Individuality and slow dynamics in bacterial growth homeostasis

Mechanistic basis for non-exponential bacterial growth

Bacterial populations typically exhibit exponential growth under resource-rich conditions, yet individual cells often deviate from this pattern. Recent work has shown that the elongation rates of Escherichia coli and Caulobacter crescentus increase throughout the cell cycle (super-exponential growth), while Bacillus subtilis displays a mid-cycle minimum (convex growth), and Mycobacterium tuberculosis grows linearly. Here, we develop a single-cell model linking gene expression, proteome allocation, and mass growth to explain these diverse growth trajectories. By calibrating model parameters with experimental data, we show that DNA-proportional mRNA transcription produces near-exponential growth, whereas deviations from this proportionality yield the observed non-exponential growth patterns. Analysis of gene expression perturbations reveals that ribosome expression primarily controls dry mass growth rate, whereas envelope expression more strongly affects cell elongation rate. Fitting our model to single-cell experimental data reproduces convex, super-exponential, and linear modes of growth, demonstrating how envelope and ribosome expression schedules drive cell-cycle-specific behaviors. These findings provide a mechanistic basis for non-exponential single-cell growth and offer insights into how bacterial cells dynamically regulate elongation rates within each generation.

Evolutionary Advantage of Cell Size Control

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

Single-cell data reveal heterogeneity of investment in ribosomes across a bacterial population

Ribosomes are responsible for the synthesis of proteins, the major component of cellular biomass. Classical experiments have established a linear relationship between the fraction of resources invested in ribosomal proteins and the rate of balanced growth of a microbial population. Very little is known, however, about how the investment in ribosomes varies over individual cells in a population. We therefore extended the study of ribosomal resource allocation from populations to single cells, using a combination of time-lapse fluorescence microscopy and statistical inference. We found a large variability of ribosome concentrations and growth rates in conditions of balanced growth of the model bacterium Escherichia coli in a given medium, which cannot be accounted for by the population-level growth law. A large variability in the allocation of resources to ribosomes was also found during the transition of the bacteria from a poor to a rich growth medium. While some cells immediately adapt their ribosome synthesis rate to the new environment, others do so only gradually. Our results thus reveal a range of strategies for investing resources in the molecular machines at the heart of cellular self-replication. This raises the fundamental question whether the observed variability is an intrinsic consequence of the stochastic nature of the underlying biochemical processes or whether it improves the fitness of Escherichia coli in its natural environment.

The Brain's Best Kept Secret Is Its Degenerate Structure

Degeneracy is defined as multiple sets of solutions that can produce very similar system performance. Degeneracy is seen across phylogenetic scales, in all kinds of organisms. In neuroscience, degeneracy can be seen in the constellation of biophysical properties that produce a neuron's characteristic intrinsic properties and/or the constellation of mechanisms that determine circuit outputs or behavior. Here, we present examples of degeneracy at multiple levels of organization, from single-cell behavior, small circuits, large circuits, and, in cognition, drawing conclusions from work ranging from bacteria to human cognition. Degeneracy allows the individual-to-individual variability within a population that creates potential for evolution.

Nonlethal deleterious mutation-induced stress accelerates bacterial aging

Random mutagenesis, including when it leads to loss of gene function, is a key mechanism enabling microorganisms' long-term adaptation to new environments. However, loss-of-function mutations are often deleterious, triggering, in turn, cellular stress and complex homeostatic stress responses, called "allostasis," to promote cell survival. Here, we characterize the differential impacts of 65 nonlethal, deleterious single-gene deletions on Escherichia coli growth in three different growth environments. Further assessments of select mutants, namely, those bearing single adenosine triphosphate (ATP) synthase subunit deletions, reveal that mutants display reorganized transcriptome profiles that reflect both the environment and the specific gene deletion. We also find that ATP synthase α-subunit deleted (ΔatpA) cells exhibit elevated metabolic rates while having slower growth compared to wild-type (wt) E. coli cells. At the single-cell level, compared to wt cells, individual ΔatpA cells display near normal proliferation profiles but enter a postreplicative state earlier and exhibit a distinct senescence phenotype. These results highlight the complex interplay between genomic diversity, adaptation, and stress response and uncover an "aging cost" to individual bacterial cells for maintaining population-level resilience to environmental and genetic stress; they also suggest potential bacteriostatic antibiotic targets and -as select human genetic diseases display highly similar phenotypes, - a bacterial origin of some human diseases.

Effects of Molecular Noise on Cell Size Control

Cells employ control strategies to maintain a stable size. Dividing at a target size (the "sizer" strategy) is thought to produce the tightest size distribution. However, this result follows from phenomenological models that ignore the molecular mechanisms required to implement the strategy. Here we investigate a simple mechanistic model for exponentially growing cells whose division is triggered at a molecular abundance threshold. We find that size noise inherits the molecular noise and is consequently minimized not by the sizer but by the "adder" strategy, where a cell divides after adding a target amount to its birth size. We derive a lower bound on size noise that agrees with publicly available data from six microfluidic studies on Escherichia coli bacteria.

Chaos in a bacterial stress response

Cellular responses to environmental changes are often highly heterogeneous and exhibit seemingly random dynamics. The astonishing insight of chaos theory is that such unpredictable patterns can, in principle, arise without the need for any random processes, i.e., purely deterministically without noise. However, while chaos is well understood in mathematics and physics, its role in cell biology remains unclear because the complexity and noisiness of biological systems make testing difficult. Here, we show that chaos explains the heterogeneous response of Escherichia coli cells to oxidative stress. We developed a theoretical model of the gene expression dynamics and demonstrate that chaotic behavior arises from rapid molecular feedbacks that are coupled with cell growth dynamics and cell-cell interactions. Based on theoretical predictions, we then designed single-cell experiments to show we can shift gene expression from periodic oscillations to chaos on demand. Our work suggests that chaotic gene regulation can be employed by cell populations to generate strong and variable responses to changing environments.

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.

Bacterial cell-size changes resulting from altering the relative expression of Min proteins

The timing of cell division, and thus cell size in bacteria, is determined in part by the accumulation dynamics of the protein FtsZ, which forms the septal ring. FtsZ localization depends on membrane-associated Min proteins, which inhibit FtsZ binding to the cell pole membrane. Changes in the relative concentrations of Min proteins can disrupt FtsZ binding to the membrane, which in turn can delay cell division until a certain cell size is reached, in which the dynamics of Min proteins frees the cell membrane long enough to allow FtsZ ring formation. Here, we study the effect of Min proteins relative expression on the dynamics of FtsZ ring formation and cell size in individual Escherichia coli bacteria. Upon inducing overexpression of minE, cell size increases gradually to a new steady-state value. Concurrently, the time required to initiate FtsZ ring formation grows as the size approaches the new steady-state, at which point the ring formation initiates as early as before induction. These results highlight the contribution of Min proteins to cell size control, which may be partially responsible for the size fluctuations observed in bacterial populations, and may clarify how the size difference acquired during asymmetric cell division is offset.

Multigenerational memory in bacterial size control

Cells maintain a stable size as they grow and divide. Inspired by the available experimental data, most proposed models for size homeostasis assume size-control mechanisms that act on a timescale of one generation. Such mechanisms lead to short-lived autocorrelations in size fluctuations that decay within less than two generations. However, recent evidence from comparing sister lineages suggests that correlations in size fluctuations can persist for many generations. Here we develop a minimal model that explains these seemingly contradictory results. Our model proposes that different environments result in different control parameters, leading to distinct inheritance patterns. Multigenerational memory is revealed in constant environments but obscured when averaging over many different environments. Inferring the parameters of our model from Escherichia coli size data in microfluidic experiments, we recapitulate the observed statistics. Our paper elucidates the impact of the environment on cell homeostasis and growth and division dynamics.

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

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

Super-exponential growth and stochastic size dynamics in rod-like bacteria

Proliferating bacterial cells exhibit stochastic growth and size dynamics, but the regulation of noise in bacterial growth and morphogenesis remains poorly understood. A quantitative understanding of morphogenetic noise control, and how it changes under different growth conditions, would provide better insights into cell-to-cell variability and intergenerational fluctuations in cell physiology. Using multigenerational growth and width data of single Escherichia coli and Caulobacter crescentus cells, we deduce the equations governing growth and size dynamics of rod-like bacterial cells. Interestingly, we find that both E. coli and C. crescentus cells deviate from exponential growth within the cell cycle. In particular, the exponential growth rate increases during the cell cycle irrespective of nutrient or temperature conditions. We propose a mechanistic model that explains the emergence of super-exponential growth from autocatalytic production of ribosomes coupled to the rate of cell elongation and surface area synthesis. Using this new model and statistical inference on large datasets, we construct the Langevin equations governing cell growth and size dynamics of E. coli cells in different nutrient conditions. The single-cell level model predicts how noise in intragenerational and intergenerational processes regulate variability in cell morphology and generation times, revealing quantitative strategies for cellular resource allocation and morphogenetic noise control in different growth conditions.

Evolutionary scaling of maximum growth rate with organism size

Data from nearly 1000 species reveal the upper bound to rates of biomass production achievable by natural selection across the Tree of Life. For heterotrophs, maximum growth rates scale positively with organism size in bacteria but negatively in eukaryotes, whereas for phototrophs, the scaling is negligible for cyanobacteria and weakly negative for eukaryotes. These results have significant implications for understanding the bioenergetic consequences of the transition from prokaryotes to eukaryotes, and of the expansion of some groups of the latter into multicellularity. The magnitudes of the scaling coefficients for eukaryotes are significantly lower than expected under any proposed physical-constraint model. Supported by genomic, bioenergetic, and population-genetic data and theory, an alternative hypothesis for the observed negative scaling in eukaryotes postulates that growth-diminishing mutations with small effects passively accumulate with increasing organism size as a consequence of associated increases in the power of random genetic drift. In contrast, conditional on the structural and functional features of ribosomes, natural selection has been able to promote bacteria with the fastest possible growth rates, implying minimal conflicts with both bioenergetic constraints and random genetic drift. If this extension of the drift-barrier hypothesis is correct, the interpretations of comparative studies of biological traits that have traditionally ignored differences in population-genetic environments will require revisiting.

Optimization and Fabrication of Multi-Level Microchannels for Long-Term Imaging of Bacterial Growth and Expansion

Bacteria are unicellular organisms whose length is usually around a few micrometers. Advances in microfabrication techniques have enabled the design and implementation of microdevices to confine and observe bacterial colony growth. Microstructures hosting the bacteria and microchannels for nutrient perfusion usually require separate microfabrication procedures due to different feature size requirements. This fact increases the complexity of device integration and assembly process. Furthermore, long-term imaging of bacterial dynamics over tens of hours requires stability in the microscope focusing mechanism to ensure less than one-micron drift in the focal axis. In this work, we design and fabricate an integrated multi-level, hydrodynamically-optimized microfluidic chip to study long-term Escherichia coli population dynamics in confined microchannels. Reliable long-term microscopy imaging and analysis has been limited by focus drifting and ghost effect, probably caused by the shear viscosity changes of aging microscopy immersion oil. By selecting a microscopy immersion oil with the most stable viscosity, we demonstrate successful captures of focally stable time-lapse bacterial images for ≥72 h. Our fabrication and imaging methodology should be applicable to other single-cell studies requiring long-term imaging.

Multiple timescales in bacterial growth homeostasis

In balanced exponential growth, bacteria maintain many properties statistically stable for a long time: cell size, cell cycle time, and more. As these are strongly coupled variables, it is not a-priori obvious which are directly regulated and which are stabilized through interactions. Here, we address this problem by separating timescales in bacterial single-cell dynamics. Disentangling homeostatic set points from fluctuations around them reveals that some variables, such as growth-rate, cell size and cycle time, are "sloppy" with highly volatile set points. Quantifying the relative contribution of environmental and internal sources, we find that sloppiness is primarily driven by the environment. Other variables such as fold-change define "stiff" combinations of coupled variables with robust set points. These results are manifested geometrically as a control manifold in the space of variables: set points span a wide range of values within the manifold, whereas out-of-manifold deviations are constrained. Our work offers a generalizable data-driven approach for identifying control variables in a multidimensional system.

A unified framework for measuring selection on cellular lineages and traits

Intracellular states probed by gene expression profiles and metabolic activities are intrinsically noisy, causing phenotypic variations among cellular lineages. Understanding the adaptive and evolutionary roles of such variations requires clarifying their linkage to population growth rates. Extending a cell lineage statistics framework, here we show that a population's growth rate can be expanded by the cumulants of a fitness landscape that characterize how fitness distributes in a population. The expansion enables quantifying the contribution of each cumulant, such as variance and skewness, to population growth. We introduce a function that contains all the essential information of cell lineage statistics, including mean lineage fitness and selection strength. We reveal a relation between fitness heterogeneity and population growth rate response to perturbation. We apply the framework to experimental cell lineage data from bacteria to mammalian cells, revealing distinct levels of growth rate gain from fitness heterogeneity across environments and organisms. Furthermore, third or higher order cumulants' contributions are negligible under constant growth conditions but could be significant in regrowing processes from growth-arrested conditions. We identify cellular populations in which selection leads to an increase of fitness variance among lineages in retrospective statistics compared to chronological statistics. The framework assumes no particular growth models or environmental conditions, and is thus applicable to various biological phenomena for which phenotypic heterogeneity and cellular proliferation are important.

Protein concentration fluctuations in the high expression regime: Taylor's law and its mechanistic origin

Protein concentration in a living cell fluctuates over time due to noise in growth and division processes. In the high expression regime, variance of the protein concentration in a cell was found to scale with the square of the mean, which belongs to a general phenomenon called Taylor's law (TL). To understand the origin for these fluctuations, we measured protein concentration dynamics in single E. coli cells from a set of strains with a variable expression of fluorescent proteins. The protein expression is controlled by a set of constitutive promoters with different strength, which allows to change the expression level over 2 orders of magnitude without introducing noise from fluctuations in transcription regulators. Our data confirms the square TL, but the prefactor A has a cell-to-cell variation independent of the promoter strength. Distributions of the normalized protein concentration for different promoters are found to collapse onto the same curve. To explain these observations, we used a minimal mechanistic model to describe the stochastic growth and division processes in a single cell with a feedback mechanism for regulating cell division. In the high expression regime where extrinsic noise dominates, the model reproduces our experimental results quantitatively. By using a mean-field approximation in the minimal model, we showed that the stochastic dynamics of protein concentration is described by a Langevin equation with multiplicative noise. The Langevin equation has a scale invariance which is responsible for the square TL. By solving the Langevin equation, we obtained an analytical solution for the protein concentration distribution function that agrees with experiments. The solution shows explicitly how the prefactor A depends on strength of different noise sources, which explains its cell-to-cell variability. By using this approach to analyze our single-cell data, we found that the noise in production rate dominates the noise from cell division. The deviation from the square TL in the low expression regime can also be captured in our model by including intrinsic noise in the production rate.

Exponential trajectories, cell size fluctuations, and the adder property in bacteria follow from simple chemical dynamics and division control

Experiments on steady-state bacterial cultures have uncovered several quantitative regularities at the system level. These include, first, the exponential growth of cell size with time and the balanced growth of intracellular chemicals between cell birth and division, which are puzzling given the nonlinear and decentralized chemical dynamics in the cell. We model a cell as a set of chemical populations undergoing nonlinear mass action kinetics in a container whose volume is a linear function of the chemical populations. This turns out to be a special class of dynamical systems that generically has attractors in which all populations grow exponentially with time at the same rate. This explains exponential balanced growth of bacterial cells without invoking any regulatory mechanisms and suggests that this could be a robust property of protocells as well. Second, we consider the hypothesis that cells commit themselves to division when a certain internal chemical population reaches a threshold of N molecules. We show that this hypothesis leads to a simple explanation of some of the variability observed across cells in a bacterial culture. In particular, it reproduces the adder property of cell size fluctuations observed recently in E. coli; the observed correlations among interdivision time, birth volume, and added volume in a generation; and the observed scale of the fluctuations (CV ≈ 10-30%) when N is between 10 and 100. Third, upon including a suitable regulatory mechanism that optimizes the growth rate of the cell, the model reproduces the observed bacterial growth laws including the dependence of the growth rate and ribosomal protein fraction on the medium. Thus, the models provide a framework for unifying diverse aspects of bacterial growth physiology under one roof. They also suggest new questions for experimental and theoretical enquiry.

Roadmap on biology in time varying environments

Biological organisms experience constantly changing environments, from sudden changes in physiology brought about by feeding, to the regular rising and setting of the Sun, to ecological changes over evolutionary timescales. Living organisms have evolved to thrive in this changing world but the general principles by which organisms shape and are shaped by time varying environments remain elusive. Our understanding is particularly poor in the intermediate regime with no separation of timescales, where the environment changes on the same timescale as the physiological or evolutionary response. Experiments to systematically characterize the response to dynamic environments are challenging since such environments are inherently high dimensional. This roadmap deals with the unique role played by time varying environments in biological phenomena across scales, from physiology to evolution, seeking to emphasize the commonalities and the challenges faced in this emerging area of research.

Bacterial Growth Control Mechanisms Inferred from Multivariate Statistical Analysis of Single-Cell Measurements

Analysis of single-cell measurements of bacterial growth and division often relied on testing preconceived models of cell size control mechanisms. Such an approach could limit the scope of data analysis and prevent us from uncovering new information. Here, we take an "agnostic" approach by applying regression methods to multiple simultaneously measured cellular variables, which allow us to infer dependencies among those variables from their apparent correlations. Besides previously observed correlations attributed to particular cell size control mechanisms, we identify dependencies that point to potentially new mechanisms. In particular, cells born smaller than their sisters tend to grow faster and make up for the size difference acquired during division. We also find that sister cells are correlated beyond what single-cell, size-control models predict. These trends are consistently found in repeat experiments, although the dependencies vary quantitatively. Such variation highlights the sensitivity of cell growth to environmental variations and the limitation of currently used experimental setups.

Non-genetic inheritance restraint of cell-to-cell variation

Heterogeneity in physical and functional characteristics of cells (e.g. size, cycle time, growth rate, protein concentration) proliferates within an isogenic population due to stochasticity in intracellular biochemical processes and in the distribution of resources during divisions. Conversely, it is limited in part by the inheritance of cellular components between consecutive generations. Here we introduce a new experimental method for measuring proliferation of heterogeneity in bacterial cell characteristics, based on measuring how two sister cells become different from each other over time. Our measurements provide the inheritance dynamics of different cellular properties, and the 'inertia' of cells to maintain these properties along time. We find that inheritance dynamics are property specific and can exhibit long-term memory (∼10 generations) that works to restrain variation among cells. Our results can reveal mechanisms of non-genetic inheritance in bacteria and help understand how cells control their properties and heterogeneity within isogenic cell populations.

Bacterial cell proliferation: from molecules to cells

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

Cell Cycle Heritability and Localization Phase Transition in Growing Populations

The cell cycle duration is a variable cellular phenotype that underlies long-term population growth and age structures. By analyzing the stationary solutions of a branching process with heritable cell division times, we demonstrate the existence of a phase transition, which can be continuous or first order, by which a nonzero fraction of the population becomes localized at a minimal division time. Just below the transition, we demonstrate the coexistence of localized and delocalized age-structure phases and the power law decay of correlation functions. Above it, we observe the self-synchronization of cell cycles, collective divisions, and the slow "aging" of population growth rates.

Filtering input fluctuations in intensity and in time underlies stochastic transcriptional pulses without feedback

Stochastic pulsatile dynamics have been observed in an increasing number of biological circuits with known mechanism involving feedback control and bistability. Surprisingly, recent single-cell experiments in Escherichia coli flagellar synthesis showed that flagellar genes are activated in stochastic pulses without the means of feedback. However, the mechanism for pulse generation in these feedbackless circuits has remained unclear. Here, by developing a system-level stochastic model constrained by a large set of single-cell E. coli flagellar synthesis data from different strains and mutants, we identify the general underlying design principles for generating stochastic transcriptional pulses without feedback. Our study shows that an inhibitor (YdiV) of the transcription factor (FlhDC) creates a monotonic ultrasensitive switch that serves as a digital filter to eliminate small-amplitude FlhDC fluctuations. Furthermore, we find that the high-frequency (fast) fluctuations of FlhDC are filtered out by integration over a timescale longer than the timescale of the input fluctuations. Together, our results reveal a filter-and-integrate design for generating stochastic pulses without feedback. This filter-and-integrate mechanism enables a general strategy for cells to avoid premature activation of the expensive downstream gene expression by filtering input fluctuations in both intensity and time so that the system only responds to input signals that are both strong and persistent.

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.

Bacterial Growth: Cell-Cycle Dependent Growth-Rate Homeostasis

In the study of bacterial growth, the prevailing conclusion is that cells grow exponentially at a constant rate throughout the cell cycle. Using a new approach, Nordholt et al. reveal that bacterial growth is biphasic; immediately after division, the cell grows linearly, transitioning to exponential growth towards the end of the cell cycle.

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.

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.

Heterogeneity in efflux pump expression predisposes antibiotic-resistant cells to mutation

Antibiotic resistance is often the result of mutations that block drug activity; however, bacteria also evade antibiotics by transiently expressing genes such as multidrug efflux pumps. A crucial question is whether transient resistance can promote permanent genetic changes. Previous studies have established that antibiotic treatment can select tolerant cells that then mutate to achieve permanent resistance. Whether these mutations result from antibiotic stress or preexist within the population is unclear. To address this question, we focused on the multidrug pump AcrAB-TolC. Using time-lapse microscopy, we found that cells with higher acrAB expression have lower expression of the DNA mismatch repair gene mutS, lower growth rates, and higher mutation frequencies. Thus, transient antibiotic resistance from elevated acrAB expression can promote spontaneous mutations within single cells.

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.

Antibiotic export by efflux pumps affects growth of neighboring bacteria

Cell-cell interactions play an important role in bacterial antibiotic resistance. Here, we asked whether neighbor proximity is sufficient to generate single-cell variation in antibiotic resistance due to local differences in antibiotic concentrations. To test this, we focused on multidrug efflux pumps because recent studies have revealed that expression of pumps is heterogeneous across populations. Efflux pumps can export antibiotics, leading to elevated resistance relative to cells with low or no pump expression. In this study, we co-cultured cells with and without AcrAB-TolC pump expression and used single-cell time-lapse microscopy to quantify growth rate as a function of a cell’s neighbors. In inhibitory concentrations of chloramphenicol, we found that cells lacking functional efflux pumps (ΔacrB) grow more slowly when they are surrounded by cells with AcrAB-TolC pumps than when surrounded by ΔacrB cells. To help explain our experimental results, we developed an agent-based mathematical model, which demonstrates the impact of neighbors based on efflux efficiency. Our findings hold true for co-cultures of Escherichia coli with and without pump expression and also in co-cultures of E. coli and Salmonella typhumirium. These results show how drug export and local microenvironments play a key role in defining single-cell level antibiotic resistance.