FlyEx, the quantitative atlas on segmentation gene expression at cellular resolution

Dynamic regulation of eve stripe 2 expression reveals transcriptional bursts in living Drosophila embryos

We present the use of recently developed live imaging methods to examine the dynamic regulation of even-skipped (eve) stripe 2 expression in the precellular Drosophila embryo. Nascent transcripts were visualized via MS2 RNA stem loops. The eve stripe 2 transgene exhibits a highly dynamic pattern of de novo transcription, beginning with a broad domain of expression during nuclear cycle 12 (nc12), and progressive refinement during nc13 and nc14. The mature stripe 2 pattern is surprisingly transient, constituting just ∼15 min of the ∼90-min period of expression. Nonetheless, this dynamic transcription profile faithfully predicts the limits of the mature stripe visualized by conventional in situ detection methods. Analysis of individual transcription foci reveals intermittent bursts of de novo transcription, with duration cycles of 4-10 min. We discuss a multistate model of transcription regulation and speculate on its role in the dynamic repression of the eve stripe 2 expression pattern during development.

Bioimage Informatics in the context of Drosophila research

Modern biological research relies heavily on microscopic imaging. The advanced genetic toolkit of Drosophila makes it possible to label molecular and cellular components with unprecedented level of specificity necessitating the application of the most sophisticated imaging technologies. Imaging in Drosophila spans all scales from single molecules to the entire populations of adult organisms, from electron microscopy to live imaging of developmental processes. As the imaging approaches become more complex and ambitious, there is an increasing need for quantitative, computer-mediated image processing and analysis to make sense of the imagery. Bioimage Informatics is an emerging research field that covers all aspects of biological image analysis from data handling, through processing, to quantitative measurements, analysis and data presentation. Some of the most advanced, large scale projects, combining cutting edge imaging with complex bioimage informatics pipelines, are realized in the Drosophila research community. In this review, we discuss the current research in biological image analysis specifically relevant to the type of systems level image datasets that are uniquely available for the Drosophila model system. We focus on how state-of-the-art computer vision algorithms are impacting the ability of Drosophila researchers to analyze biological systems in space and time. We pay particular attention to how these algorithmic advances from computer science are made usable to practicing biologists through open source platforms and how biologists can themselves participate in their further development.

Quantitative modeling of a gene's expression from its intergenic sequence

Modeling a gene's expression from its intergenic locus and trans-regulatory context is a fundamental goal in computational biology. Owing to the distributed nature of cis-regulatory information and the poorly understood mechanisms that integrate such information, gene locus modeling is a more challenging task than modeling individual enhancers. Here we report the first quantitative model of a gene's expression pattern as a function of its locus. We model the expression readout of a locus in two tiers: 1) combinatorial regulation by transcription factors bound to each enhancer is predicted by a thermodynamics-based model and 2) independent contributions from multiple enhancers are linearly combined to fit the gene expression pattern. The model does not require any prior knowledge about enhancers contributing toward a gene's expression. We demonstrate that the model captures the complex multi-domain expression patterns of anterior-posterior patterning genes in the early Drosophila embryo. Altogether, we model the expression patterns of 27 genes; these include several gap genes, pair-rule genes, and anterior, posterior, trunk, and terminal genes. We find that the model-selected enhancers for each gene overlap strongly with its experimentally characterized enhancers. Our findings also suggest the presence of sequence-segments in the locus that would contribute ectopic expression patterns and hence were "shut down" by the model. We applied our model to identify the transcription factors responsible for forming the stripe boundaries of the studied genes. The resulting network of regulatory interactions exhibits a high level of agreement with known regulatory influences on the target genes. Finally, we analyzed whether and why our assumption of enhancer independence was necessary for the genes we studied. We found a deterioration of expression when binding sites in one enhancer were allowed to influence the readout of another enhancer. Thus, interference between enhancer activities was a possible factor necessitating enhancer independence in our model.

Ancestral resurrection of the Drosophila S2E enhancer reveals accessible evolutionary paths through compensatory change

Upstream regulatory sequences that control gene expression evolve rapidly, yet the expression patterns and functions of most genes are typically conserved. To address this paradox, we have reconstructed computationally and resurrected in vivo the cis-regulatory regions of the ancestral Drosophila eve stripe 2 element and evaluated its evolution using a mathematical model of promoter function. Our feed-forward transcriptional model predicts gene expression patterns directly from enhancer sequence. We used this functional model along with phylogenetics to generate a set of possible ancestral eve stripe 2 sequences for the common ancestors of 1) D. simulans and D. sechellia; 2) D. melanogaster, D. simulans, and D. sechellia; and 3) D. erecta and D. yakuba. These ancestral sequences were synthesized and resurrected in vivo. Using a combination of quantitative and computational analysis, we find clear support for functional compensation between the binding sites for Bicoid, Giant, and Krüppel over the course of 40-60 My of Drosophila evolution. We show that this compensation is driven by a coupling interaction between Bicoid activation and repression at the anterior and posterior border necessary for proper placement of the anterior stripe 2 border. A multiplicity of mechanisms for binding site turnover exemplified by Bicoid, Giant, and Krüppel sites, explains how rapid sequence change may occur while maintaining the function of the cis-regulatory element.

Reverse-engineering post-transcriptional regulation of gap genes in Drosophila melanogaster

Systems biology proceeds through repeated cycles of experiment and modeling. One way to implement this is reverse engineering, where models are fit to data to infer and analyse regulatory mechanisms. This requires rigorous methods to determine whether model parameters can be properly identified. Applying such methods in a complex biological context remains challenging. We use reverse engineering to study post-transcriptional regulation in pattern formation. As a case study, we analyse expression of the gap genes Krüppel, knirps, and giant in Drosophila melanogaster. We use detailed, quantitative datasets of gap gene mRNA and protein expression to solve and fit a model of post-transcriptional regulation, and establish its structural and practical identifiability. Our results demonstrate that post-transcriptional regulation is not required for patterning in this system, but is necessary for proper control of protein levels. Our work demonstrates that the uniqueness and specificity of a fitted model can be rigorously determined in the context of spatio-temporal pattern formation. This greatly increases the potential of reverse engineering for the study of development and other, similarly complex, biological processes.

The analysis of pattern-forming gene networks is largely focussed on transcriptional regulation. However, post-transcriptional events, such as translation and regulation of protein stability also play important roles in the establishment of protein expression patterns and levels. In this study, we use a reverse-engineering approach—fitting mathematical models to quantitative expression data—to analyse post-transcriptional regulation of the Drosophila gap genes Krüppel, knirps and giant, involved in segment determination during early embryogenesis. Rigorous fitting requires us to establish whether our models provide a robust and unique solution. We demonstrate, for the first time, that this can be done in the context of a complex spatio-temporal regulatory system. This is an important methodological advance for reverse-engineering developmental processes. Our results indicate that post-transcriptional regulation is not required for pattern formation, but is necessary for proper regulation of gap protein levels. Specifically, we predict that translation rates must be tuned for rapid early accumulation, and protein stability must be increased for persistence of high protein levels at late stages of gap gene expression.

Evaluating thermodynamic models of enhancer activity on cellular resolution gene expression data

With the advent of high throughput sequencing and high resolution transcriptomic technologies, there exists today an unprecedented opportunity to understand gene regulation at a quantitative level. State of the art models of the relationship between regulatory sequence and gene expression have shown great promise, but also suffer from some major shortcomings. In this paper, we identify and address methodological challenges pertaining to quantitative modeling of gene expression from sequence, and test our models on the anterior-posterior patterning system in the Drosophila embryo. We first develop a framework to process cellular resolution three-dimensional gene expression data from the Drosophila embryo and create data sets on which quantitative models can be trained. Next we propose a new score, called 'weighted pattern generating potential' (w-PGP), to evaluate model predictions, and show its advantages over the two most common scoring schemes in use today. The model building exercise uses w-PGP as the evaluation score and adopts a systematic strategy to increase a model's complexity while guarding against over-fitting. Our model identifies three transcription factors--ZELDA, SLOPPY-PAIRED, and NUBBIN--that have not been previously incorporated in quantitative models of this system, as having significant regulatory influence. Finally, we show how fitting quantitative models on data sets comprising a handful of enhancers, as reported in earlier work, may lead to unreliable models.

Rearrangements of 2.5 kilobases of noncoding DNA from the Drosophila even-skipped locus define predictive rules of genomic cis-regulatory logic

Rearrangements of about 2.5 kilobases of regulatory DNA located 5' of the transcription start site of the Drosophila even-skipped locus generate large-scale changes in the expression of even-skipped stripes 2, 3, and 7. The most radical effects are generated by juxtaposing the minimal stripe enhancers MSE2 and MSE3 for stripes 2 and 3 with and without small "spacer" segments less than 360 bp in length. We placed these fusion constructs in a targeted transformation site and obtained quantitative expression data for these transformants together with their controlling transcription factors at cellular resolution. These data demonstrated that the rearrangements can alter expression levels in stripe 2 and the 2-3 interstripe by a factor of more than 10. We reasoned that this behavior would place tight constraints on possible rules of genomic cis-regulatory logic. To find these constraints, we confronted our new expression data together with previously obtained data on other constructs with a computational model. The model contained representations of thermodynamic protein-DNA interactions including steric interference and cooperative binding, short-range repression, direct repression, activation, and coactivation. The model was highly constrained by the training data, which it described within the limits of experimental error. The model, so constrained, was able to correctly predict expression patterns driven by enhancers for other Drosophila genes; even-skipped enhancers not included in the training set; stripe 2, 3, and 7 enhancers from various Drosophilid and Sepsid species; and long segments of even-skipped regulatory DNA that contain multiple enhancers. The model further demonstrated that elevated expression driven by a fusion of MSE2 and MSE3 was a consequence of the recruitment of a portion of MSE3 to become a functional component of MSE2, demonstrating that cis-regulatory "elements" are not elementary objects.

Lack of tailless leads to an increase in expression variability in Drosophila embryos

Developmental processes are robust, or canalised: dynamic patterns of gene expression across space and time are regulated reliably and precisely in the presence of genetic and environmental perturbations. It remains unclear whether canalisation relies on specific regulatory factors (such as heat-shock proteins), or whether it is based on more general redundancy and distributed robustness at the network level. The latter explanation implies that mutations in many regulatory factors should exhibit loss of canalisation. Here, we present a quantitative characterisation of segmentation gene expression patterns in mutants of the terminal gap gene tailless (tll) in Drosophila melanogaster. Our analysis provides new insights into the dynamic mechanisms underlying gap gene regulation, and reveals significantly increased variability of gene expression in the mutant compared to the wild-type background. We show that both position and timing of posterior segmentation gene expression domains vary strongly from embryo-to-embryo in tll mutants. This variability must be caused by a vulnerability in the regulatory system which is hidden or buffered in the wild-type, but becomes uncovered by the deletion of tll. Our analysis provides evidence that loss of canalisation in mutants could be more widespread than previously thought.

Quantitative dynamics and increased variability of segmentation gene expression in the Drosophila Krüppel and knirps mutants

Here we characterize the response of the Drosophila segmentation system to mutations in two gap genes, Kr and kni, in the form of single or double homozygotes and single heterozygotes. Segmentation gene expression in these genotypes was quantitatively monitored with cellular resolution in space and 6.5 to 13min resolution in time. As is the case with wild type, we found that gene expression domains in the posterior portion of the embryo shift to the anterior over time. In certain cases, such as the gt posterior domain in Kr mutants, the shifts are significantly larger than is seen in wild type embryos. We also investigated the effects of Kr and kni on the variability of gene expression. Mutations often produce variable phenotypes, and it is well known that the cuticular phenotype of Kr mutants is variable. We sought to understand the molecular basis of this effect. We find that throughout cycle 14A the relative levels of eve and ftz expression in stripes 2 and 3 are variable among individual embryos. Moreover, in Kr and kni mutants, unlike wild type, the variability in positioning of the posterior Hb domain and eve stripe 7 is not decreased or filtered with time. The posterior Gt domain in Kr mutants is highly variable at early times, but this variability decreases when this domain shifts in the anterior direction to the position of the neighboring Kni domain. In contrast to these findings, positional variability throughout the embryo does not decrease over time in double Kr;kni mutants. In heterozygotes the early expression patterns of segmentation genes resemble patterns seen in homozygous mutants but by the onset of gastrulation they become similar to the wild type patterns. Finally, we note that gene expression levels are reduced in Kr and kni mutant embryos and have a tendency to decrease over time. This is a surprising result in view of the role that mutual repression is thought to play in the gap gene system.

Accurate measurements of dynamics and reproducibility in small genetic networks

Quantification of gene expression has become a central tool for understanding genetic networks. In many systems, the only viable way to measure protein levels is by immunofluorescence, which is notorious for its limited accuracy. Using the early Drosophila embryo as an example, we show that careful identification and control of experimental error allows for highly accurate gene expression measurements. We generated antibodies in different host species, allowing for simultaneous staining of four Drosophila gap genes in individual embryos. Careful error analysis of hundreds of expression profiles reveals that less than ∼20% of the observed embryo-to-embryo fluctuations stem from experimental error. These measurements make it possible to extract not only very accurate mean gene expression profiles but also their naturally occurring fluctuations of biological origin and corresponding cross-correlations. We use this analysis to extract gap gene profile dynamics with ∼1 min accuracy. The combination of these new measurements and analysis techniques reveals a twofold increase in profile reproducibility owing to a collective network dynamics that relays positional accuracy from the maternal gradients to the pair-rule genes.

The importance of geometry in mathematical models of developing systems

Understanding the interaction between the spatial variation of extracellular signals and the interpretation of such signals in embryonic development is difficult without a mathematical model, but the inherent limitations of a model can have a profound impact on its utility. A central issue is the level of abstraction needed, and here we focus on the role of geometry in models and how the choice of the spatial dimension can influence the conclusions reached. A widely studied system in which the proper choice of geometry is critical is embryonic development of Drosophila melanogaster, and we discuss recent work in which 3D embryo-scale modeling is used to identify key modes of transport, analyze gap gene expression, and test BMP-mediated positive feedback mechanisms.

Medium-throughput processing of whole mount in situ hybridisation experiments into gene expression domains

Understanding the function and evolution of developmental regulatory networks requires the characterisation and quantification of spatio-temporal gene expression patterns across a range of systems and species. However, most high-throughput methods to measure the dynamics of gene expression do not preserve the detailed spatial information needed in this context. For this reason, quantification methods based on image bioinformatics have become increasingly important over the past few years. Most available approaches in this field either focus on the detailed and accurate quantification of a small set of gene expression patterns, or attempt high-throughput analysis of spatial expression through binary pattern extraction and large-scale analysis of the resulting datasets. Here we present a robust, “medium-throughput” pipeline to process in situ hybridisation patterns from embryos of different species of flies. It bridges the gap between high-resolution, and high-throughput image processing methods, enabling us to quantify graded expression patterns along the antero-posterior axis of the embryo in an efficient and straightforward manner. Our method is based on a robust enzymatic (colorimetric) in situ hybridisation protocol and rapid data acquisition through wide-field microscopy. Data processing consists of image segmentation, profile extraction, and determination of expression domain boundary positions using a spline approximation. It results in sets of measured boundaries sorted by gene and developmental time point, which are analysed in terms of expression variability or spatio-temporal dynamics. Our method yields integrated time series of spatial gene expression, which can be used to reverse-engineer developmental gene regulatory networks across species. It is easily adaptable to other processes and species, enabling the in silico reconstitution of gene regulatory networks in a wide range of developmental contexts.

Modeling of gap gene expression in Drosophila Kruppel mutants

The segmentation gene network in Drosophila embryo solves the fundamental problem of embryonic patterning: how to establish a periodic pattern of gene expression, which determines both the positions and the identities of body segments. The gap gene network constitutes the first zygotic regulatory tier in this process. Here we have applied the systems-level approach to investigate the regulatory effect of gap gene Kruppel (Kr) on segmentation gene expression. We acquired a large dataset on the expression of gap genes in Kr null mutants and demonstrated that the expression levels of these genes are significantly reduced in the second half of cycle 14A. To explain this novel biological result we applied the gene circuit method which extracts regulatory information from spatial gene expression data. Previous attempts to use this formalism to correctly and quantitatively reproduce gap gene expression in mutants for a trunk gap gene failed, therefore here we constructed a revised model and showed that it correctly reproduces the expression patterns of gap genes in Kr null mutants. We found that the remarkable alteration of gap gene expression patterns in Kr mutants can be explained by the dynamic decrease of activating effect of Cad on a target gene and exclusion of Kr gene from the complex network of gap gene interactions, that makes it possible for other interactions, in particular, between hb and gt, to come into effect. The successful modeling of the quantitative aspects of gap gene expression in mutant for the trunk gap gene Kr is a significant achievement of this work. This result also clearly indicates that the oversimplified representation of transcriptional regulation in the previous models is one of the reasons for unsuccessful attempts of mutant simulations.

Systems biology is aimed to develop an understanding of biological function or process as a system of interacting components. Here we apply the systems-level approach to understand how the blueprints for segments in the fruit fly Drosophila embryo arise. We obtain gene expression data and use the gene circuits method which allow us to reconstruct the segment determination process in the computer. To understand the system we need not only to describe it in detail, but also to comprehend what happens when certain stimuli or disruptions occur. Previous attempts to model segmentation gene expression patterns in a mutant for a trunk gap gene were unsuccessful. Here we describe the extension of the model that allows us to solve this problem in the context of Kruppel (Kr) gene. We show that remarkable alteration of gap gene expression patterns in Kr mutants can be explained by dynamic decrease of the activating effect of Cad on a target gene and exclusion of Kr from the complex network of gap gene interactions, that makes it possible for other interactions, in particular between hb and gt, to come into effect.

Efficient reverse-engineering of a developmental gene regulatory network

Understanding the complex regulatory networks underlying development and evolution of multi-cellular organisms is a major problem in biology. Computational models can be used as tools to extract the regulatory structure and dynamics of such networks from gene expression data. This approach is called reverse engineering. It has been successfully applied to many gene networks in various biological systems. However, to reconstitute the structure and non-linear dynamics of a developmental gene network in its spatial context remains a considerable challenge. Here, we address this challenge using a case study: the gap gene network involved in segment determination during early development of Drosophila melanogaster. A major problem for reverse-engineering pattern-forming networks is the significant amount of time and effort required to acquire and quantify spatial gene expression data. We have developed a simplified data processing pipeline that considerably increases the throughput of the method, but results in data of reduced accuracy compared to those previously used for gap gene network inference. We demonstrate that we can infer the correct network structure using our reduced data set, and investigate minimal data requirements for successful reverse engineering. Our results show that timing and position of expression domain boundaries are the crucial features for determining regulatory network structure from data, while it is less important to precisely measure expression levels. Based on this, we define minimal data requirements for gap gene network inference. Our results demonstrate the feasibility of reverse-engineering with much reduced experimental effort. This enables more widespread use of the method in different developmental contexts and organisms. Such systematic application of data-driven models to real-world networks has enormous potential. Only the quantitative investigation of a large number of developmental gene regulatory networks will allow us to discover whether there are rules or regularities governing development and evolution of complex multi-cellular organisms.

Mechanisms of developmental robustness

We present a review of noise buffering mechanisms responsible for developmental robustness. We focus on functions of chaperone Hsp90, miRNA, and cross-regulation of gap genes in Drosophila. The noise buffering mechanisms associated with these functions represent specific examples of the developmental canalization, reducing the phenotypical variability in presence of either genetic or environmental perturbations. We demonstrate that robustness often appears as a function of a network of interacting elements and that the system level approach is needed to understand the mechanisms of noise filtering.

Gaussian process modelling for bicoid mRNA regulation in spatio-temporal Bicoid profile

MOTIVATION

Bicoid protein molecules, translated from maternally provided bicoid mRNA, establish a concentration gradient in Drosophila early embryonic development. There is experimental evidence that the synthesis and subsequent destruction of this protein is regulated at source by precise control of the stability of the maternal mRNA. Can we infer the driving function at the source from noisy observations of the spatio-temporal protein profile? We use non-parametric Gaussian process regression for modelling the propagation of Bicoid in the embryo and infer aspects of source regulation as a posterior function.

RESULTS

With synthetic data from a 1D diffusion model with a source simulated to model mRNA stability regulation, our results establish that the Gaussian process method can accurately infer the driving function and capture the spatio-temporal dynamics of embryonic Bicoid propagation. On real data from the FlyEx database, too, the reconstructed source function is indicative of stability regulation, but is temporally smoother than what we expected, partly due to the fact that the dataset is only partially observed. To be in line with recent thinking on the subject, we also analyse this model with a spatial gradient of maternal mRNA, rather than being fixed at only the anterior pole.

CONTACT

m.niranjan@southampton.ac.uk

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Gene network inference and visualization tools for biologists: application to new human transcriptome datasets

Gene regulatory networks inferred from RNA abundance data have generated significant interest, but despite this, gene network approaches are used infrequently and often require input from bioinformaticians. We have assembled a suite of tools for analysing regulatory networks, and we illustrate their use with microarray datasets generated in human endothelial cells. We infer a range of regulatory networks, and based on this analysis discuss the strengths and limitations of network inference from RNA abundance data. We welcome contact from researchers interested in using our inference and visualization tools to answer biological questions.

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.

Temporal coordination of gene networks by Zelda in the early Drosophila embryo

In past years, much attention has focused on the gene networks that regulate early developmental processes, but less attention has been paid to how multiple networks and processes are temporally coordinated. Recently the discovery of the transcriptional activator Zelda (Zld), which binds to CAGGTAG and related sequences present in the enhancers of many early-activated genes in Drosophila, hinted at a mechanism for how batteries of genes could be simultaneously activated. Here we use genome-wide binding and expression assays to identify Zld target genes in the early embryo with the goal of unraveling the gene circuitry regulated by Zld. We found that Zld binds to genes involved in early developmental processes such as cellularization, sex determination, neurogenesis, and pattern formation. In the absence of Zld, many target genes failed to be activated, while others, particularly the patterning genes, exhibited delayed transcriptional activation, some of which also showed weak and/or sporadic expression. These effects disrupted the normal sequence of patterning-gene interactions and resulted in highly altered spatial expression patterns, demonstrating the significance of a timing mechanism in early development. In addition, we observed prevalent overlap between Zld-bound regions and genomic "hotspot" regions, which are bound by many developmental transcription factors, especially the patterning factors. This, along with the finding that the most over-represented motif in hotspots, CAGGTA, is the Zld binding site, implicates Zld in promoting hotspot formation. We propose that Zld promotes timely and robust transcriptional activation of early-gene networks so that developmental events are coordinated and cell fates are established properly in the cellular blastoderm embryo.

The role of regulated mRNA stability in establishing bicoid morphogen gradient in Drosophila embryonic development

The Bicoid morphogen is amongst the earliest triggers of differential spatial pattern of gene expression and subsequent cell fate determination in the embryonic development of Drosophila. This maternally deposited morphogen is thought to diffuse in the embryo, establishing a concentration gradient which is sensed by downstream genes. In most model based analyses of this process, the translation of the bicoid mRNA is thought to take place at a fixed rate from the anterior pole of the embryo and a supply of the resulting protein at a constant rate is assumed. Is this process of morphogen generation a passive one as assumed in the modelling literature so far, or would available data support an alternate hypothesis that the stability of the mRNA is regulated by active processes? We introduce a model in which the stability of the maternal mRNA is regulated by being held constant for a length of time, followed by rapid degradation. With this more realistic model of the source, we have analysed three computational models of spatial morphogen propagation along the anterior-posterior axis: (a) passive diffusion modelled as a deterministic differential equation, (b) diffusion enhanced by a cytoplasmic flow term; and (c) diffusion modelled by stochastic simulation of the corresponding chemical reactions. Parameter estimation on these models by matching to publicly available data on spatio-temporal Bicoid profiles suggests strong support for regulated stability over either a constant supply rate or one where the maternal mRNA is permitted to degrade in a passive manner.

Mechanisms of gap gene expression canalization in the Drosophila blastoderm

BACKGROUND

Extensive variation in early gap gene expression in the Drosophila blastoderm is reduced over time because of gap gene cross regulation. This phenomenon is a manifestation of canalization, the ability of an organism to produce a consistent phenotype despite variations in genotype or environment. The canalization of gap gene expression can be understood as arising from the actions of attractors in the gap gene dynamical system.

RESULTS

In order to better understand the processes of developmental robustness and canalization in the early Drosophila embryo, we investigated the dynamical effects of varying spatial profiles of Bicoid protein concentration on the formation of the expression border of the gap gene hunchback. At several positions on the anterior-posterior axis of the embryo, we analyzed attractors and their basins of attraction in a dynamical model describing expression of four gap genes with the Bicoid concentration profile accounted as a given input in the model equations. This model was tested against a family of Bicoid gradients obtained from individual embryos. These gradients were normalized by two independent methods, which are based on distinct biological hypotheses and provide different magnitudes for Bicoid spatial variability. We showed how the border formation is dictated by the biological initial conditions (the concentration gradient of maternal Hunchback protein) being attracted to specific attracting sets in a local vicinity of the border. Different types of these attracting sets (point attractors or one dimensional attracting manifolds) define several possible mechanisms of border formation. The hunchback border formation is associated with intersection of the spatial gradient of the maternal Hunchback protein and a boundary between the attraction basins of two different point attractors. We demonstrated how the positional variability for hunchback is related to the corresponding variability of the basin boundaries. The observed reduction in variability of the hunchback gene expression can be accounted for by specific geometrical properties of the basin boundaries.

CONCLUSION

We clarified the mechanisms of gap gene expression canalization in early Drosophila embryos. These mechanisms were specified in the case of hunchback in well defined terms of the dynamical system theory.

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.

An atlas of gene regulatory networks reveals multiple three-gene mechanisms for interpreting morphogen gradients

Although >450 different topologies can achieve the same multicellular patterning function, they can be grouped into six main classes, which operate using different underlying dynamics.

Alternative designs for the same functions can therefore split into two types: (a) topology alterations that retain the same underlying dynamics and (b) alterations that utilize a completely different underlying dynamical mechanism.

This segregation of networks into distinct dynamical mechanisms can be revealed by the shape of the topology atlas itself.

Cell–cell communication is not usually part of the causal mechanism underlying a band-pass response during morphogen interpretation, but it can tune the result or increase robustness.

Understanding how gene regulatory networks (GRNs) achieve particular biological functions is a central question in systems biology. Systems biology promises to go beyond a case-by-case understanding of individual networks to map out the complete design space of mechanistic possibilities that underlie biological functions. Can such maps serve as useful theoretical frameworks in which to explore the general design principles for these functions? Towards addressing these questions, we created the first design space for a morphogen interpretation function.

In order to generate a design space for such a function, we enumerated all possible wiring designs of GRNs consisting of three genes and tested their ability to perform one particular morphogen interpretation function; stripe formation, as it represents a simplified form of the much studied French flag problem and is a commonly found gene expression pattern (Figure 1A). We found that only 5% of GRNs had the ability to generate a single stripe of gene expression when simulated with a fixed morphogen input in a one-dimensional model.

We hypothesized that the core mechanisms for producing the stripe of gene expression should be represented by topologies that contain only the necessary and sufficient gene–gene interactions for that function. Hence, we utilized the notions of complexity and neighborhood to generate a complexity atlas. GRNs of such an atlas (represented by nodes) are considered neighbors if they differ by a single gene–gene interaction (neighboring GRN nodes are connected by edges). Such a metagraph (graph of graphs) can then be reorganized using complexity (number of gene–gene interactions) to determine a GRNs position in the y axis, whereas GRNs are spaced in the x axis with the aim of reducing edge crossing (Figure 5A). This reorganization reveals a striking structure, where ‘stalactites' of complexity can be seen protruding from the bottom of the atlas. Each of these stalactites converges on a single ‘core' topology that by extensive analysis we find represents a distinct mechanism.

The mechanisms employ a diverse range of distinct space–time behaviors, and the underlying core topologies display design features such as modularity and feed-forward. We mapped the mechanisms to the complexity atlas by analyzing how each particular GRN of the atlas was working. The GRNs functioning via the different mechanisms are highlighted by the different colors in Figure 5A. Mechanisms thus occupy large regions of separated topology space, suggesting them to be discrete. Analyzing transitions between mechanisms through parameter space confirms this to be the case.

We find that three of the mechanisms are employed in real patterning systems, including both blastoderm patterning in Drosophila and mesoderm specification in Xenopus (Figure 5B). The remaining three mechanisms are thus candidates for employment in other patterning systems. We explored the performance features of these mechanisms, which suggest that some have features such as robustness to parameter variation that make them highly likely to be employed in particular patterning contexts.

Only one of the six-core mechanisms absolutely requires cell–cell communication for functionality, prompting us to predict that cell–cell communication will rarely be responsible for the basic dose response of morphogen interpretation networks. However, we show how cell–cell communication has an important role in robust stripe generation in the face of a noisy morphogen input and in fine tuning the quantitative details of stripe patterning.

In summary, the complexity atlas approach is an amendable approach to any system with a clear genotype–function relationship. We demonstrate how certain functions such as morphogen interpretation may have a range of potential solutions in contrast to previous studies that analyzed more constrained functions. Furthermore, we demonstrate how such an approach can be utilized to define a ‘design space' for a given biological function that describes the different mechanistic possibilities and how they relate to one another (Figure 5). Such a design space can be used practically as a guide to discern which patterning mechanisms are likely be at work in a particular context throwing up less intuitive possibilities with powerful performance features.

The interpretation of morphogen gradients is a pivotal concept in developmental biology, and several mechanisms have been proposed to explain how gene regulatory networks (GRNs) achieve concentration-dependent responses. However, the number of different mechanisms that may exist for cells to interpret morphogens, and the importance of design features such as feedback or local cell–cell communication, is unclear. A complete understanding of such systems will require going beyond a case-by-case analysis of real morphogen interpretation mechanisms and mapping out a complete GRN ‘design space.' Here, we generate a first atlas of design space for GRNs capable of patterning a homogeneous field of cells into discrete gene expression domains by interpreting a fixed morphogen gradient. We uncover multiple very distinct mechanisms distributed discretely across the atlas, thereby expanding the repertoire of morphogen interpretation network motifs. Analyzing this diverse collection of mechanisms also allows us to predict that local cell–cell communication will rarely be responsible for the basic dose-dependent response of morphogen interpretation networks.

[Studies of stability mechanisms of early embryonal development of fruit fly Drosophila]

Living organisms well adapt themselves to changes in the environment and are robust to potential damage such as mutations. The epigenetic mechanism whereby the suppression of phenotypic variation is achieved has been called canalization. This paper summarizes results of research that employed experimental and theoretical approaches to uncover the mechanisms of canalization of variation in expression of segmentation genes.

DEEP-differential evolution entirely parallel method for gene regulatory networks

The Differential Evolution Entirely Parallel (DEEP) method is applied to the biological data fitting problem. We introduce a new migration scheme, in which the best member of the branch substitutes the oldest member of the next branch that provides a high speed of the algorithm convergence. We analyze the performance and efficiency of the developed algorithm on a test problem of finding the regulatory interactions within the network of gap genes that control the development of early Drosophila embryo. The parameters of a set of nonlinear differential equations are determined by minimizing the total error between the model behavior and experimental observations. The age of the individuum is defined by the number of iterations this individuum survived without changes. We used a ring topology for the network of computational nodes. The computer codes are available upon request.

The gap gene network

Gap genes are involved in segment determination during the early development of the fruit fly Drosophila melanogaster as well as in other insects. This review attempts to synthesize the current knowledge of the gap gene network through a comprehensive survey of the experimental literature. I focus on genetic and molecular evidence, which provides us with an almost-complete picture of the regulatory interactions responsible for trunk gap gene expression. I discuss the regulatory mechanisms involved, and highlight the remaining ambiguities and gaps in the evidence. This is followed by a brief discussion of molecular regulatory mechanisms for transcriptional regulation, as well as precision and size-regulation provided by the system. Finally, I discuss evidence on the evolution of gap gene expression from species other than Drosophila. My survey concludes that studies of the gap gene system continue to reveal interesting and important new insights into the role of gene regulatory networks in development and evolution.

Image processing challenges in the creation of spatiotemporal gene expression atlases of developing embryos

To properly understand and model animal embryogenesis it is crucial to obtain detailed measurements, both in time and space, about their gene expression domains and cell dynamics. Such challenge has been confronted in recent years by a surge of atlases which integrate a statistically relevant number of different individuals to get robust, complete information about their spatiotemporal locations of gene patterns. This paper will discuss the fundamental image analysis strategies required to build such models and the most common problems found along the way. We also discuss the main challenges and future goals in the field.

Calibration and validation of a genetic regulatory network model describing the production of the protein Hunchback in Drosophila early development

We fit the parameters of a differential equations model describing the production of gap-gene proteins Hunchback and Knirps along the antero-posterior axis of the embryo of Drosophila. As initial data for the differential equations model, we take the antero-posterior distribution of the proteins Bicoid, Hunchback and Tailless at the beginning of cleavage cycle 14. We calibrate and validate the model with experimental data using single- and multi-objective evolutionary optimization techniques. In the multi-objective optimization technique, we compute the associated Pareto fronts. We analyze the cross regulation mechanism between the gap-genes protein pair Hunchback-Knirps and we show that the posterior distribution of Hunchback follow the experimental data if Hunchback is negatively regulated by the Huckebein protein. This approach enables to us predict the posterior localization on the embryo of the protein Huckebein, and to validate with the experimental data the genetic regulatory network responsible for the antero-posterior distribution of the gap-gene protein Hunchback. We discuss the importance of Pareto multi-objective optimization techniques in the calibration and validation of biological models.

HLH54F is required for the specification and migration of longitudinal gut muscle founders from the caudal mesoderm of Drosophila

HLH54F, the Drosophila ortholog of the vertebrate basic helix-loop-helix domain-encoding genes capsulin and musculin, is expressed in the founder cells and developing muscle fibers of the longitudinal midgut muscles. These cells descend from the posterior-most portion of the mesoderm, termed the caudal visceral mesoderm (CVM), and migrate onto the trunk visceral mesoderm prior to undergoing myoblast fusion and muscle fiber formation. We show that HLH54F expression in the CVM is regulated by a combination of terminal patterning genes and snail. We generated HLH54F mutations and show that this gene is crucial for the specification, migration and survival of the CVM cells and the longitudinal midgut muscle founders. HLH54F mutant embryos, larvae, and adults lack all longitudinal midgut muscles, which causes defects in gut morphology and integrity. The function of HLH54F as a direct activator of gene expression is exemplified by our analysis of a CVM-specific enhancer from the Dorsocross locus, which requires combined inputs from HLH54F and Biniou in a feed-forward fashion. We conclude that HLH54F is the earliest specific regulator of CVM development and that it plays a pivotal role in all major aspects of development and differentiation of this largely twist-independent population of mesodermal cells.

A software tool to model genetic regulatory networks. Applications to the modeling of threshold phenomena and of spatial patterning in Drosophila

We present a general methodology in order to build mathematical models of genetic regulatory networks. This approach is based on the mass action law and on the Jacob and Monod operon model. The mathematical models are built symbolically by the Mathematica software package GeneticNetworks. This package accepts as input the interaction graphs of the transcriptional activators and repressors of a biological process and, as output, gives the mathematical model in the form of a system of ordinary differential equations. All the relevant biological parameters are chosen automatically by the software. Within this framework, we show that concentration dependent threshold effects in biology emerge from the catalytic properties of genes and its associated conservation laws. We apply this methodology to the segment patterning in Drosophila early development and we calibrate the genetic transcriptional network responsible for the patterning of the gap gene proteins Hunchback and Knirps, along the antero-posterior axis of the Drosophila embryo. In this approach, the zygotically produced proteins Hunchback and Knirps do not diffuse along the antero-posterior axis of the embryo of Drosophila, developing a spatial pattern due to concentration dependent thresholds. This shows that patterning at the gap genes stage can be explained by the concentration gradients along the embryo of the transcriptional regulators.

Systems biology of embryogenesis

The development of a complete organism from a single cell involves extraordinarily complex orchestration of biological processes that vary intricately across space and time. Systems biology seeks to describe how all elements of a biological system interact in order to understand, model and ultimately predict aspects of emergent biological processes. Embryogenesis represents an extraordinary opportunity (and challenge) for the application of systems biology. Systems approaches have already been used successfully to study various aspects of development, from complex intracellular networks to four-dimensional models of organogenesis. Going forward, great advancements and discoveries can be expected from systems approaches applied to embryogenesis and developmental biology.

mRNA diffusion explains protein gradients in Drosophila early development

We propose a new model describing the production and the establishment of the stable gradient of the Bicoid protein along the antero-posterior axis of the embryo of Drosophila. In this model, we consider that bicoid mRNA diffuses along the antero-posterior axis of the embryo and the protein is produced in the ribosomes localized near the syncytial nuclei. Bicoid protein stays localized near the syncytial nuclei as observed in experiments. We calibrate the parameters of the mathematical model with experimental data taken during the cleavage stages 11-14 of the developing embryo of Drosophila. We obtain good agreement between the experimental and the model gradients, with relative errors in the range 5-8%. The inferred diffusion coefficient of bicoid mRNA is in the range 4.6 x 10(-12)-1.5 x 10(-11)m(2)s(-1), in agreement with the theoretical predictions and experimental measurements for the diffusion of macromolecules in the cytoplasm. We show that the model based on the mRNA diffusion hypothesis is consistent with the known observational data, supporting the recent experimental findings of the gradient of bicoid mRNA in Drosophila [Spirov et al. (2009). Development 136, 605-614].

Reverse engineering a gene network using an asynchronous parallel evolution strategy

BACKGROUND

The use of reverse engineering methods to infer gene regulatory networks by fitting mathematical models to gene expression data is becoming increasingly popular and successful. However, increasing model complexity means that more powerful global optimisation techniques are required for model fitting. The parallel Lam Simulated Annealing (pLSA) algorithm has been used in such approaches, but recent research has shown that island Evolutionary Strategies can produce faster, more reliable results. However, no parallel island Evolutionary Strategy (piES) has yet been demonstrated to be effective for this task.

RESULTS

Here, we present synchronous and asynchronous versions of the piES algorithm, and apply them to a real reverse engineering problem: inferring parameters in the gap gene network. We find that the asynchronous piES exhibits very little communication overhead, and shows significant speed-up for up to 50 nodes: the piES running on 50 nodes is nearly 10 times faster than the best serial algorithm. We compare the asynchronous piES to pLSA on the same test problem, measuring the time required to reach particular levels of residual error, and show that it shows much faster convergence than pLSA across all optimisation conditions tested.

CONCLUSIONS

Our results demonstrate that the piES is consistently faster and more reliable than the pLSA algorithm on this problem, and scales better with increasing numbers of nodes. In addition, the piES is especially well suited to further improvements and adaptations: Firstly, the algorithm's fast initial descent speed and high reliability make it a good candidate for being used as part of a global/local search hybrid algorithm. Secondly, it has the potential to be used as part of a hierarchical evolutionary algorithm, which takes advantage of modern multi-core computing architectures.

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.

Gene circuit analysis of the terminal gap gene huckebein

The early embryo of Drosophila melanogaster provides a powerful model system to study the role of genes in pattern formation. The gap gene network constitutes the first zygotic regulatory tier in the hierarchy of the segmentation genes involved in specifying the position of body segments. Here, we use an integrative, systems-level approach to investigate the regulatory effect of the terminal gap gene huckebein (hkb) on gap gene expression. We present quantitative expression data for the Hkb protein, which enable us to include hkb in gap gene circuit models. Gap gene circuits are mathematical models of gene networks used as computational tools to extract regulatory information from spatial expression data. This is achieved by fitting the model to gap gene expression patterns, in order to obtain estimates for regulatory parameters which predict a specific network topology. We show how considering variability in the data combined with analysis of parameter determinability significantly improves the biological relevance and consistency of the approach. Our models are in agreement with earlier results, which they extend in two important respects: First, we show that Hkb is involved in the regulation of the posterior hunchback (hb) domain, but does not have any other essential function. Specifically, Hkb is required for the anterior shift in the posterior border of this domain, which is now reproduced correctly in our models. Second, gap gene circuits presented here are able to reproduce mutants of terminal gap genes, while previously published models were unable to reproduce any null mutants correctly. As a consequence, our models now capture the expression dynamics of all posterior gap genes and some variational properties of the system correctly. This is an important step towards a better, quantitative understanding of the developmental and evolutionary dynamics of the gap gene network.

GCPReg package for registration of the segmentation gene expression data in Drosophila

In modern functional genomics registration techniques areused to construct reference gene expression patterns and createa spatiotemporal atlas of the expression of all the genes in anetwork. In this paper we present a software package calledGCPReg, which can be used to register the expression patterns ofsegmentation genes in the early Drosophila embryo. The key task,which this package performs, is the extraction of spatially localizedcharacteristic features of expression patterns. To facilitatethis task, we have developed an easy-to-use interactive graphicalinterface. We describe GCPReg usage and demonstrate how thispackage can be applied to register gene expression patterns inwild type and mutants. GCPReg has been designed to operate ona UNIX platform and is freely available via the Internet at http://urchin.spbcas.ru/downloads/GCPReg/GCPReg.htm.