A discrete model of Drosophila eggshell patterning reveals cell-autonomous and juxtacrine effects

Finishing the egg

Gamete development is a fundamental process that is highly conserved from early eukaryotes to mammals. As germ cells develop, they must coordinate a dynamic series of cellular processes that support growth, cell specification, patterning, the loading of maternal factors (RNAs, proteins, and nutrients), differentiation of structures to enable fertilization and ensure embryonic survival, and other processes that make a functional oocyte. To achieve these goals, germ cells integrate a complex milieu of environmental and developmental signals to produce fertilizable eggs. Over the past 50 years, Drosophila oogenesis has risen to the forefront as a system to interrogate the sophisticated mechanisms that drive oocyte development. Studies in Drosophila have defined mechanisms in germ cells that control meiosis, protect genome integrity, facilitate mRNA trafficking, and support the maternal loading of nutrients. Work in this system has provided key insights into the mechanisms that establish egg chamber polarity and patterning as well as the mechanisms that drive ovulation and egg activation. Using the power of Drosophila genetics, the field has begun to define the molecular mechanisms that coordinate environmental stresses and nutrient availability with oocyte development. Importantly, the majority of these reproductive mechanisms are highly conserved throughout evolution, and many play critical roles in the development of somatic tissues as well. In this chapter, we summarize the recent progress in several key areas that impact egg chamber development and ovulation. First, we discuss the mechanisms that drive nutrient storage and trafficking during oocyte maturation and vitellogenesis. Second, we examine the processes that regulate follicle cell patterning and how that patterning impacts the construction of the egg shell and the establishment of embryonic polarity. Finally, we examine regulatory factors that control ovulation, egg activation, and successful fertilization.

Reducing Boolean networks with backward equivalence

BACKGROUND

Boolean Networks (BNs) are a popular dynamical model in biology where the state of each component is represented by a variable taking binary values that express, for instance, activation/deactivation or high/low concentrations. Unfortunately, these models suffer from the state space explosion, i.e., there are exponentially many states in the number of BN variables, which hampers their analysis.

RESULTS

We present Boolean Backward Equivalence (BBE), a novel reduction technique for BNs which collapses system variables that, if initialized with same value, maintain matching values in all states. A large-scale validation on 86 models from two online model repositories reveals that BBE is effective, since it is able to reduce more than 90% of the models. Furthermore, on such models we also show that BBE brings notable analysis speed-ups, both in terms of state space generation and steady-state analysis. In several cases, BBE allowed the analysis of models that were originally intractable due to the complexity. On two selected case studies, we show how one can tune the reduction power of BBE using model-specific information to preserve all dynamics of interest, and selectively exclude behavior that does not have biological relevance.

CONCLUSIONS

BBE complements existing reduction methods, preserving properties that other reduction methods fail to reproduce, and vice versa. BBE drops all and only the dynamics, including attractors, originating from states where BBE-equivalent variables have been initialized with different activation values The remaining part of the dynamics is preserved exactly, including the length of the preserved attractors, and their reachability from given initial conditions, without adding any spurious behaviours. Given that BBE is a model-to-model reduction technique, it can be combined with further reduction methods for BNs.

On the effects of the modularity of gene regulatory networks on phenotypic variability and its association with robustness

Biological adaptations depend on natural selection sorting out those individuals that exhibit characters fit to their environment. Selection, in turn, depends on the phenotypic variation present in a population. Thus, evolutionary outcomes depend, to a certain extent, on the kind of variation that organisms can produce through random genetic perturbation, that is, their phenotypic variability. Moreover, the properties of developmental mechanisms that produce the organisms affect their phenotypic variability. Two of these properties are modularity and robustness. Modularity is the degree to which interactions occur mostly within groups of the system's elements and scarcely between elements in different groups. Robustness is the propensity of a system to endure perturbations while preserving its phenotype. In this paper, we used a model of gene regulatory networks (GRNs) to study the relationship between modularity and robustness in developmental processes and how modularity affects the variation that random genetic mutations produce in the expression patterns of GRNs. Our results show that modularity and robustness are correlated in multifunctional GRNs and that selection for one of these properties affects the other as well. We contend that these observations may help to understand why modularity and robustness are widespread in biological systems. Additionally, we found that modular networks tend to produce new expression patterns with subtle changes localized in the expression of a few groups of genes. This effect in the phenotypic variability of modular GRNs may bear important consequences for adaptive evolution: it may help to adjust the expression of one group of genes at a time, with few alterations on other previously evolved expression patterns.

WebMaBoSS: A Web Interface for Simulating Boolean Models Stochastically

WebMaBoSS is an easy-to-use web interface for conversion, storage, simulation and analysis of Boolean models that allows to get insight from these models without any specific knowledge of modeling or coding. It relies on an existing software, MaBoSS, which simulates Boolean models using a stochastic approach: it applies continuous time Markov processes over the Boolean network. It was initially built to fill the gap between Boolean and continuous formalisms, i.e., providing semi-quantitative results using a simple representation with a minimum number of parameters to fit. The goal of WebMaBoSS is to simplify the use and the analysis of Boolean models coping with two main issues: 1) the simulation of Boolean models of intracellular processes with MaBoSS, or any modeling tool, may appear as non-intuitive for non-experts; 2) the simulation of already-published models available in current model databases (e.g., Cell Collective, BioModels) may require some extra steps to ensure compatibility with modeling tools such as MaBoSS. With WebMaBoSS, new models can be created or imported directly from existing databases. They can then be simulated, modified and stored in personal folders. Model simulations are performed easily, results visualized interactively, and figures can be exported in a preferred format. Extensive model analyses such as mutant screening or parameter sensitivity can also be performed. For all these tasks, results are stored and can be subsequently filtered to look for specific outputs. This web interface can be accessed at the address: https://maboss.curie.fr/webmaboss/ and deployed locally using docker. This application is open-source under LGPL license, and available at https://github.com/sysbio-curie/WebMaBoSS.

A system-level mechanistic explanation for asymmetric stem cell fates: Arabidopsis thaliana root niche as a study system

Asymmetric divisions maintain long-term stem cell populations while producing new cells that proliferate and then differentiate. Recent reports in animal systems show that divisions of stem cells can be uncoupled from their progeny differentiation, and the outcome of a division could be influenced by microenvironmental signals. But the underlying system-level mechanisms, and whether this dynamics also occur in plant stem cell niches (SCN), remain elusive. This article presents a cell fate regulatory network model that contributes to understanding such mechanism and identify critical cues for cell fate transitions in the root SCN. Novel computational and experimental results show that the transcriptional regulator SHR is critical for the most frequent asymmetric division previously described for quiescent centre stem cells. A multi-scale model of the root tip that simulated each cell's intracellular regulatory network, and the dynamics of SHR intercellular transport as a cell-cell coupling mechanism, was developed. It revealed that quiescent centre cell divisions produce two identical cells, that may acquire different fates depending on the feedback between SHR's availability and the state of the regulatory network. Novel experimental data presented here validates our model, which in turn, constitutes the first proposed systemic mechanism for uncoupled SCN cell division and differentiation.

The proneural wave in the Drosophila optic lobe is driven by an excitable reaction-diffusion mechanism

In living organisms, self-organised waves of signalling activity propagate spatiotemporal information within tissues. During the development of the largest component of the visual processing centre of the Drosophila brain, a travelling wave of proneural gene expression initiates neurogenesis in the larval optic lobe primordium and drives the sequential transition of neuroepithelial cells into neuroblasts. Here, we propose that this 'proneural wave' is driven by an excitable reaction-diffusion system involving epidermal growth factor receptor (EGFR) signalling interacting with the proneural gene l'sc. Within this framework, a propagating transition zone emerges from molecular feedback and diffusion. Ectopic activation of EGFR signalling in clones within the neuroepithelium demonstrates that a transition wave can be excited anywhere in the tissue by inducing signalling activity, consistent with a key prediction of the model. Our model illuminates the physical and molecular underpinnings of proneural wave progression and suggests a generic mechanism for regulating the sequential differentiation of tissues.

On logical bifurcation diagrams

Bifurcation theory provides a powerful framework to analyze the dynamics of differential systems as a function of specific parameters. Abou-Jaoudé et al. (2009) introduced the concept of logical bifurcation diagrams, an analog of bifurcation diagrams for the logical modeling framework. In this work, we propose a formal definition of this concept. Since logical models are inherently discrete, we use the piecewise differential (PWLD) framework to introduce the underlying bifurcation parameters. Given a regulatory graph, a set of PWLD models is mapped to a set of logical models consistent with this graph, thereby linking continuous changes of bifurcation parameters to sequences of valuations of logical parameters. A logical bifurcation diagram corresponds then to a sequence of valuations of the logical parameters (with their associated set of attractors) consistent with at least one bifurcation diagram of the set of PWLD models. Necessary conditions on logical bifurcation diagrams in the general case, as well as a characterization of these diagrams in the Boolean case, exploiting a partial order between the logical parameters, are provided. We also propose a procedure to determine a logical bifurcation diagram of maximum length, starting from an initial valuation of the logical parameters, in the Boolean case. Finally, we apply our methodology to the analysis of a biological model of the p53-Mdm2 network.

A Novel Data-Driven Boolean Model for Genetic Regulatory Networks

A Boolean model is a simple, discrete and dynamic model without the need to consider the effects at the intermediate levels. However, little effort has been made into constructing activation, inhibition, and protein decay networks, which could indicate the direct roles of a gene (or its synthesized protein) as an activator or inhibitor of a target gene. Therefore, we propose to focus on the general Boolean functions at the subfunction level taking into account the effectiveness of protein decay, and further split the subfunctions into the activation and inhibition domains. As a consequence, we developed a novel data-driven Boolean model; namely, the Fundamental Boolean Model (FBM), to draw insights into gene activation, inhibition, and protein decay. This novel Boolean model provides an intuitive definition of activation and inhibition pathways and includes mechanisms to handle protein decay issues. To prove the concept of the novel model, we implemented a platform using R language, called FBNNet. Our experimental results show that the proposed FBM could explicitly display the internal connections of the mammalian cell cycle between genes separated into the connection types of activation, inhibition and protein decay. Moreover, the method we proposed to infer the gene regulatory networks for the novel Boolean model can be run in parallel and; hence, the computation cost is affordable. Finally, the novel Boolean model and related Fundamental Boolean Networks (FBNs) could show significant trajectories in genes to reveal how genes regulated each other over a given period. This new feature could facilitate further research on drug interventions to detect the side effects of a newly-proposed drug.

EpiLog: A software for the logical modelling of epithelial dynamics

Cellular responses are governed by regulatory networks subject to external signals from surrounding cells and to other micro-environmental cues. The logical (Boolean or multi-valued)  framework proved well suited to study such processes at the cellular level, by specifying qualitative models of involved signalling pathways and gene regulatory networks.  Here, we describe and illustrate the main features of EpiLog, a computational tool that implements an extension of the logical framework to the tissue level. EpiLog defines a collection of hexagonal cells over a 2D grid, which embodies a mono-layer epithelium. Basically, it defines a cellular automaton in which cell behaviours are driven by associated logical models subject to external signals.  EpiLog is freely available on the web at http://epilog-tool.org. It is implemented in Java (version ≥1.7 required) and the source code is provided at https://github.com/epilog-tool/epilog under a GNU General Public License v3.0.

Logical Modeling and Analysis of Cellular Regulatory Networks With GINsim 3.0

The logical formalism is well adapted to model large cellular networks, in particular when detailed kinetic data are scarce. This tutorial focuses on this well-established qualitative framework. Relying on GINsim (release 3.0), a software implementing this formalism, we guide the reader step by step toward the definition, the analysis and the simulation of a four-node model of the mammalian p53-Mdm2 network.

Gene regulation during Drosophila eggshell patterning

A common path to the formation of complex 3D structures starts with an epithelial sheet that is patterned by inductive cues that control the spatiotemporal activities of transcription factors. These activities are then interpreted by the cis-regulatory regions of the genes involved in cell differentiation and tissue morphogenesis. Although this general strategy has been documented in multiple developmental contexts, the range of experimental models in which each of the steps can be examined in detail and evaluated in its effect on the final structure remains very limited. Studies of the Drosophila eggshell patterning provide unique insights into the multiscale mechanisms that connect gene regulation and 3D epithelial morphogenesis. Here we review the current understanding of this system, emphasizing how the recent identification of cis-regulatory regions of genes within the eggshell patterning network enables mechanistic analysis of its spatiotemporal dynamics and evolutionary diversification. It appears that cis-regulatory changes can account for only some aspects of the morphological diversity of Drosophila eggshells, such as the prominent differences in the number of the respiratory dorsal appendages. Other changes, such as the appearance of the respiratory eggshell ridges, are caused by changes in the spatial distribution of inductive signals. Both types of mechanisms are at play in this rapidly evolving system, which provides an excellent model of developmental patterning and morphogenesis.

The repertoire of epithelial morphogenesis on display: Progressive elaboration of Drosophila egg structure

Epithelial structures are foundational for tissue organization in all metazoans. Sheets of epithelial cells form lateral adhesive junctions and acquire apico-basal polarity perpendicular to the surface of the sheet. Genetic analyses in the insect model, Drosophila melanogaster, have greatly advanced our understanding of how epithelial organization is established, and how it is modulated during tissue morphogenesis. Major insights into collective cell migrations have come from analyses of morphogenetic movements within the adult follicular epithelium that cooperates with female germ cells to build a mature egg. Epithelial follicle cells progress through tightly choreographed phases of proliferation, patterning, reorganization and migrations, before they differentiate to form the elaborate structures of the eggshell. Distinct structural domains are organized by differential adhesion, within which lateral junctions are remodeled to further shape the organized epithelia. During collective cell migrations, adhesive interactions mediate supracellular organization of planar polarized macromolecules, and facilitate crawling over the basement membrane or traction against adjacent cell surfaces. Comparative studies with other insects are revealing the diversification of morphogenetic movements for elaboration of epithelial structures. This review surveys the repertoire of follicle cell morphogenesis, to highlight the coordination of epithelial plasticity with progressive differentiation of a secretory epithelium. Technological advances will keep this tissue at the leading edge for interrogating the precise spatiotemporal regulation of normal epithelial reorganization events, and provide a framework for understanding pathological tissue dysplasia.

Logical Modeling and Dynamical Analysis of Cellular Networks

The logical (or logic) formalism is increasingly used to model regulatory and signaling networks. Complementing these applications, several groups contributed various methods and tools to support the definition and analysis of logical models. After an introduction to the logical modeling framework and to several of its variants, we review here a number of recent methodological advances to ease the analysis of large and intricate networks. In particular, we survey approaches to determine model attractors and their reachability properties, to assess the dynamical impact of variations of external signals, and to consistently reduce large models. To illustrate these developments, we further consider several published logical models for two important biological processes, namely the differentiation of T helper cells and the control of mammalian cell cycle.

Toward a study of gene regulatory constraints to morphological evolution of the Drosophila ocellar region

The morphology and function of organs depend on coordinated changes in gene expression during development. These changes are controlled by transcription factors, signaling pathways, and their regulatory interactions, which are represented by gene regulatory networks (GRNs). Therefore, the structure of an organ GRN restricts the morphological and functional variations that the organ can experience—its potential morphospace. Therefore, two important questions arise when studying any GRN: what is the predicted available morphospace and what are the regulatory linkages that contribute the most to control morphological variation within this space. Here, we explore these questions by analyzing a small “three-node” GRN model that captures the Hh-driven regulatory interactions controlling a simple visual structure: the ocellar region of Drosophila. Analysis of the model predicts that random variation of model parameters results in a specific non-random distribution of morphological variants. Study of a limited sample of drosophilids and other dipterans finds a correspondence between the predicted phenotypic range and that found in nature. As an alternative to simulations, we apply Bayesian networks methods in order to identify the set of parameters with the largest contribution to morphological variation. Our results predict the potential morphological space of the ocellar complex and identify likely candidate processes to be responsible for ocellar morphological evolution using Bayesian networks. We further discuss the assumptions that the approach we have taken entails and their validity.

Complementing ODE-Based System Analysis Using Boolean Networks Derived from an Euler-Like Transformation

In this paper, we present a systematic transition scheme for a large class of ordinary differential equations (ODEs) into Boolean networks. Our transition scheme can be applied to any system of ODEs whose right hand sides can be written as sums and products of monotone functions. It performs an Euler-like step which uses the signs of the right hand sides to obtain the Boolean update functions for every variable of the corresponding discrete model. The discrete model can, on one hand, be considered as another representation of the biological system or, alternatively, it can be used to further the analysis of the original ODE model. Since the generic transformation method does not guarantee any property conservation, a subsequent validation step is required. Depending on the purpose of the model this step can be based on experimental data or ODE simulations and characteristics. Analysis of the resulting Boolean model, both on its own and in comparison with the ODE model, then allows to investigate system properties not accessible in a purely continuous setting. The method is exemplarily applied to a previously published model of the bovine estrous cycle, which leads to new insights regarding the regulation among the components, and also indicates strongly that the system is tailored to generate stable oscillations.