Phenotypic variability of growing cellular populations

How Does Escherichia coli Allocate Proteome?

Microorganisms are shown to actively partition their intracellular resources, such as proteins, for growth optimization. Recent experiments have begun to reveal molecular components unpinning the partition; however, quantitatively, it remains unclear how individual parts orchestrate to yield precise resource allocation that is both robust and dynamic. Here, we developed a coarse-grained mathematical framework that centers on guanosine pentaphosphate (ppGpp)-mediated regulation and used it to systematically uncover the design principles of proteome allocation in Escherichia coli. Our results showed that the cellular ability of resource partition lies in an ultrasensitive, negative feedback-controlling topology with the ultrasensitivity arising from zero-order amino acid kinetics and the negative feedback from ppGpp-controlled ribosome synthesis. In addition, together with the time-scale separation between slow ribosome kinetics and fast turnovers of ppGpp and amino acids, the network topology confers the organism an optimization mechanism that mimics sliding mode control, a nonlinear optimization strategy that is widely used in man-made systems. We further showed that such a controlling mechanism is robust against parameter variations and molecular fluctuations and is also efficient for biomass production over time. This work elucidates the fundamental controlling mechanism of E. coli proteome allocation, thereby providing insights into quantitative microbial physiology as well as the design of synthetic gene networks.

Collective behavior and self-organization in neural rosette morphogenesis

Neural rosettes develop from the self-organization of differentiating human pluripotent stem cells. This process mimics the emergence of the embryonic central nervous system primordium, i.e., the neural tube, whose formation is under close investigation as errors during such process result in severe diseases like spina bifida and anencephaly. While neural tube formation is recognized as an example of self-organization, we still do not understand the fundamental mechanisms guiding the process. Here, we discuss the different theoretical frameworks that have been proposed to explain self-organization in morphogenesis. We show that an explanation based exclusively on stem cell differentiation cannot describe the emergence of spatial organization, and an explanation based on patterning models cannot explain how different groups of cells can collectively migrate and produce the mechanical transformations required to generate the neural tube. We conclude that neural rosette development is a relevant experimental 2D in-vitro model of morphogenesis because it is a multi-scale self-organization process that involves both cell differentiation and tissue development. Ultimately, to understand rosette formation, we first need to fully understand the complex interplay between growth, migration, cytoarchitecture organization, and cell type evolution.

Agent-Based Modeling of Microbial Communities

Microbial communities are complex living systems that populate the planet with diverse functions and are increasingly harnessed for practical human needs. To deepen the fundamental understanding of their organization and functioning as well as to facilitate their engineering for applications, mathematical modeling has played an increasingly important role. Agent-based models represent a class of powerful quantitative frameworks for investigating microbial communities because of their individualistic nature in describing cells, mechanistic characterization of molecular and cellular processes, and intrinsic ability to produce emergent system properties. This review presents a comprehensive overview of recent advances in agent-based modeling of microbial communities. It surveys the state-of-the-art algorithms employed to simulate intracellular biomolecular events, single-cell behaviors, intercellular interactions, and interactions between cells and their environments that collectively serve as the driving forces of community behaviors. It also highlights three lines of applications of agent-based modeling, namely, the elucidation of microbial range expansion and colony ecology, the design of synthetic gene circuits and microbial populations for desired behaviors, and the characterization of biofilm formation and dispersal. The review concludes with a discussion of existing challenges, including the computational cost of the modeling, and potential mitigation strategies.

Exact Probability Landscapes of Stochastic Phenotype Switching in Feed-Forward Loops: Phase Diagrams of Multimodality

Feed-forward loops (FFLs) are among the most ubiquitously found motifs of reaction networks in nature. However, little is known about their stochastic behavior and the variety of network phenotypes they can exhibit. In this study, we provide full characterizations of the properties of stochastic multimodality of FFLs, and how switching between different network phenotypes are controlled. We have computed the exact steady-state probability landscapes of all eight types of coherent and incoherent FFLs using the finite-butter Accurate Chemical Master Equation (ACME) algorithm, and quantified the exact topological features of their high-dimensional probability landscapes using persistent homology. Through analysis of the degree of multimodality for each of a set of 10,812 probability landscapes, where each landscape resides over 10⁵–10⁶ microstates, we have constructed comprehensive phase diagrams of all relevant behavior of FFL multimodality over broad ranges of input and regulation intensities, as well as different regimes of promoter binding dynamics. In addition, we have quantified the topological sensitivity of the multimodality of the landscapes to regulation intensities. Our results show that with slow binding and unbinding dynamics of transcription factor to promoter, FFLs exhibit strong stochastic behavior that is very different from what would be inferred from deterministic models. In addition, input intensity play major roles in the phenotypes of FFLs: At weak input intensity, FFL exhibit monomodality, but strong input intensity may result in up to 6 stable phenotypes. Furthermore, we found that gene duplication can enlarge stable regions of specific multimodalities and enrich the phenotypic diversity of FFL networks, providing means for cells toward better adaptation to changing environment. Our results are directly applicable to analysis of behavior of FFLs in biological processes such as stem cell differentiation and for design of synthetic networks when certain phenotypic behavior is desired.

Circuit-Host Coupling Induces Multifaceted Behavioral Modulations of a Gene Switch

Quantitative modeling of gene circuits is fundamentally important to synthetic biology, as it offers the potential to transform circuit engineering from trial-and-error construction to rational design and, hence, facilitates the advance of the field. Currently, typical models regard gene circuits as isolated entities and focus only on the biochemical processes within the circuits. However, such a standard paradigm is getting challenged by increasing experimental evidence suggesting that circuits and their host are intimately connected, and their interactions can potentially impact circuit behaviors. Here we systematically examined the roles of circuit-host coupling in shaping circuit dynamics by using a self-activating gene switch as a model circuit. Through a combination of deterministic modeling, stochastic simulation, and Fokker-Planck equation formalism, we found that circuit-host coupling alters switch behaviors across multiple scales. At the single-cell level, it slows the switch dynamics in the high protein production regime and enlarges the difference between stable steady-state values. At the population level, it favors cells with low protein production through differential growth amplification. Together, the two-level coupling effects induce both quantitative and qualitative modulations of the switch, with the primary component of the effects determined by the circuit's architectural parameters. This study illustrates the complexity and importance of circuit-host coupling in modulating circuit behaviors, demonstrating the need for a new paradigm-integrated modeling of the circuit-host system-for quantitative understanding of engineered gene networks.

Rate-limiting steps in transcription dictate sensitivity to variability in cellular components

Cell-to-cell variability in cellular components generates cell-to-cell diversity in RNA and protein production dynamics. As these components are inherited, this should also cause lineage-to-lineage variability in these dynamics. We conjectured that these effects on transcription are promoter initiation kinetics dependent. To test this, first we used stochastic models to predict that variability in the numbers of molecules involved in upstream processes, such as the intake of inducers from the environment, acts only as a transient source of variability in RNA production numbers, while variability in the numbers of a molecular species controlling transcription of an active promoter acts as a constant source. Next, from single-cell, single-RNA level time-lapse microscopy of independent lineages of Escherichia coli cells, we demonstrate the existence of lineage-to-lineage variability in gene activation times and mean RNA production rates, and that these variabilities differ between promoters and inducers used. Finally, we provide evidence that this can be explained by differences in the kinetics of the rate-limiting steps in transcription between promoters and induction schemes. We conclude that cell-to-cell and consequent lineage-to-lineage variability in RNA and protein numbers are both promoter sequence-dependent and subject to regulation.

Population-Dynamic Modeling of Bacterial Horizontal Gene Transfer by Natural Transformation

Natural transformation is a major mechanism of horizontal gene transfer (HGT) and plays an essential role in bacterial adaptation, evolution, and speciation. Although its molecular underpinnings have been increasingly revealed, natural transformation is not well characterized in terms of its quantitative ecological roles. Here, by using Neisseria gonorrhoeae as an example, we developed a population-dynamic model for natural transformation and analyzed its dynamic characteristics with nonlinear tools and simulations. Our study showed that bacteria capable of natural transformation can display distinct population behaviors ranging from extinction to coexistence and to bistability, depending on their HGT rate and selection coefficient. With the model, we also illustrated the roles of environmental DNA sources-active secretion and passive release-in impacting population dynamics. Additionally, by constructing and utilizing a stochastic version of the model, we examined how noise shapes the steady and dynamic behaviors of the system. Notably, we found that distinct waiting time statistics for HGT events, namely a power-law distribution, an exponential distribution, and a mix of the both, are associated with the dynamics in the regimes of extinction, coexistence, and bistability accordingly. This work offers a quantitative illustration of natural transformation by revealing its complex population dynamics and associated characteristics, therefore advancing our ecological understanding of natural transformation as well as HGT in general.

Stochastic sensitivity analysis and kernel inference via distributional data

Cellular processes are noisy due to the stochastic nature of biochemical reactions. As such, it is impossible to predict the exact quantity of a molecule or other attributes at the single-cell level. However, the distribution of a molecule over a population is often deterministic and is governed by the underlying regulatory networks relevant to the cellular functionality of interest. Recent studies have started to exploit this property to infer network states. To facilitate the analysis of distributional data in a general experimental setting, we introduce a computational framework to efficiently characterize the sensitivity of distributional output to changes in external stimuli. Further, we establish a probability-divergence-based kernel regression model to accurately infer signal level based on distribution measurements. Our methodology is applicable to any biological system subject to stochastic dynamics and can be used to elucidate how population-based information processing may contribute to organism-level functionality. It also lays the foundation for engineering synthetic biological systems that exploit population decoding to more robustly perform various biocomputation tasks, such as disease diagnostics and environmental-pollutant sensing.

Slow and steady wins the race: a bacterial exploitative competition strategy in fluctuating environments

One promising frontier for synthetic biology is the development of synthetic ecologies, whereby interacting species form an additional layer of connectivity for engineered gene circuits. Toward this goal, an important step is to understand different types of bacterial interactions in natural settings, among which competition is the most prevalent. By constructing a two-species population dynamics model, here, we mimicked bacterial growth in nature with resource-limited fluctuating environments and searched for optimal strategies for bacterial exploitative competition. In a simple game with two strategy options (constant or susceptible growth), we found that the species playing the constant growth strategy always outplays or is evenly matched with its competitor, suggesting that constant growth is a "no-loss" good bet. We also showed that adoption of sophisticated strategies enables a species to maximize its fitness when its competitor grows susceptibly. The pursuit of fitness maximization is, however, associated with potential loss if both species are capable of strategy adjustment, indicating an intrinsic risk-return trade-off. These findings offer new insights into bacterial competition and may also facilitate the engineering of microbial consortia for synthetic biology applications.

Programming the group behaviors of bacterial communities with synthetic cellular communication

Synthetic biology is a newly emerged research discipline that focuses on the engineering of novel cellular behaviors and functionalities through the creation of artificial gene circuits. One important class of synthetic circuits currently under active development concerns the programming of bacterial cellular communication and collective population-scale behaviors. Because of the ubiquity of cell-cell interactions within bacterial communities, having an ability of engineering these circuits is vital to programming robust cellular behaviors. Here, we highlight recent advances in communication-based synthetic gene circuits by first discussing natural communication systems and then surveying various functional engineered circuits, including those for population density control, temporal synchronization, spatial organization, and ecosystem formation. We conclude by summarizing recent advances, outlining existing challenges, and discussing potential applications and future opportunities.

A multi-phenotypic cancer model with cell plasticity

The conventional cancer stem cell (CSC) theory indicates a hierarchy of CSCs and non-stem cancer cells (NSCCs), that is, CSCs can differentiate into NSCCs but not vice versa. However, an alternative paradigm of CSC theory with reversible cell plasticity among cancer cells has received much attention very recently. Here we present a generalized multi-phenotypic cancer model by integrating cell plasticity with the conventional hierarchical structure of cancer cells. We prove that under very weak assumption, the nonlinear dynamics of multi-phenotypic proportions in our model has only one stable steady state and no stable limit cycle. This result theoretically explains the phenotypic equilibrium phenomena reported in various cancer cell lines. Furthermore, according to the transient analysis of our model, it is found that cancer cell plasticity plays an essential role in maintaining the phenotypic diversity in cancer especially during the transient dynamics. Two biological examples with experimental data show that the phenotypic conversions from NCSSs to CSCs greatly contribute to the transient growth of CSCs proportion shortly after the drastic reduction of it. In particular, an interesting overshooting phenomenon of CSCs proportion arises in three-phenotypic example. Our work may pave the way for modeling and analyzing the multi-phenotypic cell population dynamics with cell plasticity.

Extinction, coexistence, and localized patterns of a bacterial population with contact-dependent inhibition

BACKGROUND

Contact-dependent inhibition (CDI) has been recently revealed as an intriguing but ubiquitous mechanism for bacterial competition in which a species injects toxins into its competitors through direct physical contact for growth suppression. Although the molecular and genetic aspects of CDI systems are being increasingly explored, a quantitative and systematic picture of how CDI systems benefit population competition and hence alter corresponding competition outcomes is not well elucidated.

RESULTS

By constructing a mathematical model for a population consisting of CDI+ and CDI- species, we have systematically investigated the dynamics and possible outcomes of population competition. In the well-mixed case, we found that the two species are mutually exclusive: Competition always results in extinction for one of the two species, with the winner determined by the tradeoff between the competitive benefit of the CDI+ species and its growth disadvantage from increased metabolic burden. Initial conditions in certain circumstances can also alter the outcome of competition. In the spatial case, in addition to exclusive extinction, coexistence and localized patterns may emerge from population competition. For spatial coexistence, population diffusion is also important in influencing the outcome. Using a set of illustrative examples, we further showed that our results hold true when the competition of the population is extended from one to two dimensional space.

CONCLUSIONS

We have revealed that the competition of a population with CDI can produce diverse patterns, including extinction, coexistence, and localized aggregation. The emergence, relative abundance, and characteristic features of these patterns are collectively determined by the competitive benefit of CDI and its growth disadvantage for a given rate of population diffusion. Thus, this study provides a systematic and statistical view of CDI-based bacterial population competition, expanding the spectrum of our knowledge about CDI systems and possibly facilitating new experimental tests for a deeper understanding of bacterial interactions.

Noise minimisation in gene expression switches

Gene expression is subject to stochastic variation which leads to fluctuations in the rate of protein production. Recently, a study in yeast at a genomic scale showed that, in some cases, gene expression variability alters phenotypes while, in other cases, these remain unchanged despite fluctuations in the expression of other genes. These studies suggested that noise in gene expression is a physiologically relevant trait and, to prevent harmful stochastic variation in the expression levels of some genes, it can be subject to minimisation. However, the mechanisms for noise minimisation are still unclear. In the present work, we analysed how noise expression depends on the architecture of the cis-regulatory system, in particular on the number of regulatory binding sites. Using analytical calculations and stochastic simulations, we found that the fluctuation level in noise expression decreased with the number of regulatory sites when regulatory transcription factors interacted with only one other bound transcription factor. In contrast, we observed that there was an optimal number of binding sites when transcription factors interacted with many bound transcription factors. This finding suggested a new mechanism for preventing large fluctuations in the expression of genes which are sensitive to the concentration of regulators.

Metabolic variability in micro-populations

Biological cells in a population are variable in practically every property. Much is known about how variability of single cells is reflected in the statistical properties of infinitely large populations; however, many biologically relevant situations entail finite times and intermediate-sized populations. The statistical properties of an ensemble of finite populations then come into focus, raising questions concerning inter-population variability and dependence on initial conditions. Recent technologies of microfluidic and microdroplet-based population growth realize these situations and make them immediately relevant for experiments and biotechnological application. We here study the statistical properties, arising from metabolic variability of single cells, in an ensemble of micro-populations grown to saturation in a finite environment such as a micro-droplet. We develop a discrete stochastic model for this growth process, describing the possible histories as a random walk in a phenotypic space with an absorbing boundary. Using a mapping to Polya’s Urn, a classic problem of probability theory, we find that distributions approach a limiting inoculum-dependent form after a large number of divisions. Thus, population size and structure are random variables whose mean, variance and in general their distribution can reflect initial conditions after many generations of growth. Implications of our results to experiments and to biotechnology are discussed.

Automatic compilation from high-level biologically-oriented programming language to genetic regulatory networks

BACKGROUND

The field of synthetic biology promises to revolutionize our ability to engineer biological systems, providing important benefits for a variety of applications. Recent advances in DNA synthesis and automated DNA assembly technologies suggest that it is now possible to construct synthetic systems of significant complexity. However, while a variety of novel genetic devices and small engineered gene networks have been successfully demonstrated, the regulatory complexity of synthetic systems that have been reported recently has somewhat plateaued due to a variety of factors, including the complexity of biology itself and the lag in our ability to design and optimize sophisticated biological circuitry.

METHODOLOGY/PRINCIPAL FINDINGS

To address the gap between DNA synthesis and circuit design capabilities, we present a platform that enables synthetic biologists to express desired behavior using a convenient high-level biologically-oriented programming language, Proto. The high level specification is compiled, using a regulatory motif based mechanism, to a gene network, optimized, and then converted to a computational simulation for numerical verification. Through several example programs we illustrate the automated process of biological system design with our platform, and show that our compiler optimizations can yield significant reductions in the number of genes (~ 50%) and latency of the optimized engineered gene networks.

CONCLUSIONS/SIGNIFICANCE

Our platform provides a convenient and accessible tool for the automated design of sophisticated synthetic biological systems, bridging an important gap between DNA synthesis and circuit design capabilities. Our platform is user-friendly and features biologically relevant compiler optimizations, providing an important foundation for the development of sophisticated biological systems.

Exact time-dependent solutions for a self-regulating gene

The exact time-dependent solution for the stochastic equations governing the behavior of a binary self-regulating gene is presented. Using the generating function technique to rephrase the master equations in terms of partial differential equations, we show that the model is totally integrable and the analytical solutions are the celebrated confluent Heun functions. Self-regulation plays a major role in the control of gene expression, and it is remarkable that such a microscopic model is completely integrable in terms of well-known complex functions.

Noise regulation by quorum sensing in low mRNA copy number systems

Background

Cells must face the ubiquitous presence of noise at the level of signaling molecules. The latter constitutes a major challenge for the regulation of cellular functions including communication processes. In the context of prokaryotic communication, the so-called quorum sensing (QS) mechanism relies on small diffusive molecules that are produced and detected by cells. This poses the intriguing question of how bacteria cope with the fluctuations for setting up a reliable information exchange.

Results

We present a stochastic model of gene expression that accounts for the main biochemical processes that describe the QS mechanism close to its activation threshold. Within that framework we study, both numerically and analytically, the role that diffusion plays in the regulation of the dynamics and the fluctuations of signaling molecules. In addition, we unveil the contribution of different sources of noise, intrinsic and transcriptional, in the QS mechanism.

Conclusions

The interplay between noisy sources and the communication process produces a repertoire of dynamics that depends on the diffusion rate. Importantly, the total noise shows a non-monotonic behavior as a function of the diffusion rate. QS systems seems to avoid values of the diffusion that maximize the total noise. These results point towards the direction that bacteria have adapted their communication mechanisms in order to improve the signal-to-noise ratio.

Gene expression variations are predictive for stochastic noise

Fluctuations in protein abundance among single cells are primarily due to the inherent stochasticity in transcription and translation processes, such stochasticity can often confer phenotypic heterogeneity among isogenic cells. It has been proposed that expression noise can be triggered as an adaptation to environmental stresses and genetic perturbations, and as a mechanism to facilitate gene expression evolution. Thus, elucidating the relationship between expression noise, measured at the single-cell level, and expression variation, measured on population of cells, can improve our understanding on the variability and evolvability of gene expression. Here, we showed that noise levels are significantly correlated with conditional expression variations. We further demonstrated that expression variations are highly predictive for noise level, especially in TATA-box containing genes. Our results suggest that expression variabilities can serve as a proxy for noise level, suggesting that these two properties share the same underlining mechanism, e.g. chromatin regulation. Our work paves the way for the study of stochastic noise in other single-cell organisms.

Robust growth of Escherichia coli

The quantitative study of the cell growth has led to many fundamental insights in our understanding of a wide range of subjects, from the cell cycle to senescence. Of particular importance is the growth rate, whose constancy represents a physiological steady state of an organism. Recent studies, however, suggest that the rate of elongation during exponential growth of bacterial cells decreases cumulatively with replicative age for both asymmetrically and symmetrically dividing organisms, implying that a "steady-state" population consists of individual cells that are never in a steady state of growth. To resolve this seeming paradoxical observation, we studied the long-term growth and division patterns of Escherichia coli cells by employing a microfluidic device designed to follow steady-state growth and division of a large number of cells at a defined reproductive age. Our analysis of approximately 10(5) individual cells reveals a remarkable stability of growth whereby the mother cell inherits the same pole for hundreds of generations. We further show that death of E. coli is not purely stochastic but is the result of accumulating damages. We conclude that E. coli, unlike all other aging model systems studied to date, has a robust mechanism of growth that is decoupled from cell death.

Tuning and controlling gene expression noise in synthetic gene networks

Synthetic gene networks can be used to control gene expression and cellular phenotypes in a variety of applications. In many instances, however, such networks can behave unreliably due to gene expression noise. Accordingly, there is a need to develop systematic means to tune gene expression noise, so that it can be suppressed in some cases and harnessed in others, e.g. in cellular differentiation to create population-wide heterogeneity. Here, we present a method for controlling noise in synthetic eukaryotic gene expression systems, utilizing reduction of noise levels by TATA box mutations and noise propagation in transcriptional cascades. Specifically, we introduce TATA box mutations into promoters driving TetR expression and show that these mutations can be used to effectively tune the noise of a target gene while decoupling it from the mean, with negligible effects on the dynamic range and basal expression. We apply mathematical and computational modeling to explain the experimentally observed effects of TATA box mutations. This work, which highlights some important aspects of noise propagation in gene regulatory cascades, has practical implications for implementing gene expression control in synthetic gene networks.

Dosage compensation on the active X chromosome minimizes transcriptional noise of X-linked genes in mammals

Comparison of gene expression variation in autosomal and X-linked genes reveals that high transcriptional noise is not a necessary consequence of haploid expression.

Background

Theory predicts that haploid-expressed genes should have noisier expression than comparable diploid-expressed ones with the same expression level. However, in mammals there are several classes of gene that are monoallelically expressed, including X-linked genes, imprinted genes and some other autosomal genes. Does it follow that the evolution of X chromosomes in eukaryotes comes at the cost of increased transcriptional noise in the heterogametic sex? Moreover, is escaping X-inactivation in mammalian females associated with an increase in transcriptional variation? To address these questions, we analyze gene expression variation between replicate samples of diverse mammalian cell lines in steady-state using microarray data.

Results

We observe that transcriptional variation of X-linked genes is no different to that of autosomal genes both before and after control for transcript abundance. By contrast, autosomal genes subject to allelic exclusion do have unusually high noise levels even allowing for their low transcript abundance. The prior theory we suggest was insufficient, at least as regards X-chromosomes, as it failed to appreciate the regulatory complexity of gene expression, not least the effects of genomic neighborhood.

Conclusions

These results suggest that high noise is not a necessary consequence of haploid expression and emphasize the primacy of expression level as a determinant of noise. The latter has consequences for understanding the etiology of haplo-insufficiency and the evolution of gene expression levels. Given the coupling between expression level and noise on the X-chromosome, we suggest that part of the selective advantage of dosage compensation is noise abatement of X-linked genes.

The importance of being persistent: heterogeneity of bacterial populations under antibiotic stress

While the DNA sequence is largely responsible for transmitting phenotypic traits over evolutionary time, organisms are also considerably affected by phenotypic variations that persist for more than one generation, with no direct change in the organisms' DNA sequence. In contrast to genetic variation, which is passed on over many generations, the phenotypic variation generated by nongenetic mechanisms is difficult to study due to the inherently limited life time of states that are not encoded in the DNA sequence, but makes it possible for the 'memory' of past environments to influence future organisms. One striking example of phenotypic variation is the phenomenon of bacterial persistence, whereby genetically identical bacterial populations respond heterogeneously to antibiotic treatment. Our aim is to review several experimental and theoretical approaches to the study of persistence. We define persistence as a characteristic of a heterogeneous bacterial population that is taken as a generic example through which we illustrate the approach and study the dynamics of population variability. The clinical and evolutionary implications of persistence are discussed in light of the mathematical description. This approach should be of relevance to the study of other phenomena in which nongenetic variability is involved, such as cellular differentiation or the response of cancer cells to treatment.

Intrinsic and measured statistics of discrete stochastic populations

The notion that the nature of a measurement is critical to its outcome is usually associated with quantum phenomena. In this paper, we show that the observed statistical properties are also a function of the measurement technique in the case of simple classical populations. In particular, the measured and intrinsic statistics of a single population may be different, while correlation and transfer of individuals between two populations may be hidden from the observer.

Regulatory control and the costs and benefits of biochemical noise

Experiments in recent years have vividly demonstrated that gene expression can be highly stochastic. How protein concentration fluctuations affect the growth rate of a population of cells is, however, a wide-open question. We present a mathematical model that makes it possible to quantify the effect of protein concentration fluctuations on the growth rate of a population of genetically identical cells. The model predicts that the population's growth rate depends on how the growth rate of a single cell varies with protein concentration, the variance of the protein concentration fluctuations, and the correlation time of these fluctuations. The model also predicts that when the average concentration of a protein is close to the value that maximizes the growth rate, fluctuations in its concentration always reduce the growth rate. However, when the average protein concentration deviates sufficiently from the optimal level, fluctuations can enhance the growth rate of the population, even when the growth rate of a cell depends linearly on the protein concentration. The model also shows that the ensemble or population average of a quantity, such as the average protein expression level or its variance, is in general not equal to its time average as obtained from tracing a single cell and its descendants. We apply our model to perform a cost-benefit analysis of gene regulatory control. Our analysis predicts that the optimal expression level of a gene regulatory protein is determined by the trade-off between the cost of synthesizing the regulatory protein and the benefit of minimizing the fluctuations in the expression of its target gene. We discuss possible experiments that could test our predictions.

Biochemical networks, consisting of biomolecules such as proteins and DNA that chemically and physically interact with one another, are the processing devices of life. Metabolic networks allow living cells to process food, while signal transduction pathways and gene regulatory networks allow living cells to process information. Experiments in recent years have demonstrated that these networks are often very “noisy”: the protein concentrations often fluctuate strongly. However, how this “biochemical noise” affects the growth rate or fitness of an organism is poorly understood. We present here a mathematical model that makes it possible to predict quantitatively how protein concentration fluctuations affect the growth rate of a cell population. The model predicts that fluctuations reduce the growth rate when evolution has tuned the average protein concentration to the level that maximizes the growth rate; however, when the average concentration deviates sufficiently from the optimal one, fluctuations can actually enhance the growth rate. Our analysis also predicts that the optimal design of a regulatory network is determined by the trade-off between the cost of synthesizing the proteins that constitute the regulatory network and the benefit of reducing the fluctuations in the network that it controls. Our predictions can be tested in wild-type and synthetic networks.

A molecular noise generator

Recent studies have demonstrated that intracellular variations in the rate of gene expression are of fundamental importance to cellular function and development. While such 'noise' is often considered detrimental in the context of perturbing genetic systems, it can be beneficial in processes such as species diversification and facilitation of evolution. A major difficulty in exploring such effects is that the magnitude and spectral properties of the induced variations arise from some intrinsic cellular process that is difficult to manipulate. Here, we present two designs of a molecular noise generator that allow for the flexible modulation of the noise profile of a target gene. The first design uses a dual-signal mechanism that enables independent tuning of the mean and variability of an output protein. This is achieved through the combinatorial control of two signals that regulate transcription and translation separately. We then extend the design to allow for DNA copy-number regulation, which leads to a wider tuning spectrum for the output molecule. To gain a deeper understanding of the circuit's functionality in a realistic environment, we introduce variability in the input signals in order to ascertain the degree of noise induced by the control process itself. We conclude by illustrating potential applications of the noise generator, demonstrating how it could be used to ascertain the robust or fragile properties of a genetic circuit.