Is cell size a spandrel?

Wine Fermentation as a Model System for Microbial Ecology and Evolution

In vitro microbial communities have proven to be invaluable model systems for studying ecological and evolutionary processes experimentally. However, it remains unclear whether quantitative insights obtained from these laboratory systems can be applied to complex communities assembling and evolving in their natural ecological context. To bridge the gap between the lab and the 'real-world', there is a need for laboratory model systems that better approximate natural and semi-natural ecosystems. Wine fermentation presents an ideal system for this purpose, balancing experimental tractability with rich ecological and evolutionary dynamics. In this perspective piece we outline the key features that make wine fermentation a fruitful model system for ecologists and evolutionary biologists. We highlight the diversity of environmentally mediated interactions that shape community dynamics during fermentation, the complex evolutionary history of wine microbial populations, and the opportunity to study the impact of complex ecologies on evolutionary dynamics. By integrating knowledge from both wine research and microbial ecology and evolution we aim to enhance understanding and foster collaboration between these fields.

Evolutionary Advantage of Cell Size Control

We analyze the advantage of cell size control strategies in growing populations under mortality constraints and show that growth-dependent mortality can select for accurate size control. We determine how mortality, noise, and nongenetic heritability of cell size impact long-term population growth. We derive an analytical expression for the optimal cell size. We demonstrate that size heritability enables selection to act on the distribution of cell sizes in a population to avoid viability thresholds and adapt to size- and growth-dependent mortality landscapes.

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.

Hunting the Cell Cycle Snark

In this very personal hunt for the meaning of the bacterial cell cycle, the snark, I briefly revisit and update some of the mechanisms we and many others have proposed to regulate the bacterial cell cycle. These mechanisms, which include the dynamics of calcium, membranes, hyperstructures, and networks, are based on physical and physico-chemical concepts such as ion condensation, phase transition, crowding, liquid crystal immiscibility, collective vibrational modes, reptation, and water availability. I draw on ideas from subjects such as the 'prebiotic ecology' and phenotypic diversity to help with the hunt. Given the fundamental nature of the snark, I would expect that its capture would make sense of other parts of biology. The route, therefore, followed by the hunt has involved trying to answer questions like "why do cells replicate their DNA?", "why is DNA replication semi-conservative?", "why is DNA a double helix?", "why do cells divide?", "is cell division a spandrel?", and "how are catabolism and anabolism balanced?". Here, I propose some relatively unexplored, experimental approaches to testing snark-related hypotheses and, finally, I propose some possibly original ideas about DNA packing, about phase separations, and about computing with populations of virtual bacteria.

Open Questions about the Roles of DnaA, Related Proteins, and Hyperstructure Dynamics in the Cell Cycle

The DnaA protein has long been considered to play the key role in the initiation of chromosome replication in modern bacteria. Many questions about this role, however, remain unanswered. Here, we raise these questions within a framework based on the dynamics of hyperstructures, alias large assemblies of molecules and macromolecules that perform a function. In these dynamics, hyperstructures can (1) emit and receive signals or (2) fuse and separate from one another. We ask whether the DnaA-based initiation hyperstructure acts as a logic gate receiving information from the membrane, the chromosome, and metabolism to trigger replication; we try to phrase some of these questions in terms of DNA supercoiling, strand opening, glycolytic enzymes, SeqA, ribonucleotide reductase, the macromolecular synthesis operon, post-translational modifications, and metabolic pools. Finally, we ask whether, underpinning the regulation of the cell cycle, there is a physico-chemical clock inherited from the first protocells, and whether this clock emits a single signal that triggers both chromosome replication and cell division.

Evolution of a minimal cell

Possessing only essential genes, a minimal cell can reveal mechanisms and processes that are critical for the persistence and stability of life1,2. Here we report on how an engineered minimal cell3,4 contends with the forces of evolution compared with the Mycoplasma mycoides non-minimal cell from which it was synthetically derived. Mutation rates were the highest among all reported bacteria, but were not affected by genome minimization. Genome streamlining was costly, leading to a decrease in fitness of greater than 50%, but this deficit was regained during 2,000 generations of evolution. Despite selection acting on distinct genetic targets, increases in the maximum growth rate of the synthetic cells were comparable. Moreover, when performance was assessed by relative fitness, the minimal cell evolved 39% faster than the non-minimal cell. The only apparent constraint involved the evolution of cell size. The size of the non-minimal cell increased by 80%, whereas the minimal cell remained the same. This pattern reflected epistatic effects of mutations in ftsZ, which encodes a tubulin-homologue protein that regulates cell division and morphology5,6. Our findings demonstrate that natural selection can rapidly increase the fitness of one of the simplest autonomously growing organisms. Understanding how species with small genomes overcome evolutionary challenges provides critical insights into the persistence of host-associated endosymbionts, the stability of streamlined chassis for biotechnology and the targeted refinement of synthetically engineered cells2,7-9.

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

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

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.

Fundamental limits on the rate of bacterial growth and their influence on proteomic composition

Despite abundant measurements of bacterial growth rate, cell size, and protein content, we lack a rigorous understanding of what sets the scale of these quantities and when protein abundances should (or should not) depend on growth rate. Here, we estimate the basic requirements and physical constraints on steady-state growth by considering key processes in cellular physiology across a collection of Escherichia coli proteomic data covering ≈4,000 proteins and 36 growth rates. Our analysis suggests that cells are predominantly tuned for the task of cell doubling across a continuum of growth rates; specific processes do not limit growth rate or dictate cell size. We present a model of proteomic regulation as a function of nutrient supply that reconciles observed interdependences between protein synthesis, cell size, and growth rate and propose that a theoretical inability to parallelize ribosomal synthesis places a firm limit on the achievable growth rate. A record of this paper's transparent peer review process is included in the supplemental information.

Changes in Cell Size and Shape during 50,000 Generations of Experimental Evolution with Escherichia coli

Bacteria adopt a wide variety of sizes and shapes, with many species exhibiting stereotypical morphologies. How morphology changes, and over what timescales, is less clear. Previous work examining cell morphology in an experiment with Escherichia coli showed that populations evolved larger cells and, in some cases, cells that were less rod-like. That experiment has now run for over two more decades. Meanwhile, genome sequence data are available for these populations, and new computational methods enable high-throughput microscopic analyses. In this study, we measured stationary-phase cell volumes for the ancestor and 12 populations at 2,000, 10,000, and 50,000 generations, including measurements during exponential growth at the last time point. We measured the distribution of cell volumes for each sample using a Coulter counter and microscopy, the latter of which also provided data on cell shape. Our data confirm the trend toward larger cells while also revealing substantial variation in size and shape across replicate populations. Most populations first evolved wider cells but later reverted to the ancestral length-to-width ratio. All but one population evolved mutations in rod shape maintenance genes. We also observed many ghost-like cells in the only population that evolved the novel ability to grow on citrate, supporting the hypothesis that this lineage struggles with maintaining balanced growth. Lastly, we show that cell size and fitness remain correlated across 50,000 generations. Our results suggest that larger cells are beneficial in the experimental environment, while the reversion toward ancestral length-to-width ratios suggests partial compensation for the less favorable surface area-to-volume ratios of the evolved cells.IMPORTANCE Bacteria exhibit great morphological diversity, yet we have only a limited understanding of how their cell sizes and shapes evolve and of how these features affect organismal fitness. This knowledge gap reflects, in part, the paucity of the fossil record for bacteria. In this study, we revived and analyzed samples extending over 50,000 generations from 12 populations of experimentally evolving Escherichia coli to investigate the relation between cell size, shape, and fitness. Using this "frozen fossil record," we show that all 12 populations evolved larger cells concomitant with increased fitness, with substantial heterogeneity in cell size and shape across the replicate lines. Our work demonstrates that cell morphology can readily evolve and diversify, even among populations living in identical environments.

Bacterial cell proliferation: from molecules to cells

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

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.

Evolution of Microbial Growth Traits Under Serial Dilution

Selection of mutants in a microbial population depends on multiple cellular traits. In serial-dilution evolution experiments, three key traits are the lag time when transitioning from starvation to growth, the exponential growth rate, and the yield (number of cells per unit resource). Here, we investigate how these traits evolve in laboratory evolution experiments using a minimal model of population dynamics, where the only interaction between cells is competition for a single limiting resource. We find that the fixation probability of a beneficial mutation depends on a linear combination of its growth rate and lag time relative to its immediate ancestor, even under clonal interference. The relative selective pressure on growth rate and lag time is set by the dilution factor; a larger dilution factor favors the adaptation of growth rate over the adaptation of lag time. The model shows that yield, however, is under no direct selection. We also show how the adaptation speeds of growth and lag depend on experimental parameters and the underlying supply of mutations. Finally, we investigate the evolution of covariation between these traits across populations, which reveals that the population growth rate and lag time can evolve a nonzero correlation even if mutations have uncorrelated effects on the two traits. Altogether these results provide useful guidance to future experiments on microbial evolution.

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

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

Mechanistic Origin of Cell-Size Control and Homeostasis in Bacteria

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

Cell size homeostasis: Metabolic control of growth and cell division

Joint regulation of growth rate and cell division rate determines cell size. Here we discuss how animal cells achieve cell size homeostasis potentially involving multiple signaling pathways converging at metabolic regulation of growth rate and cell cycle progression. While several models have been developed to explain cell size control, comparison of the two predominant models shows that size homeostasis is dependent on the ability to adjust cellular growth rate based on cell size. Consequently, maintenance of size homeostasis requires that larger cells can grow slower than small cells in relative terms. We review recent experimental evidence showing that such size adjustment occurs primarily at or immediately before the G1/S transition of the cell cycle. We further propose that bidirectional feedback between growth rate and size results in cell size sensing and discuss potential mechanisms how this may be accomplished.

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

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

A Markovian Approach towards Bacterial Size Control and Homeostasis in Anomalous Growth Processes

Regardless of the progress achieved during recent years, the mechanisms coupling growth and division to attain cell size homeostasis in bacterial populations are still not well understood. In particular, there is a gap of knowledge about the mechanisms controlling anomalous growth events that are ubiquitous even in wild-type phenotypes. Thus, when cells exceed the doubling size the divisome dynamics sets a characteristic length scale that suggests a sizer property. Yet, it has been recently shown that the size at birth and the size increment still satisfy an adder-like correlation. Herein we propose a Markov chain model, that we complement with computational and experimental approaches, to clarify this issue. In this context, we show that classifying cells as a function of the characteristic size set by the divisome dynamics provides a compelling framework to understand size convergence, growth, and division at the large length scale, including the adaptation to, and rescue from, filamentation processes. Our results reveal the independence of size homeostasis on the division pattern of long cells and help to reconcile sizer concepts at the single cell level with an adder-like behavior at a population level.

Decoupling of Nuclear Division Cycles and Cell Size during the Coenocytic Growth of the Ichthyosporean Sphaeroforma arctica

Coordination of the cell division cycle with the growth of the cell is critical to achieve cell size homeostasis [1]. Mechanisms coupling the cell division cycle with cell growth have been described across diverse eukaryotic taxa [2, 3, 4], but little is known about how these processes are coordinated in organisms that undergo more complex life cycles, such as coenocytic growth. Coenocytes (multinucleate cells formed by sequential nuclear divisions without cytokinesis) are commonly found across the eukaryotic kingdom, including in animal and plant tissues and several lineages of unicellular eukaryotes [5]. Among the organisms that form coenocytes are ichthyosporeans, a lineage of unicellular holozoans that are of significant interest due to their phylogenetic placement as one of the closest relatives of animals [6]. Here, we characterize the coenocytic cell division cycle in the ichthyosporean Sphaeroforma arctica. We observe that, in laboratory conditions, S. arctica cells undergo a uniform and easily synchronizable coenocytic cell cycle, reaching up to 128 nuclei per cell before cellularization and release of daughter cells. Cycles of nuclear division occur synchronously within the coenocyte and in regular time intervals (11–12 hr). We find that the growth of cell volume is dependent on concentration of nutrients in the media; in contrast, the rate of nuclear division cycles is constant over a range of nutrient concentrations. Together, the results suggest that nuclear division cycles in the coenocytic growth of S. arctica are driven by a timer, which ensures periodic and synchronous nuclear cycles independent of the cell size and growth.

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Synchronous coenocytic growth in S. arctica, a close unicellular relative of animals

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Cells grow from 1 to 64–128 nuclei before cellularization and release

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Nuclear division cycles are periodic and driven by a time-keeping mechanism

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The nuclear division timer is independent of cell volume and growth rate

Constriction Rate Modulation Can Drive Cell Size Control and Homeostasis in C. crescentus

Rod-shaped bacteria typically grow first via sporadic and dispersed elongation along their lateral walls and then via a combination of zonal elongation and constriction at the division site to form the poles of daughter cells. Although constriction comprises up to half of the cell cycle, its impact on cell size control and homeostasis has rarely been considered. To reveal the roles of cell elongation and constriction in bacterial size regulation during cell division, we captured the shape dynamics of Caulobacter crescentus with time-lapse structured illumination microscopy and used molecular markers as cell-cycle landmarks. We perturbed the constriction rate using a hyperconstriction mutant or fosfomycin ([(2R,3S)-3-methyloxiran-2-yl]phosphonic acid) inhibition. We report that the constriction rate contributes to both size control and homeostasis, by determining elongation during constriction and by compensating for variation in pre-constriction elongation on a single-cell basis.

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Perturbing constriction rate changes cell length

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Faster constriction rate results in blunter cell poles

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Early constriction rate modulation balances elongation before and during constriction

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We propose that constriction rate is set by the accumulation of precursors during elongation

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.

Bacterial Cell Size: Multifactorial and Multifaceted

How cells establish, maintain, and modulate size has always been an area of great interest and fascination. Until recently, technical limitations curtailed our ability to understand the molecular basis of bacterial cell size control. In the past decade, advances in microfluidics, imaging, and high-throughput single-cell analysis, however, have led to a flurry of work revealing size to be a highly complex trait involving the integration of three core aspects of bacterial physiology: metabolism, growth, and cell cycle progression.

Heterogeneity and Robustness in Plant Morphogenesis: From Cells to Organs

Development is remarkably reproducible, producing organs with the same size, shape, and function repeatedly from individual to individual. For example, every flower on the Antirrhinum stalk has the same snapping dragon mouth. This reproducibility has allowed taxonomists to classify plants and animals according to their morphology. Yet these reproducible organs are composed of highly variable cells. For example, neighboring cells grow at different rates in Arabidopsis leaves, sepals, and shoot apical meristems. This cellular variability occurs in normal, wild-type organisms, indicating that cellular heterogeneity (or diversity in a characteristic such as growth rate) is either actively maintained or, at a minimum, not entirely suppressed. In fact, cellular heterogeneity can contribute to producing invariant organs. Here, we focus on how plant organs are reproducibly created during development from these highly variable cells.

Different Amounts of DNA in Newborn Cells of Escherichia coli Preclude a Role for the Chromosome in Size Control According to the "Adder" Model

According to the recently-revived adder model for cell size control, newborn cells of Escherichia coli will grow and divide after having added a constant size or length, ΔL, irrespective of their size at birth. Assuming exponential elongation, this implies that large newborns will divide earlier than small ones. The molecular basis for the constant size increment is still unknown. As DNA replication and cell growth are coordinated, the constant ΔL could be based on duplication of an equal amount of DNA, ΔG, present in newborn cells. To test this idea, we measured amounts of DNA and lengths of nucleoids in DAPI-stained cells growing in batch culture at slow and fast rates. Deeply-constricted cells were divided in two subpopulations of longer and shorter lengths than average; these were considered to represent large and small prospective daughter cells, respectively. While at slow growth, large and small prospective daughter cells contained similar amounts of DNA, fast growing cells with multiforked replicating chromosomes, showed a significantly higher amount of DNA (20%) in the larger cells. This observation precludes the hypothesis that ΔL is based on the synthesis of a constant ΔG. Growth curves were constructed for siblings generated by asymmetric division and growing according to the adder model. Under the assumption that all cells at the same growth rate exhibit the same time between initiation of DNA replication and cell division (i.e., constant C+D-period), the constructions predict that initiation occurs at different sizes (Li) and that, at fast growth, large newborn cells transiently contain more DNA than small newborns, in accordance with the observations. Because the state of segregation, measured as the distance between separated nucleoids, was found to be more advanced in larger deeply-constricted cells, we propose that in larger newborns nucleoid separation occurs faster and at a shorter length, allowing them to divide earlier. We propose a composite model in which both differential initiation and segregation leads to an adder-like behavior of large and small newborn cells.

Cell size control and gene expression homeostasis in single-cells

Growth of a cell and its subsequent division into daughters is a fundamental aspect of all cellular living systems. During these processes, how do individual cells correct size aberrations so that they do not grow abnormally large or small? How do cells ensure that the concentration of essential gene products are maintained at desired levels, in spite of dynamic/stochastic changes in cell size during growth and division? Both these questions have fascinated researchers for over a century. We review how advances in singe-cell technologies and measurements are providing unique insights into these questions across organisms from prokaryotes to human cells. More specifically, diverse strategies based on timing of cell-cycle events, regulating growth, and number of daughters are employed to maintain cell size homeostasis. Interestingly, size homeostasis often results in size optimality - proliferation of individual cells in a population is maximized at an optimal cell size. We further discuss how size-dependent expression or gene-replication timing can buffer concentration of a gene product from cell-to-cell size variations within a population. Finally, we speculate on an intriguing hypothesis that specific size control strategies may have evolved as a consequence of gene-product concentration homeostasis.

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

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

Learning from Noise: How Observing Stochasticity May Aid Microbiology

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

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

In nature, microorganisms exhibit different volumes spanning six orders of magnitude ¹ . Despite their capability to create different sizes, a clonal population in a given environment maintains a uniform size across individual cells. Recent studies in eukaryotic and bacterial organisms showed that this homogeneity in cell size can be accomplished by growing a constant size between two cell cycle events (that is, the adder model ^2-6 ). Demonstration of the adder model led to the hypothesis that this phenomenon is a consequence of convergent evolution. Given that archaeal cells share characteristics with both bacteria and eukaryotes, we investigated whether and how archaeal cells exhibit control over cell size. To this end, we developed a soft-lithography method of growing the archaeal cells to enable quantitative time-lapse imaging and single-cell analysis, which would be useful for other microorganisms. Using this method, we demonstrated that Halobacterium salinarum, a hypersaline-adapted archaeal organism, grows exponentially at the single-cell level and maintains a narrow-size distribution by adding a constant length between cell division events. Interestingly, the archaeal cells exhibited greater variability in cell division placement and exponential growth rate across individual cells in a population relative to those observed in Escherichia coli ^6-9 . Here, we present a theoretical framework that explains how these larger fluctuations in archaeal cell cycle events contribute to cell size variability and control.

Does the eclipse limit bacterial nucleoid complexity and cell width?

Cell size of bacteria M is related to 3 temporal parameters: chromosome replication time C, period from replication-termination to subsequent division D, and doubling time τ. Steady-state, bacillary cells grow exponentially by extending length L only, but their constant width W is larger at shorter τ's or longer C's, in proportion to the number of chromosome replication positions n (= C/τ), at least in Escherichia coli and Salmonella typhimurium. Extending C by thymine limitation of fast-growing thyA mutants result in continuous increase of M, associated with rising W, up to a limit before branching. A set of such puzzling observations is qualitatively consistent with the view that the actual cell mass (or volume) at the time of replication-initiation Mi (or Vi), usually relatively constant in growth at varying τ's, rises with time under thymine limitation of fast-growing, thymine-requiring E. coli strains. The hypothesis will be tested that presumes existence of a minimal distance l_min between successive moving replisomes, translated into the time needed for a replisome to reach l_min before a new replication-initiation at oriC is allowed, termed Eclipse E. Preliminary analysis of currently available data is inconsistent with a constant E under all conditions, hence other explanations and ways to test them are proposed in an attempt to elucidate these and other results. The complex hypothesis takes into account much of what is currently known about Bacterial Physiology: the relationships between cell dimensions, growth and cycle parameters, particularly nucleoid structure, replication and position, and the mode of peptidoglycan biosynthesis. Further experiments are mentioned that are necessary to test the discussed ideas and hypotheses.

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

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

A Parallel Adder Coordinates Mycobacterial Cell-Cycle Progression and Cell-Size Homeostasis in the Context of Asymmetric Growth and Organization

In model bacteria, such as E. coli and B. subtilis, regulation of cell-cycle progression and cellular organization achieves consistency in cell size, replication dynamics, and chromosome positioning [1-3]. Mycobacteria elongate and divide asymmetrically, giving rise to significant variation in cell size and elongation rate among closely related cells [4, 5]. Given the physical asymmetry of mycobacteria, the models that describe coordination of cellular organization and cell-cycle progression in model bacteria are not directly translatable [1, 2, 6-8]. Here, we used time-lapse microscopy and fluorescent reporters of DNA replication and chromosome positioning to examine the coordination of growth, division, and chromosome dynamics at a single-cell level in Mycobacterium smegmatis (M. smegmatis) and Mycobacterium bovis Bacillus Calmette-Guérin (BCG). By analyzing chromosome and replisome localization, we demonstrated that chromosome positioning is asymmetric and proportional to cell size. Furthermore, we found that cellular asymmetry is maintained throughout the cell cycle and is not established at division. Using measurements and stochastic modeling of mycobacterial cell size and cell-cycle timing in both slow and fast growth conditions, we found that well-studied models of cell-size control are insufficient to explain the mycobacterial cell cycle. Instead, we showed that mycobacterial cell-cycle progression is regulated by an unprecedented mechanism involving parallel adders (i.e., constant growth increments) that start at replication initiation. Together, these adders enable mycobacterial populations to regulate cell size, growth, and heterogeneity in the face of varying environments.

The Effects of Stochasticity at the Single-Cell Level and Cell Size Control on the Population Growth

Establishing a quantitative connection between the population growth rate and the generation times of single cells is a prerequisite for understanding evolutionary dynamics of microbes. However, existing theories fail to account for the experimentally observed correlations between mother-daughter generation times that are unavoidable when cell size is controlled for, which is essentially always the case. Here, we study population-level growth in the presence of cell size control and corroborate our theory using experimental measurements of single-cell growth rates. We derive a closed formula for the population growth rate and demonstrate that it only depends on the single-cell growth rate variability, not other sources of stochasticity. Our work provides an evolutionary rationale for the narrow growth rate distributions often observed in nature: when single-cell growth rates are less variable but have a fixed mean, the population will exhibit an enhanced population growth rate as long as the correlations between the mother and daughter cells' growth rates are not too strong.

Analysis of Noise Mechanisms in Cell-Size Control

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

Cell size control - a mechanism for maintaining fitness and function

The maintenance of cell size homeostasis has been studied for years in different cellular systems. With the focus on 'what regulates cell size', the question 'why cell size needs to be maintained' has been largely overlooked. Recent evidence indicates that animal cells exhibit nonlinear cell size dependent growth rates and mitochondrial metabolism, which are maximal in intermediate sized cells within each cell population. Increases in intracellular distances and changes in the relative cell surface area impose biophysical limitations on cells, which can explain why growth and metabolic rates are maximal in a specific cell size range. Consistently, aberrant increases in cell size, for example through polyploidy, are typically disadvantageous to cellular metabolism, fitness and functionality. Accordingly, cellular hypertrophy can potentially predispose to or worsen metabolic diseases. We propose that cell size control may have emerged as a guardian of cellular fitness and metabolic activity.