Noise and Epigenetic Inheritance of Single-Cell Division Times Influence Population Fitness

Criticality in the Luria-Delbrück Model with an Arbitrary Mutation Rate

The Luria-Delbrück model is a classic model of population dynamics with random mutations, that has been used historically to prove that random mutations drive evolution. In typical scenarios, the relevant mutation rate is exceedingly small, and mutants are counted only at the final time point. Here, inspired by recent experiments on DNA repair, we study a mathematical model that is formally equivalent to the Luria-Delbrück setup, with the repair rate p playing the role of mutation rate, albeit taking on large values, of order unity per cell division. We find that although at large times the fraction of repaired cells approaches one, the variance of the number of repaired cells undergoes a phase transition: when p>1/2 the variance decreases with time, but, intriguingly, for p<1/2 even though the fraction of repaired cells approaches 1, the variance in the number of repaired cells increases with time. Analyzing DNA-repair experiments, we find that in order to explain the data the model should also take into account the probability of a successful repair process once it is initiated. Taken together, our work shows how the study of variability can lead to surprising phase transitions as well as provide biological insights into the process of DNA repair.

An expanded view of cell competition

Cell competition arises in heterogeneous tissues when neighbouring cells sense their relative fitness and undergo selection. It has been a challenge to define contexts in which cell competition is a physiologically relevant phenomenon and to understand the cellular features that underlie fitness and fitness sensing. Drawing on examples across a range of contexts and length scales, we illuminate molecular and cellular features that could underlie fitness in diverse tissue types and processes to promote and reinforce long-term maintenance of tissue function. We propose that by broadening the scope of how fitness is defined and the circumstances in which cell competition can occur, the field can unlock the potential of cell competition as a lens through which heterogeneity and its role in the fundamental principles of complex tissue organisation can be understood.

Accelerating Diverse Cell-Based Therapies Through Scalable Design

Augmenting cells with novel, genetically encoded functions will support therapies that expand beyond natural capacity for immune surveillance and tissue regeneration. However, engineering cells at scale with transgenic cargoes remains a challenge in realizing the potential of cell-based therapies. In this review, we introduce a range of applications for engineering primary cells and stem cells for cell-based therapies. We highlight tools and advances that have launched mammalian cell engineering from bioproduction to precision editing of therapeutically relevant cells. Additionally, we examine how transgenesis methods and genetic cargo designs can be tailored for performance. Altogether, we offer a vision for accelerating the translation of innovative cell-based therapies by harnessing diverse cell types, integrating the expanding array of synthetic biology tools, and building cellular tools through advanced genome writing techniques.

Equations describing semi-confluent cell growth (I) Analytical approximations

A set of differential equations with analytical solutions are presented that can quantitatively account for variable degrees of contact inhibition on cell growth in two- and three-dimensional cultures. The developed equations can be used for comparative purposes when assessing contribution of higher-order effects, such as culture geometry and nutrient depletion, on mean cell growth rate. These equations also offer experimentalists the opportunity to characterize cell culture experiments using a single reductive parameter.

Collective effects of cell cleavage dynamics

A conserved process of early embryonic development in metazoans is the reductive cell divisions following oocyte fertilization, termed cell cleavages. Cell cleavage cycles usually start synchronously, lengthen differentially between the embryonic cells becoming asynchronous, and cease before major morphogenetic events, such as germ layer formation and gastrulation. Despite exhibiting species-specific characteristics, the regulation of cell cleavage dynamics comes down to common controllers acting mostly at the single cell/nucleus level, such as nucleus-to-cytoplasmic ratio and zygotic genome activation. Remarkably, recent work has linked cell cleavage dynamics to the emergence of collective behavior during embryogenesis, including pattern formation and changes in embryo-scale mechanics, raising the question how single-cell controllers coordinate embryo-scale processes. In this review, we summarize studies across species where an association between cell cleavages and collective behavior was made, discuss the underlying mechanisms, and propose that cell-to-cell variability in cell cleavage dynamics can serve as a mechanism of long-range coordination in developing embryos.

MIL-CELL: a tool for multi-scale simulation of yeast replication and prion transmission

The single-celled baker's yeast, Saccharomyces cerevisiae, can sustain a number of amyloid-based prions, the three most prominent examples being [URE3], [PSI+], and [PIN+]. In the laboratory, haploid S. cerevisiae cells of a single mating type can acquire an amyloid prion in one of two ways (i) spontaneous nucleation of the prion within the yeast cell, and (ii) receipt via mother-to-daughter transmission during the cell division cycle. Similarly, prions can be lost due to (i) dissolution of the prion amyloid by its breakage into non-amyloid monomeric units, or (ii) preferential donation/retention of prions between the mother and daughter during cell division. Here we present a computational tool (Monitoring Induction and Loss of prions in Cells; MIL-CELL) for modelling these four general processes using a multiscale approach describing both spatial and kinetic aspects of the yeast life cycle and the amyloid-prion behavior. We describe the workings of the model, assumptions upon which it is based and some interesting simulation results pertaining to the wave-like spread of the epigenetic prion elements through the yeast population. MIL-CELL is provided as a stand-alone GUI executable program for free download with the paper. MIL-CELL is equipped with a relational database allowing all simulated properties to be searched, collated and graphed. Its ability to incorporate variation in heritable properties means MIL-CELL is also capable of simulating loss of the isogenic nature of a cell population over time. The capability to monitor both chronological and reproductive age also makes MIL-CELL potentially useful in studies of cell aging.

The σB alternative sigma factor circuit modulates noise to generate different types of pulsing dynamics

Single-cell approaches are revealing a high degree of heterogeneity, or noise, in gene expression in isogenic bacteria. How gene circuits modulate this noise in gene expression to generate robust output dynamics is unclear. Here we use the Bacillus subtilis alternative sigma factor σB as a model system for understanding the role of noise in generating circuit output dynamics. σB controls the general stress response in B. subtilis and is activated by a range of energy and environmental stresses. Recent single-cell studies have revealed that the circuit can generate two distinct outputs, stochastic pulsing and a single pulse response, but the conditions under which each response is generated are under debate. We implement a stochastic mathematical model of the σB circuit to investigate this and find that the system's core circuit can generate both response types. This is despite one response (stochastic pulsing) being stochastic in nature, and the other (single response pulse) being deterministic. We demonstrate that the main determinant for whichever response is generated is the degree with which the input pathway activates the core circuit, although the noise properties of the input pathway also biases the system towards one or the other type of output. Thus, our work shows how stochastic modelling can reveal the mechanisms behind non-intuitive gene circuit output dynamics.

Transcriptional bursting: stochasticity in deterministic development

The transcription of DNA by RNA polymerase occurs as a discontinuous process described as transcriptional bursting. This bursting behavior is observed across species and has been quantified using various stochastic modeling approaches. There is a large body of evidence that suggests the bursts are actively modulated by transcriptional machinery and play a role in regulating developmental processes. Under a commonly used two-state model of transcription, various enhancer-, promoter- and chromatin microenvironment-associated features are found to differentially influence the size and frequency of bursting events - key parameters of the two-state model. Advancement of modeling and analysis tools has revealed that the simple two-state model and associated parameters may not sufficiently characterize the complex relationship between these features. The majority of experimental and modeling findings support the view of bursting as an evolutionarily conserved transcriptional control feature rather than an unintended byproduct of the transcription process. Stochastic transcriptional patterns contribute to enhanced cellular fitness and execution of proper development programs, which posit this mode of transcription as an important feature in developmental gene regulation. In this Review, we present compelling examples of the role of transcriptional bursting in development and explore the question of how stochastic transcription leads to deterministic organism development.

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.

Exploring the expanse between theoretical questions and experimental approaches in the modern study of evolvability

Despite several decades of computational and experimental work across many systems, evolvability remains on the periphery with regards to its status as a widely accepted and regularly applied theoretical concept. Here we propose that its marginal status is partly a result of large gaps between the diverse but disconnected theoretical treatments of evolvability and the relatively narrower range of studies that have tested it empirically. To make this case, we draw on a range of examples-from experimental evolution in microbes, to molecular evolution in proteins-where attempts have been made to mend this disconnect. We highlight some examples of progress that has been made and point to areas where synthesis and translation of existing theory can lead to further progress in the still-new field of empirical measurements of evolvability.

Phenotypic plasticity as a facilitator of microbial evolution

Tossed about by the tides of history, the inheritance of acquired characteristics has found a safe harbor at last in the rapidly expanding field of epigenetics. The slow pace of genetic variation and high opportunity cost associated with maintaining a diverse genetic pool are well-matched by the flexibility of epigenetic traits, which can enable low-cost exploration of phenotypic space and reactive tuning to environmental pressures. Aiding in the generation of a phenotypically plastic population, epigenetic mechanisms often provide a hotbed of innovation for countering environmental pressures, while the potential for genetic fixation can lead to strong epigenetic-genetic evolutionary synergy. At the level of cells and cellular populations, we begin this review by exploring the breadth of mechanisms for the storage and intergenerational transmission of epigenetic information, followed by a brief review of common and exotic epigenetically regulated phenotypes. We conclude by offering an in-depth coverage of recent papers centered around two critical issues: the evolvability of epigenetic traits through Baldwinian adaptive phenotypic plasticity and the potential for synergy between epigenetic and genetic evolution.

Do microbes have a memory? History-dependent behavior in the adaptation to variable environments

Microbes are constantly confronted with changes and challenges in their environment. A proper response to these environmental cues is needed for optimal cellular functioning and fitness. Interestingly, past exposure to environmental cues can accelerate or boost the response when this condition returns, even in daughter cells that have not directly encountered the initial cue. Moreover, this behavior is mostly epigenetic and often goes hand in hand with strong heterogeneity in the strength and speed of the response between isogenic cells of the same population, which might function as a bet-hedging strategy. In this review, we discuss examples of history-dependent behavior (HDB) or “memory,” with a specific focus on HDB in fluctuating environments. In most examples discussed, the lag time before the response to an environmental change is used as an experimentally measurable proxy for HDB. We highlight different mechanisms already implicated in HDB, and by using HDB in fluctuating carbon conditions as a case study, we showcase how the metabolic state of a cell can be a key determining factor for HDB. Finally, we consider possible evolutionary causes and consequences of such HDB.

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.

Proteasome-dependent truncation of the negative heterochromatin regulator Epe1 mediates antifungal resistance

Epe1 histone demethylase restricts H3K9-methylation-dependent heterochromatin, preventing it from spreading over, and silencing, gene-containing regions in fission yeast. External stress induces an adaptive response allowing heterochromatin island formation that confers resistance on surviving wild-type lineages. Here we investigate the mechanism by which Epe1 is regulated in response to stress. Exposure to caffeine or antifungals results in Epe1 ubiquitylation and proteasome-dependent removal of the N-terminal 150 residues from Epe1, generating truncated Epe1 (tEpe1) which accumulates in the cytoplasm. Constitutive tEpe1 expression increases H3K9 methylation over several chromosomal regions, reducing expression of underlying genes and enhancing resistance. Reciprocally, constitutive non-cleavable Epe1 expression decreases resistance. tEpe1-mediated resistance requires a functional JmjC demethylase domain. Moreover, caffeine-induced Epe1-to-tEpe1 cleavage is dependent on an intact cell integrity MAP kinase stress signaling pathway, mutations in which alter resistance. Thus, environmental changes elicit a mechanism that curtails the function of this key epigenetic modifier, allowing heterochromatin to reprogram gene expression, thereby bestowing resistance to some cells within a population. H3K9me-heterochromatin components are conserved in human and crop-plant fungal pathogens for which a limited number of antifungals exist. Our findings reveal how transient heterochromatin-dependent antifungal resistant epimutations develop and thus inform on how they might be countered.

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.

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.

How to characterize a strain? Clonal heterogeneity in industrial Saccharomyces influences both phenotypes and heterogeneity in phenotypes

Populations of microbes are constantly evolving heterogeneity that selection acts upon, yet heterogeneity is nontrivial to assess methodologically. The necessary practice of isolating single-cell colonies and thus subclone lineages for establishing, transferring, and using a strain results in single-cell bottlenecks with a generally neglected effect on the characteristics of the strain itself. Here, we present evidence that various subclone lineages for industrial yeasts sequenced for recent genomic studies show considerable differences, ranging from loss of heterozygosity to aneuploidies. Subsequently, we assessed whether phenotypic heterogeneity is also observable in industrial yeast, by individually testing subclone lineages obtained from products. Phenotyping of industrial yeast samples and their newly isolated subclones showed that single-cell bottlenecks during isolation can indeed considerably influence the observable phenotype. Next, we decoupled fitness distributions on the level of individual cells from clonal interference by plating single-cell colonies and quantifying colony area distributions. We describe and apply an approach using statistical modeling to compare the heterogeneity in phenotypes across samples and subclone lineages. One strain was further used to show how individual subclonal lineages are remarkably different not just in phenotype but also in the level of heterogeneity in phenotype. With these observations, we call attention to the fact that choosing an initial clonal lineage from an industrial yeast strain may vastly influence downstream performances and observations on karyotype, on phenotype, and also on heterogeneity.

Variation, Variegation and Heritable Gene Repression in S. cerevisiae

Phenotypic heterogeneity provides growth advantages for a population upon changes of the environment. In S. cerevisiae, such heterogeneity has been observed as "on/off" states in the expression of individual genes in individual cells. These variations can persist for a limited or extended number of mitotic divisions. Such traits are known to be mediated by heritable chromatin structures, by the mitotic transmission of transcription factors involved in gene regulatory circuits or by the cytoplasmic partition of prions or other unstructured proteins. The significance of such epigenetic diversity is obvious, however, we have limited insight into the mechanisms that generate it. In this review, we summarize the current knowledge of epigenetically maintained heterogeneity of gene expression and point out similarities and converging points between different mechanisms. We discuss how the sharing of limiting repression or activation factors can contribute to cell-to-cell variations in gene expression and to the coordination between short- and long- term epigenetic strategies. Finally, we discuss the implications of such variations and strategies in adaptation and aging.

Insights on the Control of Yeast Single-Cell Growth Variability by Members of the Trehalose Phosphate Synthase (TPS) Complex

Single-cell variability of growth is a biological phenomenon that has attracted growing interest in recent years. Important progress has been made in the knowledge of the origin of cell-to-cell heterogeneity of growth, especially in microbial cells. To better understand the origins of such heterogeneity at the single-cell level, we developed a new methodological pipeline that coupled cytometry-based cell sorting with automatized microscopy and image analysis to score the growth rate of thousands of single cells. This allowed investigating the influence of the initial amount of proteins of interest on the subsequent growth of the microcolony. As a preliminary step to validate this experimental setup, we referred to previous findings in yeast where the expression level of Tsl1, a member of the Trehalose Phosphate Synthase (TPS) complex, negatively correlated with cell division rate. We unfortunately could not find any influence of the initial TSL1 expression level on the growth rate of the microcolonies. We also analyzed the effect of the natural variations of trehalose-6-phosphate synthase (TPS1) expression on cell-to-cell growth heterogeneity, but we did not find any correlation. However, due to the already known altered growth of the tps1Δ mutants, we tested this strain at the single-cell level on a permissive carbon source. This mutant showed an outstanding lack of reproducibility of growth rate distributions as compared to the wild-type strain, with variable proportions of non-growing cells between cultivations and more heterogeneous microcolonies in terms of individual growth rates. Interestingly, this variable behavior at the single-cell level was reminiscent to the high variability that is also stochastically suffered at the population level when cultivating this tps1Δ strain, even when using controlled bioreactors.

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.

The Path towards Predicting Evolution as Illustrated in Yeast Cell Polarity

A bottom-up route towards predicting evolution relies on a deep understanding of the complex network that proteins form inside cells. In a rapidly expanding panorama of experimental possibilities, the most difficult question is how to conceptually approach the disentangling of such complex networks. These can exhibit varying degrees of hierarchy and modularity, which obfuscate certain protein functions that may prove pivotal for adaptation. Using the well-established polarity network in budding yeast as a case study, we first organize current literature to highlight protein entrenchments inside polarity. Following three examples, we see how alternating between experimental novelties and subsequent emerging design strategies can construct a layered understanding, potent enough to reveal evolutionary targets. We show that if you want to understand a cell’s evolutionary capacity, such as possible future evolutionary paths, seemingly unimportant proteins need to be mapped and studied. Finally, we generalize this research structure to be applicable to other systems of interest.

Microbial metabolic noise

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

A Similar Speciation Process Relying on Cellular Stochasticity in Microbial and Cancer Cell Populations

Similarities between microbial and cancer cells were noticed in recent years and serve as a basis for an atavism theory of cancer. Cancer cells would rely on the reactivation of an ancestral "genetic program" that would have been repressed in metazoan cells. Here we argue that cancer cells resemble unicellular organisms mainly in their similar way to exploit cellular stochasticity to produce cell specialization and maximize proliferation. Indeed, the relationship between low stochasticity, specialization, and quiescence found in normal differentiated metazoan cells is lost in cancer. On the contrary, low stochasticity and specialization are associated with high proliferation among cancer cells, as it is observed for the "specialist" cells in microbial populations that fully exploit nutritional resources to maximize proliferation. Thus, we propose a model where the appearance of cancer phenotypes can be solely due to an adaptation and a speciation process based on initial increase in cellular stochasticity.

Heritable gene expression variability and stochasticity govern clonal heterogeneity in circadian period

A ubiquitous feature of the circadian clock across life forms is its organization as a network of cellular oscillators, with individual cellular oscillators within the network often exhibiting considerable heterogeneity in their intrinsic periods. The interaction of coupling and heterogeneity in circadian clock networks is hypothesized to influence clock’s entrainability, but our knowledge of mechanisms governing period heterogeneity within circadian clock networks remains largely elusive. In this study, we aimed to explore the principles that underlie intercellular period variation in circadian clock networks (clonal period heterogeneity). To this end, we employed a laboratory selection approach and derived a panel of 25 clonal cell populations exhibiting circadian periods ranging from 22 to 28 h. We report that a single parent clone can produce progeny clones with a wide distribution of circadian periods, and this heterogeneity, in addition to being stochastically driven, has a heritable component. By quantifying the expression of 20 circadian clock and clock-associated genes across our clone panel, we found that inheritance of expression patterns in at least three clock genes might govern clonal period heterogeneity in circadian clock networks. Furthermore, we provide evidence suggesting that heritable epigenetic variation in gene expression regulation might underlie period heterogeneity.

How do genetically identical cells exhibit a different circadian phenotype? This study reveals that a single parent clone can produce progeny with a wide distribution of circadian periods and that this heterogeneity, in addition to being stochastically driven, has a heritable component, likely via heritable epigenetic variation in gene expression regulation.

A new protocol for single-cell RNA-seq reveals stochastic gene expression during lag phase in budding yeast

Current methods for single-cell RNA sequencing (scRNA-seq) of yeast cells do not match the throughput and relative simplicity of the state-of-the-art techniques that are available for mammalian cells. In this study, we report how 10x Genomics' droplet-based single-cell RNA sequencing technology can be modified to allow analysis of yeast cells. The protocol, which is based on in-droplet spheroplasting of the cells, yields an order-of-magnitude higher throughput in comparison to existing methods. After extensive validation of the method, we demonstrate its use by studying the dynamics of the response of isogenic yeast populations to a shift in carbon source, revealing the heterogeneity and underlying molecular processes during this shift. The method we describe opens new avenues for studies focusing on yeast cells, as well as other cells with a degradable cell wall.

Exact solution of stochastic gene expression models with bursting, cell cycle and replication dynamics

The bulk of stochastic gene expression models in the literature do not have an explicit description of the age of a cell within a generation and hence they cannot capture events such as cell division and DNA replication. Instead, many models incorporate the cell cycle implicitly by assuming that dilution due to cell division can be described by an effective decay reaction with first-order kinetics. If it is further assumed that protein production occurs in bursts, then the stationary protein distribution is a negative binomial. Here we seek to understand how accurate these implicit models are when compared with more detailed models of stochastic gene expression. We derive the exact stationary solution of the chemical master equation describing bursty protein dynamics, binomial partitioning at mitosis, age-dependent transcription dynamics including replication, and random interdivision times sampled from Erlang or more general distributions; the solution is different for single lineage and population snapshot settings. We show that protein distributions are well approximated by the solution of implicit models (a negative binomial) when the mean number of mRNAs produced per cycle is low and the cell cycle length variability is large. When these conditions are not met, the distributions are either almost bimodal or else display very flat regions near the mode and cannot be described by implicit models. We also show that for genes with low transcription rates, the size of protein noise has a strong dependence on the replication time, it is almost independent of cell cycle variability for lineage measurements, and increases with cell cycle variability for population snapshot measurements. In contrast for large transcription rates, the size of protein noise is independent of replication time and increases with cell cycle variability for both lineage and population measurements.

Investigation of chemical noise in multisite phosphorylation chain using linear noise approximation

Quantitative and qualitative nature of chemical noise propagation in biochemical reaction networks depend crucially on the topology of the networks. Multisite reversible phosphorylation-dephosphorylation of target proteins is one such recurrently found topology that regulates host of key functions in living cells. Here we analytically calculated the stochasticity in multistep reversible chemical reactions by determining variance of phosphorylated species at the steady state using linear noise approximation to investigate the effect of mass action and Michaelis-Menten kinetics on the noise of phosphorylated species. We probed the dependence of noise on the number of phosphorylation sites and the equilibrium constants of the reaction equilibria to investigate the chemical noise propagation in the multisite phosphorylation chain.

Epigenetic switching as a strategy for quick adaptation while attenuating biochemical noise

Epigenetic switches are bistable, molecular systems built from self-reinforcing feedback loops that can spontaneously switch between heritable phenotypes in the absence of DNA mutation. It has been hypothesized that epigenetic switches first evolved as a mechanism of bet-hedging and adaptation, but the evolutionary trajectories and conditions by which an epigenetic switch can outcompete adaptation through genetic mutation remain unknown. Here, we used computer simulations to evolve a mechanistic, biophysical model of a self-activating genetic circuit, which can both adapt genetically through mutation and exhibit epigenetic switching. We evolved these genetic circuits under a fluctuating environment that alternatively selected for low and high protein expression levels. In all tested conditions, the population first evolved by genetic mutation towards a region of genotypes where genetic adaptation can occur faster after each environmental transition. Once in this region, the self-activating genetic circuit can exhibit epigenetic switching, which starts competing with genetic adaptation. We show a trade-off between either minimizing the adaptation time or increasing the robustness of the phenotype to biochemical noise. Epigenetic switching was superior in a fast fluctuating environment because it adapted faster than genetic mutation after an environmental transition, while still attenuating the effect of biochemical noise on the phenotype. Conversely, genetic adaptation was favored in a slowly fluctuating environment because it maximized the phenotypic robustness to biochemical noise during the constant environment between transitions, even if this resulted in slower adaptation. This simple trade-off predicts the conditions and trajectories under which an epigenetic switch evolved to outcompete genetic adaptation, shedding light on possible mechanisms by which bet-hedging strategies might emerge and persist in natural populations.

Epigenetic switches regulate cell fate decisions during development in multicellular organisms, but their origin predates multicellularity because they are found in viruses, bacteria, and unicellular eukaryotes. It has been suggested that epigenetic switches first evolved as a mechanism of bet-hedging and adaptation to fluctuating environments. To discern the evolutionary pressures that select for epigenetic switches, we used computer simulations to evolve a mechanistic, biophysical model of a self-activating genetic circuit, which can both adapt genetically and exhibit epigenetic switching. Unlike laboratory evolution experiments, this in silico experiment was run many times over a range of evolutionary parameters (population size, selection pressure, mutation step-size, fluctuation frequency) and different model assumptions to uncover statistical regularities in the evolutionary trajectories. Using this computational approach, we could elucidate simple principles that predict the conditions that favor adaptation by epigenetic switching over genetic mutation in a fluctuating environment.

A general approach for detecting expressed mutations in AML cells using single cell RNA-sequencing

Virtually all tumors are genetically heterogeneous, containing mutationally-defined subclonal cell populations that often have distinct phenotypes. Single-cell RNA-sequencing has revealed that a variety of tumors are also transcriptionally heterogeneous, but the relationship between expression heterogeneity and subclonal architecture is unclear. Here, we address this question in the context of Acute Myeloid Leukemia (AML) by integrating whole genome sequencing with single-cell RNA-sequencing (using the 10x Genomics Chromium Single Cell 5’ Gene Expression workflow). Applying this approach to five cryopreserved AML samples, we identify hundreds to thousands of cells containing tumor-specific mutations in each case, and use the results to distinguish AML cells (including normal-karyotype AML cells) from normal cells, identify expression signatures associated with subclonal mutations, and find cell surface markers that could be used to purify subclones for further study. This integrative approach for connecting genotype to phenotype is broadly applicable to any sample that is phenotypically and genetically heterogeneous.

The advent of single-cell RNA sequencing has revealed significant transcriptional heterogeneity in cancer, but its relationship to genomic heterogeneity remains unclear. Focusing on acute myeloid leukemia samples, the authors describe a general approach for linking mutation-containing cells to their transcriptional phenotypes using single-cell RNA sequencing data.

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.

Epigenetic Modifications in Acute Myeloid Leukemia: Prognosis, Treatment, and Heterogeneity

Leukemia, specifically acute myeloid leukemia (AML), is a common malignancy that can be differentiated into multiple subtypes based on leukemogenic history and etiology. Although genetic aberrations, particularly cytogenetic abnormalities and mutations in known oncogenes, play an integral role in AML development, epigenetic processes have been shown as a significant and sometimes independent dynamic in AML pathophysiology. Here, we summarize how tumors evolve and describe AML through an epigenetic lens, including discussions on recent discoveries that include prognostics from epialleles, changes in RNA function for hematopoietic stem cells and the epitranscriptome, and novel epigenetic treatment options. We further describe the limitations of treatment in the context of the high degree of heterogeneity that characterizes acute myeloid leukemia.

Intrinsic and extrinsic noise of gene expression in lineage trees

Cell-to-cell heterogeneity is driven by stochasticity in intracellular reactions and the population dynamics. While these sources are usually studied separately, we develop an agent-based framework that accounts for both factors while tracking every single cell of a growing population. Apart from the common intrinsic variability, the framework also predicts extrinsic noise without the need to introduce fluctuating rate constants. Instead, extrinsic fluctuations are explained by cell cycle fluctuations and differences in cell age. We provide explicit formulas to quantify mean molecule numbers, intrinsic and extrinsic noise statistics in two-colour experiments. We find that these statistics differ significantly depending on the experimental setup used to observe the cells. We illustrate this fact using (i) averages over an isolated cell lineage tracked over many generations as observed in the mother machine, (ii) population snapshots with known cell ages as recorded in time-lapse microscopy, and (iii) snapshots with unknown cell ages as measured from static images or flow cytometry. Applying the method to models of stochastic gene expression and feedback regulation elucidates that isolated lineages, as compared to snapshot data, can significantly overestimate the mean number of molecules, overestimate extrinsic noise but underestimate intrinsic noise and have qualitatively different sensitivities to cell cycle fluctuations.

On the duration of the microbial lag phase

When faced with environmental changes, microbes enter a lag phase during which cell growth is arrested, allowing cells to adapt to the new situation. The discovery of the lag phase started the field of gene regulation and led to the unraveling of underlying mechanisms. However, the factors determining the exact duration and dynamics of the lag phase remain largely elusive. Naively, one would expect that cells adapt as quickly as possible, so they can resume growth and compete with other organisms. However, recent studies show that the lag phase can last from several hours up to several days. Moreover, some cells within the same population take much longer than others, despite being genetically identical. In addition, the lag phase duration is also influenced by the past, with recent exposure to a given environment leading to a quicker adaptation when that environment returns. Genome-wide screens in Saccharomyces cerevisiae on carbon source shifts now suggest that the length of the lag phase, the heterogeneity in lag times of individual cells, and the history-dependent behavior are not determined by the time it takes to induce a few specific genes related to uptake and metabolism of a new carbon source. Instead, a major shift in general metabolism, and in particular a switch between fermentation and respiration, is the major bottleneck that determines lag duration. This suggests that there may be a fitness trade-off between complete adaptation of a cell’s metabolism to a given environment, and a short lag phase when the environment changes.

Unbiased Fitness Estimation of Pooled Barcode or Amplicon Sequencing Studies

Standard practice for phenotyping complex cell pools is to measure the fold enrichment of genotype-specific amplicons after a period of competitive growth. Here, we show that fold-enrichment measures cannot be compared across genotype pools with different fitness distributions. We develop a method to calculate an unbiased estimate of relative fitness by tracking abundances over several time points and show how to optimize experimental protocols to minimize fitness measurement error.

Scaling of G1 Duration with Population Doubling Time by a Cyclin in Saccharomyces cerevisiae

The longer cells stay in particular phases of the cell cycle, the longer it will take these cell populations to increase. However, the above qualitative description has very little predictive value, unless it can be codified mathematically. A quantitative relation that defines the population doubling time (Td) as a function of the time eukaryotic cells spend in specific cell cycle phases would be instrumental for estimating rates of cell proliferation and for evaluating introduced perturbations. Here, we show that in human cells, the length of the G1 phase (TG1) regressed on Td with a slope of ≈0.75, while in the yeast Saccharomyces cerevisiae, the slope was slightly smaller, at ≈0.60. On the other hand, cell size was not strongly associated with Td or TG1 in cell cultures that were proliferating at different rates. Furthermore, we show that levels of the yeast G1 cyclin Cln3p were positively associated with rates of cell proliferation over a broad range, at least in part through translational control mediated by a short upstream ORF (uORF) in the CLN3 transcript. Cln3p was also necessary for the proper scaling between TG1 and Td In contrast, yeast lacking the Whi5p transcriptional repressor maintained the scaling between TG1 and Td These data reveal fundamental scaling relationships between the duration of eukaryotic cell cycle phases and rates of cell proliferation, point to the necessary role of Cln3p in these relationships in yeast, and provide a mechanistic basis linking Cln3p levels to proliferation rates and the scaling of G1 with doubling time.

Transition between fermentation and respiration determines history-dependent behavior in fluctuating carbon sources

Cells constantly adapt to environmental fluctuations. These physiological changes require time and therefore cause a lag phase during which the cells do not function optimally. Interestingly, past exposure to an environmental condition can shorten the time needed to adapt when the condition re-occurs, even in daughter cells that never directly encountered the initial condition. Here, we use the molecular toolbox of Saccharomyces cerevisiae to systematically unravel the molecular mechanism underlying such history-dependent behavior in transitions between glucose and maltose. In contrast to previous hypotheses, the behavior does not depend on persistence of proteins involved in metabolism of a specific sugar. Instead, presence of glucose induces a gradual decline in the cells' ability to activate respiration, which is needed to metabolize alternative carbon sources. These results reveal how trans-generational transitions in central carbon metabolism generate history-dependent behavior in yeast, and provide a mechanistic framework for similar phenomena in other cell types.

A systematic study of the determinants of protein abundance memory in cell lineage

Proteins are essential players of life activities. Intracellular protein levels directly affect cellular functions and cell fate. Upon cell division, the proteins in the mother cell are inherited by the daughters. However, what factors and by how much they affect this epigenetic inheritance of protein abundance remains unclear. Using both computational and experimental approaches, we systematically investigated this problem. We derived an analytical expression for the dependence of protein inheritance on various factors and showed that it agreed with numerical simulations of protein production and experimental results. Our work provides a framework for quantitative studies of protein inheritance and for the potential application of protein memory manipulation.

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.

Statistical mechanics for metabolic networks during steady state growth

Which properties of metabolic networks can be derived solely from stoichiometry? Predictive results have been obtained by flux balance analysis (FBA), by postulating that cells set metabolic fluxes to maximize growth rate. Here we consider a generalization of FBA to single-cell level using maximum entropy modeling, which we extend and test experimentally. Specifically, we define for Escherichia coli metabolism a flux distribution that yields the experimental growth rate: the model, containing FBA as a limit, provides a better match to measured fluxes and it makes a wide range of predictions: on flux variability, regulation, and correlations; on the relative importance of stoichiometry vs. optimization; on scaling relations for growth rate distributions. We validate the latter here with single-cell data at different sub-inhibitory antibiotic concentrations. The model quantifies growth optimization as emerging from the interplay of competitive dynamics in the population and regulation of metabolism at the level of single cells.

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.

Links between evolutionary processes and phenotypic robustness in microbes

The costs and benefits of random phenotypic heterogeneity in microbes have been vigorously debated and experimental tested for decades; yet, this conversation is largely independent from discussion of phenotypic robustness in other disciplines. In this review I connect microbial examples of stochasticity with studies on the ecological and population-genetic consequences of phenotypic variability. These topics illustrate the complexity of selection pressures on phenotypic robustness and provide inspiration that this complexity can be parsed with theoretical advances and the experimental power of microbial systems.

Heritable stress response dynamics revealed by single-cell genealogy

Cells often respond to environmental stimuli by activating specific transcription factors. Upon exposure to glucose limitation stress, it is known that yeast Saccharomyces cerevisiae cells dephosphorylate the general stress response factor Msn2, leading to its nuclear localization, which in turn activates the expression of many genes. However, the precise dynamics of Msn2 nucleocytoplasmic translocations and whether they are inherited over multiple generations in a stress-dependent manner are not well understood. Tracking Msn2 localization events in yeast lineages grown on a microfluidic chip, here we report how cells modulate the amplitude, duration, frequency, and dynamic pattern of the localization events in response to glucose limitation stress. Single yeast cells were found to modulate the amplitude and frequency of Msn2 nuclear localization, but not its duration. Moreover, the Msn2 localization frequency was epigenetically inherited in descendants of mother cells, leading to a decrease in cell-to-cell variation in localization frequency. An analysis of the time dynamic patterns of nuclear localizations between genealogically related cell pairs using an information theory approach found that the magnitude of pattern similarity increased with stress intensity and was strongly inherited by the descendant cells at the highest stress level. By dissecting how general stress response dynamics is contributed by different modulation schemes over long time scales, our work provides insight into which scheme evolution might have acted on to optimize fitness in stressful environments.