Understanding Pattern Formation in Embryos: Experiment, Theory, and Simulation

Contrasting philosophical and scientific views in the long history of studying the generation of form in development

Focusing on the opposing ways of thinking of philosophers and scientists to explain the generation of form in biological development, I show that today's controversies over explanations of early development bear fundamental similarities to the dichotomy of preformation theory versus epigenesis in Greek antiquity. They are related to the acceptance or rejection of the idea of a physical form of what today would be called information for the generating of the embryo as a necessary pre-requisite for specific development and heredity. As a recent example, I scrutinize the dichotomy of genomic causality versus self-organization in 20th and 21st century theories of the generation of form. On the one hand, the generation of patterns and form, as well as the constant outcome in development, are proposed to be causally related to something that is "preformed" in the germ cells, the nucleus of germ cells, or the genome. On the other hand, it is proposed that there is no pre-existing form or information, and development is seen as a process where genuinely new characters emerge from formless matter, either by immaterial "forces of life," or by physical-chemical processes of self-organization. I also argue that these different ways of thinking and the research practices associated with them are not equivalent, and maintain that it is impossible to explain the generation of form and constant outcome of development without the assumption of the transmission of pre-existing information in the form of DNA sequences in the genome. Only in this framework of "preformed" information can "epigenesis" in the form of physical and chemical processes of self-organization play an important role.

A mathematical framework for measuring and tuning tempo in developmental gene regulatory networks

Embryo development is a dynamic process governed by the regulation of timing and sequences of gene expression, which control the proper growth of the organism. Although many genetic programmes coordinating these sequences are common across species, the timescales of gene expression can vary significantly among different organisms. Currently, substantial experimental efforts are focused on identifying molecular mechanisms that control these temporal aspects. In contrast, the capacity of established mathematical models to incorporate tempo control while maintaining the same dynamical landscape remains less understood. Here, we address this gap by developing a mathematical framework that links the functionality of developmental programmes to the corresponding gene expression orbits (or landscapes). This unlocks the ability to find tempo differences as perturbations in the dynamical system that preserve its orbits. We demonstrate that this framework allows for the prediction of molecular mechanisms governing tempo, through both numerical and analytical methods. Our exploration includes two case studies: a generic network featuring coupled production and degradation, with a particular application to neural progenitor differentiation; and the repressilator. In the latter, we illustrate how altering the dimerisation rates of transcription factors can decouple the tempo from the shape of the resulting orbits. We conclude by highlighting how the identification of orthogonal molecular mechanisms for tempo control can inform the design of circuits with specific orbits and tempos.

The salt-and-pepper pattern in mouse blastocysts is compatible with signaling beyond the nearest neighbors

Embryos develop in a concerted sequence of spatiotemporal arrangements of cells. In the preimplantation mouse embryo, the distribution of the cells in the inner cell mass evolves from a salt-and-pepper pattern to spatial segregation of two distinct cell types. The exact properties of the salt-and-pepper pattern have not been analyzed so far. We investigate the spatiotemporal distribution of NANOG- and GATA6-expressing cells in the ICM of the mouse blastocysts with quantitative three-dimensional single-cell-based neighborhood analyses. A combination of spatial statistics and agent-based modeling reveals that the cell fate distribution follows a local clustering pattern. Using ordinary differential equations modeling, we show that this pattern can be established by a distance-based signaling mechanism enabling cells to integrate information from the whole inner cell mass into their cell fate decision. Our work highlights the importance of longer-range signaling to ensure coordinated decisions in groups of cells to successfully build embryos.

Self-Organization and Genomic Causality in Models of Morphogenesis

The debate about what causes the generation of form and structure in embryological development goes back to antiquity. Most recently, it has focused on the divergent views as to whether the generation of patterns and form in development is a largely self-organized process or is mainly determined by the genome, in particular, complex developmental gene regulatory processes. This paper presents and analyzes pertinent models of pattern formation and form generation in a developing organism in the past and the present, with a special emphasis on Alan Turing's 1952 reaction-diffusion model. I first draw attention to the fact that Turing's paper remained, at first, without a noticeable impact on the community of biologists because purely physical-chemical models were unable to explain embryological development and often also simple repetitive patterns. I then show that from the year 2000 and onwards, Turing's 1952 paper was increasingly cited also by biologists. The model was updated to include gene products and now seemed able to account for the generation of biological patterns, though discrepancies between models and biological reality remained. I then point out Eric Davidson's successful theory of early embryogenesis based on gene-regulatory network analysis and its mathematical modeling that not only was able to provide a mechanistic and causal explanation for gene regulatory events controlling developmental cell fate specification but, unlike reaction-diffusion models, also addressed the effects of evolution and organisms' longstanding developmental and species stability. The paper concludes with an outlook on further developments of the gene regulatory network model.

Ethanol exposure perturbs sea urchin development and disrupts developmental timing

Ethanol is a known vertebrate teratogen that causes craniofacial defects as a component of fetal alcohol syndrome (FAS). Our results show that sea urchin embryos treated with ethanol similarly show broad skeletal patterning defects, potentially analogous to the defects associated with FAS. The sea urchin larval skeleton is a simple patterning system that involves only two cell types: the primary mesenchymal cells (PMCs) that secrete the calcium carbonate skeleton and the ectodermal cells that provide migratory, positional, and differentiation cues for the PMCs. Perturbations in RA biosynthesis and Hh signaling pathways are thought to be causal for the FAS phenotype in vertebrates. Surprisingly, our results indicate that these pathways are not functionally relevant for the teratogenic effects of ethanol in developing sea urchins. We found that developmental morphology as well as the expression of some ectodermal and PMC genes was delayed by ethanol exposure. Temporal transcriptome analysis revealed significant impacts of ethanol on signaling and metabolic gene expression, and a disruption in the timing of GRN gene expression that includes both delayed and precocious gene expression throughout the specification network. We conclude that the skeletal patterning perturbations in ethanol-treated embryos likely arise from a loss of temporal synchrony within and between the instructive and responsive tissues.

A pendulum of induction between the epiblast and extra-embryonic endoderm supports post-implantation progression

Embryogenesis is supported by dynamic loops of cellular interactions. Here, we create a partial mouse embryo model to elucidate the principles of epiblast (Epi) and extra-embryonic endoderm co-development (XEn). We trigger naive mouse embryonic stem cells to form a blastocyst-stage niche of Epi-like cells and XEn-like cells (3D, hydrogel free and serum free). Once established, these two lineages autonomously progress in minimal medium to form an inner pro-amniotic-like cavity surrounded by polarized Epi-like cells covered with visceral endoderm (VE)-like cells. The progression occurs through reciprocal inductions by which the Epi supports the primitive endoderm (PrE) to produce a basal lamina that subsequently regulates Epi polarization and/or cavitation, which, in return, channels the transcriptomic progression to VE. This VE then contributes to Epi bifurcation into anterior- and posterior-like states. Similarly, boosting the formation of PrE-like cells within blastoids supports developmental progression. We argue that self-organization can arise from lineage bifurcation followed by a pendulum of induction that propagates over time.

The Nasonia pair-rule gene regulatory network retains its function over 300 million years of evolution

Insect segmentation is a well-studied and tractable system with which to investigate the genetic regulation of development. Though insects segment their germband using a variety of methods, modelling work implies that a single gene regulatory network can underpin the two main types of insect segmentation. This means limited genetic changes are required to explain significant differences in segmentation mode between different insects. This idea needs to be tested in a wider variety of species, and the nature of the gene regulatory network (GRN) underlying this model has not been tested. Some insects, e.g. Nasonia vitripennis and Apis mellifera segment progressively, a pattern not examined in previous studies of this segmentation model, producing stripes at different times progressively through the embryo, but not from a segment addition zone. Here, we aim to understand the GRNs patterning Nasonia using a simulation-based approach. We found that an existing model of Drosophila segmentation ( Clark, 2017) can be used to recapitulate the progressive segmentation of Nasonia, if provided with altered inputs in the form of expression of the timer genes Nv-caudal and Nv-odd paired. We predict limited topological changes to the pair-rule network and show, by RNAi knockdown, that Nv-odd paired is required for morphological segmentation. Together this implies that very limited changes to the Drosophila network are required to simulate Nasonia segmentation, despite significant differences in segmentation modes, implying that Nasonia use a very similar version of an ancestral GRN used by Drosophila, which must therefore have been conserved for at least 300 million years.

Summary: The gene regulatory network that controls segmentation in the wasp Nasonia is functionally similar to that of Drosophila, despite different modes of segmentation and 300 million years of divergence.

Minimal Developmental Computation: A Causal Network Approach to Understand Morphogenetic Pattern Formation

What information-processing strategies and general principles are sufficient to enable self-organized morphogenesis in embryogenesis and regeneration? We designed and analyzed a minimal model of self-scaling axial patterning consisting of a cellular network that develops activity patterns within implicitly set bounds. The properties of the cells are determined by internal ‘genetic’ networks with an architecture shared across all cells. We used machine-learning to identify models that enable this virtual mini-embryo to pattern a typical axial gradient while simultaneously sensing the set boundaries within which to develop it from homogeneous conditions—a setting that captures the essence of early embryogenesis. Interestingly, the model revealed several features (such as planar polarity and regenerative re-scaling capacity) for which it was not directly selected, showing how these common biological design principles can emerge as a consequence of simple patterning modes. A novel “causal network” analysis of the best model furthermore revealed that the originally symmetric model dynamically integrates into intercellular causal networks characterized by broken-symmetry, long-range influence and modularity, offering an interpretable macroscale-circuit-based explanation for phenotypic patterning. This work shows how computation could occur in biological development and how machine learning approaches can generate hypotheses and deepen our understanding of how featureless tissues might develop sophisticated patterns—an essential step towards predictive control of morphogenesis in regenerative medicine or synthetic bioengineering contexts. The tools developed here also have the potential to benefit machine learning via new forms of backpropagation and by leveraging the novel distributed self-representation mechanisms to improve robustness and generalization.

Sox9CreER-mediated deletion of β-catenin in palatal mesenchyme results in delayed palatal elevation accompanied with repressed canonical Wnt signaling and reduced actin polymerization

Cleft palate is a good model to pushing us toward a deeper understanding of the molecular mechanisms of spatiotemporal patterns in tissues and organisms because of the multiple-step processes such as elevation and fusion. Previous studies have shown that the epithelial β-catenin is crucial for palatal fusion, however, the function of the mesenchymal β-catenin remains elusive. We investigate the role of mesenchymal β-catenin in palatal development by generating a β-catenin conditional knockout mouse (CKO) (Sox9CreER; Ctnnb1^F/F ). We found that the CKO mice exhibited delayed palatal elevation, leading to cleft palate in both in vivo and ex vivo. Abnormal cell proliferation and repressed mesenchymal canonical Wnt signaling were found in the CKO palate. Interestingly, Filamentous actin (F-actin) polymerization was significantly reduced in the palatal mesenchyme of mutant embryos. Furthermore, overexpression of adenovirus-mediated transfection with Acta1 in the mutant could help to elevate the palatal shelves but could not prevent cleft palate in ex vivo. Our results suggest that conditionally knock out β-catenin in the palatal mesenchyme by Sox9CreER leading to delayed palatal elevation, which results in repressed mesenchymal canonical Wnt signaling, decreased cell proliferation, and reduced actin polymerization, finally causes cleft palate.

Neural tube patterning: from a minimal model for rostrocaudal patterning toward an integrated 3D model

Rostrocaudal patterning of the neural tube is a defining event in vertebrate brain development. This process is driven by morphogen gradients which specify the fate of neural progenitor cells, leading to the partitioning of the tube. Although this is extensively studied experimentally, an integrated view of the genetic circuitry is lacking. Here, we present a minimal gene regulatory model for rostrocaudal patterning, whose tristable topology was determined in a data-driven way. Using this model, we identified the repression of hindbrain fate as promising strategy for the improvement of current protocols for the generation of dopaminergic neurons. Furthermore, we combined our model with an established minimal model for dorsoventral patterning on a realistic 3D neural tube and found that key features of neural tube patterning could be recapitulated. Doing so, we demonstrate how data and models from different sources can be combined to simulate complex in vivo processes.

Cross-species comparisons and in vitro models to study tempo in development and homeostasis

Time is inherent to biological processes. It determines the order of events and the speed at which they take place. However, we still need to refine approaches to measure the course of time in biological systems and understand what controls the pace of development. Here, we argue that the comparison of biological processes across species provides molecular insight into the timekeeping mechanisms in biology. We discuss recent findings and the open questions in the field and highlight the use of in vitro systems as tools to investigate cell-autonomous control as well as the coordination of temporal mechanisms within tissues. Further, we discuss the relevance of studying tempo for tissue transplantation, homeostasis and lifespan.

Implications of diffusion and time-varying morphogen gradients for the dynamic positioning and precision of bistable gene expression boundaries

The earliest models for how morphogen gradients guide embryonic patterning failed to account for experimental observations of temporal refinement in gene expression domains. Following theoretical and experimental work in this area, dynamic positional information has emerged as a conceptual framework to discuss how cells process spatiotemporal inputs into downstream patterns. Here, we show that diffusion determines the mathematical means by which bistable gene expression boundaries shift over time, and therefore how cells interpret positional information conferred from morphogen concentration. First, we introduce a metric for assessing reproducibility in boundary placement or precision in systems where gene products do not diffuse, but where morphogen concentrations are permitted to change in time. We show that the dynamics of the gradient affect the sensitivity of the final pattern to variation in initial conditions, with slower gradients reducing the sensitivity. Second, we allow gene products to diffuse and consider gene expression boundaries as propagating wavefronts with velocity modulated by local morphogen concentration. We harness this perspective to approximate a PDE model as an ODE that captures the position of the boundary in time, and demonstrate the approach with a preexisting model for Hunchback patterning in fruit fly embryos. We then propose a design that employs antiparallel morphogen gradients to achieve accurate boundary placement that is robust to scaling. Throughout our work we draw attention to tradeoffs among initial conditions, boundary positioning, and the relative timescales of network and gradient evolution. We conclude by suggesting that mathematical theory should serve to clarify not just our quantitative, but also our intuitive understanding of patterning processes.

Principles of Self-Organization of the Mammalian Embryo

Early embryogenesis is a conserved and self-organized process. In the mammalian embryo, the potential for self-organization is manifested in its extraordinary developmental plasticity, allowing a correctly patterned embryo to arise despite experimental perturbation. The underlying mechanisms enabling such regulative development have long been a topic of study. In this Review, we summarize our current understanding of the self-organizing principles behind the regulative nature of the early mammalian embryo. We argue that geometrical constraints, feedback between mechanical and biochemical factors, and cellular heterogeneity are all required to ensure the developmental plasticity of mammalian embryo development.

Cell-in-the-loop pattern formation with optogenetically emulated cell-to-cell signaling

Designing and implementing synthetic biological pattern formation remains challenging due to underlying theoretical complexity as well as the difficulty of engineering multicellular networks biochemically. Here, we introduce a cell-in-the-loop approach where living cells interact through in silico signaling, establishing a new testbed to interrogate theoretical principles when internal cell dynamics are incorporated rather than modeled. We present an easy-to-use theoretical test to predict the emergence of contrasting patterns in gene expression among laterally inhibiting cells. Guided by the theory, we experimentally demonstrate spontaneous checkerboard patterning in an optogenetic setup, where cell-to-cell signaling is emulated with light inputs calculated in silico from real-time gene expression measurements. The scheme successfully produces spontaneous, persistent checkerboard patterns for systems of sixteen patches, in quantitative agreement with theoretical predictions. Our research highlights how tools from dynamical systems theory may inform our understanding of patterning, and illustrates the potential of cell-in-the-loop for engineering synthetic multicellular systems.