Noise reduction by diffusional dissipation in a minimal quorum sensing motif

N -acylhomoserine lactone-degrading activity of Trichoderma species and its application in the inhibition of bacterial quorum sensing

Many gram-negative pathogens can activate virulence factors under the control of N-acylhomoserine lactone (AHL）-mediated quorum sensing. AHL-degrading enzymes have been investigated for their application in disease control. Trichoderma is a genus of fungi inhabiting various types of soil and are widely used as biocontrol agents for plant pathogens. When the AHL-degrading activity of 33 strains belonging to Trichoderma species was investigated, most strains can degrade AHL. AHL lactonase catalyzes AHL ring opening by hydrolyzing lactone. Two model strains, Trichoderma atroviride MAFF 242473 and MAFF 242475, degrade AHL using their AHL lactonase activity and rapidly metabolize ring-opening AHL. Moreover, co-inoculation with MAFF 242473 and MAFF 242475 effectively inhibited AHL production by the plant pathogens, Pantoea ananatis and Pectobacterium carotovorum subsp. carotovorum. Our study suggested that Trichoderma might be an effective biocontrol agent to inhibit the expression of virulence factors via AHL-mediated quorum sensing.

Emergent robustness of bacterial quorum sensing in fluid flow

Bacteria use intercellular signaling, or quorum sensing (QS), to share information and respond collectively to aspects of their surroundings. The autoinducers that carry this information are exposed to the external environment; consequently, they are affected by factors such as removal through fluid flow, a ubiquitous feature of bacterial habitats ranging from the gut and lungs to lakes and oceans. To understand how QS genetic architectures in cells promote appropriate population-level phenotypes throughout the bacterial life cycle requires knowledge of how these architectures determine the QS response in realistic spatiotemporally varying flow conditions. Here we develop and apply a general theory that identifies and quantifies the conditions required for QS activation in fluid flow by systematically linking cell- and population-level genetic and physical processes. We predict that when a subset of the population meets these conditions, cell-level positive feedback promotes a robust collective response by overcoming flow-induced autoinducer concentration gradients. By accounting for a dynamic flow in our theory, we predict that positive feedback in cells acts as a low-pass filter at the population level in oscillatory flow, allowing a population to respond only to changes in flow that occur over slow enough timescales. Our theory is readily extendable and provides a framework for assessing the functional roles of diverse QS network architectures in realistic flow conditions.

Investigating the dynamics of microbial consortia in spatially structured environments

The spatial organization of microbial communities arises from a complex interplay of biotic and abiotic interactions, and is a major determinant of ecosystem functions. Here we design a microfluidic platform to investigate how the spatial arrangement of microbes impacts gene expression and growth. We elucidate key biochemical parameters that dictate the mapping between spatial positioning and gene expression patterns. We show that distance can establish a low-pass filter to periodic inputs and can enhance the fidelity of information processing. Positive and negative feedback can play disparate roles in the synchronization and robustness of a genetic oscillator distributed between two strains to spatial separation. Quantification of growth and metabolite release in an amino-acid auxotroph community demonstrates that the interaction network and stability of the community are highly sensitive to temporal perturbations and spatial arrangements. In sum, our microfluidic platform can quantify spatiotemporal parameters influencing diffusion-mediated interactions in microbial consortia.

Bacteria Floc, but Do They Flock? Insights from Population Interaction Models of Quorum Sensing

Quorum sensing (QS) enables coordinated, population-wide behavior. QS-active bacteria "communicate" their number density using autoinducers which they synthesize, collect, and interpret. Tangentially, chemotactic bacteria migrate, seeking out nutrients and other molecules. It has long been hypothesized that bacterial behaviors, such as chemotaxis, were the primordial progenitors of complex behaviors of higher-order organisms. Recently, QS was linked to chemotaxis, yet the notion that these behaviors can together contribute to higher-order behaviors has not been shown. Here, we mathematically link flocking behavior, commonly observed in fish and birds, to bacterial chemotaxis and QS by constructing a phenomenological model of population-scale QS-mediated phenomena. Specifically, we recast a previously developed mathematical model of flocking and found that simulated bacterial behaviors aligned well with well-known QS behaviors. This relatively simple system of ordinary differential equations affords analytical analysis of asymptotic behavior and describes cell position and velocity, QS-mediated protein expression, and the surrounding concentrations of an autoinducer. Further, heuristic explorations of the model revealed that the emergence of "migratory" subpopulations occurs only when chemotaxis is directly linked to QS. That is, behaviors were simulated when chemotaxis was coupled to QS and when not. When coupled, the bacterial flocking model predicts the formation of two distinct groups of cells migrating at different speeds in their journey toward an attractant. This is qualitatively similar to phenomena spotted in our Escherichiacoli chemotaxis experiments as well as in analogous work observed over 50 years ago.IMPORTANCE Our modeling efforts show how cell density can affect chemotaxis; they help to explain the roots of subgroup formation in bacterial populations. Our work also reinforces the notion that bacterial mechanisms are at times exhibited in higher-order organisms.

Logic of two antagonizing intra-species quorum sensing systems in bacteria

Bacteria release signaling molecules into the surrounding environment and sense them when present in their proximity. Using this strategy, a cell estimates the number of neighbors in its surrounding. Upon sensing a critical number of individuals, bacteria coordinate a number of cellular processes. This density-dependent control of gene expression and physiology is called quorum sensing (QS). Quorum sensing controls a wide variety of functions in bacteria, including those related to motility, growth, virulence etc. Quorum sensing has been widely observed in bacteria while the individuals of the same species or different species compete and cooperate each other. Interestingly, many species possess more than one QS system (intra-species) and these QS systems interact each other to perform quorum sensing. Thus, several logical arrangements can be possible based on the interaction among intra-species QS systems - parallel, series, antagonizing, and agonizing. In this work, we perform simulations to understand the logic of interaction between two antagonizing intra-species QS systems. In such an interaction, one QS system gets fully expressed and the other only gets partially expressed. This is found to be dictated by the interplay between autoinducer's diffusivity and antagonizing strength. In addition, we speculate an important role of the intracellular regulators (eg. LuxR) in maintaining the uniform response among the individual cells from the different localities. We also expect the interplay between the autoinducer's diffusivity and distribution of cells in fine tuning the collective response. Interestingly, in a localized niche with a heterogeneous cell distribution, the cells are expected to perform a global quorum sensing via fully expressed QS system and a local quorum sensing via partially expressed QS system.

Errors in mutagenesis and the benefit of cell-to-cell signalling in the evolution of stress-induced mutagenesis

Stress-induced mutagenesis is a widely observed phenomenon. Theoretical models have shown that stress-induced mutagenesis can be favoured by natural selection due to the beneficial mutations it generates. These models, however, assumed an error-free regulation of mutation rate in response to stress. Here, we explore the effects of errors in the regulation of mutagenesis on the evolution of stress-induced mutagenesis, and consider the role of cell-to-cell signalling. Using theoretical models, we show (i) that stress-induced mutagenesis can be disadvantageous if errors are common; and (ii) that cell-to-cell signalling can allow stress-induced mutagenesis to be favoured by selection even when error rates are high. We conclude that cell-to-cell signalling can facilitate the evolution of stress-induced mutagenesis in microbes through second-order selection.

Engineered Control of Genetic Variability Reveals Interplay among Quorum Sensing, Feedback Regulation, and Biochemical Noise

Stochastic fluctuations in gene expression trigger both beneficial and harmful consequences for cell behavior. Therefore, achieving a desired mean protein expression level while minimizing noise is of interest in many applications, including robust protein production systems in industrial biotechnology. Here, we consider a synthetic gene circuit combining intracellular negative feedback and cell-to-cell communication based on quorum sensing. Accounting for both intrinsic and extrinsic noise, stochastic simulations allow us to analyze the capability of the circuit to reduce noise strength as a function of its parameters. We obtain mean expression levels and noise strengths for all species under different scenarios, showing good agreement with system-wide available experimental data of protein abundance and noise in Escherichia coli. Our in silico experiments, validated by preliminary in vivo results, reveal significant noise attenuation in gene expression through the interplay between quorum sensing and negative feedback and highlight the differential role that they play in regard to intrinsic and extrinsic noise.

Mathematical Modelling of Bacterial Quorum Sensing: A Review

Bacterial quorum sensing (QS) refers to the process of cell-to-cell bacterial communication enabled through the production and sensing of the local concentration of small molecules called autoinducers to regulate the production of gene products (e.g. enzymes or virulence factors). Through autoinducers, bacteria interact with individuals of the same species, other bacterial species, and with their host. Among QS-regulated processes mediated through autoinducers are aggregation, biofilm formation, bioluminescence, and sporulation. Autoinducers are therefore "master" regulators of bacterial lifestyles. For over 10 years, mathematical modelling of QS has sought, in parallel to experimental discoveries, to elucidate the mechanisms regulating this process. In this review, we present the progress in mathematical modelling of QS, highlighting the various theoretical approaches that have been used and discussing some of the insights that have emerged. Modelling of QS has benefited almost from the onset of the involvement of experimentalists, with many of the papers which we review, published in non-mathematical journals. This review therefore attempts to give a broad overview of the topic to the mathematical biology community, as well as the current modelling efforts and future challenges.

Conversation game: talking bacteria

The story of autonomous unicellular organisms, bacteria with unimaginable computational and evolutionary capabilities along with collective behavior has been running since the first six decades of the twentieth Century. However, do not consider them to be small and simple, because they possess the generic term quorum sensing adopted to describe the cell communication process which co-ordinate gene expression, when the population has reached a high cell density. Bacteria release diffusible signal molecules known as autoinducers or quorum sensing molecules. In recent research, the direction for activating or deactivating nature of a wave of gene expression is predicted experimentally which control bacterial populations subject to a diffusing autoinducer signal. On the other hand, it has been observed that the accumulation of the quorum sensing molecules leads to a negative diffusion coefficient in the solution of governing differential equation.

Quorum Sensing Desynchronization Leads to Bimodality and Patterned Behaviors

Quorum Sensing (QS) drives coordinated phenotypic outcomes among bacterial populations. Its role in mediating infectious disease has led to the elucidation of numerous autoinducers and their corresponding QS signaling pathways. Among them, the Lsr (LuxS-regulated) QS system is conserved in scores of bacteria, and its signal molecule, autoinducer-2 (AI-2), is synthesized as a product of 1-carbon metabolism. Lsr signal transduction processes, therefore, may help organize population scale activities in numerous bacterial consortia. Conceptions of how Lsr QS organizes population scale behaviors remain limited, however. Using mathematical simulations, we examined how desynchronized Lsr QS activation, arising from cell-to-cell population heterogeneity, could lead to bimodal Lsr signaling and fractional activation. This has been previously observed experimentally. Governing these processes are an asynchronous AI-2 uptake, where positive intracellular feedback in Lsr expression is combined with negative feedback between cells. The resulting activation patterns differ from that of the more widely studied LuxIR system, the topology of which consists of only positive feedback. To elucidate differences, both QS systems were simulated in 2D, where cell populations grow and signal each other via traditional growth and diffusion equations. Our results demonstrate that the LuxIR QS system produces an ‘outward wave’ of autoinduction, and the Lsr QS system yields dispersed autoinduction from spatially-localized secretion and uptake profiles. In both cases, our simulations mirror previously demonstrated experimental results. As a whole, these models inform QS observations and synthetic biology designs.

Bacterial behavior is responsive to a multitude of soluble molecular cues. Among them are self-secreted autoinducers that control quorum sensing (QS) processes. While new quorum sensing systems are constantly being discovered, several systems have been well defined in terms of their molecular and genetic topologies, each influencing a variety of resultant phenotypes. These quorum sensing systems include LuxIR homologs that use an array of species specific autoinducers and Lsr system homologs that share a single autoinducer among numerous species. Here we suggest that the regulatory topology of these two systems mark them as opposites of a sort. Whereas the LuxIR system bears a strong positive intercellular feedback mechanism, the Lsr system bears strong negative intercellular feedback. In our simulations these differences are manifested in distinct patterns of signaling. This was readily visualized in the outward spread of autogenous LuxIR expression in a growing bacterial 2D ‘colony’ whereas a dispersed activity was produced by autogenous Lsr expression in an otherwise identical colony. Here, this dispersed activity is a reflection of bimodal Lsr expression. We show that this bimodality could arise from desynchronized Lsr driven autoinducer import (intercellular negative feedback). This may have consequences on the arrangement of downstream phenotypes.

Single Cell Analysis of a Bacterial Sender-Receiver System

Monitoring gene expression dynamics on the single cell level provides important information on cellular heterogeneity and stochasticity, and potentially allows for more accurate quantitation of gene expression processes. We here study bacterial senders and receivers genetically engineered with components of the quorum sensing system derived from Aliivibrio fischeri on the single cell level using microfluidics-based bacterial chemostats and fluorescence video microscopy. We track large numbers of bacteria over extended periods of time, which allows us to determine bacterial lineages and filter out subpopulations within a heterogeneous population. We quantitatively determine the dynamic gene expression response of receiver bacteria to varying amounts of the quorum sensing inducer N-3-oxo-C6-homoserine lactone (AHL). From this we construct AHL response curves and characterize gene expression dynamics of whole bacterial populations by investigating the statistical distribution of gene expression activity over time. The bacteria are found to display heterogeneous induction behavior within the population. We therefore also characterize gene expression in a homogeneous bacterial subpopulation by focusing on single cell trajectories derived only from bacteria with similar induction behavior. The response at the single cell level is found to be more cooperative than that obtained for the heterogeneous total population. For the analysis of systems containing both AHL senders and receiver cells, we utilize the receiver cells as ‘bacterial sensors’ for AHL. Based on a simple gene expression model and the response curves obtained in receiver-only experiments, the effective AHL concentration established by the senders and their ‘sending power’ is determined.

Addressing biological uncertainties in engineering gene circuits

Synthetic biology has grown tremendously over the past fifteen years. It represents a new strategy to develop biological understanding and holds great promise for diverse practical applications. Engineering of a gene circuit typically involves computational design of the circuit, selection of circuit components, and test and optimization of circuit functions. A fundamental challenge in this process is the predictable control of circuit function due to multiple layers of biological uncertainties. These uncertainties can arise from different sources. We categorize these uncertainties into incomplete quantification of parts, interactions between heterologous components and the host, or stochastic dynamics of chemical reactions and outline potential design strategies to minimize or exploit them.

Molecular-Level Tuning of Cellular Autonomy Controls the Collective Behaviors of Cell Populations

A rigorous understanding of how multicellular behaviors arise from the actions of single cells requires quantitative frameworks that bridge the gap between genetic circuits, the arrangement of cells in space, and population-level behaviors. Here, we provide such a framework for a ubiquitous class of multicellular systems-namely, "secrete-and-sense cells" that communicate by secreting and sensing a signaling molecule. By using formal, mathematical arguments and introducing the concept of a phenotype diagram, we show how these cells tune their degrees of autonomous and collective behavior to realize distinct single-cell and population-level phenotypes; these phenomena have biological analogs, such as quorum sensing or paracrine signaling. We also define the "entropy of population," a measurement of the number of arrangements that a population of cells can assume, and demonstrate how a decrease in the entropy of population accompanies the formation of ordered spatial patterns. Our conceptual framework ties together diverse systems, including tissues and microbes, with common principles.

Artificial cell-cell communication as an emerging tool in synthetic biology applications

Cell-cell communication is a widespread phenomenon in nature, ranging from bacterial quorum sensing and fungal pheromone communication to cellular crosstalk in multicellular eukaryotes. These communication modes offer the possibility to control the behavior of an entire community by modifying the performance of individual cells in specific ways. Synthetic biology, i.e., the implementation of artificial functions within biological systems, is a promising approach towards the engineering of sophisticated, autonomous devices based on specifically functionalized cells. With the growing complexity of the functions performed by such systems, both the risk of circuit crosstalk and the metabolic burden resulting from the expression of numerous foreign genes are increasing. Therefore, systems based on a single type of cells are no longer feasible. Synthetic biology approaches with multiple subpopulations of specifically functionalized cells, wired by artificial cell-cell communication systems, provide an attractive and powerful alternative. Here we review recent applications of synthetic cell-cell communication systems with a specific focus on recent advances with fungal hosts.

Microstructured block copolymer surfaces for control of microbe adhesion and aggregation

The attachment and arrangement of microbes onto a substrate is influenced by both the biochemical and physical surface properties. In this report, we develop lectin-functionalized substrates containing patterned, three-dimensional polymeric structures of varied shapes and densities and use these to investigate the effects of topology and spatial confinement on lectin-mediated microbe immobilization. Films of poly(glycidyl methacrylate)-block-4,4-dimethyl-2-vinylazlactone (PGMA-b-PVDMA) were patterned on silicon surfaces into line arrays or square grid patterns with 5 μm wide features and varied pitch. The patterned films had three-dimensional geometries with 900 nm film thickness. After surface functionalization with wheat germ agglutinin, the size of Pseudomonas fluorescens aggregates immobilized was dependent on the pattern dimensions. Films patterned as parallel lines or square grids with a pitch of 10 μm or less led to the immobilization of individual microbes with minimal formation of aggregates. Both geometries allowed for incremental increases in aggregate size distribution with each increase in pitch. These engineered surfaces combine spatial confinement with affinity-based capture to control the extent of microbe adhesion and aggregation, and can also be used as a platform to investigate intercellular interactions and biofilm formation in microbial populations of controlled sizes.

Modeling and validation of autoinducer-mediated bacterial gene expression in microfluidic environments

Biosensors exploiting communication within genetically engineered bacteria are becoming increasingly important for monitoring environmental changes. Currently, there are a variety of mathematical models for understanding and predicting how genetically engineered bacteria respond to molecular stimuli in these environments, but as sensors have miniaturized towards microfluidics and are subjected to complex time-varying inputs, the shortcomings of these models have become apparent. The effects of microfluidic environments such as low oxygen concentration, increased biofilm encapsulation, diffusion limited molecular distribution, and higher population densities strongly affect rate constants for gene expression not accounted for in previous models. We report a mathematical model that accurately predicts the biological response of the autoinducer N-acyl homoserine lactone-mediated green fluorescent protein expression in reporter bacteria in microfluidic environments by accommodating these rate constants. This generalized mass action model considers a chain of biomolecular events from input autoinducer chemical to fluorescent protein expression through a series of six chemical species. We have validated this model against experimental data from our own apparatus as well as prior published experimental results. Results indicate accurate prediction of dynamics (e.g., 14% peak time error from a pulse input) and with reduced mean-squared error with pulse or step inputs for a range of concentrations (10 μM-30 μM). This model can help advance the design of genetically engineered bacteria sensors and molecular communication devices.

Stochastic noise reduction upon complexification: positively correlated birth-death type systems

Cell systems consist of a huge number of various molecules that display specific patterns of interactions, which have a determining influence on the cell׳s functioning. In general, such complexity is seen to increase with the complexity of the organism, with a concomitant increase of the accuracy and specificity of the cellular processes. The question thus arises how the complexification of systems - modeled here by simple interacting birth-death type processes - can lead to a reduction of the noise - described by the variance of the number of molecules. To gain understanding of this issue, we investigated the difference between a single system containing molecules that are produced and degraded, and the same system - with the same average number of molecules - connected to a buffer. We modeled these systems using Itō stochastic differential equations in discrete time, as they allow straightforward analytical developments. In general, when the molecules in the system and the buffer are positively correlated, the variance on the number of molecules in the system is found to decrease compared to the equivalent system without a buffer. Only buffers that are too noisy themselves tend to increase the noise in the main system. We tested this result on two model cases, in which the system and the buffer contain proteins in their active and inactive state, or protein monomers and homodimers. We found that in the second test case, where the interconversion terms are non-linear in the number of molecules, the noise reduction is much more pronounced; it reaches up to 20% reduction of the Fano factor with the parameter values tested in numerical simulations on an unperturbed birth-death model. We extended our analysis to two arbitrary interconnected systems, and found that the sum of the noise levels in the two systems generally decreases upon interconnection if the molecules they contain are positively correlated.

Mosaic physiology from developmental noise: within-organism physiological diversity as an alternative to phenotypic plasticity and phenotypic flexibility

A key problem in organismal biology is to explain the origins of functional diversity. In the context of organismal biology, functional diversity describes the set of phenotypes, across scales of biological organization and through time, that a single genotype, or genome, or organism, can produce. Functional diversity encompasses many phenomena: differences in cell types within organisms; physiological and morphological differences among tissues and organs; differences in performance; morphological shifts in external phenotype; and changes in behavior. How can single genomes produce so many different phenotypes? Modern biology proposes two general mechanisms. The first is developmental programs, by which single cells and their single genomes diversify, via relatively deterministic processes, into the sets of cell types, tissues and organs that we see in most multicellular organisms. The second general mechanism is phenotypic modification stemming from interactions between organisms and their environments – modifications known either as phenotypic plasticity or as phenotypic flexibility, depending on the time scale of the response and the degree of reversibility. These two diversity-generating mechanisms are related because phenotypic modifications may sometimes arise as a consequence of environments influencing developmental programs. Here, I propose that functional diversity also arises via a third fundamental mechanism: stochastic developmental events giving rise to mosaics of physiological diversity within individual organisms. In biological systems, stochasticity stems from the inherently random actions of small numbers of molecules interacting with one another. Although stochastic effects occur in many biological contexts, available evidence suggests that they can be especially important in gene networks, specifically as a consequence of low transcript numbers in individual cells. I briefly review known mechanisms by which organisms control such stochasticity, and how they may use it to create adaptive functional diversity. I then fold this idea into modern thinking on phenotypic plasticity and flexibility, proposing that multicellular organisms exhibit ‘mosaic physiology’. Mosaic physiology refers to sets of diversified phenotypes, within individual organisms, that carry out related functions at the same time, but that are distributed in space. Mosaic physiology arises from stochasticity-driven differentiation of cells, early during cell diversification, which is then amplified by cell division and growth into macroscopic phenotypic modules (cells, tissues, organs) making up the physiological systems of later life stages. Mosaic physiology provides a set of standing, diversified phenotypes, within single organisms, that raise the likelihood of the organism coping well with novel environmental challenges. These diversified phenotypes can be distinct, akin to polyphenisms at the organismal level; or they can be continuously distributed, creating a kind of standing, simultaneously expressed reaction norm of physiological capacities.

Noise propagation through extracellular signaling leads to fluctuations in gene expression

BACKGROUND

Cell-to-cell variability in mRNA and proteins has been observed in many biological systems, including the human innate immune response to viral infection. Most of these studies have focused on variability that arises from (a) intrinsic stochastic fluctuations in gene expression and (b) extrinsic sources (e.g. fluctuations in transcription factors). The main focus of our study is the effect of extracellular signaling on enhancing intrinsic stochastic fluctuations. As a new source of noise, the communication between cells with fluctuating numbers of components has received little attention. We use agent-based modeling to study this contribution to noise in a system of human dendritic cells responding to viral infection.

RESULTS

Our results, validated by single-cell experiments, show that in the transient state cell-to-cell variability in an interferon-stimulated gene (DDX58) arises from the interplay between the spatial randomness of the cellular sources of the interferon and the temporal stochasticity of its own production. The numerical simulations give insight into the time scales on which autocrine and paracrine signaling act in a heterogeneous population of dendritic cells upon viral infection. We study the effect of different factors that influence the magnitude of the cell-to-cell-variability of the induced gene, including the cell density, multiplicity of infection, and the time scale over which the cellular sources begin producing the cytokine.

CONCLUSIONS

We propose a mechanism of noise propagation through extracellular communication and establish conditions under which the mechanism is operative. The cellular stochasticity of gene induction, which we investigate, is not limited to the specific interferon-induced gene we have studied; a broad distribution of copy numbers across cells is to be expected for other interferon-stimulated genes. This can lead to functional consequences for the system-level response to a viral challenge.

Dynamics of the quorum sensing switch: stochastic and non-stationary effects

Background

A wide range of bacteria species are known to communicate through the so called quorum sensing (QS) mechanism by means of which they produce a small molecule that can freely diffuse in the environment and in the cells. Upon reaching a threshold concentration, the signalling molecule activates the QS-controlled genes that promote phenotypic changes. This mechanism, for its simplicity, has become the model system for studying the emergence of a global response in prokaryotic cells. Yet, how cells precisely measure the signal concentration and act coordinately, despite the presence of fluctuations that unavoidably affects cell regulation and signalling, remains unclear.

Results

We propose a model for the QS signalling mechanism in Vibrio fischeri based on the synthetic strains lux01 and lux02. Our approach takes into account the key regulatory interactions between LuxR and LuxI, the autoinducer transport, the cellular growth and the division dynamics. By using both deterministic and stochastic models, we analyze the response and dynamics at the single-cell level and compare them to the global response at the population level. Our results show how fluctuations interfere with the synchronization of the cell activation and lead to a bimodal phenotypic distribution. In this context, we introduce the concept of precision in order to characterize the reliability of the QS communication process in the colony. We show that increasing the noise in the expression of LuxR helps cells to get activated at lower autoinducer concentrations but, at the same time, slows down the global response. The precision of the QS switch under non-stationary conditions decreases with noise, while at steady-state it is independent of the noise value.

Conclusions

Our in silico experiments show that the response of the LuxR/LuxI system depends on the interplay between non-stationary and stochastic effects and that the burst size of the transcription/translation noise at the level of LuxR controls the phenotypic variability of the population. These results, together with recent experimental evidences on LuxR regulation in wild-type species, suggest that bacteria have evolved mechanisms to regulate the intensity of those fluctuations.

Tuning positive feedback for signal detection in noisy dynamic environments

Learning from previous actions is a key feature of decision-making. Diverse biological systems, from neuronal assemblies to insect societies, use a combination of positive feedback and forgetting of stored memories to process and respond to input signals. Here we look how these systems deal with a dynamic two-armed bandit problem of detecting a very weak signal in the presence of a high degree of noise. We show that by tuning the form of positive feedback and the decay rate to appropriate values, a single tracking variable can effectively detect dynamic inputs even in the presence of a large degree of noise. In particular, we show that when tuned appropriately a simple positive feedback algorithm is Fisher efficient, in that it can track changes in a signal on a time of order L(h)=(|h|/σ)(-2), where |h| is the magnitude of the signal and σ the magnitude of the noise.

Noise drives sharpening of gene expression boundaries in the zebrafish hindbrain

Morphogens provide positional information for spatial patterns of gene expression during development. However, stochastic effects such as local fluctuations in morphogen concentration and noise in signal transduction make it difficult for cells to respond to their positions accurately enough to generate sharp boundaries between gene expression domains. During development of rhombomeres in the zebrafish hindbrain, the morphogen retinoic acid (RA) induces expression of hoxb1a in rhombomere 4 (r4) and krox20 in r3 and r5. Fluorescent in situ hybridization reveals rough edges around these gene expression domains, in which cells co-express hoxb1a and krox20 on either side of the boundary, and these sharpen within a few hours. Computational analysis of spatial stochastic models shows, surprisingly, that noise in hoxb1a/krox20 expression actually promotes sharpening of boundaries between adjacent segments. In particular, fluctuations in RA initially induce a rough boundary that requires noise in hoxb1a/krox20 expression to sharpen. This finding suggests a novel noise attenuation mechanism that relies on intracellular noise to induce switching and coordinate cellular decisions during developmental patterning.

Computation of steady-state probability distributions in stochastic models of cellular networks

Cellular processes are "noisy". In each cell, concentrations of molecules are subject to random fluctuations due to the small numbers of these molecules and to environmental perturbations. While noise varies with time, it is often measured at steady state, for example by flow cytometry. When interrogating aspects of a cellular network by such steady-state measurements of network components, a key need is to develop efficient methods to simulate and compute these distributions. We describe innovations in stochastic modeling coupled with approaches to this computational challenge: first, an approach to modeling intrinsic noise via solution of the chemical master equation, and second, a convolution technique to account for contributions of extrinsic noise. We show how these techniques can be combined in a streamlined procedure for evaluation of different sources of variability in a biochemical network. Evaluation and illustrations are given in analysis of two well-characterized synthetic gene circuits, as well as a signaling network underlying the mammalian cell cycle entry.

Programming microbial population dynamics by engineered cell-cell communication

A major aim of synthetic biology is to program novel cellular behavior using engineered gene circuits. Early endeavors focused on building simple circuits that fulfill simple functions, such as logic gates, bistable toggle switches, and oscillators. These gene circuits have primarily focused on single-cell behaviors since they operate intracellularly. Thus, they are often susceptible to cell-cell variations due to stochastic gene expression. Cell-cell communication offers an efficient strategy to coordinate cellular behavior at the population level. To this end, we review recent advances in engineering cell-cell communication to achieve reliable population dynamics, spanning from communication within single species to multispecies, from one-way sender-receiver communication to two-way communication in synthetic microbial ecosystems. These engineered systems serve as well-defined model systems to better understand design principles of their naturally occurring counterparts and to facilitate novel biotechnology applications.

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.

Heterogeneous response to a quorum-sensing signal in the luminescence of individual Vibrio fischeri

The marine bacterium Vibrio fischeri regulates its bioluminescence through a quorum sensing mechanism: the bacterium releases diffusible small molecules (autoinducers) that accumulate in the environment as the population density increases. This accumulation of autoinducer (AI) eventually activates transcriptional regulators for bioluminescence as well as host colonization behaviors. Although V. fischeri quorum sensing has been extensively characterized in bulk populations, far less is known about how it performs at the level of the individual cell, where biochemical noise is likely to limit the precision of luminescence regulation. We have measured the time-dependence and AI-dependence of light production by individual V. fischeri cells that are immobilized in a perfusion chamber and supplied with a defined concentration of exogenous AI. We use low-light level microscopy to record and quantify the photon emission from the cells over periods of several hours as they respond to the introduction of AI. We observe an extremely heterogeneous response to the AI signal. Individual cells differ widely in the onset time for their luminescence and in their resulting brightness, even in the presence of high AI concentrations that saturate the light output from a bulk population. The observed heterogeneity shows that although a given concentration of quorum signal may determine the average light output from a population of cells, it provides far weaker control over the luminescence output of each individual cell.

Stochastic E2F activation and reconciliation of phenomenological cell-cycle models

A new, stochastic model of entry into the mammalian cell cycle provides a mechanistic understanding of the temporal variability observed across populations of cells and reconciles previously proposed phenomenological cell-cycle models.

The transition of the mammalian cell from quiescence to proliferation is a highly variable process. Over the last four decades, two lines of apparently contradictory, phenomenological models have been proposed to account for such temporal variability. These include various forms of the transition probability (TP) model and the growth control (GC) model, which lack mechanistic details. The GC model was further proposed as an alternative explanation for the concept of the restriction point, which we recently demonstrated as being controlled by a bistable Rb-E2F switch. Here, through a combination of modeling and experiments, we show that these different lines of models in essence reflect different aspects of stochastic dynamics in cell cycle entry. In particular, we show that the variable activation of E2F can be described by stochastic activation of the bistable Rb-E2F switch, which in turn may account for the temporal variability in cell cycle entry. Moreover, we show that temporal dynamics of E2F activation can be recast into the frameworks of both the TP model and the GC model via parameter mapping. This mapping suggests that the two lines of phenomenological models can be reconciled through the stochastic dynamics of the Rb-E2F switch. It also suggests a potential utility of the TP or GC models in defining concise, quantitative phenotypes of cell physiology. This may have implications in classifying cell types or states.

Mammalian cells enter the division cycle in response to appropriate growth signals. For each cell, the decision to do so is critically dependent on the interplay between environmental cues and the internal state of the cell and is influenced by random fluctuations in cellular processes. Indeed, experimental evidence indicates that cell cycle entry is highly variable from cell to cell, even within a clonal population. To account for such variability, a number of phenomenological models have been previously proposed. These models primarily fall into two types depending on their fundamental assumptions on the origin of the variability. “Transition probability” models presume that variability in cell cycle entry originates from the fact that entry in each individual cell is random but also governed by a fixed probability. In contrast, “growth-controlled” models assume that the growth rates across a population are variable and result in cells that are out of phase developmentally. While both kinds of models provide a good fit to experimental data, their lack of mechanistic details limits their predictive power and has led to unresolved debate between their practitioners. In this study, we developed a mechanistically based stochastic model of the temporal dynamics of activation of the E2F transcription factor, which is used here as a marker of the transition of cells from quiescence to active cell cycling. Using this model, we show that “transition probability” and “growth-controlled” models can be reconciled by incorporation of a small number of basic cellular parameters related to protein synthesis and turnover, protein modification, stochasticity, and the like. Essentially our work shows that each kind of phenomenological model holds true for describing a particular aspect of the cell cycle transition. We suggest that incorporation of basic cellular parameters in this manner into phenomenological models may constitute a broadly applicable approach to defining concise, quantitative phenotypes of cell physiology.

A mathematical model of the Gac/Rsm quorum sensing network in Pseudomonas fluorescens

I present a deterministic model of the dynamics of signal transduction and gene expression in the Gac/Rsm network of the soil-dwelling bacterium Pseudomonas fluorescens. The network is involved in quorum sensing and governs antifungal production in this important biocontrol agent. A central role is played by small untranslated RNAs, which sequester regulatory mRNA-binding proteins. The model provides a reasonable match to the available data, which consists primarily of time series from reporter gene fusions. I use the model to investigate the information-processing properties of the Gac/Rsm network, in part by comparing it to a simplified model capable of quorum sensing. The results suggest that the complexity and redundancy of the Gac/Rsm network have evolved to meet the conflicting requirements of high sensitivity to environmental conditions and a conservative, robust response to variability in parameter values. Similar systems exist in a wide variety of bacteria, where they control a diverse set of population-dependent behaviors. This makes them important subjects for mathematical models that can help link empirical understanding of network structure to theoretical insights into how these networks have evolved to function under natural conditions.

Engineering multicellular systems by cell-cell communication

Synthetic biology encompasses the design of new biological parts and systems as well as the modulation of existing biological networks to generate novel functions. In recent years, increasing emphasis has been placed on the engineering of population-level behaviors using cell-cell communication. From the engineering perspective, cell-cell communication serves as a versatile regulatory module that enables coordination among cells in and between populations and facilitates the generation of reliable dynamics. In addition to exploring biological 'design principles' via the construction of increasingly complex dynamics, communication-based synthetic systems can be used as well-defined model systems to study ecological and social interactions such as competition, cooperation, and predation. Here we discuss the dynamic properties of cell-cell communication modules, how they can be engineered for synthetic circuit design, and applications of these systems.

Decoding biological principles using gene circuits

A major flavor of synthetic biology is the creation of artificial gene circuits to perform user-defined tasks. One aspect of this area is to realize ever-increasingly more complicated circuit behavior. Such efforts have led to the identification and evaluation of design strategies that enable robust control of dynamics in single cells and in cell populations. On the other hand, there is increasing emphasis on using artificial systems programmed by simple circuits to explore fundamental biological questions of broad significance.

What is stochastic resonance? Definitions, misconceptions, debates, and its relevance to biology

Stochastic resonance is said to be observed when increases in levels of unpredictable fluctuations--e.g., random noise--cause an increase in a metric of the quality of signal transmission or detection performance, rather than a decrease. This counterintuitive effect relies on system nonlinearities and on some parameter ranges being "suboptimal". Stochastic resonance has been observed, quantified, and described in a plethora of physical and biological systems, including neurons. Being a topic of widespread multidisciplinary interest, the definition of stochastic resonance has evolved significantly over the last decade or so, leading to a number of debates, misunderstandings, and controversies. Perhaps the most important debate is whether the brain has evolved to utilize random noise in vivo, as part of the "neural code". Surprisingly, this debate has been for the most part ignored by neuroscientists, despite much indirect evidence of a positive role for noise in the brain. We explore some of the reasons for this and argue why it would be more surprising if the brain did not exploit randomness provided by noise--via stochastic resonance or otherwise--than if it did. We also challenge neuroscientists and biologists, both computational and experimental, to embrace a very broad definition of stochastic resonance in terms of signal-processing "noise benefits", and to devise experiments aimed at verifying that random variability can play a functional role in the brain, nervous system, or other areas of biology.

Timing cellular decision making under noise via cell-cell communication

Many cellular processes require decision making mechanisms, which must act reliably even in the unavoidable presence of substantial amounts of noise. However, the multistable genetic switches that underlie most decision-making processes are dominated by fluctuations that can induce random jumps between alternative cellular states. Here we show, via theoretical modeling of a population of noise-driven bistable genetic switches, that reliable timing of decision-making processes can be accomplished for large enough population sizes, as long as cells are globally coupled by chemical means. In the light of these results, we conjecture that cell proliferation, in the presence of cell-cell communication, could provide a mechanism for reliable decision making in the presence of noise, by triggering cellular transitions only when the whole cell population reaches a certain size. In other words, the summation performed by the cell population would average out the noise and reduce its detrimental impact.

Signal discrimination by differential regulation of protein stability in quorum sensing

Quorum sensing (QS) is a communication mechanism exploited by a large variety of bacteria to coordinate gene expression at the population level. In Gram-negative bacteria, QS occurs via synthesis and detection of small chemical signals, most of which belong to the acyl-homoserine lactone class. In such a system, binding of an acyl-homoserine lactone signal to its cognate transcriptional regulator (R-protein) often induces stabilization and subsequent dimerization of the R-protein, which results in the regulation of downstream gene expression. Existence of diverse QS systems within and among species of bacteria indicates that each bacterium needs to distinguish among a myriad of structurally similar chemical signals. We show, using a mathematical model, that fast degradation of an R-protein monomer can facilitate discrimination of signals that differentially stabilize it. Furthermore, our results suggest an inverse correlation between the stability of an R-protein and the achievable limits of fidelity in signal discrimination. In particular, an unstable R-protein tends to be more specific to its cognate signal, whereas a stable R-protein tends to be more promiscuous. These predictions are consistent with experimental data on well-studied natural and engineered R-proteins and thus have implications for understanding the functional design of QS systems.