Spatial bistability generates hunchback expression sharpness in the Drosophila embryo

Body plan evolvability: The role of variability in gene regulatory networks

Recent computational modeling of early fruit fly (Drosophila) development has characterized the degree to which gene regulation networks can be robust to natural variability. In the first few hours of development, broad spatial gradients of maternally derived transcription factors activate embryonic gap genes. These gap patterns determine the subsequent segmented insect body plan through pair-rule gene expression. Gap genes are expressed with greater spatial precision than the maternal patterns. Computational modeling of the gap-gap regulatory interactions provides a mechanistic understanding for this robustness to maternal variability in wild-type (WT) patterning. A long-standing question in evolutionary biology has been how a system which is robust, such as the developmental program creating any particular species' body plan, is also evolvable, i.e. how can a system evolve or speciate, if the WT form is strongly buffered and protected? In the present work, we use the WT model to explore the breakdown of such Waddington-type 'canalization'. What levels of variability will push the system out of the WT form; are there particular pathways in the gene regulatory mechanism which are more susceptible to losing the WT form; and when robustness is lost, what types of forms are most likely to occur (i.e. what forms lie near the WT)? Manipulating maternal effects in several different pathways, we find a common gap 'peak-to-step' pattern transition in the loss of WT. We discuss these results in terms of the evolvability of insect segmentation, and in terms of experimental perturbations and mutations which could test the model predictions. We conclude by discussing the prospects for using continuum models of pattern dynamics to investigate a wider range of evo-devo problems.

A bistable autoregulatory module in the developing embryo commits cells to binary expression fates

Bistable autoactivation has been proposed as a mechanism for cells to adopt binary fates during embryonic development. However, it is unclear whether the autoactivating modules found within developmental gene regulatory networks are bistable, unless their parameters are quantitatively determined. Here, we combine in vivo live imaging with mathematical modeling to dissect the binary cell fate dynamics of the fruit fly pair-rule gene fushi tarazu (ftz), which is regulated by two known enhancers: the early (non-autoregulating) element and the autoregulatory element. Live imaging of transcription and protein concentration in the blastoderm revealed that binary Ftz fates are achieved as Ftz expression rapidly transitions from being dictated by the early element to the autoregulatory element. Moreover, we discovered that Ftz concentration alone is insufficient to activate the autoregulatory element, and that this element only becomes responsive to Ftz at a prescribed developmental time. Based on these observations, we developed a dynamical systems model and quantitated its kinetic parameters directly from experimental measurements. Our model demonstrated that the ftz autoregulatory module is indeed bistable and that the early element transiently establishes the content of the binary cell fate decision to which the autoregulatory module then commits. Further in silico analysis revealed that the autoregulatory element locks the Ftz fate quickly, within 35 min of exposure to the transient signal of the early element. Overall, our work confirms the widely held hypothesis that autoregulation can establish developmental fates through bistability and, most importantly, provides a framework for the quantitative dissection of cellular decision-making.

Shaping the scaling characteristics of gap gene expression patterns in Drosophila

How patterns are formed to scale with tissue size remains an unresolved problem. Here we investigate embryonic patterns of gap gene expression along the anterior-posterior (AP) axis in Drosophila. We use embryos that greatly differ in length and, importantly, possess distinct length-scaling characteristics of the Bicoid (Bcd) gradient. We systematically analyze the dynamic movements of gap gene expression boundaries in relation to both embryo length and Bcd input as a function of time. We document the process through which such dynamic movements drive both an emergence of a global scaling landscape and evolution of boundary-specific scaling characteristics. We show that, despite initial differences in pattern scaling characteristics that mimic those of Bcd in the anterior, such characteristics of final patterns converge. Our study thus partitions the contributions of Bcd input and regulatory dynamics inherent to the AP patterning network in shaping embryonic pattern's scaling characteristics.

Spatiotemporal Patterning Enabled by Gene Regulatory Networks

Spatiotemporal pattern formation plays a key role in various biological phenomena including embryogenesis and neural network formation. Though the reaction-diffusion systems enabling pattern formation have been studied phenomenologically, the biomolecular mechanisms behind these processes have not been modeled in detail. Here, we study the emergence of spatiotemporal patterns due to simple, synthetic and commonly observed two- and three-node gene regulatory network motifs coupled with their molecular diffusion in one- and two-dimensional space. We investigate the patterns formed due to the coupling of inherent multistable and oscillatory behavior of the toggle switch, toggle switch with double self-activation, toggle triad, and repressilator with the effect of spatial diffusion of these molecules. We probe multiple parameter regimes corresponding to different regions of stability (monostable, multistable, oscillatory) and assess the impact of varying diffusion coefficients. This analysis offers valuable insights into the design principles of pattern formation facilitated by these network motifs, and it suggests the mechanistic underpinnings of biological pattern formation.

Implications of diffusion and time-varying morphogen gradients for the dynamic positioning and precision of bistable gene expression boundaries

The earliest models for how morphogen gradients guide embryonic patterning failed to account for experimental observations of temporal refinement in gene expression domains. Following theoretical and experimental work in this area, dynamic positional information has emerged as a conceptual framework to discuss how cells process spatiotemporal inputs into downstream patterns. Here, we show that diffusion determines the mathematical means by which bistable gene expression boundaries shift over time, and therefore how cells interpret positional information conferred from morphogen concentration. First, we introduce a metric for assessing reproducibility in boundary placement or precision in systems where gene products do not diffuse, but where morphogen concentrations are permitted to change in time. We show that the dynamics of the gradient affect the sensitivity of the final pattern to variation in initial conditions, with slower gradients reducing the sensitivity. Second, we allow gene products to diffuse and consider gene expression boundaries as propagating wavefronts with velocity modulated by local morphogen concentration. We harness this perspective to approximate a PDE model as an ODE that captures the position of the boundary in time, and demonstrate the approach with a preexisting model for Hunchback patterning in fruit fly embryos. We then propose a design that employs antiparallel morphogen gradients to achieve accurate boundary placement that is robust to scaling. Throughout our work we draw attention to tradeoffs among initial conditions, boundary positioning, and the relative timescales of network and gradient evolution. We conclude by suggesting that mathematical theory should serve to clarify not just our quantitative, but also our intuitive understanding of patterning processes.

A reaction-diffusion network model predicts a dual role of Cactus/IκB to regulate Dorsal/NFκB nuclear translocation in Drosophila

Dorsal-ventral patterning of the Drosophila embryo depends on the NFκB superfamily transcription factor Dorsal (Dl). Toll receptor activation signals for degradation of the IκB inhibitor Cactus (Cact), leading to a ventral-to-dorsal nuclear Dl gradient. Cact is critical for Dl nuclear import, as it binds to and prevents Dl from entering the nuclei. Quantitative analysis of cact mutants revealed an additional Cact function to promote Dl nuclear translocation in ventral regions of the embryo. To investigate this dual Cact role, we developed a predictive model based on a reaction-diffusion regulatory network. This network distinguishes non-uniform Toll-dependent Dl nuclear import and Cact degradation, from the Toll-independent processes of Cact degradation and reversible nuclear-cytoplasmic Dl flow. In addition, it incorporates translational control of Cact levels by Dl. Our model successfully reproduces wild-type data and emulates the Dl nuclear gradient in mutant dl and cact allelic combinations. Our results indicate that the dual role of Cact depends on the dynamics of Dl-Cact trimers along the dorsal-ventral axis: In the absence of Toll activation, free Dl-Cact trimers retain Dl in the cytoplasm, limiting the flow of Dl into the nucleus; in ventral-lateral regions, Dl-Cact trimers are recruited by Toll activation into predominant signaling complexes and promote Dl nuclear translocation. Simulations suggest that the balance between Toll-dependent and Toll-independent processes are key to this dynamics and reproduce the full assortment of Cact effects. Considering the high evolutionary conservation of these pathways, our analysis should contribute to understanding NFκB/c-Rel activation in other contexts such as in the vertebrate immune system and disease.

In Drosophila, Toll pathway establishes spatially distinct gene expression territories that define the embryonic dorsal-ventral axis. Toll activation leads to degradation of the IκB inhibitor Cactus, releasing the NFκB superfamily transcription factor Dorsal for nuclear entry. Recently, quantitative analysis of cact mutants revealed that Cact displays an additional function to promote Dl nuclear translocation in ventral regions of the embryo. To understand this novel activity, we developed a predictive theoretical model that shows that the kinetics of Dorsal-Cactus complex formation prior to their recruitment to Toll-signaling complexes is an essential regulatory hub. Cactus controls the balance between the recruitment of these complexes by active Toll receptor and association-dissociation events that generate free Dorsal for direct nuclear import.

Multicellular sensing at a feedback-induced critical point

Feedback in sensory biochemical networks can give rise to bifurcations in cells' behavioral response. These bifurcations share many properties with thermodynamic critical points. Evidence suggests that biological systems may operate near these critical points, but the functional benefit of doing so remains poorly understood. Here we investigate a simple biochemical model with nonlinear feedback and multicellular communication to determine if criticality provides a functional benefit in terms of the ability to gain information about a stochastic chemical signal. We find that when signal fluctuations are slow, the mutual information between the signal and the intracellular readout is maximized at criticality, because the benefit of high signal susceptibility outweighs the detriment of high readout noise. When cells communicate, criticality gives rise to long-range correlations in readout molecule number among cells. Consequently, we find that communication increases the mutual information between a given cell's readout and the spatial average of the signal across the population. Finally, we find that both with and without communication, the sensory benefits of criticality compete with critical slowing down, such that the information rate, as opposed to the information itself, is minimized at the critical point. Our results reveal the costs and benefits of feedback-induced criticality for multicellular sensing.

The dynamic transmission of positional information in stau- mutants during Drosophila embryogenesis

It has been suggested that Staufen (Stau) is key in controlling the variability of the posterior boundary of the Hb anterior domain (xHb). However, the mechanism that underlies this control is elusive. Here, we quantified the dynamic 3D expression of segmentation genes in Drosophila embryos. With improved control of measurement errors, we show that the xHb of stau- mutants reproducibly moves posteriorly by 10% of the embryo length (EL) to the wild type (WT) position in the nuclear cycle (nc) 14, and that its variability over short time windows is comparable to that of the WT. Moreover, for stau- mutants, the upstream Bicoid (Bcd) gradients show equivalent relative intensity noise to that of the WT in nc12-nc14, and the downstream Even-skipped (Eve) and cephalic furrow (CF) show the same positional errors as these factors in WT. Our results indicate that threshold-dependent activation and self-organized filtering are not mutually exclusive and could both be implemented in early Drosophila embryogenesis.

Controlling spatiotemporal pattern formation in a concentration gradient with a synthetic toggle switch

The formation of spatiotemporal patterns of gene expression is frequently guided by gradients of diffusible signaling molecules. The toggle switch subnetwork, composed of two cross-repressing transcription factors, is a common component of gene regulatory networks in charge of patterning, converting the continuous information provided by the gradient into discrete abutting stripes of gene expression. We present a synthetic biology framework to understand and characterize the spatiotemporal patterning properties of the toggle switch. To this end, we built a synthetic toggle switch controllable by diffusible molecules in Escherichia coli. We analyzed the patterning capabilities of the circuit by combining quantitative measurements with a mathematical reconstruction of the underlying dynamical system. The toggle switch can produce robust patterns with sharp boundaries, governed by bistability and hysteresis. We further demonstrate how the hysteresis, position, timing, and precision of the boundary can be controlled, highlighting the dynamical flexibility of the circuit.

Lighting up the central dogma for predictive developmental biology

Although the last 30years have witnessed the mapping of the wiring diagrams of the gene regulatory networks that dictate cell fate and animal body plans, specific understanding building on such network diagrams that shows how DNA regulatory regions control gene expression lags far behind. These networks have yet to yield the predictive power necessary to, for example, calculate how the concentration dynamics of input transcription factors and DNA regulatory sequence prescribes output patterns of gene expression that, in turn, determine body plans themselves. Here, we argue that reaching a predictive understanding of developmental decision-making calls for an interplay between theory and experiment aimed at revealing how the regulation of the processes of the central dogma dictate network connections and how network topology guides cells toward their ultimate developmental fate. To make this possible, it is crucial to break free from the snapshot-based understanding of embryonic development facilitated by fixed-tissue approaches and embrace new technologies that capture the dynamics of developmental decision-making at the single cell level, in living embryos.

Artificial Gene Regulatory Networks-A Review

In nature, gene regulatory networks are a key mediator between the information stored in the DNA of living organisms (their genotype) and the structural and behavioral expression this finds in their bodies, surviving in the world (their phenotype). They integrate environmental signals, steer development, buffer stochasticity, and allow evolution to proceed. In engineering, modeling and implementations of artificial gene regulatory networks have been an expanding field of research and development over the past few decades. This review discusses the concept of gene regulation, describes the current state of the art in gene regulatory networks, including modeling and simulation, and reviews their use in artificial evolutionary settings. We provide evidence for the benefits of this concept in natural and the engineering domains.

A Tug-of-War Mechanism for Pattern Formation in a Genetic Network

Synthesizing spatial patterns with genetic networks is an ongoing challenge in synthetic biology. A successful demonstration of pattern formation would imply a better understanding of systems in the natural world and advance applications in synthetic biology. In developmental systems, transient patterning may suffice in order to imprint instructions for long-term development. In this paper we show that transient but persistent patterns can emerge from a realizable synthetic gene network based on a toggle switch. We show that a bistable system incorporating diffusible molecules can generate patterns that resemble Turing patterns but are distinctly different in the underlying mechanism: diffusion of mutually inhibiting molecules creates a prolonged "tug-of-war" between patches of cells at opposing bistable states. The patterns are transient but longer wavelength patterns persist for extended periods of time. Analysis of a representative small scale model implies the eigenvalues of the persistent modes are just above the threshold of stability. The results are verified through simulation of biologically relevant models.

Transcriptional precision and accuracy in development: from measurements to models and mechanisms

During development, genes are transcribed at specific times, locations and levels. In recent years, the emergence of quantitative tools has significantly advanced our ability to measure transcription with high spatiotemporal resolution in vivo. Here, we highlight recent studies that have used these tools to characterize transcription during development, and discuss the mechanisms that contribute to the precision and accuracy of the timing, location and level of transcription. We attempt to disentangle the discrepancies in how physicists and biologists use the term ‘precision' to facilitate interactions using a common language. We also highlight selected examples in which the coupling of mathematical modeling with experimental approaches has provided important mechanistic insights, and call for a more expansive use of mathematical modeling to exploit the wealth of quantitative data and advance our understanding of animal transcription.

Summary: This Review highlights how high-resolution quantitative tools and theoretical models have formed our current view of the mechanisms determining precision and accuracy in the timing, location and level of transcription in the Drosophila embryo.

Synthesis and materialization of a reaction-diffusion French flag pattern

During embryo development, patterns of protein concentration appear in response to morphogen gradients. These patterns provide spatial and chemical information that directs the fate of the underlying cells. Here, we emulate this process within non-living matter and demonstrate the autonomous structuration of a synthetic material. First, we use DNA-based reaction networks to synthesize a French flag, an archetypal pattern composed of three chemically distinct zones with sharp borders whose synthetic analogue has remained elusive. A bistable network within a shallow concentration gradient creates an immobile, sharp and long-lasting concentration front through a reaction-diffusion mechanism. The combination of two bistable circuits generates a French flag pattern whose 'phenotype' can be reprogrammed by network mutation. Second, these concentration patterns control the macroscopic organization of DNA-decorated particles, inducing a French flag pattern of colloidal aggregation. This experimental framework could be used to test reaction-diffusion models and fabricate soft materials following an autonomous developmental programme.

Identifying ultrasensitive HGF dose-response functions in a 3D mammalian system for synthetic morphogenesis

Nonlinear responses to signals are widespread natural phenomena that affect various cellular processes. Nonlinearity can be a desirable characteristic for engineering living organisms because it can lead to more switch-like responses, similar to those underlying the wiring in electronics. Steeper functions are described as ultrasensitive, and can be applied in synthetic biology by using various techniques including receptor decoys, multiple co-operative binding sites, and sequential positive feedbacks. Here, we explore the inherent non-linearity of a biological signaling system to identify functions that can potentially be exploited using cell genome engineering. For this, we performed genome-wide transcription profiling to identify genes with ultrasensitive response functions to Hepatocyte Growth Factor (HGF). We identified 3,527 genes that react to increasing concentrations of HGF, in Madin-Darby canine kidney (MDCK) cells, grown as cysts in 3D collagen cell culture. By fitting a generic Hill function to the dose-responses of these genes we obtained a measure of the ultrasensitivity of HGF-responsive genes, identifying a subset with higher apparent Hill coefficients (e.g. MMP1, TIMP1, SNORD75, SNORD86 and ERRFI1). The regulatory regions of these genes are potential candidates for future engineering of synthetic mammalian gene circuits requiring nonlinear responses to HGF signalling.

Genome-Wide Transcriptome and Binding Sites Analyses Identify Early FOX Expressions for Enhancing Cardiomyogenesis Efficiency of hESC Cultures

The differentiation efficiency of human embryonic stem cells (hESCs) into heart muscle cells (cardiomyocytes) is highly sensitive to culture conditions. To elucidate the regulatory mechanisms involved, we investigated hESCs grown on three distinct culture platforms: feeder-free Matrigel, mouse embryonic fibroblast feeders, and Matrigel replated on feeders. At the outset, we profiled and quantified their differentiation efficiency, transcriptome, transcription factor binding sites and DNA-methylation. Subsequent genome-wide analyses allowed us to reconstruct the relevant interactome, thereby forming the regulatory basis for implicating the contrasting differentiation efficiency of the culture conditions. We hypothesized that the parental expressions of FOXC1, FOXD1 and FOXQ1 transcription factors (TFs) are correlative with eventual cardiomyogenic outcome. Through WNT induction of the FOX TFs, we observed the co-activation of WNT3 and EOMES which are potent inducers of mesoderm differentiation. The result strengthened our hypothesis on the regulatory role of the FOX TFs in enhancing mesoderm differentiation capacity of hESCs. Importantly, the final proportions of cells expressing cardiac markers were directly correlated to the strength of FOX inductions within 72 hours after initiation of differentiation across different cell lines and protocols. Thus, we affirmed the relationship between early FOX TF expressions and cardiomyogenesis efficiency.

Sequential construction of a model for modular gene expression control, applied to spatial patterning of theDrosophilagenehunchback

Gene network simulations are increasingly used to quantify mutual gene regulation in biological tissues. These are generally based on linear interactions between single-entity regulatory and target genes. Biological genes, by contrast, commonly have multiple, partially independent, cis-regulatory modules (CRMs) for regulator binding, and can produce variant transcription and translation products. We present a modeling framework to address some of the gene regulatory dynamics implied by this biological complexity. Spatial patterning of the hunchback (hb) gene in Drosophila development involves control by three CRMs producing two distinct mRNA transcripts. We use this example to develop a differential equations model for transcription which takes into account the cis-regulatory architecture of the gene. Potential regulatory interactions are screened by a genetic algorithms (GAs) approach and compared to biological expression data.

A glance at the applications of Singular Spectrum Analysis in gene expression data

In recent years Singular Spectrum Analysis (SSA) has been used to solve many biomedical issues and is currently accepted as a potential technique in quantitative genetics studies. Presented in this article is a review of recent published genetics studies which have taken advantage of SSA. Since Singular Value Decomposition (SVD) is an important stage of this technique which can also be used as an independent analytical method in gene expression data, we also briefly touch upon some areas of the application of SVD. The review finds that at present, the most prominent area of applying SSA in genetics is filtering and signal extraction, which proves that SSA can be considered as a valuable aid and promising method for genetics analysis.

Probing the impact of temperature on molecular events in a developmental system

A well-appreciated general feature of development is the ability to achieve a normal outcome despite the inevitable variability at molecular, genetic, or environmental levels. But it is not well understood how changes in a global factor such as temperature bring about specific challenges to a developmental system in molecular terms. Here we address this question using early Drosophila embryos where the maternal gradient Bicoid (Bcd) instructs anterior-patterning (AP) patterning. We show that temperature can impact the amplitude of the Bcd gradient in the embryo. To evaluate how molecular decisions are made at different temperatures, we quantify Bcd concentrations and the expression of its target gene hunchback (hb) in individual embryos. Our results suggest a relatively robust Bcd concentration threshold in inducing hb transcription within a temperature range. Our results also reveal a complex nature of the effects of temperature on the progressions of developmental and molecular events of the embryo. Our study thus advances the concept of developmental robustness by quantitatively elaborating specific features and challenges—imposed by changes in temperature—that an embryo must resolve.

Combining protein and mRNA quantification to decipher transcriptional regulation

We combine immunofluorescence and single-molecule fluorescence in situ hybridization (smFISH), followed by automated image analysis, to quantify the concentration of nuclear transcription factors, number of transcription factors bound, and number of nascent mRNAs synthesized at individual gene loci. A theoretical model is used to decipher how transcription-factor binding modulates the stochastic kinetics of mRNA production. We demonstrate this approach by examining the regulation of hunchback in the early Drosophila embryo.

Mid-embryo patterning and precision in Drosophila segmentation: Krüppel dual regulation of hunchback

In early development, genes are expressed in spatial patterns which later define cellular identities and tissue locations. The mechanisms of such pattern formation have been studied extensively in early Drosophila (fruit fly) embryos. The gap gene hunchback (hb) is one of the earliest genes to be expressed in anterior-posterior (AP) body segmentation. As a transcriptional regulator for a number of downstream genes, the spatial precision of hb expression can have significant effects in the development of the body plan. To investigate the factors contributing to hb precision, we used fine spatial and temporal resolution data to develop a quantitative model for the regulation of hb expression in the mid-embryo. In particular, modelling hb pattern refinement in mid nuclear cleavage cycle 14 (NC14) reveals some of the regulatory contributions of simultaneously-expressed gap genes. Matching the model to recent data from wild-type (WT) embryos and mutants of the gap gene Krüppel (Kr) indicates that a mid-embryo Hb concentration peak important in thoracic development (at parasegment 4, PS4) is regulated in a dual manner by Kr, with low Kr concentration activating hb and high Kr concentration repressing hb. The processes of gene expression (transcription, translation, transport) are intrinsically random. We used stochastic simulations to characterize the noise generated in hb expression. We find that Kr regulation can limit the positional variability of the Hb mid-embryo border. This has been recently corroborated in experimental comparisons of WT and Kr- mutant embryos. Further, Kr regulation can decrease uncertainty in mid-embryo hb expression (i.e. contribute to a smooth Hb boundary) and decrease between-copy transcriptional variability within nuclei. Since many tissue boundaries are first established by interactions between neighbouring gene expression domains, these properties of Hb-Kr dynamics to diminish the effects of intrinsic expression noise may represent a general mechanism contributing to robustness in early development.

Computational and mathematical methods for morphogenetic gradient analysis, boundary formation and axonal targeting

Morphogenesis and axonal targeting are key processes during development that depend on complex interactions at molecular, cellular and tissue level. Mathematical modeling is essential to bridge this multi-scale gap in order to understand how the emergence of large structures is controlled at molecular level by interactions between various signaling pathways. We summarize mathematical modeling and computational methods for time evolution and precision of morphogenetic gradient formation. We discuss tissue patterning and the formation of borders between regions labeled by different morphogens. Finally, we review models and algorithms that reveal the interplay between morphogenetic gradients and patterned activity for axonal pathfinding and the generation of the retinotopic map in the visual system.

Dissection of a Krox20 positive feedback loop driving cell fate choices in hindbrain patterning

A positive autoregulatory loop required for the expression of the transcription factor Krox20 was dissected using in vivo quantitative data and biophysical modelling to demonstrate how Krox20 controls cell fate decision and rhombomere size in the hindbrain.

Positive autoregulation of Krox20 underpins a bistable switch that turns a transient input signal into cell fate commitment, as demonstrated in single cell analyses.

The duration and strength of the input signal control the size of the hindbrain segments by modulating the distribution between two cell fates.

The progressive extinction of Krox20 expression involves a destabilization of the loop by repressor molecules.

Although feedback loops are essential in development, their molecular implementation and precise functions remain elusive. Using enhancer knockout in mice, we demonstrate that a direct, positive autoregulatory loop amplifies and maintains the expression of Krox20, a transcription factor governing vertebrate hindbrain segmentation. By combining quantitative data collected in the zebrafish with biophysical modelling that accounts for the intrinsic stochastic molecular dynamics, we dissect the loop at the molecular level. We find that it underpins a bistable switch that turns a transient input signal into cell fate commitment, as we observe in single cell analyses. The stochasticity of the activation process leads to a graded input–output response until saturation is reached. Consequently, the duration and strength of the input signal controls the size of the hindbrain segments by modulating the distribution between the two cell fates. Moreover, segment formation is buffered from severe variations in input level. Finally, the progressive extinction of Krox20 expression involves a destabilization of the loop by repressor molecules. These mechanisms are of general significance for cell type specification and tissue patterning.

Stability of localized wave fronts in bistable systems

Localized wave fronts are a fundamental feature of biological systems from cell biology to ecology. Here, we study a broad class of bistable models subject to self-activation, degradation, and spatially inhomogeneous activating agents. We determine the conditions under which wave-front localization is possible and analyze the stability thereof with respect to extrinsic perturbations and internal noise. It is found that stability is enhanced upon regulating a positional signal and, surprisingly, also for a low degree of binding cooperativity. We further show a contrasting impact of self-activation to the stability of these two sources of destabilization.

Precision of hunchback expression in the Drosophila embryo

Activation of the gap gene hunchback (hb) by the maternal Bicoid gradient is one of the most intensively studied gene regulatory interactions in animal development. Most efforts to understand this process have focused on the classical Bicoid target enhancer located immediately upstream of the P2 promoter. However, hb is also regulated by a recently identified distal shadow enhancer as well as a neglected "stripe" enhancer, which mediates expression in both central and posterior regions of cellularizing embryos. Here, we employ BAC transgenesis and quantitative imaging methods to investigate the individual contributions of these different enhancers to the dynamic hb expression pattern. These studies reveal that the stripe enhancer is crucial for establishing the definitive border of the anterior Hb expression pattern, just beyond the initial border delineated by Bicoid. Removal of this enhancer impairs dynamic expansion of hb expression and results in variable cuticular defects in the mesothorax (T2) due to abnormal patterns of segmentation gene expression. The stripe enhancer is subject to extensive regulation by gap repressors, including Kruppel, Knirps, and Hb itself. We propose that this repression helps ensure precision of the anterior Hb border in response to variations in the Bicoid gradient.

External noise control in inherently stochastic biological systems

Biological systems are often subject to external noise from signal stimuli and environmental perturbations, as well as noises in the intracellular signal transduction pathway. Can different stochastic fluctuations interact to give rise to new emerging behaviors? How can a system reduce noise effects while still being capable of detecting changes in the input signal? Here, we study analytically and computationally the role of nonlinear feedback systems in controlling external noise with the presence of large internal noise. In addition to noise attenuation, we analyze derivatives of Fano factor to study systems' capability of differentiating signal inputs. We find effects of internal noise and external noise may be separated in one slow positive feedback loop system; in particular, the slow loop can decrease external noise and increase robustness of signaling with respect to fluctuations in rate constants, while maintaining the signal output specific to the input. For two feedback loops, we demonstrate that the influence of external noise mainly depends on how the fast loop responds to fluctuations in the input and the slow loop plays a limited role in determining the signal precision. Furthermore, in a dual loop system of one positive feedback and one negative feedback, a slower positive feedback always leads to better noise attenuation; in contrast, a slower negative feedback may not be more beneficial. Our results reveal interesting stochastic effects for systems containing both extrinsic and intrinsic noises, suggesting novel noise filtering strategies in inherently stochastic systems.

Mutual repression enhances the steepness and precision of gene expression boundaries

Embryonic development is driven by spatial patterns of gene expression that determine the fate of each cell in the embryo. While gene expression is often highly erratic, embryonic development is usually exceedingly precise. In particular, gene expression boundaries are robust not only against intra-embryonic fluctuations such as noise in gene expression and protein diffusion, but also against embryo-to-embryo variations in the morphogen gradients, which provide positional information to the differentiating cells. How development is robust against intra- and inter-embryonic variations is not understood. A common motif in the gene regulation networks that control embryonic development is mutual repression between pairs of genes. To assess the role of mutual repression in the robust formation of gene expression patterns, we have performed large-scale stochastic simulations of a minimal model of two mutually repressing gap genes in Drosophila, hunchback (hb) and knirps (kni). Our model includes not only mutual repression between hb and kni, but also the stochastic and cooperative activation of hb by the anterior morphogen Bicoid (Bcd) and of kni by the posterior morphogen Caudal (Cad), as well as the diffusion of Hb and Kni between neighboring nuclei. Our analysis reveals that mutual repression can markedly increase the steepness and precision of the gap gene expression boundaries. In contrast to other mechanisms such as spatial averaging and cooperative gene activation, mutual repression thus allows for gene-expression boundaries that are both steep and precise. Moreover, mutual repression dramatically enhances their robustness against embryo-to-embryo variations in the morphogen levels. Finally, our simulations reveal that diffusion of the gap proteins plays a critical role not only in reducing the width of the gap gene expression boundaries via the mechanism of spatial averaging, but also in repairing patterning errors that could arise because of the bistability induced by mutual repression.

The role of Bicoid cooperative binding in the patterning of sharp borders in Drosophila melanogaster

In Drosophila embryonic development, the Bicoid (Bcd) protein establishes positional information of downstream developmental genes like hunchback (hb), which has a strong anterior expression and a sharp on-off boundary in the mid-embryo. The role of Bcd cooperative binding in the positioning of the Hb pattern has been previously demonstrated. However, there are discrepancies in the reported results about the role of this mechanism in the sharp Hb border. Here, we determined the Hill coefficient (nH) required for Bcd to generate the sharp border of Hb in wild-type (WT) embryos. We found that an n(H) of approximately 6.3 (s.d. 1.4) and 10.8 (s.d. 4.0) is required to account for Hb sharpness at early and late cycle 14A, respectively. Additional mechanisms are possibly required because the high nH is likely unachievable for Bcd binding to the hb promoter. To test this idea, we determined the nH required to pattern the Hb profile of 15 embryos expressing an hb14F allele that is defective in self-activation and found nH to be 3.0 (s.d. 1.0). This result indicates that in WT embryos, the hb self-activation is important for Hb sharpness. Corroborating our results, we also found a progressive increase in the required value of n(H) spanning from 4.0 to 9.2 by determining this coefficient from averaged profiles of eight temporal classes at cycle 14A (T1 to T8). Our results indicate that there is a transition in the mechanisms responsible for the sharp Hb border during cycle 14A: in early stages of this cycle, Bcd cooperative binding is primarily responsible for Hb sharpness; in late cycle 14A, hb self-activation becomes the dominant mechanism.

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.

Whole-embryo modeling of early segmentation in Drosophila identifies robust and fragile expression domains

Segmentation of the Drosophila melanogaster embryo results from the dynamic establishment of spatial mRNA and protein patterns. Here, we exploit recent temporal mRNA and protein expression measurements on the full surface of the blastoderm to calibrate a dynamical model of the gap gene network on the entire embryo cortex. We model the early mRNA and protein dynamics of the gap genes hunchback, Kruppel, giant, and knirps, taking as regulatory inputs the maternal Bicoid and Caudal gradients, plus the zygotic Tailless and Huckebein proteins. The model captures the expression patterns faithfully, and its predictions are assessed from gap gene mutants. The inferred network shows an architecture based on reciprocal repression between gap genes that can stably pattern the embryo on a realistic geometry but requires complex regulations such as those involving the Hunchback monomer and dimers. Sensitivity analysis identifies the posterior domain of giant as among the most fragile features of an otherwise robust network, and hints at redundant regulations by Bicoid and Hunchback, possibly reflecting recent evolutionary changes in the gap-gene network in insects.

The Drosophila gap gene network is composed of two parallel toggle switches

Drosophila “gap” genes provide the first response to maternal gradients in the early fly embryo. Gap genes are expressed in a series of broad bands across the embryo during first hours of development. The gene network controlling the gap gene expression patterns includes inputs from maternal gradients and mutual repression between the gap genes themselves. In this study we propose a modular design for the gap gene network, involving two relatively independent network domains. The core of each network domain includes a toggle switch corresponding to a pair of mutually repressive gap genes, operated in space by maternal inputs. The toggle switches present in the gap network are evocative of the phage lambda switch, but they are operated positionally (in space) by the maternal gradients, so the synthesis rates for the competing components change along the embryo anterior-posterior axis. Dynamic model, constructed based on the proposed principle, with elements of fractional site occupancy, required 5–7 parameters to fit quantitative spatial expression data for gap gradients. The identified model solutions (parameter combinations) reproduced major dynamic features of the gap gradient system and explained gap expression in a variety of segmentation mutants.

A multiscale investigation of bicoid-dependent transcriptional events in Drosophila embryos

Background

Morphogen molecules form concentration gradients to provide spatial information to cells in a developing embryo. Precisely how cells decode such information to form patterns with sharp boundaries remains an open question. For example, it remains controversial whether the Drosophila morphogenetic protein Bicoid (Bcd) plays a transient or sustained role in activating its target genes to establish sharp expression boundaries during development.

Methodology/Principal Findings

In this study, we describe a method to simultaneously detect Bcd and the nascent transcripts of its target genes in developing embryos. This method allows us to investigate the relationship between Bcd and the transcriptional status of individual copies of its target genes on distinct scales. We show that, on three scales analyzed concurrently—embryonic, nuclear and local, the actively-transcribing gene copies are associated with high Bcd concentrations. These results underscore the importance of Bcd as a sustained input for transcriptional decisions of individual copies of its target genes during development. We also show that the Bcd-dependent transcriptional decisions have a significantly higher noise than Bcd-dependent gene products, suggesting that, consistent with theoretical studies, time and/or space averaging reduces the noise of Bcd-activated transcriptional output. Finally, our analysis of an X-linked Bcd target gene reveals that Bcd-dependent transcription bursts at twice the frequency in males as in females, providing a mechanism for dosage compensation in early Drosophila embryos.

Conclusion/Significance

Our study represents a first experimental uncovering of the actions of Bcd in controlling the actual transcriptional events while its positional information is decoded during development. It establishes a sustained role of Bcd in transcriptional decisions of individual copies of its target genes to generate sharp expression boundaries. It also provides an experimental evaluation of the effect of time and/or space averaging on Bcd-dependent transcriptional output, and establishes a dosage compensation mechanism in early Drosophila embryos.

Gene expression noise in spatial patterning: hunchback promoter structure affects noise amplitude and distribution in Drosophila segmentation

Positional information in developing embryos is specified by spatial gradients of transcriptional regulators. One of the classic systems for studying this is the activation of the hunchback (hb) gene in early fruit fly (Drosophila) segmentation by the maternally-derived gradient of the Bicoid (Bcd) protein. Gene regulation is subject to intrinsic noise which can produce variable expression. This variability must be constrained in the highly reproducible and coordinated events of development. We identify means by which noise is controlled during gene expression by characterizing the dependence of hb mRNA and protein output noise on hb promoter structure and transcriptional dynamics. We use a stochastic model of the hb promoter in which the number and strength of Bcd and Hb (self-regulatory) binding sites can be varied. Model parameters are fit to data from WT embryos, the self-regulation mutant hb(14F), and lacZ reporter constructs using different portions of the hb promoter. We have corroborated model noise predictions experimentally. The results indicate that WT (self-regulatory) Hb output noise is predominantly dependent on the transcription and translation dynamics of its own expression, rather than on Bcd fluctuations. The constructs and mutant, which lack self-regulation, indicate that the multiple Bcd binding sites in the hb promoter (and their strengths) also play a role in buffering noise. The model is robust to the variation in Bcd binding site number across a number of fly species. This study identifies particular ways in which promoter structure and regulatory dynamics reduce hb output noise. Insofar as many of these are common features of genes (e.g. multiple regulatory sites, cooperativity, self-feedback), the current results contribute to the general understanding of the reproducibility and determinacy of spatial patterning in early development.

Shaping a morphogen gradient for positional precision

Morphogen gradients, which provide positional information to cells in a developing tissue, could in principle adopt any nonuniform profile. To our knowledge, how the profile of a morphogen gradient affects positional precision has not been well studied experimentally. Here, we compare the positional precision provided by the Drosophila morphogenetic protein Bicoid (Bcd) in wild-type (wt) embryos with embryos lacking an interacting cofactor. The Bcd gradient in the latter case exhibits decreased positional precision around mid-embryo compared with its wt counterpart. The domain boundary of Hunchback (Hb), a target activated by Bcd, becomes more variable in mutant embryos. By considering embryo-to-embryo, internal, and measurement fluctuations, we dissect mathematically the relevant sources of fluctuations that contribute to the error in positional information. Using this approach, we show that the defect in Hb boundary positioning in mutant embryos is directly reflective of an altered Bcd gradient profile with increasing flatness toward mid-embryo. Furthermore, we find that noise in the Bcd input signal is dominated by internal fluctuations but, due to time and spatial averaging, the spatial precision of the Hb boundary is primarily affected by embryo-to-embryo variations. Our results demonstrate that the positional information provided by the wt Bcd gradient profile is highly precise and necessary for patterning precision.

Modeling bistable cell-fate choices in the Drosophila eye: qualitative and quantitative perspectives

A major goal of developmental biology is to understand the molecular mechanisms whereby genetic signaling networks establish and maintain distinct cell types within multicellular organisms. Here, we review cell-fate decisions in the developing eye of Drosophila melanogaster and the experimental results that have revealed the topology of the underlying signaling circuitries. We then propose that switch-like network motifs based on positive feedback play a central role in cell-fate choice, and discuss how mathematical modeling can be used to understand and predict the bistable or multistable behavior of such networks.

Precision and scaling in morphogen gradient read-out

Morphogen gradients infer cell fate as a function of cellular position. Experiments in Drosophila embryos have shown that the Bicoid (Bcd) gradient is precise and exhibits some degree of scaling. We present experimental results on the precision of Bcd target genes for embryos with a single, double or quadruple dose of bicoid demonstrating that precision is highest at mid-embryo and position dependent, rather than gene dependent. This confirms that the major contribution to precision is achieved already at the Bcd gradient formation. Modeling this dynamic process, we investigate precision for inter-embryo fluctuations in different parameters affecting gradient formation. Within our modeling framework, the observed precision can only be achieved by a transient Bcd profile. Studying different extensions of our modeling framework reveals that scaling is generally position dependent and decreases toward the posterior pole. Our measurements confirm this trend, indicating almost perfect scaling except for anterior most expression domains, which overcompensate fluctuations in embryo length.

How transcription factors can adjust the gene expression floodgates

The rate of transcription initiation is the main level of quantitative control of gene expression, primarily responsible for the accumulation of mRNAs in the cell. Many, if not all, molecular actors involved in transcription initiation are known but the mechanisms underlying the frequency of initiations, remain elusive. To make the connection between transcription factors and the frequency of transcription initiation, intricated aspects of this complex activity are classified i) depending on whether or not the DNA-bound transcription factors directly activate the commitment to transcription and ii) on the destructive or non-destructive effect of transcription initiation on the stability of promoter complexes. Two possible sources of synergy allowing the combinatorial specificity of transcription factors action are compared, for binding to DNA and for recruiting transcription machineries. Tentative formulations are proposed to discriminate the different micro-reversible modes of DNA binding cooperativity modulating the specificity and dosage of transcription initiation.

Modelling the Drosophila embryo

I provide a historical overview on the use of mathematical models to gain insight into pattern formation during early development of the fruit fly Drosophila melanogaster. It is my intention to illustrate how the aims and methodology of modelling have changed from the early beginnings of a theoretical developmental biology in the 1960s to modern-day systems biology. I show that even early modelling attempts addressed interesting and relevant questions, which were not tractable by experimental approaches. Unfortunately, their validation was severely hampered by a lack of specificity and appropriate experimental evidence. There is a simple lesson to be learned from this: we cannot deduce general rules for pattern formation from first principles or spurious reproduction of developmental phenomena. Instead, we must infer such rules (if any) from detailed and accurate studies of specific developmental systems. To achieve this, mathematical modelling must be closely integrated with experimental approaches. I report on progress that has been made in this direction in the past few years and illustrate the kind of novel insights that can be gained from such combined approaches. These insights demonstrate the great potential (and some pitfalls) of an integrative, systems-level investigation of pattern formation.

Stable, precise, and reproducible patterning of bicoid and hunchback molecules in the early Drosophila embryo

Precise patterning of morphogen molecules and their accurate reading out are of key importance in embryonic development. Recent experiments have visualized distributions of proteins in developing embryos and shown that the gradient of concentration of Bicoid morphogen in Drosophila embryos is established rapidly after fertilization and remains stable through syncytial mitoses. This stable Bicoid gradient is read out in a precise way to distribute Hunchback with small fluctuations in each embryo and in a reproducible way, with small embryo-to-embryo fluctuation. The mechanisms of such stable, precise, and reproducible patterning through noisy cellular processes, however, still remain mysterious. To address these issues, here we develop the one- and three-dimensional stochastic models of the early Drosophila embryo. The simulated results show that the fluctuation in expression of the hunchback gene is dominated by the random arrival of Bicoid at the hunchback enhancer. Slow diffusion of Hunchback protein, however, averages out this intense fluctuation, leading to the precise patterning of distribution of Hunchback without loss of sharpness of the boundary of its distribution. The coordinated rates of diffusion and transport of input Bicoid and output Hunchback play decisive roles in suppressing fluctuations arising from the dynamical structure change in embryos and those arising from the random diffusion of molecules, and give rise to the stable, precise, and reproducible patterning of Bicoid and Hunchback distributions.

Bistability coordinates activation of the EGFR and DPP pathways in Drosophila vein differentiation

Cell differentiation in developing tissues is controlled by a small set of signaling pathways, which must coordinate the timing and levels of activation to ensure robust and precise outcomes. Highly coordinated activation of signaling pathways can result from cross-regulatory interactions in multi-pathway networks. Here we explore the dynamics and function of pathway coordination between the EGFR and DPP pathways during Drosophila wing-vein differentiation. We show that simultaneous activation of both the EGFR and DPP pathways must be maintained for vein cell differentiation and that above-threshold ectopic activation of either pathway is sufficient to drive vein cell differentiation outside the proveins. The joint activation of the EGFR and DPP signaling systems is ensured by a positive feedback loop, in which the two pathways stimulate each other at the level of ligand production.

Monomeric bistability and the role of autoloops in gene regulation

Genetic toggle switches are widespread in gene regulatory networks (GRN). Bistability, namely the ability to choose among two different stable states, is an essential feature of switching and memory devices. Cells have many regulatory circuits able to provide bistability that endow a cell with efficient and reliable switching between different physiological modes of operation. It is often assumed that negative feedbacks with cooperative binding (i.e. the formation of dimers or multimers) are a prerequisite for bistability. Here we analyze the relation between bistability in GRN under monomeric regulation and the role of autoloops under a deterministic setting. Using a simple geometric argument, we show analytically that bistability can also emerge without multimeric regulation, provided that at least one regulatory autoloop is present.

Canalization of gene expression and domain shifts in the Drosophila blastoderm by dynamical attractors

The variation in the expression patterns of the gap genes in the blastoderm of the fruit fly Drosophila melanogaster reduces over time as a result of cross regulation between these genes, a fact that we have demonstrated in an accompanying article in PLoS Biology (see Manu et al., doi:10.1371/journal.pbio.1000049). This biologically essential process is an example of the phenomenon known as canalization. It has been suggested that the developmental trajectory of a wild-type organism is inherently stable, and that canalization is a manifestation of this property. Although the role of gap genes in the canalization process was established by correctly predicting the response of the system to particular perturbations, the stability of the developmental trajectory remains to be investigated. For many years, it has been speculated that stability against perturbations during development can be described by dynamical systems having attracting sets that drive reductions of volume in phase space. In this paper, we show that both the reduction in variability of gap gene expression as well as shifts in the position of posterior gap gene domains are the result of the actions of attractors in the gap gene dynamical system. Two biologically distinct dynamical regions exist in the early embryo, separated by a bifurcation at 53% egg length. In the anterior region, reduction in variation occurs because of stability induced by point attractors, while in the posterior, the stability of the developmental trajectory arises from a one-dimensional attracting manifold. This manifold also controls a previously characterized anterior shift of posterior region gap domains. Our analysis shows that the complex phenomena of canalization and pattern formation in the Drosophila blastoderm can be understood in terms of the qualitative features of the dynamical system. The result confirms the idea that attractors are important for developmental stability and shows a richer variety of dynamical attractors in developmental systems than has been previously recognized.

The evolutionary influence of binding site organisation on gene regulatory networks

Gene regulatory networks are shaped by selection for advantageous gene expression patterns. Can we use this fact to predict and explain the structure and properties of gene regulatory networks? Here we address this question with evolutionary simulations of small (two to four genes) transcriptional regulatory networks. Each modeled network is tested for the frequency with which it evolves to produce a bimodal spatial expression pattern of a target gene (the output), in response to a linear trigger gradient (the input). By including network features such as the organisation of binding sites that do not evolve in the model, we can compare the relative chances of evolutionary success between networks differing only in these features. Specifically, we show that networks with competitive binding sites (where binding of one transcription factor excludes another) are more likely to evolve bimodal patterns of gene repression than are networks with independent binding sites (where binding of multiple transcription factors can occur simultaneously). These predictions have implications for the likely structure of gene regulatory networks carrying out bimodal (including bistable) gene expression functions in vivo. The capacity to predict the evolution of structure-function relationships in gene regulatory networks is constrained by gaps in current understanding such as the unknown prior probabilities of the network features, and the quantitative nature of the molecular interactions involved in gene expression. Methods for the circumvention of these constraints, and the potential of the evolutionary modeling approach, are discussed.