Single-Cell Analysis of Growth and Cell Division of the Anaerobe Desulfovibrio vulgaris Hildenborough

Impact of Graphene Layers on Genetic Expression and Regulation within Sulfate-Reducing Biofilms

Bacterial adhesion and biofilm maturation is significantly influenced by surface properties, encompassing both bare surfaces and single or multi-layered coatings. Hence, there is an utmost interest in exploring the intricacies of gene regulation in sulfate-reducing bacteria (SRB) on copper and graphene-coated copper surfaces. In this study, Oleidesulfovibrio alaskensis G20 was used as the model SRB to elucidate the pathways that govern pivotal roles during biofilm formation on the graphene layers. Employing a potent reporter green fluorescent protein (GFP) tagged to O. alaskensis G20, the spatial structure of O. alaskensis G20 biofilm on copper foil (CuF), single-layer graphene-coated copper (Cu-GrI), and double-layer graphene-coated copper (Cu-GrII) surfaces was investigated. Biofilm formation on CuF, Cu-GrI, and Cu-GrII surfaces was quantified using CLSM z-stack images within COMSTAT v2 software. The results revealed that CuF, Cu-GrI, and Cu-GrII did not affect the formation of the GFP-tagged O. alaskensis G20 biofilm architecture. qPCR expression showed insignificant fold changes for outer membrane components regulating the quorum-sensing system, and global regulatory proteins between the uncoated and coated surfaces. Notably, a significant expression was observed within the sulfate reduction pathway confined to dissimilatory sulfite reductases on the Cu-GrII surface compared to the CuF and Cu-GrI surfaces.

Bioinformatic Assessment of Factors Affecting the Correlation between Protein Abundance and Elongation Efficiency in Prokaryotes

Protein abundance is crucial for the majority of genetically regulated cell functions to act properly in prokaryotic organisms. Therefore, developing bioinformatic methods for assessing the efficiency of different stages of gene expression is of great importance for predicting the actual protein abundance. One of these steps is the evaluation of translation elongation efficiency based on mRNA sequence features, such as codon usage bias and mRNA secondary structure properties. In this study, we have evaluated correlation coefficients between experimentally measured protein abundance and predicted elongation efficiency characteristics for 26 prokaryotes, including non-model organisms, belonging to diverse taxonomic groups The algorithm for assessing elongation efficiency takes into account not only codon bias, but also number and energy of secondary structures in mRNA if those demonstrate an impact on predicted elongation efficiency of the ribosomal protein genes. The results show that, for a number of organisms, secondary structures are a better predictor of protein abundance than codon usage bias. The bioinformatic analysis has revealed several factors associated with the value of the correlation coefficient. The first factor is the elongation efficiency optimization type-the organisms whose genomes are optimized for codon usage only have significantly higher correlation coefficients. The second factor is taxonomical identity-bacteria that belong to the class Bacilli tend to have higher correlation coefficients among the analyzed set. The third is growth rate, which is shown to be higher for the organisms with higher correlation coefficients between protein abundance and predicted translation elongation efficiency. The obtained results can be useful for further improvement of methods for protein abundance prediction.

Inhibition of Sulfate Reduction and Cell Division by Desulfovibrio desulfuricans Coated in Palladium Metal

The growth of sulfate-reducing bacteria (SRB) and associated hydrogen sulfide production can be problematic in a range of industries such that inhibition strategies are needed. A range of SRB can reduce metal ions, a strategy that has been utilized for bioremediation, metal recovery, and synthesis of precious metal catalysts. In some instances, the metal remains bound to the cell surface, and the impact of this coating on bacterial cell division and metabolism has not previously been reported. In this study, Desulfovibrio desulfuricans cells (1g dry weight) enabled the reduction of up to 1500 mmol (157.5 g) palladium (Pd) ions, resulting in cells being coated in approximately 1 μm of metal. Thickly coated cells were no longer able to metabolize or divide, ultimately leading to the death of the population. Increasing Pd coating led to prolonged inhibition of sulfate reduction, which ceased completely after cells had been coated with 1200 mmol Pd g-1 dry cells. Less Pd nanoparticle coating permitted cells to carry out sulfate reduction and divide, allowing the population to recover over time as surface-associated Pd diminished. Overcoming inhibition in this way was more rapid using lactate as the electron donor, compared to formate. When using formate as an electron donor, preferential Pd(II) reduction took place in the presence of 100 mM sulfate. The inhibition of important metabolic pathways using a biologically enabled casing in metal highlights a new mechanism for the development of microbial control strategies. IMPORTANCE Microbial reduction of sulfate to hydrogen sulfide is highly undesirable in several industrial settings. Some sulfate-reducing bacteria are also able to transform metal ions in their environment into metal phases that remain attached to their outer cell surface. This study demonstrates the remarkable extent to which Desulfovibrio desulfuricans can be coated with locally generated metal nanoparticles, with individual cells carrying more than 100 times their mass of palladium metal. Moreover, it reveals the effect of metal coating on metabolism and replication for a wide range of metal loadings, with bacteria unable to reduce sulfate to sulfide beyond a specific threshold. These findings present a foundation for a novel means of modulating the activity of sulfate-reducing bacteria.

Possibilities for an Aerial Biosphere in Temperate Sub Neptune-Sized Exoplanet Atmospheres

The search for signs of life through the detection of exoplanet atmosphere biosignature gases is gaining momentum. Yet, only a handful of rocky exoplanet atmospheres are suitable for observation with planned next-generation telescopes. To broaden prospects, we describe the possibilities for an aerial, liquid water cloud-based biosphere in the atmospheres of sub Neptune-sized temperate exoplanets, those receiving Earth-like irradiation from their host stars. One such planet is known (K2-18b) and other candidates are being followed up. Sub Neptunes are common and easier to study observationally than rocky exoplanets because of their larger sizes, lower densities, and extended atmospheres or envelopes. Yet, sub Neptunes lack any solid surface as we know it, so it is worthwhile considering whether their atmospheres can support an aerial biosphere. We review, synthesize, and build upon existing research. Passive microbial-like life particles must persist aloft in a region with liquid water clouds for long enough to metabolize, reproduce, and spread before downward transport to lower altitudes that may be too hot for life of any kind to survive. Dynamical studies are needed to flesh out quantitative details of life particle residence times. A sub Neptune would need to be a part of a planetary system with an unstable asteroid belt in order for meteoritic material to provide nutrients, though life would also need to efficiently reuse and recycle metals. The origin of life may be the most severe limiting challenge. Regardless of the uncertainties, we can keep an open mind to the search for biosignature gases as a part of general observational studies of sub Neptune exoplanets.

OrpR is a σ54 -dependent activator using an iron-sulfur cluster for redox sensing in Desulfovibrio vulgaris Hildenborough

Enhancer binding proteins (EBPs) are key players of σ⁵⁴ -regulation that control transcription in response to environmental signals. In the anaerobic microorganism Desulfovibrio vulgaris Hildenborough (DvH), orp operons have been previously shown to be coregulated by σ⁵⁴ -RNA polymerase, the integration host factor IHF and a cognate EBP, OrpR. In this study, ChIP-seq experiments indicated that the OrpR regulon consists of only the two divergent orp operons. In vivo data revealed that (i) OrpR is absolutely required for orp operons transcription, (ii) under anaerobic conditions, OrpR binds on the two dedicated DNA binding sites and leads to high expression levels of the orp operons, (iii) increasing the redox potential of the medium leads to a drastic down-regulation of the orp operons expression. Moreover, combining functional and biophysical studies on the anaerobically purified OrpR leads us to propose that OrpR senses redox potential variations via a redox-sensitive [4Fe-4S]²⁺ cluster in the sensory PAS domain. Overall, the study herein presents the first characterization of a new Fe-S redox regulator belonging to the σ⁵⁴ -dependent transcriptional regulator family probably advantageously selected by cells adapted to the anaerobic lifestyle to monitor redox stress conditions.

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.

Modeling homeostasis mechanisms that set the target cell size

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

Modulation of first-passage time for gene expression via asymmetric cell division

How to balance the size of exponentially growing cells has always been a focus of biologists. Recent experiments have uncovered that the cell is divided into two daughter cells only when the level of time-keeper protein reaches a fixed threshold and cell division in prokaryote is not completely symmetric. The timing of cell division is essentially random because gene expression is stochastic, but cells seen to manage to have precise timing of cell division events. Although the inter-cellular variability of gene expression has attracted much attention, the randomness of event timing has been rarely studied. In our analysis, the timing of cell division is formulated as the first-passage time (denoted by FPT) for time-keeper protein’s level to cross a critical threshold firstly, we derive exact analytical formulae for the mean and noise of FPT based on stochastic gene expression model with asymmetric cell division. The results of numerical simulation show that the regulatory factors (division rate, newborn cell size, exponential growth rate and threshold) have significant influence on the mean and noise of FPT. We also show that both the increase of division rate and newborn cell size could reduce the mean of FPT and increase the noise of FPT, the larger the exponential growth rate is, the smaller the mean and noise of FPT will be; and the larger the threshold value is, the higher the mean of FPT is and the lower the noise is. In addition, compared with symmetric division, asymmetric division can reduce the mean of FPT and improve the noise of FPT. In summary, our results provide insight into the relationship between regulatory factors and FPT and reveal that asymmetric division is an effective mechanism to shorten the mean of FPT.

Effect of Blastocystis sp. in dengue patients-Increase in the treatment cost and exacerbation of symptoms

Increasing incidences of dengue have become a global health threat with major clinical manifestation including high fever and gastrointestinal symptoms. These symptoms were also expressed among Blastocystis sp. infected individuals, a parasite commonly seen in human stools. This parasite has been previously reported to replicate faster upon exposure to high temperature. The present study is a hospitalized-based cross-sectional study involved the collection of faecal sample from dengue patients. Stool examination was done by in vitro cultivation to isolate Blastocystis sp. Growth pattern of all the positive isolates were analyzed to identify the multiplication rate of Blastocystis sp. isolated from dengue patients. Distribution of Blastocystis sp. among dengue patients was 23.6%. Dengue patients who were positive for Blastocystis sp. infection denoted a significantly higher fever rate reaching 38.73°C (p<0.05) compared to the non-Blastocystis sp. infected patients (38.44°C). It was also found that Blastocystis sp. infected patients complained of frequenting the toilet more than five times a day (p<0.05) compared to those who were non-Blastocystis sp. infected. At the same time, the duration of hospitalization was significantly longer (p<0.05) for Blastocystis sp. infected dengue patients compared to the non-Blastocystis sp. infected patients. Besides, Blastocystis sp. isolated from dengue patients (in vivo thermal stress) showed a higher growth rate compared to the non-dengue isolated which was exposed to high temperature (in vitro thermal stress). Our findings suggest that presence of Blastocystis sp. during dengue infection could trigger the increase of temperature which could be due to highly elevated pro inflammatory cytokines by both parasitic and virus infection. This could justify why the temperature in Blastocystis sp. infected dengue patients is higher compared to the non-Blastocystis sp. infected patients. Higher temperature could have triggered a greater parasite multiplication rate that contributed to the aggravation of the gastrointestinal symptoms.

The bacterial MrpORP is a novel Mrp/NBP35 protein involved in iron-sulfur biogenesis

Despite recent advances in understanding the biogenesis of iron-sulfur (Fe-S) proteins, most studies focused on aerobic bacteria as model organisms. Accordingly, multiple players have been proposed to participate in the Fe-S delivery step to apo-target proteins, but critical gaps exist in the knowledge of Fe-S proteins biogenesis in anaerobic organisms. Mrp/NBP35 ATP-binding proteins are a subclass of the soluble P-loop containing nucleoside triphosphate hydrolase superfamily (P-loop NTPase) known to bind and transfer Fe-S clusters in vitro. Here, we report investigations of a novel atypical two-domain Mrp/NBP35 ATP-binding protein named Mrp_ORP associating a P-loop NTPase domain with a dinitrogenase iron-molybdenum cofactor biosynthesis domain (Di-Nase). Characterization of full length Mrp_ORP, as well as of its two domains, showed that both domains bind Fe-S clusters. We provide in vitro evidence that the P-loop NTPase domain of the Mrp_ORP can efficiently transfer its Fe-S cluster to apo-target proteins of the ORange Protein (ORP) complex, suggesting that this novel protein is involved in the maturation of these Fe-S proteins. Last, we showed for the first time, by fluorescence microscopy imaging a polar localization of a Mrp/NBP35 protein.

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.

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).

Inhibitory effect of high phenol concentration in treating coal gasification wastewater in anaerobic biofilter

In this paper, the inhibition of methanogens by phenol in coal gasification wastewater (CGW) was investigated by both anaerobic toxicity tests and a lab-scale anaerobic biofilter reactor (AF). The anaerobic toxicity tests indicated that keeping the phenol concentration in the influent under 280mg/L could maintain the methanogenic activity. In the AF treating CGW, the result showed that adding glucose solution as co-substrate could be beneficial for the quick start-up of the reactor. The effluent chemical oxygen demand (COD) and total phenol reached 1200 and 100mg/L, respectively, and the methane production rate was 175mLCH₄/gCOD/day. However, if the concentration of phenol was increased, the inhibition of anaerobic micro-organisms was irreversible. The threshold of total phenol for AF operation was 200-250mg/L. The extracellular polymeric substances (EPS) and particle size distribution of anaerobic granular sludge in the different stages were also examined, and the results indicated that the influence of toxicity in the system was more serious than its effect on flocculation of EPS. Moreover, the proportion of small size anaerobic granular sludge gradually increased from 10.2% to 34.6%. The results of high through-put sequencing indicated that the abundance of the Chloroflexi and Planctomycetes was inhibited by the toxicity of the CGW, and some shifts in the microbial community were observed at different stages.

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.

In vitro and in vivo thermal stress induces proliferation of Blastocystis sp

Blastocystis sp. is known to be the most commonly found intestinal protozoan parasite in human fecal surveys and has been incriminated to cause diarrhea and abdominal bloating. Binary fission has been widely accepted as the plausible mode of reproduction for this parasite. The present study demonstrates that subjecting the parasites in vitro to higher temperature shows the proliferation of parasite numbers in cultures. Transmission electron microscopy was used to compare the morphology of Blastocystis sp. subtype 3 isolated from a dengue patient having high fever (in vivo thermal stress) and Blastocystis sp. 3 maintained at 41 °C (in vitro thermal stress) and 37 °C (control). Fluorescence stains like acridine orange (AO) and 4',6'-diamino-2-phenylindole (DAPI) were used to demonstrate the viability and nuclear content of the parasite for both the in vitro and in vivo thermal stress groups of parasites. Blastocystis sp. at 37 °C was found to be mostly vacuolar whereas the in vitro thermal stressed isolates at 41 °C were granular with electron dense material seen to protect the granules within the central body. Parasites of the in vivo thermal stressed group showed similar ultrastructure as the in vitro ones. AO and DAPI staining provided evidence that these granules are viable which develop into progenies of Blastocystis sp. These granular forms were then observed to rupture and release progenies from the mother cells whilst the peripheral cytoplasmic walls were seen to degrade. Upon exposure to high temperature both in vitro and in vivo, Blastocystis sp. in cultures show higher number of granular forms seen to be protected by the electron dense material within the central body possibly acting as a protective mechanism. This is possibly to ensure the ability to survive for the granules to be developed as viable progenies for release into the host system.

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.

Beyond the bulk: disclosing the life of single microbial cells

Microbial single cell analysis has led to discoveries that are beyond what can be resolved with population-based studies. It provides a pristine view of the mechanisms that organize cellular physiology, unbiased by population heterogeneity or uncontrollable environmental impacts. A holistic description of cellular functions at the single cell level requires analytical concepts beyond the miniaturization of existing technologies, defined but uncontrolled by the biological system itself. This review provides an overview of the latest advances in single cell technologies and demonstrates their potential. Opportunities and limitations of single cell microbiology are discussed using selected application-related examples.

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.

A mechanistic stochastic framework for regulating bacterial cell division

How exponentially growing cells maintain size homeostasis is an important fundamental problem. Recent single-cell studies in prokaryotes have uncovered the adder principle, where cells add a fixed size (volume) from birth to division, irrespective of their size at birth. To mechanistically explain the adder principle, we consider a timekeeper protein that begins to get stochastically expressed after cell birth at a rate proportional to the volume. Cell-division time is formulated as the first-passage time for protein copy numbers to hit a fixed threshold. Consistent with data, the model predicts that the noise in division timing increases with size at birth. Intriguingly, our results show that the distribution of the volume added between successive cell-division events is independent of the newborn cell size. This was dramatically seen in experimental studies, where histograms of the added volume corresponding to different newborn sizes collapsed on top of each other. The model provides further insights consistent with experimental observations: the distribution of the added volume when scaled by its mean becomes invariant of the growth rate. In summary, our simple yet elegant model explains key experimental findings and suggests a mechanism for regulating both the mean and fluctuations in cell-division timing for controlling size.