Stripe forming architecture of the gap gene system

Discovering novel phenotypes with automatically inferred dynamic models: a partial melanocyte conversion in Xenopus

Progress in regenerative medicine requires reverse-engineering cellular control networks to infer perturbations with desired systems-level outcomes. Such dynamic models allow phenotypic predictions for novel perturbations to be rapidly assessed in silico. Here, we analyzed a Xenopus model of conversion of melanocytes to a metastatic-like phenotype only previously observed in an all-or-none manner. Prior in vivo genetic and pharmacological experiments showed that individual animals either fully convert or remain normal, at some characteristic frequency after a given perturbation. We developed a Machine Learning method which inferred a model explaining this complex, stochastic all-or-none dataset. We then used this model to ask how a new phenotype could be generated: animals in which only some of the melanocytes converted. Systematically performing in silico perturbations, the model predicted that a combination of altanserin (5HTR2 inhibitor), reserpine (VMAT inhibitor), and VP16-XlCreb1 (constitutively active CREB) would break the all-or-none concordance. Remarkably, applying the predicted combination of three reagents in vivo revealed precisely the expected novel outcome, resulting in partial conversion of melanocytes within individuals. This work demonstrates the capability of automated analysis of dynamic models of signaling networks to discover novel phenotypes and predictively identify specific manipulations that can reach them.

Parallel Simulated Annealing Using an Adaptive Resampling Interval

This paper presents a parallel simulated annealing algorithm that is able to achieve 90% parallel efficiency in iteration on up to 192 processors and up to 40% parallel efficiency in time when applied to a 5000-dimension Rastrigin function. Our algorithm breaks scalability barriers in the method of Chu et al. (1999) by abandoning adaptive cooling based on variance. The resulting gains in parallel efficiency are much larger than the loss of serial efficiency from lack of adaptive cooling. Our algorithm resamples the states across processors periodically. The resampling interval is tuned according to the success rate for each specific number of processors. We further present an adaptive method to determine the resampling interval based on the adoption rate. This adaptive method is able to achieve nearly identical parallel efficiency but higher success rates compared to the fixed interval one using the best interval found.

Physiological controls of large-scale patterning in planarian regeneration: a molecular and computational perspective on growth and form

Planaria are complex metazoans that repair damage to their bodies and cease remodeling when a correct anatomy has been achieved. This model system offers a unique opportunity to understand how large-scale anatomical homeostasis emerges from the activities of individual cells. Much progress has been made on the molecular genetics of stem cell activity in planaria. However, recent data also indicate that the global pattern is regulated by physiological circuits composed of ionic and neurotransmitter signaling. Here, we overview the multi-scale problem of understanding pattern regulation in planaria, with specific focus on bioelectric signaling via ion channels and gap junctions (electrical synapses), and computational efforts to extract explanatory models from functional and molecular data on regeneration. We present a perspective that interprets results in this fascinating field using concepts from dynamical systems theory and computational neuroscience. Serving as a tractable nexus between genetic, physiological, and computational approaches to pattern regulation, planarian pattern homeostasis harbors many deep insights for regenerative medicine, evolutionary biology, and engineering.

Inferring regulatory networks from experimental morphological phenotypes: a computational method reverse-engineers planarian regeneration

Transformative applications in biomedicine require the discovery of complex regulatory networks that explain the development and regeneration of anatomical structures, and reveal what external signals will trigger desired changes of large-scale pattern. Despite recent advances in bioinformatics, extracting mechanistic pathway models from experimental morphological data is a key open challenge that has resisted automation. The fundamental difficulty of manually predicting emergent behavior of even simple networks has limited the models invented by human scientists to pathway diagrams that show necessary subunit interactions but do not reveal the dynamics that are sufficient for complex, self-regulating pattern to emerge. To finally bridge the gap between high-resolution genetic data and the ability to understand and control patterning, it is critical to develop computational tools to efficiently extract regulatory pathways from the resultant experimental shape phenotypes. For example, planarian regeneration has been studied for over a century, but despite increasing insight into the pathways that control its stem cells, no constructive, mechanistic model has yet been found by human scientists that explains more than one or two key features of its remarkable ability to regenerate its correct anatomical pattern after drastic perturbations. We present a method to infer the molecular products, topology, and spatial and temporal non-linear dynamics of regulatory networks recapitulating in silico the rich dataset of morphological phenotypes resulting from genetic, surgical, and pharmacological experiments. We demonstrated our approach by inferring complete regulatory networks explaining the outcomes of the main functional regeneration experiments in the planarian literature; By analyzing all the datasets together, our system inferred the first systems-biology comprehensive dynamical model explaining patterning in planarian regeneration. This method provides an automated, highly generalizable framework for identifying the underlying control mechanisms responsible for the dynamic regulation of growth and form.

Developmental and regenerative biology experiments are producing a huge number of morphological phenotypes from functional perturbation experiments. However, existing pathway models do not generally explain the dynamic regulation of anatomical shape due to the difficulty of inferring and testing non-linear regulatory networks responsible for appropriate form, shape, and pattern. We present a method that automates the discovery and testing of regulatory networks explaining morphological outcomes directly from the resultant phenotypes, producing network models as testable hypotheses explaining regeneration data. Our system integrates a formalization of the published results in planarian regeneration, an in silico simulator in which the patterning properties of regulatory networks can be quantitatively tested in a regeneration assay, and a machine learning module that evolves networks whose behavior in this assay optimally matches the database of planarian results. We applied our method to explain the key experiments in planarian regeneration, and discovered the first comprehensive model of anterior-posterior patterning in planaria under surgical, pharmacological, and genetic manipulations. Beyond the planarian data, our approach is readily generalizable to facilitate the discovery of testable regulatory networks in developmental biology and biomedicine, and represents the first developmental model discovered de novo from morphological outcomes by an automated 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.

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.

Dual-functioning transcription factors in the developmental gene network of Drosophila melanogaster

Background

Quantitative models for transcriptional regulation have shown great promise for advancing our understanding of the biological mechanisms underlying gene regulation. However, all of the models to date assume a transcription factor (TF) to have either activating or repressing function towards all the genes it is regulating.

Results

In this paper we demonstrate, on the example of the developmental gene network in D. melanogaster, that the data-fit can be improved by up to 40% if the model is allowing certain TFs to have dual function, that is, acting as activator for some genes and as repressor for others. We demonstrate that the improvement is not due to additional flexibility in the model but rather derived from the data itself. We also found no evidence for the involvement of other known site-specific TFs in regulating this network. Finally, we propose SUMOylation as a candidate biological mechanism allowing TFs to switch their role when a small ubiquitin-like modifier (SUMO) is covalently attached to the TF. We strengthen this hypothesis by demonstrating that the TFs predicted to have dual function also contain the known SUMO consensus motif, while TFs predicted to have only one role lack this motif.

Conclusions

We argue that a SUMOylation-dependent mechanism allowing TFs to have dual function represents a promising area for further research and might be another step towards uncovering the biological mechanisms underlying transcriptional regulation.

Mathematical model of the Drosophila circadian clock: loop regulation and transcriptional integration

Eukaryotic circadian clocks include interconnected positive and negative feedback loops. The clock-cycle dimer (CLK-CYC) and its homolog, CLK-BMAL1, are key transcriptional activators of central components of the Drosophila and mammalian circadian networks, respectively. In Drosophila, negative loops include period-timeless and vrille; positive loops include par domain protein 1. Clockwork orange (CWO) is a recently discovered negative transcription factor with unusual effects on period, timeless, vrille, and par domain protein 1. To understand the actions of this protein, we introduced a new system of ordinary differential equations to model regulatory networks. The model is faithful in the sense that it replicates biological observations. CWO loop actions elevate CLK-CYC; the transcription of direct targets responds by integrating opposing signals from CWO and CLK-CYC. Loop regulation and integration of opposite transcriptional signals appear to be central mechanisms as they also explain paradoxical effects of period gain-of-function and null mutations.

Stochastic Spatio-Temporal Dynamic Model for Gene/Protein Interaction Network in Early Drosophila Development

In order to investigate the possible mechanisms for eve stripe formation of Drosophila embryo, a spatio-temporal gene/protein interaction network model is proposed to mimic dynamic behaviors of protein synthesis, protein decay, mRNA decay, protein diffusion, transcription regulations and autoregulation to analyze the interplay of genes and proteins at different compartments in early embryogenesis. In this study, we use the maximum likelihood (ML) method to identify the stochastic 3-D Embryo Space-Time (3-DEST) dynamic model for gene/protein interaction network via 3-D mRNA and protein expression data and then use the Akaike Information Criterion (AIC) to prune the gene/protein interaction network. The identified gene/protein interaction network allows us not only to analyze the dynamic interplay of genes and proteins on the border of eve stripes but also to infer that eve stripes are established and maintained by network motifs built by the cooperation between transcription regulations and diffusion mechanisms in early embryogenesis. Literature reference with the wet experiments of gene mutations provides a clue for validating the identified network. The proposed spatio-temporal dynamic model can be extended to gene/protein network construction of different biological phenotypes, which depend on compartments, e.g. postnatal stem/progenitor cell differentiation.

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.

A developmental systems perspective on epistasis: computational exploration of mutational interactions in model developmental regulatory networks

The way in which the information contained in genotypes is translated into complex phenotypic traits (i.e. embryonic expression patterns) depends on its decoding by a multilayered hierarchy of biomolecular systems (regulatory networks). Each layer of this hierarchy displays its own regulatory schemes (i.e. operational rules such as +/− feedback) and associated control parameters, resulting in characteristic variational constraints. This process can be conceptualized as a mapping issue, and in the context of highly-dimensional genotype-phenotype mappings (GPMs) epistatic events have been shown to be ubiquitous, manifested in non-linear correspondences between changes in the genotype and their phenotypic effects. In this study I concentrate on epistatic phenomena pervading levels of biological organization above the genetic material, more specifically the realm of molecular networks. At this level, systems approaches to studying GPMs are specially suitable to shed light on the mechanistic basis of epistatic phenomena. To this aim, I constructed and analyzed ensembles of highly-modular (fully interconnected) networks with distinctive topologies, each displaying dynamic behaviors that were categorized as either arbitrary or functional according to early patterning processes in the Drosophila embryo. Spatio-temporal expression trajectories in virtual syncytial embryos were simulated via reaction-diffusion models. My in silico mutational experiments show that: 1) the average fitness decay tendency to successively accumulated mutations in ensembles of functional networks indicates the prevalence of positive epistasis, whereas in ensembles of arbitrary networks negative epistasis is the dominant tendency; and 2) the evaluation of epistatic coefficients of diverse interaction orders indicates that, both positive and negative epistasis are more prevalent in functional networks than in arbitrary ones. Overall, I conclude that the phenotypic and fitness effects of multiple perturbations are strongly conditioned by both the regulatory architecture (i.e. pattern of coupled feedback structures) and the dynamic nature of the spatio-temporal expression trajectories displayed by the simulated networks.

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

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

Canalization of gene expression in the Drosophila blastoderm by gap gene cross regulation

Developing embryos exhibit a robust capability to reduce phenotypic variations that occur naturally or as a result of experimental manipulation. This reduction in variation occurs by an epigenetic mechanism called canalization, a phenomenon which has resisted understanding because of a lack of necessary molecular data and of appropriate gene regulation models. In recent years, quantitative gene expression data have become available for the segment determination process in the Drosophila blastoderm, revealing a specific instance of canalization. These data show that the variation of the zygotic segmentation gene expression patterns is markedly reduced compared to earlier levels by the time gastrulation begins, and this variation is significantly lower than the variation of the maternal protein gradient Bicoid. We used a predictive dynamical model of gene regulation to study the effect of Bicoid variation on the downstream gap genes. The model correctly predicts the reduced variation of the gap gene expression patterns and allows the characterization of the canalizing mechanism. We show that the canalization is the result of specific regulatory interactions among the zygotic gap genes. We demonstrate the validity of this explanation by showing that variation is increased in embryos mutant for two gap genes, Krüppel and knirps, disproving competing proposals that canalization is due to an undiscovered morphogen, or that it does not take place at all. In an accompanying article in PLoS Computational Biology (doi:10.1371/journal.pcbi.1000303), we show that cross regulation between the gap genes causes their expression to approach dynamical attractors, reducing initial variation and providing a robust output. These results demonstrate that the Bicoid gradient is not sufficient to produce gap gene borders having the low variance observed, and instead this low variance is generated by gap gene cross regulation. More generally, we show that the complex multigenic phenomenon of canalization can be understood at a quantitative and predictive level by the application of a precise dynamical model.

Animals have an astonishing ability to develop reliably in spite of variable conditions during embryogenesis. More than 60 years ago, it was proposed that this property of development, called canalization, results from genetic interactions that adjust biochemical reactions so as to bring about reliable outcomes. Since then, a great deal of progress has been made in understanding the buffering of genotypic and environmental variation, and individual mutations that reveal variation have been identified. However, the mechanisms by which genetic interactions produce canalization are not yet well understood, because this requires molecular data on multiple developmental determinants and models that correctly predict complex interactions. We make use of gene expression data at both high spatial and temporal resolution for the gap genes involved in the segmentation of Drosophila. We also apply a mathematical model to show that cross regulation among the gap genes is responsible for canalization in this system. Furthermore, the model predicted specific interactions that cause canalization, and the prediction was validated experimentally. Our results show that groups of genes can act on one another to reduce variation and highlights the importance of genetic networks in generating robust development.

DuringDrosophila development, the expression patterns of gap genes are much less variable than the Bicoid morphogen gradient. Modeling and experiments show that this specific instance of canalization or developmental robustness occurs by gap gene cross regulation.

Characterization of the Drosophila segment determination morphome

Here we characterize the expression of the full system of genes which control the segmentation morphogenetic field of Drosophila at the protein level in one dimension. The data used for this characterization are quantitative with cellular resolution in space and about 6 min in time. We present the full quantitative profiles of all 14 segmentation genes which act before the onset of gastrulation. The expression patterns of these genes are first characterized in terms of their average or typical behavior. At this level, the expression of all of the genes has been integrated into a single atlas of gene expression in which the expression levels of all genes in each cell are specified. We show that expression domains do not arise synchronously, but rather each domain has its own specific dynamics of formation. Moreover, we show that the expression domains shift position in the direction of the cephalic furrow, such that domains in the anlage of the segmented germ band shift anteriorly while those in the presumptive head shift posteriorly. The expression atlas of integrated data is very close to the expression profiles of individual embryos during the latter part of the blastoderm stage. At earlier times gap gene domains show considerable variation in amplitude, and significant positional variability. Nevertheless, an average early gap domain is close to that of a median individual. In contrast, we show that there is a diversity of developmental trajectories among pair-rule genes at a variety of levels, including the order of domain formation and positional accuracy. We further show that this variation is dynamically reduced, or canalized, over time. As the first quantitatively characterized morphogenetic field, this system and its behavior constitute an extraordinarily rich set of materials for the study of canalization and embryonic regulation at the molecular level.

Efficient parameter estimation for spatio-temporal models of pattern formation: case study of Drosophila melanogaster

MOTIVATION

Diffusable and non-diffusable gene products play a major role in body plan formation. A quantitative understanding of the spatio-temporal patterns formed in body plan formation, by using simulation models is an important addition to experimental observation. The inverse modelling approach consists of describing the body plan formation by a rule-based model, and fitting the model parameters to real observed data. In body plan formation, the data are usually obtained from fluorescent immunohistochemistry or in situ hybridizations. Inferring model parameters by comparing such data to those from simulation is a major computational bottleneck. An important aspect in this process is the choice of method used for parameter estimation. When no information on parameters is available, parameter estimation is mostly done by means of heuristic algorithms.

RESULTS

We show that parameter estimation for pattern formation models can be efficiently performed using an evolution strategy (ES). As a case study we use a quantitative spatio-temporal model of the regulatory network for early development in Drosophila melanogaster. In order to estimate the parameters, the simulated results are compared to a time series of gene products involved in the network obtained with immunohistochemistry. We demonstrate that a (mu,lambda)-ES can be used to find good quality solutions in the parameter estimation. We also show that an ES with multiple populations is 5-140 times as fast as parallel simulated annealing for this case study, and that combining ES with a local search results in an efficient parameter estimation method.

On the dynamic nature of positional information

Morphogenetic fields are among the most fundamental concepts of embryology. However, they are also among the most ill-defined, since they consist of dynamic regulatory processes whose exact nature remains elusive. In order to achieve a more rigorous definition of a developmental field, Lewis Wolpert introduced the concept of positional information illustrated by his French Flag model. Here we argue that Wolpert's positional information - a static coordinate system defining a field - lacks essential properties of the original field concept. We show how data-driven mathematical modeling approaches now enable us to study regulatory processes in a way that is qualitatively different from our previous level of understanding. As an example, we review our recent analysis of segmentation gene expression in the blastoderm embryo of the fruit fly Drosophila melanogaster. Based on this analysis, we propose a revised French Flag, which incorporates the dynamic, feedback-driven nature of pattern formation in the Drosophila blastoderm.

Known maternal gradients are not sufficient for the establishment of gap domains in Drosophila melanogaster

Gap genes are among the first transcriptional targets of maternal morphogen gradients in the early Drosophila embryo. However, it remains unclear whether these gradients are indeed sufficient to establish the boundaries of localized gap gene expression patterns. In this study, we address this question using gap gene circuits, which are data-driven mathematical tools for extracting regulatory information from quantitative wild-type gene expression data. We present new, quantitative data on the mRNA expression patterns for the gap genes Krüppel (Kr), knirps (kni) and giant (gt) during the early blastoderm stage of Drosophila development. This data set shows significant differences in timing of gap gene expression compared to previous observations, and reveals that early gap gene expression is highly variable in both space and time. Gene circuit models fit to this data set were used for a detailed regulatory analysis of early gap gene expression. Our analysis shows that the proper balance of maternal repression and activation is essential for the correct positioning of gap domains, and that such balance can only be achieved for early expression of kni. In contrast, our results suggest that early expression of gt requires local neutralization of repressive input in the anterior region of the embryo, and that known maternal gradients are completely insufficient to position the boundaries of the early central Kr domain, or in fact any Kr-like domain in the central region of the blastoderm embryo. Based on this, we propose that unknown additional regulators must be involved in early gap gene regulation.

Dynamical analysis of regulatory interactions in the gap gene system of Drosophila melanogaster

Genetic studies have revealed that segment determination in Drosophila melanogaster is based on hierarchical regulatory interactions among maternal coordinate and zygotic segmentation genes. The gap gene system constitutes the most upstream zygotic layer of this regulatory hierarchy, responsible for the initial interpretation of positional information encoded by maternal gradients. We present a detailed analysis of regulatory interactions involved in gap gene regulation based on gap gene circuits, which are mathematical gene network models used to infer regulatory interactions from quantitative gene expression data. Our models reproduce gap gene expression at high accuracy and temporal resolution. Regulatory interactions found in gap gene circuits provide consistent and sufficient mechanisms for gap gene expression, which largely agree with mechanisms previously inferred from qualitative studies of mutant gene expression patterns. Our models predict activation of Kr by Cad and clarify several other regulatory interactions. Our analysis suggests a central role for repressive feedback loops between complementary gap genes. We observe that repressive interactions among overlapping gap genes show anteroposterior asymmetry with posterior dominance. Finally, our models suggest a correlation between timing of gap domain boundary formation and regulatory contributions from the terminal maternal system.

Dynamic control of positional information in the early Drosophila embryo

Morphogen gradients contribute to pattern formation by determining positional information in morphogenetic fields. Interpretation of positional information is thought to rely on direct, concentration-threshold-dependent mechanisms for establishing multiple differential domains of target gene expression. In Drosophila, maternal gradients establish the initial position of boundaries for zygotic gap gene expression, which in turn convey positional information to pair-rule and segment-polarity genes, the latter forming a segmental pre-pattern by the onset of gastrulation. Here we report, on the basis of quantitative gene expression data, substantial anterior shifts in the position of gap domains after their initial establishment. Using a data-driven mathematical modelling approach, we show that these shifts are based on a regulatory mechanism that relies on asymmetric gap-gap cross-repression and does not require the diffusion of gap proteins. Our analysis implies that the threshold-dependent interpretation of maternal morphogen concentration is not sufficient to determine shifting gap domain boundary positions, and suggests that establishing and interpreting positional information are not independent processes in the Drosophila blastoderm.

Segmenting the fly embryo: a logical analysis of the pair-rule cross-regulatory module

This manuscript reports a dynamical analysis of the pair-rule cross-regulatory module controlling segmentation in Drosophila melanogaster. We propose a logical model accounting for the ability of the pair-rule module to determine the formation of alternate juxtaposed Engrailed- and Wingless-expressing cells that form the (para)segmental boundaries. This module has the intrinsic capacity to generate four distinct expression states, each characterized by the expression of a particular combination of pair-rule genes or expression mode. The selection of one of these expression modes depends on the maternal and gap inputs, but also crucially on cross-regulations among pair-rule genes. The latter are instrumental in the interpretation of the maternal-gap pre-pattern. Our logical model allows the qualitative reproduction of the patterns of pair-rule gene expressions corresponding to the wild type situation, to loss-of-function and cis-regulatory mutations, and to ectopic pair-rule expressions. Furthermore, this model provides a formal explanation for the morphogenetic role of the initial bell-shaped expression of the gene even-skipped, i.e. for the distinct effects of different levels of the Even-skipped protein on its target pair-rule genes. It also accounts for the requirement of Even-skipped for the formation of all Engrailed-stripes. Finally, it provides new insights into the roles and evolutionary origins of the apparent redundancies in the regulatory architecture of the pair-rule module.

On schemes of combinatorial transcription logic

Cells receive a wide variety of cellular and environmental signals, which are often processed combinatorially to generate specific genetic responses. Here we explore theoretically the potentials and limitations of combinatorial signal integration at the level of cis-regulatory transcription control. Our analysis suggests that many complex transcription-control functions of the type encountered in higher eukaryotes are already implementable within the much simpler bacterial transcription system. Using a quantitative model of bacterial transcription and invoking only specific protein-DNA interaction and weak glue-like interaction between regulatory proteins, we show explicit schemes to implement regulatory logic functions of increasing complexity by appropriately selecting the strengths and arranging the relative positions of the relevant protein-binding DNA sequences in the cis-regulatory region. The architectures that emerge are naturally modular and evolvable. Our results suggest that the transcription regulatory apparatus is a "programmable" computing machine, belonging formally to the class of Boltzmann machines. Crucial to our results is the ability to regulate gene expression at a distance. In bacteria, this can be achieved for isolated genes via DNA looping controlled by the dimerization of DNA-bound proteins. However, if adopted extensively in the genome, long-distance interaction can cause unintentional intergenic cross talk, a detrimental side effect difficult to overcome by the known bacterial transcription-regulation systems. This may be a key factor limiting the genome-wide adoption of complex transcription control in bacteria. Implications of our findings for combinatorial transcription control in eukaryotes are discussed.

Modeling and simulation of genetic regulatory systems: a literature review

In order to understand the functioning of organisms on the molecular level, we need to know which genes are expressed, when and where in the organism, and to which extent. The regulation of gene expression is achieved through genetic regulatory systems structured by networks of interactions between DNA, RNA, proteins, and small molecules. As most genetic regulatory networks of interest involve many components connected through interlocking positive and negative feedback loops, an intuitive understanding of their dynamics is hard to obtain. As a consequence, formal methods and computer tools for the modeling and simulation of genetic regulatory networks will be indispensable. This paper reviews formalisms that have been employed in mathematical biology and bioinformatics to describe genetic regulatory systems, in particular directed graphs, Bayesian networks, Boolean networks and their generalizations, ordinary and partial differential equations, qualitative differential equations, stochastic equations, and rule-based formalisms. In addition, the paper discusses how these formalisms have been used in the simulation of the behavior of actual regulatory systems.

Modeling and computational analysis of EGF receptor-mediated cell communication in Drosophila oogenesis

Autocrine signaling through the Epidermal Growth Factor Receptor (EGFR) operates at various stages of development across species. A recent hypothesis suggested that a distributed network of EGFR autocrine loops was capable of spatially modulating a simple single-peaked input into a more complex two-peaked signaling pattern, specifying the formation of a pair organ in Drosophila oogenesis (two respiratory appendages on the eggshell). To test this hypothesis, we have integrated genetic and biochemical information about the EGFR network into a mechanistic model of transport and signaling. The model allows us to estimate the relative spatial ranges and time scales of the relevant feedback loops, to interpret the phenotypic transitions in eggshell morphology and to predict the effects of new genetic manipulations. We have found that the proposed mechanism with a single diffusing inhibitor is sufficient to convert a single-peaked extracellular input into a two-peaked pattern of intracellular signaling. Based on extensive computational analysis, we predict that the same mechanism is capable of generating more complex patterns. At least indirectly, this can be used to account for more complex eggshell morphologies observed in related fly species. We propose that versatility in signaling mediated by autocrine loops can be systematically explored using experiment-based mechanistic models and their analysis.

Temporal classification of Drosophila segmentation gene expression patterns by the multi-valued neural recognition method

In order to reconstruct the establishment of the body pattern over time in Drosophila embryos, we have developed automated methods for detecting the age of an embryo on the basis of knowledge about its gene expression patterns. In this paper we perform temporal classification of confocal images of expression patterns of genes controlling segmentation by means of a neural network based on multi-valued neurons (MVN). MVN are artificial neural processing elements with complex-valued weights and high functionality, which proved to be efficient for solving the image recognition problems. The results obtained by this method confirm its efficiency for image recognition and indicate that the method can detect characteristic features of expression patterns which mark their development over time.

A logical analysis of the Drosophila gap-gene system

This manuscript focuses on the formal analysis of the gap-gene network involved in Drosophila segmentation. The gap genes are expressed in defined domains along the anterior-posterior axis of the embryo, as a response to asymmetric maternal information in the oocyte. Though many of the individual interactions among maternal and gap genes are reasonably well understood, we still lack a thorough understanding of the dynamic behavior of the system as a whole. Based on a generalized logical formalization, the present analysis leads to the delineation of: (1) the minimal number of distinct, qualitative, functional levels associated with each of the key regulatory factors (the three maternal Bcd, Hb and Cad products, and the four gap Gt, Hb, Kr and Kni products); (2) the most crucial interactions and regulatory circuits of the earliest stages of the segmentation process; (3) the ordering of different regulatory interactions governed by each of these products according to corresponding concentration scales; and (4) the role of gap-gene cross-interactions in the transformation of graded maternal information into discrete gap-gene expression domains. The proposed model allows not only the qualitative reproduction of the patterns of gene expression characterized experimentally, but also the simulation and prediction of single and multiple mutant phenotypes.

How gap genes make their domains: An analytical study based on data driven approximations

We consider a mathematical formulation of the problem of protein production during segment determination in the Drosophila blastoderm, together with some preliminary results of its analytical study. We reformulate the spatial difference equations as a set of nonlinear partial differential equations and obtain their dimensionless form in the continuum limit. Using previous results obtained by the gene circuit method, we find an asymptotic statement of the problem with a small parameter. Some results of the comparison method applied to the model are obtained, and exact stationary upper solutions are derived. They exhibit distinctive features of localized bell-shaped structures. (c) 2001 American Institute of Physics.

Elegant hypothesis and inelegant fact in developmental biology

The relationship between theoretical and experimental approaches to the problem of pattern generation during embryonic development has often been uneasy. This stems at least in part from the different emphases that have typically been used in the two approaches. The spectacular success of modern genetic techniques in uncovering developmental mechanisms has led to a widespread belief that theory is no longer very relevant. However, recent examples of data-driven modelling point to new roles for theoretical approaches in exploring important issues such as the robustness and evolution of pattern-forming mechanisms.

Development, evolution, and corroboration

The cloning of genes involved in pathways fundamental to morphogenesis has opened the door to visualizing expression of developmental regulatory genes in many organisms. Expression data have become technical commonplace in analysis of mutants of Drosophila melanogaster and a handful of other genetic model systems. Many researchers have used probes and extended the logic from studies of D. melanogaster for comparisons of expression patterns to infer developmental bases for homologous structures among animals with diverse body plans. This research program has led to exciting but sweeping generalizations about how development evolves. Here we examine several underlying assumptions of this approach in terms of comparative and historical biology. First, we evaluate the logic that underlies the equation of gene expression similarity with homologous morphology. Second, we examine epistemological issues surrounding the descriptive visualization of gene expression patterns. We conclude by examining the role of phylogenetic coding and mapping of these patterns to examine the evolution of complex gene regulatory networks.

Prediction of mutant expression patterns using gene circuits

Networks of interacting transcription factors, or gene circuits, form an essential part of the metabolic pathways controlling macromolecular synthesis. This paper conveys two new results about gene circuits. We first show how a gene circuit for mutant phenotypes can be constructed from the wild type gene circuit for the same organism. We then present results of computational studies that show that mutant expression patterns can be correctly predicted using gene circuits whose parameters have been determined from wild type data only. Further computational studies demonstrate that this property is insensitive to errors as large as a factor of two in the input data. Together, these results show that gene circuits can be used to identify the regulatory mechanisms governing an entire family of genotypes from a knowledge of the wild type genotype alone. It is argued that this fact forms the basis for a new paradigm in genetics.