Generation and filtering of gene expression noise by the bacterial cell cycle

Model-guided gene circuit design for engineering genetically stable cell populations in diverse applications

Maintaining engineered cell populations' genetic stability is a key challenge in synthetic biology. Synthetic genetic constructs compete with a host cell's native genes for expression resources, burdening the cell and impairing its growth. This creates a selective pressure favouring mutations which alleviate this growth defect by removing synthetic gene expression. Non-functional mutants thus spread in cell populations, eventually making them lose engineered functions. Past work has attempted to limit mutation spread by coupling synthetic gene expression to survival. However, these approaches are highly context-dependent and must be tailor-made for each particular synthetic gene circuit to be retained. By contrast, we develop and analyse a biomolecular controller which depresses mutant cell growth independently of the mutated synthetic gene's identity. Modelling shows how our design can be deployed alongside various synthetic circuits without any re-engineering of its genetic components, outperforming extant gene-specific mutation spread mitigation strategies. Our controller's performance is evaluated using a novel simulation approach which leverages resource-aware cell modelling to directly link a circuit's design parameters to its population-level behaviour. Our design's adaptability promises to mitigate mutation spread in an expanded range of applications, while our analyses provide a blueprint for using resource-aware cell models in circuit design.

Mechanisms and implications of phenotypic switching in bacterial pathogens

Bacteria encounter various stressful conditions within a variety of dynamic environments, which they must overcome for survival. One way they achieve this is by developing phenotypic heterogeneity to introduce diversity within their population. Such distinct subpopulations can arise through endogenous fluctuations in regulatory components, wherein bacteria can express diverse phenotypes and switch between them, sometimes in a heritable and reversible manner. This switching may also lead to antigenic variation, enabling pathogenic bacteria to evade the host immune response. Therefore, phenotypic heterogeneity plays a significant role in microbial pathogenesis, immune evasion, antibiotic resistance, host niche tissue establishment, and environmental persistence. This heterogeneity can result from stochastic and responsive switches, as well as various genetic and epigenetic mechanisms. The development of phenotypic heterogeneity may create clonal populations that differ in their level of virulence, contribute to the formation of biofilms, and allow for antibiotic persistence within select morphological variants. This review delves into the current understanding of the molecular switching mechanisms underlying phenotypic heterogeneity, highlighting their roles in establishing infections caused by select bacterial pathogens.

Global transcription regulation revealed from dynamical correlations in time-resolved single-cell RNA sequencing

Single-cell transcriptomics reveals significant variations in transcriptional activity across cells. Yet, it remains challenging to identify mechanisms of transcription dynamics from static snapshots. It is thus still unknown what drives global transcription dynamics in single cells. We present a stochastic model of gene expression with cell size- and cell cycle-dependent rates in growing and dividing cells that harnesses temporal dimensions of single-cell RNA sequencing through metabolic labeling protocols and cel lcycle reporters. We develop a parallel and highly scalable approximate Bayesian computation method that corrects for technical variation and accurately quantifies absolute burst frequency, burst size, and degradation rate along the cell cycle at a transcriptome-wide scale. Using Bayesian model selection, we reveal scaling between transcription rates and cell size and unveil waves of gene regulation across the cell cycle-dependent transcriptome. Our study shows that stochastic modeling of dynamical correlations identifies global mechanisms of transcription regulation. A record of this paper's transparent peer review process is included in the supplemental information.

Direct single-cell observation of a key Escherichia coli cell-cycle oscillator

Initiation of DNA replication in Escherichia coli is coupled to cell size via the DnaA protein, whose activity is dependent on its nucleotide-bound state. However, the oscillations in DnaA activity have never been observed at the single-cell level. By measuring the volume-specific production rate of a reporter protein under control of a DnaA-regulated promoter, we could distinguish two distinct cell-cycle oscillators. The first, driven by both DnaA activity and SeqA repression, shows a causal relationship with cell size and divisions, similarly to initiation events. The second one, a reporter of DnaA activity alone, loses the synchrony and causality properties. Our results show that transient inhibition of gene expression by SeqA keeps the oscillation of volume-sensing DnaA activity in phase with the subsequent division event and suggest that DnaA activity peaks do not correspond directly to initiation events.

A phenomenological model of non-genomic variability of luminescent bacterial cells

The light emitted by a luminescent bacterium serves as a unique native channel of information regarding the intracellular processes within the individual cell. In the presence of highly sensitive equipment, it is possible to obtain the distribution of bacterial culture cells by the intensity of light emission, which correlates with the amount of luciferase in the cells. When growing on rich media, the luminescence intensity of individual cells of brightly luminous strains of the luminescent bacteria Photobacterium leiognathi and Ph. phosporeum reaches 104-105 quanta/s. The signal of such intensity can be registered using sensitive photometric equipment. All experiments were carried out with bacterial clones (genetically homogeneous populations). A typical dynamics of luminous bacterial cells distributions with respect to intensity of light emission at various stages of batch culture growth in a liquid medium was obtained. To describe experimental distributions, a phenomenological model that links the light of a bacterial cell with the history of events at the molecular level was constructed. The proposed phenomenological model with a minimum number of fitting parameters (1.5) provides a satisfactory description of the complex process of formation of cell distributions by luminescence intensity at different stages of bacterial culture growth. This may be an indication that the structure of the model describes some essential processes of the real system. Since in the process of division all cells go through the stage of release of all regulatory molecules from the DNA molecule, the resulting distributions can be attributed not only to luciferase, but also to other proteins of constitutive (and not only) synthesis.

The interplay between metabolic stochasticity and cAMP-CRP regulation in single E. coli cells

The inherent stochasticity of metabolism raises a critical question for understanding homeostasis: are cellular processes regulated in response to internal fluctuations? Here, we show that, in E. coli cells under constant external conditions, catabolic enzyme expression continuously responds to metabolic fluctuations. The underlying regulatory feedback is enabled by the cyclic AMP (cAMP) and cAMP receptor protein (CRP) system, which controls catabolic enzyme expression based on metabolite concentrations. Using single-cell microscopy, genetic constructs in which this feedback is disabled, and mathematical modeling, we show how fluctuations circulate through the metabolic and genetic network at sub-cell-cycle timescales. Modeling identifies four noise propagation modes, including one specific to CRP regulation. Together, these modes correctly predict noise circulation at perturbed cAMP levels. The cAMP-CRP system may thus have evolved to control internal metabolic fluctuations in addition to external growth conditions. We conjecture that second messengers may more broadly function to achieve cellular homeostasis.

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

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

Robustness of DNA looping across multiple cell divisions in individual bacteria

DNA looping has emerged as a central paradigm of transcriptional regulation, as it is shared across many living systems. One core property of DNA looping-based regulation is its ability to greatly enhance repression or activation of genes with only a few copies of transcriptional regulators. However, this property based on a small number of proteins raises the question of the robustness of such a mechanism with respect to the large intracellular perturbations taking place during growth and division of the cell. Here we address the issue of sensitivity to variations of intracellular parameters of gene regulation by DNA looping. We use the lac system as a prototype to experimentally identify the key features of the robustness of DNA looping in growing Escherichia coli cells. Surprisingly, we observe time intervals of tight repression spanning across division events, which can sometimes exceed 10 generations. Remarkably, the distribution of such long time intervals exhibits memoryless statistics that is mostly insensitive to repressor concentration, cell division events, and the number of distinct loops accessible to the system. By contrast, gene regulation becomes highly sensitive to these perturbations when DNA looping is absent. Using stochastic simulations, we propose that the observed robustness to division emerges from the competition between fast, multiple rebinding events of repressors and slow initiation rate of the RNA polymerase. We argue that fast rebinding events are a direct consequence of DNA looping that ensures robust gene repression across a range of intracellular perturbations.

OUP accepted manuscript

Many questions remain about the interplay between adaptive and neutral processes leading to genome expansion and the evolution of cellular complexity. Genome size appears to be tightly linked to the size of the regulatory repertoire of cells (van Nimwegen E. 2003. Scaling laws in the functional content of genomes. Trends Gen. 19(9):479–484). In the context of gene regulation, we here study the interplay between adaptive and nonadaptive forces on genome and regulatory network in a computational model of cell-cycle adaptation to different environments. Starting from the well-known Caulobacter crescentus network, we report on ten replicate in silico evolution experiments where cells evolve cell-cycle control by adapting to increasingly harsh spatial habitats.

We find adaptive expansion of the regulatory repertoire of cells. Having a large genome is inherently costly, but also allows for improved cell-cycle behavior. Replicates traverse different evolutionary trajectories leading to distinct eco-evolutionary strategies. In four replicates, cells evolve a generalist strategy to cope with a variety of nutrient levels; in two replicates, different specialist cells evolve for specific nutrient levels; in the remaining four replicates, an intermediate strategy evolves. These diverse evolutionary outcomes reveal the role of contingency in a system under strong selective forces.

This study shows that functionality of cells depends on the combination of regulatory network topology and genome organization. For example, the positions of dosage-sensitive genes are exploited to signal to the regulatory network when replication is completed, forming a de novo evolved cell cycle checkpoint. Our results underline the importance of the integration of multiple organizational levels to understand complex gene regulation and the evolution thereof.

Cis-Regulatory Logic Produces Gene-Expression Noise Describing Phenotypic Heterogeneity in Bacteria

Gene transcriptional process is random. It occurs in bursts and follows single-molecular kinetics. Intermittent bursts are measured based on their frequency and size. They influence temporal fluctuations in the abundance of total mRNA and proteins by generating distinct transcriptional variations referred to as “noise”. Noisy expression induces uncertainty because the association between transcriptional variation and the extent of gene expression fluctuation is ambiguous. The promoter architecture and remote interference of different cis-regulatory elements are the crucial determinants of noise, which is reflected in phenotypic heterogeneity. An alternative perspective considers that cellular parameters dictating genome-wide transcriptional kinetics follow a universal pattern. Research on noise and systematic perturbations of promoter sequences reinforces that both gene-specific and genome-wide regulation occur across species ranging from bacteria and yeast to animal cells. Thus, deciphering gene-expression noise is essential across different genomics applications. Amidst the mounting conflict, it is imperative to reconsider the scope, progression, and rational construction of diversified viewpoints underlying the origin of the noise. Here, we have established an indication connecting noise, gene expression variations, and bacterial phenotypic variability. This review will enhance the understanding of gene-expression noise in various scientific contexts and applications.

Cut the noise or couple up: Coordinating circadian and synthetic clocks

Circadian clocks are important to much of life on Earth and are of inherent interest to humanity, implicated in fields ranging from agriculture and ecology to developmental biology and medicine. New techniques show that it is not simply the presence of clocks, but coordination between them that is critical for complex physiological processes across the kingdoms of life. Recent years have also seen impressive advances in synthetic biology to the point where parallels can be drawn between synthetic biological and circadian oscillators. This review will emphasize theoretical and experimental studies that have revealed a fascinating dichotomy of coupling and heterogeneity among circadian clocks. We will also consolidate the fields of chronobiology and synthetic biology, discussing key design principles of their respective oscillators.

Coordination of gene expression noise with cell size: analytical results for agent-based models of growing cell populations

The chemical master equation and the Gillespie algorithm are widely used to model the reaction kinetics inside living cells. It is thereby assumed that cell growth and division can be modelled through effective dilution reactions and extrinsic noise sources. We here re-examine these paradigms through developing an analytical agent-based framework of growing and dividing cells accompanied by an exact simulation algorithm, which allows us to quantify the dynamics of virtually any intracellular reaction network affected by stochastic cell size control and division noise. We find that the solution of the chemical master equation-including static extrinsic noise-exactly agrees with the agent-based formulation when the network under study exhibits stochastic concentration homeostasis, a novel condition that generalizes concentration homeostasis in deterministic systems to higher order moments and distributions. We illustrate stochastic concentration homeostasis for a range of common gene expression networks. When this condition is not met, we demonstrate by extending the linear noise approximation to agent-based models that the dependence of gene expression noise on cell size can qualitatively deviate from the chemical master equation. Surprisingly, the total noise of the agent-based approach can still be well approximated by extrinsic noise models.

Disentangling Intrinsic and Extrinsic Gene Expression Noise in Growing Cells

Gene expression is a stochastic process. Despite the increase of protein numbers in growing cells, the protein concentrations are often found to be confined within small ranges throughout the cell cycle. Generally, the noise in protein concentration can be decomposed into an intrinsic and an extrinsic component, where the former vanishes for high expression levels. Considering the time trajectory of protein concentration as a random walker in the concentration space, an effective restoring force (with a corresponding "spring constant") must exist to prevent the divergence of concentration due to random fluctuations. In this work, we prove that the magnitude of the effective spring constant is directly related to the fraction of intrinsic noise in the total protein concentration noise. We show that one can infer the magnitude of intrinsic, extrinsic, and measurement noises of gene expression solely based on time-resolved data of protein concentration, without any a priori knowledge of the underlying gene expression dynamics. We apply this method to experimental data of single-cell bacterial gene expression. The results allow us to estimate the average copy numbers and the translation burst parameters of the studied proteins.

Dissecting the genetic basis of wheat blast resistance in the Brazilian wheat cultivar BR 18-Terena

BACKGROUND

Wheat blast, caused by Magnaporthe oryzae Triticum (MoT) pathotype, is a global threat to wheat (Triticum aestivum L.) production. Few blast resistance (R) genes have been identified to date, therefore assessing potential sources of resistance in wheat is important. The Brazilian wheat cultivar BR 18-Terena is considered one of the best sources of resistance to blast and has been widely used in Brazilian breeding programmes, however the underlying genetics of this resistance are unknown.

RESULTS

BR 18-Terena was used as the common parent in the development of two recombinant inbred line (RIL) F₆ populations with the Brazilian cultivars Anahuac 75 and BRS 179. Populations were phenotyped for resistance at the seedling and heading stage using the sequenced MoT isolate BR32, with transgressive segregation being observed. Genetic maps containing 1779 and 1318 markers, were produced for the Anahuac 75 × BR 18-Terena and BR 18-Terena × BRS 179 populations, respectively. Five quantitative trait loci (QTL) associated with seedling resistance, on chromosomes 2B, 4B (2 QTL), 5A and 6A, were identified, as were four QTL associated with heading stage resistance (1A, 2B, 4A and 5A). Seedling and heading stage QTL did not co-locate, despite a significant positive correlation between these traits, indicating that resistance at these developmental stages is likely to be controlled by different genes. BR 18-Terena provided the resistant allele for six QTL, at both developmental stages, with the largest phenotypic effect conferred by a QTL being 24.8% suggesting that BR 18-Terena possesses quantitative resistance. Haplotype analysis of 100 Brazilian wheat cultivars indicates that 11.0% of cultivars already possess a BR 18-Terena-like haplotype for more than one of the identified heading stage QTL.

CONCLUSIONS

This study suggests that BR 18-Terena possesses quantitative resistance to wheat blast, with nine QTL associated with resistance at either the seedling or heading stage being detected. Wheat blast resistance is also largely tissue-specific. Identification of durable quantitative resistances which can be combined with race-specific R gene-mediated resistance is critical to effectively control wheat blast. Collectively, this work facilitates marker-assisted selection to develop new varieties for cultivation in regions at risk from this emerging disease.

Contributions to the 'noise floor' in gene expression in a population of dividing cells

Experiments with cells reveal the existence of a lower bound for protein noise, the noise floor, in highly expressed genes. Its origins are still debated. We propose a minimal model of gene expression in a proliferating bacterial cell population. The model predicts the existence of a noise floor and it semi-quantitatively reproduces the curved shape of the experimental noise vs. mean protein concentration plots. When the cell volume increases in a different manner than does the mean protein copy number, the noise floor level is determined by the cell population’s age structure and by the dependence of the mean protein concentration on cell age. Additionally, the noise floor level may depend on a biological limit for the mean number of bursts in the cell cycle. In that case, the noise floor level depends on the burst size distribution width but it is insensitive to the mean burst size. Our model quantifies the contributions of each of these mechanisms to gene expression noise.

Emergence of Metabolite Provisioning as a By-Product of Evolved Biological Functions

Microbes commonly use metabolites produced by other organisms to compete effectively with others in their environment. As a result, microbial communities are composed of networks of metabolically interdependent organisms. How these networks evolve and shape population diversity, stability, and community function is a subject of active research. But how did these metabolic interactions develop initially? In particular, how and why are metabolites such as amino acids, cofactors, and nucleobases released for the benefit of others when there apparently is no incentive to do so? Here, we discuss the hypothesis that metabolite provisioning is not itself adaptive but rather can be a natural consequence of other evolved biological functions.

Microbes commonly use metabolites produced by other organisms to compete effectively with others in their environment. As a result, microbial communities are composed of networks of metabolically interdependent organisms. How these networks evolve and shape population diversity, stability, and community function is a subject of active research. But how did these metabolic interactions develop initially? In particular, how and why are metabolites such as amino acids, cofactors, and nucleobases released for the benefit of others when there apparently is no incentive to do so? Here, we discuss the hypothesis that metabolite provisioning is not itself adaptive but rather can be a natural consequence of other evolved biological functions. We outline two examples of metabolite provisioning as a by-product of other functions by considering cell lysis and regulated metabolite efflux outside their canonical roles and explore their potential to facilitate the emergence of interdependent metabolite sharing.

Models of protein production along the cell cycle: An investigation of possible sources of noise

In this article, we quantitatively study, through stochastic models, the effects of several intracellular phenomena, such as cell volume growth, cell division, gene replication as well as fluctuations of available RNA polymerases and ribosomes. These phenomena are indeed rarely considered in classic models of protein production and no relative quantitative comparison among them has been performed. The parameters for a large and representative class of proteins are determined using experimental measures. The main important and surprising conclusion of our study is to show that despite the significant fluctuations of free RNA polymerases and free ribosomes, they bring little variability to protein production contrary to what has been previously proposed in the literature. After verifying the robustness of this quite counter-intuitive result, we discuss its possible origin from a theoretical view, and interpret it as the result of a mean-field effect.

Existence, Transition, and Propagation of Intermediate Silencing States in Ribosomal DNA

The MET3 promoter (MET3pr) inserted into the silenced chromosome in budding yeast can overcome Sir2-dependent silencing upon induction and activate transcription in every single cell among a population. Despite the fact that MET3pr is turned on in all the cells, its activity still shows very high cell-to-cell variability. To understand the nature of such "gene expression noise," we followed the dynamics of the MET3pr-GFP expression inserted into ribosomal DNA (rDNA) using time-lapse microscopy. We found that the noisy "on" state is comprised of multiple substable states with discrete expression levels. These intermediate states stochastically transition between each other, with "up" transitions among different activated states occurring exclusively near the mitotic exit and "down" transitions occurring throughout the rest of the cell cycle. Such cell cycle dependence likely reflects the dynamic activity of the rDNA-specific RENT complex, as MET3pr-GFP expression in a telomeric locus does not have the same cell cycle dependence. The MET3pr-GFP expression in rDNA is highly correlated in mother and daughter cells after cell division, indicating that the silenced state in the mother cell is inherited in daughter cells. These states are disrupted by a brief repression and reset upon a second activation. Potential mechanisms behind these observations are further discussed.

Deciphering Metabolic Heterogeneity by Single-Cell Analysis

Single-cell analysis provides insights into cellular heterogeneity and dynamics of individual cells. This Feature highlights recent developments in key analytical techniques suited for single-cell metabolic analysis with a special focus on mass spectrometry-based analytical platforms and RNA-seq as well as imaging techniques that reveal stochasticity in metabolism.

Phenotypic heterogeneity of microbial populations under nutrient limitation

Phenotypic heterogeneity is a phenomenon in which genetically identical individuals have different characteristics. This behavior can also be found in bacteria, even if they grow as monospecies in well-mixed environments such as bioreactors. Here it is discussed how phenotypic heterogeneity is generated by internal factors and how it is promoted under nutrient-limited growth conditions. A better understanding of the molecular levels that control phenotypic heterogeneity could improve biotechnological production processes.

Exactly solvable model of gene expression in a proliferating bacterial cell population with stochastic protein bursts and protein partitioning

Many of the existing stochastic models of gene expression contain the first-order decay reaction term that may describe active protein degradation or dilution. If the model variable is interpreted as the molecule number, and not concentration, the decay term may also approximate the loss of protein molecules due to cell division as a continuous degradation process. The seminal model of that kind leads to gamma distributions of protein levels, whose parameters are defined by the mean frequency of protein bursts and mean burst size. However, such models (whether interpreted in terms of molecule numbers or concentrations) do not correctly account for the noise due to protein partitioning between daughter cells. We present an exactly solvable stochastic model of gene expression in cells dividing at random times, where we assume description in terms of molecule numbers with a constant mean protein burst size. The model is based on a population balance equation supplemented with protein production in random bursts. If protein molecules are partitioned equally between daughter cells, we obtain at steady state the analytical expressions for probability distributions similar in shape to gamma distributions, yet with quite different values of mean burst size and mean burst frequency than would result from fitting of the classical continuous-decay model to these distributions. For random partitioning of protein molecules between daughter cells, we obtain the moment equations for the protein number distribution and thus the analytical formulas for the squared coefficient of variation.

Noise propagation in an integrated model of bacterial gene expression and growth

In bacterial cells, gene expression, metabolism, and growth are highly interdependent and tightly coordinated. As a result, stochastic fluctuations in expression levels and instantaneous growth rate show intricate cross-correlations. These correlations are shaped by feedback loops, trade-offs and constraints acting at the cellular level; therefore a quantitative understanding requires an integrated approach. To that end, we here present a mathematical model describing a cell that contains multiple proteins that are each expressed stochastically and jointly limit the growth rate. Conversely, metabolism and growth affect protein synthesis and dilution. Thus, expression noise originating in one gene propagates to metabolism, growth, and the expression of all other genes. Nevertheless, under a small-noise approximation many statistical quantities can be calculated analytically. We identify several routes of noise propagation, illustrate their origins and scaling, and establish important connections between noise propagation and the field of metabolic control analysis. We then present a many-protein model containing >1000 proteins parameterized by previously measured abundance data and demonstrate that the predicted cross-correlations between gene expression and growth rate are in broad agreement with published measurements.

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.

Division rate, cell size and proteome allocation: impact on gene expression noise and implications for the dynamics of genetic circuits

The cell division rate, size and gene expression programmes change in response to external conditions. These global changes impact on average concentrations of biomolecule and their variability or noise. Gene expression is inherently stochastic, and noise levels of individual proteins depend on synthesis and degradation rates as well as on cell-cycle dynamics. We have modelled stochastic gene expression inside growing and dividing cells to study the effect of division rates on noise in mRNA and protein expression. We use assumptions and parameters relevant to Escherichia coli, for which abundant quantitative data are available. We find that coupling of transcription, but not translation rates to the rate of cell division can result in protein concentration and noise homeostasis across conditions. Interestingly, we find that the increased cell size at fast division rates, observed in E. coli and other unicellular organisms, buffers noise levels even for proteins with decreased expression at faster growth. We then investigate the functional importance of these regulations using gene regulatory networks that exhibit bi-stability and oscillations. We find that network topology affects robustness to changes in division rate in complex and unexpected ways. In particular, a simple model of persistence, based on global physiological feedback, predicts increased proportion of persister cells at slow division rates. Altogether, our study reveals how cell size regulation in response to cell division rate could help controlling gene expression noise. It also highlights that understanding circuits' robustness across growth conditions is key for the effective design of synthetic biological systems.

Division rate, cell size and proteome allocation: impact on gene expression noise and implications for the dynamics of genetic circuits

The cell division rate, size and gene expression programmes change in response to external conditions. These global changes impact on average concentrations of biomolecule and their variability or noise. Gene expression is inherently stochastic, and noise levels of individual proteins depend on synthesis and degradation rates as well as on cell-cycle dynamics. We have modelled stochastic gene expression inside growing and dividing cells to study the effect of division rates on noise in mRNA and protein expression. We use assumptions and parameters relevant to Escherichia coli, for which abundant quantitative data are available. We find that coupling of transcription, but not translation rates to the rate of cell division can result in protein concentration and noise homeostasis across conditions. Interestingly, we find that the increased cell size at fast division rates, observed in E. coli and other unicellular organisms, buffers noise levels even for proteins with decreased expression at faster growth. We then investigate the functional importance of these regulations using gene regulatory networks that exhibit bi-stability and oscillations. We find that network topology affects robustness to changes in division rate in complex and unexpected ways. In particular, a simple model of persistence, based on global physiological feedback, predicts increased proportion of persister cells at slow division rates. Altogether, our study reveals how cell size regulation in response to cell division rate could help controlling gene expression noise. It also highlights that understanding circuits' robustness across growth conditions is key for the effective design of synthetic biological systems.

Recent advances in understanding how rod-like bacteria stably maintain their cell shapes

Cell shape and cell volume are important for many bacterial functions. In recent years, we have seen a range of experimental and theoretical work that led to a better understanding of the determinants of cell shape and size. The roles of different molecular machineries for cell-wall expansion have been detailed and partially redefined, mechanical forces have been shown to influence cell shape, and new connections between metabolism and cell shape have been proposed. Yet the fundamental determinants of the different cellular dimensions remain to be identified. Here, we highlight some of the recent developments and focus on the determinants of rod-like cell shape and size in the well-studied model organisms Escherichia coli and Bacillus subtilis.

Statistics and simulation of growth of single bacterial cells: illustrations with B. subtilis and E. coli

The inherent stochasticity of molecular reactions prevents us from predicting the exact state of single-cells in a population. However, when a population grows at steady-state, the probability to observe a cell with particular combinations of properties is fixed. Here we validate and exploit existing theory on the statistics of single-cell growth in order to predict the probability of phenotypic characteristics such as cell-cycle times, volumes, accuracy of division and cell-age distributions, using real-time imaging data for Bacillus subtilis and Escherichia coli. Our results show that single-cell growth-statistics can accurately be predicted from a few basic measurements. These equations relate different phenotypic characteristics, and can therefore be used in consistency tests of experimental single-cell growth data and prediction of single-cell statistics. We also exploit these statistical relations in the development of a fast stochastic-simulation algorithm of single-cell growth and protein expression. This algorithm greatly reduces computational burden, by recovering the statistics of growing cell-populations from the simulation of only one of its lineages. Our approach is validated by comparison of simulations and experimental data. This work illustrates a methodology for the prediction, analysis and tests of consistency of single-cell growth and protein expression data from a few basic statistical principles.

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.

Taking chances and making mistakes: non-genetic phenotypic heterogeneity and its consequences for surviving in dynamic environments

Natural selection has shaped the strategies for survival and growth of microorganisms. The success of microorganisms depends not only on slow evolutionary tuning but also on the ability to adapt to unpredictable changes in their environment. In principle, adaptive strategies range from purely deterministic mechanisms to those that exploit the randomness intrinsic to many cellular and molecular processes. Depending on the environment and selective pressures, particular strategies can lie somewhere along this continuum. In recent years, non-genetic cell-to-cell differences have received a lot of attention, not least because of their potential impact on the ability of microbial populations to survive in dynamic environments. Using several examples, we describe the origins of spontaneous and induced mechanisms of phenotypic adaptation. We identify some of the commonalities of these examples and consider the potential role of chance and constraints in microbial phenotypic adaptation.

Robustness of synthetic oscillators in growing and dividing cells

Synthetic biology sets out to implement new functions in cells, and to develop a deeper understanding of biological design principles. Elowitz and Leibler [Nature (London) 403, 335 (2000)NATUAS0028-083610.1038/35002125] showed that by rational design of the reaction network, and using existing biological components, they could create a network that exhibits periodic gene expression, dubbed the repressilator. More recently, Stricker et al. [Nature (London) 456, 516 (2008)NATUAS0028-083610.1038/nature07389] presented another synthetic oscillator, called the dual-feedback oscillator, which is more stable. Detailed studies have been carried out to determine how the stability of these oscillators is affected by the intrinsic noise of the interactions between the components and the stochastic expression of their genes. However, as all biological oscillators reside in growing and dividing cells, an important question is how these oscillators are perturbed by the cell cycle. In previous work we showed that the periodic doubling of the gene copy numbers due to DNA replication can couple not only natural, circadian oscillators to the cell cycle [Paijmans et al., Proc. Natl. Acad. Sci. (USA) 113, 4063 (2016)PNASA60027-842410.1073/pnas.1507291113], but also these synthetic oscillators. Here we expand this study. We find that the strength of the locking between oscillators depends not only on the positions of the genes on the chromosome, but also on the noise in the timing of gene replication: noise tends to weaken the coupling. Yet, even in the limit of high levels of noise in the replication times of the genes, both synthetic oscillators show clear signatures of locking to the cell cycle. This work enhances our understanding of the design of robust biological oscillators inside growing and diving cells.

Intercellular Variability in Protein Levels from Stochastic Expression and Noisy Cell Cycle Processes

Inside individual cells, expression of genes is inherently stochastic and manifests as cell-to-cell variability or noise in protein copy numbers. Since proteins half-lives can be comparable to the cell-cycle length, randomness in cell-division times generates additional intercellular variability in protein levels. Moreover, as many mRNA/protein species are expressed at low-copy numbers, errors incurred in partitioning of molecules between two daughter cells are significant. We derive analytical formulas for the total noise in protein levels when the cell-cycle duration follows a general class of probability distributions. Using a novel hybrid approach the total noise is decomposed into components arising from i) stochastic expression; ii) partitioning errors at the time of cell division and iii) random cell-division events. These formulas reveal that random cell-division times not only generate additional extrinsic noise, but also critically affect the mean protein copy numbers and intrinsic noise components. Counter intuitively, in some parameter regimes, noise in protein levels can decrease as cell-division times become more stochastic. Computations are extended to consider genome duplication, where transcription rate is increased at a random point in the cell cycle. We systematically investigate how the timing of genome duplication influences different protein noise components. Intriguingly, results show that noise contribution from stochastic expression is minimized at an optimal genome-duplication time. Our theoretical results motivate new experimental methods for decomposing protein noise levels from synchronized and asynchronized single-cell expression data. Characterizing the contributions of individual noise mechanisms will lead to precise estimates of gene expression parameters and techniques for altering stochasticity to change phenotype of individual cells.

Inside individual cells, gene products often occur at low molecular counts and are subject to considerable stochastic fluctuations (noise) in copy numbers over time. An important consequence of noisy expression is that the level of a protein can vary considerably even among genetically identical cells exposed to the same environment. Such non-genetic phenotypic heterogeneity is physiologically relevant and critically influences diverse cellular processes. In addition to noise sources inherent in gene product synthesis, recent experimental studies have uncovered additional noise mechanisms that critically effect expression. For example, the time within the cell cycle when a gene duplicates, and the time taken to complete cell cycle are governed by random processes. The key contribution of this work is development of novel mathematical results quantifying how cell cycle-related noise sources combine with stochastic expression to drive intercellular variability in protein molecular counts. Derived formulas lead to many counterintuitive results, such as increasing randomness in the timing of cell division can lower noise in the level of a protein. Finally, these results inform experimental strategies to systematically dissect the contributions of different noise sources in the expression of a gene of interest.

Temporal and intrinsic factors of rifampicin tolerance in mycobacteria

Mycobacteria grow and divide asymmetrically, creating variability in growth pole age, growth properties, and antibiotic susceptibilities. Here, we investigate the importance of growth pole age and other growth properties in determining the spectrum of responses of Mycobacterium smegmatis to challenge with rifampicin. We used a combination of live-cell microscopy and modeling to prospectively identify subpopulations with altered rifampicin susceptibility. We found two subpopulations that had increased susceptibility. At the initiation of treatment, susceptible cells were either small and at early stages of the cell cycle, or large and in later stages of their cell cycle. In contrast to this temporal window of susceptibility, tolerance was associated with factors inherited at division: long birth length and mature growth poles. Thus, rifampicin response is complex and due to a combination of differences established from both asymmetric division and the timing of treatment relative to cell birth.