Robustness, flexibility, and the role of lateral inhibition in the neurogenic network

A theory for the arrangement of sensory organs in Drosophila

We study the arrangements of recurved bristles on the anterior wing margin of wild-type and mutant Drosophila. The epidermal or neural fate of a proneural cell depends on the concentrations of proteins of the achaete-scute complex. At puparium formation, concentrations of proteins are nearly identical in all cells of the anterior wing and each cell has the potential for neural fate. In wild-type flies, the action of regulatory networks drives the initial state to one where a bristle grows out of every fifth cell. Recent experiments have shown that the frequency of recurved bristles can be made to change by adjusting the mean concentrations of the zinc-finger transcription factor Senseless and the micro-RNA miR-9a. Specifically, mutant flies with reduced levels of miR-9a exhibit ectopic bristles, and those with lower levels of both miR-9a and Senseless show regular organization of recurved bristles, but with a lower periodicity of 4. We argue that these characteristics can be explained assuming an underlying Turing-type bifurcation whereby a periodic pattern spontaneously emerges from a uniform background. However, bristle patterns occur in a discrete array of cells, and are not mediated by diffusion. We argue that intracellular actions of transmembrane proteins such as Delta and Notch can play a role of diffusion in destabilizing the homogeneous state. In contrast to diffusion, intercellular actions can be activating or inhibiting; further, there can be lateral cross-species interactions. We introduce a phenomenological model to study bristle arrangements and make several model-independent predictions that can be tested in experiments. In our theory, miRNA-9a is one of the components of the underlying network and has no special regulatory role. The loss of periodicity in its absence is due to the transfer of the system to a bistable state.

Carry-over effect of larval settlement cue on postlarval gene expression in the marine gastropod Haliotis asinina

The drastic shift from pelagic larvae to benthic adult form that occurs during marine invertebrate metamorphosis is often induced by intimate interactions between settling larvae and their benthic environment. Larval experience prior to and during metamorphosis can significantly affect adult fitness, but it is presently unknown whether the exact nature of the inductive cue is an experience that matters, or by what mechanism such carry-over effects are mediated. Here we test for carry-over effects of the specific nature of inductive cues on gene expression in metamorphosing postlarvae of the tropical abalone, Haliotis asinina. Postlarvae induced by three different species of coralline algae all successfully undergo metamorphosis, yet the expression profiles of 11 of 17 metamorphosis-related genes differ according to which species of algae the larvae settled upon. Significantly, several genes continue to be differentially expressed for at least 40 h after removal of the algae from the postlarvae, clearly demonstrating a carry-over effect of inductive cue on gene expression. We observe a carryover effect in several genes with varying functions and spatial expression patterns, indicating that each algal species impacts global gene expression in a unique manner. These data unexpectedly reveal that transcriptional modulation of metamorphosis-related genes is contingent upon the precise composition of the benthic microenvironment experienced directly at induction of settlement, and highlight transcription as a mechanism that can mediate between larval and postlarval experiences. For new recruits into an abalone population, metamorphosis clearly does not represent a new transcriptional beginning.

The genotype-phenotype relationship in multicellular pattern-generating models--the neglected role of pattern descriptors

Background

A deep understanding of what causes the phenotypic variation arising from biological patterning processes, cannot be claimed before we are able to recreate this variation by mathematical models capable of generating genotype-phenotype maps in a causally cohesive way. However, the concept of pattern in a multicellular context implies that what matters is not the state of every single cell, but certain emergent qualities of the total cell aggregate. Thus, in order to set up a genotype-phenotype map in such a spatiotemporal pattern setting one is actually forced to establish new pattern descriptors and derive their relations to parameters of the original model. A pattern descriptor is a variable that describes and quantifies a certain qualitative feature of the pattern, for example the degree to which certain macroscopic structures are present. There is today no general procedure for how to relate a set of patterns and their characteristic features to the functional relationships, parameter values and initial values of an original pattern-generating model. Here we present a new, generic approach for explorative analysis of complex patterning models which focuses on the essential pattern features and their relations to the model parameters. The approach is illustrated on an existing model for Delta-Notch lateral inhibition over a two-dimensional lattice.

Results

By combining computer simulations according to a succession of statistical experimental designs, computer graphics, automatic image analysis, human sensory descriptive analysis and multivariate data modelling, we derive a pattern descriptor model of those macroscopic, emergent aspects of the patterns that we consider of interest. The pattern descriptor model relates the values of the new, dedicated pattern descriptors to the parameter values of the original model, for example by predicting the parameter values leading to particular patterns, and provides insights that would have been hard to obtain by traditional methods.

Conclusion

The results suggest that our approach may qualify as a general procedure for how to discover and relate relevant features and characteristics of emergent patterns to the functional relationships, parameter values and initial values of an underlying pattern-generating mathematical model.

The genotype-phenotype relationship in multicellular pattern-generating models--the neglected role of pattern descriptors

BACKGROUND

A deep understanding of what causes the phenotypic variation arising from biological patterning processes, cannot be claimed before we are able to recreate this variation by mathematical models capable of generating genotype-phenotype maps in a causally cohesive way. However, the concept of pattern in a multicellular context implies that what matters is not the state of every single cell, but certain emergent qualities of the total cell aggregate. Thus, in order to set up a genotype-phenotype map in such a spatiotemporal pattern setting one is actually forced to establish new pattern descriptors and derive their relations to parameters of the original model. A pattern descriptor is a variable that describes and quantifies a certain qualitative feature of the pattern, for example the degree to which certain macroscopic structures are present. There is today no general procedure for how to relate a set of patterns and their characteristic features to the functional relationships, parameter values and initial values of an original pattern-generating model. Here we present a new, generic approach for explorative analysis of complex patterning models which focuses on the essential pattern features and their relations to the model parameters. The approach is illustrated on an existing model for Delta-Notch lateral inhibition over a two-dimensional lattice.

RESULTS

By combining computer simulations according to a succession of statistical experimental designs, computer graphics, automatic image analysis, human sensory descriptive analysis and multivariate data modelling, we derive a pattern descriptor model of those macroscopic, emergent aspects of the patterns that we consider of interest. The pattern descriptor model relates the values of the new, dedicated pattern descriptors to the parameter values of the original model, for example by predicting the parameter values leading to particular patterns, and provides insights that would have been hard to obtain by traditional methods.

CONCLUSION

The results suggest that our approach may qualify as a general procedure for how to discover and relate relevant features and characteristics of emergent patterns to the functional relationships, parameter values and initial values of an underlying pattern-generating mathematical model.

Dynamical approaches to modeling developmental gene regulatory networks

The network of interacting regulatory signals within a cell comprises one of the most complex and powerful computational systems in biology. Gene regulatory networks (GRNs) play a key role in transforming the information encoded in a genome into morphological form. To achieve this feat, GRNs must respond to and integrate environmental signals with their internal dynamics in a robust and coordinated fashion. The highly dynamic nature of this process lends itself to interpretation and analysis in the language of dynamical models. Modeling provides a means of systematically untangling the complicated structure of GRNs, a framework within which to simulate the behavior of reconstructed systems and, in some cases, suites of analytic tools for exploring that behavior and its implications. This review provides a general background to the idea of treating a regulatory network as a dynamical system, and describes a variety of different approaches that have been taken to the dynamical modeling of GRNs.

Oscillatory Notch-pathway activity in a delay model of neuronal differentiation

Lateral inhibition resulting from a double-negative feedback loop underlies the assignment of different fates to cells in many developmental processes. Previous studies have shown that the presence of time delays in models of lateral inhibition can result in significant oscillatory transients before patterned steady states are reached. We study the impact of local feedback loops in a model of lateral inhibition based on the Notch signaling pathway, elucidating the roles of intracellular and intercellular delays in controlling the overall system behavior. The model exhibits both in-phase and out-of-phase oscillatory modes and oscillation death. Interactions between oscillatory modes can generate complex behaviors such as intermittent oscillations. Our results provide a framework for exploring the recent observation of transient Notch-pathway oscillations during fate assignment in vertebrate neurogenesis.

cis-Inhibition of Notch by endogenous Delta biases the outcome of lateral inhibition

Lateral inhibition mediated by Delta/Notch (Dl/N) signaling is used throughout development to limit the number of initially equivalent cells that adopt a particular fate. Although adjacent cells express both Dl ligand and N receptor, signaling between them ultimately occurs in only one direction. Classically, this has been explained entirely by feedback: activated N can downregulate Dl, amplifying even slight asymmetries in the Dl or N activities of adjacent cells. Here, however, we present an example of lateral inhibition in which unidirectional signaling depends instead on Dl's ability to inhibit N within the same cell, a phenomenon known as cis-inhibition. By genetically manipulating individual R1/R6/R7 photoreceptor precursors in the Drosophila eye, we show that loss of Dl-mediated cis-inhibition reverses the direction of lateral signaling. Based on our finding that Dl in R1/R6s requires endocytosis to trans-activate but not to cis-inhibit N, we reexamine previously published data from other examples of lateral inhibition. We conclude that cis-inhibition generally influences the direction of Dl/N signaling and should therefore be included in standard models of lateral inhibition.

Understanding physiological and degenerative natural vision mechanisms to define contrast and contour operators

BACKGROUND

Dynamical systems like neural networks based on lateral inhibition have a large field of applications in image processing, robotics and morphogenesis modeling. In this paper, we will propose some examples of dynamical flows used in image contrasting and contouring.

METHODOLOGY

First we present the physiological basis of the retina function by showing the role of the lateral inhibition in the optical illusions and pathologic processes generation. Then, based on these biological considerations about the real vision mechanisms, we study an enhancement method for contrasting medical images, using either a discrete neural network approach, or its continuous version, i.e. a non-isotropic diffusion reaction partial differential system. Following this, we introduce other continuous operators based on similar biomimetic approaches: a chemotactic contrasting method, a viability contouring algorithm and an attentional focus operator. Then, we introduce the new notion of mixed potential Hamiltonian flows; we compare it with the watershed method and we use it for contouring.

CONCLUSIONS

We conclude by showing the utility of these biomimetic methods with some examples of application in medical imaging and computed assisted surgery.

Computational models of the Notch network elucidate mechanisms of context-dependent signaling

The Notch signaling pathway controls numerous cell fate decisions during development and adulthood through diverse mechanisms. Thus, whereas it functions as an oscillator during somitogenesis, it can mediate an all-or-none cell fate switch to influence pattern formation in various tissues during development. Furthermore, while in some contexts continuous Notch signaling is required, in others a transient Notch signal is sufficient to influence cell fate decisions. However, the signaling mechanisms that underlie these diverse behaviors in different cellular contexts have not been understood. Notch1 along with two downstream transcription factors hes1 and RBP-Jk forms an intricate network of positive and negative feedback loops, and we have implemented a systems biology approach to computationally study this gene regulation network. Our results indicate that the system exhibits bistability and is capable of switching states at a critical level of Notch signaling initiated by its ligand Delta in a particular range of parameter values. In this mode, transient activation of Delta is also capable of inducing prolonged high expression of Hes1, mimicking the “ON” state depending on the intensity and duration of the signal. Furthermore, this system is highly sensitive to certain model parameters and can transition from functioning as a bistable switch to an oscillator by tuning a single parameter value. This parameter, the transcriptional repression constant of hes1, can thus qualitatively govern the behavior of the signaling network. In addition, we find that the system is able to dampen and reduce the effects of biological noise that arise from stochastic effects in gene expression for systems that respond quickly to Notch signaling.

This work thus helps our understanding of an important cell fate control system and begins to elucidate how this context dependent signaling system can be modulated in different cellular settings to exhibit entirely different behaviors.

The Notch signaling pathway is an evolutionarily conserved signaling system that is involved in various cell fate decisions, both during development of an organism and during adulthood. While the same core circuit functions in various different cellular contexts, it has experimentally been shown to elicit varied behaviors and responses. On the one hand, it functions as a cellular oscillator critical for somitogenesis, whereas in other situations, it can function as a cell fate switch to pattern developing tissue, for example in the Drosophila eye. Furthermore, malfunctioning of Notch signaling is implicated in various cancers. To better understand the underlying mechanisms that allow the network to function distinctly in different contexts, we have mathematically modeled the behavior of the Notch network, encompassing the Notch gene along with two of its downstream effector transcription factors, which together form a network of positive and negative feedback loops. Our results indicate that the qualitative and quantitative behavior of the system can readily be tuned based on key parameters to reflect its multiple roles. Furthermore, our results provide insights into alterations in the signaling system that lead to malfunction and hence disease, which could be used to identify potential drug targets for therapy.

A microRNA imparts robustness against environmental fluctuation during development

The microRNA miR-7 is perfectly conserved from annelids to humans, and yet some of the genes that it regulates in Drosophila are not regulated in mammals. We have explored the role of lineage restricted targets, using Drosophila, in order to better understand the evolutionary significance of microRNA-target relationships. From studies of two well characterized developmental regulatory networks, we find that miR-7 functions in several interlocking feedback and feedforward loops, and propose that its role in these networks is to buffer them against perturbation. To directly demonstrate this function for miR-7, we subjected the networks to temperature fluctuation and found that miR-7 is essential for the maintenance of regulatory stability under conditions of environmental flux. We suggest that some conserved microRNAs like miR-7 may enter into novel genetic relationships to buffer developmental programs against variation and impart robustness to diverse regulatory networks.

Evolution under canalization and the dual roles of microRNAs: a hypothesis

Canalization refers to the process by which phenotypes are stabilized within species. Evolution by natural selection can proceed efficiently only when phenotypes are canalized. The existence and identity of canalizing genes have thus been an important, but controversial topic. Recent evidence has increasingly hinted that microRNAs may be involved in canalizing gene expression. Their paradoxical properties (e.g., strongly conserved but functionally dispensable) suggest unconventional regulatory roles. We synthesized published and unpublished results and hypothesize that miRNAs may have dual functions -- in gene expression tuning and in expression buffering. In tuning, miRNAs modify the mean expression level of their targets, but in buffering they merely reduce the variance around a preset mean. In light of the constant emergence of new miRNAs, we further discuss the relative importance of these two functions in evolution.

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.

Effects of ploidy and recombination on evolution of robustness in a model of the segment polarity network

Many genetic networks are astonishingly robust to quantitative variation, allowing these networks to continue functioning in the face of mutation and environmental perturbation. However, the evolution of such robustness remains poorly understood for real genetic networks. Here we explore whether and how ploidy and recombination affect the evolution of robustness in a detailed computational model of the segment polarity network. We introduce a novel computational method that predicts the quantitative values of biochemical parameters from bit sequences representing genotype, allowing our model to bridge genotype to phenotype. Using this, we simulate 2,000 generations of evolution in a population of individuals under stabilizing and truncation selection, selecting for individuals that could sharpen the initial pattern of engrailed and wingless expression. Robustness was measured by simulating a mutation in the network and measuring the effect on the engrailed and wingless patterns; higher robustness corresponded to insensitivity of this pattern to perturbation. We compared robustness in diploid and haploid populations, with either asexual or sexual reproduction. In all cases, robustness increased, and the greatest increase was in diploid sexual populations; diploidy and sex synergized to evolve greater robustness than either acting alone. Diploidy conferred increased robustness by allowing most deleterious mutations to be rescued by a working allele. Sex (recombination) conferred a robustness advantage through "survival of the compatible": those alleles that can work with a wide variety of genetically diverse partners persist, and this selects for robust alleles.

Multistable decision switches for flexible control of epigenetic differentiation

It is now recognized that molecular circuits with positive feedback can induce two different gene expression states (bistability) under the very same cellular conditions. Whether, and how, cells make use of the coexistence of a larger number of stable states (multistability) is however largely unknown. Here, we first examine how autoregulation, a common attribute of genetic master regulators, facilitates multistability in two-component circuits. A systematic exploration of these modules' parameter space reveals two classes of molecular switches, involving transitions in bistable (progression switches) or multistable (decision switches) regimes. We demonstrate the potential of decision switches for multifaceted stimulus processing, including strength, duration, and flexible discrimination. These tasks enhance response specificity, help to store short-term memories of recent signaling events, stabilize transient gene expression, and enable stochastic fate commitment. The relevance of these circuits is further supported by biological data, because we find them in numerous developmental scenarios. Indeed, many of the presented information-processing features of decision switches could ultimately demonstrate a more flexible control of epigenetic differentiation.

Neutrality and robustness in evo-devo: emergence of lateral inhibition

Embryonic development is defined by the hierarchical dynamical process that translates genetic information (genotype) into a spatial gene expression pattern (phenotype) providing the positional information for the correct unfolding of the organism. The nature and evolutionary implications of genotype-phenotype mapping still remain key topics in evolutionary developmental biology (evo-devo). We have explored here issues of neutrality, robustness, and diversity in evo-devo by means of a simple model of gene regulatory networks. The small size of the system allowed an exhaustive analysis of the entire fitness landscape and the extent of its neutrality. This analysis shows that evolution leads to a class of robust genetic networks with an expression pattern characteristic of lateral inhibition. This class is a repertoire of distinct implementations of this key developmental process, the diversity of which provides valuable clues about its underlying causal principles.

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.

A mutual support mechanism through intercellular movement of CAPRICE and GLABRA3 can pattern the Arabidopsis root epidermis

The patterning of the Arabidopsis root epidermis depends on a genetic regulatory network that operates both within and between cells. Genetic studies have identified a number of key components of this network, but a clear picture of the functional logic of the network is lacking. Here, we integrate existing genetic and biochemical data in a mathematical model that allows us to explore both the sufficiency of known network interactions and the extent to which additional assumptions about the model can account for wild-type and mutant data. Our model shows that an existing hypothesis concerning the autoregulation of WEREWOLF does not account fully for the expression patterns of components of the network. We confirm the lack of WEREWOLF autoregulation experimentally in transgenic plants. Rather, our modelling suggests that patterning depends on the movement of the CAPRICE and GLABRA3 transcriptional regulators between epidermal cells. Our combined modelling and experimental studies show that WEREWOLF autoregulation does not contribute to the initial patterning of epidermal cell fates in the Arabidopsis seedling root. In contrast to a patterning mechanism relying on local activation, we propose a mechanism based on lateral inhibition with feedback. The active intercellular movements of proteins that are central to our model underlie a mechanism for pattern formation in planar groups of cells that is centred on the mutual support of two cell fates rather than on local activation and lateral inhibition.

Diverse metabolic model parameters generate similar methionine cycle dynamics

Parameter estimation constitutes a major challenge in dynamic modeling of metabolic networks. Here we examine, via computational simulations, the influence of system nonlinearity and the nature of available data on the distribution and predictive capability of identified model parameters. Simulated methionine cycle metabolite concentration data (both with and without corresponding flux data) was inverted to identify model parameters consistent with it. Thousands of diverse parameter families were found to be consistent with the data to within moderate error, with most of the parameter values spanning over 1000-fold ranges irrespective of whether flux data was included. Due to strong correlations within the extracted parameter families, model predictions were generally reliable despite the broad ranges found for individual parameters. Inclusion of flux data, by strengthening these correlations, resulted in substantially more reliable flux predictions. These findings suggest that, despite the difficulty of extracting biochemically accurate model parameters from system level data, such data may nevertheless prove adequate for driving the development of predictive dynamic metabolic models.

Innovation and robustness in complex regulatory gene networks

The history of life involves countless evolutionary innovations, a steady stream of ingenuity that has been flowing for more than 3 billion years. Very little is known about the principles of biological organization that allow such innovation. Here, we examine these principles for evolutionary innovation in gene expression patterns. To this end, we study a model for the transcriptional regulation networks that are at the heart of embryonic development. A genotype corresponds to a regulatory network of a given topology, and a phenotype corresponds to a steady-state gene expression pattern. Networks with the same phenotype form a connected graph in genotype space, where two networks are immediate neighbors if they differ by one regulatory interaction. We show that an evolutionary search on this graph can reach genotypes that are as different from each other as if they were chosen at random in genotype space, allowing evolutionary access to different kinds of innovation while staying close to a viable phenotype. Thus, although robustness to mutations may hinder innovation in the short term, we conclude that long-term innovation in gene expression patterns can only emerge in the presence of the robustness caused by connected genotype graphs.

Robustness can evolve gradually in complex regulatory gene networks with varying topology

The topology of cellular circuits (the who-interacts-with-whom) is key to understand their robustness to both mutations and noise. The reason is that many biochemical parameters driving circuit behavior vary extensively and are thus not fine-tuned. Existing work in this area asks to what extent the function of any one given circuit is robust. But is high robustness truly remarkable, or would it be expected for many circuits of similar topology? And how can high robustness come about through gradual Darwinian evolution that changes circuit topology gradually, one interaction at a time? We here ask these questions for a model of transcriptional regulation networks, in which we explore millions of different network topologies. Robustness to mutations and noise are correlated in these networks. They show a skewed distribution, with a very small number of networks being vastly more robust than the rest. All networks that attain a given gene expression state can be organized into a graph whose nodes are networks that differ in their topology. Remarkably, this graph is connected and can be easily traversed by gradual changes of network topologies. Thus, robustness is an evolvable property. This connectedness and evolvability of robust networks may be a general organizational principle of biological networks. In addition, it exists also for RNA and protein structures, and may thus be a general organizational principle of all biological systems.

The theory of biological robustness and its implication in cancer

One of the essential issues in systems biology is to identify fundamental principles that govern living organisms at the system level. In this chapter, I argue that robustness is a fundamental feature of living systems where its relationship with evolution-trade-offs among robustness, fragility, resource demands, and performance-provides a possible framework for how biological systems have evolved and been organized. In addition, diseases can be con- sidered as a manifestation of fragility of the system. In some cases, such as cancer, the disease state establishes its own robustness against therapeutic interventions. Understanding robustness and its intrinsic properties will provide us with a more profound understanding of biological systems, their anomalies, and countermeasures.

Cryptic variation in butterfly eyespot development: the importance of sample size in gene expression studies

Previous studies have shown that development can be robust to variation in parameters such as the timing or level of gene expression. This leads to the prediction that natural populations should be able to host developmental variation that has little phenotypic effect. Cryptic variation is of particular interest because it can result in selectable phenotypes when "released" by environmental or genetic factors. Currently, however, we have little idea of how variation is distributed between genes or over time in pattern formation processes. Here we survey expression of Notch (N), Spalt (Sal), and Engrailed (En) during butterfly eyespot determination to better understand how pattern formation may vary within a population. We observed substantial heterochronic variance in the progress of spatial expression patterns for all three proteins, suggesting some degree of developmental buffering in eyespot development. Peak variance for different proteins was found at both early and late stages of development, contrasting with previous models suggesting that the distribution of variance should be more temporally focused during pattern formation. We speculate that our observations are representative of a standing reservoir of cryptic variation that may contribute to phenotypic evolution under certain circumstances. Our results also provide a strong cautionary message that gene expression studies with limited sample sizes can be positively misleading in terms of inferring expression pattern time series, as well as for making cross-species phylogenetic comparisons.

Embryo stability and vulnerability in an always changing world

Contrary to the view that embryos and larvae are the most fragile stages of life, development is stable under real-world conditions. Early cleavage embryos are prepared for environmental vagaries by having high levels of cellular defenses already present in the egg before fertilization. Later in development, adaptive responses to the environment either buffer stress or produce alternative developmental phenotypes. These buffers, defenses, and alternative pathways set physiological limits for development under expected conditions; teratology occurs when embryos encounter unexpected environmental changes and when stress exceeds these limits. Of concern is that rapid anthropogenic changes to the environment are beyond the range of these protective mechanisms.

Biological robustness in complex host-pathogen systems

Infectious diseases are still the number one killer of human beings. Even in developed countries, infectious diseases continue to be a major health threat. This article explores a conceptual framework for understanding infectious diseases in the context of the complex dynamics between microbe and host, and explores theoretical strategies for anti-infectives. The central pillar of this conceptual framework is that biological robustness is a fundamental property of systems that is closely interlinked with the evolution of symbiotic host-pathogen systems. There are specific architectural features of such robust yet evolvable systems and interpretable trade-offs between robustness, fragility, resource demands, and performance. This concept applies equally to both microbes and host. Pathogens have evolved to exploit the host using various strategies as well as effective escape mechanisms. Modular pathogenicity islands (PAI) derived from horizontal gene transfer, highly variable surface molecules, and a range of other countermeasures enhance the robustness of a pathogen against attacks from the host immune system. The host has likewise evolved complex defensive mechanisms to protect itself against pathogenic threats, but the host immune system includes several trade-offs that can be exploited by pathogens and induces undesirable inflammatory reactions. Due to the complexity of the dynamics emerging from the interactions of multiple microbes and a host, effective counter-measures require an in-depth understanding of system dynamics as well as detailed molecular mechanisms of the processes that are involved.

Morpheus Unbound: Reimagining the Morphogen Gradient

The theory that the spatial organization of cell fate is orchestrated by gradients of diffusing molecules was a major contribution to 20th century developmental biology. Although the existence of morphogens is no longer in doubt, studies on the formation and function of their gradients have yielded far more puzzles than answers. On close inspection, every morphogen gradient seems to use a rich array of regulatory mechanisms, suggesting that the tasks carried out by such systems are far more extensive than previously thought.

Longevity network: Construction and implications

The vast majority of studies on longevity have focused on individual genes/proteins, without adequately addressing the possible role of interactions between them. This study is the first attempt towards constructing a "longevity network" via analysis of human protein-protein interactions (PPIs). For this purpose, we (i) compiled a complete list of established longevity genes from different species, including those that most probably affect the longevity in humans, (ii) defined the human orthologs of the longevity genes, and (iii) determined whether the encoded proteins could be organized as a network. The longevity gene-encoded proteins together with their interacting proteins form a continuous network, which fits the criteria for a scale-free network with an extremely high contribution of hubs to the network connectivity. Most of them have never been annotated before in connection with longevity. Remarkably, almost all of the hubs of the "longevity network" were reported to be involved in at least one age-related disease (ARD), with many being involved in several ARDs. This may be one of the ways by which the proteins with multiple interactions affect the longevity. The hubs offer the potential of being primary targets for longevity-promoting interventions.

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.

Stem cell biology: a view toward the future

In this essay I have attempted to provide clues relating to novel research avenues that are likely to have a broad impact on the field of stem cell biology. The specific examples, drawn from other areas, are meant to be instructive and are representative of many more similar efforts. I have suggested that the new areas of systems and synthetic biology may provide a truly deep level of understanding for many aspects of how stem cells make fate choices. Successful application of new avenues will require an integrative approach that combines experimental and computational techniques.

Canalization of development by microRNAs

Animal development is an extremely robust process resulting in stereotyped outcomes. Canalization is a design principle wherein developmental pathways are stabilized to increase phenotypic reproducibility. Recent revelations into microRNA (miRNA) function suggest that miRNAs act as key players in canalizing genetic programs. We suggest that miRNA interactions with the network of protein-coding genes evolved to buffer stochastic perturbations and thereby confer robustness to developmental genetic programs.

A novel hes5/hes6 circuitry of negative regulation controls Notch activity during neurogenesis

HES transcriptional repressors are important components of the Notch pathway that regulates neurogenesis from Drosophila to vertebrates. These proteins are normally induced by Notch activity and inhibit neural commitment by antagonizing the activity of proneural genes. We describe here four chick hes genes that are expressed during neurogenesis: three hes5-like genes (hes5-1, hes5-2 and hes5-3) and one hes6-like (hes6-2). We show that hes6-2 represses transcription of the hes5 genes, thus functioning as a negative regulator of Notch signaling. Conversely, hes6-2 may be repressed by hes5 activity. In cells committing to differentiation, we find that hes6-2 is up-regulated by proneural genes and contributes to the proneural program of neuronal commitment by preventing Notch activity in these cells. In neural progenitors, Notch signaling produces an initial burst of hes5 activity, which represses hes6-2. However, as hes5 transcription declines due to negative auto-regulation, hes6-2 may become active and inhibit the remaining hes5 activity to end Notch signaling. These cells can then enter a new cycle of fate decisions and will be kept as progenitors if a new pulse of Notch activity occurs. Maintenance of progenitors during vertebrate neurogenesis therefore requires that these cells go through successive cycles of Notch activity. We propose that the hes5/hes6 circuitry of negative cross-regulations is a conserved feature of the Notch pathway that underlies these cycles in neural progenitors.

Variability, compensation and homeostasis in neuron and network function

Neurons in most animals live a very long time relative to the half-lives of all of the proteins that govern excitability and synaptic transmission. Consequently, homeostatic mechanisms are necessary to ensure stable neuronal and network function over an animal's lifetime. To understand how these homeostatic mechanisms might function, it is crucial to understand how tightly regulated synaptic and intrinsic properties must be for adequate network performance, and the extent to which compensatory mechanisms allow for multiple solutions to the production of similar behaviour. Here, we use examples from theoretical and experimental studies of invertebrates and vertebrates to explore several issues relevant to understanding the precision of tuning of synaptic and intrinsic currents for the operation of functional neuronal circuits.

In vivo robustness analysis of cell division cycle genes in Saccharomyces cerevisiae

Intracellular biochemical parameters, such as the expression level of gene products, are considered to be optimized so that a biological system, including the parameters, works effectively. Those parameters should have some permissible range so that the systems have robustness against perturbations, such as noise in gene expression. However, little is known about the permissible range in real cells because there has been no experimental technique to test it. In this study, we developed a genetic screening method, named “genetic tug-of-war” (gTOW) that evaluates upper limit copy numbers of genes in a model eukaryote Saccharomyces cerevisiae, and we applied it for 30 cell-cycle related genes (CDC genes). The experiment provided unique quantitative data that could be used to argue the system-level properties of the cell cycle such as robustness and fragility. The data were used to evaluate the current computational model, and refinements to the model were suggested.

Robustness is a property of a system that attempts to maintain its functions against internal and external perturbations. It is one of the fundamental and ubiquitously observed system-level properties of biological systems. Understanding the cellular robustness is important, not only to gain insights in biology, but also to identify potential therapeutic targets. Robustness is estimated by measuring how much parameters can be perturbed without disrupting essential functions; comprehensive, as well as quantitative perturbations of intracellular parameters, such as gene expression, are essential for solid robustness analysis. However, the lack of experimental methodology for the comprehensive quantification and defined perturbation of parameters has prevented experimental analyses of cellular robustness. The authors developed a novel genetic screening method named “genetic tug-of-war” (gTOW) that allows systematic measurement of upper limit gene copy number. gTOW applied for the robustness analysis of cell division cycle system in the model eukaryote, Saccharomyces cerevisiae, and revealed the point of fragility in the system. The gTOW method is particularly suitable for systems biology research and demonstrates the value of comprehensive and quantitative perturbation experiment to uncover system-level properties of the cellular system.

Constructing quantitative models from qualitative mutant phenotypes: preferences in selecting sensory organ precursors

MOTIVATION

To study biology from the systems level, mathematical models that describe the time-evolution of the system offer useful insights. Quantitative information is required for constructing such models, but such information is rarely provided.

RESULTS

We propose a scheme-based on random searches over a parameter space, according to criteria set by qualitative experimental observations-for inferring quantitative parameters from qualitative experimental results. We used five mutant constraints to construct genetic network models for sensory organ precursor formation in Drosophila development. Most of the models were capable of generating expression patterns for the gene Enhancer of split that were compatible with experimental observations for wild type and two Notch mutants. We further examined factors differentiating the neural fate among cells in a proneural cluster, and found two opposite driving forces that bias the choice between middle cells and the peripheral cells. Therefore, it is possible to build numerical models from mutant screening and to study mechanisms behind the complicated network.

Discrete time piecewise affine models of genetic regulatory networks

We introduce simple models of genetic regulatory networks and we proceed to the mathematical analysis of their dynamics. The models are discrete time dynamical systems generated by piecewise affine contracting mappings whose variables represent gene expression levels. These models reduce to boolean networks in one limiting case of a parameter, and their asymptotic dynamics approaches that of a differential equation in another limiting case of this parameter. For intermediate values, the model present an original phenomenology which is argued to be due to delay effects. This phenomenology is not limited to piecewise affine model but extends to smooth nonlinear discrete time models of regulatory networks. In a first step, our analysis concerns general properties of networks on arbitrary graphs (characterisation of the attractor, symbolic dynamics, Lyapunov stability, structural stability, symmetries, etc). In a second step, focus is made on simple circuits for which the attractor and its changes with parameters are described. In the negative circuit of 2 genes, a thorough study is presented which concern stable (quasi-)periodic oscillations governed by rotations on the unit circle - with a rotation number depending continuously and monotonically on threshold parameters. These regular oscillations exist in negative circuits with arbitrary number of genes where they are most likely to be observed in genetic systems with non-negligible delay effects.

Recombination and the evolution of mutational robustness

Mutational robustness is the degree to which a phenotype, such as fitness, is resistant to mutational perturbations. Since most of these perturbations will tend to reduce fitness, robustness provides an immediate benefit for the mutated individual. However, robust systems decay due to the accumulation of deleterious mutations that would otherwise have been cleared by selection. This decay has received very little theoretical attention. At equilibrium, a population or asexual lineage is expected to have a mutation load that is invariant with respect to the selection coefficient of deleterious alleles, so the benefit of robustness (at the level of the population or asexual lineage) is temporary. However, previous work has shown that robustness can be favoured when robustness loci segregate independently of the mutating loci they act upon. We examine a simple two-locus model that allows for intermediate rates of recombination and inbreeding to show that increasing the effective recombination rate allows for the evolution of greater mutational robustness.

Filtering transcriptional noise during development: concepts and mechanisms

The assignation of cell fates during eukaryotic development relies on the coordinated and stable expression of cohorts of genes within cell populations. The precise and reproducible nature of this process is remarkable given that, at the single-cell level, the transcription of individual genes is associated with noise - random molecular fluctuations that create variability in the levels of gene expression within a cell population. Here we consider the implications of transcriptional noise for development and suggest the existence of molecular devices that are dedicated to filtering noise. On the basis of existing evidence, we propose that one such mechanism might depend on the Wnt signalling pathway.

Circuit topology and the evolution of robustness in two-gene circadian oscillators

Many parameters driving the behavior of biochemical circuits vary extensively and are thus not fine-tuned. Therefore, the topology of such circuits (the who-interacts-with-whom) is key to understanding their central properties. I here explore several hundred different topologies of a simple biochemical model of circadian oscillations to ask two questions: Do different circuits differ dramatically in their robustness to parameter change? If so, can a process of gradual molecular evolution find highly robust topologies when starting from less robust topologies? I find that the distribution of robustness among different circuit topologies is highly skewed: Most show low robustness, whereas very few topologies are highly robust. To address the second evolutionary question, I define a topology graph, each of whose nodes corresponds to one circuit topology that shows circadian oscillations. Two nodes in this graph are connected if they differ by only one regulatory interaction within the circuit. For the circadian oscillator I study, most topologies are connected in this graph, making evolutionary transitions from low to high robustness easy. A similar approach has been used to study the evolution of robustness in biological macromolecules, with similar results. This suggests that the same principles govern the evolution of robustness on different levels of biological organization. The regulatory interlocking of several oscillating gene products in biological circadian oscillators may exist because it provides robustness.

Extensive sex-specific nonadditivity of gene expression in Drosophila melanogaster

Assessment of the degree to which gene expression is additive and heritable has important implications for understanding the maintenance of variation, adaptation, phenotypic divergence, and the mapping of genotype onto phenotype. We used whole-genome transcript profiling using Agilent long-oligonucleotide microarrays representing 12,017 genes to demonstrate that gene transcription is pervasively nonadditive in Drosophila melanogaster. Comparison of adults of two isogenic lines and their reciprocal F1 hybrids revealed 5820 genes as significantly different between at least two of the four genotypes in either males or females or across both sexes. Strikingly, while 25% of all genes differ between the two parents, 33% differ between both F1's and the parents, averaged across sexes. However, only 5% of genes show overdominance, suggesting that heterosis for expression is rare.

Elucidating mechanisms underlying robustness of morphogen gradients

Morphogen gradients play a pivotal role in most phases of developmental patterning. To ensure proper patterning, reproducible gradients are established under diverse environmental conditions and genetic backgrounds. We refer to the capacity to buffer fluctuations in gene dosage or environmental conditions as 'robustness'. By theoretical analysis of mechanisms that facilitate robustness, it is possible to unravel the machinery responsible for generating the spatial distribution of morphogens.

A new measure of the robustness of biochemical networks

MOTIVATION

The robustness of a biochemical network is defined as the tolerance of variations in kinetic parameters with respect to the maintenance of steady state. Robustness also plays an important role in the fail-safe mechanism in the evolutionary process of biochemical networks. The purposes of this paper are to use the synergism and saturation system (S-system) representation to describe a biochemical network and to develop a robustness measure of a biochemical network subject to variations in kinetic parameters. Since most biochemical networks in nature operate close to the steady state, we consider only the robustness measurement of a biochemical network at the steady state.

RESULTS

We show that the upper bound of the tolerated parameter variations is related to the system matrix of a biochemical network at the steady state. Using this upper bound, we can calculate the tolerance (robustness) of a biochemical network without testing many parametric perturbations. We find that a biochemical network with a large tolerance can also better attenuate the effects of variations in rate parameters and environments. Compensatory parameter variations and network redundancy are found to be important mechanisms for the robustness of biochemical networks. Finally, four biochemical networks, such as a cascaded biochemical network, the glycolytic-glycogenolytic pathway in a perfused rat liver, the tricarboxylic acid cycle in Dictyostelium discoideum and the cAMP oscillation network in bacterial chemotaxis, are used to illustrate the usefulness of the proposed robustness measure.

Evolvability of cell specification mechanisms

The architecture of gene action during development is relevant to phenotypic evolution as it links genotype to morphological phenotype. Analysis of development at the level of cell fate specification mechanisms illuminates some of the properties of developmental evolution. In this article, we first review examples of evolutionary change in mechanisms of cell fate specification, with an emphasis on evolution in the dependence on inductive signaling and on evolution of the mechanisms that result in spatial asymmetries. We then focus on properties of development that bias possible phenotypic change and present how the distribution of phenotypes that are available by mutational change of the starting genotype can be experimentally tested by systematic mutagenesis. We finally discuss ways in which selection pressures on phenotypes can be inferred from a comparison of the phenotypic spectrum found on mutation with that found in the wild.

Metabolic syndrome and robustness tradeoffs

The metabolic syndrome is a highly complex breakdown of normal physiology characterized by obesity, insulin resistance, hyperlipidemia, and hypertension. Type 2 diabetes is a major manifestation of this syndrome, although increased risk for cardiovascular disease (CVD) often precedes the onset of frank clinical diabetes. Prevention and cure for this disease constellation is of major importance to world health. Because the metabolic syndrome affects multiple interacting organ systems (i.e., it is a systemic disease), a systems-level analysis of disease evolution is essential for both complete elucidation of its pathophysiology and improved approaches to therapy. The goal of this review is to provide a perspective on systems-level approaches to metabolic syndrome, with particular emphasis on type 2 diabetes. We consider that metabolic syndromes take over inherent dynamics of our body that ensure robustness against unstable food supply and pathogenic infections, and lead to chronic inflammation that ultimately results in CVD. This exemplifies how trade-offs between robustness against common perturbations (unstable food and infections) and fragility against unusual perturbations (high-energy content foods and low-energy utilization lifestyle) is exploited to form chronic diseases. Possible therapeutic approaches that target fragility of emergent robustness of the disease state have been discussed. A detailed molecular interaction map for adipocyte, hepatocyte, skeletal muscle cell, and pancreatic beta-cell cross-talk in the metabolic syndrome can be viewed at http://www.systems-biology.org/001/003.html.

Simulation study on effects of signaling network structure on the developmental increase in complexity

The developmental increase in structural complexity in multicellular lifeforms depends on local, often non-periodic differences in gene expression. These, in turn, depend on a network of gene-gene interactions coded within the organismal genome. To see what architectural features of a network (size, connectivity, etc.) affect the likelihood of patterns with multiple cell types (i.e. patterns where cells express > or = 3 different combinations of genes), developmental pattern formation was simulated in virtual blastoderm embryos with small artificial genomes. Several basic properties of these genomic signaling networks, such as the number of genes, the distributions of positive (inductive) and negative (repressive) interactions, and the strengths of gene-gene interactions were tested. The results show that the frequencies of complex and/or stable patterns depended not only on the existence of negative interactions, but also on the distribution of regulatory interactions: for example, coregulation of signals and their intracellular effectors increased the likelihood of pattern formation compared to differential regulation of signaling pathway components. Interestingly, neither quantitative differences in strengths of signaling interactions nor multiple response thresholds to different levels of signal concentration (as in morphogen gradients) were essential for formation of multiple, spatially unique "cell types". However, those combinations of architectural features that greatly increased the likelihood for pattern complexity tended to decrease the likelihoods for pattern stability and developmental robustness. Nevertheless, elements of complex patterns (e.g. genes, cell type order within the pattern) could differ in their developmental robustness, which may be important for the evolution of complexity. The results show that depending on the network structure, the same set of genes can produce patterns of different complexity, robustness and stability. Because of this, the evolution of metazoan complexity with a combinatorial code of gene regulation may have depended at least as much on selection for favorable distribution of connections between existing developmental regulatory genes as on the simple increase in numbers of regulatory genes.

Evolutionary diversification of pigment pattern in Danio fishes: differential fms dependence and stripe loss in D. albolineatus

The developmental bases for species differences in adult phenotypes remain largely unknown. An emerging system for studying such variation is the adult pigment pattern expressed by Danio fishes. These patterns result from several classes of pigment cells including black melanophores and yellow xanthophores, which differentiate during metamorphosis from latent stem cells of presumptive neural crest origin. In the zebrafish D. rerio, alternating light and dark horizontal stripes develop, in part, owing to interactions between melanophores and cells of the xanthophore lineage that depend on the fms receptor tyrosine kinase; zebrafish fms mutants lack xanthophores and have disrupted melanophore stripes. By contrast, the closely related species D. albolineatus exhibits a uniform pattern of melanophores, and previous interspecific complementation tests identified fms as a potential contributor to this difference between species. Here, we survey additional species and demonstrate marked variation in the fms-dependence of hybrid pigment patterns, suggesting interspecific variation in the fms pathway or fms requirements during pigment pattern formation. We next examine the cellular bases for the evolutionary loss of stripes in D. albolineatus and test the simplest model to explain this transformation, a loss of fms activity in D. albolineatus relative to D. rerio. Within D. albolineatus, we demonstrate increased rates of melanophore death and decreased melanophore migration, different from wild-type D. rerio but similar to fms mutant D. rerio. Yet, we also find persistent fms expression in D. albolineatus and enhanced xanthophore development compared with wild-type D. rerio, and in stark contrast to fms mutant D. rerio. These findings exclude the simplest model in which stripe loss in D. albolineatus results from a loss of fms-dependent xanthophores and their interactions with melanophores. Rather, our results suggest an alternative model in which evolutionary changes in pigment cell interactions themselves have contributed to stripe loss, and we test this model by manipulating melanophore numbers in interspecific hybrids. Together, these data suggest evolutionary changes in the fms pathway or fms requirements, and identify changes in cellular interactions as a likely mechanism of evolutionary change in Danio pigment patterns.

Robustness of cellular functions

Robustness, the ability to maintain performance in the face of perturbations and uncertainty, is a long-recognized key property of living systems. Owing to intimate links to cellular complexity, however, its molecular and cellular basis has only recently begun to be understood. Theoretical approaches to complex engineered systems can provide guidelines for investigating cellular robustness because biology and engineering employ a common set of basic mechanisms in different combinations. Robustness may be a key to understanding cellular complexity, elucidating design principles, and fostering closer interactions between experimentation and theory.

The Bacillus subtilis sin operon: an evolvable network motif

The strategy of combining genes from a regulatory protein and its antagonist within the same operon, but controlling their activities differentially, can lead to diverse regulatory functions. This protein-antagonist motif is ubiquitous and present in evolutionarily unrelated regulatory pathways. Using the sin operon from the Bacillus subtilis sporulation pathway as a model system, we built a theoretical model, parameterized it using data from the literature, and used bifurcation analyses to determine the circuit functions it could encode. The model demonstrated that this motif can generate a bistable switch with tunable control over the switching threshold and the degree of population heterogeneity. Further, the model predicted that a small perturbation of a single critical parameter can bias this architecture into functioning like a graded response, a bistable switch, an oscillator, or a pulse generator. By mapping the parameters of the model to specific DNA regions and comparing the genomic sequences of Bacillus species, we showed that phylogenetic variation tends to occur in those regions that tune the switch threshold without disturbing the circuit function. The dynamical plasticity of the protein-antagonist operon motif suggests that it is an evolutionarily convergent design selected not only for particular immediate function but also for its evolvability.