Random partitioning of molecules at cell division

Stochastic Gene Expression in Proliferating Cells: Differing Noise Intensity in Single-Cell and Population Perspectives

Random fluctuations (noise) in gene expression can be studied from two complementary perspectives: following expression in a single cell over time or comparing expression between cells in a proliferating population at a given time. Here, we systematically investigated scenarios where both perspectives lead to different levels of noise in a given gene product. We first consider a stable protein, whose concentration is diluted by cellular growth, and the protein inhibits growth at high concentrations, establishing a positive feedback loop. For a stochastic model with molecular bursting of gene products, we analytically predict and contrast the steady-state distributions of protein concentration in both frameworks. Although positive feedback amplifies the noise in expression, this amplification is much higher in the population framework compared to following a single cell over time. We also study other processes that lead to different noise levels even in the absence of such dilution-based feedback. When considering randomness in the partitioning of molecules between daughters during mitosis, we find that in the single-cell perspective, the noise in protein concentration is independent of noise in the cell cycle duration. In contrast, partitioning noise is amplified in the population perspective by increasing randomness in cell-cycle time. Overall, our results show that the commonly used single-cell framework that does not account for proliferating cells can, in some cases, underestimate the noise in gene product levels. These results have important implications for studying the inter-cellular variation of different stress-related expression programs across cell types that are known to inhibit cellular growth.

The purpose and ubiquity of turnover

Turnover-constant component production and destruction-is ubiquitous in biology. Turnover occurs across organisms and scales, including for RNAs, proteins, membranes, macromolecular structures, organelles, cells, hair, feathers, nails, antlers, and teeth. For many systems, turnover might seem wasteful when degraded components are often fully functional. Some components turn over with shockingly high rates and others do not turn over at all, further making this process enigmatic. However, turnover can address fundamental problems by yielding powerful properties, including regeneration, rapid repair onset, clearance of unpredictable damage and errors, maintenance of low constitutive levels of disrepair, prevention of stable hazards, and transitions. I argue that trade-offs between turnover benefits and metabolic costs, combined with constraints on turnover, determine its presence and rates across distinct contexts. I suggest that the limits of turnover help explain aging and that turnover properties and the basis for its levels underlie this fundamental component of life.

Effects of mRNA conformational switching on translational noise in gene circuits

Intragenic translational heterogeneity describes the variation in translation at the level of transcripts for an individual gene. A factor that contributes to this source of variation is the mRNA structure. Both the composition of the thermodynamic ensemble, i.e., the stationary distribution of mRNA structures, and the switching dynamics between those play a role. The effect of the switching dynamics on intragenic translational heterogeneity remains poorly understood. We present a stochastic translation model that accounts for mRNA structure switching and is derived from a Markov model via approximate stochastic filtering. We assess the approximation on various timescales and provide a method to quantify how mRNA structure dynamics contributes to translational heterogeneity. With our approach, we allow quantitative information on mRNA switching from biophysical experiments or coarse-grain molecular dynamics simulations of mRNA structures to be included in gene regulatory chemical reaction network models without an increase in the number of species. Thereby, our model bridges a gap between mRNA structure kinetics and gene expression models, which we hope will further improve our understanding of gene regulatory networks and facilitate genetic circuit design.

A dual fluorescence protein expression system detects cell cycle dependent protein noise

Inherently identical cells exhibit significant phenotypic variation. It can be essential for many biological processes and is known to arise from stochastic, 'noisy', gene expression that is determined by intrinsic and extrinsic components. It is now obvious that the noise varies as a function of inducer concentration. However, its fluctuation over the cell cycle is limited. Applying dual colour fluorescence protein reporter system, Cyan Fluorescent Protein (CFP) and Yellow fluorescent protein (YFP) tagged multi-copy plasmids, we determine variation of the noise components over the phases in lac promoter induced by Isopropyl β-D-1-thiogalactopyranoside (IPTG) and in presence of additional Magnesium, Mg2+ ion. We, also, estimate the how such system deviates from observations of single-copy plasmid. Found 25 % difference between multi-copy system and single-copy system clarifies that observed noise is considerable and estimates population behaviour during the cell cycle. We show that total variation in cells induced with IPTG is determined by higher extrinsic than intrinsic noise. It increases from Lag to Exponential phase and decreases from Retardation to Stationary phase. By observing slow and fast dividing cells, we show that 5 mM Mg2+ increases population homogeneity compared to 2.5 mM Mg2+ in the environment. The experimental data obtained using dual colour fluorescence protein reporter system demonstrates that protein expression noise, depending on intra cellular ionic concentration, is tightly controlled by phase of the cell.

Phenotypic Heterogeneity, Bidirectionality, Universal Cues, Plasticity, Mechanics, and the Tumor Microenvironment Drive Cancer Metastasis

Tumor diseases become a huge problem when they embark on a path that advances to malignancy, such as the process of metastasis. Cancer metastasis has been thoroughly investigated from a biological perspective in the past, whereas it has still been less explored from a physical perspective. Until now, the intraluminal pathway of cancer metastasis has received the most attention, while the interaction of cancer cells with macrophages has received little attention. Apart from the biochemical characteristics, tumor treatments also rely on the tumor microenvironment, which is recognized to be immunosuppressive and, as has recently been found, mechanically stimulates cancer cells and thus alters their functions. The review article highlights the interaction of cancer cells with other cells in the vascular metastatic route and discusses the impact of this intercellular interplay on the mechanical characteristics and subsequently on the functionality of cancer cells. For instance, macrophages can guide cancer cells on their intravascular route of cancer metastasis, whereby they can help to circumvent the adverse conditions within blood or lymphatic vessels. Macrophages induce microchannel tunneling that can possibly avoid mechanical forces during extra- and intravasation and reduce the forces within the vascular lumen due to vascular flow. The review article highlights the vascular route of cancer metastasis and discusses the key players in this traditional route. Moreover, the effects of flows during the process of metastasis are presented, and the effects of the microenvironment, such as mechanical influences, are characterized. Finally, the increased knowledge of cancer metastasis opens up new perspectives for cancer treatment.

Cell size homeostasis is tightly controlled throughout the cell cycle

To achieve a stable size distribution over multiple generations, proliferating cells require a means of counteracting stochastic noise in the rate of growth, the time spent in various phases of the cell cycle, and the imprecision in the placement of the plane of cell division. In the most widely accepted model, cell size is thought to be regulated at the G1/S transition, such that cells smaller than a critical size pause at the end of G1 phase until they have accumulated mass to a predetermined size threshold, at which point the cells proceed through the rest of the cell cycle. However, a model, based solely on a specific size checkpoint at G1/S, cannot readily explain why cells with deficient G1/S control mechanisms are still able to maintain a very stable cell size distribution. Furthermore, such a model would not easily account for stochastic variation in cell size during the subsequent phases of the cell cycle, which cannot be anticipated at G1/S. To address such questions, we applied computationally enhanced quantitative phase microscopy (ceQPM) to populations of cultured human cell lines, which enables highly accurate measurement of cell dry mass of individual cells throughout the cell cycle. From these measurements, we have evaluated the factors that contribute to maintaining cell mass homeostasis at any point in the cell cycle. Our findings reveal that cell mass homeostasis is accurately maintained, despite disruptions to the normal G1/S machinery or perturbations in the rate of cell growth. Control of cell mass is generally not confined to regulation of the G1 length. Instead mass homeostasis is imposed throughout the cell cycle. In the cell lines examined, we find that the coefficient of variation (CV) in dry mass of cells in the population begins to decline well before the G1/S transition and continues to decline throughout S and G2 phases. Among the different cell types tested, the detailed response of cell growth rate to cell mass differs. However, in general, when it falls below that for exponential growth, the natural increase in the CV of cell mass is effectively constrained. We find that both mass-dependent cell cycle regulation and mass-dependent growth rate modulation contribute to reducing cell mass variation within the population. Through the interplay and coordination of these 2 processes, accurate cell mass homeostasis emerges. Such findings reveal previously unappreciated and very general principles of cell size control in proliferating cells. These same regulatory processes might also be operative in terminally differentiated cells. Further quantitative dynamical studies should lead to a better understanding of the underlying molecular mechanisms of cell size control.

A heritable iron memory enables decision-making in Escherichia coli

The importance of memory in bacterial decision-making is relatively unexplored. We show here that a prior experience of swarming is remembered when Escherichia coli encounters a new surface, improving its future swarming efficiency. We conducted >10,000 single-cell swarm assays to discover that cells store memory in the form of cellular iron levels. This "iron" memory preexists in planktonic cells, but the act of swarming reinforces it. A cell with low iron initiates swarming early and is a better swarmer, while the opposite is true for a cell with high iron. The swarming potential of a mother cell, which tracks with its iron memory, is passed down to its fourth-generation daughter cells. This memory is naturally lost by the seventh generation, but artificially manipulating iron levels allows it to persist much longer. A mathematical model with a time-delay component faithfully recreates the observed dynamic interconversions between different swarming potentials. We demonstrate that cellular iron levels also track with biofilm formation and antibiotic tolerance, suggesting that iron memory may impact other physiologies.

Measuring prion propagation in single bacteria elucidates a mechanism of loss

Prions are self-propagating protein aggregates formed by specific proteins that can adopt alternative folds. Prions were discovered as the cause of the fatal transmissible spongiform encephalopathies in mammals, but prions can also constitute nontoxic protein-based elements of inheritance in fungi and other species. Prion propagation has recently been shown to occur in bacteria for more than a hundred cell divisions, yet a fraction of cells in these lineages lost the prion through an unknown mechanism. Here, we investigate prion propagation in single bacterial cells as they divide using microfluidics and fluorescence microscopy. We show that the propagation occurs in two distinct modes. In a fraction of the population, cells had multiple small visible aggregates and lost the prion through random partitioning of aggregates to one of the two daughter cells at division. In the other subpopulation, cells had a stable large aggregate localized to the pole; upon division the mother cell retained this polar aggregate and a daughter cell was generated that contained small aggregates. Extending our findings to prion domains from two orthologous proteins, we observe similar propagation and loss properties. Our findings also provide support for the suggestion that bacterial prions can form more than one self-propagating state. We implement a stochastic version of the molecular model of prion propagation from yeast and mammals that recapitulates all the observed single-cell properties. This model highlights challenges for prion propagation that are unique to prokaryotes and illustrates the conservation of fundamental characteristics of prion propagation.

Phenotypic heterogeneity in human genetic diseases: ultrasensitivity-mediated threshold effects as a unifying molecular mechanism

Phenotypic heterogeneity is very common in genetic systems and in human diseases and has important consequences for disease diagnosis and treatment. In addition to the many genetic and non-genetic (e.g., epigenetic, environmental) factors reported to account for part of the heterogeneity, we stress the importance of stochastic fluctuation and regulatory network topology in contributing to phenotypic heterogeneity. We argue that a threshold effect is a unifying principle to explain the phenomenon; that ultrasensitivity is the molecular mechanism for this threshold effect; and discuss the three conditions for phenotypic heterogeneity to occur. We suggest that threshold effects occur not only at the cellular level, but also at the organ level. We stress the importance of context-dependence and its relationship to pleiotropy and edgetic mutations. Based on this model, we provide practical strategies to study human genetic diseases. By understanding the network mechanism for ultrasensitivity and identifying the critical factor, we may manipulate the weak spot to gently nudge the system from an ultrasensitive state to a stable non-disease state. Our analysis provides a new insight into the prevention and treatment of genetic diseases.

PyEcoLib: a python library for simulating stochastic cell size dynamics

Recently, there has been an increasing need for tools to simulate cell size regulation due to important applications in cell proliferation and gene expression. However, implementing the simulation usually presents some difficulties, as the division has a cycle-dependent occurrence rate. In this article, we gather a recent theoretical framework inPyEcoLib, a python-based library to simulate the stochastic dynamics of the size of bacterial cells. This library can simulate cell size trajectories with an arbitrarily small sampling period. In addition, this simulator can include stochastic variables, such as the cell size at the beginning of the experiment, the cycle duration timing, the growth rate, and the splitting position. Furthermore, from a population perspective, the user can choose between tracking a single lineage or all cells in a colony. They can also simulate the most common division strategies (adder, timer, and sizer) using the division rate formalism and numerical methods. As an example of PyecoLib applications, we explain how to couple size dynamics with gene expression predicting, from simulations, how the noise in protein levels increases by increasing the noise in division timing, the noise in growth rate and the noise in cell splitting position. The simplicity of this library and its transparency about the underlying theoretical framework yield the inclusion of cell size stochasticity in complex models of gene expression.

Iron Memory in E. coli

The importance of memory in bacterial decision-making is relatively unexplored. We show here that a prior experience of swarming is remembered when E. coli encounters a new surface, improving its future swarming efficiency. We conducted >10,000 single-cell swarm assays to discover that cells store memory in the form of cellular iron levels. This memory pre-exists in planktonic cells, but the act of swarming reinforces it. A cell with low iron initiates swarming early and is a better swarmer, while the opposite is true for a cell with high iron. The swarming potential of a mother cell, whether low or high, is passed down to its fourth-generation daughter cells. This memory is naturally lost by the seventh generation, but artificially manipulating iron levels allows it to persist much longer. A mathematical model with a time-delay component faithfully recreates the observed dynamic interconversions between different swarming potentials. We also demonstrate that iron memory can integrate multiple stimuli, impacting other bacterial behaviors such as biofilm formation and antibiotic tolerance.

Phenotypic heterogeneity in the bacterial oxidative stress response is driven by cell-cell interactions

Genetically identical bacterial cells commonly display different phenotypes. This phenotypic heterogeneity is well known for stress responses, where it is often explained as bet hedging against unpredictable environmental threats. Here, we explore phenotypic heterogeneity in a major stress response of Escherichia coli and find it has a fundamentally different basis. We characterize the response of cells exposed to hydrogen peroxide (H2O2) stress in a microfluidic device under constant growth conditions. A machine-learning model reveals that phenotypic heterogeneity arises from a precise and rapid feedback between each cell and its immediate environment. Moreover, we find that the heterogeneity rests upon cell-cell interaction, whereby cells shield each other from H2O2 via their individual stress responses. Our work shows how phenotypic heterogeneity in bacterial stress responses can emerge from short-range cell-cell interactions and result in a collective phenotype that protects a large proportion of the population.

Measuring prion propagation in single bacteria elucidates mechanism of loss

Prions are self-propagating protein aggregates formed by specific proteins that can adopt alternative folds. Prions were discovered as the cause of the fatal transmissible spongiform encephalopathies in mammals, but prions can also constitute non-toxic protein-based elements of inheritance in fungi and other species. Prion propagation has recently been shown to occur in bacteria for more than a hundred cell divisions, yet a fraction of cells in these lineages lost the prion through an unknown mechanism. Here, we investigate prion propagation in single bacterial cells as they divide using microfluidics and fluorescence microscopy. We show that the propagation occurs in two distinct modes with distinct stability and inheritance characteristics. We find that the prion is lost through random partitioning of aggregates to one of the two daughter cells at division. Extending our findings to prion domains from two orthologous proteins, we observe similar propagation and loss properties. Our findings also provide support for the suggestion that bacterial prions can form more than one self-propagating state. We implement a stochastic version of the molecular model of prion propagation from yeast and mammals that recapitulates all the observed single-cell properties. This model highlights challenges for prion propagation that are unique to prokaryotes and illustrates the conservation of fundamental characteristics of prion propagation across domains of life.

Epigenetic memory acquired during long-term EMT induction governs the recovery to the epithelial state

Epithelial-mesenchymal transition (EMT) and its reverse mesenchymal-epithelial transition (MET) are critical during embryonic development, wound healing and cancer metastasis. While phenotypic changes during short-term EMT induction are reversible, long-term EMT induction has been often associated with irreversibility. Here, we show that phenotypic changes seen in MCF10A cells upon long-term EMT induction by TGFβ need not be irreversible, but have relatively longer time scales of reversibility than those seen in short-term induction. Next, using a phenomenological mathematical model to account for the chromatin-mediated epigenetic silencing of the miR-200 family by ZEB family, we highlight how the epigenetic memory gained during long-term EMT induction can slow the recovery to the epithelial state post-TGFβ withdrawal. Our results suggest that epigenetic modifiers can govern the extent and time scale of EMT reversibility and advise caution against labelling phenotypic changes seen in long-term EMT induction as 'irreversible'.

Microtubule-mitochondrial attachment facilitates cell division symmetry and mitochondrial partitioning in fission yeast

Association with microtubules inhibits the fission of mitochondria in Schizosaccharomyces pombe. Here, we show that this attachment of mitochondria to microtubules is an important cell-intrinsic factor in determining cell division symmetry. By comparing mutant cells that exhibited enhanced attachment and no attachment of mitochondria to microtubules (Dnm1Δ and Mmb1Δ, respectively), we show that microtubules in these mutants displayed aberrant dynamics compared to wild-type cells, which resulted in errors in nuclear positioning. This translated to cell division asymmetry in a significant proportion of both Dnm1Δ and Mmb1Δ cells. Asymmetric division in Dnm1Δ and Mmb1Δ cells resulted in unequal distribution of mitochondria, with the daughter cell that received more mitochondria growing faster than the other daughter cell. Taken together, we show the existence of homeostatic feedback controls between mitochondria and microtubules in fission yeast, which directly influence mitochondrial partitioning and, thereby, cell growth. This article has an associated First Person interview with the first author of the paper.

Efficient Quantification of Extrinsic Fluctuations via Stochastic Simulations

At the molecular level, all the biological processes are exposed to fluctuations emanating from various sources in and around the cellular system. Often these fluctuations dictate the outcome of a cell-fate decision-making event. Thus, having an accurate estimate of these fluctuations for any biological network is extremely important. There are well-established theoretical and numerical methods to quantify the intrinsic fluctuation present within a biological network arising due to the low copy numbers of cellular components. Unfortunately, the extrinsic fluctuations arising due to cell division events, epigenetic regulation, etc. have received very little attention. However, recent studies demonstrate that these extrinsic fluctuations significantly affect the transcriptional heterogeneity of certain important genes. Herein, we propose a new stochastic simulation algorithm to efficiently estimate these extrinsic fluctuations for experimentally constructed bidirectional transcriptional reporter systems along with the intrinsic variability. We use the Nanog transcriptional regulatory network and its variants to illustrate our numerical method. Our method reconciled experimental observations related to Nanog transcription, made exciting predictions, and can be applied to quantify intrinsic and extrinsic fluctuations for any similar transcriptional regulatory network.

Collective behavior and nongenetic inheritance allow bacterial populations to adapt to changing environments

Collective behaviors require coordination among a group of individuals. As a result, individuals that are too phenotypically different from the rest of the group can be left out, reducing heterogeneity, but increasing coordination. If individuals also reproduce, the offspring can have different phenotypes from their parent(s). This raises the question of how these two opposing processes-loss of diversity by collective behaviors and generation of it through growth and inheritance-dynamically shape the phenotypic composition of an isogenic population. We examine this question theoretically using collective migration of chemotactic bacteria as a model system, where cells of different swimming phenotypes are better suited to navigate in different environments. We find that the differential loss of phenotypes caused by collective migration is environment-dependent. With cell growth, this differential loss enables migrating populations to dynamically adapt their phenotype compositions to the environment, enhancing migration through multiple environments. Which phenotypes are produced upon cell division depends on the level of nongenetic inheritance, and higher inheritance leads to larger composition adaptation and faster migration at steady state. However, this comes at the cost of slower responses to new environments. Due to this trade-off, there is an optimal level of inheritance that maximizes migration speed through changing environments, which enables a diverse population to outperform a nondiverse one. Growing populations might generally leverage the selection-like effects provided by collective behaviors to dynamically shape their own phenotype compositions, without mutations.

Quantifying biochemical reaction rates from static population variability within incompletely observed complex networks

Quantifying biochemical reaction rates within complex cellular processes remains a key challenge of systems biology even as high-throughput single-cell data have become available to characterize snapshots of population variability. That is because complex systems with stochastic and non-linear interactions are difficult to analyze when not all components can be observed simultaneously and systems cannot be followed over time. Instead of using descriptive statistical models, we show that incompletely specified mechanistic models can be used to translate qualitative knowledge of interactions into reaction rate functions from covariability data between pairs of components. This promises to turn a globally intractable problem into a sequence of solvable inference problems to quantify complex interaction networks from incomplete snapshots of their stochastic fluctuations.

Long-term imaging of individual mRNA molecules in living cells

Single-cell imaging of individual mRNAs has revealed core mechanisms of the central dogma. However, most approaches require cell fixation or have limited sensitivity for live-cell applications. Here, we describe SunRISER (SunTag-based reporter for imaging signal-enriched mRNA), a computationally and experimentally optimized approach for unambiguous detection of single mRNA molecules in living cells. When viewed by epifluorescence microscopy, SunRISER-labeled mRNAs show strong signal to background and resistance to photobleaching, which together enable long-term mRNA imaging studies. SunRISER variants, using 8× and 10× stem-loop arrays, demonstrate effective mRNA detection while significantly reducing alterations to target mRNA sequences. We characterize SunRISER to observe mRNA inheritance during mitosis and find that stressors enhance diversity among post-mitotic sister cells. Taken together, SunRISER enables a glimpse into living cells to observe aspects of the central dogma and the role of mRNAs in rare and dynamical trafficking events.

Types and functions of heterogeneity in mycobacteria

The remarkable ability of Mycobacterium tuberculosis to survive attacks from the host immune response and drug treatment is due to the resilience of a few bacilli rather than a result of survival of the entire population. Maintenance of mycobacterial subpopulations with distinct phenotypic characteristics is key for survival in the face of dynamic and variable stressors encountered during infection. Mycobacterial populations develop a wide range of phenotypes through an innate asymmetric growth pattern and adaptation to fluctuating microenvironments during infection that point to heterogeneity being a vital survival strategy. In this Review, we describe different types of mycobacterial heterogeneity and discuss how heterogeneity is generated and regulated in response to environmental cues. We discuss how this heterogeneity may have a key role in recording memory of their environment at both the single-cell level and the population level to give mycobacterial populations plasticity to withstand complex stressors.

Phenotypic heterogeneity in persisters: a novel 'hunker' theory of persistence

Persistence has been linked to treatment failure since its discovery over 70 years ago and understanding formation, nature and survival of this key antibiotic refractory subpopulation is crucial to enhancing treatment success and combatting the threat of antimicrobial resistance (AMR). The term 'persistence' is often used interchangeably with other terms such as tolerance or dormancy. In this review we focus on 'antibiotic persistence' which we broadly define as a feature of a subpopulation of bacterial cells that possesses the non-heritable character of surviving exposure to one or more antibiotics; and persisters as cells that possess this characteristic. We discuss novel molecular mechanisms involved in persister cell formation, as well as environmental factors which can contribute to increased antibiotic persistence in vivo, highlighting recent developments advanced by single-cell studies. We also aim to provide a comprehensive model of persistence, the 'hunker' theory which is grounded in intrinsic heterogeneity of bacterial populations and a myriad of 'hunkering down' mechanisms which can contribute to antibiotic survival of the persister subpopulation. Finally, we discuss antibiotic persistence as a 'stepping-stone' to AMR and stress the urgent need to develop effective anti-persister treatment regimes to treat this highly clinically relevant bacterial sub-population.

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.

Pathway dynamics can delineate the sources of transcriptional noise in gene expression

Single-cell expression profiling opens up new vistas on cellular processes. Extensive cell-to-cell variability at the transcriptomic and proteomic level has been one of the stand-out observations. Because most experimental analyses are destructive we only have access to snapshot data of cellular states. This loss of temporal information presents significant challenges for inferring dynamics, as well as causes of cell-to-cell variability. In particular, we typically cannot separate dynamic variability from within cells ('intrinsic noise') from variability across the population ('extrinsic noise'). Here, we make this non-identifiability mathematically precise, allowing us to identify new experimental set-ups that can assist in resolving this non-identifiability. We show that multiple generic reporters from the same biochemical pathways (e.g. mRNA and protein) can infer magnitudes of intrinsic and extrinsic transcriptional noise, identifying sources of heterogeneity. Stochastic simulations support our theory, and demonstrate that 'pathway-reporters' compare favourably to the well-known, but often difficult to implement, dual-reporter method.

Towards a synthetic cell cycle

Recent developments in synthetic biology may bring the bottom-up generation of a synthetic cell within reach. A key feature of a living synthetic cell is a functional cell cycle, in which DNA replication and segregation as well as cell growth and division are well integrated. Here, we describe different approaches to recreate these processes in a synthetic cell, based on natural systems and/or synthetic alternatives. Although some individual machineries have recently been established, their integration and control in a synthetic cell cycle remain to be addressed. In this Perspective, we discuss potential paths towards an integrated synthetic cell cycle.

Challenges of analysing stochastic gene expression in bacteria using single-cell time-lapse experiments

Stochastic gene expression causes phenotypic heterogeneity in a population of genetically identical bacterial cells. Such non-genetic heterogeneity can have important consequences for the population fitness, and therefore cells implement regulation strategies to either suppress or exploit such heterogeneity to adapt to their circumstances. By employing time-lapse microscopy of single cells, the fluctuation dynamics of gene expression may be analysed, and their regulatory mechanisms thus deciphered. However, a careful consideration of the experimental design and data-analysis is needed to produce useful data for deriving meaningful insights from them. In the present paper, the individual steps and challenges involved in a time-lapse experiment are discussed, and a rigorous framework for designing, performing, and extracting single-cell gene expression dynamics data from such experiments is outlined.

The influence of methylation status on a stochastic model of MGMT dynamics in glioblastoma: Phenotypic selection can occur with and without a downshift in promoter methylation status

Glioblastoma originates in the brain and is one of the most aggressive cancer types. Glioblastoma represents 15% of all brain tumours, with a median survival of 15 months. Although the current standard of care for such a tumour (the Stupp protocol) has shown positive results for the prognosis of patients, O-6-methylguanine-DNA methyltransferase (MGMT) driven drug resistance has been an issue of increasing concern and hence requires innovative approaches. In addition to the well established drug resistance factors such as tumour location and blood brain barriers, it is also important to understand how the genetic and epigenetic dynamics of the glioblastoma cells can play a role. One important aspect of this is the study of methylation status of MGMT following administration of temozolomide. In this paper, we extend our previously published model that simulated MGMT expression in glioblastoma cells to incorporate the promoter methylation status of MGMT. This methylation status has clinical significance and is used as a marker for patient outcomes. Using this model, we investigate the causative relationship between temozolomide treatment and the methylation status of the MGMT promoter in a population of cells. In addition by constraining the model to relevant biological data using Approximate Bayesian Computation, we were able to identify parameter regimes that yield different possible modes of resistances, namely, phenotypic selection of MGMT, a downshift in the methylation status of the MGMT promoter or both simultaneously. We analysed each of the parameter sets associated with the different modes of resistance, presenting representative solutions as well as discovering some similarities between them as well as unique requirements for each of them. Finally, we used them to devise optimal strategies for inhibiting MGMT expression with the aim of minimising live glioblastoma cell numbers.

Orthogonal control of mean and variability of endogenous genes in a human cell line

Stochastic fluctuations at the transcriptional level contribute to isogenic cell-to-cell heterogeneity in mammalian cell populations. However, we still have no clear understanding of the repercussions of this heterogeneity, given the lack of tools to independently control mean expression and variability of a gene. Here, we engineer a synthetic circuit to modulate mean expression and heterogeneity of transgenes and endogenous human genes. The circuit, a Tunable Noise Rheostat (TuNR), consists of a transcriptional cascade of two inducible transcriptional activators, where the output mean and variance can be modulated by two orthogonal small molecule inputs. In this fashion, different combinations of the inputs can achieve the same mean but with different population variability. With TuNR, we achieve low basal expression, over 1000-fold expression of a transgene product, and up to 7-fold induction of the endogenous gene NGFR. Importantly, for the same mean expression level, we are able to establish varying degrees of heterogeneity in expression within an isogenic population, thereby decoupling gene expression noise from its mean. TuNR is therefore a modular tool that can be used in mammalian cells to enable direct interrogation of the implications of cell-to-cell variability.

Mathematical Modeling of Plasticity and Heterogeneity in EMT

The epithelial-mesenchymal transition (EMT) and the corresponding reverse process, mesenchymal-epithelial transition (MET), are dynamic and reversible cellular programs orchestrated by many changes at both biochemical and morphological levels. A recent surge in identifying the molecular mechanisms underlying EMT/MET has led to the development of various mathematical models that have contributed to our improved understanding of dynamics at single-cell and population levels: (a) multi-stability-how many phenotypes can cells attain during an EMT/MET?, (b) reversibility/irreversibility-what time and/or concentration of an EMT inducer marks the "tipping point" when cells induced to undergo EMT cannot revert?, (c) symmetry in EMT/MET-do cells take the same path when reverting as they took during the induction of EMT?, and (d) non-cell autonomous mechanisms-how does a cell undergoing EMT alter the tendency of its neighbors to undergo EMT? These dynamical traits may facilitate a heterogenous response within a cell population undergoing EMT/MET. Here, we present a few examples of designing different mathematical models that can contribute to decoding EMT/MET dynamics.

Phenotypic Heterogeneity in Tumor Progression, and Its Possible Role in the Onset of Cancer

Heterogeneity among isogenic cells/individuals has been known for at least 150 years. Even Mendel, working on pea plants, realized that not all tall plants were identical. However, Mendel was more interested in the discontinuous variation between genetically distinct individuals. The concept of environment dictating distinct phenotypes among isogenic individuals has since been shown to impact the evolution of populations in numerous examples at different scales of life. In this review, we discuss how phenotypic heterogeneity and its evolutionary implications exist at all levels of life, from viruses to mammals. In particular, we discuss how a particular disease condition (cancer) is impacted by heterogeneity among isogenic cells, and propose a potential role that phenotypic heterogeneity might play toward the onset of the disease.

Asymmetry of nanoparticle inheritance upon cell division: Effect on the coefficient of variation

Several previous studies have shown that when a cell that has taken up nanoparticles divides, the nanoparticles are inherited by the two daughter cells in an asymmetrical fashion, with one daughter cell receiving more nanoparticles than the other. This interesting observation is typically demonstrated either indirectly using mathematical modelling of high-throughput experimental data or more directly by imaging individual cells as they divide. Here we suggest that measurements of the coefficient of variation (standard deviation over mean) of the number of nanoparticles per cell over the cell population is another means of assessing the degree of asymmetry. Using simulations of an evolving cell population, we show that the coefficient of variation is sensitive to the degree of asymmetry and note its characteristic evolution in time. As the coefficient of variation is readily measurable using high-throughput techniques, this should allow a more rapid experimental assessment of the degree of asymmetry.

Fine-tuning Nanog expression heterogeneity in embryonic stem cells by regulating a Nanog transcript-specific microRNA

In embryonic stem cells (ESCs), the transcription factor Nanog maintains the stemness of ESCs despite exhibiting heterogeneous expression patterns under varied culture conditions. Efficient fine-tuning of Nanog expression heterogeneity could enable ESC proliferation and differentiation along specific lineages to be regulated. Herein, by employing a stochastic modeling approach, we show that Nanog expression heterogeneity can be controlled by modulating the regulatory features of a Nanog transcript-specific microRNA, mir-296. We demonstrate how and why the extent of origin-dependent fluctuations in Nanog expression level can be altered by varying either the binding efficiency of the microRNA-mRNA complex or the expression level of mir-296. Moreover, our model makes experimentally feasible and insightful predictions to maneuver Nanog expression heterogeneity explicitly to achieve cell-type-specific differentiation of ESCs.

Contributions to the 'noise floor' in gene expression in a population of dividing cells

Experiments with cells reveal the existence of a lower bound for protein noise, the noise floor, in highly expressed genes. Its origins are still debated. We propose a minimal model of gene expression in a proliferating bacterial cell population. The model predicts the existence of a noise floor and it semi-quantitatively reproduces the curved shape of the experimental noise vs. mean protein concentration plots. When the cell volume increases in a different manner than does the mean protein copy number, the noise floor level is determined by the cell population’s age structure and by the dependence of the mean protein concentration on cell age. Additionally, the noise floor level may depend on a biological limit for the mean number of bursts in the cell cycle. In that case, the noise floor level depends on the burst size distribution width but it is insensitive to the mean burst size. Our model quantifies the contributions of each of these mechanisms to gene expression noise.

Epigenetic feedback and stochastic partitioning during cell division can drive resistance to EMT

Epithelial-mesenchymal transition (EMT) and its reverse process mesenchymal-epithelial transition (MET) are central to metastatic aggressiveness and therapy resistance in solid tumors. While molecular determinants of both processes have been extensively characterized, the heterogeneity in the response of tumor cells to EMT and MET inducers has come into focus recently, and has been implicated in the failure of anti-cancer therapies. Recent experimental studies have shown that some cells can undergo an irreversible EMT depending on the duration of exposure to EMT-inducing signals. While the irreversibility of MET, or equivalently, resistance to EMT, has not been studied in as much detail, evidence supporting such behavior is slowly emerging. Here, we identify two possible mechanisms that can underlie resistance of cells to undergo EMT: epigenetic feedback in ZEB1/GRHL2 feedback loop and stochastic partitioning of biomolecules during cell division. Identifying the ZEB1/GRHL2 axis as a key determinant of epithelial-mesenchymal plasticity across many cancer types, we use mechanistic mathematical models to show how GRHL2 can be involved in both the abovementioned processes, thus driving an irreversible MET. Our study highlights how an isogenic population may contain subpopulation with varying degrees of susceptibility or resistance to EMT, and proposes a next set of questions for detailed experimental studies characterizing the irreversibility of MET/resistance to EMT.

Effects of cell cycle variability on lineage and population measurements of messenger RNA abundance

Many models of gene expression do not explicitly incorporate a cell cycle description. Here, we derive a theory describing how messenger RNA (mRNA) fluctuations for constitutive and bursty gene expression are influenced by stochasticity in the duration of the cell cycle and the timing of DNA replication. Analytical expressions for the moments show that omitting cell cycle duration introduces an error in the predicted mean number of mRNAs that is a monotonically decreasing function of η, which is proportional to the ratio of the mean cell cycle duration and the mRNA lifetime. By contrast, the error in the variance of the mRNA distribution is highest for intermediate values of η consistent with genome-wide measurements in many organisms. Using eukaryotic cell data, we estimate the errors in the mean and variance to be at most 3% and 25%, respectively. Furthermore, we derive an accurate negative binomial mixture approximation to the mRNA distribution. This indicates that stochasticity in the cell cycle can introduce fluctuations in mRNA numbers that are similar to the effect of bursty transcription. Finally, we show that for real experimental data, disregarding cell cycle stochasticity can introduce errors in the inference of transcription rates larger than 10%.

Phenotypic selection through cell death: stochastic modelling of O-6-methylguanine-DNA methyltransferase dynamics

Glioblastoma (GBM) is the most aggressive malignant primary brain tumour with a median overall survival of 15 months. To treat GBM, patients currently undergo a surgical resection followed by exposure to radiotherapy and concurrent and adjuvant temozolomide (TMZ) chemotherapy. However, this protocol often leads to treatment failure, with drug resistance being the main reason behind this. To date, many studies highlight the role of O-6-methylguanine-DNA methyltransferase (MGMT) in conferring drug resistance. The mechanism through which MGMT confers resistance is not well studied-particularly in terms of computational models. With only a few reasonable biological assumptions, we were able to show that even a minimal model of MGMT expression could robustly explain TMZ-mediated drug resistance. In particular, we showed that for a wide range of parameter values constrained by novel cell growth and viability assays, a model accounting for only stochastic gene expression of MGMT coupled with cell growth, division, partitioning and death was able to exhibit phenotypic selection of GBM cells expressing MGMT in response to TMZ. Furthermore, we found this selection allowed the cells to pass their acquired phenotypic resistance onto daughter cells in a stable manner (as long as TMZ is provided). This suggests that stochastic gene expression alone is enough to explain the development of chemotherapeutic resistance.

Single-molecule imaging of transcription dynamics in somatic stem cells

Molecular noise is a natural phenomenon inherent to all biological systems^1,2. How stochastic processes give rise to the robust outcomes supportive of tissue homeostasis is a conundrum. Here, to quantitatively investigate this issue, we use single-molecule mRNA FISH (smFISH) on stem cells derived from hematopoietic tissue to measure the transcription dynamics of three key transcription factor (TF) genes: PU.1, Gata1 and Gata2. Our results indicate that infrequent, stochastic bursts of transcription result in the co-expression of these antagonistic TF in the majority of hematopoietic stem and progenitor cells. Moreover, by pairing smFISH to time-lapse microscopy and the analysis of pedigrees, we find that while individual stem cell clones produce offspring that are in transcriptionally related states, akin to a transcriptional priming phenomenon, the underlying transition dynamics between states are nevertheless best captured by stochastic and reversible models. As such, the outcome of a stochastic process can produce cellular behaviors that may be incorrectly inferred to have arisen from deterministic dynamics. In light of our findings, we propose a model whereby the intrinsic stochasticity of gene expression facilitates, rather than impedes, concomitant maintenance of transcriptional plasticity and stem cell robustness.

Inheritance and variability of kinetic gene expression parameters in microbial cells: modeling and inference from lineage tree data

Motivation

Modern experimental technologies enable monitoring of gene expression dynamics in individual cells and quantification of its variability in isogenic microbial populations. Among the sources of this variability is the randomness that affects inheritance of gene expression factors at cell division. Known parental relationships among individually observed cells provide invaluable information for the characterization of this extrinsic source of gene expression noise. Despite this fact, most existing methods to infer stochastic gene expression models from single-cell data dedicate little attention to the reconstruction of mother–daughter inheritance dynamics.

Results

Starting from a transcription and translation model of gene expression, we propose a stochastic model for the evolution of gene expression dynamics in a population of dividing cells. Based on this model, we develop a method for the direct quantification of inheritance and variability of kinetic gene expression parameters from single-cell gene expression and lineage data. We demonstrate that our approach provides unbiased estimates of mother–daughter inheritance parameters, whereas indirect approaches using lineage information only in the post-processing of individual-cell parameters underestimate inheritance. Finally, we show on yeast osmotic shock response data that daughter cell parameters are largely determined by the mother, thus confirming the relevance of our method for the correct assessment of the onset of gene expression variability and the study of the transmission of regulatory factors.

Availability and implementation

Software code is available at https://github.com/almarguet/IdentificationWithARME. Lineage tree data is available upon request.

Supplementary information

Supplementary material is available at Bioinformatics online.

Allocation of gene products to daughter cells is determined by the age of the mother in single Escherichia coli cells

Gene expression and growth rate are highly stochastic in Escherichia coli. Some of the growth rate variations result from the deterministic and asymmetric partitioning of damage by the mother to its daughters. One daughter, denoted the old daughter, receives more damage, grows more slowly and ages. To determine if expressed gene products are also allocated asymmetrically, we compared the levels of expressed green fluorescence protein in growing daughters descending from the same mother. Our results show that old daughters were less fluorescent than new daughters. Moreover, old mothers, which were born as old daughters, produced daughters that were more asymmetric when compared to new mothers. Thus, variation in gene products in a clonal E. coli population also has a deterministic component. Because fluorescence levels and growth rates were positively correlated, the aging of old daughters appears to result from both the presence of both more damage and fewer expressed gene products.

Plasmid expression level heterogeneity monitoring via heterologous eGFP production at the single-cell level in Cupriavidus necator

A methodology for plasmid expression level monitoring of eGFP expression suitable for dynamic processes was assessed during fermentation. This technique was based on the expression of a fluorescent biosensor (eGFP) encoded on a recombinant plasmid coupled to single-cell analysis. Fluorescence intensity at single-cell level was measured by flow cytometry. We demonstrated that promoter evaluation based on single-cell analysis versus classic global analysis brings valuable insights. Single-cell analysis pointed out the fact that intrinsic fluorescence increased with the strength of the promoter up to a threshold. Beyond that, cell permeability increases to excrete the fluorescent protein in the medium. The metabolic load due to the increase in the eGFP production in the case of strong constitutive promoters leads to slower growth kinetics compared with plasmid-free cells. With the strain Cupriavidus necator Re2133, growth rate losses were measured from 3% with the weak constitutive promoter P_lac to 56% with the strong constitutive promoter P_j5. Through this work, it seems crucial to find a compromise between the fluorescence intensity in single cells and the metabolic load; in our conditions, the best compromise found was the weak promoter P_lac. The plasmid expression level monitoring method was tested in the presence of a heterogeneous population induced by plasmid-curing methods. For all the identified subpopulations, the plasmid expression level heterogeneity was significantly detected at the level of fluorescence intensity in single cells. After cell sorting, growth rate and cultivability were assessed for each subpopulation. In conclusion, this eGFP biosensor makes it possible to follow the variations in the level of plasmid expression under conditions of population heterogeneity.Key Points•Development of a plasmid expression level monitoring method at the single-cell level by flow cytometry.•Promoter evaluation by single-cell analysis: cell heterogeneity and strain robustness.•Reporter system optimization for efficient subpopulation detection in pure cultures.

Stochastic models coupling gene expression and partitioning in cell division in Escherichia coli

Regulation of future RNA and protein numbers is a key process by which cells continuously best fit the environment. In bacteria, RNA and proteins exist in small numbers and their regulatory processes are stochastic. Consequently, there is cell-to-cell variability in these numbers, even between sister cells. Traditionally, the two most studied sources of this variability are gene expression and RNA and protein degradation, with evidence suggesting that the latter is subject to little regulation, when compared to the former. However, time-lapse microscopy and single molecule fluorescent tagging have produced evidence that cell division can also be a significant source of variability due to asymmetries in the partitioning of RNA and proteins. Relevantly, the impact of this noise differs from noise in production and degradation since, unlike these, it is not continuous. Rather, it occurs at specific time points, at which moment it can introduce major fluctuations. Several models have now been proposed that integrate noise from cell division, in addition to noise in gene expression, to mimic the dynamics of RNA and protein numbers of cell lineages. This is expected to be particularly relevant in genetic circuits, where significant fluctuations in one component protein, at specific time moments, are expected to perturb near-equilibrium states of the circuits, which can have long-lasting consequences. Here we review stochastic models coupling these processes in Escherichia coli, from single genes to small circuits.

Noise-driven cell differentiation and the emergence of spatiotemporal patterns

The emergence of phenotypic diversity in a population of cells and their arrangement in space and time is one of the most fascinating features of living systems. In fact, understanding multicellularity is unthinkable without explaining the proximate and the ultimate causes of cell differentiation in time and space. Simpler forms of cell differentiation can be found in unicellular organisms, such as bacterial biofilm, where reversible cell differentiation results in phenotypically diverse populations. In this manuscript, we attempt to start with the simple case of reversible nongenetic phenotypic to construct a model of differentiation and pattern formation. Our model, which we refer to as noise-driven differentiation (NDD) model, is an attempt to consider the prevalence of noise in biological systems, alongside what is known about genetic switches and signaling, to create a simple model which generates spatiotemporal patterns from bottom-up. Our simulations indicate that the presence of noise in cells can lead to reversible differentiation and the addition of signaling can create spatiotemporal pattern.

DivIVA Controls Progeny Morphology and Diverse ParA Proteins Regulate Cell Division or Gliding Motility in Bdellovibrio bacteriovorus

The predatory bacterium B. bacteriovorus grows and divides inside the periplasm of Gram-negative bacteria, forming a structure known as a bdelloplast. Cell division of predators inside the dead prey cell is not by binary fission but instead by synchronous division of a single elongated filamentous cell into odd or even numbers of progeny cells. Bdellovibrio replication and cell division processes are dependent on the finite level of nutrients available from inside the prey bacterium. The filamentous growth and division process of the predator maximizes the number of progeny produced by the finite nutrients in a way that binary fission could not. To learn more about such an unusual growth profile, we studied the role of DivIVA in the growing Bdellovibrio cell. This protein is well known for its link to polar cell growth and spore formation in Gram-positive bacteria, but little is known about its function in a predatory growth context. We show that DivIVA is expressed in the growing B. bacteriovorus cell and controls cell morphology during filamentous cell division, but not the number of progeny produced. Bacterial Two Hybrid (BTH) analysis shows DivIVA may interact with proteins that respond to metabolic indicators of amino-acid biosynthesis or changes in redox state. Such changes may be relevant signals to the predator, indicating the consumption of prey nutrients within the sealed bdelloplast environment. ParA, a chromosome segregation protein, also contributes to bacterial septation in many species. The B. bacteriovorus genome contains three ParA homologs; we identify a canonical ParAB pair required for predatory cell division and show a BTH interaction between a gene product encoded from the same operon as DivIVA with the canonical ParA. The remaining ParA proteins are both expressed in Bdellovibrio but are not required for predator cell division. Instead, one of these ParA proteins coordinates gliding motility, changing the frequency at which the cells reverse direction. Our work will prime further studies into how one bacterium can co-ordinate its cell division with the destruction of another bacterium that it dwells within.

Probing Mechanisms of Transcription Elongation Through Cell-to-Cell Variability of RNA Polymerase

The process of transcription initiation and elongation are primary points of control in the regulation of gene expression. Although biochemical studies have uncovered the mechanisms involved in controlling transcription at each step, how these mechanisms manifest in vivo at the level of individual genes is still unclear. Recent experimental advances have enabled single-cell measurements of RNA polymerase (RNAP) molecules engaged in the process of transcribing a gene of interest. In this article, we use Gillespie simulations to show that measurements of cell-to-cell variability of RNAP numbers and interpolymerase distances can reveal the prevailing mode of regulation of a given gene. Mechanisms of regulation at each step, from initiation to elongation dynamics, produce qualitatively distinct signatures, which can further be used to discern between them. Most intriguingly, depending on the initiation kinetics, stochastic elongation can either enhance or suppress cell-to-cell variability at the RNAP level. To demonstrate the value of this framework, we analyze RNAP number distribution data for ribosomal genes in Saccharomyces cerevisiae from three previously published studies and show that this approach provides crucial mechanistic insights into the transcriptional regulation of these genes.

Specification of the First Mammalian Cell Lineages In Vivo and In Vitro

Our understanding of how the first mammalian cell lineages arise has been shaped largely by studies of the preimplantation mouse embryo. Painstaking work over many decades has begun to reveal how a single totipotent cell is transformed into a multilayered structure representing the foundations of the body plan. Here, we review how the first lineage decision is initiated by epigenetic regulation but consolidated by the integration of morphological features and transcription factor activity. The establishment of pluripotent and multipotent stem cell lines has enabled deeper analysis of molecular and epigenetic regulation of cell fate decisions. The capability to assemble these stem cells into artificial embryos is an exciting new avenue of research that offers a long-awaited window into cell fate specification in the human embryo. Together, these approaches are poised to profoundly increase our understanding of how the first lineage decisions are made during mammalian embryonic development.

Digital Microfluidics for Single Bacteria Capture and Selective Retrieval Using Optical Tweezers

When screening microbial populations or consortia for interesting cells, their selective retrieval for further study can be of great interest. To this end, traditional fluorescence activated cell sorting (FACS) and optical tweezers (OT) enabled methods have typically been used. However, the former, although allowing cell sorting, fails to track dynamic cell behavior, while the latter has been limited to complex channel-based microfluidic platforms. In this study, digital microfluidics (DMF) was integrated with OT for selective trapping, relocation, and further proliferation of single bacterial cells, while offering continuous imaging of cells to evaluate dynamic cell behavior. To enable this, magnetic beads coated with Salmonella Typhimurium-targeting antibodies were seeded in the microwell array of the DMF platform, and used to capture single cells of a fluorescent S. Typhimurium population. Next, OT were used to select a bead with a bacterium of interest, based on its fluorescent expression, and to relocate this bead to a different microwell on the same or different array. Using an agar patch affixed on top, the relocated bacterium was subsequently allowed to proliferate. Our OT-integrated DMF platform thus successfully enabled selective trapping, retrieval, relocation, and proliferation of bacteria of interest at single-cell level, thereby enabling their downstream analysis.

Analytical distributions for detailed models of stochastic gene expression in eukaryotic cells

The stochasticity of gene expression presents significant challenges to the modeling of genetic networks. A two-state model describing promoter switching, transcription, and messenger RNA (mRNA) decay is the standard model of stochastic mRNA dynamics in eukaryotic cells. Here, we extend this model to include mRNA maturation, cell division, gene replication, dosage compensation, and growth-dependent transcription. We derive expressions for the time-dependent distributions of nascent mRNA and mature mRNA numbers, provided two assumptions hold: 1) nascent mRNA dynamics are much faster than those of mature mRNA; and 2) gene-inactivation events occur far more frequently than gene-activation events. We confirm that thousands of eukaryotic genes satisfy these assumptions by using data from yeast, mouse, and human cells. We use the expressions to perform a sensitivity analysis of the coefficient of variation of mRNA fluctuations averaged over the cell cycle, for a large number of genes in mouse embryonic stem cells, identifying degradation and gene-activation rates as the most sensitive parameters. Furthermore, it is shown that, despite the model's complexity, the time-dependent distributions predicted by our model are generally well approximated by the negative binomial distribution. Finally, we extend our model to include translation, protein decay, and auto-regulatory feedback, and derive expressions for the approximate time-dependent protein-number distributions, assuming slow protein decay. Our expressions enable us to study how complex biological processes contribute to the fluctuations of gene products in eukaryotic cells, as well as allowing a detailed quantitative comparison with experimental data via maximum-likelihood methods.

A mechanism for epithelial-mesenchymal heterogeneity in a population of cancer cells

Epithelial-mesenchymal heterogeneity implies that cells within the same tumor can exhibit different phenotypes-epithelial, mesenchymal, or one or more hybrid epithelial-mesenchymal phenotypes. This behavior has been reported across cancer types, both in vitro and in vivo, and implicated in multiple processes associated with metastatic aggressiveness including immune evasion, collective dissemination of tumor cells, and emergence of cancer cell subpopulations with stem cell-like properties. However, the ability of a population of cancer cells to generate, maintain, and propagate this heterogeneity has remained a mystifying feature. Here, we used a computational modeling approach to show that epithelial-mesenchymal heterogeneity can emerge from the noise in the partitioning of biomolecules (such as RNAs and proteins) among daughter cells during the division of a cancer cell. Our model captures the experimentally observed temporal changes in the fractions of different phenotypes in a population of murine prostate cancer cells, and describes the hysteresis in the population-level dynamics of epithelial-mesenchymal plasticity. The model is further able to predict how factors known to promote a hybrid epithelial-mesenchymal phenotype can alter the phenotypic composition of a population. Finally, we used the model to probe the implications of phenotypic heterogeneity and plasticity for different therapeutic regimens and found that co-targeting of epithelial and mesenchymal cells is likely to be the most effective strategy for restricting tumor growth. By connecting the dynamics of an intracellular circuit to the phenotypic composition of a population, our study serves as a first step towards understanding the generation and maintenance of non-genetic heterogeneity in a population of cancer cells, and towards the therapeutic targeting of phenotypic heterogeneity and plasticity in cancer cell populations.

Models of protein production along the cell cycle: An investigation of possible sources of noise

In this article, we quantitatively study, through stochastic models, the effects of several intracellular phenomena, such as cell volume growth, cell division, gene replication as well as fluctuations of available RNA polymerases and ribosomes. These phenomena are indeed rarely considered in classic models of protein production and no relative quantitative comparison among them has been performed. The parameters for a large and representative class of proteins are determined using experimental measures. The main important and surprising conclusion of our study is to show that despite the significant fluctuations of free RNA polymerases and free ribosomes, they bring little variability to protein production contrary to what has been previously proposed in the literature. After verifying the robustness of this quite counter-intuitive result, we discuss its possible origin from a theoretical view, and interpret it as the result of a mean-field effect.

Microbial phenotypic heterogeneity in response to a metabolic toxin: Continuous, dynamically shifting distribution of formaldehyde tolerance in Methylobacterium extorquens populations

While microbiologists often make the simplifying assumption that genotype determines phenotype in a given environment, it is becoming increasingly apparent that phenotypic heterogeneity (in which one genotype generates multiple phenotypes simultaneously even in a uniform environment) is common in many microbial populations. The importance of phenotypic heterogeneity has been demonstrated in a number of model systems involving binary phenotypic states (e.g., growth/non-growth); however, less is known about systems involving phenotype distributions that are continuous across an environmental gradient, and how those distributions change when the environment changes. Here, we describe a novel instance of phenotypic diversity in tolerance to a metabolic toxin within wild-type populations of Methylobacterium extorquens, a ubiquitous phyllosphere methylotroph capable of growing on the methanol periodically released from plant leaves. The first intermediate in methanol metabolism is formaldehyde, a potent cellular toxin that is lethal in high concentrations. We have found that at moderate concentrations, formaldehyde tolerance in M. extorquens is heterogeneous, with a cell's minimum tolerance level ranging between 0 mM and 8 mM. Tolerant cells have a distinct gene expression profile from non-tolerant cells. This form of heterogeneity is continuous in terms of threshold (the formaldehyde concentration where growth ceases), yet binary in outcome (at a given formaldehyde concentration, cells either grow normally or die, with no intermediate phenotype), and it is not associated with any detectable genetic mutations. Moreover, tolerance distributions within the population are dynamic, changing over time in response to growth conditions. We characterized this phenomenon using bulk liquid culture experiments, colony growth tracking, flow cytometry, single-cell time-lapse microscopy, transcriptomics, and genome resequencing. Finally, we used mathematical modeling to better understand the processes by which cells change phenotype, and found evidence for both stochastic, bidirectional phenotypic diversification and responsive, directed phenotypic shifts, depending on the growth substrate and the presence of toxin.

Scientists tend to appreciate microbes for their simplicity and predictability: a population of genetically identical cells inhabiting a uniform environment is expected to behave in a uniform way. However, counter-examples to this assumption are frequently being discovered, forcing a re-examination of the relationship between genotype and phenotype. In most such examples, bacterial cells are found to split into two discrete populations, for instance growing and non-growing. Here, we report the discovery of a novel example of microbial phenotypic heterogeneity in which cells are distributed along a gradient of phenotypes, ranging from low to high tolerance of a toxic chemical. Furthermore, we demonstrate that the distribution of phenotypes changes in different growth conditions, and we use mathematical modeling to show that cells may change their phenotype either randomly or in a particular direction in response to the environment. Our work expands our understanding of how a bacterial cell's genome, family history, and environment all contribute to its behavior, with implications for the diverse situations in which we care to understand the growth of any single-celled populations.

Decoding the grammar of transcriptional regulation from RNA polymerase measurements: models and their applications

The genomic revolution has indubitably brought about a paradigm shift in the field of molecular biology, wherein we can sequence, write and re-write genomes. In spite of achieving such feats, we still lack a quantitative understanding of how cells integrate environmental and intra-cellular signals at the promoter and accordingly regulate the production of messenger RNAs. This current state of affairs is being redressed by recent experimental breakthroughs which enable the counting of RNA polymerase molecules (or the corresponding nascent RNAs) engaged in the process of transcribing a gene at the single-cell level. Theorists, in conjunction, have sought to unravel the grammar of transcriptional regulation by harnessing the various statistical properties of these measurements. In this review, we focus on the recent progress in developing falsifiable models of transcription that aim to connect the molecular mechanisms of transcription to single-cell polymerase measurements. We discuss studies where the application of such models to the experimental data have led to novel mechanistic insights into the process of transcriptional regulation. Such interplay between theory and experiments will likely contribute towards the exciting journey of unfurling the governing principles of transcriptional regulation ranging from bacteria to higher organisms.