Inferring fitness landscapes and selection on phenotypic states from single-cell genealogical data

Phenotypic resistant single-cell characteristics under recurring ampicillin antibiotic exposure in Escherichia coli

Non-heritable, phenotypic drug resistance toward antibiotics challenges antibiotic therapies. Characteristics of such phenotypic resistance have implications for the evolution of heritable resistance. Diverse forms of phenotypic resistance have been described, but phenotypic resistance characteristics remain less explored than genetic resistance. Here, we add novel combinations of single-cell characteristics of phenotypic resistant E. coli cells and compare those to characteristics of susceptible cells of the parental population by exposure to different levels of recurrent ampicillin antibiotic. Contrasting expectations, we did not find commonly described characteristics of phenotypic resistant cells that arrest growth or near growth. We find that under ampicillin exposure, phenotypic resistant cells reduced their growth rate by about 50% compared to growth rates prior to antibiotic exposure. The growth reduction is a delayed alteration to antibiotic exposure, suggesting an induced response and not a stochastic switch or caused by a predetermined state as frequently described. Phenotypic resistant cells exhibiting constant slowed growth survived best under ampicillin exposure and, contrary to expectations, not only fast-growing cells suffered high mortality triggered by ampicillin but also growth-arrested cells. Our findings support diverse modes of phenotypic resistance, and we revealed resistant cell characteristics that have been associated with enhanced genetically fixed resistance evolution, which supports claims of an underappreciated role of phenotypic resistant cells toward genetic resistance evolution. A better understanding of phenotypic resistance will benefit combatting genetic resistance by developing and engulfing effective anti-phenotypic resistance strategies.

IMPORTANCE

Antibiotic resistance is a major challenge for modern medicine. Aside from genetic resistance to antibiotics, phenotypic resistance that is not heritable might play a crucial role for the evolution of antibiotic resistance. Using a highly controlled microfluidic system, we characterize single cells under recurrent exposure to antibiotics. Fluctuating antibiotic exposure is likely experienced under common antibiotic therapies. These phenotypic resistant cell characteristics differ from previously described phenotypic resistance, highlighting the diversity of modes of resistance. The phenotypic characteristics of resistant cells we identify also imply that such cells might provide a stepping stone toward genetic resistance, thereby causing treatment failure.

Feedback between stochastic gene networks and population dynamics enables cellular decision-making

Phenotypic selection occurs when genetically identical cells are subject to different reproductive abilities due to cellular noise. Such noise arises from fluctuations in reactions synthesizing proteins and plays a crucial role in how cells make decisions and respond to stress or drugs. We propose a general stochastic agent-based model for growing populations capturing the feedback between gene expression and cell division dynamics. We devise a finite state projection approach to analyze gene expression and division distributions and infer selection from single-cell data in mother machines and lineage trees. We use the theory to quantify selection in multi-stable gene expression networks and elucidate that the trade-off between phenotypic switching and selection enables robust decision-making essential for synthetic circuits and developmental lineage decisions. Using live-cell data, we demonstrate that combining theory and inference provides quantitative insights into bet-hedging-like response to DNA damage and adaptation during antibiotic exposure in Escherichia coli.

Stochastic chemical kinetics of cell fate decision systems: From single cells to populations and back

Stochastic chemical kinetics is a widely used formalism for studying stochasticity of chemical reactions inside single cells. Experimental studies of reaction networks are generally performed with cells that are part of a growing population, yet the population context is rarely taken into account when models are developed. Models that neglect the population context lose their validity whenever the studied system influences traits of cells that can be selected in the population, a property that naturally arises in the complex interplay between single-cell and population dynamics of cell fate decision systems. Here, we represent such systems as absorbing continuous-time Markov chains. We show that conditioning on non-absorption allows one to derive a modified master equation that tracks the time evolution of the expected population composition within a growing population. This allows us to derive consistent population dynamics models from a specification of the single-cell process. We use this approach to classify cell fate decision systems into two types that lead to different characteristic phases in emerging population dynamics. Subsequently, we deploy the gained insights to experimentally study a recurrent problem in biology: how to link plasmid copy number fluctuations and plasmid loss events inside single cells to growth of cell populations in dynamically changing environments.

Generalization of Powell's results to population out of steady state

Since the seminal work of Powell, the relationships between the population growth rate, the probability distributions of generation time, and the distribution of cell age have been known for the bacterial population in a steady state of exponential growth. Here we generalize these relationships to include an unsteady (transient) state for both the batch culture and the mother machine experiment. In particular, we derive a time-dependent Euler-Lotka equation (relating the generation-time distributions to the population growth rate) and a generalization of the inequality between the mean generation time and the population doubling time. To do this, we use a model proposed by Lebowitz and Rubinow, in which each cell is described by its age and generation time. We show that our results remain valid for a class of more complex models that use other state variables in addition to cell age and generation time, as long as the integration of these additional variables reduces the model to Lebowitz-Rubinow form. As an application of this formalism, we calculate the fitness landscapes for phenotypic traits (cell age, generation time) in a population that is not growing exponentially. We clarify that the known fitness landscape formula for the cell age as a phenotypic trait is an approximation to the exact time-dependent formula.

Statistical theory of asymmetric damage segregation in clonal cell populations

Asymmetric damage segregation (ADS) is ubiquitous among unicellular organisms: After a mother cell divides, its two daughter cells receive sometimes slightly, sometimes strongly different fractions of damaged proteins accumulated in the mother cell. Previous studies demonstrated that ADS provides a selective advantage over symmetrically dividing cells by rejuvenating and perpetuating the population as a whole. In this work we focus on the statistical properties of damage in individual lineages and the overall damage distributions in growing populations for a variety of ADS models with different rules governing damage accumulation, segregation, and the lifetime dependence on damage. We show that for a large class of deterministic ADS rules the trajectories of damage along the lineages are chaotic, and the distributions of damage in cells born at a given time asymptotically becomes fractal. By exploiting the analogy of linear ADS models with the Iterated Function Systems known in chaos theory, we derive the Frobenius-Perron equation for the stationary damage density distribution and analytically compute the damage distribution moments and fractal dimensions. We also investigate nonlinear and stochastic variants of ADS models and show the robustness of the salient features of the damage distributions.

Statistical Theory of Asymmetric Damage Segregation in Clonal Cell Populations

Asymmetric damage segregation (ADS) is ubiquitous among unicellular organisms: After a mother cell divides, its two daughter cells receive sometimes slightly, sometimes strongly different fractions of damaged proteins accumulated in the mother cell. Previous studies demonstrated that ADS provides a selective advantage over symmetrically dividing cells by rejuvenating and perpetuating the population as a whole. In this work we focus on the statistical properties of damage in individual lineages and the overall damage distributions in growing populations for a variety of ADS models with different rules governing damage accumulation, segregation, and the lifetime dependence on damage. We show that for a large class of deterministic ADS rules the trajectories of damage along the lineages are chaotic, and the distributions of damage in cells born at a given time asymptotically becomes fractal. By exploiting the analogy of linear ADS models with the Iterated Function Systems known in chaos theory, we derive the Frobenius-Perron equation for the stationary damage density distribution and analytically compute the damage distribution moments and fractal dimensions. We also investigate nonlinear and stochastic variants of ADS models and show the robustness of the salient features of the damage distributions.

Patterns of interdivision time correlations reveal hidden cell cycle factors

The time taken for cells to complete a round of cell division is a stochastic process controlled, in part, by intracellular factors. These factors can be inherited across cellular generations which gives rise to, often non-intuitive, correlation patterns in cell cycle timing between cells of different family relationships on lineage trees. Here, we formulate a framework of hidden inherited factors affecting the cell cycle that unifies known cell cycle control models and reveals three distinct interdivision time correlation patterns: aperiodic, alternator, and oscillator. We use Bayesian inference with single-cell datasets of cell division in bacteria, mammalian and cancer cells, to identify the inheritance motifs that underlie these datasets. From our inference, we find that interdivision time correlation patterns do not identify a single cell cycle model but generally admit a broad posterior distribution of possible mechanisms. Despite this unidentifiability, we observe that the inferred patterns reveal interpretable inheritance dynamics and hidden rhythmicity of cell cycle factors. This reveals that cell cycle factors are commonly driven by circadian rhythms, but their period may differ in cancer. Our quantitative analysis thus reveals that correlation patterns are an emergent phenomenon that impact cell proliferation and these patterns may be altered in disease.

Analytical cell size distribution: lineage-population bias and parameter inference

We derive analytical steady-state cell size distributions for size-controlled cells in single-lineage experiments, such as the mother machine, which are fundamentally different from batch cultures where populations of cells grow freely. For exponential single-cell growth, characterizing most bacteria, the lineage-population bias is obtained explicitly. In addition, if volume is evenly split between the daughter cells at division, we show that cells are on average smaller in populations than in lineages. For more general power-law growth rates and deterministic volume partitioning, both symmetric and asymmetric, we derive the exact lineage distribution. This solution is in good agreement with Escherichia coli mother machine data and can be used to infer cell cycle parameters such as the strength of the size control and the asymmetry of the division. When introducing stochastic volume partitioning, we derive the large-size and small-size tails of the lineage distribution and show that the lineage-population bias only depends on the single-cell growth rate. These asymptotic behaviours are extended to the adder model of cell size control. When considering noisy single-cell growth rate, we derive the large-size lineage and population distributions. Finally, we show that introducing noise, either on the volume partitioning or on the single-cell growth rate, can cancel the lineage-population bias.

Cell size homeostasis under the circadian regulation of cell division in cyanobacteria

Bacterial cells maintain their characteristic cell size over many generations. Several rod-shaped bacteria, such as Escherichia coli and the cyanobacteria Synechococcus elongatus, divide after adding a constant length to their length at birth. Through this division control known as the adder mechanism, perturbation in cell length due to physiological fluctuation decays over generations at a rate of 2^-1 per cell division. However, previous experiments have shown that the circadian clock in cyanobacteria reduces cell division frequency at a specific time of day under constant light. This circadian gating should modulate the division control by the adder mechanism, but its significance remains unknown. Here we address how the circadian gating affects cell length, doubling time, and cell length stability in cyanobacteria by using mathematical models. We show that a cell subject to circadian gating grows for a long time, and gives birth to elongated daughter cells. These elongated daughter cells grow faster than the previous generation, as elongation speed is proportional to cell length and divide in a short time before the next gating. Hence, the distributions of doubling time and cell length become bimodal, as observed in experimental data. Interestingly, the average doubling time over the population of cells is independent of gating because the extension of doubling time by gating is compensated by its reduction in the subsequent generation. On the other hand, average cell length is increased by gating, suggesting that the circadian clock controls cell length. We then show that the decay rate of perturbation in cell length depends on the ratio of delay in division by the gating τ_G to the average doubling time τ₀ as [Formula: see text] . We estimated τ_G≈2.5, τ₀≈13.6 hours, and τ_G/τ₀≈0.18 from experimental data, indicating that a long doubling time in cyanobacteria maintains the decay rate similar to that of the adder mechanism. Thus, our analysis suggests that the acquisition of the circadian clock during evolution did not impose a constraint on cell size homeostasis in cyanobacteria.

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.

Density fluctuations, homeostasis, and reproduction effects in bacteria

Single-cells grow by increasing their biomass and size. Here, we report that while mass and size accumulation rates of single Escherichia coli cells are exponential, their density and, thus, the levels of macromolecular crowding fluctuate during growth. As such, the average rates of mass and size accumulation of a single cell are generally not the same, but rather cells differentiate into increasing one rate with respect to the other. This differentiation yields a density homeostasis mechanism that we support mathematically. Further, we observe that density fluctuations can affect the reproduction rates of single cells, suggesting a link between the levels of macromolecular crowding with metabolism and overall population fitness. We detail our experimental approach and the “invisible” microfluidic arrays that enabled increased precision and throughput. Infections and natural communities start from a few cells, thus, emphasizing the significance of density-fluctuations when taking non-genetic variability into consideration.

Quantitative imaging, invisible microfluidics, and mathematical models demonstrate how the density of single E. coli cells fluctuates during the cell cycle, unmasking key homeostasis and population fitness effects.

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.

Generalized Euler-Lotka equation for correlated cell divisions

Cell division times in microbial populations display significant fluctuations that impact the population growth rate in a nontrivial way. If fluctuations are uncorrelated among different cells, the population growth rate is predicted by the Euler-Lotka equation, which is a classic result in mathematical biology. However, cell division times can be significantly correlated, due to physical properties of cells that are passed through generations. In this Letter, we derive an equation remarkably similar to the Euler-Lotka equation which is valid in the presence of correlations. Our exact result is based on large deviation theory and does not require particularly strong assumptions on the underlying dynamics. We apply our theory to a phenomenological model of bacterial cell division in E. coli and to experimental data. We find that the discrepancy between the growth rate predicted by the Euler-Lotka equation and our generalized version is relatively small, but large enough to be measurable by our approach.

Reconstructing an epigenetic landscape using a genetic pulling approach

Cells use genetic switches to shift between alternate stable gene expression states, e.g., to adapt to new environments or to follow a developmental pathway. Conceptually, these stable phenotypes can be considered as attractive states on an epigenetic landscape with phenotypic changes being transitions between states. Measuring these transitions is challenging because they are both very rare in the absence of appropriate signals and very fast. As such, it has proved difficult to experimentally map the epigenetic landscapes that are widely believed to underly developmental networks. Here, we introduce a nonequilibrium perturbation method to help reconstruct a regulatory network's epigenetic landscape. We derive the mathematical theory needed and then use the method on simulated data to reconstruct the landscapes. Our results show that with a relatively small number of perturbation experiments it is possible to recover an accurate representation of the true epigenetic landscape. We propose that our theory provides a general method by which epigenetic landscapes can be studied. Finally, our theory suggests that the total perturbation impulse required to induce a switch between metastable states is a fundamental quantity in developmental dynamics.

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.

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.

Large Deviation Principle Linking Lineage Statistics to Fitness in Microbial Populations

In exponentially proliferating populations of microbes, the population doubles at a rate less than the average doubling time of a single-cell due to variability at the single-cell level. It is known that the distribution of generation times obtained from a single lineage is, in general, insufficient to determine a population's growth rate. Is there an explicit relationship between observables obtained from a single lineage and the population growth rate? We show that a population's growth rate can be represented in terms of averages over isolated lineages. This lineage representation is related to a large deviation principle that is a generic feature of exponentially proliferating populations. Due to the large deviation structure of growing populations, the number of lineages needed to obtain an accurate estimate of the growth rate depends exponentially on the duration of the lineages, leading to a nonmonotonic convergence of the estimate, which we verify in both synthetic and experimental data sets.

Fluctuation relations and fitness landscapes of growing cell populations

We construct a pathwise formulation of a growing population of cells, based on two different samplings of lineages within the population, namely the forward and backward samplings. We show that a general symmetry relation, called fluctuation relation relates these two samplings, independently of the model used to generate divisions and growth in the cell population. These relations lead to estimators of the population growth rate, which can be very efficient as we demonstrate by an analysis of a set of mother machine data. These fluctuation relations lead to general and important inequalities between the mean number of divisions and the doubling time of the population. We also study the fitness landscape, a concept based on the two samplings mentioned above, which quantifies the correlations between a phenotypic trait of interest and the number of divisions. We obtain explicit results when the trait is the age or the size, for age and size-controlled models.

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.

Linking lineage and population observables in biological branching processes

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

Cell Size Regulation Induces Sustained Oscillations in the Population Growth Rate

We study the effect of correlations in generation times on the dynamics of population growth of microorganisms. We show that any nonzero correlation that is due to cell-size regulation, no matter how small, induces long-term oscillations in the population growth rate. The population only reaches its steady state when we include the often-neglected variability in the growth rates of individual cells. We discover that the relaxation timescale of the population to its steady state is determined by the distribution of single-cell growth rates and is surprisingly independent of details of the division process such as the noise in the timing of division and the mechanism of cell-size regulation. We validate the predictions of our model using existing experimental data and propose an experimental method to measure single-cell growth variability by observing how long it takes for the population to reach its steady state or balanced growth.

Toward Experimental Evolution with Giant Vesicles

Experimental evolution in chemical models of cells could reveal the fundamental mechanisms of cells today. Various chemical cell models, water-in-oil emulsions, oil-on-water droplets, and vesicles have been constructed in order to conduct research on experimental evolution. In this review, firstly, recent studies with these candidate models are introduced and discussed with regards to the two hierarchical directions of experimental evolution (chemical evolution and evolution of a molecular self-assembly). Secondly, we suggest giant vesicles (GVs), which have diameters larger than 1 µm, as promising chemical cell models for studying experimental evolution. Thirdly, since technical difficulties still exist in conventional GV experiments, recent developments of microfluidic devices to deal with GVs are reviewed with regards to the realization of open-ended evolution in GVs. Finally, as a future perspective, we link the concept of messy chemistry to the promising, unexplored direction of experimental evolution in GVs.

Fitness effects of altering gene expression noise in Saccharomyces cerevisiae

Gene expression noise is an evolvable property of biological systems that describes differences in expression among genetically identical cells in the same environment. Prior work has shown that expression noise is heritable and can be shaped by selection, but the impact of variation in expression noise on organismal fitness has proven difficult to measure. Here, we quantify the fitness effects of altering expression noise for the TDH3 gene in Saccharomyces cerevisiae. We show that increases in expression noise can be deleterious or beneficial depending on the difference between the average expression level of a genotype and the expression level maximizing fitness. We also show that a simple model relating single-cell expression levels to population growth produces patterns consistent with our empirical data. We use this model to explore a broad range of average expression levels and expression noise, providing additional insight into the fitness effects of variation in expression noise.

Making sense of snapshot data: ergodic principle for clonal cell populations

Population growth is often ignored when quantifying gene expression levels across clonal cell populations. We develop a framework for obtaining the molecule number distributions in an exponentially growing cell population taking into account its age structure. In the presence of generation time variability, the average acquired across a population snapshot does not obey the average of a dividing cell over time, apparently contradicting ergodicity between single cells and the population. Instead, we show that the variation observed across snapshots with known cell age is captured by cell histories, a single-cell measure obtained from tracking an arbitrary cell of the population back to the ancestor from which it originated. The correspondence between cells of known age in a population with their histories represents an ergodic principle that provides a new interpretation of population snapshot data. We illustrate the principle using analytical solutions of stochastic gene expression models in cell populations with arbitrary generation time distributions. We further elucidate that the principle breaks down for biochemical reactions that are under selection, such as the expression of genes conveying antibiotic resistance, which gives rise to an experimental criterion with which to probe selection on gene expression fluctuations.

Individuality and slow dynamics in bacterial growth homeostasis

Microbial cells go through repeated cycles of growth and division. These cycles are not perfect: the time and size at division can fluctuate from one cycle to the next. Still, cell size is kept tightly controlled, and fluctuations do not accumulate to large deviations. How this control is implemented in single cells is still not fully understood. We performed experiments that follow individual bacteria in microfluidic traps for hundreds of generations. This enables us to identify distinct individual dynamic properties that are maintained over many cycles of growth and division. Surprisingly, we find that each cell suppresses fluctuations with a different strength; this variability defines an “individual” behavior for each cell, which is inherited along many generations.

Microbial growth and division are fundamental processes relevant to many areas of life science. Of particular interest are homeostasis mechanisms, which buffer growth and division from accumulating fluctuations over multiple cycles. These mechanisms operate within single cells, possibly extending over several division cycles. However, all experimental studies to date have relied on measurements pooled from many distinct cells. Here, we disentangle long-term measured traces of individual cells from one another, revealing subtle differences between temporal and pooled statistics. By analyzing correlations along up to hundreds of generations, we find that the parameter describing effective cell size homeostasis strength varies significantly among cells. At the same time, we find an invariant cell size, which acts as an attractor to all individual traces, albeit with different effective attractive forces. Despite the common attractor, each cell maintains a distinct average size over its finite lifetime with suppressed temporal fluctuations around it, and equilibration to the global average size is surprisingly slow (>150 cell cycles). To show a possible source of variable homeostasis strength, we construct a mathematical model relying on intracellular interactions, which integrates measured properties of cell size with those of highly expressed proteins. Effective homeostasis strength is then influenced by interactions and by noise levels and generally varies among cells. A predictable and measurable consequence of variable homeostasis strength appears as distinct oscillatory patterns in cell size and protein content over many generations. We discuss implications of our results to understanding mechanisms controlling division in single cells and their characteristic timescales.

Mycobacteria Modify Their Cell Size Control under Sub-Optimal Carbon Sources

The decision to divide is the most important one that any cell must make. Recent single cell studies suggest that most bacteria follow an “adder” model of cell size control, incorporating a fixed amount of cell wall material before dividing. Mycobacteria, including the causative agent of tuberculosis Mycobacterium tuberculosis, are known to divide asymmetrically resulting in heterogeneity in growth rate, doubling time, and other growth characteristics in daughter cells. The interplay between asymmetric cell division and adder size control has not been extensively investigated. Moreover, the impact of changes in the environment on growth rate and cell size control have not been addressed for mycobacteria. Here, we utilize time-lapse microscopy coupled with microfluidics to track live Mycobacterium smegmatis cells as they grow and divide over multiple generations, under a variety of growth conditions. We demonstrate that, under optimal conditions, M. smegmatis cells robustly follow the adder principle, with constant added length per generation independent of birth size, growth rate, and inherited pole age. However, the nature of the carbon source induces deviations from the adder model in a manner that is dependent on pole age. Understanding how mycobacteria maintain cell size homoeostasis may provide crucial targets for the development of drugs for the treatment of tuberculosis, which remains a leading cause of global mortality.