is widespread in all three domains of life — Archaea, Bacteria and Eukarya. Tubulins build the microtubules of the eukaryotic cytoskeleton, whereas members of the homologous FtsZ family construct the division ring in prokaryotes and some eukaryotic organelles. Their functions are relatively poorly understood in archaea, yet these microbes contain a remarkable diversity of tubulin superfamily proteins, including FtsZ for division, a newly described major family called CetZ that is involved in archaeal cell shape control, and several other divergent families of unclear function that are implicated in a variety of cell envelope-remodelling contexts. Archaeal model organisms, particularly halophilic archaea such as Haloferax volcanii, have sufficiently developed genetic tools and we show why their large, flattened cells that are capable of controlled differentiation are also well suited to cell biological investigations by live-cell high-resolution light and electron microscopy. As most archaea only have a glycoprotein lattice S-layer, rather than a peptidoglycan cell wall like bacteria, the activity of the tubulin-like cytoskeletal proteins at the cell envelope is expected to vary significantly, and may involve direct membrane remodelling or directed synthesis or insertion of the S-layer protein subunits. Further studies of archaeal cell biology will provide fresh insight into the evolution of cells and the principles in common to their fundamental activities across the full spectrum of cellular life.

Homeostasis of protein and mRNA concentrations in growing cells

Many experiments show that the numbers of mRNA and protein are proportional to the cell volume in growing cells. However, models of stochastic gene expression often assume constant transcription rate per gene and constant translation rate per mRNA, which are incompatible with these experiments. Here, we construct a minimal gene expression model to fill this gap. Assuming ribosomes and RNA polymerases are limiting in gene expression, we show that the numbers of proteins and mRNAs both grow exponentially during the cell cycle and that the concentrations of all mRNAs and proteins achieve cellular homeostasis; the competition between genes for the RNA polymerases makes the transcription rate independent of the genome number. Furthermore, by extending the model to situations in which DNA (mRNA) can be saturated by RNA polymerases (ribosomes) and becomes limiting, we predict a transition from exponential to linear growth of cell volume as the protein-to-DNA ratio increases.

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.

Archaeal imaging: leading the hunt for new discoveries

Since the identification of the archaeal domain in the mid-1970s, we have collected a great deal of metagenomic, biochemical, and structural information from archaeal species. However, there is still little known about how archaeal cells organize their internal cellular components in space and time. In contrast, live-cell imaging has allowed bacterial and eukaryotic cell biologists to learn a lot about biological processes by observing the motions of cells, the dynamics of their internal organelles, and even the motions of single molecules. The explosion of knowledge gained via live-cell imaging in prokaryotes and eukaryotes has motivated an ever-improving set of imaging technologies that could allow analogous explorations into archaeal biology. Furthermore, previous studies of essential biological processes in prokaryotic and eukaryotic organisms give methodological roadmaps for the investigation of similar processes in archaea. In this perspective, we highlight a few fundamental cellular processes in archaea, reviewing our current state of understanding about each, and compare how imaging approaches helped to advance the study of similar processes in bacteria and eukaryotes.

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.