Intercellular coupling amplifies fate segregation during Caenorhabditis elegans vulval development

Analysis of Pattern Formation by Colored Petri Nets With Quantitative Regulation of Gene Expression Level

Modeling and simulation are becoming indispensable tools for studying multicellular events such as pattern formation during embryonic development. In this paper, we propose a new approach for analyzing multicellular biological phenomena by combining colored hybrid Petri nets (ColHPNs) with newly devised biological experiments that can control level of a gene quantitatively. With this approach, we analyzed patterning of the boundary cells in the Drosophila large intestine, where one-cell-wide domain of boundary cells differentiate through Delta-Notch signaling. Biological experiments regulating the level of Delta resulted in six distinct patterns of boundary cells correlating with the level of Delta. All these patterns were successfully reproduced by simulation based on ColHPN modeling only by changing the parameter related to the level of Delta. By monitoring the concentration of the active form of Notch in each cell during simulation, it was revealed that these distinct modes of patterning correlate with the fluctuation range of active Notch. Combination of simulation and quantitative manipulation of a gene activity described here is a reliable and powerful approach for analyzing and understanding the patterning process regulated by Notch signaling. This approach can be easily adapted to address other similar pattern formation issues in the systems biology area.

Cell fate determination is influenced by Notch heterogeneity

Notch signaling (NS) determines the fate of adjacent cells during metazoans development. This intercellular signaling mechanism regulates diverse development processes like cell differentiation, proliferation, survival and is considered responsible for maintaining cellular homeostasis. In this study, we elucidate the role of Notch heterogeneity (NH) in cell fate determination. We studied the role of NH at intercellular, intracellular and the coexistence of Notch variation simultaneously at the intracellular and intercellular level in direct cell-cell signaling on an irregular cell mosaic. In addition, the effect of intracellular Notch receptor diffusion on an irregular cell lattice is also taken into account during Delta-Notch lateral inhibition (LI) process. Through mathematical and computational models, we discovered that the classical checkerboard pattern formation can be reproduced with an accuracy of 70-81% by accounting for NH in a realistic epithelial layer of multicellular organisms.

Outstanding questions in developmental ERK signaling

The extracellular signal-regulated kinase (ERK) pathway leads to activation of the effector molecule ERK, which controls downstream responses by phosphorylating a variety of substrates, including transcription factors. Crucial insights into the regulation and function of this pathway came from studying embryos in which specific phenotypes arise from aberrant ERK activation. Despite decades of research, several important questions remain to be addressed for deeper understanding of this highly conserved signaling system and its function. Answering these questions will require quantifying the first steps of pathway activation, elucidating the mechanisms of transcriptional interpretation and measuring the quantitative limits of ERK signaling within which the system must operate to avoid developmental defects.

Enhanced Delta-Notch Lateral Inhibition Model Incorporating Intracellular Notch Heterogeneity and Tension-Dependent Rate of Delta-Notch Binding that Reproduces Sprouting Angiogenesis Patterns

Endothelial cells adopt unique cell fates during sprouting angiogenesis, differentiating into tip or stalk cells. The fate selection process is directed by Delta-Notch lateral inhibition pathway. Classical Delta-Notch models produce a spatial pattern of tip cells separated by a single stalk cell, or the salt-and-pepper pattern. However, classical models cannot explain alternative tip-stalk patterning, such as tip cells that are separated by two or more stalk cells. We show that lateral inhibition models involving only Delta and Notch proteins can also recapitulate experimental tip-stalk patterns by invoking two mechanisms, specifically, intracellular Notch heterogeneity and tension-dependent rate of Delta-Notch binding. We introduce our computational model and analysis where we establish that our enhanced Delta-Notch lateral inhibition model can recapitulate a greater variety of tip-stalk patterning which is previously not possible using classical lateral inhibition models. In our enhanced Delta-Notch lateral inhibition model, we observe the existence of a hybrid cell type displaying intermediate tip and stalk cells’ characteristics. We validate the existence of such hybrid cells by immuno-staining of endothelial cells with tip cell markers, Delta and CD34, which substantiates our enhanced model.

Tinkering and the Origins of Heritable Anatomical Variation in Vertebrates

Evolutionary change comes from natural and other forms of selection acting on existing anatomical and physiological variants. While much is known about selection, little is known about the details of how genetic mutation leads to the range of heritable anatomical variants that are present within any population. This paper takes a systems-based view to explore how genomic mutation in vertebrate genomes works its way upwards, though changes to proteins, protein networks, and cell phenotypes to produce variants in anatomical detail. The evidence used in this approach mainly derives from analysing anatomical change in adult vertebrates and the protein networks that drive tissue formation in embryos. The former indicate which processes drive variation-these are mainly patterning, timing, and growth-and the latter their molecular basis. The paper then examines the effects of mutation and genetic drift on these processes, the nature of the resulting heritable phenotypic variation within a population, and the experimental evidence on the speed with which new variants can appear under selection. The discussion considers whether this speed is adequate to explain the observed rate of evolutionary change or whether other non-canonical, adaptive mechanisms of heritable mutation are needed. The evidence to hand suggests that they are not, for vertebrate evolution at least.

A computational model predicts genetic nodes that allow switching between species-specific responses in a conserved signaling network

Alterations to only specific parameters in a model including EGF, Wnt and Notch lead to cell behavior differences.

A Primer on Quantitative Modeling

Caenorhabditis elegans is particularly suitable for obtaining quantitative data about behavior, neuronal activity, gene expression, ecological interactions, quantitative traits, and much more. To exploit the full potential of these data one seeks to interpret them within quantitative models. Using two examples from the C. elegans literature we briefly explore several types of modeling approaches relevant to worm biology, and show how they might be used to interpret data, formulate testable hypotheses, and suggest new experiments. We emphasize that the choice of modeling approach is strongly dependent on the questions of interest and the type of available knowledge.

The origins of mutational robustness

Biological systems are resistant to genetic changes; a property known as mutational robustness, the origin of which remains an open question. In recent years, researchers have explored emergent properties of biological systems and mechanisms of genetic redundancy to reveal how mutational robustness emerges and persists. Several mechanisms have been proposed to explain the origin of mutational robustness, including molecular chaperones and gene duplication. The latter has received much attention, but its role in robustness remains controversial. Here, I examine recent findings linking genetic redundancy through gene duplication and mutational robustness. Experimental evolution and genome resequencing have made it possible to test the role of gene duplication in tolerating mutations at both the coding and regulatory levels. This evidence as well as previous findings on regulatory reprogramming of duplicates support the role of gene duplication in the origin of robustness.

Collective motion of cells: from experiments to models

Swarming or collective motion of living entities is one of the most common and spectacular manifestations of living systems that have been extensively studied in recent years. A number of general principles have been established. The interactions at the level of cells are quite different from those among individual animals, therefore the study of collective motion of cells is likely to reveal some specific important features which we plan to overview in this paper. In addition to presenting the most appealing results from the quickly growing related literature we also deliver a critical discussion of the emerging picture and summarize our present understanding of collective motion at the cellular level. Collective motion of cells plays an essential role in a number of experimental and real-life situations. In most cases the coordinated motion is a helpful aspect of the given phenomenon and results in making a related process more efficient (e.g., embryogenesis or wound healing), while in the case of tumor cell invasion it appears to speed up the progression of the disease. In these mechanisms cells both have to be motile and adhere to one another, the adherence feature being the most specific to this sort of collective behavior. One of the central aims of this review is to present the related experimental observations and treat them in light of a few basic computational models so as to make an interpretation of the phenomena at a quantitative level as well.

Cells change their sensitivity to an EGF morphogen gradient to control EGF-induced gene expression

How cells in developing organisms interpret the quantitative information contained in morphogen gradients is an open question. Here we address this question using a novel integrative approach that combines quantitative measurements of morphogen-induced gene expression at single-mRNA resolution with mathematical modelling of the induction process. We focus on the induction of Notch ligands by the LIN-3/EGF morphogen gradient during vulva induction in Caenorhabditis elegans. We show that LIN-3/EGF-induced Notch ligand expression is highly dynamic, exhibiting an abrupt transition from low to high expression. Similar transitions in Notch ligand expression are observed in two highly divergent wild C. elegans isolates. Mathematical modelling and experiments show that this transition is driven by a dynamic increase in the sensitivity of the induced cells to external LIN-3/EGF. Furthermore, this increase in sensitivity is independent of the presence of LIN-3/EGF. Our integrative approach might be useful to study induction by morphogen gradients in other systems.

A model of the regulatory network involved in the control of the cell cycle and cell differentiation in the Caenorhabditis elegans vulva

BACKGROUND

There are recent experimental reports on the cross-regulation between molecules involved in the control of the cell cycle and the differentiation of the vulval precursor cells (VPCs) of Caenorhabditis elegans. Such discoveries provide novel clues on how the molecular mechanisms involved in the cell cycle and cell differentiation processes are coordinated during vulval development. Dynamic computational models are helpful to understand the integrated regulatory mechanisms affecting these cellular processes.

RESULTS

Here we propose a simplified model of the regulatory network that includes sufficient molecules involved in the control of both the cell cycle and cell differentiation in the C. elegans vulva to recover their dynamic behavior. We first infer both the topology and the update rules of the cell cycle module from an expected time series. Next, we use a symbolic algorithmic approach to find which interactions must be included in the regulatory network. Finally, we use a continuous-time version of the update rules for the cell cycle module to validate the cyclic behavior of the network, as well as to rule out the presence of potential artifacts due to the synchronous updating of the discrete model. We analyze the dynamical behavior of the model for the wild type and several mutants, finding that most of the results are consistent with published experimental results.

CONCLUSIONS

Our model shows that the regulation of Notch signaling by the cell cycle preserves the potential of the VPCs and the three vulval fates to differentiate and de-differentiate, allowing them to remain completely responsive to the concentration of LIN-3 and lateral signal in the extracellular microenvironment.

Logic programming to predict cell fate patterns and retrodict genotypes in organogenesis

Caenorhabditis elegans vulval development is a paradigm system for understanding cell differentiation in the process of organogenesis. Through temporal and spatial controls, the fate pattern of six cells is determined by the competition of the LET-23 and the Notch signalling pathways. Modelling cell fate determination in vulval development using state-based models, coupled with formal analysis techniques, has been established as a powerful approach in predicting the outcome of combinations of mutations. However, computing the outcomes of complex and highly concurrent models can become prohibitive. Here, we show how logic programs derived from state machines describing the differentiation of C. elegans vulval precursor cells can increase the speed of prediction by four orders of magnitude relative to previous approaches. Moreover, this increase in speed allows us to infer, or 'retrodict', compatible genomes from cell fate patterns. We exploit this technique to predict highly variable cell fate patterns resulting from dig-1 reduced-function mutations and let-23 mosaics. In addition to the new insights offered, we propose our technique as a platform for aiding the design and analysis of experimental data.

MODELING AND ANALYZING BIOLOGICAL SYSTEMS USING COLORED HIERARCHICAL PETRI NETS ILLUSTRATED BYC. ELEGANSVULVAL DEVELOPMENT

Colored Petri nets allow compact, parameterizable and scalable representations of large-scale biological models by encoding, e.g., species as colored tokens, and offer a variety of analysis techniques, e.g., structural analysis, simulation and model checking to analyze biological models. However, so far colored Petri nets have not been widely used and well explored in systems biology. In this paper, we aim to present a systematic approach to modeling and analyzing complex biological systems using colored Petri nets in order to help biologists to easily use them. We first describe a framework comprising a family of related colored Petri nets: colored qualitative Petri net (𝒬𝒫𝒩𝒞), colored stochastic Petri net (𝒮𝒫𝒩𝒞) and colored continuous Petri net (𝒞𝒫𝒩𝒞). They share structure, but are specialized by their kinetic information. Based on this framework, we present our colored Petri net approach to modeling and analyzing complex biological systems. First a biological system is modeled as a hierarchical 𝒬𝒫𝒩𝒞model, animated and analyzed by structural analysis; then it is converted into a 𝒮𝒫𝒩𝒞or 𝒞𝒫𝒩𝒞model, to be further analyzed using stochastic or continuous simulation, and simulative or numerical model checking. We demonstrate this approach using a nontrivial example, Caenorhabditis elegans vulval development.

A network model for the specification of vulval precursor cells and cell fusion control in Caenorhabditis elegans

The vulva of Caenorhabditis elegans has been long used as an experimental model of cell differentiation and organogenesis. While it is known that the signaling cascades of Wnt, Ras/MAPK, and NOTCH interact to form a molecular network, there is no consensus regarding its precise topology and dynamical properties. We inferred the molecular network, and developed a multivalued synchronous discrete dynamic model to study its behavior. The model reproduces the patterns of activation reported for the following types of cell: vulval precursor, first fate, second fate, second fate with reversed polarity, third fate, and fusion fate. We simulated the fusion of cells, the determination of the first, second, and third fates, as well as the transition from the second to the first fate. We also used the model to simulate all possible single loss- and gain-of-function mutants, as well as some relevant double and triple mutants. Importantly, we associated most of these simulated mutants to multivulva, vulvaless, egg-laying defective, or defective polarity phenotypes. The model shows that it is necessary for RAL-1 to activate NOTCH signaling, since the repression of LIN-45 by RAL-1 would not suffice for a proper second fate determination in an environment lacking DSL ligands. We also found that the model requires the complex formed by LAG-1, LIN-12, and SEL-8 to inhibit the transcription of eff-1 in second fate cells. Our model is the largest reconstruction to date of the molecular network controlling the specification of vulval precursor cells and cell fusion control in C. elegans. According to our model, the process of fate determination in the vulval precursor cells is reversible, at least until either the cells fuse with the ventral hypoderm or divide, and therefore the cell fates must be maintained by the presence of extracellular signals.

Mathematical study of the role of Delta/Notch lateral inhibition during primary branching of Drosophila trachea development

A wide range of cellular developmental processes employ intercellular signaling via the Delta/Notch lateral inhibitory pathway to achieve stable spatial patterning. Recent genetic experiments have shown the importance of Delta/Notch lateral inhibition for regulating the number of tip cells in the tracheal primary branching of Drosophila. To examine the role of Delta/Notch regulation in the tip-cell selection, we analyzed a mathematical model of a simple lateral inhibitory system having input signals. Mathematical and numerical analyses revealed that the lateral inhibition did not amplify the signal difference between neighboring cells over the parameter ranges in which the spatial pattern of tip selection was realized. We also show that the number of tip cells becomes less affected by a fluctuation of the input gradient signal as the lateral inhibition becomes stronger. In addition, we demonstrate that the lateral inhibitory regulation enhances the robustness of the tip-cell selection compared with a system regulated by self-inhibition, an alternative means of inhibitory regulation. These results suggest that the lateral inhibition promotes the robustness of tip-cell selection in the tracheal development of Drosophila.

Geometry, epistasis, and developmental patterning

Developmental signaling networks are composed of dozens of components whose interactions are very difficult to quantify in an embryo. Geometric reasoning enumerates a discrete hierarchy of phenotypic models with a few composite variables whose parameters may be defined by in vivo data. Vulval development in the nematode Caenorhabditis elegans is a classic model for the integration of two signaling pathways; induction by EGF and lateral signaling through Notch. Existing data for the relative probabilities of the three possible terminal cell types in diverse genetic backgrounds as well as timed ablation of the inductive signal favor one geometric model and suffice to fit most of its parameters. The model is fully dynamic and encompasses both signaling and commitment. It then predicts the correlated cell fate probabilities for a cross between any two backgrounds/conditions. The two signaling pathways are combined additively, without interactions, and epistasis only arises from the nonlinear dynamical flow in the landscape defined by the geometric model. In this way, the model quantitatively fits genetic experiments purporting to show mutual pathway repression. The model quantifies the contributions of extrinsic vs. intrinsic sources of noise in the penetrance of mutant phenotypes in signaling hypomorphs and explains available experiments with no additional parameters. Data for anchor cell ablation fix the parameters needed to define Notch autocrine signaling.

Hybrid Modeling of Cell Signaling and Transcriptional Reprogramming and Its Application in C. elegans Development

Modeling of signal driven transcriptional reprogramming is critical for understanding of organism development, human disease, and cell biology. Many current modeling techniques discount key features of the biological sub-systems when modeling multiscale, organism-level processes. We present a mechanistic hybrid model, GESSA, which integrates a novel pooled probabilistic Boolean network model of cell signaling and a stochastic simulation of transcription and translation responding to a diffusion model of extracellular signals. We apply the model to simulate the well studied cell fate decision process of the vulval precursor cells (VPCs) in C. elegans, using experimentally derived rate constants wherever possible and shared parameters to avoid overfitting. We demonstrate that GESSA recovers (1) the effects of varying scaffold protein concentration on signal strength, (2) amplification of signals in expression, (3) the relative external ligand concentration in a known geometry, and (4) feedback in biochemical networks. We demonstrate that setting model parameters based on wild-type and LIN-12 loss-of-function mutants in C. elegans leads to correct prediction of a wide variety of mutants including partial penetrance of phenotypes. Moreover, the model is relatively insensitive to parameters, retaining the wild-type phenotype for a wide range of cell signaling rate parameters.

Quantitative variation in autocrine signaling and pathway crosstalk in the Caenorhabditis vulval network

BACKGROUND

Biological networks experience quantitative change in response to environmental and evolutionary variation. Computational modeling allows exploration of network parameter space corresponding to such variations. The intercellular signaling network underlying Caenorhabditis vulval development specifies three fates in a row of six precursor cells, yielding a quasi-invariant 3°3°2°1°2°3° cell fate pattern. Two seemingly conflicting verbal models of vulval precursor cell fate specification have been proposed: sequential induction by the EGF-MAP kinase and Notch pathways, or morphogen-based induction by the former.

RESULTS

To study the mechanistic and evolutionary system properties of this network, we combine experimental studies with computational modeling, using a model that keeps the network architecture constant but varies parameters. We first show that the Delta autocrine loop can play an essential role in 2° fate specification. With this autocrine loop, the same network topology can be quantitatively tuned to use in the six-cell-row morphogen-based or sequential patterning mechanisms, which may act singly, cooperatively, or redundantly. Moreover, different quantitative tunings of this same network can explain vulval patterning observed experimentally in C. elegans, C. briggsae, C. remanei, and C. brenneri. We experimentally validate model predictions, such as interspecific differences in isolated vulval precursor cell behavior and in spatial regulation of Notch activity.

CONCLUSIONS

Our study illustrates how quantitative variation in the same network comprises developmental patterning modes that were previously considered qualitatively distinct and also accounts for evolution among closely related species.

The zebrafish: scalable in vivo modeling for systems biology

The zebrafish offers a scalable vertebrate model for many areas of biologic investigation. There is substantial conservation of genetic and genomic features and, at a higher order, conservation of intermolecular networks, as well as physiologic systems and phenotypes. We highlight recent work demonstrating the extent of this homology, and efforts to develop high-throughput phenotyping strategies suited to genetic or chemical screening on a scale compatible with in vivo validation for systems biology. We discuss the implications of these approaches for functional annotation of the genome, elucidation of multicellular processes in vivo, and mechanistic exploration of hypotheses generated by a broad range of 'unbiased' 'omic technologies such as expression profiling and genome-wide association. Finally, we outline potential strategies for the application of the zebrafish to the systematic study of phenotypic architecture, disease heterogeneity and drug responses.

The natural and engineered 3D microenvironment as a regulatory cue during stem cell fate determination

The concept of using stem cells as self-renewing sources of healthy cells in regenerative medicine has existed for decades, but most applications have yet to achieve clinical success. A main reason for the lack of successful stem cell therapies is the difficulty in fully recreating the maintenance and control of the native stem cell niche. Improving the performance of transplanted stem cells therefore requires a better understanding of the cellular mechanisms guiding stem cell behavior in both native and engineered three-dimensional (3D) microenvironments. Most techniques, however, for uncovering mechanisms controlling cell behavior in vitro have been developed using 2D cell cultures and are of limited use in 3D environments such as engineered tissue constructs. Deciphering the mechanisms controlling stem cell fate in native and engineered 3D environments, therefore, requires rigorous quantitative techniques that permit mechanistic, hypothesis-driven studies of cell-microenvironment interactions. Here, we review the current understanding of 2D and 3D stem cell control mechanisms and propose an approach to uncovering the mechanisms that govern stem cell behavior in 3D.

[Genetic and environmental variations in an intercellular signaling network]

Interindividual variation, be it of environmental or genetic origin, is crucial for biological evolution as well as in the medical context. This variation is not always directly visible, yet may be revealed under some environmental or genetic condition. In this essay is presented the example of the developmental model system underlying vulva formation in the nematode Caenorhabditis elegans, where an intercellular signaling network (EGF-Ras-MAP kinase, Notch and Wnt pathways) is involved in spatial patterning of the fates of the vulva precursor cells. Variation may be studied at two levels: (1) rare deviations in the system's output, i.e. the spatial pattern of vulva precursor cell fates ; (2) so-called << cryptic >> variation in the underlying intercellular signaling network, without change in the system's output. Like every biological system, this network displays genetic and -environmental epistasis.

Predicting phenotypic diversity and the underlying quantitative molecular transitions

During development, signaling networks control the formation of multicellular patterns. To what extent quantitative fluctuations in these complex networks may affect multicellular phenotype remains unclear. Here, we describe a computational approach to predict and analyze the phenotypic diversity that is accessible to a developmental signaling network. Applying this framework to vulval development in C. elegans, we demonstrate that quantitative changes in the regulatory network can render ∼500 multicellular phenotypes. This phenotypic capacity is an order-of-magnitude below the theoretical upper limit for this system but yet is large enough to demonstrate that the system is not restricted to a select few outcomes. Using metrics to gauge the robustness of these phenotypes to parameter perturbations, we identify a select subset of novel phenotypes that are the most promising for experimental validation. In addition, our model calculations provide a layout of these phenotypes in network parameter space. Analyzing this landscape of multicellular phenotypes yielded two significant insights. First, we show that experimentally well-established mutant phenotypes may be rendered using non-canonical network perturbations. Second, we show that the predicted multicellular patterns include not only those observed in C. elegans, but also those occurring exclusively in other species of the Caenorhabditis genus. This result demonstrates that quantitative diversification of a common regulatory network is indeed demonstrably sufficient to generate the phenotypic differences observed across three major species within the Caenorhabditis genus. Using our computational framework, we systematically identify the quantitative changes that may have occurred in the regulatory network during the evolution of these species. Our model predictions show that significant phenotypic diversity may be sampled through quantitative variations in the regulatory network without overhauling the core network architecture. Furthermore, by comparing the predicted landscape of phenotypes to multicellular patterns that have been experimentally observed across multiple species, we systematically trace the quantitative regulatory changes that may have occurred during the evolution of the Caenorhabditis genus.

The diversity of metazoan life forms that we experience today arose as multicellular systems continually sampled new phenotypes that withstood ever changing selective pressures. This phenotypic diversification is driven by variations in the underlying regulatory network that instructs cells to form multicellular patterns and structures. Here, we computationally construct the phenotypic diversity that may be accessible through quantitative tuning of the regulatory network that drives multicellular patterning during C. elegans vulval development. We show that significant phenotypic diversity may be sampled through quantitative variations without overhauling the core regulatory network architecture. Furthermore, by comparing the predicted landscape of phenotypes to multicellular patterns that have been experimentally observed across multiple species, we systematically deduce the quantitative molecular changes that may have transpired during the evolution of the Caenorhabditis genus.

Plasticity and errors of a robust developmental system in different environments

Many developmental processes generate invariant phenotypes in a wide range of ecological conditions. Such robustness to environmental variation is a fundamental biological property, yet its extent, limits, and adaptive significance have rarely been assessed empirically. Here we tested how environmental variation affects vulval formation in Caenorhabditis nematodes. In different environments, a correct vulval pattern develops with high precision, but rare deviant patterns reveal the system's limits and how its mechanisms respond to environmental challenges. Key features of the apparent robustness are functional redundancy among vulval precursor cells and tolerance to quantitative variation in Ras, Notch, and Wnt pathway activities. The observed environmental responses and precision of vulval patterning vary within and between Caenorhabditis species. These results highlight the complex response of developmental systems to the environment and illustrate how a robust and invariant phenotype may result through cellular and molecular processes that are highly plastic--across environments and evolution.

Modeling the dynamics of transcriptional gene regulatory networks for animal development

The dynamic process of cell fate specification is regulated by networks of regulatory genes. The architecture of the network defines the temporal order of specification events. To understand the dynamic control of the developmental process, the kinetics of mRNA and protein synthesis and the response of the cis-regulatory modules to transcription factor concentration must be considered. Here we review mathematical models for mRNA and protein synthesis kinetics which are based on experimental measurements of the rates of the relevant processes. The model comprises the response functions of cis-regulatory modules to their transcription factor inputs, by incorporating binding site occupancy and its dependence on biologically measurable quantities. We use this model to simulate gene expression, to distinguish between cis-regulatory execution of "AND" and "OR" logic functions, rationalize the oscillatory behavior of certain transcriptional auto-repressors and to show how linked subcircuits can be dealt with. Model simulations display the effects of mutation of binding sites, or perturbation of upstream gene expression. The model is a generally useful tool for understanding gene regulation and the dynamics of cell fate specification.

Intraspecific evolution of the intercellular signaling network underlying a robust developmental system

Many biological systems produce an invariant output when faced with stochastic or environmental variation. This robustness of system output to variation affecting the underlying process may allow for "cryptic" genetic evolution within the system without change in output. We studied variation of cell fate patterning of Caenorhabditis elegans vulva precursors, a developmental system that relies on a simple intercellular signaling network and yields an invariant output of cell fates and lineages among C. elegans wild isolates. We first investigated the system's genetic variation in C. elegans by means of genetic tools and cell ablation to break down its buffering mechanisms. We uncovered distinct architectures of quantitative variation along the Ras signaling cascade, including compensatory variation, and differences in cell sensitivity to induction along the anteroposterior axis. In the unperturbed system, we further found variation between isolates in spatio-temporal dynamics of Ras pathway activity, which can explain the phenotypic differences revealed upon perturbation. Finally, the variation mostly affects the signaling pathways in a tissue-specific manner. We thus demonstrate and characterize microevolution of a developmental signaling network. In addition, our results suggest that the vulva genetic screens would have yielded a different mutation spectrum, especially for Wnt pathway mutations, had they been performed in another C. elegans genetic background.

Executable cell biology

Computational modeling of biological systems is becoming increasingly important in efforts to better understand complex biological behaviors. In this review, we distinguish between two types of biological models--mathematical and computational--which differ in their representations of biological phenomena. We call the approach of constructing computational models of biological systems 'executable biology', as it focuses on the design of executable computer algorithms that mimic biological phenomena. We survey the main modeling efforts in this direction, emphasize the applicability and benefits of executable models in biological research and highlight some of the challenges that executable biology poses for biology and computer science. We claim that for executable biology to reach its full potential as a mainstream biological technique, formal and algorithmic approaches must be integrated into biological research. This will drive biology toward a more precise engineering discipline.

Negative autoregulation by FAS mediates robust fetal erythropoiesis

Tissue development is regulated by signaling networks that control developmental rate and determine ultimate tissue mass. Here we present a novel computational algorithm used to identify regulatory feedback and feedforward interactions between progenitors in developing erythroid tissue. The algorithm makes use of dynamic measurements of red cell progenitors between embryonic days 12 and 15 in the mouse. It selects for intercellular interactions that reproduce the erythroid developmental process and endow it with robustness to external perturbations. This analysis predicts that negative autoregulatory interactions arise between early erythroblasts of similar maturation stage. By studying embryos mutant for the death receptor FAS, or for its ligand, FASL, and by measuring the rate of FAS-mediated apoptosis in vivo, we show that FAS and FASL are pivotal negative regulators of fetal erythropoiesis, in the manner predicted by the computational model. We suggest that apoptosis in erythroid development mediates robust homeostasis regulating the number of red blood cells reaching maturity.

What lies at the interface of regenerative medicine and developmental biology?

At a recent Keystone Symposium on `Developmental Biology and Tissue Engineering', new findings in areas ranging from stem cell differentiation,embryonic pattern formation and organ regeneration to engineered cell microenvironments, synthetic biomaterials and artificial tissue fabrication were described. Although these new advances were exciting, this symposium clarified that biologists and engineers often view the challenge of tissue formation from different, and sometimes conflicting, perspectives. These dichotomies raise questions regarding the definition of regenerative medicine,but offer the promise of exciting new interdisciplinary approaches to tissue and organ regeneration, if effective alliances can be established.

Cryptic quantitative evolution of the vulva intercellular signaling network in Caenorhabditis

BACKGROUND

The Caenorhabditis vulva is formed from a row of Pn.p precursor cells, which adopt a spatial cell-fate pattern-3 degrees 3 degrees 2 degrees 1 degrees 2 degrees 3 degrees -centered on the gonadal anchor cell. This pattern is robustly specified by an intercellular signaling network including EGF/Ras induction from the anchor cell and Delta/Notch signaling between the precursor cells. It is unknown how the roles and quantitative contributions of these signaling pathways have evolved in closely related Caenorhabditis species.

RESULTS

Cryptic evolution in the network is uncovered by quantification of cell-fate-pattern frequencies obtained after displacement of the system out of its normal range, either by anchor-cell ablations or through LIN-3/EGF overexpression. Silent evolution in the Caenorhabditis genus covers a large neutral space of cell-fate patterns. Direct induction of the 1 degrees fate as in C. elegans appeared within the genus. C. briggsae displays a graded induction of 1 degrees and 2 degrees fates, with 1 degrees fate induction requiring a longer time than in C. elegans, and a reduced lateral inhibition of adjacent 1 degrees fates. C. remanei displays a strong lateral induction of 2 degrees fates relative to vulval-fate activation in the central cell. This evolution in cell-fate pattern space can be experimentally reconstituted by mild variations of Ras, Wnt, and Notch pathway activities in C. elegans and C. briggsae.

CONCLUSIONS

Quantitative evolution in the roles of graded induction by LIN-3/EGF and Notch signaling is demonstrated for the Caenorhabditis vulva signaling network. This evolutionary system biology approach provides a quantitative view of the variational properties of this biological system.

Biology by numbers: mathematical modelling in developmental biology

In recent years, mathematical modelling of developmental processes has earned new respect. Not only have mathematical models been used to validate hypotheses made from experimental data, but designing and testing these models has led to testable experimental predictions. There are now impressive cases in which mathematical models have provided fresh insight into biological systems, by suggesting, for example, how connections between local interactions among system components relate to their wider biological effects. By examining three developmental processes and corresponding mathematical models, this Review addresses the potential of mathematical modelling to help understand development.

Mechanisms and evolution of environmental responses in Caenorhabditis elegans

We review mechanistic and evolutionary aspects of interactions between the model organism Caenorhabditis elegans and its environment. In particular, we focus on environmental effects affecting developmental mechanisms. We describe natural and laboratory environments of C. elegans and provide an overview of the different environmental responses of this organism. We then show how two developmental processes respond to changes in the environment. First, we discuss the development of alternative juvenile stages, the dauer and non-dauer larva. This example illustrates how development responds to variation in the environment to generate complex phenotypic variation. Second, we discuss the development of the C. elegans vulva. This example illustrates how development responds to variation in the environment while generating an invariant final phenotype.

Synchronization in coupled cells with activator-inhibitor pathways

The functional dynamics exhibited by cell collectives are fascinating examples of robust, synchronized, collective behavior in spatially extended biological systems. To investigate the roles of local cellular dynamics and interaction strength in the spatiotemporal dynamics of cell collectives of different sizes, we study a model system consisting of a ring of coupled cells incorporating a three-step biochemical pathway of regulated activator-inhibitor reactions. The isolated individual cells display very complex dynamics as a result of the nonlinear interactions common in cellular processes. On coupling the cells to nearest neighbors, through diffusion of the pathway end product, the ring of cells yields a host of interesting and unusual dynamical features such as, suppression of chaos, phase synchronization, traveling waves, and intermittency, for varying interaction strengths and system sizes. But robust complete synchronization can be induced in these coupled cells with a small degree of random coupling among them even where regular coupling yielded only intermittent synchronization. Our studies indicate that robustness in synchronized functional dynamics in tissues and cell populations in nature can be ensured by a few transient random connections among the cells. Such connections are being discovered only recently in real cellular systems.

Robustness and evolution: concepts, insights and challenges from a developmental model system

Robustness, the persistence of an organismal trait under perturbations, is a ubiquitous property of complex living systems. We here discuss key concepts related to robustness with examples from vulva development in the nematode Caenorhabditis elegans. We emphasize the need to be clear about the perturbations a trait is (or is not) robust to. We discuss two prominent mechanistic causes of robustness, namely redundancy and distributed robustness. We also discuss possible evolutionary causes of robustness, one of which does not involve natural selection. To better understand robustness is of paramount importance for understanding organismal evolution. Part of the reason is that highly robust systems can accumulate cryptic variation that can serve as a source of new adaptations and evolutionary innovations. We point to some key challenges in improving our understanding of robustness.

Curvature and spatial organization in biological membranes

Cellular membranes bend and curve into a multitude of shapes as they perform various functions. These deformations make use of the remarkable material properties of biological membranes inherent in their nature as two-dimensional fluids. The curvature of membranes is controlled by the constituent proteins and lipids, but conversely, curvature itself provides mechanisms for organizing mobile membrane molecules. In this article we survey recent experiments that have uncovered intriguing connections between mechanics and biochemistry at membranes, focusing on the influence of molecular shape on curvature, links between phase separation and curvature, and membrane bending at inter-cellular contacts. We describe the concepts that emerge from these studies, especially the existence of long-range, curvature-mediated mechanisms for spatial organization in membranes, and highlight open areas for future research.

Quantitative Models of Developmental Pattern Formation

Pattern formation in developing organisms can be regulated at a variety of levels, from gene sequence to anatomy. At this level of complexity, mechanistic models of development become essential for integrating data, guiding future experiments, and predicting the effects of genetic and physical perturbations. However, the formulation and analysis of quantitative models of development are limited by high levels of uncertainty in experimental measurements, a large number of both known and unknown system components, and the multiscale nature of development. At the same time, an expanding arsenal of experimental tools can constrain models and directly test their predictions, making the modeling efforts not only necessary, but feasible. Using a number of problems in fruit fly development, we discuss how models can be used to test the feasibility of proposed patterning mechanisms and characterize their systems-level properties.