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

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.

Effective bet-hedging through growth rate dependent stability

Microbes in the wild face highly variable and unpredictable environments and are naturally selected for their average growth rate across environments. Apart from using sensory regulatory systems to adapt in a targeted manner to changing environments, microbes employ bet-hedging strategies where cells in an isogenic population switch stochastically between alternative phenotypes. Yet, bet-hedging suffers from a fundamental trade-off: Increasing the phenotype-switching rate increases the rate at which maladapted cells explore alternative phenotypes but also increases the rate at which cells switch out of a well-adapted state. Consequently, it is currently believed that bet-hedging strategies are effective only when the number of possible phenotypes is limited and when environments last for sufficiently many generations. However, recent experimental results show that gene expression noise generally decreases with growth rate, suggesting that phenotype-switching rates may systematically decrease with growth rate. Such growth rate dependent stability (GRDS) causes cells to be more explorative when maladapted and more phenotypically stable when well-adapted, and we show that GRDS can almost completely overcome the trade-off that limits bet-hedging, allowing for effective adaptation even when environments are diverse and change rapidly. We further show that even a small decrease in switching rates of faster-growing phenotypes can substantially increase long-term fitness of bet-hedging strategies. Together, our results suggest that stochastic strategies may play an even bigger role for microbial adaptation than hitherto appreciated.

Emergent expression of fitness-conferring genes by phenotypic selection

Genotypic and phenotypic adaptation is the consequence of ongoing natural selection in populations and is key to predicting and preventing drug resistance. Whereas classic antibiotic persistence is all-or-nothing, here we demonstrate that an antibiotic resistance gene displays linear dose-responsive selection for increased expression in proportion to rising antibiotic concentration in growing Escherichia coli populations. Furthermore, we report the potentially wide-spread nature of this form of emergent gene expression (EGE) by instantaneous phenotypic selection process under bactericidal and bacteriostatic antibiotic treatment, as well as an amino acid synthesis pathway enzyme under a range of auxotrophic conditions. We propose an analogy to Ohm's law in electricity (V = IR), where selection pressure acts similarly to voltage (V), gene expression to current (I), and resistance (R) to cellular machinery constraints and costs. Lastly, mathematical modeling using agent-based models of stochastic gene expression in growing populations and Bayesian model selection reveal that the EGE mechanism requires variability in gene expression within an isogenic population, and a cellular "memory" from positive feedbacks between growth and expression of any fitness-conferring gene. Finally, we discuss the connection of the observed phenomenon to a previously described general fluctuation-response relationship in biology.

Bacillus subtilis Histidine Kinase KinC Activates Biofilm Formation by Controlling Heterogeneity of Single-Cell Responses

In Bacillus subtilis, biofilm and sporulation pathways are both controlled by a master regulator, Spo0A, which is activated by phosphorylation via a phosphorelay-a cascade of phosphotransfer reactions commencing with autophosphorylation of histidine kinases KinA, KinB, KinC, KinD, and KinE. However, it is unclear how the kinases, despite acting via the same regulator, Spo0A, differentially regulate downstream pathways, i.e., how KinA mainly activates sporulation genes and KinC mainly activates biofilm genes. In this work, we found that KinC also downregulates sporulation genes, suggesting that KinC has a negative effect on Spo0A activity. To explain this effect, with a mathematical model of the phosphorelay, we revealed that unlike KinA, which always activates Spo0A, KinC has distinct effects on Spo0A at different growth stages: during fast growth, KinC acts as a phosphate source and activates Spo0A, whereas during slow growth, KinC becomes a phosphate sink and contributes to decreasing Spo0A activity. However, under these conditions, KinC can still increase the population-mean biofilm matrix production activity. In a population, individual cells grow at different rates, and KinC would increase the Spo0A activity in the fast-growing cells but reduce the Spo0A activity in the slow-growing cells. This mechanism reduces single-cell heterogeneity of Spo0A activity, thereby increasing the fraction of cells that activate biofilm matrix production. Thus, KinC activates biofilm formation by controlling the fraction of cells activating biofilm gene expression. IMPORTANCE In many bacterial and eukaryotic systems, multiple cell fate decisions are activated by a single master regulator. Typically, the activities of the regulators are controlled posttranslationally in response to different environmental stimuli. The mechanisms underlying the ability of these regulators to control multiple outcomes are not understood in many systems. By investigating the regulation of Bacillus subtilis master regulator Spo0A, we show that sensor kinases can use a novel mechanism to control cell fate decisions. By acting as a phosphate source or sink, kinases can interact with one another and provide accurate regulation of the phosphorylation level. Moreover, this mechanism affects the cell-to-cell heterogeneity of the transcription factor activity and eventually determines the fraction of different cell types in the population. These results demonstrate the importance of intercellular heterogeneity for understanding the effects of genetic perturbations on cell fate decisions. Such effects can be applicable to a wide range of cellular systems.

The effect of natural selection on the propagation of protein expression noise to bacterial growth

In bacterial cells, protein expression is a highly stochastic process. Gene expression noise moreover propagates through the cell and adds to fluctuations in the cellular growth rate. A common intuition is that, due to their relatively high noise amplitudes, proteins with a low mean expression level are the most important drivers of fluctuations in physiological variables. In this work, we challenge this intuition by considering the effect of natural selection on noise propagation. Mathematically, the contribution of each protein species to the noise in the growth rate depends on two factors: the noise amplitude of the protein’s expression level, and the sensitivity of the growth rate to fluctuations in that protein’s concentration. We argue that natural selection, while shaping mean abundances to increase the mean growth rate, also affects cellular sensitivities. In the limit in which cells grow optimally fast, the growth rate becomes most sensitive to fluctuations in highly abundant proteins. This causes abundant proteins to overall contribute strongly to the noise in the growth rate, despite their low noise levels. We further explore this result in an experimental data set of protein abundances, and test key assumptions in an evolving, stochastic toy model of cellular growth.

Gene expression in bacterial cells is intrinsically stochastic: copy numbers of all proteins vary between genetically identical cells, even in a homogeneous environment. Such noise in gene expression affects metabolic fluxes and even propagates to the cellular level. Indeed, also the growth rate of individual cells, an important proxy for fitness, fluctuates strongly. This beckons the question as to which protein species contribute most to the noise in the cell’s growth rate. We here derive general mathematical predictions stating that if cells have been optimised by evolution to grow fast, abundant protein species contribute most to the noise in the growth rate. This result is counter-intuitive, because the noise levels in the expression of those highly expressed proteins are small.

Microbial metabolic noise

From the time a cell was first placed under the microscope, it became apparent that identifying two clonal cells that "look" identical is extremely challenging. Since then, cell-to-cell differences in shape, size, and protein content have been carefully examined, informing us of the ultimate limits that hinder two cells from occupying an identical phenotypic state. Here, we present recent experimental and computational evidence that similar limits emerge also in cellular metabolism. These limits pertain to stochastic metabolic dynamics and, thus, cell-to-cell metabolic variability, including the resulting adapting benefits. We review these phenomena with a focus on microbial metabolism and conclude with a brief outlook on the potential relationship between metabolic noise and adaptive evolution. This article is categorized under: Metabolic Diseases > Computational Models Metabolic Diseases > Biomedical Engineering.

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

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

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

An analytical theory of balanced cellular growth

The biological fitness of microbes is largely determined by the rate with which they replicate their biomass composition. Mathematical models that maximize this balanced growth rate while accounting for mass conservation, reaction kinetics, and limits on dry mass per volume are inevitably non-linear. Here, we develop a general theory for such models, termed Growth Balance Analysis (GBA), which provides explicit expressions for protein concentrations, fluxes, and growth rates. These variables are functions of the concentrations of cellular components, for which we calculate marginal fitness costs and benefits that are related to metabolic control coefficients. At maximal growth rate, the net benefits of all concentrations are equal. Based solely on physicochemical constraints, GBA unveils fundamental quantitative principles of cellular resource allocation and growth; it accurately predicts the relationship between growth rates and ribosome concentrations in E. coli and yeast and between growth rate and dry mass density in E. coli.

Gene expression noise in a complex artificial toxin expression system

Gene expression is an intrinsically stochastic process. Fluctuations in transcription and translation lead to cell-to-cell variations in mRNA and protein levels affecting cellular function and cell fate. Here, using fluorescence time-lapse microscopy, we quantify noise dynamics in an artificial operon in Escherichia coli, which is based on the native operon of ColicinE2, a toxin. In the natural system, toxin expression is controlled by a complex regulatory network; upon induction of the bacterial SOS response, ColicinE2 is produced (cea gene) and released (cel gene) by cell lysis. Using this ColicinE2-based operon, we demonstrate that upon induction of the SOS response noise of cells expressing the operon is significantly lower for the (mainly) transcriptionally regulated gene cea compared to the additionally post-transcriptionally regulated gene cel. Likewise, we find that mutations affecting the transcriptional regulation by the repressor LexA do not significantly alter the population noise, whereas specific mutations to post-transcriptionally regulating units, strongly influence noise levels of both genes. Furthermore, our data indicate that global factors, such as the plasmid copy number of the operon encoding plasmid, affect gene expression noise of the entire operon. Taken together, our results provide insights on how noise in a native toxin-producing operon is controlled and underline the importance of post-transcriptional regulation for noise control in this system.

Segregostat: a novel concept to control phenotypic diversification dynamics on the example of Gram-negative bacteria

Controlling and managing the degree of phenotypic diversification of microbial populations is a challenging task. This task not only requires detailed knowledge regarding diversification mechanisms but also advanced technical set-ups for the real-time analyses and control of population behaviour on single-cell level. In this work, set-up, design and operation of the so called segregostat are described which, in contrast to a traditional chemostat, allows the control of phenotypic diversification of microbial populations over time. Two exemplary case studies will be discussed, i.e. phenotypic diversification dynamics of Eschericia coli and Pseudomonas putida based on outer membrane permeabilization, emphasizing the applicability and versatility of the proposed approach. Upon nutrient limitation, cell population tends to diversify into several subpopulations exhibiting distinct phenotypic features (non-permeabilized and permeabilized cells). Online analysis leads to the determination of the ratio between cells in these two states, which in turn triggers the addition of glucose pulses in order to maintain a predefined diversification ratio. These results prove that phenotypic diversification can be controlled by means of defined pulse-frequency modulation within continuously running bioreactor set-ups. This lays the foundation for systematic studies, not only of phenotypic diversification but also for all processes where dynamics single-cell approaches are required, such as synthetic co-culture processes.

Sources, propagation and consequences of stochasticity in cellular growth

Growth impacts a range of phenotypic responses. Identifying the sources of growth variation and their propagation across the cellular machinery can thus unravel mechanisms that underpin cell decisions. We present a stochastic cell model linking gene expression, metabolism and replication to predict growth dynamics in single bacterial cells. Alongside we provide a theory to analyse stochastic chemical reactions coupled with cell divisions, enabling efficient parameter estimation, sensitivity analysis and hypothesis testing. The cell model recovers population-averaged data on growth-dependence of bacterial physiology and how growth variations in single cells change across conditions. We identify processes responsible for this variation and reconstruct the propagation of initial fluctuations to growth and other processes. Finally, we study drug-nutrient interactions and find that antibiotics can both enhance and suppress growth heterogeneity. Our results provide a predictive framework to integrate heterogeneous data and draw testable predictions with implications for antibiotic tolerance, evolutionary and synthetic biology.

The drivers of growth rate variability in bacteria are yet unknown. Here, the authors present a theory to predict the growth dynamics of individual cells and use a stochastic cell model integrating metabolism, gene expression and replication to identify the processes that underlie growth variation.