Characterization of the Drosophila segment determination morphome

Multifaceted effects on even-skipped transcriptional dynamics upon Krüppel dosage changes

Although fluctuations in transcription factor (TF) dosage are often well tolerated, TF dosage modulation can change the target gene expression dynamics and result in significant non-lethal developmental phenotypes. Using MS2/MCP-mediated quantitative live imaging in early Drosophila embryos, we analyzed how changing levels of the gap gene Krüppel (Kr) affects transcriptional dynamics of the pair-rule gene even-skipped (eve). Halving the Kr dosage leads to a transient posterior expansion of the eve stripe 2 and an anterior shift of stripe 5. Surprisingly, the most significant changes are observed in eve stripes 3 and 4, the enhancers of which do not contain Kr-binding sites. In Kr heterozygous embryos, both stripes 3 and 4 display narrower widths, anteriorly shifted boundaries and reduced mRNA production levels. We show that Kr dosage indirectly affects stripe 3 and 4 dynamics by modulating other gap gene dynamics. We quantitatively correlate moderate body segment phenotypes of Kr heterozygotes with spatiotemporal changes in eve expression. Our results indicate that nonlinear relationships between TF dosage and phenotypes underlie direct TF-DNA and indirect TF-TF interactions.

Global repression by tailless during segmentation

The orphan nuclear receptor Tailless (Tll) exhibits conserved roles in brain formation and maintenance that are shared, for example, with vertebrate orthologous forms (Tlx). However, the early expression of tll in two gap domains in the segmentation cascade of Drosophila is unusual even for most other insects. Here we investigate tll regulation on pair-rule stripes. With ectopic misexpression of tll we detected unexpected repression of almost all pair-rule stripes of hairy (h), even-skipped (eve), runt (run), and fushi-tarazu (ftz). Examining Tll embryonic ChIP-chip data with regions mapped as Cis-Regulatory Modules (CRMs) of pair-rule stripes we verified Tll interactions to these regions. With the ChIP-chip data we also verified Tll interactions to the CRMs of gap domains and in the misexpression assay, Tll-mediated repression on Kruppel (Kr), kni (kni) and giant (gt) according to their differential sensitivity to Tll. These results with gap genes confirmed previous data from the literature and argue against indirect repression roles of Tll in the striped pattern. Moreover, the prediction of Tll binding sites in the CRMs of eve stripes and the mathematical modeling of their removal using an experimentally validated theoretical framework shows effects on eve stripes compatible with the absence of a repressor binding to the CRMs. In addition, modeling increased tll levels in the embryo results in the differential repression of eve stripes, agreeing well with the results of the misexpression assay. In genetic assays we investigated eve 5, that is strongly repressed by the ectopic domain and representative of more central stripes not previously implied to be under direct regulation of tll. While this stripe is little affected in tll-, its posterior border is expanded in gt- but detected with even greater expansion in gt-;tll-. We end up by discussing tll with key roles in combinatorial repression mechanisms to contain the expression of medial patterns of the segmentation cascade in the extremities of the embryo.

Scale invariance in early embryonic development

The body plan of the fruit fly is determined by the expression of just a handful of genes. We show that the spatial patterns of expression for several of these genes scale precisely with the size of the embryo. Concretely, discrete positional markers such as the peaks in striped patterns have absolute positions along the anterior-posterior axis that are proportional to embryo length, with better than 1% accuracy. Further, the information (in bits) that graded patterns of expression provide about position can be decomposed into information about fractional or scaled position and information about absolute position or embryo length; all of the available information is about scaled position, again with ~1% accuracy. These observations suggest that the underlying genetic network exhibits scale invariance in a deeper mathematical sense. Taking this mathematical statement seriously requires that the network dynamics have a zero mode, which connects to many other observations on this system.

Precisely timed regulation of enhancer activity defines the binary expression pattern of Fushi tarazu in the Drosophila embryo

The genes that drive development each typically have many different enhancers. Properly coordinating the action of these different enhancers is crucial to correctly specifying cell-fate decisions, yet it remains poorly understood how their activity is choregraphed in time. To shed light on this question, we used recently developed single-cell live imaging tools to dissect the regulation of Fushi tarazu (Ftz) in Drosophila melanogaster embryos. Ftz is a transcription factor that is expressed in asymmetric stripes by two distinct enhancers: autoregulatory and zebra. The anterior edge of each stripe needs to be sharply defined to specify essential lineage boundaries. Here, we tracked how boundary cells commit to either a high-Ftz or low-Ftz fate by measuring Ftz protein traces in real time and simultaneously quantifying transcription from the endogenous locus and individual enhancers. This revealed that the autoregulatory enhancer does not establish this fate choice. Instead, it perpetuates the decision defined by zebra. This is contrary to the prevailing view that autoregulation drives the fate decision by causing bi-stable Ftz expression. Furthermore, we showed that the autoregulatory enhancer is not activated based on a Ftz-concentration threshold but through a timing-based mechanism. We hypothesize that this is regulated by several ubiquitously expressed pioneer-like transcription factors, which have recently been shown to act as timers in the embryo. Our work provides new insight into how precisely timed enhancer activity can directly regulate the dynamics of gene regulatory networks, which may be a general mechanism for ensuring that embryogenesis runs like clockwork.

Anterior-posterior patterning of segments in Anopheles stephensi offers insights into the transition from sequential to simultaneous segmentation in holometabolous insects

The gene regulatory network for segmentation in arthropods offers valuable insights into how networks evolve owing to the breadth of species examined and the extremely detailed knowledge gained in the model organism Drosophila melanogaster. These studies have shown that Drosophila's network represents a derived state that acquired changes to accelerate segment patterning, whereas most insects specify segments gradually as the embryo elongates. Such heterochronic shifts in segmentation have potentially emerged multiple times within holometabolous insects, resulting in many mechanistic variants and difficulties in isolating underlying commonalities that permit such shifts. Recent studies identified regulatory genes that work as timing factors, coordinating gene expression transitions during segmentation. These studies predict that changes in timing factor deployment explain shifts in segment patterning relative to other developmental events. Here, we test this hypothesis by characterizing the temporal and spatial expression of the pair-rule patterning genes in the malaria vector mosquito, Anopheles stephensi. This insect is a Dipteran (fly), like Drosophila, but represents an ancient divergence within this clade, offering a useful counterpart for evo-devo studies. In mosquito embryos, we observe anterior to posterior sequential addition of stripes for many pair-rule genes and a wave of broad timer gene expression across this axis. Segment polarity gene stripes are added sequentially in the wake of the timer gene wave and the full pattern is not complete until the embryo is fully elongated. This "progressive segmentation" mode in Anopheles displays commonalities with both Drosophila's rapid segmentation mechanism and sequential modes used by more distantly related insects.

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.

A timer gene network is spatially regulated by the terminal system in the Drosophila embryo

In insect embryos, anteroposterior patterning is coordinated by the sequential expression of the 'timer' genes caudal, Dichaete, and odd-paired, whose expression dynamics correlate with the mode of segmentation. In Drosophila, the timer genes are expressed broadly across much of the blastoderm, which segments simultaneously, but their expression is delayed in a small 'tail' region, just anterior to the hindgut, which segments during germband extension. Specification of the tail and the hindgut depends on the terminal gap gene tailless, but beyond this the regulation of the timer genes is poorly understood. We used a combination of multiplexed imaging, mutant analysis, and gene network modelling to resolve the regulation of the timer genes, identifying 11 new regulatory interactions and clarifying the mechanism of posterior terminal patterning. We propose that a dynamic Tailless expression gradient modulates the intrinsic dynamics of a timer gene cross-regulatory module, delineating the tail region and delaying its developmental maturation.

Data-driven modeling predicts gene regulatory network dynamics during the differentiation of multipotential hematopoietic progenitors

Cellular differentiation during hematopoiesis is guided by gene regulatory networks (GRNs) comprising transcription factors (TFs) and the effectors of cytokine signaling. Based largely on analyses conducted at steady state, these GRNs are thought to be organized as a hierarchy of bistable switches, with antagonism between Gata1 and PU.1 driving red- and white-blood cell differentiation. Here, we utilize transient gene expression patterns to infer the genetic architecture—the type and strength of regulatory interconnections—and dynamics of a twelve-gene GRN including key TFs and cytokine receptors. We trained gene circuits, dynamical models that learn genetic architecture, on high temporal-resolution gene-expression data from the differentiation of an inducible cell line into erythrocytes and neutrophils. The model is able to predict the consequences of gene knockout, knockdown, and overexpression experiments and the inferred interconnections are largely consistent with prior empirical evidence. The inferred genetic architecture is densely interconnected rather than hierarchical, featuring extensive cross-antagonism between genes from alternative lineages and positive feedback from cytokine receptors. The analysis of the dynamics of gene regulation in the model reveals that PU.1 is one of the last genes to be upregulated in neutrophil conditions and that the upregulation of PU.1 and other neutrophil genes is driven by Cebpa and Gfi1 instead. This model inference is confirmed in an independent single-cell RNA-Seq dataset from mouse bone marrow in which Cebpa and Gfi1 expression precedes the neutrophil-specific upregulation of PU.1 during differentiation. These results demonstrate that full PU.1 upregulation during neutrophil development involves regulatory influences extrinsic to the Gata1-PU.1 bistable switch. Furthermore, although there is extensive cross-antagonism between erythroid and neutrophil genes, it does not have a hierarchical structure. More generally, we show that the combination of high-resolution time series data and data-driven dynamical modeling can uncover the dynamics and causality of developmental events that might otherwise be obscured.

The supply of blood cells is replenished by the maturation of hematopoietic progenitor cells into different cell types. Which cell type a progenitor cell develops into is determined by a complex network of genes whose protein products directly or indirectly regulate each others’ expression and that of downstream genes characteristic of the cell type. We inferred the nature and causality of the regulatory connections in a 12-gene network known to affect the decision between erythrocyte and neutrophil cell fates using a predictive machine-learning approach. Our analysis showed that the overall architecture of the network is densely interconnected and not hierarchical. Furthermore, the model inferred that PU.1, considered a master regulator of all white-blood cell lineages, is upregulated during neutrophil development by two other proteins, Cebpa and Gfi1. We validated this prediction by showing that Cebpa and Gfi1 expression precedes that of PU.1 in single-cell gene expression data from mouse bone marrow. These results revise the architecture of the gene network and the causality of regulatory events guiding hematopoiesis. The results also show that combining machine learning approaches with time course data can help resolve causality during development.

Application of Domain- and Genotype-Specific Models to Infer Post-Transcriptional Regulation of Segmentation Gene Expression in Drosophila

Unlike transcriptional regulation, the post-transcriptional mechanisms underlying zygotic segmentation gene expression in early Drosophila embryo have been insufficiently investigated. Condition-specific post-transcriptional regulation plays an important role in the development of many organisms. Our recent study revealed the domain- and genotype-specific differences between mRNA and the protein expression of Drosophila hb, gt, and eve genes in cleavage cycle 14A. Here, we use this dataset and the dynamic mathematical model to recapitulate protein expression from the corresponding mRNA patterns. The condition-specific nonuniformity in parameter values is further interpreted in terms of possible post-transcriptional modifications. For hb expression in wild-type embryos, our results predict the position-specific differences in protein production. The protein synthesis rate parameter is significantly higher in hb anterior domain compared to the posterior domain. The parameter sets describing Gt protein dynamics in wild-type embryos and Kr mutants are genotype-specific. The spatial discrepancy between gt mRNA and protein posterior expression in Kr mutants is well reproduced by the whole axis model, thus rejecting the involvement of post-transcriptional mechanisms. Our models fail to describe the full dynamics of eve expression, presumably due to its complex shape and the variable time delays between mRNA and protein patterns, which likely require a more complex model. Overall, our modeling approach enables the prediction of regulatory scenarios underlying the condition-specific differences between mRNA and protein expression in early embryo.

Patterning with clocks and genetic cascades: Segmentation and regionalization of vertebrate versus insect body plans

Oscillatory and sequential processes have been implicated in the spatial patterning of many embryonic tissues. For example, molecular clocks delimit segmental boundaries in vertebrates and insects and mediate lateral root formation in plants, whereas sequential gene activities are involved in the specification of regional identities of insect neuroblasts, vertebrate neural tube, vertebrate limb, and insect and vertebrate body axes. These processes take place in various tissues and organisms, and, hence, raise the question of what common themes and strategies they share. In this article, we review 2 processes that rely on the spatial regulation of periodic and sequential gene activities: segmentation and regionalization of the anterior-posterior (AP) axis of animal body plans. We study these processes in species that belong to 2 different phyla: vertebrates and insects. By contrasting 2 different processes (segmentation and regionalization) in species that belong to 2 distantly related phyla (arthropods and vertebrates), we elucidate the deep logic of patterning by oscillatory and sequential gene activities. Furthermore, in some of these organisms (e.g., the fruit fly Drosophila), a mode of AP patterning has evolved that seems not to overtly rely on oscillations or sequential gene activities, providing an opportunity to study the evolution of pattern formation mechanisms.

The fushi tarazu zebra element is not required for Drosophila viability or fertility

Expression of genes in precisely controlled spatiotemporal patterns is essential for embryonic development. Much of our understanding of mechanisms regulating gene expression comes from the study of cis-regulatory elements (CREs) that direct expression of reporter genes in transgenic organisms. This reporter-transgene approach identifies genomic regions sufficient to drive expression but fails to provide information about quantitative and qualitative contributions to endogenous expression, although such conclusions are often inferred. Here we evaluated the endogenous function of a classic Drosophila CRE, the fushi tarazu (ftz) zebra element. ftz is a pair-rule segmentation gene expressed in seven stripes during embryogenesis, necessary for formation of alternate body segments. Reporter transgenes identified the promoter-proximal zebra element as a major driver of the seven ftz stripes. We generated a precise genomic deletion of the zebra element (ftzΔZ) to assess its role in the context of native chromatin and neighboring CREs, expecting large decreases in ftz seven-stripe expression. However, significant reduction in expression was found for only one stripe, ftz stripe 4, expressed at ∼25% of wild type levels in ftzΔZ homozygotes. Defects in corresponding regions of ftzΔZ mutants suggest this level of expression borders the threshold required to promote morphological segmentation. Further, we established true-breeding lines of homozygous ftzΔZ flies, demonstrating that the body segments missing in the mutants are not required for viability or fertility. These results highlight the different types of conclusions drawn from different experimental designs and emphasize the importance of examining transcriptional regulatory mechanisms in the context of the native genomic environment.

Quantitative Analysis of the Dynamics of Maternal Gradients in the Early Drosophila Embryo

Predetermination, formation, and maintenance of the primary morphogenetic gradient (bicoid, bcd) of the early Drosophila embryo involves many interrelated processes. Here we focus on the biological systems analysis of the bcd mRNA redistribution in an early embryo. The results of the quantitative analysis of experimental data, together with the results of their dynamic modeling, substantiate the role of active transport in the redistribution of the bcd mRNA. The role of the nonlinearity of degradation mechanisms in the mRNA pattern robustness is discussed.

Time and space in segmentation

Arthropod segmentation and vertebrate somitogenesis are leading fields in the experimental and theoretical interrogation of developmental patterning. However, despite the sophistication of current research, basic conceptual issues remain unresolved. These include: (i) the mechanistic origins of spatial organization within the segment addition zone (SAZ); (ii) the mechanistic origins of segment polarization; (iii) the mechanistic origins of axial variation; and (iv) the evolutionary origins of simultaneous patterning. Here, I explore these problems using coarse-grained models of cross-regulating dynamical processes. In the morphogenetic framework of a row of cells undergoing axial elongation, I simulate interactions between an 'oscillator', a 'switch' and up to three 'timers', successfully reproducing essential patterning behaviours of segmenting systems. By comparing the output of these largely cell-autonomous models to variants that incorporate positional information, I find that scaling relationships, wave patterns and patterning dynamics all depend on whether the SAZ is regulated by temporal or spatial information. I also identify three mechanisms for polarizing oscillator output, all of which functionally implicate the oscillator frequency profile. Finally, I demonstrate significant dynamical and regulatory continuity between sequential and simultaneous modes of segmentation. I discuss these results in the context of the experimental literature.

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.

Fully interpretable deep learning model of transcriptional control

Motivation

The universal expressibility assumption of Deep Neural Networks (DNNs) is the key motivation behind recent worksin the systems biology community to employDNNs to solve important problems in functional genomics and moleculargenetics. Typically, such investigations have taken a ‘black box’ approach in which the internal structure of themodel used is set purely by machine learning considerations with little consideration of representing the internalstructure of the biological system by the mathematical structure of the DNN. DNNs have not yet been applied to thedetailed modeling of transcriptional control in which mRNA production is controlled by the binding of specific transcriptionfactors to DNA, in part because such models are in part formulated in terms of specific chemical equationsthat appear different in form from those used in neural networks.

Results

In this paper, we give an example of a DNN whichcan model the detailed control of transcription in a precise and predictive manner. Its internal structure is fully interpretableand is faithful to underlying chemistry of transcription factor binding to DNA. We derive our DNN from asystems biology model that was not previously recognized as having a DNN structure. Although we apply our DNNto data from the early embryo of the fruit fly Drosophila, this system serves as a test bed for analysis of much larger datasets obtained by systems biology studies on a genomic scale. .

Availability and implementation

The implementation and data for the models used in this paper are in a zip file in the supplementary material.

Supplementary information

Supplementary data are available at Bioinformatics online.

Dynamic Modeling of Transcriptional Gene Regulatory Networks

Diverse cellular phenotypes are determined by groups of transcription factors (TFs) and other regulators that influence each others' gene expression, forming transcriptional gene regulatory networks (GRNs). In many biological contexts, especially in development and associated diseases, the expression of the genes in GRNs is not static but evolves in time. Modeling the dynamics of GRN state is an important approach for understanding diverse cellular phenomena such as cell-fate specification, pluripotency and cell-fate reprogramming, oncogenesis, and tissue regeneration. In this protocol, we describe how to model GRNs using a data-driven dynamic modeling methodology, gene circuits. Gene circuits do not require knowledge of the GRN topology and connectivity but instead learn them from training data, making them very general and applicable to diverse biological contexts. We utilize the MATLAB-based gene circuit modeling software Fast Inference of Gene Regulation (FIGR) for training the model on quantitative gene expression data and simulating the GRN. We describe all the steps in the modeling life cycle, from formulating the model, training the model using FIGR, simulating the GRN, to analyzing and interpreting the model output. This protocol highlights these steps with the example of a dynamical model of the gap gene GRN involved in Drosophila segmentation and includes example MATLAB statements for each step.

Kinetic sculpting of the seven stripes of the Drosophila even-skipped gene

We used live imaging to visualize the transcriptional dynamics of the Drosophila melanogaster even-skipped gene at single-cell and high-temporal resolution as its seven stripe expression pattern forms, and developed tools to characterize and visualize how transcriptional bursting varies over time and space. We find that despite being created by the independent activity of five enhancers, even-skipped stripes are sculpted by the same kinetic phenomena: a coupled increase of burst frequency and amplitude. By tracking the position and activity of individual nuclei, we show that stripe movement is driven by the exchange of bursting nuclei from the posterior to anterior stripe flanks. Our work provides a conceptual, theoretical and computational framework for dissecting pattern formation in space and time, and reveals how the coordinated transcriptional activity of individual nuclei shapes complex developmental patterns.

Transcriptional Enhancers in Drosophila

Key discoveries in Drosophila have shaped our understanding of cellular "enhancers." With a special focus on the fly, this chapter surveys properties of these adaptable cis-regulatory elements, whose actions are critical for the complex spatial/temporal transcriptional regulation of gene expression in metazoa. The powerful combination of genetics, molecular biology, and genomics available in Drosophila has provided an arena in which the developmental role of enhancers can be explored. Enhancers are characterized by diverse low- or high-throughput assays, which are challenging to interpret, as not all of these methods of identifying enhancers produce concordant results. As a model metazoan, the fly offers important advantages to comprehensive analysis of the central functions that enhancers play in gene expression, and their critical role in mediating the production of phenotypes from genotype and environmental inputs. A major challenge moving forward will be obtaining a quantitative understanding of how these cis-regulatory elements operate in development and disease.

Gene regulatory networks in Drosophila early embryonic development as a model for the study of the temporal identity of neuroblasts

Genes belonging to the "gap" and "gap-like" family constitute the best-studied gene regulatory networks (GRNs) in Drosophila embryogenesis. Gap genes are a core of two subnetworks controlling embryonic segmentation: (hunchback, hb; Krüppel, Kr; giant, gt; and knirps, kni) and (hb; Kr; pou-domain, pdm; and, probably, castor, cas). Of particular interest is that (hb, Kr, pdm, cas) also specifies the temporal identity of stem cells, neuroblasts, in Drosophila neurogenesis. This GRN controls the sequential differentiation of neuroblasts during the asymmetric cell division. In the last decades, modeling of the patterning of gene ensemble (hb, Kr, gt, kni) in segmentation was in the center of attention. We show that our previously published and extensively studied model at a certain level of external factors is able to reproduce temporal patterns of (hb, Kr, pdm, cas) in neurogenesis with minor evolutionary explicable modifications. This result testifies in favor of a hypothesis that the similarity of two gene ensembles active in segmentation and neurogenesis is a result of co-option of the network architecture in evolution from the common ancestral form. By means of the model dynamical analysis, it is shown that the establishment of the robust patterns in both systems could be explained in terms of the action of attractors in the gap gene dynamical system. We formulate the common principles underlying the robustness of both GRNs in segmentation and neurogenesis due to the similar functional organization of the gene ensembles as having the same evolutionary origin.

Evolution and Developmental System Drift in the Endoderm Gene Regulatory Network of Caenorhabditis and Other Nematodes

Developmental gene regulatory networks (GRNs) underpin metazoan embryogenesis and have undergone substantial modification to generate the tremendous variety of animal forms present on Earth today. The nematode Caenorhabditis elegans has been a central model for advancing many important discoveries in fundamental mechanistic biology and, more recently, has provided a strong base from which to explore the evolutionary diversification of GRN architecture and developmental processes in other species. In this short review, we will focus on evolutionary diversification of the GRN for the most ancient of the embryonic germ layers, the endoderm. Early embryogenesis diverges considerably across the phylum Nematoda. Notably, while some species deploy regulative development, more derived species, such as C. elegans, exhibit largely mosaic modes of embryogenesis. Despite the relatively similar morphology of the nematode gut across species, widespread variation has been observed in the signaling inputs that initiate the endoderm GRN, an exemplar of developmental system drift (DSD). We will explore how genetic variation in the endoderm GRN helps to drive DSD at both inter- and intraspecies levels, thereby resulting in a robust developmental system. Comparative studies using divergent nematodes promise to unveil the genetic mechanisms controlling developmental plasticity and provide a paradigm for the principles governing evolutionary modification of an embryonic GRN.

Multimodal transcriptional control of pattern formation in embryonic development

Predicting how interactions between transcription factors and regulatory DNA sequence dictate rates of transcription and, ultimately, drive developmental outcomes remains an open challenge in physical biology. Using stripe 2 of the even-skipped gene in Drosophila embryos as a case study, we dissect the regulatory forces underpinning a key step along the developmental decision-making cascade: the generation of cytoplasmic mRNA patterns via the control of transcription in individual cells. Using live imaging and computational approaches, we found that the transcriptional burst frequency is modulated across the stripe to control the mRNA production rate. However, we discovered that bursting alone cannot quantitatively recapitulate the formation of the stripe and that control of the window of time over which each nucleus transcribes even-skipped plays a critical role in stripe formation. Theoretical modeling revealed that these regulatory strategies (bursting and the time window) respond in different ways to input transcription factor concentrations, suggesting that the stripe is shaped by the interplay of 2 distinct underlying molecular processes.

Evolution of larval segment position across 12 Drosophila species

Many developmental traits that are critical to the survival of the organism are also robust. These robust traits are resistant to phenotypic change in the face of variation. This presents a challenge to evolution. In this article, we asked whether and how a well‐established robust trait, Drosophila segment patterning, changed over the evolutionary history of the genus. We compared segment position scaled to body length at the first‐instar larval stage among 12 Drosophila species. We found that relative segment position has changed many times across the phylogeny. Changes were frequent, but primarily small in magnitude. Phylogenetic analysis demonstrated that rates of change in segment position are variable along the Drosophila phylogenetic tree, and that these changes can occur in short evolutionary timescales. Correlation between position shifts of segments decreased as the distance between two segments increased, suggesting local control of segment position. The posterior‐most abdominal segment showed the highest magnitude of change on average, had the highest rate of evolution between species, and appeared to be evolving more independently as compared to the rest of the segments. This segment was exceptionally elongated in the cactophilic species in our dataset, raising questions as to whether this change may be adaptive.

Dynamic positional information: Patterning mechanism versus precision in gradient-driven systems

There is much talk about information in biology. In developmental biology, this takes the form of "positional information," especially in the context of morphogen-based pattern formation. Unfortunately, the concept of "information" is rarely defined in any precise manner. Here, we provide two alternative interpretations of "positional information," and examine the complementary meanings and uses of each concept. Positional information defined as Shannon information helps us understand decoding and error propagation in patterning systems. General relativistic positional information, in contrast, provides a metric to assess the output of pattern-forming mechanisms. Both interpretations provide powerful conceptual tools that do not compete, but are best used in combination to gain a proper mechanistic understanding of robust patterning.

Classification-Based Inference of Dynamical Models of Gene Regulatory Networks

Cell-fate decisions during development are controlled by densely interconnected gene regulatory networks (GRNs) consisting of many genes. Inferring and predictively modeling these GRNs is crucial for understanding development and other physiological processes. Gene circuits, coupled differential equations that represent gene product synthesis with a switch-like function, provide a biologically realistic framework for modeling the time evolution of gene expression. However, their use has been limited to smaller networks due to the computational expense of inferring model parameters from gene expression data using global non-linear optimization. Here we show that the switch-like nature of gene regulation can be exploited to break the gene circuit inference problem into two simpler optimization problems that are amenable to computationally efficient supervised learning techniques. We present FIGR (Fast Inference of Gene Regulation), a novel classification-based inference approach to determining gene circuit parameters. We demonstrate FIGR’s effectiveness on synthetic data generated from random gene circuits of up to 50 genes as well as experimental data from the gap gene system of Drosophila melanogaster, a benchmark for inferring dynamical GRN models. FIGR is faster than global non-linear optimization by a factor of 600 and its computational complexity scales much better with GRN size. On a practical level, FIGR can accurately infer the biologically realistic gap gene network in under a minute on desktop-class hardware instead of requiring hours of parallel computing. We anticipate that FIGR would enable the inference of much larger biologically realistic GRNs than was possible before.

An in silico analysis of robust but fragile gene regulation links enhancer length to robustness

Organisms must ensure that expression of genes is directed to the appropriate tissues at the correct times, while simultaneously ensuring that these gene regulatory systems are robust to perturbation. This idea is captured by a mathematical concept called r-robustness, which says that a system is robust to a perturbation in up to r - 1 randomly chosen parameters. r-robustness implies that the biological system has a small number of sensitive parameters and that this number can be used as a robustness measure. In this work we use this idea to investigate the robustness of gene regulation using a sequence level model of the Drosophila melanogaster gene even-skipped. We consider robustness with respect to mutations of the enhancer sequence and with respect to changes of the transcription factor concentrations. We find that gene regulation is r-robust with respect to mutations in the enhancer sequence and identify a number of sensitive nucleotides. In both natural and in silico predicted enhancers, the number of nucleotides that are sensitive to mutation correlates negatively with the length of the sequence, meaning that longer sequences are more robust. The exact degree of robustness obtained is dependent not only on DNA sequence, but also on the local concentration of regulatory factors. We find that gene regulation can be remarkably sensitive to changes in transcription factor concentrations at the boundaries of expression features, while it is robust to perturbation elsewhere.

Arthropod segmentation

There is now compelling evidence that many arthropods pattern their segments using a clock-and-wavefront mechanism, analogous to that operating during vertebrate somitogenesis. In this Review, we discuss how the arthropod segmentation clock generates a repeating sequence of pair-rule gene expression, and how this is converted into a segment-polarity pattern by ‘timing factor’ wavefronts associated with axial extension. We argue that the gene regulatory network that patterns segments may be relatively conserved, although the timing of segmentation varies widely, and double-segment periodicity appears to have evolved at least twice. Finally, we describe how the repeated evolution of a simultaneous (Drosophila-like) mode of segmentation within holometabolan insects can be explained by heterochronic shifts in timing factor expression plus extensive pre-patterning of the pair-rule genes.

Modularity, criticality, and evolvability of a developmental gene regulatory network

The existence of discrete phenotypic traits suggests that the complex regulatory processes which produce them are functionally modular. These processes are usually represented by networks. Only modular networks can be partitioned into intelligible subcircuits able to evolve relatively independently. Traditionally, functional modularity is approximated by detection of modularity in network structure. However, the correlation between structure and function is loose. Many regulatory networks exhibit modular behaviour without structural modularity. Here we partition an experimentally tractable regulatory network—the gap gene system of dipteran insects—using an alternative approach. We show that this system, although not structurally modular, is composed of dynamical modules driving different aspects of whole-network behaviour. All these subcircuits share the same regulatory structure, but differ in components and sensitivity to regulatory interactions. Some subcircuits are in a state of criticality, while others are not, which explains the observed differential evolvability of the various expression features in the system.

ATAC-seq reveals regional differences in enhancer accessibility during the establishment of spatial coordinates in the Drosophila blastoderm

Establishment of spatial coordinates during Drosophila embryogenesis relies on differential regulatory activity of axis patterning enhancers. Concentration gradients of activator and repressor transcription factors (TFs) provide positional information to each enhancer, which in turn promotes transcription of a target gene in a specific spatial pattern. However, the interplay between an enhancer regulatory activity and its accessibility as determined by local chromatin organization is not well understood. We profiled chromatin accessibility with ATAC-seq in narrow, genetically tagged domains along the antero-posterior axis in the Drosophila blastoderm. We demonstrate that one-quarter of the accessible genome displays significant regional variation in its ATAC-seq signal immediately after zygotic genome activation. Axis patterning enhancers are enriched among the most variable intervals, and their accessibility changes correlate with their regulatory activity. In an embryonic domain where an enhancer receives a net activating TF input and promotes transcription, it displays elevated accessibility in comparison to a domain where it receives a net repressive input. We propose that differential accessibility is a signature of patterning cis-regulatory elements in the Drosophila blastoderm and discuss potential mechanisms by which accessibility of enhancers may be modulated by activator and repressor TFs.

Optimal Decoding of Cellular Identities in a Genetic Network

In developing organisms, spatially prescribed cell identities are thought to be determined by the expression levels of multiple genes. Quantitative tests of this idea, however, require a theoretical framework capable of exposing the rules and precision of cell specification over developmental time. We use the gap gene network in the early fly embryo as an example to show how expression levels of the four gap genes can be jointly decoded into an optimal specification of position with 1% accuracy. The decoder correctly predicts, with no free parameters, the dynamics of pair-rule expression patterns at different developmental time points and in various mutant backgrounds. Precise cellular identities are thus available at the earliest stages of development, contrasting the prevailing view of positional information being slowly refined across successive layers of the patterning network. Our results suggest that developmental enhancers closely approximate a mathematically optimal decoding strategy.

Quantitative analysis reveals genotype- and domain- specific differences between mRNA and protein expression of segmentation genes in Drosophila

In many biological systems gene expression at mRNA and protein levels is not identical. Rigorous comparison of such differences on a spatio-temporal scale is still not feasible by high-throughput transcriptomic and proteomic analyses of early embryo development. Here, we characterize differences between mRNA and protein expression of Drosophila segmentation genes at the level of individual gene expression domains. We obtained quantitative imaging data on expression of gap genes gt and hb and pair-rule gene eve for Drosophila wild type embryos, Kr null mutants and Kr+/Kr- heterozygotes. To compare mRNA and protein expression we use several criteria including difference in amplitude and positions of expression domains, pattern shape and positional variability. For a number of gene expression domains we show examples where protein expression does not repeat mRNA expression even after a temporal delay. We calculated time delays between eve pattern formation at the level of mRNA and protein for wild type embryos, Kr mutants and Kr+/Kr- heterozygotes. We detect that in wild type embryos, the amplitudes of eve stripes 3 and 7 do not differ significantly at the level of mRNA, however, stripe 3 is higher than stripe 7 at the protein level. We further show that hb mRNA and protein expression in both anterior and posterior domains significantly differs at specific time points. The formation of hb PS4 stripe at the mRNA level proceeds five times faster than at the level of protein. With regard to spatial expression, we show that the offset between posterior gt mRNA and protein domains is much larger in Kr mutants than in wild type embryos and heterozygotes. Finally, we analyze differences in positional variability of eve stripe 7 expression in Kr mutants and Kr+/Kr- heterozygotes at the level of mRNA and protein. These results enable further perspectives to uncover mechanisms underlying discrepancies between mRNA and protein expression in early embryo.

Lessons and perspectives for applications of stochastic models in biological and cancer research

The effects of randomness, an unavoidable feature of intracellular environments, are observed at higher hierarchical levels of living matter organization, such as cells, tissues, and organisms. Additionally, the many compounds interacting as a well-orchestrated network of reactions increase the difficulties of assessing these systems using only experiments. This limitation indicates that elucidation of the dynamics of biological systems is a complex task that will benefit from the establishment of principles to help describe, categorize, and predict the behavior of these systems. The theoretical machinery already available, or ones to be discovered to help solve biological problems, might play an important role in these processes. Here, we demonstrate the application of theoretical tools by discussing some biological problems that we have approached mathematically: fluctuations in gene expression and cell proliferation in the context of loss of contact inhibition. We discuss the methods that have been employed to provide the reader with a biologically motivated phenomenological perspective of the use of theoretical methods. Finally, we end this review with a discussion of new research perspectives motivated by our results.

Two-Exponential Models of Gene Expression Patterns for Noisy Experimental Data

Spatial pattern formation of the primary anterior-posterior morphogenetic gradient of the transcription factor Bicoid (Bcd) has been studied experimentally and computationally for many years. Bcd specifies positional information for the downstream segmentation genes, affecting the fly body plan. More recently, a number of researchers have focused on the patterning dynamics of the underlying bcd messenger RNA (mRNA) gradient, which is translated into Bcd protein. New, more accurate techniques for visualizing bcd mRNA need to be combined with quantitative signal extraction techniques to reconstruct the bcd mRNA distribution. Here, we present a robust technique for quantifying gradients with a two-exponential model. This approach (1) has natural, biologically relevant parameters and (2) is invariant to linear transformations of the data arising due to variation in experimental conditions (e.g., microscope settings, nonspecific background signal). This allows us to quantify bcd mRNA gradient variability from embryo to embryo (important for studying the robustness of developmental regulatory networks); sort out atypical gradients; and classify embryos to developmental stage by quantitative gradient parameters.

Temporal dynamics of pair-rule stripes in living Drosophila embryos

Traditional studies of gene regulation in the Drosophila embryo centered primarily on the analysis of fixed tissues. These methods provided considerable insight into the spatial control of gene activity, such as the borders of eve stripe 2, but yielded only limited information about temporal dynamics. The advent of quantitative live-imaging and genome-editing methods permits the detailed examination of the temporal control of endogenous gene activity. Here, we present evidence that the pair-rule genes fushi tarazu (ftz) and even-skipped (eve) undergo dynamic shifts in gene expression. We observe sequential anterior shifting of the stripes along the anterior to posterior axis, with stripe 1 exhibiting movement before stripe 2 and the more posterior stripes. Conversely, posterior stripes shift over greater distances (two or three nuclei) than anterior stripes (one or two nuclei). Shifting of the ftz and eve stripes are slightly offset, with ftz moving faster than eve This observation is consistent with previous genetic studies, suggesting that eve is epistatic to ftz The precision of pair-rule temporal dynamics might depend on enhancer-enhancer interactions within the eve locus, since removal of the endogenous eve stripe 1 enhancer via CRISPR/Cas9 genome editing led to precocious and expanded expression of eve stripe 2. These observations raise the possibility of an added layer of complexity in the positional information encoded by the segmentation gene regulatory network.

Evidence for the temporal regulation of insect segmentation by a conserved sequence of transcription factors

Long-germ insects, such as the fruit fly Drosophila melanogaster, pattern their segments simultaneously, whereas short-germ insects, such as the beetle Tribolium castaneum, pattern their segments sequentially, from anterior to posterior. While the two modes of segmentation at first appear quite distinct, much of this difference might simply reflect developmental heterochrony. We now show here that, in both Drosophila and Tribolium, segment patterning occurs within a common framework of sequential Caudal, Dichaete, and Odd-paired expression. In Drosophila these transcription factors are expressed like simple timers within the blastoderm, while in Tribolium they form wavefronts that sweep from anterior to posterior across the germband. In Drosophila, all three are known to regulate pair-rule gene expression and influence the temporal progression of segmentation. We propose that these regulatory roles are conserved in short-germ embryos, and that therefore the changing expression profiles of these genes across insects provide a mechanistic explanation for observed differences in the timing of segmentation. In support of this hypothesis we demonstrate that Odd-paired is essential for segmentation in Tribolium, contrary to previous reports.

A damped oscillator imposes temporal order on posterior gap gene expression in Drosophila

Insects determine their body segments in two different ways. Short-germband insects, such as the flour beetle Tribolium castaneum, use a molecular clock to establish segments sequentially. In contrast, long-germband insects, such as the vinegar fly Drosophila melanogaster, determine all segments simultaneously through a hierarchical cascade of gene regulation. Gap genes constitute the first layer of the Drosophila segmentation gene hierarchy, downstream of maternal gradients such as that of Caudal (Cad). We use data-driven mathematical modelling and phase space analysis to show that shifting gap domains in the posterior half of the Drosophila embryo are an emergent property of a robust damped oscillator mechanism, suggesting that the regulatory dynamics underlying long- and short-germband segmentation are much more similar than previously thought. In Tribolium, Cad has been proposed to modulate the frequency of the segmentation oscillator. Surprisingly, our simulations and experiments show that the shift rate of posterior gap domains is independent of maternal Cad levels in Drosophila. Our results suggest a novel evolutionary scenario for the short- to long-germband transition and help explain why this transition occurred convergently multiple times during the radiation of the holometabolan insects.

Different insect species exhibit one of two distinct modes of determining their body segments (known as segmentation) during development: they either use a molecular oscillator to position segments sequentially, or they generate segments simultaneously through a hierarchical gene-regulatory cascade. The sequential mode is ancestral, while the simultaneous mode has been derived from it independently several times during evolution. In this paper, we present evidence suggesting that simultaneous segmentation also involves an oscillator in the posterior end of the embryo of the vinegar fly, Drosophila melanogaster. This surprising result indicates that both modes of segment determination are much more similar than previously thought. Such similarity provides an important step towards our understanding of the frequent evolutionary transitions observed between sequential and simultaneous segmentation.

Synthetic enhancer design by in silico compensatory evolution reveals flexibility and constraint in cis-regulation

BACKGROUND

Models that incorporate specific chemical mechanisms have been successful in describing the activity of Drosophila developmental enhancers as a function of underlying transcription factor binding motifs. Despite this, the minimum set of mechanisms required to reconstruct an enhancer from its constituent parts is not known. Synthetic biology offers the potential to test the sufficiency of known mechanisms to describe the activity of enhancers, as well as to uncover constraints on the number, order, and spacing of motifs.

RESULTS

Using a functional model and in silico compensatory evolution, we generated putative synthetic even-skipped stripe 2 enhancers with varying degrees of similarity to the natural enhancer. These elements represent the evolutionary trajectories of the natural stripe 2 enhancer towards two synthetic enhancers designed ab initio. In the first trajectory, spatially regulated expression was maintained, even after more than a third of binding sites were lost. In the second, sequences with high similarity to the natural element did not drive expression, but a highly diverged sequence about half the length of the minimal stripe 2 enhancer drove ten times greater expression. Additionally, homotypic clusters of Zelda or Stat92E motifs, but not Bicoid, drove expression in developing embryos.

CONCLUSIONS

Here, we present a functional model of gene regulation to test the degree to which the known transcription factors and their interactions explain the activity of the Drosophila even-skipped stripe 2 enhancer. Initial success in the first trajectory showed that the gene regulation model explains much of the function of the stripe 2 enhancer. Cases where expression deviated from prediction indicates that undescribed factors likely act to modulate expression. We also showed that activation driven Bicoid and Hunchback is highly sensitive to spatial organization of binding motifs. In contrast, Zelda and Stat92E drive expression from simple homotypic clusters, suggesting that activation driven by these factors is less constrained. Collectively, the 40 sequences generated in this work provides a powerful training set for building future models of gene regulation.

Conservation and variation in pair-rule gene expression and function in the intermediate-germ beetle Dermestes maculatus

A set of pair-rule (PR) segmentation genes (PRGs) promotes the formation of alternate body segments in Drosophila melanogaster Whereas Drosophila embryos are long-germ, with segments specified more or less simultaneously, most insects add segments sequentially as the germband elongates. The hide beetle Dermestes maculatus represents an intermediate between short- and long-germ development, ideal for comparative study of PRGs. We show that eight of nine Drosophila PRG orthologs are expressed in stripes in Dermestes Functional results parse these genes into three groups: Dmac-eve, -odd and -run play roles in both germband elongation and PR patterning; Dmac-slp and -prd function exclusively as complementary, classic PRGs, supporting functional decoupling of elongation and segment formation; and orthologs of ftz, ftz-f1, h and opa show more variable function in Dermestes and other species. While extensive cell death generally prefigured Dermestes PRG RNAi-mediated cuticle defects, an organized region with high mitotic activity near the margin of the segment addition zone is likely to have contributed to truncation of eve^RNAi embryos. Our results suggest general conservation of clock-like regulation of PR stripe addition in sequentially segmenting species while highlighting regulatory rewiring involving a subset of PRG orthologs.

Optimizing bicoid signal extraction

Signal extraction and analysis is of great importance, not only in fields such as economics and meteorology, but also in genetics and even biomedicine. There exists a range of parametric and nonparametric techniques which can perform signal extractions. However, the aim of this paper is to define a new approach for optimising signal extraction from bicoid gene expression profile. Having studied both parametric and nonparametric signal extraction techniques, we identified the lack of specific criteria enabling users to select the optimal signal extraction parameters. Exploiting the expression profile of bicoid gene, which is a maternal segmentation coordinate gene found in Drosophila melanogaster, we introduce a new approach for optimising the signal extraction using a nonparametric technique. The underlying criteria are based on the distribution of the residual, more specifically its skewness.

Translating natural genetic variation to gene expression in a computational model of the Drosophila gap gene regulatory network

Annotating the genotype-phenotype relationship, and developing a proper quantitative description of the relationship, requires understanding the impact of natural genomic variation on gene expression. We apply a sequence-level model of gap gene expression in the early development of Drosophila to analyze single nucleotide polymorphisms (SNPs) in a panel of natural sequenced D. melanogaster lines. Using a thermodynamic modeling framework, we provide both analytical and computational descriptions of how single-nucleotide variants affect gene expression. The analysis reveals that the sequence variants increase (decrease) gene expression if located within binding sites of repressors (activators). We show that the sign of SNP influence (activation or repression) may change in time and space and elucidate the origin of this change in specific examples. The thermodynamic modeling approach predicts non-local and non-linear effects arising from SNPs, and combinations of SNPs, in individual fly genotypes. Simulation of individual fly genotypes using our model reveals that this non-linearity reduces to almost additive inputs from multiple SNPs. Further, we see signatures of the action of purifying selection in the gap gene regulatory regions. To infer the specific targets of purifying selection, we analyze the patterns of polymorphism in the data at two phenotypic levels: the strengths of binding and expression. We find that combinations of SNPs show evidence of being under selective pressure, while individual SNPs do not. The model predicts that SNPs appear to accumulate in the genotypes of the natural population in a way biased towards small increases in activating action on the expression pattern. Taken together, these results provide a systems-level view of how genetic variation translates to the level of gene regulatory networks via combinatorial SNP effects.

Dynamic patterning by the Drosophila pair-rule network reconciles long-germ and short-germ segmentation

Drosophila segmentation is a well-established paradigm for developmental pattern formation. However, the later stages of segment patterning, regulated by the "pair-rule" genes, are still not well understood at the system level. Building on established genetic interactions, I construct a logical model of the Drosophila pair-rule system that takes into account the demonstrated stage-specific architecture of the pair-rule gene network. Simulation of this model can accurately recapitulate the observed spatiotemporal expression of the pair-rule genes, but only when the system is provided with dynamic "gap" inputs. This result suggests that dynamic shifts of pair-rule stripes are essential for segment patterning in the trunk and provides a functional role for observed posterior-to-anterior gap domain shifts that occur during cellularisation. The model also suggests revised patterning mechanisms for the parasegment boundaries and explains the aetiology of the even-skipped null mutant phenotype. Strikingly, a slightly modified version of the model is able to pattern segments in either simultaneous or sequential modes, depending only on initial conditions. This suggests that fundamentally similar mechanisms may underlie segmentation in short-germ and long-germ arthropods.

A sequence level model of an intact locus predicts the location and function of nonadditive enhancers

Metazoan gene expression is controlled through the action of long stretches of noncoding DNA that contain enhancers-shorter sequences responsible for controlling a single aspect of a gene's expression pattern. Models built on thermodynamics have shown how enhancers interpret protein concentration in order to determine specific levels of gene expression, but the emergent regulatory logic of a complete regulatory locus shows qualitative and quantitative differences from isolated enhancers. Such differences may arise from steric competition limiting the quantity of DNA that can simultaneously influence the transcription machinery. We incorporated this competition into a mechanistic model of gene regulation, generated efficient algorithms for this computation, and applied it to the regulation of Drosophila even-skipped (eve). This model finds the location of enhancers and identifies which factors control the boundaries of eve expression. This model predicts a new enhancer that, when assayed in vivo, drives expression in a non-eve pattern. Incorporation of chromatin accessibility eliminates this inconsistency.

Ancient role of ten-m/odz in segmentation and the transition from sequential to syncytial segmentation

Background

Until recently, mechanisms of segmentation established for Drosophila served as a paradigm for arthropod segmentation. However, with the discovery of gene expression waves in vertebrate segmentation, another paradigm based on oscillations linked to axial growth was established. The Notch pathway and hairy delay oscillator are basic components of this mechanism, as is the wnt pathway. With the establishment of oscillations during segmentation of the beetle Tribolium, a common segmentation mechanism may have been present in the last common ancestor of vertebrates and arthropods. However, the Notch pathway is not involved in segmentation of the initial Drosophila embryo. In arthropods, the engrailed, wingless pair has a much more conserved function in segmentation than most of the hierarchy established for Drosophila.

Results

Here, we work backwards from this conserved pair by discussing possible mechanisms which could have taken over the role of the Notch pathway. We propose a pivotal role for the large transmembrane protein Ten-m/Odz. Ten-m/Odz may have had an ancient role in cell-cell communication, parallel to the Notch and wnt pathways. The Ten-m protein binds to the membrane with properties which resemble other membrane-based biochemical oscillators.

Conclusion

We propose that such a simple transition could have formed the initial scaffold, on top of which the hierarchy, observed in the syncytium of dipterans, could have evolved.

Transcriptional bursting in Drosophila development: Stochastic dynamics of eve stripe 2 expression

Anterior-posterior (AP) body segmentation of the fruit fly (Drosophila) is first seen in the 7-stripe spatial expression patterns of the pair-rule genes, which regulate downstream genes determining specific segment identities. Regulation of pair-rule expression has been extensively studied for the even-skipped (eve) gene. Recent live imaging, of a reporter for the 2^ndeve stripe, has demonstrated the stochastic nature of this process, with ‘bursts’ in the number of RNA transcripts being made over time. We developed a stochastic model of the spatial and temporal expression of eve stripe 2 (binding by transcriptional activators (Bicoid and Hunchback proteins) and repressors (Giant and Krüppel proteins), transcriptional initiation and termination; with all rate parameters constrained by features of the experimental data) in order to analyze the noisy experimental time series and test hypotheses for how eve transcription is regulated. These include whether eve transcription is simply OFF or ON, with a single ON rate, or whether it proceeds by a more complex mechanism, with multiple ON rates. We find that both mechanisms can produce long (multi-minute) RNA bursts, but that the short-time (minute-to-minute) statistics of the data is indicative of eve being transcribed with at least two distinct ON rates, consistent with data on the joint activation of eve by Bicoid and Hunchback. We also predict distinct statistical signatures for cases in which eve is repressed (e.g. along the edges of the stripe) vs. cases in which activation is reduced (e.g. by mutagenesis of transcription factor binding sites). Fundamental developmental processes such as gene transcription are intrinsically noisy; our approach presents a new way to quantify and analyze time series data during developmental patterning in order to understand regulatory mechanisms and how they propagate noise and impact embryonic robustness.

Causality analysis detects the regulatory role of maternal effect genes in the early Drosophila embryo

In developmental studies, inferring regulatory interactions of segmentation genetic network play a vital role in unveiling the mechanism of pattern formation. As such, there exists an opportune demand for theoretical developments and new mathematical models which can result in a more accurate illustration of this genetic network. Accordingly, this paper seeks to extract the meaningful regulatory role of the maternal effect genes using a variety of causality detection techniques and to explore whether these methods can suggest a new analytical view to the gene regulatory networks. We evaluate the use of three different powerful and widely-used models representing time and frequency domain Granger causality and convergent cross mapping technique with the results being thoroughly evaluated for statistical significance. Our findings show that the regulatory role of maternal effect genes is detectable in different time classes and thereby the method is applicable to infer the possible regulatory interactions present among the other genes of this network.

Dynamic Maternal Gradients Control Timing and Shift-Rates for Drosophila Gap Gene Expression

Pattern formation during development is a highly dynamic process. In spite of this, few experimental and modelling approaches take into account the explicit time-dependence of the rules governing regulatory systems. We address this problem by studying dynamic morphogen interpretation by the gap gene network in Drosophila melanogaster. Gap genes are involved in segment determination during early embryogenesis. They are activated by maternal morphogen gradients encoded by bicoid (bcd) and caudal (cad). These gradients decay at the same time-scale as the establishment of the antero-posterior gap gene pattern. We use a reverse-engineering approach, based on data-driven regulatory models called gene circuits, to isolate and characterise the explicitly time-dependent effects of changing morphogen concentrations on gap gene regulation. To achieve this, we simulate the system in the presence and absence of dynamic gradient decay. Comparison between these simulations reveals that maternal morphogen decay controls the timing and limits the rate of gap gene expression. In the anterior of the embyro, it affects peak expression and leads to the establishment of smooth spatial boundaries between gap domains. In the posterior of the embryo, it causes a progressive slow-down in the rate of gap domain shifts, which is necessary to correctly position domain boundaries and to stabilise the spatial gap gene expression pattern. We use a newly developed method for the analysis of transient dynamics in non-autonomous (time-variable) systems to understand the regulatory causes of these effects. By providing a rigorous mechanistic explanation for the role of maternal gradient decay in gap gene regulation, our study demonstrates that such analyses are feasible and reveal important aspects of dynamic gene regulation which would have been missed by a traditional steady-state approach. More generally, it highlights the importance of transient dynamics for understanding complex regulatory processes in development.

Animal development is a highly dynamic process. Biochemical or environmental signals can cause the rules that shape it to change over time. We know little about the effects of such changes. For the sake of simplicity, we usually leave them out of our models and experimental assays. Here, we do exactly the opposite. We characterise precisely those aspects of pattern formation caused by changing signalling inputs to a gene regulatory network, the gap gene system of Drosophila melanogaster. Gap genes are involved in determining the body segments of flies and other insects during early development. Gradients of maternal morphogens activate the expression of the gap genes. These gradients are highly dynamic themselves, as they decay while being read out. We show that this decay controls the peak concentration of gap gene products, produces smooth boundaries of gene expression, and slows down the observed positional shifts of gap domains in the posterior of the embryo, thereby stabilising the spatial pattern. Our analysis demonstrates that the dynamics of gene regulation not only affect the timing, but also the positioning of gene expression. This suggests that we must pay closer attention to transient dynamic aspects of development than is currently the case.