Cell-size control and homeostasis in bacteria

General quantitative relations linking cell growth and the cell cycle in Escherichia coli

Growth laws emerging from studies of cell populations provide essential constraints on the global mechanisms that coordinate cell growth^1-3. The foundation of bacterial cell cycle studies relies on two interconnected dogmas that were proposed more than 50 years ago-the Schaechter-Maaloe-Kjeldgaard growth law that relates cell mass to growth rate¹ and Donachie's hypothesis of a growth-rate-independent initiation mass⁴. These dogmas spurred many efforts to understand their molecular bases and physiological consequences^5-14. Although they are generally accepted in the fast-growth regime, that is, for doubling times below 1 h, extension of these dogmas to the slow-growth regime has not been consistently achieved. Here, through a quantitative physiological study of Escherichia coli cell cycles over an extensive range of growth rates, we report that neither dogma holds in either the slow- or fast-growth regime. In their stead, linear relations between the cell mass and the rate of chromosome replication-segregation were found across the range of growth rates. These relations led us to propose an integral-threshold model in which the cell cycle is controlled by a licensing process, the rate of which is related in a simple way to chromosomal dynamics. These results provide a quantitative basis for predictive understanding of cell growth-cell cycle relationships.

Lineage EM algorithm for inferring latent states from cellular lineage trees

SUMMARY

Phenotypic variability in a population of cells can work as the bet-hedging of the cells under an unpredictably changing environment, the typical example of which is the bacterial persistence. To understand the strategy to control such phenomena, it is indispensable to identify the phenotype of each cell and its inheritance. Although recent advancements in microfluidic technology offer us useful lineage data, they are insufficient to directly identify the phenotypes of the cells. An alternative approach is to infer the phenotype from the lineage data by latent-variable estimation. To this end, however, we must resolve the bias problem in the inference from lineage called survivorship bias. In this work, we clarify how the survivorship bias distorts statistical estimations. We then propose a latent-variable estimation algorithm without the survivorship bias from lineage trees based on an expectation-maximization (EM) algorithm, which we call lineage EM algorithm (LEM). LEM provides a statistical method to identify the traits of the cells applicable to various kinds of lineage data.

AVAILABILITY AND IMPLEMENTATION

An implementation of LEM is available at https://github.com/so-nakashima/Lineage-EM-algorithm.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

On the Molecular Mechanisms Regulating Animal Cell Size Homeostasis

Cell size is fundamental to cell physiology because it sets the scale of intracellular geometry, organelles, and biosynthetic processes. In animal cells, size homeostasis is controlled through two phenomenologically distinct mechanisms. First, size-dependent cell cycle progression ensures that smaller cells delay cell cycle progression to accumulate more biomass than larger cells prior to cell division. Second, size-dependent cell growth ensures that larger and smaller cells grow slower per unit mass than more optimally sized cells. This decade has seen dramatic progress in single-cell technologies establishing the diverse phenomena of cell size control in animal cells. Here, we review this recent progress and suggest pathways forward to determine the underlying molecular mechanisms.

Nucleoid Size Scaling and Intracellular Organization of Translation across Bacteria

The scaling of organelles with cell size is thought to be exclusive to eukaryotes. Here, we demonstrate that similar scaling relationships hold for the bacterial nucleoid. Despite the absence of a nuclear membrane, nucleoid size strongly correlates with cell size, independent of changes in DNA amount and across various nutrient conditions. This correlation is observed in diverse bacteria, revealing a near-constant ratio between nucleoid and cell size for a given species. As in eukaryotes, the nucleocytoplasmic ratio in bacteria varies greatly among species. This spectrum of nucleocytoplasmic ratios is independent of genome size, and instead it appears linked to the average population cell size. Bacteria with different nucleocytoplasmic ratios have a cytoplasm with different biophysical properties, impacting ribosome mobility and localization. Together, our findings identify new organizational principles and biophysical features of bacterial cells, implicating the nucleocytoplasmic ratio and cell size as determinants of the intracellular organization of translation.

Variable cell division time and asymmetric division site lead to filament-to-rod cell cycle of Lysinibacillus varians

All well-established cell size homeostasis paradigms are based on the researches of rod bacteria like B. subtilis and E. coli, suggesting a constant division time (timer model), division size (sizer model) or added size (adder model) before division. However, Lysinibacillus varians, a new species with regular filament-to-rod cell cycle, is inconsistent with existing models. In this study, the cell size parameters of the type strain GY32, were investigated by combing multiple microscopy techniques and single-cell approach. Our results showed that the filaments of strain GY32 were unicellular cells with multiple nucleoids. The division time of GY32 cells was variable and their daughter cells produced by asymmetric binary fission had different birth sizes, which were proportional to their elongation rates, resulting in high heterogeneity among the sister cells. Furthermore, the added size from birth to division was significantly shorter than birth size (p < 0.01) and decreased along generations. The results above revealed that the asymmetric division site and varied cell size parameters resulted in filament-to-rod cell cycle of L. varians and cell size homeostasis could be a more complex and dynamic process than previously assumed. These findings would be helpful in elucidating the open questions in cell division and cell size heterogeneity.

A G1 Sizer Coordinates Growth and Division in the Mouse Epidermis

Cell size homeostasis is often achieved by coupling cell-cycle progression to cell growth. Growth has been shown to drive cell-cycle progression in bacteria and yeast through "sizers," wherein cells of varying birth size divide at similar final sizes [1-3], and "adders," wherein cells increase in size a fixed amount per cell cycle [4-6]. Intermediate control phenomena are also observed, and even the same organism can exhibit different control phenomena depending on growth conditions [2, 7, 8]. Although studying unicellular organisms in laboratory conditions may give insight into their growth control in the wild, this is less apparent for studies of mammalian cells growing outside the organism. Sizers, adders, and intermediate phenomena have been observed in vitro [9-12], but it is unclear how this relates to mammalian cell proliferation in vivo. To address this question, we analyzed time-lapse images of the mouse epidermis taken over 1 week during normal tissue turnover [13]. We quantified the 3D volume growth and cell-cycle progression of single cells within the mouse skin. In dividing epidermal stem cells, we found that cell growth is coupled to division through a sizer operating largely in the G1 phase of the cell cycle. Thus, although the majority of tissue culture studies have identified adders, our analysis demonstrates that sizers are important in vivo and highlights the need to determine their underlying molecular origin.

Loss of phenotypic inheritance associated with ydcI mutation leads to increased frequency of small, slow persisters in Escherichia coli

Whenever a genetically homogenous population of bacterial cells is exposed to antibiotics, a tiny fraction of cells survives the treatment, the phenomenon known as bacterial persistence [G.L. Hobby et al., Exp. Biol. Med. 50, 281-285 (1942); J. Bigger, The Lancet 244, 497-500 (1944)]. Despite its biomedical relevance, the origin of the phenomenon is still unknown, and as a rare, phenotypically resistant subpopulation, persisters are notoriously hard to study and define. Using computerized tracking we show that persisters are small at birth and slowly replicating. We also determine that the high-persister mutant strain of Escherichia coli, HipQ, is associated with the phenotype of reduced phenotypic inheritance (RPI). We identify the gene responsible for RPI, ydcI, which encodes a transcription factor, and propose a mechanism whereby loss of phenotypic inheritance causes increased frequency of persisters. These results provide insight into the generation and maintenance of phenotypic variation and provide potential targets for the development of therapeutic strategies that tackle persistence in bacterial infections.

Quantitative Connection between Cell Size and Growth Rate by Phospholipid Metabolism

The processes involved in cell growth are extremely complicated even for a single cell organism such as Escherichia coli, while the relationship between growth rate and cell size is simple. We aimed to reveal the systematic link between them from the aspect of the genome-scale metabolic network. Since the growth rate reflects metabolic rates of bacteria and the cell size relates to phospholipid synthesis, a part of bacterial metabolic networks, we calculated the cell length from the cardiolipin synthesis rate, where the cardiolipin synthesis reaction is able to represent the phospholipid metabolism of Escherichia coli in the exponential growth phase. Combined with the flux balance analysis, it enables us to predict cell length and to examine the quantitative relationship between cell length and growth rate. By simulating bacteria growing in various nutrient media with the flux balance analysis and calculating the corresponding cell length, we found that the increase of the synthesis rate of phospholipid, the cell width, and the protein fraction in membranes caused the increase of cell length with growth rate. Different tendencies of phospholipid synthesis rate changing with growth rate result in different relationships between cell length and growth rate. The effects of gene deletions on cell size and growth rate are also examined. Knocking out the genes, such as Δ tktA, Δ tktB, Δ yqaB, Δ pgm, and Δ cysQ, affects growth rate largely while affecting cell length slightly. Results of this method are in good agreement with experiments.

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.

Microfluidic Single-Cell Analytics

What is the impact of cellular heterogeneity on process performance? How do individual cells contribute to averaged process productivity? Single-cell analysis is a key technology for answering such key questions of biotechnology, beyond bulky measurements with populations. The analysis of cellular individuality, its origins, and the dependency of process performance on cellular heterogeneity has tremendous potential for optimizing biotechnological processes in terms of metabolic, reaction, and process engineering. Microfluidics offer unmatched environmental control of the cellular environment and allow massively parallelized cultivation of single cells. However, the analytical accessibility to a cell's physiology is of crucial importance for obtaining the desired information on the single-cell production phenotype. Highly sensitive analytics are required to detect and quantify the minute amounts of target analytes and small physiological changes in a single cell. For their application to biotechnological questions, single-cell analytics must evolve toward the measurement of kinetics and specific rates of the smallest catalytic unit, the single cell. In this chapter, we focus on an introduction to the latest single-cell analytics and their application for obtaining physiological parameters in a biotechnological context from single cells. We present and discuss recent advancements in single-cell analytics that enable the analysis of cell-specific growth, uptake, and production kinetics, as well as the gene expression and regulatory mechanisms at a single-cell level.

PDE MODELS OF ADDER MECHANISMS IN CELLULAR PROLIFERATION

Cell division is a process that involves many biochemical steps and complex biophysical mechanisms. To simplify the understanding of what triggers cell division, three basic models that subsume more microscopic cellular processes associated with cell division have been proposed. Cells can divide based on the time elapsed since their birth, their size, and/or the volume added since their birth-the timer, sizer, and adder models, respectively. Here, we propose unified adder-sizer models and investigate some of the properties of different adder processes arising in cellular proliferation. Although the adder-sizer model provides a direct way to model cell population structure, we illustrate how it is mathematically related to the well-known model in which cell division depends on age and size. Existence and uniqueness of weak solutions to our 2+1-dimensional PDE model are proved, leading to the convergence of the discretized numerical solutions and allowing us to numerically compute the dynamics of cell population densities. We then generalize our PDE model to incorporate recent experimental findings of a system exhibiting mother-daughter correlations in cellular growth rates. Numerical experiments illustrating possible average cell volume blowup and the dynamical behavior of cell populations with mother-daughter correlated growth rates are carried out. Finally, motivated by new experimental findings, we extend our adder model cases where the controlling variable is the added size between DNA replication initiation points in the cell cycle.

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.

Quantitation and Comparison of Phenotypic Heterogeneity Among Single Cells of Monoclonal Microbial Populations

Phenotypic heterogeneity within microbial populations arises even when the cells are exposed to putatively constant and homogeneous conditions. The outcome of this phenomenon can affect the whole function of the population, resulting in, for example, new "adapted" metabolic strategies and impacting its fitness at given environmental conditions. Accounting for phenotypic heterogeneity becomes thus necessary, due to its relevance in medical and applied microbiology as well as in environmental processes. Still, a comprehensive evaluation of this phenomenon requires a common and unique method of quantitation, which allows for the comparison between different studies carried out with different approaches. Consequently, in this study, two widely applicable indices for quantitation of heterogeneity were developed. The heterogeneity coefficient (HC) is valid when the population follows unimodal activity, while the differentiation tendency index (DTI) accounts for heterogeneity implying outbreak of subpopulations and multimodal activity. We demonstrated the applicability of HC and DTI for heterogeneity quantitation on stable isotope probing with nanoscale secondary ion mass spectrometry (SIP-nanoSIMS), flow cytometry, and optical microscopy datasets. The HC was found to provide a more accurate and precise measure of heterogeneity, being at the same time consistent with the coefficient of variation (CV) applied so far. The DTI is able to describe the differentiation in single-cell activity within monoclonal populations resolving subpopulations with low cell abundance, individual cells with similar phenotypic features (e.g., isotopic content close to natural abundance, as detected with nanoSIMS). The developed quantitation approach allows for a better understanding on the impact and the implications of phenotypic heterogeneity in environmental, medical and applied microbiology, microbial ecology, cell biology, and biotechnology.

Control of Bacillus subtilis Replication Initiation during Physiological Transitions and Perturbations

Bacillus subtilis and Escherichia coli are evolutionarily divergent model organisms whose analysis has enabled elucidation of fundamental differences between Gram-positive and Gram-negative bacteria, respectively. Despite their differences in cell cycle control at the molecular level, the two organisms follow the same phenomenological principle, known as the adder principle, for cell size homeostasis. We thus asked to what extent B. subtilis and E. coli share common physiological principles in coordinating growth and the cell cycle. We measured physiological parameters of B. subtilis under various steady-state growth conditions with and without translation inhibition at both the population and single-cell levels. These experiments revealed core physiological principles shared between B. subtilis and E. coli Specifically, both organisms maintain an invariant cell size per replication origin at initiation, under all steady-state conditions, and even during nutrient shifts at the single-cell level. Furthermore, the two organisms also inherit the same "hierarchy" of physiological parameters. On the basis of these findings, we suggest that the basic principles of coordination between growth and the cell cycle in bacteria may have been established early in evolutionary history.IMPORTANCE High-throughput, quantitative approaches have enabled the discovery of fundamental principles describing bacterial physiology. These principles provide a foundation for predicting the behavior of biological systems, a widely held aspiration. However, these approaches are often exclusively applied to the best-known model organism, E. coli In this report, we investigate to what extent quantitative principles discovered in Gram-negative E. coli are applicable to Gram-positive B. subtilis We found that these two extremely divergent bacterial species employ deeply similar strategies in order to coordinate growth, cell size, and the cell cycle. These similarities mean that the quantitative physiological principles described here can likely provide a beachhead for others who wish to understand additional, less-studied prokaryotes.

A Visual Framework for Classifying Determinants of Cell Size

Cells control their size by coordinating cell cycle progression with volume growth. Size control is typically studied at specific cell cycle transitions that are delayed or accelerated depending on size. This focus is well suited for revealing mechanisms acting at these transitions, but neglects the dynamics in other cell cycle phases, and is therefore inherently limited for studying how the characteristic cell size is determined. We address this limitation through a formalism that intuitively visualizes the characteristic size emerging from integrated cell cycle dynamics of individual cells. Applying this formalism to budding yeast, we describe the contributions of the un-budded (G1) and budded (S-G2-M) phase to size adjustments following environmental or genetic perturbations. We show that although the budded phase can be perturbed with little consequences for G1 dynamics, perturbations in G1 propagate to the budded phase. Our study provides an integrated view on cell size determinants in budding yeast.

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An intuitive visualization framework for cell size control is described

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Cell size control in different environments or mutant backgrounds can be compared

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Mutual dependencies between size control at different cell cycle phases are described

The Simplified Human Intestinal Microbiota (SIHUMIx) Shows High Structural and Functional Resistance against Changing Transit Times in In Vitro Bioreactors

Many functions in host-microbiota interactions are potentially influenced by intestinal transit times, but little is known about the effects of altered transition times on the composition and functionality of gut microbiota. To analyze these effects, we cultivated the model community SIHUMIx in bioreactors in order to determine the effects of varying transit times (TT) on the community structure and function. After five days of continuous cultivation, we investigated the influence of different medium TT of 12 h, 24 h, and 48 h. For profiling the microbial community, we applied flow cytometric fingerprinting and revealed changes in the community structure of SIHUMIx during the change of TT, which were not associated with changes in species abundances. For pinpointing metabolic alterations, we applied metaproteomics and metabolomics and found, along with shortening the TT, a slight decrease in glycan biosynthesis, carbohydrate, and amino acid metabolism and, furthermore, a reduction in butyrate, methyl butyrate, isobutyrate, valerate, and isovalerate concentrations. Specifically, B. thetaiotaomicron was identified to be affected in terms of butyrate metabolism. However, communities could recover to the original state afterward. This study shows that SIHUMIx showed high structural stability when TT changed-even four-fold. Resistance values remained high, which suggests that TTs did not interfere with the structure of the community to a certain degree.

Frontiers in Microfluidics, a Teaching Resource Review

This is a literature teaching resource review for biologically inspired microfluidics courses or exploring the diverse applications of microfluidics. The structure is around key papers and model organisms. While courses gradually change over time, a focus remains on understanding how microfluidics has developed as well as what it can and cannot do for researchers. As a primary starting point, we cover micro-fluid mechanics principles and microfabrication of devices. A variety of applications are discussed using model prokaryotic and eukaryotic organisms from the set of bacteria (Escherichia coli), trypanosomes (Trypanosoma brucei), yeast (Saccharomyces cerevisiae), slime molds (Physarum polycephalum), worms (Caenorhabditis elegans), flies (Drosophila melangoster), plants (Arabidopsis thaliana), and mouse immune cells (Mus musculus). Other engineering and biochemical methods discussed include biomimetics, organ on a chip, inkjet, droplet microfluidics, biotic games, and diagnostics. While we have not yet reached the end-all lab on a chip, microfluidics can still be used effectively for specific applications.

Isolating live cells after high-throughput, long-term, time-lapse microscopy

Single-cell genetic screens can be incredibly powerful, but current high-throughput platforms do not track dynamic processes, and even for non-dynamic properties they struggle to separate mutants of interest from phenotypic outliers of the wild-type population. Here we introduce SIFT, single-cell isolation following time-lapse imaging, to address these limitations. After imaging and tracking individual bacteria for tens of consecutive generations under tightly controlled growth conditions, cells of interest are isolated and propagated for downstream analysis, free of contamination and without genetic or physiological perturbations. This platform can characterize tens of thousands of cell lineages per day, making it possible to accurately screen complex phenotypes without the need for barcoding or genetic modifications. We applied SIFT to identify a set of ultraprecise synthetic gene oscillators, with circuit variants spanning a 30-fold range of average periods. This revealed novel design principles in synthetic biology and demonstrated the power of SIFT to reliably screen diverse dynamic phenotypes.

Mono- to Multilayer Transition in Growing Bacterial Colonies

The transition from monolayers to multilayered structures in bacterial colonies is a fundamental step in biofilm development. Observed across different morphotypes and species, this transition is triggered within freely growing bacterial microcolonies comprising a few hundred cells. Using a combination of numerical simulations and analytical modeling, here we demonstrate that this transition originates from the competition between growth-induced in-plane active stresses and vertical restoring forces, due to the cell-substrate interactions. Using a simple chainlike colony of laterally confined cells, we show that the transition sets when individual cells become unstable to rotations; thus it is localized and mechanically deterministic. Asynchronous cell division renders the process stochastic, so that all the critical parameters that control the onset of the transition are continuously distributed random variables. Here we demonstrate that the occurrence of the first division in the colony can be approximated as a Poisson process in the limit of large cell numbers. This allows us to approximately calculate the probability distribution function of the position and time associated with the first extrusion. The rate of such a Poisson process can be identified as the order parameter of the transition, thus highlighting its mixed deterministic-stochastic nature.

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.

High-throughput detection and tracking of cells and intracellular spots in mother machine experiments

The analysis of bacteria at the single-cell level is essential to characterization of processes in which cellular heterogeneity plays an important role. BACMMAN (bacteria mother machine analysis) is a software allowing fast and reliable automated image analysis of high-throughput 2D or 3D time-series images from experiments using the 'mother machine', a very popular microfluidic device allowing biological processes in bacteria to be investigated at the single-cell level. Here, we describe how to use some of the BACMMAN features, including (i) segmentation and tracking of bacteria and intracellular fluorescent spots, (ii) visualization and editing of the results, (iii) configuration of the image-processing pipeline for different datasets and (iv) BACMMAN coupling to data analysis software for visualization and analysis of data subsets with specific properties. Among software specifically dedicated to the analysis of mother machine data, only BACMMAN allows segmentation and tracking of both bacteria and intracellular spots. For a single position, single channel with 1,000 frames (2-GB dataset), image processing takes ~6 min on a regular computer. Numerous implemented algorithms, easy configuration and high modularity ensure wide applicability of the BACMMAN software.

Surface-to-volume scaling and aspect ratio preservation in rod-shaped bacteria

Rod-shaped bacterial cells can readily adapt their lengths and widths in response to environmental changes. While many recent studies have focused on the mechanisms underlying bacterial cell size control, it remains largely unknown how the coupling between cell length and width results in robust control of rod-like bacterial shapes. In this study we uncover a conserved surface-to-volume scaling relation in Escherichia coli and other rod-shaped bacteria, resulting from the preservation of cell aspect ratio. To explain the mechanistic origin of aspect-ratio control, we propose a quantitative model for the coupling between bacterial cell elongation and the accumulation of an essential division protein, FtsZ. This model reveals a mechanism for why bacterial aspect ratio is independent of cell size and growth conditions, and predicts cell morphological changes in response to nutrient perturbations, antibiotics, MreB or FtsZ depletion, in quantitative agreement with experimental data.

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.

Does the Nucleoid Determine Cell Dimensions in Escherichia coli?

Bacillary, Gram-negative bacteria grow by elongation with no discernible change in width, but during faster growth in richer media the cells are also wider. The mechanism regulating the change in cell width W during transitions from slow to fast growth is a fundamental, unanswered question in molecular biology. The value of W that changes in the divisome and during the division process only, is related to the nucleoid complexity, determined by the rates of growth and of chromosome replication; the former is manipulated by nutritional conditions and the latter-by thymine limitation of thyA mutants. Such spatio-temporal regulation is supported by existence of a minimal possible distance between successive replisomes, so-called eclipse that limits the number of replisomes to a maximum. Breaching this limit by slowing replication in fast growing cells results in maximal nucleoid complexity that is associated with maximum cell width, supporting the notion of Nucleoid-to-Divisome signal transmission. Physical signal(s) may be delivered from the nucleoid to assemble the divisome and to fix the value of W in the nascent cell pole.

Bayesian inference of distributed time delay in transcriptional and translational regulation

MOTIVATION

Advances in experimental and imaging techniques have allowed for unprecedented insights into the dynamical processes within individual cells. However, many facets of intracellular dynamics remain hidden, or can be measured only indirectly. This makes it challenging to reconstruct the regulatory networks that govern the biochemical processes underlying various cell functions. Current estimation techniques for inferring reaction rates frequently rely on marginalization over unobserved processes and states. Even in simple systems this approach can be computationally challenging, and can lead to large uncertainties and lack of robustness in parameter estimates. Therefore we will require alternative approaches to efficiently uncover the interactions in complex biochemical networks.

RESULTS

We propose a Bayesian inference framework based on replacing uninteresting or unobserved reactions with time delays. Although the resulting models are non-Markovian, recent results on stochastic systems with random delays allow us to rigorously obtain expressions for the likelihoods of model parameters. In turn, this allows us to extend MCMC methods to efficiently estimate reaction rates, and delay distribution parameters, from single-cell assays. We illustrate the advantages, and potential pitfalls, of the approach using a birth-death model with both synthetic and experimental data, and show that we can robustly infer model parameters using a relatively small number of measurements. We demonstrate how to do so even when only the relative molecule count within the cell is measured, as in the case of fluorescence microscopy.

AVAILABILITY AND IMPLEMENTATION

Accompanying code in R is available at https://github.com/cbskust/DDE_BD.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Cell Boundary Confinement Sets the Size and Position of the E. coli Chromosome

Although the spatiotemporal structure of the genome is crucial to its biological function, many basic questions remain unanswered on the morphology and segregation of chromosomes. Here, we experimentally show in Escherichia coli that spatial confinement plays a dominant role in determining both the chromosome size and position. In non-dividing cells with lengths increased to 10 times normal, single chromosomes are observed to expand > 4-fold in size. Chromosomes show pronounced internal dynamics but exhibit a robust positioning where single nucleoids reside robustly at mid-cell, whereas two nucleoids self-organize at 1/4 and 3/4 positions. The cell-size-dependent expansion of the nucleoid is only modestly influenced by deletions of nucleoid-associated proteins, whereas osmotic manipulation experiments reveal a prominent role of molecular crowding. Molecular dynamics simulations with model chromosomes and crowders recapitulate the observed phenomena and highlight the role of entropic effects caused by confinement and molecular crowding in the spatial organization of the chromosome.

Cell population heterogeneity driven by stochastic partition and growth optimality

A fundamental question in biology is how cell populations evolve into different subtypes based on homogeneous processes at the single cell level. Here we show that population bimodality can emerge even when biological processes are homogenous at the cell level and the environment is kept constant. Our model is based on the stochastic partitioning of a cell component with an optimal copy number. We show that the existence of unimodal or bimodal distributions depends on the variance of partition errors and the growth rate tolerance around the optimal copy number. In particular, our theory provides a consistent explanation for the maintenance of aneuploid states in a population. The proposed model can also be relevant for other cell components such as mitochondria and plasmids, whose abundances affect the growth rate and are subject to stochastic partition at cell division.

Quantitative modelling of nutrient-limited growth of bacterial colonies in microfluidic cultivation

Nutrient gradients and limitations play a pivotal role in the life of all microbes, both in their natural habitat as well as in artificial, microfluidic systems. Spatial concentration gradients of nutrients in densely packed cell configurations may locally affect the bacterial growth leading to heterogeneous micropopulations. A detailed understanding and quantitative modelling of cellular behaviour under nutrient limitations is thus highly desirable. We use microfluidic cultivations to investigate growth and microbial behaviour of the model organism Corynebacterium glutamicum under well-controlled conditions. With a reaction-diffusion-type model, parameters are extracted from steady-state experiments with a one-dimensional nutrient gradient. Subsequently, we employ particle-based simulations with these parameters to predict the dynamical growth of a colony in two dimensions. Comparing the results of those simulations with microfluidic experiments yields excellent agreement. Our modelling approach lays the foundation for a better understanding of dynamic microbial growth processes, both in nature and in applied biotechnology.

Cell Size: Fat Makes Cells Fat

Nutrients are required for the multiple biosynthetic pathways that result in cell growth, and faster growth due to increased nutrient supply results in larger cell volume. A new study demonstrates that fatty-acid availability limits growth rate and cell envelope capacity, revealing that fatty-acid synthesis is the primary determinant of cell size in bacteria and in budding yeast.

A critical analysis of Powell's results on the interdivision time distribution

The cell-age and interdivision-time probability density functions (PDFs) have been extensively investigated since the 1940s due to their fundamental role in cell growth. The pioneering work of Powell established the first relationship between the interdivision-time and cell-age PDFs. In the literature, two definitions for the interdivision-time PDF have been proposed. One stands for the age-at-rupture PDF and is experimentally observable, whereas the other is the probability density that a cell divides at a certain age and is unobservable. From Powell’s results pertaining to the unobservable interdivision-time PDF, Painter and Marr derived an inequality that is true but is incorrectly used by experimentalists to analyse single-cell data. Unfortunately, the confusion between these two PDFs persists. To dissipate this confusion, exact relationships between the cell-age and the interdivision-time PDFs are derived in this work from an age-structured model, which can be used by experimentalists to analyse cell growth in batch and continuous culture modes.

Simulations reveal challenges to artificial community selection and possible strategies for success

Multispecies microbial communities often display "community functions" arising from interactions of member species. Interactions are often difficult to decipher, making it challenging to design communities with desired functions. Alternatively, similar to artificial selection for individuals in agriculture and industry, one could repeatedly choose communities with the highest community functions to reproduce by randomly partitioning each into multiple "Newborn" communities for the next cycle. However, previous efforts in selecting complex communities have generated mixed outcomes that are difficult to interpret. To understand how to effectively enact community selection, we simulated community selection to improve a community function that requires 2 species and imposes a fitness cost on one or both species. Our simulations predict that improvement could be easily stalled unless various aspects of selection are carefully considered. These aspects include promoting species coexistence, suppressing noncontributors, choosing additional communities besides the highest functioning ones to reproduce, and reducing stochastic fluctuations in the biomass of each member species in Newborn communities. These considerations can be addressed experimentally. When executed effectively, community selection is predicted to improve costly community function, and may even force species to evolve slow growth to achieve species coexistence. Our conclusions hold under various alternative model assumptions and are therefore applicable to a variety of communities.

Does the Semiconservative Nature of DNA Replication Facilitate Coherent Phenotypic Diversity?

It has been clear for over sixty years that the principal method whereby cells replicate and segregate their DNA is semiconservative. It is much less clear why it should be like this rather than, say, conservative. Recently, evidence has accumulated that supports the hypothesis that one of the functions of the cell cycle is to generate phenotypically different daughter cells, even in nondifferentiating bacteria such as Escherichia coli Evidence has also accumulated that the bacterial phenotype is determined by the functioning of extended assemblies of macromolecules termed hyperstructures. One class of these hyperstructures is attached dynamically to a DNA strand by the coupling of transcription and translation. Previously, we proposed in the strand segregation model that one set of hyperstructures accompanies one parental strand into one daughter cell while another set of hyperstructures accompanies the other parental strand into the other daughter cell. This epigenetic mechanism results in daughter cells having different phenotypes. Here, I propose that one of the reasons why semiconservative replication has been selected is because it allows the generation of a population containing cells with very different growth rates even in steady-state conditions.

One is Nothing without the Other: Theoretical and Empirical Analysis of Cell Growth and Cell Cycle Progression

Small, fast-growing bacteria make ideal subjects for genetic and quantitative analysis alike. Long the darling of theoreticians, efforts to understand the relationship between cell growth and cell cycle progression in bacterial systems have been propelled by modelers and empiricist in equal measure. Taking a historical approach, here we break down early work in this area, the impact it had on how the bacterial cell cycle is understood and interrogated, and changes brought by the advent of high-throughput techniques for the analysis of individual bacterial cells in culture.

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.

Bacillus subtilis cell diameter is determined by the opposing actions of two distinct cell wall synthetic systems

Rod-shaped bacteria grow by adding material into their cell wall via the action of two spatially distinct enzymatic systems: the Rod complex moves around the cell circumference, whereas class A penicillin-binding proteins (aPBPs) do not. To understand how the combined action of these two systems defines bacterial dimensions, we examined how each affects the growth and width of Bacillus subtilis as well as the mechanical anisotropy and orientation of material within their sacculi. Rod width is not determined by MreB, rather it depends on the balance between the systems: the Rod complex reduces diameter, whereas aPBPs increase it. Increased Rod-complex activity correlates with an increased density of directional MreB filaments and a greater fraction of directional PBP2a enzymes. This increased circumferential synthesis increases the relative quantity of oriented material within the sacculi, making them more resistant to stretching across their width, thereby reinforcing rod shape. Together, these experiments explain how the combined action of the two main cell wall synthetic systems builds and maintains rods of different widths. Escherichia coli Rod mutants also show the same correlation between width and directional MreB filament density, suggesting this model may be generalizable to bacteria that elongate via the Rod complex.

Growing from a few cells: combined effects of initial stochasticity and cell-to-cell variability

The growth of a cell population from a large inoculum appears deterministic, although the division process is stochastic at the single-cell level. Microfluidic observations, however, display wide variations in the growth of small populations. Here we combine theory, simulations and experiments to explore the link between single-cell stochasticity and the growth of a population starting from a small number of individuals. The study yields descriptors of the probability distribution function (PDF) of the population size under three sources of stochasticity: cell-to-cell variability, uncertainty in the number of initial cells and generation-dependent division times. The PDF, rescaled to account for the exponential growth of the population, is found to converge to a stationary distribution. All moments of the PDF grow exponentially with the same growth rate, which depends solely on cell-to-cell variability. The shape of the PDF, however, contains the signature of all sources of stochasticity, and is dominated by the early stages of growth, and not by the cell-to-cell variability. Thus, probabilistic predictions of the growth of bacterial populations can be obtained with implications for both naturally occurring conditions and technological applications of single-cell microfluidics.

3D dynamics of bacteria wall entrapment at a water-air interface

Swimming bacteria can be trapped for prolonged times at the surface of an impenetrable boundary. The subsequent surface confined motility is found to be very sensitive to the physico-chemical properties of the interfaces which determine the boundary conditions for the flow. The quantitative understanding of this complex dynamics requires detailed and systematic experimental data to validate theoretical models for both flagellar propulsion and interfacial dynamics. Using a combination of optical trapping and holographic imaging we study the 3D dynamics of wall entrapment of swimming bacteria that are sequentially released towards a surfactant-covered liquid-air interface. We find that an incompressible surfactant model for the interface quantitatively accounts for the observed normal and tangential speed of bacteria as they approach the boundary. Surprisingly we also find that, although bacteria circulate over the air phase in counterclockwise circular trajectories, typical of free-slip interfaces, the body axis is still tilted "nose down" as found for no-slip interfaces.

Multiparameter antibiotic resistance detection based on hydrodynamic trapping of individual E. coli

There is an urgent need to develop novel methods for assessing the response of bacteria to antibiotics in a timely manner. Antibiotics are traditionally assessed via their effect on bacteria in a culture medium, which takes 24-48 h and exploits only a single parameter, i.e. growth. Here, we present a multiparameter approach at the single-cell level that takes approximately an hour from spiking the culture to correctly classify susceptible and resistant strains. By hydrodynamically trapping hundreds of bacteria, we simultaneously monitor the evolution of motility and morphology of individual bacteria upon drug administration. We show how this combined detection method provides insights into the activity of antimicrobials at the onset of their action which single parameter and traditional tests cannot offer. Our observations complement the current growth-based methods and highlight the need for future antimicrobial susceptibility tests to take multiple parameters into account.

Linking lineage and population observables in biological branching processes

Using a population dynamics inspired by an ensemble of growing cells, a set of fluctuation theorems linking observables measured at the lineage and population levels is derived. One of these relations implies specific inequalities comparing the population doubling time with the mean generation time at the lineage or population levels. While these inequalities have been derived before for age-controlled models with negligible mother-daughter correlations, we show that they also hold for a broad class of size-controlled models. We discuss the implications of this result for the interpretation of a recent experiment in which the growth of bacteria strains has been probed at the single-cell level.

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.

Stringent response leads to continued cell division and a temporal restart of DNA replication after initial shutdown in Vibrio cholerae

Vibrio cholerae is an aquatic bacterium with the potential to infect humans and cause the cholera disease. While most bacteria have single chromosomes, the V. cholerae genome is encoded on two replicons of different size. This study focuses on the DNA replication and cell division of this bi-chromosomal bacterium during the stringent response induced by starvation stress. V. cholerae cells were found to initially shut DNA replication initiation down upon stringent response induction by the serine analog serine hydroxamate. Surprisingly, cells temporarily restart their DNA replication before finally reaching a state with fully replicated single chromosome sets. This division-replication pattern is very different to that of the related single chromosome model bacterium Escherichia coli. Within the replication restart phase, both chromosomes of V. cholerae maintained their known order of replication timing to achieve termination synchrony. Using flow cytometry combined with mathematical modeling, we established that a phase of cellular regrowth be the reason for the observed restart of DNA replication after the initial shutdown. Our study shows that although the stringent response induction itself is widely conserved, bacteria developed different ways of how to react to the sensed nutrient limitation, potentially reflecting their individual lifestyle requirements.

Spatiotemporal establishment of dense bacterial colonies growing on hard agar

The physical interactions of growing bacterial cells with each other and with their surroundings significantly affect the structure and dynamics of biofilms. Here a 3D agent-based model is formulated to describe the establishment of simple bacterial colonies expanding by the physical force of their growth. With a single set of parameters, the model captures key dynamical features of colony growth by non-motile, non EPS-producing E. coli cells on hard agar. The model, supported by experiment on colony growth in different types and concentrations of nutrients, suggests that radial colony expansion is not limited by nutrients as commonly believed, but by mechanical forces. Nutrient penetration instead governs vertical colony growth, through thin layers of vertically oriented cells lifting up their ancestors from the bottom. Overall, the model provides a versatile platform to investigate the influences of metabolic and environmental factors on the growth and morphology of bacterial colonies.

Successive Paradigm Shifts in the Bacterial Cell Cycle and Related Subjects

A paradigm shift in one field can trigger paradigm shifts in other fields. This is illustrated by the paradigm shifts that have occurred in bacterial physiology following the discoveries that bacteria are not unstructured, that the bacterial cell cycle is not controlled by the dynamics of peptidoglycan, and that the growth rates of bacteria in the same steady-state population are not at all the same. These paradigm shifts are having an effect on longstanding hypotheses about the regulation of the bacterial cell cycle, which appear increasingly to be inadequate. I argue that, just as one earthquake can trigger others, an imminent paradigm shift in the regulation of the bacterial cell cycle will have repercussions or "paradigm quakes" on hypotheses about the origins of life and about the regulation of the eukaryotic cell cycle.

Bacterial surface colonization, preferential attachment and fitness under periodic stress

Early bacterial surface colonization is not a random process wherein cells arbitrarily attach to surfaces and grow; but rather, attachment events, movement and cellular interactions induce non-random spatial organization. We have only begun to understand how the apparent self-organization affects the fitness of the population. A key factor contributing to fitness is the tradeoff between solitary-planktonic and aggregated surface-attached biofilm lifestyles. Though planktonic cells typically grow faster, bacteria in aggregates are more resistant to stress such as desiccation, antibiotics and predation. Here we ask if and to what extent informed surface-attachments improve fitness during early surface colonization under periodic stress conditions. We use an individual-based modeling approach to simulate foraging planktonic cells colonizing a surface under alternating wet-dry cycles. Such cycles are common in the largest terrestrial microbial habitats–soil, roots, and leaf surfaces–that are not constantly saturated with water and experience daily periods of desiccation stress. We compared different surface-attachment strategies, and analyzed the emerging spatio-temporal dynamics of surface colonization and population yield as a measure of fitness. We demonstrate that a simple strategy of preferential attachment (PA), biased to dense sites, carries a large fitness advantage over any random attachment across a broad range of environmental conditions–particularly under periodic stress.

A vast portion of bacterial life on Earth takes place on surfaces. In many of these surfaces cells collectively organize into biofilms that are known to provide them protection from various environmental stresses. Early bacterial colonization of surfaces, prior to the development of mature biofilm, is a critical stage during which cells attempt to establish a sustainable population. It is not a random process wherein cells arbitrarily attach to surfaces and grow to form micro-colonies. Rather, surface-attachments, movement and cellular interactions take place to yield non-random organization. Using computer simulations, based on individual-based modeling, we demonstrate that simple attachment strategies, where planktonic cells preferentially attach to existing surface-attached aggregates, may confer fitness advantage over random attachment. The advantage of preferential attachment is particularly substantial under periodic stress–a common characteristic of many natural microbial habitats. This is due to a more efficient recruitment of planktonic cells that accelerates the formation of stress-protected aggregates.

Phenomenological models as effective tools to discover cellular design principles

Microbes have proved useful to us in many different ways. To utilize microbes, we have mostly focused on maximizing growth, to improve yield of chemicals derived from the microbes. However, to truly tap into their potential, we should also aim to understand microbial physiology. We present a historical perspective of the developments in the field of Microbial Biotechnology, focusing on how the growth-modelling approaches have changed. Starting from simple empirical growth models, we have evolved towards mechanistic and phenomenological models which use molecular and physiological details to drastically improve prediction power of these models. Lastly, we explore the as of yet unsolved questions in microbial physiology, and discuss how the ability to monitor microbial growth at single cell resolution using the lab-on-a-chip technologies is uncovering previously unobservable causal principles underlying microbial growth.

The Dream of a Mycobacterium

How do mycobacteria divide? Cell division has been studied extensively in the model rod-shaped bacteria Escherichia coli and Bacillus subtilis, but much less is understood about cell division in mycobacteria, a genus that includes the major human pathogens M. tuberculosis and M. leprae. In general, bacterial cell division requires the concerted effort of many proteins in both space and time to elongate the cell, replicate and segregate the chromosome, and construct and destruct the septum - processes which result in the creation of two new daughter cells. Here, we describe these distinct stages of cell division in B. subtilis and follow with the current knowledge in mycobacteria. As will become apparent, there are many differences between mycobacteria and B. subtilis in terms of both the broad outline of cell division and the molecular details. So, while the fundamental challenge of spatially and temporally organizing cell division is shared between these rod-shaped bacteria, they have solved these challenges in often vastly different ways.