Waddington’s epigenetic landscape is an intuitive metaphor for the
developmental and evolutionary potential of biological regulatory processes. It
emphasises time-dependence and transient behaviour. Nowadays, we can derive this
landscape by modelling a specific regulatory network as a dynamical system and
calculating its so-called potential surface. In this sense, potential surfaces are
the mathematical equivalent of the Waddingtonian landscape metaphor. In order to
fully capture the time-dependent (non-autonomous) transient behaviour of
biological processes, we must be able to characterise potential landscapes and how
they change over time. However, currently available mathematical tools focus on
the asymptotic (steady-state) behaviour of autonomous dynamical systems, which
restricts how biological systems are studied.
We present a pragmatic first step towards a methodology for dealing with transient
behaviours in non-autonomous systems. We propose a classification scheme for
different kinds of such dynamics based on the simulation of a simple genetic
toggle-switch model with time-variable parameters. For this low-dimensional
system, we can calculate and explicitly visualise numerical approximations to the
potential landscape. Focussing on transient dynamics in non-autonomous systems
reveals a range of interesting and biologically relevant behaviours that would be
missed in steady-state analyses of autonomous systems. Our simulation-based
approach allows us to identify four qualitatively different kinds of dynamics:
transitions, pursuits, and two kinds of captures. We describe these in detail, and
illustrate the usefulness of our classification scheme by providing a number of
examples that demonstrate how it can be employed to gain specific mechanistic
insights into the dynamics of gene regulation.
The practical aim of our proposed classification scheme is to make the analysis of
explicitly time-dependent transient behaviour tractable, and to encourage the
wider use of non-autonomous models in systems biology. Our method is applicable to
a large class of biological processes.
Model organisms, such as Drosophila melanogaster, provide powerful experimental tools for the study of development. However, approaches using model systems need to be complemented by comparative studies for us to gain a deeper understanding of the functional properties and evolution of developmental processes. New model organisms need to be established to enable such comparative work. The establishment of new model system requires a detailed description of its life cycle and development. The resulting staging scheme is essential for providing morphological context for molecular studies, and allows us to homologise developmental processes between species. In this paper, we provide a staging scheme and morphological characterisation of the life cycle for an emerging non-drosophilid dipteran model system: the scuttle fly Megaselia abdita. We pay particular attention to early embryogenesis (cleavage and blastoderm stages up to gastrulation), the formation and retraction of extraembryonic tissues, and the determination and formation of germ (pole) cells. Despite the large evolutionary distance between the two species (approximately 150 million years), we find that M. abdita development is remarkably similar to D. melanogaster in terms of developmental landmarks and their relative timing.
Model organisms, such as Drosophila melanogaster, allow us to address a wide range of biological questions with experimental rigour. However, studies in model species need to be complemented by comparative studies if we are to fully understand the functional properties and evolutionary history of developmental processes. The establishment of new model organisms is crucial for this purpose. One of the first essential steps to establish a species as an experimental model is to carefully describe its life cycle and development. The resulting staging scheme serves as a framework for molecular studies, and allows us to homologise developmental processes between species. In this paper, we have characterised the life cycle and development of an emerging non-drosophilid dipteran model system: the moth midge Clogmia albipunctata. In particular, we focus on early embryogenesis (cleavage and blastoderm cycles before gastrulation), on formation and retraction of extraembryonic tissues, and on formation of the germ line. Considering the large evolutionary distance between the two species (approximately 250 million years), we find that the development of C. albipunctata is remarkably conserved compared to D. melanogaster. On the other hand, we detect significant differences in morphology and timing affecting the development of extraembryonic tissues and the germ line. Moreover, C. albipunctata shows several heterochronic shifts, and lacks head involution and associated processes during late stages of development.
Comparative studies of developmental processes are one of the main approaches to evolutionary developmental biology (evo-devo). Over recent years, there has been a shift of focus from the comparative study of particular regulatory genes to the level of whole gene networks. Reverse-engineering methods can be used to computationally reconstitute and analyze the function and dynamics of such networks. These methods require quantitative spatio-temporal expression data for model fitting. Obtaining such data in non-model organisms remains a major technical challenge, impeding the wider application of data-driven mathematical modeling to evo-devo.
We have raised antibodies against four segmentation gene products in the moth midge Clogmia albipunctata, a non-drosophilid dipteran species. We have used these antibodies to create a quantitative atlas of protein expression patterns for the gap gene hunchback (hb), and the pair-rule gene even-skipped (eve). Our data reveal differences in the dynamics of Hb boundary positioning and Eve stripe formation between C. albipunctata and Drosophila melanogaster. Despite these differences, the overall relative spatial arrangement of Hb and Eve domains is remarkably conserved between these two distantly related dipteran species.
We provide a proof of principle that it is possible to acquire quantitative gene expression data at high accuracy and spatio-temporal resolution in non-model organisms. Our quantitative data extend earlier qualitative studies of segmentation gene expression in C. albipunctata, and provide a starting point for comparative reverse-engineering studies of the evolutionary and developmental dynamics of the segmentation gene system.
Clogmia albipunctata; Non-drosophilid diptera; Non-model organism; Pattern formation; Comparative network analysis; Segmentation gene network; Hunchback; Even-skipped; Image bioinformatics; Quantitative expression data
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.
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.
► We present a quantitative analysis of spatial gene expression in Drosophila mutants. ► Dynamic gap domain shifts do not depend on expression of terminal gap genes or hb. ► Expression variability is greatly increased in a tll mutant background. ► This indicates de-canalisation (loss of developmental robustness) in the mutant. ► Such de-canalisation is a common phenomenon in mutants of developmental regulators.
Drosophila embryogenesis; Segmentation gene network; Quantitative expression analysis; Pattern formation; Robustness/canalisation; Genetic capacitance
Bone morphogenetic proteins (BMPs) play key roles in development. In Drosophila melanogaster, there are three BMP-encoding genes: decapentaplegic (dpp), glass bottom boat (gbb) and screw (scw). dpp and gbb are found in all groups of insects. In contrast, the origin of scw via duplication of an ancestral gbb homologue is more recent, with new evidence placing it within the Diptera. Recent studies show that scw appeared basal to the Schizophora, since scw orthologues exist in aschizan cyclorrhaphan flies. In order to further localise the origin of scw, we have utilised new genomic resources for the nematoceran moth midge Clogmia albipunctata (Psychodidae). We identified the BMP subclass members dpp and gbb from an early embryonic transcriptome and show that their expression patterns in the blastoderm differ considerably from those seen in cyclorrhaphan flies. Further searches of the genome of C. albipunctata were unable to identify a scw-like gbb duplicate, but confirm the presence of dpp and gbb. Our phylogenetic analysis shows these to be clear orthologues of dpp and gbb from other non-cyclorrhaphan insects, with C. albipunctata gbb branching ancestrally to the cyclorrhaphan gbb/scw split. Furthermore, our analysis suggests that scw is absent from all Nematocera, including the Bibionomorpha. We conclude that the gbb/scw duplication occurred between the separation of the lineage leading to Brachycera and the origin of cyclorrhaphan flies 200–150 Ma ago.
Electronic supplementary material
The online version of this article (doi:10.1007/s00427-013-0445-9) contains supplementary material, which is available to authorized users.
Bone morphogenetic proteins (BMPs); Phylogenetic analysis; Gene duplication; Diptera; Clogmia albipunctata
Modern sequencing technologies have massively increased the amount of data available for comparative genomics. Whole-transcriptome shotgun sequencing (RNA-seq) provides a powerful basis for comparative studies. In particular, this approach holds great promise for emerging model species in fields such as evolutionary developmental biology (evo-devo).
We have sequenced early embryonic transcriptomes of two non-drosophilid dipteran species: the moth midge Clogmia albipunctata, and the scuttle fly Megaselia abdita. Our analysis includes a third, published, transcriptome for the hoverfly Episyrphus balteatus. These emerging models for comparative developmental studies close an important phylogenetic gap between Drosophila melanogaster and other insect model systems. In this paper, we provide a comparative analysis of early embryonic transcriptomes across species, and use our data for a phylogenomic re-evaluation of dipteran phylogenetic relationships.
We show how comparative transcriptomics can be used to create useful resources for evo-devo, and to investigate phylogenetic relationships. Our results demonstrate that de novo assembly of short (Illumina) reads yields high-quality, high-coverage transcriptomic data sets. We use these data to investigate deep dipteran phylogenetic relationships. Our results, based on a concatenation of 160 orthologous genes, provide support for the traditional view of Clogmia being the sister group of Brachycera (Megaselia, Episyrphus, Drosophila), rather than that of Culicomorpha (which includes mosquitoes and blackflies).
Non-drosophilid diptera; Clogmia albipunctata; Megaselia abdita; Episyrphus balteatus; Comparative transcriptomics; RNA-seq; De novo assembly; Automated annotation; Evolutionary developmental biology; Phylogenomics
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.
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.
To better understand multi-cellular organisms we need a better and more systematic understanding of the complex regulatory networks that govern their development and evolution. However, this problem is far from trivial. Regulatory networks involve many factors interacting in a non-linear manner, which makes it difficult to study them without the help of computers. Here, we investigate a computational method, reverse engineering, which allows us to reconstitute real-world regulatory networks in silico. As a case study, we investigate the gap gene network involved in determining the position of body segments during early development of Drosophila. We visualise spatial gap gene expression patterns using in situ hybridisation and microscopy. The resulting embryo images are quantified to measure the position of expression domain boundaries. We then use computational models as tools to extract regulatory information from the data. We investigate what kind, and how much data are required for successful network inference. Our results reveal that much less effort is required for reverse-engineering networks than previously thought. This opens the possibility of investigating a large number of developmental networks using this approach, which in turn will lead to a more general understanding of the rules and principles underlying development in animals and plants.
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.
Developmental biology; Evolution; Segment determination; Pattern formation; Gene regulatory network; Transcriptional regulation; Patterning precision; Size regulation
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.
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.
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.
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.
Currently, there are two very different approaches to the study of pattern formation: Traditional developmental genetics investigates the role of particular factors in great mechanistic detail, while newly developed systems-biology methods study many factors in parallel but usually remain rather general in their conclusions. Here, we attempt to bridge the gap between the two by studying the expression pattern and function of a particular developmental gene—the terminal gap gene huckebein (hkb) in the fruit fly Drosophila melanogaster—in great quantitative detail using a systems-level approach called the gene circuit method. Gene circuits are mathematical models which allow us to reconstitute a developmental process in the computer. This allows us to study the function of the hkb gene in its wild-type regulatory context with unprecedented accuracy and resolution. Our results confirm earlier, qualitative evidence, and show that hkb plays a small, but crucial role in gap gene regulation. Understanding hkb's regulatory contributions is essential for our wider understanding of dynamic shifts in the position of gap gene expression domains which play important roles during both development and evolution.
Quantitative measurements and mathematical modeling finally allow us to probe the limits of precision in developmental systems and reveal the importance of feedback regulation for developmental robustness.
Mathematical modeling of real-life processes often requires the estimation of unknown parameters. Once the parameters are found by means of optimization, it is important to assess the quality of the parameter estimates, especially if parameter values are used to draw biological conclusions from the model.
In this paper we describe how the quality of parameter estimates can be analyzed. We apply our methodology to assess parameter determinability for gene circuit models of the gap gene network in early Drosophila embryos.
Our analysis shows that none of the parameters of the considered model can be determined individually with reasonable accuracy due to correlations between parameters. Therefore, the model cannot be used as a tool to infer quantitative regulatory weights. On the other hand, our results show that it is still possible to draw reliable qualitative conclusions on the regulatory topology of the gene network. Moreover, it improves previous analyses of the same model by allowing us to identify those interactions for which qualitative conclusions are reliable, and those for which they are ambiguous.
A fundamental problem in functional genomics is to determine the structure and dynamics of genetic networks based on expression data. We describe a new strategy for solving this problem and apply it to recently published data on early Drosophila melanogaster development. Our method is orders of magnitude faster than current fitting methods and allows us to fit different types of rules for expressing regulatory relationships. Specifically, we use our approach to fit models using a smooth nonlinear formalism for modeling gene regulation (gene circuits) as well as models using logical rules based on activation and repression thresholds for transcription factors. Our technique also allows us to infer regulatory relationships de novo or to test network structures suggested by the literature. We fit a series of models to test several outstanding questions about gap gene regulation, including regulation of and by hunchback and the role of autoactivation. Based on our modeling results and validation against the experimental literature, we propose a revised network structure for the gap gene system. Interestingly, some relationships in standard textbook models of gap gene regulation appear to be unnecessary for or even inconsistent with the details of gap gene expression during wild-type development.
Modeling dynamical systems involves determining which elements of the system interact with which, and what is the nature of the interaction. In the context of modeling gene expression dynamics, this question equates to determining regulatory relationships between genes. Perkins and colleagues present a new computational method for fitting differential equation models of time series data, and apply it to expression data from the well-known segmentation network of Drosophila melanogaster. The method is orders of magnitude faster than other approaches that produce fits of comparable quality, such as Simulated Annealing. The authors show that it is possible to detect interactions de novo as well as to test existing regulatory hypotheses, and they propose a revised network structure for the gap gene system, based on their modeling efforts and on other experimental literature.