Noise-driven growth rate gain in clonal cellular populations

Smectic-like bundle formation of planktonic bacteria upon nutrient starvation

Bacteria aggregate through various intercellular interactions to build biofilms, but the effect of environmental changes on them remains largely unexplored. Here, by using an experimental device that overcomes past difficulties, we observed the collective response of Escherichia coli aggregates to dynamic changes in the growth conditions. We discovered that nutrient starvation caused bacterial cells to arrange themselves into bundle-shaped clusters, developing a structure akin to that of smectic liquid crystals. The degree of the smectic-like bundle order was evaluated by a deep learning approach. Our experiments suggest that both the depletion attraction by extracellular polymeric substances and the growth arrest are essential for the bundle formation. Since these effects of nutrient starvation at the single-cell level are common to many bacterial species, bundle formation might also be a common collective behavior that bacterial cells may exhibit under harsh environments.

From noisy cell size control to population growth: When variability can be beneficial

Single-cell experiments revealed substantial variability in generation times, growth rates, but also in birth and division sizes between genetically identical cells. Understanding how these fluctuations determine the fitness of the population, i.e., its growth rate, is necessary in any quantitative theory of evolution. Here, we develop a biologically relevant model which accounts for the stochasticity in single-cell growth rates, birth sizes, and division sizes. We derive expressions for the population growth rate and mean birth size in the population in terms of single-cell fluctuations. Allowing division sizes to fluctuate reveals how the mechanism of cell size control (timer, sizer, and adder) influences population growth. Surprisingly, we find that fluctuations in single-cell growth rates can be beneficial for population growth when slow-growing cells tend to divide at smaller sizes than fast-growing cells. Our framework is not limited to exponentially growing cells like Escherichia coli, and we derive similar expressions for cells with linear and bilinear growth laws, such as Mycobacterium tuberculosis and fission yeast Schizosaccharomyces pombe, respectively.

DeepKymoTracker: A tool for accurate construction of cell lineage trees for highly motile cells

Time-lapse microscopy has long been used to record cell lineage trees. Successful construction of a lineage tree requires tracking and preserving the identity of multiple cells across many images. If a single cell is misidentified the identity of all its progeny will be corrupted and inferences about heritability may be incorrect. Successfully avoiding such identity errors is challenging, however, when studying highly-motile cells such as T lymphocytes which readily change shape from one image to the next. To address this problem, we developed DeepKymoTracker, a pipeline for combined tracking and segmentation. Central to DeepKymoTracker is the use of a seed, a marker for each cell which transmits information about cell position and identity between sets of images during tracking, as well as between tracking and segmentation steps. The seed allows a 3D convolutional neural network (CNN) to detect and associate cells across several consecutive images in an integrated way, reducing the risk of a single poor image corrupting cell identity. DeepKymoTracker was trained extensively on synthetic and experimental T lymphocyte images. It was benchmarked against five publicly available, automatic analysis tools and outperformed them in almost all respects. The software is written in pure Python and is freely available. We suggest this tool is particularly suited to the tracking of cells in suspension, whose fast motion makes lineage assembly particularly difficult.

Diversification of single-cell growth dynamics under starvation influences subsequent reproduction in a clonal bacterial population

Most of the microbes in nature infrequently receive nutrients and are thus in slow- or non-growing states. How quickly they can resume their growth upon an influx of new resources is crucial to occupy environmental niches. Isogenic microbial populations are known to harbor only a fraction of cells with rapid growth resumption, yet little is known about the physiological characteristics of those cells and their emergence in the population. Here, we tracked growth of individual Escherichia coli cells in populations under fluctuating nutrient conditions. We found that shifting from high- to low-nutrient conditions caused stalling of cell growth with few cells continuing to divide extremely slowly, a process which was dependent on lipid turnover. Resuming high-nutrient inflow after low-nutrient conditions resulted in cells resuming growth and division, but with different lag times and leading to varying progeny. The history of cell growth during low-nutrient but not high-nutrient conditions was determinant for resumption of growth, which cellular genealogy analysis suggested to originate from inherited physiological differences. Our results demonstrate that cellular growth dynamics become diverse by nutrient limitations, under which a fraction of cells experienced a particular growth history can reproduce progeny with new resources in the future.

Dimensional reduction and adaptation-development-evolution relation in evolved biological systems

Living systems are complex and hierarchical, with diverse components at different scales, yet they sustain themselves, grow, and evolve over time. How can a theory of such complex biological states be developed? Here we note that for a hierarchical biological system to be robust, it must achieve consistency between micro-scale (e.g., molecular) and macro-scale (e.g., cellular) phenomena. This allows for a universal theory of adaptive change in cells based on biological robustness and consistency between cellular growth and molecular replication. Here, we show how adaptive changes in high-dimensional phenotypes (biological states) are constrained to low-dimensional space, leading to the derivation of a macroscopic law for cellular states. The theory is then extended to evolution, leading to proportionality between evolutionary and environmental responses, as well as proportionality between phenotypic variances due to noise and due to genetic changes. The universality of the results across several models and experiments is demonstrated. Then, by further extending the theory of evolutionary dimensional reduction to multicellular systems, the relationship between multicellular development and evolution, in particular, the developmental hourglass, is demonstrated. Finally, the possibility of collapse of dimensional reduction under nutrient limitation is discussed.

Fragmented micro-growth habitats present opportunities for alternative competitive outcomes

Bacteria in nature often thrive in fragmented environments, like soil pores, plant roots or plant leaves, leading to smaller isolated habitats, shared with fewer species. This spatial fragmentation can significantly influence bacterial interactions, affecting overall community diversity. To investigate this, we contrast paired bacterial growth in tiny picoliter droplets (1-3 cells per 35 pL up to 3-8 cells per species in 268 pL) with larger, uniform liquid cultures (about 2 million cells per 140 µl). We test four interaction scenarios using different bacterial strains: substrate competition, substrate independence, growth inhibition, and cell killing. In fragmented environments, interaction outcomes are more variable and sometimes even reverse compared to larger uniform cultures. Both experiments and simulations show that these differences stem mostly from variation in initial cell population growth phenotypes and their sizes. These effects are most significant with the smallest starting cell populations and lessen as population size increases. Simulations suggest that slower-growing species might survive competition by increasing growth variability. Our findings reveal how microhabitat fragmentation promotes diverse bacterial interaction outcomes, contributing to greater species diversity under competitive conditions.

Asynchronous abundance fluctuations can drive giant genotype frequency fluctuations

Large stochastic population abundance fluctuations are ubiquitous across the tree of life1-7, impacting the predictability of population dynamics and influencing eco-evolutionary outcomes. It has generally been thought that these large abundance fluctuations do not strongly impact evolution, as the relative frequencies of alleles in the population will be unaffected if the abundance of all alleles fluctuate in unison. However, we argue that large abundance fluctuations can lead to significant genotype frequency fluctuations if different genotypes within a population experience these fluctuations asynchronously. By serially diluting mixtures of two closely related E. coli strains, we show that such asynchrony can occur, leading to giant frequency fluctuations that far exceed expectations from models of genetic drift. We develop a flexible, effective model that explains the abundance fluctuations as arising from correlated offspring numbers between individuals, and the large frequency fluctuations result from even slight decoupling in offspring numbers between genotypes. This model accurately describes the observed abundance and frequency fluctuation scaling behaviors. Our findings suggest chaotic dynamics underpin these giant fluctuations, causing initially similar trajectories to diverge exponentially; subtle environmental changes can be magnified, leading to batch correlations in identical growth conditions. Furthermore, we present evidence that such decoupling noise is also present in mixed-genotype S. cerevisiae populations. We demonstrate that such decoupling noise can strongly influence evolutionary outcomes, in a manner distinct from genetic drift. Given the generic nature of asynchronous fluctuations, we anticipate that they are widespread in biological populations, significantly affecting evolutionary and ecological dynamics.

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.

Scaling of stochastic growth and division dynamics: A comparative study of individual rod-shaped cells in the Mother Machine and SChemostat platforms

Microfluidic platforms enable long-term quantification of stochastic behaviors of individual bacterial cells under precisely controlled growth conditions. Yet, quantitative comparisons of physiological parameters and cell behaviors of different microorganisms in different experimental and device modalities is not available due to experiment-specific details affecting cell physiology. To rigorously assess the effects of mechanical confinement, we designed, engineered, and performed side-by-side experiments under otherwise identical conditions in the Mother Machine (with confinement) and the SChemostat (without confinement), using the latter as the ideal comparator. We established a protocol to cultivate a suitably engineered rod-shaped mutant of Caulobacter crescentus in the Mother Machine and benchmarked the differences in stochastic growth and division dynamics with respect to the SChemostat. While the single-cell growth rate distributions are remarkably similar, the mechanically confined cells in the Mother Machine experience a substantial increase in interdivision times. However, we find that the division ratio distribution precisely compensates for this increase, which in turn reflects identical emergent simplicities governing stochastic intergenerational homeostasis of cell sizes across device and experimental configurations, provided the cell sizes are appropriately mean-rescaled in each condition. Our results provide insights into the nature of the robustness of the bacterial growth and division machinery.

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.

Synergistic and antagonistic effects of deterministic and stochastic cell-cell variations

By diversifying, cells in a clonal population can together overcome the limits of individuals. Diversity in single-cell growth rates allows the population to survive environmental stresses, such as antibiotics, and grow faster than the undiversified population. These functional cell-cell variations can arise stochastically, from noise in biochemical reactions, or deterministically, by asymmetrically distributing damaged components. While each of the mechanisms is well understood, the effect of the combined mechanisms is unclear. To evaluate the contribution of the deterministic component we developed a mathematical model by mapping the growing population to the Ising model. To analyze the combined effects of stochastic and deterministic contributions we introduced the analytical results of the Ising-mapping into an Euler-Lotka framework. Model results, confirmed by simulations and experimental data, show that deterministic cell-cell variations increase near-linearly with stress. As a consequence, we predict that the gain in population doubling time from cell-cell variations is primarily stochastic at low stress but may cross over to deterministic at higher stresses. Furthermore, we find that while the deterministic component minimizes population damage, stochastic variations antagonize this effect. Together our results may help identifying stress-tolerant pathogenic cells and thus inspire novel antibiotic strategies.

Kobayashi T. Population dynamics models for various forms of adaptation

Adaptability to changing environments is one of the universal characteristics of living organisms. Because individual modes of adaptation are diverse, a unified understanding of these diverse modes is essential to comprehend adaptation. Adaptations can be categorized from at least two perspectives with respect to information. One is the passivity and activity of adaptation and the other is the type of information transmission. In Darwinian natural selection, organisms are selected among randomly generated traits under which individual organisms are passive in the sense that they do not process any environmental information. On the other hand, organisms can also adapt by sensing their environment and changing their traits. This is an active adaptation in that it makes use of environmental information. In terms of information transfer, adaptation through phenotypic heterogeneity, such as bacterial bet-hedging, is intragenerational in which traits are not passed on to the next generation. In contrast, adaptation through genetic diversity is intergenerational. The theory of population dynamics enables us to unify these various modes of adaptations and their properties can be analyzed qualitatively and quantitatively using techniques from quantitative genetics and information thermodynamics. In addition, such methods can be applied to situations where organisms can learn from past experiences and pass them on from generation to generation. In this work, we introduce the unified theory of biological adaptation based on population dynamics and show its potential applications to evaluate the fitness value of information and to analyze experimental lineage tree data. Finally, we discuss future perspectives for its development. This review article is an extended version of the Japanese article in SEIBUTSU BUTSURI Vol. 57, p. 287-290 (2017).

Evolutionary dynamics in non-Markovian models of microbial populations

In the past decade, great strides have been made to quantify the dynamics of single-cell growth and division in microbes. In order to make sense of the evolutionary history of these organisms, we must understand how features of single-cell growth and division influence evolutionary dynamics. This requires us to connect processes on the single-cell scale to population dynamics. Here, we consider a model of microbial growth in finite populations which explicitly incorporates the single-cell dynamics. We study the behavior of a mutant population in such a model and ask: can the evolutionary dynamics be coarse-grained so that the forces of natural selection and genetic drift can be expressed in terms of the long-term fitness? We show that it is in fact not possible, as there is no way to define a single fitness parameter (or reproductive rate) that defines the fate of an organism even in a constant environment. This is due to fluctuations in the population averaged division rate. As a result, various details of the single-cell dynamics affect the fate of a new mutant independently from how they affect the long-term growth rate of the mutant population. In particular, we show that in the case of neutral mutations, variability in generation times increases the rate of genetic drift, and in the case of beneficial mutations, variability decreases its fixation probability. Furthermore, we explain the source of the persistent division rate fluctuations and provide analytic solutions for the fixation probability as a multispecies generalization of the Euler-Lotka equation.

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.

Dynamic fluctuations in a bacterial metabolic network

The operation of the central metabolism is typically assumed to be deterministic, but dynamics and high connectivity of the metabolic network make it potentially prone to generating fluctuations. However, time-resolved measurements of metabolite levels in individual cells that are required to characterize such fluctuations remained a challenge, particularly in small bacterial cells. Here we use single-cell metabolite measurements based on Förster resonance energy transfer, combined with computer simulations, to explore the real-time dynamics of the metabolic network of Escherichia coli. We observe that steplike exposure of starved E. coli to glycolytic carbon sources elicits large periodic fluctuations in the intracellular concentration of pyruvate in individual cells. These fluctuations are consistent with predicted oscillatory dynamics of E. coli metabolic network, and they are primarily controlled by biochemical reactions around the pyruvate node. Our results further indicate that fluctuations in glycolysis propagate to other cellular processes, possibly leading to temporal heterogeneity of cellular states within a population.

Metabolic activity grows in human cancers pushed by phenotypic variability

Different evolutionary processes push cancers to increasingly aggressive behaviors, energetically sustained by metabolic reprogramming. The collective signature emerging from this transition is macroscopically displayed by positron emission tomography (PET). In fact, the most readily PET measure, the maximum standardized uptake value (SUV_max), has been found to have prognostic value in different cancers. However, few works have linked the properties of this metabolic hotspot to cancer evolutionary dynamics. Here, by analyzing diagnostic PET images from 512 patients with cancer, we found that SUV_max scales superlinearly with the mean metabolic activity (SUV_mean), reflecting a dynamic preferential accumulation of activity on the hotspot. Additionally, SUV_max increased with metabolic tumor volume (MTV) following a power law. The behavior from the patients data was accurately captured by a mechanistic evolutionary dynamics model of tumor growth accounting for phenotypic transitions. This suggests that non-genetic changes may suffice to fuel the observed sustained increases in tumor metabolic activity.

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.

Intercellular interaction mechanisms promote diversity in intracellular ATP concentration in Escherichia coli populations

In fluctuating environments, many microorganisms acquire phenotypic heterogeneity as a survival tactic to increase the likelihood of survival of the overall population. One example of this interindividual heterogeneity is the diversity of ATP concentration among members of Escherichia coli populations under glucose deprivation. Despite the importance of such environmentally driven phenotypic heterogeneity, how the differences in intracellular ATP concentration emerge among individual E. coli organisms is unknown. In this study, we focused on the mechanism through which individual E. coli achieve high intracellular ATP concentrations. First, we measured the ATP retained by E. coli over time when cultured at low (0.1 mM) and control (22.2 mM) concentrations of glucose and obtained the chronological change in ATP concentrations. Then, by comparing these chronological change of ATP concentrations and analyzing whether stochastic state transitions, periodic oscillations, cellular age, and intercellular communication-which have been reported as molecular biological mechanisms for generating interindividual heterogeneity-are involved, we showed that the appearance of high ATP-holding individuals observed among E. coli can be explained only by intercellular transmission. By performing metabolomic analysis of post-culture medium, we revealed a significant increase in the ATP, especially at low glucose, and that the number of E. coli that retain significantly higher ATP can be controlled by adding large amounts of ATP to the medium, even in populations cultured under control glucose concentrations. These results reveal for the first time that ATP-mediated intercellular transmission enables some individuals in E. coli populations grown at low glucose to retain large amounts of ATP.

Drug resistant tuberculosis: Implications for transmission, diagnosis, and disease management

Drug resistant tuberculosis contributes significantly to the global burden of antimicrobial resistance, often consuming a large proportion of the healthcare budget and associated resources in many endemic countries. The rapid emergence of resistance to newer tuberculosis therapies signals the need to ensure appropriate antibiotic stewardship, together with a concerted drive to develop new regimens that are active against currently circulating drug resistant strains. Herein, we highlight that the current burden of drug resistant tuberculosis is driven by a combination of ongoing transmission and the intra-patient evolution of resistance through several mechanisms. Global control of tuberculosis will require interventions that effectively address these and related aspects. Interrupting tuberculosis transmission is dependent on the availability of novel rapid diagnostics which provide accurate results, as near-patient as is possible, together with appropriate linkage to care. Contact tracing, longitudinal follow-up for symptoms and active mapping of social contacts are essential elements to curb further community-wide spread of drug resistant strains. Appropriate prophylaxis for contacts of drug resistant index cases is imperative to limit disease progression and subsequent transmission. Preventing the evolution of drug resistant strains will require the development of shorter regimens that rapidly eliminate all populations of mycobacteria, whilst concurrently limiting bacterial metabolic processes that drive drug tolerance, mutagenesis and the ultimate emergence of resistance. Drug discovery programs that specifically target bacterial genetic determinants associated with these processes will be paramount to tuberculosis eradication. In addition, the development of appropriate clinical endpoints that quantify drug tolerant organisms in sputum, such as differentially culturable/detectable tubercle bacteria is necessary to accurately assess the potential of new therapies to effectively shorten treatment duration. When combined, this holistic approach to addressing the critical problems associated with drug resistance will support delivery of quality care to patients suffering from tuberculosis and bolster efforts to eradicate this disease.

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.

A compressed logistic equation bacteria growth: Inferring time-dependent growth rate

We propose a compressed logistic model for bacterial growth by invoking a time-dependent rate instead of the intrinsic growth rate (constant), which was adopted in traditional logistic models. The new model may have a better physiological basis than the traditional ones, and it replicates experimental observations, such as the case example for E. coli, Salmonella, and Staphylococcus aureus. Stochastic colonial growth at a different rate may have a fractal-like nature, which should be an origin of the time-dependent reaction rate. The present model, from a stochastic viewpoint, is approximated as a Gaussian time evolution of bacteria (error function).

Single mutation makes Escherichia coli an insect mutualist

Microorganisms often live in symbiosis with their hosts, and some are considered mutualists, where all species involved benefit from the interaction. How free-living microorganisms have evolved to become mutualists is unclear. Here we report an experimental system in which non-symbiotic Escherichia coli evolves into an insect mutualist. The stinkbug Plautia stali is typically associated with its essential gut symbiont, Pantoea sp., which colonizes a specialized symbiotic organ. When sterilized newborn nymphs were infected with E. coli rather than Pantoea sp., only a few insects survived, in which E. coli exhibited specific localization to the symbiotic organ and vertical transmission to the offspring. Through transgenerational maintenance with P. stali, several hypermutating E. coli lines independently evolved to support the host's high adult emergence and improved body colour; these were called 'mutualistic' E. coli. These mutants exhibited slower bacterial growth, smaller size, loss of flagellar motility and lack of an extracellular matrix. Transcriptomic and genomic analyses of 'mutualistic' E. coli lines revealed independent mutations that disrupted the carbon catabolite repression global transcriptional regulator system. Each mutation reproduced the mutualistic phenotypes when introduced into wild-type E. coli, confirming that single carbon catabolite repression mutations can make E. coli an insect mutualist. These findings provide an experimental system for future work on host-microbe symbioses and may explain why microbial mutualisms are omnipresent in nature.

History-dependent physiological adaptation to lethal genetic modification under antibiotic exposure

Genetic modifications, such as gene deletion and mutations, could lead to significant changes in physiological states or even cell death. Bacterial cells can adapt to diverse external stresses, such as antibiotic exposure, but can they also adapt to detrimental genetic modification? To address this issue, we visualized the response of individual Escherichia coli cells to deletion of the antibiotic resistance gene under chloramphenicol (Cp) exposure, combining the light-inducible genetic recombination and microfluidic long-term single-cell tracking. We found that a significant fraction (∼40%) of resistance-gene-deleted cells demonstrated a gradual restoration of growth and stably proliferated under continuous Cp exposure without the resistance gene. Such physiological adaptation to genetic modification was not observed when the deletion was introduced in 10 hr or more advance before Cp exposure. Resistance gene deletion under Cp exposure disrupted the stoichiometric balance of ribosomal large and small subunit proteins (RplS and RpsB). However, the balance was gradually recovered in the cell lineages with restored growth. These results demonstrate that bacterial cells can adapt even to lethal genetic modifications by plastically gaining physiological resistance. However, the access to the resistance states is limited by the environmental histories and the timings of genetic modification.

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.

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.

Population genetics in microchannels

Many microbial populations proliferate in small channels. In such environments, reproducing cells organize in parallel lanes. Reproducing cells shift these lanes, potentially expelling other cells from the channel. In this paper, we combine theory and experiments to understand how these dynamics affects the diversity of a microbial population. We theoretically predict that genetic diversity is quickly lost along lanes of cells. Our experiments confirm that a population of proliferating Escherichia coli in a microchannel organizes into lanes of genetically identical cells within a few generations. Our findings elucidate the effect of lane formation on populations evolution, with potential applications ranging from microbial ecology in soil to dynamics of epithelial tissues in higher organisms.

Spatial constraints, such as rigid barriers, affect the dynamics of cell populations, potentially altering the course of natural evolution. In this paper, we investigate the population genetics of Escherichia coli proliferating in microchannels with open ends. Our analysis is based on a population model, in which reproducing cells shift entire lanes of cells toward the open ends of the channel. The model predicts that diversity is lost very rapidly within lanes but at a much slower pace among lanes. As a consequence, two mixed, neutral E. coli strains competing in a microchannel must organize into an ordered regular stripe pattern in the course of a few generations. These predictions are in quantitative agreement with our experiments. We also demonstrate that random mutations appearing in the middle of the channel are much more likely to reach fixation than those occurring elsewhere. Our results illustrate fundamental mechanisms of microbial evolution in spatially confined space.

Tracking the stochastic growth of bacterial populations in microfluidic droplets

Bacterial growth in microfluidic droplets is relevant in biotechnology, in microbial ecology, and in understanding stochastic population dynamics in small populations. However, it has proved challenging to automate measurement of absolute bacterial numbers within droplets, forcing the use of proxy measures for population size. Here we present a microfluidic device and imaging protocol that allows high-resolution imaging of thousands of droplets, such that individual bacteria stay in the focal plane and can be counted automatically. Using this approach, we track the stochastic growth of hundreds of replicateEscherichia colipopulations within droplets. We find that, for early times, the statistics of the growth trajectories obey the predictions of the Bellman-Harris model, in which there is no inheritance of division time. Our approach should allow further testing of models for stochastic growth dynamics, as well as contributing to broader applications of droplet-based bacterial culture.

Kinetic Modeling of Saccharomyces cerevisiae Central Carbon Metabolism: Achievements, Limitations, and Opportunities

Central carbon metabolism comprises the metabolic pathways in the cell that process nutrients into energy, building blocks and byproducts. To unravel the regulation of this network upon glucose perturbation, several metabolic models have been developed for the microorganism Saccharomyces cerevisiae. These dynamic representations have focused on glycolysis and answered multiple research questions, but no commonly applicable model has been presented. This review systematically evaluates the literature to describe the current advances, limitations, and opportunities. Different kinetic models have unraveled key kinetic glycolytic mechanisms. Nevertheless, some uncertainties regarding model topology and parameter values still limit the application to specific cases. Progressive improvements in experimental measurement technologies as well as advances in computational tools create new opportunities to further extend the model scale. Notably, models need to be made more complex to consider the multiple layers of glycolytic regulation and external physiological variables regulating the bioprocess, opening new possibilities for extrapolation and validation. Finally, the onset of new data representative of individual cells will cause these models to evolve from depicting an average cell in an industrial fermenter, to characterizing the heterogeneity of the population, opening new and unseen possibilities for industrial fermentation improvement.

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.

Continuous rate modeling of bacterial stochastic size dynamics

Bacterial division is an inherently stochastic process with effects on fluctuations of protein concentration and phenotype variability. Current modeling tools for the stochastic short-term cell-size dynamics are scarce and mainly phenomenological. Here we present a general theoretical approach based on the Chapman-Kolmogorov equation incorporating continuous growth and division events as jump processes. This approach allows us to include different division strategies, noisy growth, and noisy cell splitting. Considering bacteria synchronized from their last division, we predict oscillations in both the central moments of the size distribution and its autocorrelation function. These oscillations, barely discussed in past studies, can arise as a consequence of the discrete time displacement invariance of the system with a period of one doubling time, and they do not disappear when including stochasticity on either division times or size heterogeneity on the starting population but only after inclusion of noise in either growth rate or septum position. This result illustrates the usefulness of having a solid mathematical description that explicitly incorporates the inherent stochasticity in various biological processes, both to understand the process in detail and to evaluate the effect of various sources of variability when creating simplified descriptions.

Evolution of phenotypic fluctuation under host-parasite interactions

Robustness and plasticity are essential features that allow biological systems to cope with complex and variable environments. In a constant environment, robustness, i.e., insensitivity of phenotypes, is expected to increase, whereas plasticity, i.e., the changeability of phenotypes, tends to diminish. Under a variable environment, existence of plasticity will be relevant. The robustness and plasticity, on the other hand, are related to phenotypic variances. As phenotypic variances decrease with the increase in robustness to perturbations, they are expected to decrease through the evolution. However, in nature, phenotypic fluctuation is preserved to a certain degree. One possible cause for this is environmental variation, where one of the most important “environmental” factors will be inter-species interactions. As a first step toward investigating phenotypic fluctuation in response to an inter-species interaction, we present the study of a simple two-species system that comprises hosts and parasites. Hosts are expected to evolve to achieve a phenotype that optimizes fitness. Then, the robustness of the corresponding phenotype will be increased by reducing phenotypic fluctuations. Conversely, plasticity tends to evolve to avoid certain phenotypes that are attacked by parasites. By using a dynamic model of gene expression for the host, we investigate the evolution of the genotype-phenotype map and of phenotypic variances. If the host–parasite interaction is weak, the fittest phenotype of the host evolves to reduce phenotypic variances. In contrast, if there exists a sufficient degree of interaction, the phenotypic variances of hosts increase to escape parasite attacks. For the latter case, we found two strategies: if the noise in the stochastic gene expression is below a certain threshold, the phenotypic variance increases via genetic diversification, whereas above this threshold, it is increased mediated by noise-induced phenotypic fluctuation. We examine how the increase in the phenotypic variances caused by parasite interactions influences the growth rate of a single host, and observed a trade-off between the two. Our results help elucidate the roles played by noise and genetic mutations in the evolution of phenotypic fluctuation and robustness in response to host–parasite interactions.

Plasticity and phenotypic variability induced by internal or external perturbations are common features of biological systems. However, under evolution for given environmental conditions, phenotypic variability is not advantageous, because it leads to the deviation from the fittest state. This has been demonstrated by previous laboratory and computer experiments. As a possible origin for the remnant phenotypic variance, we investigated the role of host–parasite interactions such as those between bacteria and phages. Different parasite-types attack hosts of certain phenotypes. Through numerical simulations of the evolution of the host genotype–phenotype mapping, we found that hosts increase phenotypic variation by increasing phenotypic fluctuations if the interaction is sufficiently strong. Depending on the degree of noise in gene expression dynamics, there are two distinct strategies for increasing phenotypic variances: stochasticity in gene expression or genetic variances. The former strategy, which can work over a faster time scale, leads to a decline in fitness, whereas the latter reduces the robustness of the fitted state. Our results provide insights into how phenotypic variances are preserved and how hosts can escape being attacked by parasites whose genes mutate to adapt to changes in parasites. These two host strategies, which depend on internal and external conditions, can be verified experimentally via the transcriptome analysis of microorganisms.

Analytics and visualization tools to characterize single-cell stochasticity using bacterial single-cell movie cytometry data

Background

Time-lapse microscopy live-cell imaging is essential for studying the evolution of bacterial communities at single-cell resolution. It allows capturing detailed information about the morphology, gene expression, and spatial characteristics of individual cells at every time instance of the imaging experiment. The image analysis of bacterial "single-cell movies" (videos) generates big data in the form of multidimensional time series of measured bacterial attributes. If properly analyzed, these datasets can help us decipher the bacterial communities' growth dynamics and identify the sources and potential functional role of intra- and inter-subpopulation heterogeneity. Recent research has highlighted the importance of investigating the role of biological "noise" in gene regulation, cell growth, cell division, etc. Single-cell analytics of complex single-cell movie datasets, capturing the interaction of multiple micro-colonies with thousands of cells, can shed light on essential phenomena for human health, such as the competition of pathogens and benign microbiome cells, the emergence of dormant cells (“persisters”), the formation of biofilms under different stress conditions, etc. However, highly accurate and automated bacterial bioimage analysis and single-cell analytics methods remain elusive, even though they are required before we can routinely exploit the plethora of data that single-cell movies generate.

Results

We present visualization and single-cell analytics using R (ViSCAR), a set of methods and corresponding functions, to visually explore and correlate single-cell attributes generated from the image processing of complex bacterial single-cell movies. They can be used to model and visualize the spatiotemporal evolution of attributes at different levels of the microbial community organization (i.e., cell population, colony, generation, etc.), to discover possible epigenetic information transfer across cell generations, infer mathematical and statistical models describing various stochastic phenomena (e.g., cell growth, cell division), and even identify and auto-correct errors introduced unavoidably during the bioimage analysis of a dense movie with thousands of overcrowded cells in the microscope's field of view.

Conclusions

ViSCAR empowers researchers to capture and characterize the stochasticity, uncover the mechanisms leading to cellular phenotypes of interest, and decipher a large heterogeneous microbial communities' dynamic behavior. ViSCAR source code is available from GitLab at https://gitlab.com/ManolakosLab/viscar.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-021-04409-9.

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.

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.

Modeling the impact of single-cell stochasticity and size control on the population growth rate in asymmetrically dividing cells

Microbial populations show striking diversity in cell growth morphology and lifecycle; however, our understanding of how these factors influence the growth rate of cell populations remains limited. We use theory and simulations to predict the impact of asymmetric cell division, cell size regulation and single-cell stochasticity on the population growth rate. Our model predicts that coarse-grained noise in the single-cell growth rate λ decreases the population growth rate, as previously seen for symmetrically dividing cells. However, for a given noise in λ we find that dividing asymmetrically can enhance the population growth rate for cells with strong size control (between a “sizer” and an “adder”). To reconcile this finding with the abundance of symmetrically dividing organisms in nature, we propose that additional constraints on cell growth and division must be present which are not included in our model, and we explore the effects of selected extensions thereof. Further, we find that within our model, epigenetically inherited generation times may arise due to size control in asymmetrically dividing cells, providing a possible explanation for recent experimental observations in budding yeast. Taken together, our findings provide insight into the complex effects generated by non-canonical growth morphologies.

How rapidly a population of single-celled organisms can grow will strongly impact their long-term success. Prior work has shown that many factors impact this population growth rate, including the rate at which single cells grow, random variability between cells, and whether cells regulate their own size. Here we show that cell division asymmetry can also have a strong impact on the population growth rate. We use theory and computer simulations to study the growth rate of cells that divide asymmetrically, producing one smaller cell and one larger cell with each cell division event. We show that variability in how fast single cells grow will still decrease the population growth rate, when asymmetry is moderate or size control is weak, but that cells with strong size control can diminish this decrease by dividing more asymmetrically. We also demonstrate that cell cycle lengths can be positively correlated for closely related cells when they both divide asymmetrically and regulate their size. This counter-intuitive result contrasts with previous findings based on cell size regulation in symmetrically dividing cells that if cells grow for “too long” in one cell cycle, this will be corrected for by reduced growth during a shorter, subsequent cell cycle.

Initial cell density encodes proliferative potential in cancer cell populations

Individual cells exhibit specific proliferative responses to changes in microenvironmental conditions. Whether such potential is constrained by the cell density throughout the growth process is however unclear. Here, we identify a theoretical framework that captures how the information encoded in the initial density of cancer cell populations impacts their growth profile. By following the growth of hundreds of populations of cancer cells, we found that the time they need to adapt to the environment decreases as the initial cell density increases. Moreover, the population growth rate shows a maximum at intermediate initial densities. With the support of a mathematical model, we show that the observed interdependence of adaptation time and growth rate is significantly at odds both with standard logistic growth models and with the Monod-like function that governs the dependence of the growth rate on nutrient levels. Our results (i) uncover and quantify a previously unnoticed heterogeneity in the growth dynamics of cancer cell populations; (ii) unveil how population growth may be affected by single-cell adaptation times; (iii) contribute to our understanding of the clinically-observed dependence of the primary and metastatic tumor take rates on the initial density of implanted cancer cells.

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.

Intrinsic growth heterogeneity of mouse leukemia cells underlies differential susceptibility to a growth-inhibiting anticancer drug

Cancer cell populations consist of phenotypically heterogeneous cells. Growing evidence suggests that pre-existing phenotypic differences among cancer cells correlate with differential susceptibility to anticancer drugs and eventually lead to a relapse. Such phenotypic differences can arise not only externally driven by the environmental heterogeneity around individual cells but also internally by the intrinsic fluctuation of cells. However, the quantitative characteristics of intrinsic phenotypic heterogeneity emerging even under constant environments and their relevance to drug susceptibility remain elusive. Here we employed a microfluidic device, mammalian mother machine, for studying the intrinsic heterogeneity of growth dynamics of mouse lymphocytic leukemia cells (L1210) across tens of generations. The generation time of this cancer cell line had a distribution with a long tail and a heritability across generations. We determined that a minority of cell lineages exist in a slow-cycling state for multiple generations. These slow-cycling cell lineages had a higher chance of survival than the fast-cycling lineages under continuous exposure to the anticancer drug Mitomycin C. This result suggests that heritable heterogeneity in cancer cells’ growth in a population influences their susceptibility to anticancer drugs.

The impact of mistranslation on phenotypic variability and fitness

Phenotypic variation is widespread in natural populations, and can significantly alter population ecology and evolution. Phenotypic variation often reflects underlying genetic variation, but also manifests via non-heritable mechanisms. For instance, translation errors result in about 10% of cellular proteins carrying altered sequences. Thus, proteome diversification arising from translation errors can potentially generate phenotypic variability, in turn increasing variability in the fate of cells or of populations. However, the link between protein diversity and phenotypic variability remains unverified. We manipulated mistranslation levels in Escherichia coli, and measured phenotypic variability between single cells (individual-level variation), as well as replicate populations (population-level variation). Monitoring growth and survival, we find that mistranslation indeed increases variation across E. coli cells, but does not consistently increase variability in growth parameters across replicate populations. Interestingly, although any deviation from the wild-type (WT) level of mistranslation reduces fitness in an optimal environment, the increased variation is associated with a survival benefit under stress. Hence, we suggest that mistranslation-induced phenotypic variation can impact growth and survival and has the potential to alter evolutionary trajectories.

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.

From single-cell variability to population growth

Single-cell experiments have revealed cell-to-cell variability in generation times and growth rates for genetically identical cells. Theoretical models relating the fluctuating generation times of single cells to the population growth rate are usually based on the assumption that the generation times of mother and daughter cells are uncorrelated. This assumption, however, is inconsistent with the exponential growth of cell volume in time observed for many cell types. Here we develop a more general and biologically relevant model in which cells grow exponentially and generation times are correlated in a manner which controls cell size. In addition to the fluctuating generation times, we also allow the single-cell growth rates to fluctuate and account for their correlations across the lineage tree. Surprisingly, we find that the population growth rate only depends on the distribution of single-cell growth rates and their correlations.

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.

The impact of random microenvironmental fluctuations on tumor control probability

The tumor control probability (TCP) is a metric used to calculate the probability of controlling or eradicating tumors through radiotherapy. Cancer cells vary in their response to radiation, and although many factors are involved, the tumor microenvironment is a crucial one that determines radiation efficacy. The tumor microenvironment plays a significant role in cancer initiation and propagation, as well as in treatment outcome. We have developed stochastic formulations to study the impact of arbitrary microenvironmental fluctuations on TCP and extinction probability (EP), which is defined as the probability of cancer cells removal in the absence of treatment. Since the derivation of analytical solutions are not possible for complicated cases, we employ a modified Gillespie algorithm to analyze TCP and EP, considering the random variations in cellular proliferation and death rates. Our results show that increasing the standard deviation in kinetic rates initially enhances the probability of tumor eradication. However, if the EP does not reach a probability of 1, the increase in the standard deviation subsequently has a negative impact on probability of cancer cells removal, decreasing the EP over time. The greatest effect on EP has been observed when both birth and death rates are being randomly modified and are anticorrelated. In addition, similar results are observed for TCP, where radiotherapy is included, indicating that increasing the standard deviation in kinetic rates at first enhances the probability of tumor eradication. But, it has a negative impact on treatment effectiveness if the TCP does not reach a probability of 1.

Influence of reduced levels or suppression of sodium nitrite on the outgrowth and toxinogenesis of psychrotrophic Clostridium botulinum Group II type B in cooked ham

Outgrowth and toxinogenesis of Clostridium botulinum Group II (non-proteolytic) type B were studied in cooked ham prepared with different NaNO₂ (ranging from 0 to 80 mg/kg) and sodium chloride (NaCl, ranging from 12 to 19 g/kg) incorporation rates. Cured ground pork batters were inoculated with a cocktail of 3 strains of C. botulinum Group II type B at 3.5 log₁₀ CFU/g, portioned and samples of 50 g were vacuum packed then cooked and cooled based on thermal processing employed by the meat processing industry. These cooked ham model samples were stored under reasonably foreseeable conditions of use and storage i.e. for 14 days at 4 °C, followed by a cold chain break for 1 h at 20 °C then up to 33 days at 8 °C. Storage times and temperatures were used to mimic those commonly encountered along the supply chain. Enumeration of C. botulinum and detection of the botulinum neurotoxin type B (BoNT/B) were performed in triplicate at different storage times. Under these experimental conditions, incorporation rates of NaNO₂ ≥ 30 mg/kg prevented the outgrowth and toxinogenesis of C. botulinum Group II type B in the cooked ham model, regardless of the NaCl concentrations tested. In contrast, total removal of nitrite allowed outgrowth and toxin production during storage of the processed meat product. Results showed that the maximum ingoing amount of nitrite (i.e. 150 mg/kg) that may be added according to the EU legislation (Regulation (EC) No 1333/2008) can be reduced in cooked ham while still ensuring control of C. botulinum Group II type B. According to the multiple factors that could affect C. botulinum behavior in processing meat products, outgrowth and toxin production of C. botulinum should be evaluated on a case by case basis, depending on the recipe, manufacturing process, food matrix and storage conditions.

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.

A novel tracking and analysis system for time-lapse cell imaging of Saccharomyces cerevisiae

Recent studies have revealed that tracking single cells using time-lapse fluorescence microscopy is an optimal tool for spatiotemporal evaluation of proteins of interest. Using this approach with Saccharomyces cerevisiae as a model organism, we previously found that heterochromatin regions involved in epigenetic regulation differ between individual cells. Determining the regularity of this phenomenon requires measurement of spatiotemporal epigenetic-dependent changes in protein levels across more than one generation. In past studies, we conducted these analyses manually to obtain a dendrogram, but this required more than 15 h, even for a single set of microscopic cell images. Thus, in this study, we developed a software-based analysis system to analyze time-lapse cellular images of S. cerevisiae, which allowed automatic generation of a dendrogram from a given set of time-lapse cell images. This approach is divided into two phases: a cell extraction and tracking phase, and an analysis phase. The cell extraction and tracking phase generates a set of necessary information for each cell, such as geometrical properties and the daughter-mother relationships, using image processing-based analysis techniques. Then, based on this information, the analysis phase allows generation of the final dendrogram by analyzing the fluorescent characteristics of each cell. The system is equipped with manual error correction to correct for the inevitable errors that occur in these analyses. The time required to obtain the final dendrograms was drastically reduced from 15 h in manual analysis to 0.8 h using this novel system.

Aging a little: On the optimality of limited senescence in Escherichia coli

Recent studies have shown that even in the absence of extrinsic stress, the morphologically symmetrically dividing model bacteria Escherichia coli do not generate offspring with equal reproductive fitness. Instead, daughter cells exhibit asymmetric division times that converge to two distinct growth states. This represents a limited senescence/rejuvenation process derived from asymmetric division that is stable for hundreds of generations. It remains unclear why the bacteria do not continue the senescence beyond this asymptote. Although there are inherent fitness benefits for heterogeneity in population growth rates, the two growth equilibria are surprisingly similar, differing by a few percent. In this work we derive an explicit model for the growth of a bacterial population with two growth equilibria, based on a generalized Fibonacci recurrence, in order to quantify the fitness benefit of a limited senescence process and examine costs associated with asymmetry that could generate the observed behavior. We find that a simple saturating effect of asymmetric partitioning of subcellular components is sufficient to explain why two distinct but similar growth states may be optimal while providing evolutionarily significant growth advantages.

The interplay of phenotypic variability and fitness in finite microbial populations

In isogenic microbial populations, phenotypic variability is generated by a combination of stochastic mechanisms, such as gene expression, and deterministic factors, such as asymmetric segregation of cell volume. Here we address the question: how does phenotypic variability of a microbial population affect its fitness? While this question has previously been studied for exponentially growing populations, the situation when the population size is kept fixed has received much less attention, despite its relevance to many natural scenarios. We show that the outcome of competition between multiple microbial species can be determined from the distribution of phenotypes in the culture using a generalization of the well-known Euler-Lotka equation, which relates the steady-state distribution of phenotypes to the population growth rate. We derive a generalization of the Euler-Lotka equation for finite cultures, which relates the distribution of phenotypes among cells in the culture to the exponential growth rate. Our analysis reveals that in order to predict fitness from phenotypes, it is important to understand how distributions of phenotypes obtained from different subsets of the genealogical history of a population are related. To this end, we derive a mapping between the various ways of sampling phenotypes in a finite population and show how to obtain the equivalent distributions from an exponentially growing culture. Finally, we use this mapping to show that species with higher growth rates in exponential growth conditions will have a competitive advantage in the finite culture.

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.