Noise in biology

Gene switching rate determines response to extrinsic perturbations in the self-activation transcriptional network motif

Gene switching dynamics is a major source of randomness in genetic networks, also in the case of large concentrations of the transcription factors. In this work, we consider a common network motif - the positive feedback of a transcription factor on its own synthesis - and assess its response to extrinsic noises perturbing gene deactivation in a variety of settings where the network might operate. These settings are representative of distinct cellular types, abundance of transcription factors and ratio between gene switching and protein synthesis rates. By investigating noise-induced transitions among the different network operative states, our results suggest that gene switching rates are key parameters to shape network response to external perturbations, and that such response depends on the particular biological setting, i.e. the characteristic time scales and protein abundance. These results might have implications on our understanding of irreversible transitions for noise-related phenomena such as cellular differentiation. In addition these evidences suggest to adopt the appropriate mathematical model of the network in order to analyze the system consistently to the reference biological setting.

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.

Redundancy in information transmission in a two-step cascade

We present a stochastic framework to study signal transmission in a generic two-step cascade S→X→Y. Starting from a set of Langevin equations obeying Gaussian noise processes we calculate the variance and covariance while considering both linear and nonlinear production terms for different biochemical species of the cascade. These quantities are then used to calculate the net synergy within the purview of partial information decomposition. We show that redundancy in information transmission is essentially an important consequence of Markovian property of the two-step cascade motif. We also show that redundancy increases fidelity of the signaling pathway.

Proteolytic crosstalk in multi-protease networks

Processive proteases, such as ClpXP in E. coli, are conserved enzyme assemblies that can recognize and rapidly degrade proteins. These proteases are used for a number of purposes, including degrading mistranslated proteins and controlling cellular stress response. However, proteolytic machinery within the cell is limited in capacity and can lead to a bottleneck in protein degradation, whereby many proteins compete ('queue') for proteolytic resources. Previous work has demonstrated that such queueing can lead to pronounced statistical relationships between different protein counts when proteins compete for a single common protease. However, real cells contain many different proteases, e.g. ClpXP, ClpAP, and Lon in E. coli, and it is not clear how competition between proteins for multiple classes of protease would influence the dynamics of cellular networks. In the present work, we theoretically demonstrate that a multi-protease proteolytic bottleneck can substantially couple the dynamics for both simple and complex (oscillatory) networks, even between substrates with substantially different affinities for protease. For these networks, queueing often leads to strong positive correlations between protein counts, and these correlations are strongest near the queueing theoretic point of balance. Furthermore, we find that the qualitative behavior of these networks depends on the relative size of the absolute affinity of substrate to protease compared to the cross affinity of substrate to protease, leading in certain regimes to priority queue statistics.

Noise propagation with interlinked feed-forward pathways

Functionally similar pathways are often seen in biological systems, forming feed-forward controls. The robustness in network motifs such as feed-forward loops (FFLs) has been reported previously. In this work, we studied noise propagation in a development network that has multiple interlinked FFLs. A FFL has the potential of asymmetric noise-filtering (i.e., it works at either the “ON” or the “OFF” state in the target gene). With multiple, interlinked FFLs, we show that the propagated noises are largely filtered regardless of the states in the input genes. The noise-filtering property of an interlinked FFL can be largely derived from that of the individual FFLs, and with interlinked FFLs, it is possible to filter noises in both “ON” and “OFF” states in the output. We demonstrated the noise filtering effect in the developmental regulatory network of Caenorhabditis elegans that controls the timing of distal tip cell (DTC) migration. The roles of positive feedback loops involving blmp-1 and the degradation regulation of DRE-1 also studied. Our analyses allow for better inference from network structures to noise-filtering properties, and provide insights into the mechanisms behind the precise DTC migration controls in space and time.

CABeRNET: a Cytoscape app for augmented Boolean models of gene regulatory NETworks

BACKGROUND

Dynamical models of gene regulatory networks (GRNs) are highly effective in describing complex biological phenomena and processes, such as cell differentiation and cancer development. Yet, the topological and functional characterization of real GRNs is often still partial and an exhaustive picture of their functioning is missing.

RESULTS

We here introduce CABERNET, a Cytoscape app for the generation, simulation and analysis of Boolean models of GRNs, specifically focused on their augmentation when a only partial topological and functional characterization of the network is available. By generating large ensembles of networks in which user-defined entities and relations are added to the original core, CABERNET allows to formulate hypotheses on the missing portions of real networks, as well to investigate their generic properties, in the spirit of complexity science.

CONCLUSIONS

CABERNET offers a series of innovative simulation and modeling functions and tools, including (but not being limited to) the dynamical characterization of the gene activation patterns ruling cell types and differentiation fates, and sophisticated robustness assessments, as in the case of gene knockouts. The integration within the widely used Cytoscape framework for the visualization and analysis of biological networks, makes CABERNET a new essential instrument for both the bioinformatician and the computational biologist, as well as a computational support for the experimentalist. An example application concerning the analysis of an augmented T-helper cell GRN is provided.

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.

Chemical communication between bacteria and cell-free gene expression systems within linear chains of emulsion droplets

Position-dependent gene expression in gradients of morphogens is one of the key processes involved in cellular differentiation during development. Here, we study a simple artificial differentiation process, which is based on the diffusion of genetic inducers within one-dimensional arrangements of 50 μm large water-in-oil droplets. The droplets are filled with either bacteria or cell-free gene expression systems, both equipped with genetic constructs that produce inducers or respond to them via expression of a fluorescent protein. We quantitatively study the coupled diffusion-gene expression process and demonstrate that gene expression can be made position-dependent both within bacteria-containing and cell-free droplets. By generating diffusing quorum sensing signals in situ, we also establish communication between artificial cell-free sender cells and bacterial receivers, and vice versa.

Providing data science support for systems pharmacology and its implications to drug discovery

INTRODUCTION

The conventional one-drug-one-target-one-disease drug discovery process has been less successful in tracking multi-genic, multi-faceted complex diseases. Systems pharmacology has emerged as a new discipline to tackle the current challenges in drug discovery. The goal of systems pharmacology is to transform huge, heterogeneous, and dynamic biological and clinical data into interpretable and actionable mechanistic models for decision making in drug discovery and patient treatment. Thus, big data technology and data science will play an essential role in systems pharmacology.

AREAS COVERED

This paper critically reviews the impact of three fundamental concepts of data science on systems pharmacology: similarity inference, overfitting avoidance, and disentangling causality from correlation. The authors then discuss recent advances and future directions in applying the three concepts of data science to drug discovery, with a focus on proteome-wide context-specific quantitative drug target deconvolution and personalized adverse drug reaction prediction.

EXPERT OPINION

Data science will facilitate reducing the complexity of systems pharmacology modeling, detecting hidden correlations between complex data sets, and distinguishing causation from correlation. The power of data science can only be fully realized when integrated with mechanism-based multi-scale modeling that explicitly takes into account the hierarchical organization of biological systems from nucleic acid to proteins, to molecular interaction networks, to cells, to tissues, to patients, and to populations.

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.

Spontaneous Chiral Symmetry Breaking for Finite Systems

Theoretical clues are desirable to help uncover the origin of bio-homochirality in life, as well as the mechanisms for the asymmetric production of functional chiral substances. Here, an open-to-matter reaction network based on a model proposed by Plasson et al. is studied. In the extended model, the statistical fluctuations lead the system to break chiral symmetry autonomously, that is, without any initial enantiomeric excess or external influence. In the stability diagrams, we observe regions of parameter space that correspond to racemic, homochiral, chiral oscillatory, and, to our knowledge, for the first time in a chiral model, chaotic regimes. The dependencies of the final concentrations of chiral substances on the parameters are determined analytically and discussed for both the racemic and homochiral regimes.

Transcriptional Bursting in Gene Expression: Analytical Results for General Stochastic Models

Gene expression in individual cells is highly variable and sporadic, often resulting in the synthesis of mRNAs and proteins in bursts. Such bursting has important consequences for cell-fate decisions in diverse processes ranging from HIV-1 viral infections to stem-cell differentiation. It is generally assumed that bursts are geometrically distributed and that they arrive according to a Poisson process. On the other hand, recent single-cell experiments provide evidence for complex burst arrival processes, highlighting the need for analysis of more general stochastic models. To address this issue, we invoke a mapping between general stochastic models of gene expression and systems studied in queueing theory to derive exact analytical expressions for the moments associated with mRNA/protein steady-state distributions. These results are then used to derive noise signatures, i.e. explicit conditions based entirely on experimentally measurable quantities, that determine if the burst distributions deviate from the geometric distribution or if burst arrival deviates from a Poisson process. For non-Poisson arrivals, we develop approaches for accurate estimation of burst parameters. The proposed approaches can lead to new insights into transcriptional bursting based on measurements of steady-state mRNA/protein distributions.

One of the fundamental problems in biology is understanding how phenotypic variations arise among individuals in a population. Recent research has shown that phenotypic variations can arise due to probabilistic cell-fate decisions driven by inherent randomness (noise) in the process of gene expression. One of the manifestations of such stochasticity in gene expression is the production of mRNAs and proteins in bursts. Bursting in gene expression is known to impact cell-fate in diverse systems ranging from latency in HIV-1 viral infections to cellular differentiation. Recent single-cell experiments provide evidence for complex arrival processes leading to bursting, however an analytical framework connecting such burst arrival processes with the corresponding higher moments of mRNA/protein distributions is currently lacking. We address this issue by invoking a mapping between general models of gene expression and systems studied in queueing theory. The framework developed and the results derived lead to new approaches for testing commonly used assumptions in modeling gene expression and for accurate estimation of burst parameters. Notably, the phenomenon of stochastic bursting has been observed in a wide range of disciplines ranging from neuroscience and finance to cell biology. The approaches developed and results obtained in this work will thus contribute towards quantitative characterization of burst processes in diverse systems of current interest.

Small-scale properties of a stochastic cubic-autocatalytic reaction-diffusion model

We investigate the small-scale properties of a stochastic cubic-autocatalytic reaction-diffusion (CARD) model using renormalization techniques. We renormalize noise-induced ultraviolet divergences and obtain β functions for the decay rate and coupling at one loop. Assuming colored (power-law) noise, our results show that the behavior of both decay rate and coupling with scale depends crucially on the noise exponent. Interpreting the CARD model as a proxy for a (very simple) living system, our results suggest that power-law correlations in environmental fluctuations can both decrease or increase the growth of structures at smaller scales.

Formation and dissolution of bacterial colonies

Many organisms form colonies for a transient period of time to withstand environmental pressure. Bacterial biofilms are a prototypical example of such behavior. Despite significant interest across disciplines, physical mechanisms governing the formation and dissolution of bacterial colonies are still poorly understood. Starting from a kinetic description of motile and interacting cells we derive a hydrodynamic equation for their density on a surface, where most of the kinetic coefficients are estimated from experimental data for N. gonorrhoeae bacteria. We use it to describe the formation of multiple colonies with sizes consistent with experimental observations. Finally, we show how the changes in the cell-to-cell interactions lead to the dissolution of the bacterial colonies. The successful application of kinetic theory to a complex far from equilibrium system such as formation and dissolution of living bacterial colonies potentially paves the way for the physical quantification of the initial stages of biofilm formation.

Random bursts determine dynamics of active filaments

Constituents of living or synthetic active matter have access to a local energy supply that serves to keep the system out of thermal equilibrium. The statistical properties of such fluctuating active systems differ from those of their equilibrium counterparts. Using the actin filament gliding assay as a model, we studied how nonthermal distributions emerge in active matter. We found that the basic mechanism involves the interplay between local and random injection of energy, acting as an analog of a thermal heat bath, and nonequilibrium energy dissipation processes associated with sudden jump-like changes in the system's dynamic variables. We show here how such a mechanism leads to a nonthermal distribution of filament curvatures with a non-Gaussian shape. The experimental curvature statistics and filament relaxation dynamics are reproduced quantitatively by stochastic computer simulations and a simple kinetic model.

Closed-form stochastic solutions for non-equilibrium dynamics and inheritance of cellular components over many cell divisions

Stochastic dynamics govern many important processes in cellular biology, and an underlying theoretical approach describing these dynamics is desirable to address a wealth of questions in biology and medicine. Mathematical tools exist for treating several important examples of these stochastic processes, most notably gene expression and random partitioning at single-cell divisions or after a steady state has been reached. Comparatively little work exists exploring different and specific ways that repeated cell divisions can lead to stochastic inheritance of unequilibrated cellular populations. Here we introduce a mathematical formalism to describe cellular agents that are subject to random creation, replication and/or degradation, and are inherited according to a range of random dynamics at cell divisions. We obtain closed-form generating functions describing systems at any time after any number of cell divisions for binomial partitioning and divisions provoking a deterministic or random, subtractive or additive change in copy number, and show that these solutions agree exactly with stochastic simulation. We apply this general formalism to several example problems involving the dynamics of mitochondrial DNA during development and organismal lifetimes.

Emergent properties arising from the assembly of amphiphiles. Artificial vesicle membranes as reaction promoters and regulators

This article deals with artificial vesicles and their membranes as reaction promoters and regulators. Among the various molecular assemblies which can form in an aqueous medium from amphiphilic molecules, vesicle systems are unique. Vesicles compartmentalize the aqueous solution in which they exist, independent on whether the vesicles are biological vesicles (existing in living systems) or whether they are artificial vesicles (formed in vitro from natural or synthetic amphiphiles). After the formation of artificial vesicles, their aqueous interior (the endovesicular volume) may become - or may be made - chemically different from the external medium (the exovesicular solution), depending on how the vesicles are prepared. The existence of differences between endo- and exovesicular composition is one of the features on the basis of which biological vesicles contribute to the complex functioning of living organisms. Furthermore, artificial vesicles can be formed from mixtures of amphiphiles in such a way that the vesicle membranes become molecularly, compositionally and organizationally highly complex, similarly to the lipidic matrix of biological membranes. All the various properties of artificial vesicles as membranous compartment systems emerge from molecular assembly as these properties are not present in the individual molecules the system is composed of. One particular emergent property of vesicle membranes is their possible functioning as promoters and regulators of chemical reactions caused by the localization of reaction components, and possibly catalysts, within or on the surface of the membranes. This specific feature is reviewed and highlighted with a few selected examples which range from the promotion of decarboxylation reactions, the selective binding of DNA or RNA to suitable vesicle membranes, and the reactivation of fragmented enzymes to the regulation of the enzymatic synthesis of polymers. Such type of emergent properties of vesicle membranes may have been important for the prebiological evolution of protocells, the hypothetical compartment systems preceding the first cells in those chemical and physico-chemical processes that led to the origin of life.

Optimizing information flow in small genetic networks. IV. Spatial coupling

We typically think of cells as responding to external signals independently by regulating their gene expression levels, yet they often locally exchange information and coordinate. Can such spatial coupling be of benefit for conveying signals subject to gene regulatory noise? Here we extend our information-theoretic framework for gene regulation to spatially extended systems. As an example, we consider a lattice of nuclei responding to a concentration field of a transcriptional regulator (the input) by expressing a single diffusible target gene. When input concentrations are low, diffusive coupling markedly improves information transmission; optimal gene activation functions also systematically change. A qualitatively different regulatory strategy emerges where individual cells respond to the input in a nearly steplike fashion that is subsequently averaged out by strong diffusion. While motivated by early patterning events in the Drosophila embryo, our framework is generically applicable to spatially coupled stochastic gene expression models.

Generalized model of island biodiversity

The dynamics of a local community of competing species with weak immigration from a static regional pool is studied. Implementing the generalized competitive Lotka-Volterra model with demographic noise, a rich dynamics with four qualitatively distinct phases is unfolded. When the overall interspecies competition is weak, the island species recapitulate the mainland species. For higher values of the competition parameter, the system still admits an equilibrium community, but now some of the mainland species are absent on the island. Further increase in competition leads to an intermittent "disordered" phase, where the dynamics is controlled by invadable combinations of species and the turnover rate is governed by the migration. Finally, the strong competition phase is glasslike, dominated by uninvadable states and noise-induced transitions. Our model contains, as a special case, the celebrated neutral island theories of Wilson-MacArthur and Hubbell. Moreover, we show that slight deviations from perfect neutrality may lead to each of the phases, as the Hubbell point appears to be quadracritical.

Microbial individuality: how single-cell heterogeneity enables population level strategies

Much of our knowledge of microbial life is only a description of average population behaviours, but modern technologies provide a more inclusive view and reveal that microbes also have individuality. It is now acknowledged that isogenic cell-to-cell heterogeneity is common across organisms and across different biological processes. This heterogeneity can be regulated and functional, rather than just reflecting tolerance to noisy biochemistry. Here, we review recent advances in our understanding of microbial heterogeneity, with an emphasis on the pervasiveness of heterogeneity, the mechanisms that sustain it, and how heterogeneity enables collective function.

Noisy localized structures induced by large noise

We investigate the influence of large noise on the formation of localized patterns in the framework of the cubic-quintic complex Ginzburg-Landau equation. The interaction of localization and noise can lead to filling in or noisy localized structures for fixed noise strength. To focus on the interaction between noise and localization we cover a region in parameter space, in particular, subcriticality, for which stationary stable deterministic pulses do not exist. Possible experimental tests of the work presented for autocatalytic chemical reactions and bioinspired systems are outlined.

Extracting physics of life at the molecular level: A review of single-molecule data analyses

Studying individual biomolecules at the single-molecule level has proved very insightful recently. Single-molecule experiments allow us to probe both the equilibrium and nonequilibrium properties as well as make quantitative connections with ensemble experiments and equilibrium thermodynamics. However, it is important to be careful about the analysis of single-molecule data because of the noise present and the lack of theoretical framework for processes far away from equilibrium. Biomolecular motion, whether it is free in solution, on a substrate, or under force, involves thermal fluctuations in varying degrees, which makes the motion noisy. In addition, the noise from the experimental setup makes it even more complex. The details of biologically relevant interactions, conformational dynamics, and activities are hidden in the noisy single-molecule data. As such, extracting biological insights from noisy data is still an active area of research. In this review, we will focus on analyzing both fluorescence-based and force-based single-molecule experiments and gaining biological insights at the single-molecule level. Inherently nonequilibrium nature of biological processes will be highlighted. Simulated trajectories of biomolecular diffusion will be used to compare and validate various analysis techniques.

Toxin effect on protein biosynthesis in eukaryotic cells: a simple kinetic model

A model for toxin inhibition of protein synthesis inside eukaryotic cells is presented. Mitigation of this effect by introduction of an antibody is also studied. Antibody and toxin (ricin) initially are delivered outside the cell. The model describes toxin internalization from the extracellular into the intracellular domain, its transport to the endoplasmic reticulum (ER) and the cleavage inside the ER into the RTA and RTB chains, the release of RTA into the cytosol, inactivation (depurination) of ribosomes, and the effect on translation. The model consists of a set of ODEs which are solved numerically. Numerical results are illustrated by figures and discussed.

Positional information, positional error, and readout precision in morphogenesis: a mathematical framework

The concept of positional information is central to our understanding of how cells determine their location in a multicellular structure and thereby their developmental fates. Nevertheless, positional information has neither been defined mathematically nor quantified in a principled way. Here we provide an information-theoretic definition in the context of developmental gene expression patterns and examine the features of expression patterns that affect positional information quantitatively. We connect positional information with the concept of positional error and develop tools to directly measure information and error from experimental data. We illustrate our framework for the case of gap gene expression patterns in the early Drosophila embryo and show how information that is distributed among only four genes is sufficient to determine developmental fates with nearly single-cell resolution. Our approach can be generalized to a variety of different model systems; procedures and examples are discussed in detail.

Nonlinearity arising from noncooperative transcription factor binding enhances negative feedback and promotes genetic oscillations

We study the effects of multiple binding sites in the promoter of a genetic oscillator. We evaluate the regulatory function of a promoter with multiple binding sites in the absence of cooperative binding, and consider different hypotheses for how the number of bound repressors affects transcription rate. Effective Hill exponents of the resulting regulatory functions reveal an increase in the nonlinearity of the feedback with the number of binding sites. We identify optimal configurations that maximize the nonlinearity of the feedback. We use a generic model of a biochemical oscillator to show that this increased nonlinearity is reflected in enhanced oscillations, with larger amplitudes over wider oscillatory ranges. Although the study is motivated by genetic oscillations in the zebrafish segmentation clock, our findings may reveal a general principle for gene regulation.

Amorphous computing in the presence of stochastic disturbances

Amorphous computing is a non-standard computing paradigm that relies on massively parallel execution of computer code by a large number of small, spatially distributed, weakly interacting processing units. Over the last decade or so, amorphous computing has attracted a great deal of interest both as an alternative model of computing and as an inspiration to understand developmental biology. A number of algorithms have been developed that can take advantage of the massive parallelism of this computing paradigm to solve specific problems. One of the interesting properties of amorphous computers is that they are robust with respect to the loss of individual processing units, in the sense that a removal of some of them should not impact on the computation as a whole. However, much less understood is to what extent amorphous computers are robust with respect to minor disturbances to the individual processing units, such as random motion or occasional faulty computation short of total component failure. In this article we address this question. As an example problem we choose an algorithm to calculate a straight line between two points. Using this example, we find that amorphous computers are not in general robust with respect to Brownian motion and noise, but we find strategies that restore reliable computation even in their presence. We will argue that these strategies are generally applicable and not specific to the particular AC we consider, or even specific to electronic computers.

Synchronization of degrade-and-fire oscillations via a common activator

The development of synthetic gene oscillators has not only demonstrated our ability to forward engineer reliable circuits in living cells, but it has also proven to be an excellent testing ground for the statistical behavior of coupled noisy oscillators. Previous experimental studies demonstrated that a shared positive feedback can reliably synchronize such oscillators, though the theoretical mechanism was not studied in detail. In the present work, we examine an experimentally motivated stochastic model for coupled degrade-and-fire gene oscillators, where a core delayed negative feedback establishes oscillations within each cell, and a shared delayed positive feedback couples all cells. We use analytic and numerical techniques to investigate conditions for one cluster and multicluster synchrony. A nonzero delay in the shared positive feedback, as expected for the experimental systems, is found to be important for synchrony to occur.