Tunability and Noise Dependence in Differentiation Dynamics

Adaptation through proportion

Adaptation is a ubiquitous feature in biological sensory and signaling networks. It has been suggested that adaptive systems may follow certain simple design principles across diverse organisms, cells and pathways. One class of networks that can achieve adaptation utilizes an incoherent feedforward control, in which two parallel signaling branches exert opposite but proportional effects on the output at steady state. In this paper, we generalize this adaptation mechanism by establishing a steady-state proportionality relationship among a subset of nodes in a network. Adaptation can be achieved by using any two nodes in the sub-network to respectively regulate the output node positively and negatively. We focus on enzyme networks and first identify basic regulation motifs consisting of two and three nodes that can be used to build small networks with proportional relationships. Larger proportional networks can then be constructed modularly similar to LEGOs. Our method provides a general framework to construct and analyze a class of proportional and/or adaptation networks with arbitrary size, flexibility and versatile functional features.

Dissecting Embryonic Stem Cell Self-Renewal and Differentiation Commitment from Quantitative Models

To model quantitatively embryonic stem cell (ESC) self-renewal and differentiation by computational approaches, we developed a unified mathematical model for gene expression involved in cell fate choices. Our quantitative model comprised ESC master regulators and lineage-specific pivotal genes. It took the factors of multiple pathways as input and computed expression as a function of intrinsic transcription factors, extrinsic cues, epigenetic modifications, and antagonism between ESC master regulators and lineage-specific pivotal genes. In the model, the differential equations of expression of genes involved in cell fate choices from regulation relationship were established according to the transcription and degradation rates. We applied this model to the Murine ESC self-renewal and differentiation commitment and found that it modeled the expression patterns with good accuracy. Our model analysis revealed that Murine ESC was an attractor state in culture and differentiation was predominantly caused by antagonism between ESC master regulators and lineage-specific pivotal genes. Moreover, antagonism among lineages played a critical role in lineage reprogramming. Our results also uncovered that the ordered expression alteration of ESC master regulators over time had a central role in ESC differentiation fates. Our computational framework was generally applicable to most cell-type maintenance and lineage reprogramming.

Transitions in a genetic transcriptional regulatory system under Lévy motion

Based on a stochastic differential equation model for a single genetic regulatory system, we examine the dynamical effects of noisy fluctuations, arising in the synthesis reaction, on the evolution of the transcription factor activator in terms of its concentration. The fluctuations are modeled by Brownian motion and α-stable Lévy motion. Two deterministic quantities, the mean first exit time (MFET) and the first escape probability (FEP), are used to analyse the transitions from the low to high concentration states. A shorter MFET or higher FEP in the low concentration region facilitates such a transition. We have observed that higher noise intensities and larger jumps of the Lévy motion shortens the MFET and thus benefits transitions. The Lévy motion activates a transition from the low concentration region to the non-adjacent high concentration region, while Brownian motion can not induce this phenomenon. There are optimal proportions of Gaussian and non-Gaussian noises, which maximise the quantities MFET and FEP for each concentration, when the total sum of noise intensities are kept constant. Because a weaker stability indicates a higher transition probability, a new geometric concept is introduced to quantify the basin stability of the low concentration region, characterised by the escaping behaviour.

A part toolbox to tune genetic expression in Bacillus subtilis

Libraries of well-characterised components regulating gene expression levels are essential to many synthetic biology applications. While widely available for the Gram-negative model bacterium Escherichia coli, such libraries are lacking for the Gram-positive model Bacillus subtilis, a key organism for basic research and biotechnological applications. Here, we engineered a genetic toolbox comprising libraries of promoters, Ribosome Binding Sites (RBS), and protein degradation tags to precisely tune gene expression in B. subtilis. We first designed a modular Expression Operating Unit (EOU) facilitating parts assembly and modifications and providing a standard genetic context for gene circuits implementation. We then selected native, constitutive promoters of B. subtilis and efficient RBS sequences from which we engineered three promoters and three RBS sequence libraries exhibiting ∼14 000-fold dynamic range in gene expression levels. We also designed a collection of SsrA proteolysis tags of variable strength. Finally, by using fluorescence fluctuation methods coupled with two-photon microscopy, we quantified the absolute concentration of GFP in a subset of strains from the library. Our complete promoters and RBS sequences library comprising over 135 constructs enables tuning of GFP concentration over five orders of magnitude, from 0.05 to 700 μM. This toolbox of regulatory components will support many research and engineering applications in B. subtilis.

Individual cell heterogeneity in Predictive Food Microbiology: Challenges in predicting a "noisy" world

Gene expression is a fundamentally noisy process giving rise to a significant cell to cell variability at the phenotype level. The phenotypic noise is manifested in a wide range of microbial traits. Heterogeneous behavior of individual cells is observed at the growth, survival and inactivation responses and should be taken into account in the context of Predictive Food Microbiology (PMF). Recent methodological advances can be employed for the study and modeling of single cell dynamics leading to a new generation of mechanistic models which can provide insight into the link between phenotype, gene-expression, protein and metabolic functional units at the single cell level. Such models however, need to deal with an enormous amount of interactions and processes that influence each other, forming an extremely complex system. In this review paper, we discuss the importance of noise and present the future challenges in predicting the "noisy" microbial responses in foods.

Fitness Trade-Offs in Competence Differentiation of Bacillus subtilis

In the stationary phase, Bacillus subtilis differentiates stochastically and transiently into the state of competence for transformation (K-state). The latter is associated with growth arrest, and it is unclear how the ability to develop competence is stably maintained, despite its cost. To quantify the effect differentiation has on the competitive fitness of B. subtilis, we characterized the competition dynamics between strains with different probabilities of entering the K-state. The relative fitness decreased with increasing differentiation probability both during the stationary phase and during outgrowth. When exposed to antibiotics inhibiting cell wall synthesis, transcription, and translation, cells that differentiated into the K-state showed a selective advantage compared to differentiation-deficient bacteria; this benefit did not require transformation. Although beneficial, the K-state was not induced by sub-MIC concentrations of antibiotics. Increasing the differentiation probability beyond the wt level did not significantly affect the competition dynamics with transient antibiotic exposure. We conclude that the competition dynamics are very sensitive to the fraction of competent cells under benign conditions but less sensitive during antibiotic exposure, supporting the picture of stochastic differentiation as a fitness trade-off.

Stochastic Simulation of Biomolecular Networks in Dynamic Environments

Simulation of biomolecular networks is now indispensable for studying biological systems, from small reaction networks to large ensembles of cells. Here we present a novel approach for stochastic simulation of networks embedded in the dynamic environment of the cell and its surroundings. We thus sample trajectories of the stochastic process described by the chemical master equation with time-varying propensities. A comparative analysis shows that existing approaches can either fail dramatically, or else can impose impractical computational burdens due to numerical integration of reaction propensities, especially when cell ensembles are studied. Here we introduce the Extrande method which, given a simulated time course of dynamic network inputs, provides a conditionally exact and several orders-of-magnitude faster simulation solution. The new approach makes it feasible to demonstrate—using decision-making by a large population of quorum sensing bacteria—that robustness to fluctuations from upstream signaling places strong constraints on the design of networks determining cell fate. Our approach has the potential to significantly advance both understanding of molecular systems biology and design of synthetic circuits.

Simulation algorithms have become indispensable tools in modern quantitative biology, providing deep insight into many biochemical systems, including gene regulatory networks. However, current stochastic simulation approaches handle the effects of fluctuating extracellular signals and upstream processes poorly, either failing to give qualitatively reliable predictions or being very inefficient computationally. Here we introduce the Extrande method, a novel approach for simulation of biomolecular networks embedded in the dynamic environment of the cell and its surroundings. The method is accurate and computationally efficient, and hence fills an important gap in the field of stochastic simulation. In particular, we employ it to study a bacterial decision-making network and demonstrate that robustness to fluctuations from upstream signaling places strong constraints on the design of networks determining cell fate.

Growth against entropy in bacterial metabolism: the phenotypic trade-off behind empirical growth rate distributions in E. coli

The solution space of genome-scale models of cellular metabolism provides a map between physically viable flux configurations and cellular metabolic phenotypes described, at the most basic level, by the corresponding growth rates. By sampling the solution space of E. coli's metabolic network, we show that empirical growth rate distributions recently obtained in experiments at single-cell resolution can be explained in terms of a trade-off between the higher fitness of fast-growing phenotypes and the higher entropy of slow-growing ones. Based on this, we propose a minimal model for the evolution of a large bacterial population that captures this trade-off. The scaling relationships observed in experiments encode, in such frameworks, for the same distance from the maximum achievable growth rate, the same degree of growth rate maximization, and/or the same rate of phenotypic change. Being grounded on genome-scale metabolic network reconstructions, these results allow for multiple implications and extensions in spite of the underlying conceptual simplicity.

Slowdown of growth controls cellular differentiation

How can changes in growth rate affect the regulatory networks behavior and the outcomes of cellular differentiation? We address this question by focusing on starvation response in sporulating Bacillus subtilis We show that the activity of sporulation master regulator Spo0A increases with decreasing cellular growth rate. Using a mathematical model of the phosphorelay-the network controlling Spo0A-we predict that this increase in Spo0A activity can be explained by the phosphorelay protein accumulation and lengthening of the period between chromosomal replication events caused by growth slowdown. As a result, only cells growing slower than a certain rate reach threshold Spo0A activity necessary for sporulation. This growth threshold model accurately predicts cell fates and explains the distribution of sporulation deferral times. We confirm our predictions experimentally and show that the concentration rather than activity of phosphorelay proteins is affected by the growth slowdown. We conclude that sensing the growth rates enables cells to indirectly detect starvation without the need for evaluating specific stress signals.

A population-based temporal logic gate for timing and recording chemical events

Engineered bacterial sensors have potential applications in human health monitoring, environmental chemical detection, and materials biosynthesis. While such bacterial devices have long been engineered to differentiate between combinations of inputs, their potential to process signal timing and duration has been overlooked. In this work, we present a two‐input temporal logic gate that can sense and record the order of the inputs, the timing between inputs, and the duration of input pulses. Our temporal logic gate design relies on unidirectional DNA recombination mediated by bacteriophage integrases to detect and encode sequences of input events. For an E. coli strain engineered to contain our temporal logic gate, we compare predictions of Markov model simulations with laboratory measurements of final population distributions for both step and pulse inputs. Although single cells were engineered to have digital outputs, stochastic noise created heterogeneous single‐cell responses that translated into analog population responses. Furthermore, when single‐cell genetic states were aggregated into population‐level distributions, these distributions contained unique information not encoded in individual cells. Thus, final differentiated sub‐populations could be used to deduce order, timing, and duration of transient chemical events.

Phenotypic Evolution With and Beyond Genome Evolution

DNA does not make phenotypes on its own. In this volume entitled "Genes and Phenotypic Evolution," the present review draws the attention on the process of phenotype construction-including development of multicellular organisms-and the multiple interactions and feedbacks between DNA, organism, and environment at various levels and timescales in the evolutionary process. First, during the construction of an individual's phenotype, DNA is recruited as a template for building blocks within the cellular context and may in addition be involved in dynamical feedback loops that depend on the environmental and organismal context. Second, in the production of phenotypic variation among individuals, stochastic, environmental, genetic, and parental sources of variation act jointly. While in controlled laboratory settings, various genetic and environmental factors can be tested one at a time or in various combinations, they cannot be separated in natural populations because the environment is not controlled and the genotype can rarely be replicated. Third, along generations, genotype and environment each have specific properties concerning the origin of their variation, the hereditary transmission of this variation, and the evolutionary feedbacks. Natural selection acts as a feedback from phenotype and environment to genotype. This review integrates recent results and concrete examples that illustrate these three points. Although some themes are shared with recent calls and claims to a new conceptual framework in evolutionary biology, the viewpoint presented here only means to add flesh to the standard evolutionary synthesis.

Noise Expands the Response Range of the Bacillus subtilis Competence Circuit

Gene regulatory circuits must contend with intrinsic noise that arises due to finite numbers of proteins. While some circuits act to reduce this noise, others appear to exploit it. A striking example is the competence circuit in Bacillus subtilis, which exhibits much larger noise in the duration of its competence events than a synthetically constructed analog that performs the same function. Here, using stochastic modeling and fluorescence microscopy, we show that this larger noise allows cells to exit terminal phenotypic states, which expands the range of stress levels to which cells are responsive and leads to phenotypic heterogeneity at the population level. This is an important example of how noise confers a functional benefit in a genetic decision-making circuit.

Fluctuations, or “noise”, in the response of a system is usually thought to be harmful. However, it is becoming increasingly clear that in single-celled organisms, noise can sometimes help cells survive. This is because noise can enhance the diversity of responses within a cell population. In this study, we identify a novel benefit of noise in the competence response of a population of Bacillus subtilis bacteria, where competence is the ability of bacteria to take in DNA from their environment when under stress. We use computational modeling and experiments to show that noise increases the range of stress levels for which these bacteria exhibit a highly dynamic response, meaning that they are neither unresponsive, nor permanently in the competent state. Since a dynamic response is thought to be optimal for survival, this study suggests that noise is exploited to increase the fitness of the bacterial population.

Division of Labor in Biofilms: the Ecology of Cell Differentiation

The dense aggregation of cells on a surface, as seen in biofilms, inevitably results in both environmental and cellular heterogeneity. For example, nutrient gradients can trigger cells to differentiate into various phenotypic states. Not only do cells adapt physiologically to the local environmental conditions, but they also differentiate into cell types that interact with each other. This allows for task differentiation and, hence, the division of labor. In this article, we focus on cell differentiation and the division of labor in three bacterial species: Myxococcus xanthus, Bacillus subtilis, and Pseudomonas aeruginosa. During biofilm formation each of these species differentiates into distinct cell types, in some cases leading to cooperative interactions. The division of labor and the cooperative interactions between cell types are assumed to yield an emergent ecological benefit. Yet in most cases the ecological benefits have yet to be elucidated. A notable exception is M. xanthus, in which cell differentiation within fruiting bodies facilitates the dispersal of spores. We argue that the ecological benefits of the division of labor might best be understood when we consider the dynamic nature of both biofilm formation and degradation.

Single-cell differences in matrix gene expression do not predict matrix deposition

Mesenchymal stem cells (MSCs) display substantial cell-to-cell heterogeneity, complicating their use in regenerative medicine. However, conventional bulk assays mask this variability. Here we show that both chondrocytes and chondrogenically induced MSCs exhibit substantial mRNA expression heterogeneity. Single-molecule RNA FISH to measure mRNA expression of differentiation markers in single cells reveals that sister cell pairs have high levels of mRNA variability, suggesting that marker expression is not heritable. Surprisingly, this variability does not correlate with cell-to-cell differences in cartilage-like matrix production. Transcriptome-wide analysis suggests that no combination of markers can predict functional potential. De-differentiating chondrocytes also show a disconnect between mRNA expression of the cartilage marker aggrecan and cartilage-like matrix accumulation. Altogether, these quantitative analyses suggest that sorting subpopulations based on these markers would only marginally enrich the progenitor population for ‘superior' MSCs. Our results suggest that instantaneous mRNA abundance of canonical markers is tenuously linked to the chondrogenic phenotype at the single-cell level.

Regenerative tissue engineering with mesenchymal stem cells is hampered by bulk methods of assessing differentiation status and a general assumption that expression of individual markers of stem cell differentiation correlate with functional capacity. Here the authors debunk this assumption by applying single-cell techniques to disassociate aggrecan mRNA abundance and matrix deposition.

A Low Dimensional Approximation For Competence In Bacillus Subtilis

The behaviour of a high dimensional stochastic system described by a chemical master equation (CME) depends on many parameters, rendering explicit simulation an inefficient method for exploring the properties of such models. Capturing their behaviour by low-dimensional models makes analysis of system behaviour tractable. In this paper, we present low dimensional models for the noise-induced excitable dynamics in Bacillus subtilis, whereby a key protein ComK, which drives a complex chain of reactions leading to bacterial competence, gets expressed rapidly in large quantities (competent state) before subsiding to low levels of expression (vegetative state). These rapid reactions suggest the application of an adiabatic approximation of the dynamics of the regulatory model that, however, lead to competence durations that are incorrect by a factor of 2. We apply a modified version of an iterative functional procedure that faithfully approximates the time-course of the trajectories in terms of a two-dimensional model involving proteins ComK and ComS. Furthermore, in order to describe the bimodal bivariate marginal probability distribution obtained from the Gillespie simulations of the CME, we introduce a tunable multiplicative noise term in a two-dimensional Langevin model whose stationary state is described by the time-independent solution of the corresponding Fokker-Planck equation.

NF-κB oscillations translate into functionally related patterns of gene expression

Several transcription factors (TFs) oscillate, periodically relocating between the cytoplasm and the nucleus. NF-κB, which plays key roles in inflammation and cancer, displays oscillations whose biological advantage remains unclear. Recent work indicated that NF-κB displays sustained oscillations that can be entrained, that is, reach a persistent synchronized state through small periodic perturbations. We show here that for our GFP-p65 knock-in cells NF-κB behaves as a damped oscillator able to synchronize to a variety of periodic external perturbations with no memory. We imposed synchronous dynamics to prove that transcription of NF-κB-controlled genes also oscillates, but mature transcript levels follow three distinct patterns. Two sets of transcripts accumulate fast or slowly, respectively. Another set, comprising chemokine and chemokine receptor mRNAs, oscillates and resets at each new stimulus, with no memory of the past. We propose that TF oscillatory dynamics is a means of segmenting time to provide renewing opportunity windows for decision.

From noise to synthetic nucleoli: can synthetic biology achieve new insights?

Synthetic biology aims to re-organise and control biological components to make functional devices. Along the way, the iterative process of designing and testing gene circuits has the potential to yield many insights into the functioning of the underlying chassis of cells. Thus, synthetic biology is converging with disciplines such as systems biology and even classical cell biology, to give a new level of predictability to gene expression, cell metabolism and cellular signalling networks. This review gives an overview of the contributions that synthetic biology has made in understanding gene expression, in terms of cell heterogeneity (noise), the coupling of growth and energy usage to expression, and spatiotemporal considerations. We mainly compare progress in bacterial and mammalian systems, which have some of the most-developed engineering frameworks. Overall, one view of synthetic biology can be neatly summarised as "creating in order to understand."

Gene expression variability in clonal populations: Causes and consequences

During the last decade it has been shown that among cell variation in gene expression plays an important role within clonal populations. Here, we provide an overview of the different mechanisms contributing to gene expression variability in clonal populations. These are ranging from inherent variations in the biochemical process of gene expression itself, such as intrinsic noise, extrinsic noise and bistability to individual responses to variations in the local micro-environment, a phenomenon called phenotypic plasticity. Also genotypic variations caused by clonal evolution and phase variation can contribute to gene expression variability. Consequently, gene expression studies need to take these fluctuations in expression into account. However, frequently used techniques for expression quantification, such as microarrays, RNA sequencing, quantitative PCR and gene reporter fusions classically determine the population average of gene expression. Here, we discuss how these techniques can be adapted towards single cell analysis by integration with single cell isolation, RNA amplification and microscopy. Alternatively more qualitative selection-based techniques, such as mutant screenings, in vivo expression technology (IVET) and recombination-based IVET (RIVET) can be applied for detection of genes expressed only within a subpopulation. Finally, differential fluorescence induction (DFI), a protocol specially designed for single cell expression is discussed.

A minimal fate-selection switch

To preserve fitness in unpredictable, fluctuating environments, a range of biological systems probabilistically generate variant phenotypes--a process often referred to as 'bet-hedging', after the financial practice of diversifying assets to minimize risk in volatile markets. The molecular mechanisms enabling bet-hedging have remained elusive. Here, we review how HIV makes a bet-hedging decision between active replication and proviral latency, a long-lived dormant state that is the chief barrier to an HIV cure. The discovery of a virus-encoded bet-hedging circuit in HIV revealed an ancient evolutionary role for latency and identified core regulatory principles, such as feedback and stochastic 'noise', that enable cell-fate decisions. These core principles were later extended to fate selection in stem cells and cancer, exposed new therapeutic targets for HIV, and led to a potentially broad strategy of using 'noise modulation' to redirect cell fate.

The female gametophyte: an emerging model for cell type-specific systems biology in plant development

Systems biology, a holistic approach describing a system emerging from the interactions of its molecular components, critically depends on accurate qualitative determination and quantitative measurements of these components. Development and improvement of large-scale profiling methods ("omics") now facilitates comprehensive measurements of many relevant molecules. For multicellular organisms, such as animals, fungi, algae, and plants, the complexity of the system is augmented by the presence of specialized cell types and organs, and a complex interplay within and between them. Cell type-specific analyses are therefore crucial for the understanding of developmental processes and environmental responses. This review first gives an overview of current methods used for large-scale profiling of specific cell types exemplified by recent advances in plant biology. The focus then lies on suitable model systems to study plant development and cell type specification. We introduce the female gametophyte of flowering plants as an ideal model to study fundamental developmental processes. Moreover, the female reproductive lineage is of importance for the emergence of evolutionary novelties such as an unequal parental contribution to the tissue nurturing the embryo or the clonal production of seeds by asexual reproduction (apomixis). Understanding these processes is not only interesting from a developmental or evolutionary perspective, but bears great potential for further crop improvement and the simplification of breeding efforts. We finally highlight novel methods, which are already available or which will likely soon facilitate large-scale profiling of the specific cell types of the female gametophyte in both model and non-model species. We conclude that it may take only few years until an evolutionary systems biology approach toward female gametogenesis may decipher some of its biologically most interesting and economically most valuable processes.

The Low Noise Limit in Gene Expression

Protein noise measurements are increasingly used to elucidate biophysical parameters. Unfortunately noise analyses are often at odds with directly measured parameters. Here we show that these inconsistencies arise from two problematic analytical choices: (i) the assumption that protein translation rate is invariant for different proteins of different abundances, which has inadvertently led to (ii) the assumption that a large constitutive extrinsic noise sets the low noise limit in gene expression. While growing evidence suggests that transcriptional bursting may set the low noise limit, variability in translational bursting has been largely ignored. We show that genome-wide systematic variation in translational efficiency can–and in the case of E. coli does–control the low noise limit in gene expression. Therefore constitutive extrinsic noise is small and only plays a role in the absence of a systematic variation in translational efficiency. These results show the existence of two distinct expression noise patterns: (1) a global noise floor uniformly imposed on all genes by expression bursting; and (2) high noise distributed to only a select group of genes.

The asymmetry of telomere replication contributes to replicative senescence heterogeneity

In eukaryotes, the absence of telomerase results in telomere shortening, eventually leading to replicative senescence, an arrested state that prevents further cell divisions. While replicative senescence is mainly controlled by telomere length, the heterogeneity of its onset is not well understood. This study proposes a mathematical model based on the molecular mechanisms of telomere replication and shortening to decipher the causes of this heterogeneity. Using simulations fitted on experimental data obtained from individual lineages of senescent Saccharomyces cerevisiae cells, we decompose the sources of senescence heterogeneity into interclonal and intraclonal components, and show that the latter is based on the asymmetry of the telomere replication mechanism. We also evidence telomere rank-switching events with distinct frequencies in short-lived versus long-lived lineages, revealing that telomere shortening dynamics display important variations. Thus, the intrinsic heterogeneity of replicative senescence and its consequences find their roots in the asymmetric structure of telomeres.

A master equation and moment approach for biochemical systems with creation-time-dependent bimolecular rate functions

Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-to-cell variability even in clonal populations. Stochastic biochemical networks have been traditionally modeled as continuous-time discrete-state Markov processes whose probability density functions evolve according to a chemical master equation (CME). In diffusion reaction systems on membranes, the Markov formalism, which assumes constant reaction propensities is not directly appropriate. This is because the instantaneous propensity for a diffusion reaction to occur depends on the creation times of the molecules involved. In this work, we develop a chemical master equation for systems of this type. While this new CME is computationally intractable, we make rational dimensional reductions to form an approximate equation, whose moments are also derived and are shown to yield efficient, accurate results. This new framework forms a more general approach than the Markov CME and expands upon the realm of possible stochastic biochemical systems that can be efficiently modeled.

Noise and low-level dynamics can coordinate multicomponent bet hedging mechanisms

To counter future uncertainty, cells can stochastically express stress response mechanisms to diversify their population and hedge against stress. This approach allows a small subset of the population to survive without the prohibitive cost of constantly expressing resistance machinery at the population level. However, expression of multiple genes in concert is often needed to ensure survival, requiring coordination of infrequent events across many downstream targets. This raises the question of how cells orchestrate the timing of multiple rare events without adding cost. To investigate this, we used a stochastic model to study regulation of downstream target genes by a transcription factor. We compared several upstream regulator profiles, including constant expression, pulsatile dynamics, and noisy expression. We found that pulsatile dynamics and noise are sufficient to coordinate expression of multiple downstream genes. Notably, this is true even when fluctuations in the upstream regulator are far below the dissociation constants of the regulated genes, as with infrequently activated genes. As an example, we simulated the dynamics of the multiple antibiotic resistance activator (MarA) and 40 diverse downstream genes it regulates, determining that low-level dynamics in MarA are sufficient to coordinate expression of resistance mechanisms. We also demonstrated that noise can play a similar coordinating role. Importantly, we found that these benefits are present without a corresponding increase in the population-level cost. Therefore, our model suggests that low-level dynamics or noise in a transcription factor can coordinate expression of multiple stress response mechanisms by engaging them simultaneously without adding to the overall cost.

Are Quasi-Steady-State Approximated Models Suitable for Quantifying Intrinsic Noise Accurately?

Large gene regulatory networks (GRN) are often modeled with quasi-steady-state approximation (QSSA) to reduce the huge computational time required for intrinsic noise quantification using Gillespie stochastic simulation algorithm (SSA). However, the question still remains whether the stochastic QSSA model measures the intrinsic noise as accurately as the SSA performed for a detailed mechanistic model or not? To address this issue, we have constructed mechanistic and QSSA models for few frequently observed GRNs exhibiting switching behavior and performed stochastic simulations with them. Our results strongly suggest that the performance of a stochastic QSSA model in comparison to SSA performed for a mechanistic model critically relies on the absolute values of the mRNA and protein half-lives involved in the corresponding GRN. The extent of accuracy level achieved by the stochastic QSSA model calculations will depend on the level of bursting frequency generated due to the absolute value of the half-life of either mRNA or protein or for both the species. For the GRNs considered, the stochastic QSSA quantifies the intrinsic noise at the protein level with greater accuracy and for larger combinations of half-life values of mRNA and protein, whereas in case of mRNA the satisfactory accuracy level can only be reached for limited combinations of absolute values of half-lives. Further, we have clearly demonstrated that the abundance levels of mRNA and protein hardly matter for such comparison between QSSA and mechanistic models. Based on our findings, we conclude that QSSA model can be a good choice for evaluating intrinsic noise for other GRNs as well, provided we make a rational choice based on experimental half-life values available in literature.

Chance and Necessity in Bacillus subtilis Development

Bacillus subtilis is an important model bacterium for the study of developmental adaptations that enhance survival in the face of fluctuating environmental challenges. These adaptations include sporulation, biofilm formation, motility, cannibalism, and competence. Remarkably, not all the cells in a given population exhibit the same response. The choice of fate by individual cells is random but is also governed by complex signal transduction pathways and cross talk mechanisms that reinforce decisions once made. The interplay of stochastic and deterministic mechanisms governing the selection of developmental fate on the single-cell level is discussed in this article.

Stochastic Switching of Cell Fate in Microbes

Microbes transiently differentiate into distinct, specialized cell types to generate functional diversity and cope with changing environmental conditions. Though alternate programs often entail radically different physiological and morphological states, recent single-cell studies have revealed that these crucial decisions are often left to chance. In these cases, the underlying genetic circuits leverage the intrinsic stochasticity of intracellular chemistry to drive transition between states. Understanding how these circuits transform transient gene expression fluctuations into lasting phenotypic programs will require a combination of quantitative modeling and extensive, time-resolved observation of switching events in single cells. In this article, we survey microbial cell fate decisions demonstrated to involve a random element, describe theoretical frameworks for understanding stochastic switching between states, and highlight recent advances in microfluidics that will enable characterization of key dynamic features of these circuits.

Effect and evolution of gene expression noise on the fitness landscape

Gene expression is a stochastic process that affects cellular and population fitness. Noise in gene expression can enhance fitness by increasing cell to cell variability as well as the time cells spend in favorable expression states. Using a stochastic model of gene expression together with a fitness function that incorporates the costs and benefits of gene expression in a stressful environment, we show that the fitness landscape is shaped by gene expression noise in more complex ways than previously anticipated. We find that mutations modulating the properties of expression noise enable cell populations to optimize their position on the fitness landscape. Additionally, we find that low levels of expression noise evolve under conditions where the fitness benefits of expression exceed the fitness costs, and that high levels of expression noise evolve when the expression costs exceed the fitness benefits. The results presented in this study expand our understanding of the interplay between stochastic gene expression and fitness in selective environments.

Fluctuation and noise propagation in phenotypic transition cascades of clonal populations

Quantitative modeling of fluctuations of each phenotype is a crucial step towards a fundamental understanding of noise propagation through various phenotypic transition cascades. The theoretical formulas for noise propagation in various phenotypic transition cascades are derived by using the linear noise approximation of master equation and the logarithmic gain. By virtue of the theoretical formulas, we study the noise propagation in bidirectional and unidirectional phenotypic transition cascades, respectively. It is found that noise propagation in these two phenotypic transition cascades evidently differs: In the bidirectional cascade, a systemic random environment is provided by a correlated global component. The total noise of each phenotype is mainly determined by the intrinsic noise and the transmitted noise from other phenotypes. The intrinsic noise enlarged by interconversion through an added part shows a novel noise propagation mechanism. However, in the unidirectional cascade, the random environment of each downstream phenotype is provided by upstream phenotypes. The total noise of each downstream phenotype is mainly determined by the transmitted noises from upstream phenotypes. The intrinsic noise and the conversion noise can propagate in both bidirectional and unidirectional phenotypic transition cascades.

Modularity and predictability in cell signaling and decision making

Cells make decisions to differentiate, divide, or apoptose based on multiple signals of internal and external origin. These decisions are discrete outputs from dynamic networks comprised of signaling pathways. Yet the validity of this decomposition of regulatory proteins into distinct pathways is unclear because many regulatory proteins are pleiotropic and interact through cross-talk with components of other pathways. In addition to the deterministic complexity of interconnected networks, there is stochastic complexity arising from the fluctuations in concentrations of regulatory molecules. Even within a genetically identical population of cells grown in the same environment, cell-to-cell variations in mRNA and protein concentrations can be as high as 50% in yeast and even higher in mammalian cells. Thus, if everything is connected and stochastic, what hope could we have for a quantitative understanding of cellular decisions? Here we discuss the implications of recent advances in genomics, single-cell, and single-cell genomics technology for network modularity and cellular decisions. On the basis of these recent advances, we argue that most gene expression stochasticity and pathway interconnectivity is nonfunctional and that cellular decisions are likely much more predictable than previously expected.

A noisy linear map underlies oscillations in cell size and gene expression in bacteria

During bacterial growth, a cell approximately doubles in size before division, after which it splits into two daughter cells. This process is subjected to the inherent perturbations of cellular noise and thus requires regulation for cell-size homeostasis. The mechanisms underlying the control and dynamics of cell size remain poorly understood owing to the difficulty in sizing individual bacteria over long periods of time in a high-throughput manner. Here we measure and analyse long-term, single-cell growth and division across different Escherichia coli strains and growth conditions. We show that a subset of cells in a population exhibit transient oscillations in cell size with periods that stretch across several (more than ten) generations. Our analysis reveals that a simple law governing cell-size control-a noisy linear map-explains the origins of these cell-size oscillations across all strains. This noisy linear map implements a negative feedback on cell-size control: a cell with a larger initial size tends to divide earlier, whereas one with a smaller initial size tends to divide later. Combining simulations of cell growth and division with experimental data, we demonstrate that this noisy linear map generates transient oscillations, not just in cell size, but also in constitutive gene expression. Our work provides new insights into the dynamics of bacterial cell-size regulation with implications for the physiological processes involved.

ComGA-RelA interaction and persistence in the Bacillus subtilis K-state

The bistably expressed K-state of Bacillus subtilis is characterized by two distinct features; transformability and arrested growth when K-state cells are exposed to fresh medium. The arrest is manifested by a failure to assemble replisomes and by decreased rates of cell growth and rRNA synthesis. These phenotypes are all partially explained by the presence of the AAA(+) protein ComGA, which is also required for the binding of transforming DNA to the cell surface and for the assembly of the transformation pilus that mediates DNA transport. We have discovered that ComGA interacts with RelA and that the ComGA-dependent inhibition of rRNA synthesis is largely bypassed in strains that cannot synthesize the alarmone (p)ppGpp. We propose that the interaction of ComGA with RelA prevents the hydrolysis of (p)ppGpp in K-state cells, which are thus trapped in a non-growing state until ComGA is degraded. We show that some K-state cells exhibit tolerance to antibiotics, a form of type 1 persistence, and we propose that the bistable expression of both transformability and the growth arrest are bet-hedging adaptations that improve fitness in the face of varying environments, such as those presumably encountered by B. subtilis in the soil.

Thioflavin T as a fluorescence probe for monitoring RNA metabolism at molecular and cellular levels

The intrinsically stochastic dynamics of mRNA metabolism have important consequences on gene regulation and non-genetic cell-to-cell variability; however, no generally applicable methods exist for studying such stochastic processes quantitatively. Here, we describe the use of the amyloid-binding probe Thioflavin T (ThT) for monitoring RNA metabolism in vitro and in vivo. ThT fluoresced strongly in complex with bacterial total RNA than with genomic DNA. ThT bound purine oligoribonucleotides preferentially over pyrimidine oligoribonucleotides and oligodeoxyribonucleotides. This property enabled quantitative real-time monitoring of poly(A) synthesis and phosphorolysis by polyribonucleotide phosphorylase in vitro. Cellular analyses, in combination with genetic approaches and the transcription-inhibitor rifampicin treatment, demonstrated that ThT mainly stained mRNA in actively dividing Escherichia coli cells. ThT also facilitated mRNA metabolism profiling at the single-cell level in diverse bacteria. Furthermore, ThT can also be used to visualise transitions between non-persister and persister cell states, a phenomenon of isogenic subpopulations of antibiotic-sensitive bacteria that acquire tolerance to multiple antibiotics due to stochastically induced dormant states. Collectively, these results suggest that probing mRNA dynamics with ThT is a broadly applicable approach ranging from the molecular level to the single-cell level.

Coupled positive and negative feedbacks produce diverse gene expression patterns in colonies

Formation of patterns is a common feature in the development of multicellular organism as well as of microbial communities. To investigate the formation of gene expression patterns in colonies, we build a mathematical model of two-dimensional colony growth, where cells carry a coupled positive-and-negative-feedback circuit. We demonstrate that the model can produce sectored, target (concentric), uniform, and scattered expression patterns of regulators, depending on gene expression dynamics and nutrient diffusion. We reconstructed the same regulatory structure in Escherichia coli cells and found gene expression patterns on the surface of colonies similar to the ones produced by the computer simulations. By comparing computer simulations and experimental results, we observed that very simple rules of gene expression can yield a spectrum of well-defined patterns in a growing colony. Our results suggest that variations of the protein content among cells lead to a high level of heterogeneity in colonies.

Importance Formation of patterns is a common feature in the development of microbial communities. In this work, we show that a simple genetic circuit composed of a positive-feedback loop and a negative-feedback loop can produce diverse expression patterns in colonies. We obtained similar sets of gene expression patterns in the simulations and in the experiments. Because the combination of positive feedback and negative feedback is common in intracellular molecular networks, our results suggest that the protein content of cells is highly diversified in colonies.

Formation of patterns is a common feature in the development of microbial communities. In this work, we show that a simple genetic circuit composed of a positive-feedback loop and a negative-feedback loop can produce diverse expression patterns in colonies. We obtained similar sets of gene expression patterns in the simulations and in the experiments. Because the combination of positive feedback and negative feedback is common in intracellular molecular networks, our results suggest that the protein content of cells is highly diversified in colonies.

Spatial fluctuations in expression of the heterocyst differentiation regulatory gene hetR in Anabaena filaments

Under nitrogen deprivation, filaments of the cyanobacterium Anabaena undergo a process of development, resulting in a one-dimensional pattern of nitrogen-fixing heterocysts separated by about ten photosynthetic vegetative cells. Many aspects of gene expression before nitrogen deprivation and during the developmental process remain to be elucidated. Furthermore, the coupling of gene expression fluctuations between cells along a multicellular filament is unknown. We studied the statistics of fluctuations of gene expression of HetR, a transcription factor essential for heterocyst differentiation, both under steady-state growth in nitrogen-rich conditions and at different times following nitrogen deprivation, using a chromosomally-encoded translational hetR-gfp fusion. Statistical analysis of fluorescence at the individual cell level in wild-type and mutant filaments demonstrates that expression fluctuations of hetR in nearby cells are coupled, with a characteristic spatial range of circa two to three cells, setting the scale for cellular interactions along a filament. Correlations between cells predominantly arise from intercellular molecular transfer and less from cell division. Fluctuations after nitrogen step-down can build up on those under nitrogen-replete conditions. We found that under nitrogen-rich conditions, basal, steady-state expression of the HetR inhibitor PatS, cell-cell communication influenced by the septal protein SepJ and positive HetR auto-regulation are essential determinants of fluctuations in hetR expression and its distribution along filaments. A comparison between the expression of hetR-gfp under nitrogen-rich and nitrogen-poor conditions highlights the differences between the two HetR inhibitors PatS and HetN, as well as the differences in specificity between the septal proteins SepJ and FraC/FraD. Activation, inhibition and cell-cell communication lie at the heart of developmental processes. Our results show that proteins involved in these basic ingredients combine together in the presence of inevitable stochasticity in gene expression, to control the coupled fluctuations of gene expression that give rise to a one-dimensional developmental pattern in this organism.

Under prolonged nitrogen deprivation, one-dimensional filaments of the multicellular cyanobacterium Anabaena undergo a process of development, forming a pattern consisting of cells specialized for nitrogen fixation-heterocysts-, separated by a chain of about ten photosynthetic vegetative cells. The developmental program uses activation, inhibition, and transport to create spatial and temporal patterns of gene expression, in the presence of unavoidable stochastic fluctuations in gene expression among cells. Using a chromosomally-encoded fluorescent marker, we followed the expression of the important regulator HetR in individual cells along filaments, both under abundant nitrogen conditions as well as at different times after nitrogen deprivation. The results of our statistical analysis of these fluctuations illuminate the fundamental role that positive feedback, lateral inhibition and cell-cell communication play in the developmental program, not only after exposure to the external cue that triggers differentiation but also under non-inducing conditions. Furthermore our results establish the spatial extent to which gene expression is correlated along filaments.

Sealable femtoliter chamber arrays for cell-free biology

Cell-free systems provide a flexible platform for probing specific networks of biological reactions isolated from the complex resource sharing (e.g., global gene expression, cell division) encountered within living cells. However, such systems, used in conventional macro-scale bulk reactors, often fail to exhibit the dynamic behaviors and efficiencies characteristic of their living micro-scale counterparts. Understanding the impact of internal cell structure and scale on reaction dynamics is crucial to understanding complex gene networks. Here we report a microfabricated device that confines cell-free reactions in cellular scale volumes while allowing flexible characterization of the enclosed molecular system. This multilayered poly(dimethylsiloxane) (PDMS) device contains femtoliter-scale reaction chambers on an elastomeric membrane which can be actuated (open and closed). When actuated, the chambers confine Cell-Free Protein Synthesis (CFPS) reactions expressing a fluorescent protein, allowing for the visualization of the reaction kinetics over time using time-lapse fluorescent microscopy. Here we demonstrate how this device may be used to measure the noise structure of CFPS reactions in a manner that is directly analogous to those used to characterize cellular systems, thereby enabling the use of noise biology techniques used in cellular systems to characterize CFPS gene circuits and their interactions with the cell-free environment.

Napoleon Is in Equilibrium

It has been said that the cell is the test tube of the twenty-first century. If so, the theoretical tools needed to quantitatively and predictively describe what goes on in such test tubes lag sorely behind the stunning experimental advances in biology seen in the decades since the molecular biology revolution began. Perhaps surprisingly, one of the theoretical tools that has been used with great success on problems ranging from how cells communicate with their environment and each other to the nature of the organization of proteins and lipids within the cell membrane is statistical mechanics. A knee-jerk reaction to the use of statistical mechanics in the description of cellular processes is that living organisms are so far from equilibrium that one has no business even thinking about it. But such reactions are probably too hasty given that there are many regimes in which, because of a separation of timescales, for example, such an approach can be a useful first step. In this article, we explore the power of statistical mechanical thinking in the biological setting, with special emphasis on cell signaling and regulation. We show how such models are used to make predictions and describe some recent experiments designed to test them. We also consider the limits of such models based on the relative timescales of the processes of interest.

An integrative approach for modeling and simulation of heterocyst pattern formation in cyanobacteria filaments

Heterocyst differentiation in cyanobacteria filaments is one of the simplest examples of cellular differentiation and pattern formation in multicellular organisms. Despite of the many experimental studies addressing the evolution and sustainment of heterocyst patterns and the knowledge of the genetic circuit underlying the behavior of single cyanobacterium under nitrogen deprivation, there is still a theoretical gap connecting these two macroscopic and microscopic processes. As an attempt to shed light on this issue, here we explore heterocyst differentiation under the paradigm of systems biology. This framework allows us to formulate the essential dynamical ingredients of the genetic circuit of a single cyanobacterium into a set of differential equations describing the time evolution of the concentrations of the relevant molecular products. As a result, we are able to study the behavior of a single cyanobacterium under different external conditions, emulating nitrogen deprivation, and simulate the dynamics of cyanobacteria filaments by coupling their respective genetic circuits via molecular diffusion. These two ingredients allow us to understand the principles by which heterocyst patterns can be generated and sustained. In particular, our results point out that, by including both diffusion and noisy external conditions in the computational model, it is possible to reproduce the main features of the formation and sustainment of heterocyst patterns in cyanobacteria filaments as observed experimentally. Finally, we discuss the validity and possible improvements of the model.

Bursty gene expression in the intact mammalian liver

Bursts of nascent mRNA have been shown to lead to substantial cell-cell variation in unicellular organisms, facilitating diverse responses to environmental challenges. It is unknown whether similar bursts and gene-expression noise occur in mammalian tissues. To address this, we combine single molecule transcript counting with dual-color labeling and quantification of nascent mRNA to characterize promoter states, transcription rates, and transcript lifetimes in the intact mouse liver. We find that liver gene expression is highly bursty, with promoters stochastically switching between transcriptionally active and inactive states. Promoters of genes with short mRNA lifetimes are active longer, facilitating rapid response while reducing burst-associated noise. Moreover, polyploid hepatocytes exhibit less noise than diploid hepatocytes, suggesting a possible benefit to liver polyploidy. Thus, temporal averaging and liver polyploidy dampen the intrinsic variability associated with transcriptional bursts. Our approach can be used to study transcriptional bursting in diverse mammalian tissues.

Heredity and self-organization: partners in the generation and evolution of phenotypes

In this review we examine the role of self-organization in the context of the evolution of morphogenesis. We provide examples to show that self-organized behavior is ubiquitous, and suggest it is a mechanism that can permit high levels of biodiversity without the invention of ever-increasing numbers of genes. We also examine the implications of self-organization for understanding the "internal descriptions" of organisms and the concept of a genotype-phenotype map.

Promoter architecture dictates cell-to-cell variability in gene expression

Variability in gene expression among genetically identical cells has emerged as a central preoccupation in the study of gene regulation; however, a divide exists between the predictions of molecular models of prokaryotic transcriptional regulation and genome-wide experimental studies suggesting that this variability is indifferent to the underlying regulatory architecture. We constructed a set of promoters in Escherichia coli in which promoter strength, transcription factor binding strength, and transcription factor copy numbers are systematically varied, and used messenger RNA (mRNA) fluorescence in situ hybridization to observe how these changes affected variability in gene expression. Our parameter-free models predicted the observed variability; hence, the molecular details of transcription dictate variability in mRNA expression, and transcriptional noise is specifically tunable and thus represents an evolutionarily accessible phenotypic parameter.

Systematic identification and quantification of phase variation in commensal and pathogenic Escherichia coli

Bacteria have been shown to generate constant genetic variation in a process termed phase variation. We present a tool based on whole genome sequencing that allows detection and quantification of coexisting genotypes mediated by genomic inversions in bacterial cultures. We tested our method on widely used strains of Escherichia coli, and detected stable and reproducible phase variation in several invertible loci. These are shown here to be responsible for maintaining constant variation in populations grown from a single colony. Applying this tool on other bacterial strains can shed light on how pathogens adjust to hostile environments by diversifying their genomes.

Mixed Poisson distributions in exact solutions of stochastic autoregulation models

In this paper we study the interplay between stochastic gene expression and system design using simple stochastic models of autoactivation and autoinhibition. Using the Poisson representation, a technique whose particular usefulness in the context of nonlinear gene regulation models we elucidate, we find exact results for these feedback models in the steady state. Further, we exploit this representation to analyze the parameter spaces of each model, determine which dimensionless combinations of rates are the shape determinants for each distribution, and thus demarcate where in the parameter space qualitatively different behaviors arise. These behaviors include power-law-tailed distributions, bimodal distributions, and sub-Poisson distributions. We also show how these distribution shapes change when the strength of the feedback is tuned. Using our results, we reexamine how well the autoinhibition and autoactivation models serve their conventionally assumed roles as paradigms for noise suppression and noise exploitation, respectively.

The physics of bacterial decision making

The choice that bacteria make between sporulation and competence when subjected to stress provides a prototypical example of collective cell fate determination that is stochastic on the individual cell level, yet predictable (deterministic) on the population level. This collective decision is performed by an elaborated gene network. Considerable effort has been devoted to simplify its complexity by taking physics approaches to untangle the basic functional modules that are integrated to form the complete network: (1) A stochastic switch whose transition probability is controlled by two order parameters-population density and internal/external stress. (2) An adaptable timer whose clock rate is normalized by the same two previous order parameters. (3) Sensing units which measure population density and external stress. (4) A communication module that exchanges information about the cells' internal stress levels. (5) An oscillating gate of the stochastic switch which is regulated by the timer. The unique circuit architecture of the gate allows special dynamics and noise management features. The gate opens a window of opportunity in time for competence transitions, during which the circuit generates oscillations that are translated into a chain of short intervals with high transition probability. In addition, the unique architecture of the gate allows filtering of external noise and robustness against variations in circuit parameters and internal noise. We illustrate that a physics approach can be very valuable in investigating the decision process and in identifying its general principles. We also show that both cell-cell variability and noise have important functional roles in the collectively controlled individual decisions.

Evolution of the cancer stem cell model

Genetic analyses have shaped much of our understanding of cancer. However, it is becoming increasingly clear that cancer cells display features of normal tissue organization, where cancer stem cells (CSCs) can drive tumor growth. Although often considered as mutually exclusive models to describe tumor heterogeneity, we propose that the genetic and CSC models of cancer can be harmonized by considering the role of genetic diversity and nongenetic influences in contributing to tumor heterogeneity. We offer an approach to integrating CSCs and cancer genetic data that will guide the field in interpreting past observations and designing future studies.