The clockfront and wavefront model revisited

The currently accepted interpretation of the clock and wavefront model of somitogenesis is that a posteriorly moving molecular gradient sequentially slows the rate of clock oscillations, resulting in a spatial readout of temporal oscillations. However, while molecular components of the clocks and wavefronts have now been identified in the pre-somitic mesoderm (PSM), there is not yet conclusive evidence demonstrating that the observed molecular wavefronts act to slow clock oscillations. Here we present an alternative formulation of the clock and wavefront model in which oscillator coupling, already known to play a key role in oscillator synchronisation, plays a fundamentally important role in the slowing of oscillations along the anterior–posterior (AP) axis. Our model has three parameters which can be determined, in any given species, by the measurement of three quantities: the clock period in the posterior PSM, somite length and the length of the PSM. A travelling wavefront, which slows oscillations along the AP axis, is an emergent feature of the model. Using the model we predict: (a) the distance between moving stripes of gene expression; (b) the number of moving stripes of gene expression and (c) the oscillator period profile along the AP axis. Predictions regarding the stripe data are verified using existing zebrafish data. We simulate a range of experimental perturbations and demonstrate how the model can be used to unambiguously define a reference frame along the AP axis. Comparing data from zebrafish, chick, mouse and snake, we demonstrate that: (a) variation in patterning profiles is accounted for by a single nondimensional parameter; the ratio of coupling strengths; and (b) the period profile along the AP axis is conserved across species. Thus the model is consistent with the idea that, although the genes involved in pattern propagation in the PSM vary, there is a conserved patterning mechanism across species

Spatiotemporal oscillations of Notch1, Dll1 and NICD are coordinated across the mouse PSM

During somitogenesis, epithelial somites form from the pre-somitic mesoderm (PSM) in a periodic manner. This periodicity is regulated by a molecular oscillator, known as the ‘segmentation clock’, that is characterised by an oscillatory pattern of gene expression that sweeps the PSM in a caudal-rostral direction. Key components of the segmentation clock are intracellular components of the Notch, Wnt and FGF pathways, and it is widely accepted that intracellular negative-feedback loops regulate oscillatory gene expression. However, an open question in the field is how intracellular oscillations are coordinated, in the form of spatiotemporal waves of expression, across the PSM. In this study, we provide a potential mechanism for this process. We show at the mRNA level that the Notch1 receptor and Delta-like 1 (Dll1) ligand vary dynamically across the PSM of both chick and mouse. Remarkably, we also demonstrate similar dynamics at the protein level; hence, the pathway components that mediate intercellular coupling themselves exhibit oscillatory dynamics. Moreover, we quantify the dynamic expression patterns of Dll1 and Notch1, and show they are highly correlated with the expression patterns of two known clock components [Lfng mRNA and the activated form of the Notch receptor (cleaved Notch intracellular domain, NICD)]. Lastly, we show that Notch1 is a target of Notch signalling, whereas Dll1 is Wnt regulated. Regulation of Dll1 and Notch1 expression thus links the activity of Wnt and Notch, the two main signalling pathways driving the clock

Left-Right Function of dmrt2 Genes Is Not Conserved between Zebrafish and Mouse

Background: Members of the Dmrt family, generally associated with sex determination, were shown to be involved in several other functions during embryonic development. Dmrt2 has been studied in the context of zebrafish development where, due to a duplication event, two paralog genes dmrt2a and dmrt2b are present. Both zebrafish dmrt2a/terra and dmrt2b are important to regulate left-right patterning in the lateral plate mesoderm. In addition, dmrt2a/terra is necessary for symmetric somite formation while dmrt2b regulates somite differentiation impacting on slow muscle development. One dmrt2 gene is also expressed in the mouse embryo, where it is necessary for somite differentiation but with an impact on axial skeleton development. However, nothing was known about its role during left-right patterning in the lateral plate mesoderm or in the symmetric synchronization of somite formation. Methodology/Principal Findings: Using a dmrt2 mutant mouse line, we show that this gene is not involved in symmetric somite formation and does not regulate the laterality pathway that controls left-right asymmetric organ positioning. We reveal that dmrt2a/terra is present in the zebrafish laterality organ, the Kupffer’s vesicle, while its homologue is excluded from the mouse equivalent structure, the node. On the basis of evolutionary sub-functionalization and neo-functionalization theories we discuss this absence of functional conservation. Conclusions/Significance: Our results show that the role of dmrt2 gene is not conserved during zebrafish and mous

Mathematical models for somite formation

Somitogenesis is the process of division of the anterior–posterior vertebrate embryonic axis into similar morphological units known as somites. These segments generate the prepattern which guides formation of the vertebrae, ribs and other associated features of the body trunk. In this work, we review and discuss a series of mathematical models which account for different stages of somite formation. We begin by presenting current experimental information and mechanisms explaining somite formation, highlighting features which will be included in the models. For each model we outline the mathematical basis, show results of numerical simulations, discuss their successes and shortcomings and avenues for future exploration. We conclude with a brief discussion of the state of modeling in the field and current challenges which need to be overcome in order to further our understanding in this area

Mathematical models for somite formation

Somitogenesis is the process of division of the anterior–posterior vertebrate embryonic axis into similar morphological units known as somites. These segments generate the prepattern which guides formation of the vertebrae, ribs and other associated features of the body trunk. In this work, we review and discuss a series of mathematical models which account for different stages of somite formation. We begin by presenting current experimental information and mechanisms explaining somite formation, highlighting features which will be included in the models. For each model we outline the mathematical basis, show results of numerical simulations, discuss their successes and shortcomings and avenues for future exploration. We conclude with a brief discussion of the state of modeling in the field and current challenges which need to be overcome in order to further our understanding in this area

Comparison of Pattern Detection Methods in Microarray Time Series of the Segmentation Clock

While genome-wide gene expression data are generated at an increasing rate, the repertoire of approaches for pattern discovery in these data is still limited. Identifying subtle patterns of interest in large amounts of data (tens of thousands of profiles) associated with a certain level of noise remains a challenge. A microarray time series was recently generated to study the transcriptional program of the mouse segmentation clock, a biological oscillator associated with the periodic formation of the segments of the body axis. A method related to Fourier analysis, the Lomb-Scargle periodogram, was used to detect periodic profiles in the dataset, leading to the identification of a novel set of cyclic genes associated with the segmentation clock. Here, we applied to the same microarray time series dataset four distinct mathematical methods to identify significant patterns in gene expression profiles. These methods are called: Phase consistency, Address reduction, Cyclohedron test and Stable persistence, and are based on different conceptual frameworks that are either hypothesis- or data-driven. Some of the methods, unlike Fourier transforms, are not dependent on the assumption of periodicity of the pattern of interest. Remarkably, these methods identified blindly the expression profiles of known cyclic genes as the most significant patterns in the dataset. Many candidate genes predicted by more than one approach appeared to be true positive cyclic genes and will be of particular interest for future research. In addition, these methods predicted novel candidate cyclic genes that were consistent with previous biological knowledge and experimental validation in mouse embryos. Our results demonstrate the utility of these novel pattern detection strategies, notably for detection of periodic profiles, and suggest that combining several distinct mathematical approaches to analyze microarray datasets is a valuable strategy for identifying genes that exhibit novel, interesting transcriptional patterns

Spots & stripes: pleomorphic patterning of stem cells via p-ERK-depenendent cell chemotaxis shown by feather morphogenesis & mathematical simulation

A key issue in stem cell biology is the differentiation of homogeneous stem cells towards different fates which are also organized into desired configurations. Little is known about the mechanisms underlying the process of periodic patterning. Feather explants offer a fundamental and testable model in which multi-potential cells are organized into hexagonally arranged primordia and the spacing between primordia. Previous work explored roles of a Turing reaction–diffusion mechanism in establishing chemical patterns. Here we show that a continuum of feather patterns, ranging from stripes to spots, can be obtained when the level of p-ERK activity is adjusted with chemical inhibitors. The patterns are dose-dependent, tissue stage-dependent, and irreversible. Analyses show that ERK activity-dependent mesenchymal cell chemotaxis is essential for converting micro-signaling centers into stable feather primordia. A mathematical model based on short-range activation, long-range inhibition, and cell chemotaxis is developed and shown to simulate observed experimental results. This generic cell behavior model can be applied to model stem cell patterning behavior at large

A balance of positive and negative regulators determines the pace of the segmentation clock

Somitogenesis is regulated by a molecular oscillator that drives dynamic gene expression within the pre-somitic mesoderm. Previous mathematical models of the somitogenesis clock that invoke the mechanism of delayed negative feedback predict that its oscillation period depends on the sum of delays inherent to negative-feedback loops and inhibitor half-lives. We develop a mathematical model that explores the possibility that positive feedback also plays a role in determining the period of clock oscillations. The model predicts that increasing the half-life of the positive regulator, Notch intracellular domain (NICD), can lead to elevated NICD levels and an increase in the oscillation period. To test this hypothesis, we investigate a phenotype induced by various small molecule inhibitors in which the clock is slowed. We observe elevated levels and a prolonged half-life of NICD. Reducing NICD production rescues these effects. These data provide the first indication that tight control of the turnover of positive as well as negative regulators of the clock determines its periodicity. DOI: http://dx.doi.org/10.7554/eLife.05842.00

Somitogenesis Clock-Wave Initiation Requires Differential Decay and Multiple Binding Sites for Clock Protein

Somitogenesis is a process common to all vertebrate embryos in which repeated blocks of cells arise from the presomitic mesoderm (PSM) to lay a foundational pattern for trunk and tail development. Somites form in the wake of passing waves of periodic gene expression that originate in the tailbud and sweep posteriorly across the PSM. Previous work has suggested that the waves result from a spatiotemporally graded control protein that affects the oscillation rate of clock-gene expression. With a minimally constructed mathematical model, we study the contribution of two control mechanisms to the initial formation of this gene-expression wave. We test four biologically motivated model scenarios with either one or two clock protein transcription binding sites, and with or without differential decay rates for clock protein monomers and dimers. We examine the sensitivity of wave formation with respect to multiple model parameters and robustness to heterogeneity in cell population. We find that only a model with both multiple binding sites and differential decay rates is able to reproduce experimentally observed waveforms. Our results show that the experimentally observed characteristics of somitogenesis wave initiation constrain the underlying genetic control mechanisms

Unmasking Chaotic Attributes in Time Series of Living Cell Populations

. Such complicated dynamics are generally the result of a combination of stochastic events and deterministic regulation. Assessing the role, if any, of chaotic regulation is difficult. However, unmasking chaotic dynamics is essential for analysis of cellular processes related to proliferation rate, including metabolic activity, telomere homeostasis, gene expression, and tumor growth.Using a simple, original, nonlinear method based on return maps, we previously found a geometrical deterministic structure coordinating such fluctuations in populations of various cell types. However, nonlinearity and determinism are only necessary conditions for chaos; they do not by themselves constitute a proof of chaotic dynamics. Therefore, we used the same analytical method to analyze the oscillations of four well-known, low-dimensional, chaotic oscillators, originally designed in diverse settings and all possibly well-adapted to model the fluctuations of cell populations: the Lorenz, Rössler, Verhulst and Duffing oscillators. All four systems also display this geometrical structure, coordinating the oscillations of one or two variables of the oscillator. No such structure could be observed in periodic or stochastic fluctuations.Theoretical models predict various cell population dynamics, from stable through periodically oscillating to a chaotic regime. Periodic and stochastic fluctuations were first described long ago in various mammalian cells, but by contrast, chaotic regulation had not previously been evidenced. The findings with our nonlinear geometrical approach are entirely consistent with the notion that fluctuations of cell populations can be chaotically controlled