The Clock and Wavefront Self-Organizing model recreates the dynamics of mouse somitogenesis in vivo and in vitro.

During mouse development, presomitic mesoderm cells synchronize Wnt and Notch oscillations, creating sequential phase waves that pattern somites. Traditional somitogenesis models attribute phase waves to a global modulation of the oscillation frequency. However, increasing evidence suggests that they could arise in a self-organizing manner. Here, we introduce the Sevilletor, a novel reaction-diffusion system that serves as a framework to compare different somitogenesis patterning hypotheses. Using this framework, we propose the Clock and Wavefront Self-Organizing model that considers an excitable self-organizing region where phase waves form independent of global frequency gradients. The model recapitulates the change in relative phase of Wnt and Notch observed during mouse somitogenesis and provides a theoretical basis for understanding the excitability of mouse presomitic mesoderm cells in vitro.

From embryos to embryoids: How external signals and self-organization drive embryonic development.

Embryonic development has been traditionally seen as an inductive process directed by exogenous maternal inputs and extra-embryonic signals. Increasing evidence, however, is showing that, in addition to exogenous signals, the development of the embryo involves endogenous self-organization. Recently, this self-organizing potential has been highlighted by a number of stem cell models known as embryoids that can recapitulate different aspects of embryogenesis in vitro. Here, we review the self-organizing behaviors observed in different embryoid models and seek to reconcile this new evidence with classical knowledge of developmental biology. This analysis leads to reexamine embryonic development as a guided self-organizing process, where patterning and morphogenesis are controlled by a combination of exogenous signals and endogenous self-organization. Finally, we discuss the multidisciplinary approach required to investigate the genetic and cellular basis of self-organization.

Virtual meeting, real and sound science: report of the 17th Meeting of the Spanish Society for Developmental Biology (SEBD-2020).

The Spanish Society for Developmental Biology (SEBD) organized its 17th meeting in November 2020 (herein referred to as SEBD2020). This meeting, originally programmed to take place in the city of Bilbao, was forced onto an online format due to the SARS-CoV2, COVID-19 pandemic. Although, we missed the live personal interactions and missed out on the Bilbao social scene, we were able to meet online to present our work and discuss our latest results. An overview of the activities that took place around the meeting, the different scientific sessions and the speakers involved are presented here. The pros and cons of virtual meetings are discussed.

Scale-invariant patterning by size-dependent inhibition of Nodal signalling.

Individuals can vary substantially in size, but the proportions of their body plans are often maintained. We generated smaller zebrafish by removing 30% of their cells at the blastula stages and found that these embryos developed into normally patterned individuals. Strikingly, the proportions of all germ layers adjusted to the new embryo size within 2 hours after cell removal. As Nodal-Lefty signalling controls germ-layer patterning, we performed a computational screen for scale-invariant models of this activator-inhibitor system. This analysis predicted that the concentration of the highly diffusive inhibitor Lefty increases in smaller embryos, leading to a decreased Nodal activity range and contracted germ-layer dimensions. In vivo studies confirmed that Lefty concentration increased in smaller embryos, and embryos with reduced Lefty levels or with diffusion-hindered Lefty failed to scale their tissue proportions. These results reveal that size-dependent inhibition of Nodal signalling allows scale-invariant patterning.

The fin-to-limb transition as the re-organization of a Turing pattern.

A Turing mechanism implemented by BMP, SOX9 and WNT has been proposed to control mouse digit patterning. However, its generality and contribution to the morphological diversity of fins and limbs has not been explored. Here we provide evidence that the skeletal patterning of the catshark Scyliorhinus canicula pectoral fin is likely driven by a deeply conserved Bmp-Sox9-Wnt Turing network. In catshark fins, the distal nodular elements arise from a periodic spot pattern of Sox9 expression, in contrast to the stripe pattern in mouse digit patterning. However, our computer model shows that the Bmp-Sox9-Wnt network with altered spatial modulation can explain the Sox9 expression in catshark fins. Finally, experimental perturbation of Bmp or Wnt signalling in catshark embryos produces skeletal alterations which match in silico predictions. Together, our results suggest that the broad morphological diversity of the distal fin and limb elements arose from the spatial re-organization of a deeply conserved Turing mechanism.

High-throughput mathematical analysis identifies Turing networks for patterning with equally diffusing signals.

The Turing reaction-diffusion model explains how identical cells can self-organize to form spatial patterns. It has been suggested that extracellular signaling molecules with different diffusion coefficients underlie this model, but the contribution of cell-autonomous signaling components is largely unknown. We developed an automated mathematical analysis to derive a catalog of realistic Turing networks. This analysis reveals that in the presence of cell-autonomous factors, networks can form a pattern with equally diffusing signals and even for any combination of diffusion coefficients. We provide a software (available at http://www.RDNets.com) to explore these networks and to constrain topologies with qualitative and quantitative experimental data. We use the software to examine the self-organizing networks that control embryonic axis specification and digit patterning. Finally, we demonstrate how existing synthetic circuits can be extended with additional feedbacks to form Turing reaction-diffusion systems. Our study offers a new theoretical framework to understand multicellular pattern formation and enables the wide-spread use of mathematical biology to engineer synthetic patterning systems.

Data-driven modelling of a gene regulatory network for cell fate decisions in the growing limb bud.

Parameter optimization coupled with model selection is a convenient approach to infer gene regulatory networks from experimental gene expression data, but so far it has been limited to single cells or static tissues where growth is not significant. Here, we present a computational study in which we determine an optimal gene regulatory network from the spatiotemporal dynamics of gene expression patterns in a complex 2D growing tissue (non-isotropic and heterogeneous growth rates). We use this method to predict the regulatory mechanisms that underlie proximodistal (PD) patterning of the developing limb bud. First, we map the expression patterns of the PD markers Meis1, Hoxa11 and Hoxa13 into a dynamic description of the tissue movements that drive limb morphogenesis. Secondly, we use reverse-engineering to test how different gene regulatory networks can interpret the opposing gradients of fibroblast growth factors (FGF) and retinoic acid (RA) to pattern the PD markers. Finally, we validate and extend the best model against various previously published manipulative experiments, including exogenous application of RA, surgical removal of the FGF source and genetic ectopic expression of Meis1. Our approach identifies the most parsimonious gene regulatory network that can correctly pattern the PD markers downstream of FGF and RA. This network reveals a new model of PD regulation which we call the "crossover model", because the proximal morphogen (RA) controls the distal boundary of Hoxa11, while conversely the distal morphogens (FGFs) control the proximal boundary.

Hox genes regulate digit patterning by controlling the wavelength of a Turing-type mechanism.

The formation of repetitive structures (such as stripes) in nature is often consistent with a reaction-diffusion mechanism, or Turing model, of self-organizing systems. We used mouse genetics to analyze how digit patterning (an iterative digit/nondigit pattern) is generated. We showed that the progressive reduction in Hoxa13 and Hoxd11-Hoxd13 genes (hereafter referred to as distal Hox genes) from the Gli3-null background results in progressively more severe polydactyly, displaying thinner and densely packed digits. Combined with computer modeling, our results argue for a Turing-type mechanism underlying digit patterning, in which the dose of distal Hox genes modulates the digit period or wavelength. The phenotypic similarity with fish-fin endoskeleton patterns suggests that the pentadactyl state has been achieved through modification of an ancestral Turing-type mechanism.

Turing patterns in development: what about the horse part?

For many years Turing patterns-the repetitive patterns which Alan Turing proved could arise from simple diffusing and interacting factors-have remained an interesting theoretical possibility, rather than a central concern of the developmental biology community. Recently however, this has started to change, with an increasing number of studies combining both experimental and theoretical work to reveal how Turing models may underlie a variety of patterning or morphogenetic processes. We review here the recent developments in this field across a wide range of model systems.

A computational clonal analysis of the developing mouse limb bud.

A comprehensive spatio-temporal description of the tissue movements underlying organogenesis would be an extremely useful resource to developmental biology. Clonal analysis and fate mappings are popular experiments to study tissue movement during morphogenesis. Such experiments allow cell populations to be labeled at an early stage of development and to follow their spatial evolution over time. However, disentangling the cumulative effects of the multiple events responsible for the expansion of the labeled cell population is not always straightforward. To overcome this problem, we develop a novel computational method that combines accurate quantification of 2D limb bud morphologies and growth modeling to analyze mouse clonal data of early limb development. Firstly, we explore various tissue movements that match experimental limb bud shape changes. Secondly, by comparing computational clones with newly generated mouse clonal data we are able to choose and characterize the tissue movement map that better matches experimental data. Our computational analysis produces for the first time a two dimensional model of limb growth based on experimental data that can be used to better characterize limb tissue movement in space and time. The model shows that the distribution and shapes of clones can be described as a combination of anisotropic growth with isotropic cell mixing, without the need for lineage compartmentalization along the AP and PD axis. Lastly, we show that this comprehensive description can be used to reassess spatio-temporal gene regulations taking tissue movement into account and to investigate PD patterning hypothesis.