A geometrical model of cell fate specification in the mouse blastocyst.

The lineage decision that generates the epiblast and primitive endoderm from the inner cell mass (ICM) is a paradigm for cell fate specification. Recent mathematics has formalized Waddington's landscape metaphor and proven that lineage decisions in detailed gene network models must conform to a small list of low-dimensional stereotypic changes called bifurcations. The most plausible bifurcation for the ICM is the so-called heteroclinic flip that we define and elaborate here. Our re-analysis of recent data suggests that there is sufficient cell movement in the ICM so the FGF signal, which drives the lineage decision, can be treated as spatially uniform. We thus extend the bifurcation model for a single cell to the entire ICM by means of a self-consistently defined time-dependent FGF signal. This model is consistent with available data and we propose additional dynamic experiments to test it further. This demonstrates that simplified, quantitative and intuitively transparent descriptions are possible when attention is shifted from specific genes to lineages. The flip bifurcation is a very plausible model for any situation where the embryo needs control over the relative proportions of two fates by a morphogen feedback.

A geometrical perspective on development.

Cell fate decisions emerge as a consequence of a complex set of gene regulatory networks. Models of these networks are known to have more parameters than data can determine. Recent work, inspired by Waddington's metaphor of a landscape, has instead tried to understand the geometry of gene regulatory networks. Here, we describe recent results on the appropriate mathematical framework for constructing these landscapes. This allows the construction of minimally parameterized models consistent with cell behavior. We review existing examples where geometrical models have been used to fit experimental data on cell fate and describe how spatial interactions between cells can be understood geometrically.

Deep-learning analysis of micropattern-based organoids enables high-throughput drug screening of Huntington's disease models.

Organoids are carrying the promise of modeling complex disease phenotypes and serving as a powerful basis for unbiased drug screens, potentially offering a more efficient drug-discovery route. However, unsolved technical bottlenecks of reproducibility and scalability have prevented the use of current organoids for high-throughput screening. Here, we present a method that overcomes these limitations by using deep-learning-driven analysis for phenotypic drug screens based on highly standardized micropattern-based neural organoids. This allows us to distinguish between disease and wild-type phenotypes in complex tissues with extremely high accuracy as well as quantify two predictors of drug success: efficacy and adverse effects. We applied our approach to Huntington's disease (HD) and discovered that bromodomain inhibitors revert complex phenotypes induced by the HD mutation. This work demonstrates the power of combining machine learning with phenotypic drug screening and its successful application to reveal a potentially new druggable target for HD.

Mechanisms underlying WNT-mediated priming of human embryonic stem cells.

Embryogenesis is guided by a limited set of signaling pathways dynamically expressed in different places. How a context-dependent signaling response is generated has been a central question of developmental biology, which can now be addressed with in vitro models of human embryos that are derived from embryonic stem cells (hESCs). Our previous work demonstrated that during early stages of hESC differentiation, cells chronicle signaling hierarchy. Only cells that have been exposed (primed) by WNT signaling can respond to subsequent activin exposure and differentiate to mesendodermal (ME) fates. Here, we show that WNT priming does not alter SMAD2 binding nor its chromatin opening but, instead, acts by inducing the expression of the SMAD2 co-factor EOMES. Expression of EOMES is sufficient to replace WNT upstream of activin-mediated ME differentiation, thus unveiling the mechanistic basis for priming and cellular memory in early development.

In vitro attachment and symmetry breaking of a human embryo model assembled from primed embryonic stem cells.

Our knowledge of the molecular mechanisms surrounding human embryo implantation and gastrulation is lacking, largely due to technical and ethical limitations of experimenting with human embryos. Alternatives to human embryos have been reported, in which 3D clusters of embryonic stem cells are differentiated in a stepwise manner to model aspects of human embryogenesis. Yet it remains challenging to model the events past attachment. We propose a strategy of modeling the post-attachment human embryo by assembling a pre-formed polarized epithelial epiblast and extraembryonic cells, allowing them to self-organize into a structure that mimics the dish-attached human embryo. The model attaches in vitro and, in the absence of exogenous morphogens, breaks anteroposterior symmetry, giving rise to early gastrulation cell types. Our assembloid approach enables in a modular way to upgrade or exchange extraembryonic tissues to access more advanced stages of post-attachment development while complying with ethical policies.

Statistically derived geometrical landscapes capture principles of decision-making dynamics during cell fate transitions.

Fate decisions in developing tissues involve cells transitioning between discrete cell states, each defined by distinct gene expression profiles. The Waddington landscape, in which the development of a cell is viewed as a ball rolling through a valley filled terrain, is an appealing way to describe differentiation. To construct and validate accurate landscapes, quantitative methods based on experimental data are necessary. We combined principled statistical methods with a framework based on catastrophe theory and approximate Bayesian computation to formulate a quantitative dynamical landscape that accurately predicts cell fate outcomes of pluripotent stem cells exposed to different combinations of signaling factors. Analysis of the landscape revealed two distinct ways in which cells make a binary choice between one of two fates. We suggest that these represent archetypal designs for developmental decisions. The approach is broadly applicable for the quantitative analysis of differentiation and for determining the logic of developmental decisions.

Mechanical regulation of early vertebrate embryogenesis.

Embryonic cells grow in environments that provide a plethora of physical cues, including mechanical forces that shape the development of the entire embryo. Despite their prevalence, the role of these forces in embryonic development and their integration with chemical signals have been mostly neglected, and scrutiny in modern molecular embryology tilted, instead, towards the dissection of molecular pathways involved in cell fate determination and patterning. It is now possible to investigate how mechanical signals induce downstream genetic regulatory networks to regulate key developmental processes in the embryo. Here, we review the insights into mechanical control of early vertebrate development, including the role of forces in tissue patterning and embryonic axis formation. We also highlight recent in vitro approaches using individual embryonic stem cells and self-organizing multicellular models of human embryos, which have been instrumental in expanding our understanding of how mechanics tune cell fate and cellular rearrangements during human embryonic development.

Human neural tube morphogenesis in vitro by geometric constraints.

Understanding human organ formation is a scientific challenge with far-reaching medical implications1,2. Three-dimensional stem-cell cultures have provided insights into human cell differentiation3,4. However, current approaches use scaffold-free stem-cell aggregates, which develop non-reproducible tissue shapes and variable cell-fate patterns. This limits their capacity to recapitulate organ formation. Here we present a chip-based culture system that enables self-organization of micropatterned stem cells into precise three-dimensional cell-fate patterns and organ shapes. We use this system to recreate neural tube folding from human stem cells in a dish. Upon neural induction5,6, neural ectoderm folds into a millimetre-long neural tube covered with non-neural ectoderm. Folding occurs at 90% fidelity, and anatomically resembles the developing human neural tube. We find that neural and non-neural ectoderm are necessary and sufficient for folding morphogenesis. We identify two mechanisms drive folding: (1) apical contraction of neural ectoderm, and (2) basal adhesion mediated via extracellular matrix synthesis by non-neural ectoderm. Targeting these two mechanisms using drugs leads to morphological defects similar to neural tube defects. Finally, we show that neural tissue width determines neural tube shape, suggesting that morphology along the anterior-posterior axis depends on neural ectoderm geometry in addition to molecular gradients7. Our approach provides a new route to the study of human organ morphogenesis in health and disease.

Geometry of gene regulatory dynamics.

Embryonic development leads to the reproducible and ordered appearance of complexity from egg to adult. The successive differentiation of different cell types that elaborate this complexity results from the activity of gene networks and was likened by Waddington to a flow through a landscape in which valleys represent alternative fates. Geometric methods allow the formal representation of such landscapes and codify the types of behaviors that result from systems of differential equations. Results from Smale and coworkers imply that systems encompassing gene network models can be represented as potential gradients with a Riemann metric, justifying the Waddington metaphor. Here, we extend this representation to include parameter dependence and enumerate all three-way cellular decisions realizable by tuning at most two parameters, which can be generalized to include spatial coordinates in a tissue. All diagrams of cell states vs. model parameters are thereby enumerated. We unify a number of standard models for spatial pattern formation by expressing them in potential form (i.e., as topographic elevation). Turing systems appear nonpotential, yet in suitable variables the dynamics are low dimensional and potential. A time-independent embedding recovers the original variables. Lateral inhibition is described by a saddle point with many unstable directions. A model for the patterning of the Drosophila eye appears as relaxation in a bistable potential. Geometric reasoning provides intuitive dynamic models for development that are well adapted to fit time-lapse data.

Differential compartmentalization of BMP4/NOGGIN requires NOGGIN trans-epithelial transport.

Using self-organizing human models of gastrulation, we previously showed that (1) BMP4 initiates the cascade of events leading to gastrulation, (2) BMP4 signal reception is restricted to the basolateral domain, and (3) in a human-specific manner, BMP4 directly induces the expression of NOGGIN. Here, we report the surprising discovery that in human epiblasts, NOGGIN and BMP4 were secreted into opposite extracellular spaces. Interestingly, apically presented NOGGIN could inhibit basally delivered BMP4. Apically imposed microfluidic flow demonstrated that NOGGIN traveled in the apical extracellular space. Our co-localization analysis detailed the endocytotic route that trafficked NOGGIN from the apical space to the basolateral intercellular space where BMP4 receptors were located. This apical-basal transcytosis was indispensable for NOGGIN inhibition. Taken together, the segregation of activator/inhibitor into distinct extracellular spaces challenges classical views of morphogen movement. We propose that the transport of morphogen inhibitors regulates the spatial availability of morphogens during embryogenesis.

In vitro modeling of early mammalian embryogenesis.

Synthetic embryology endeavors to use stem cells to recapitulate the first steps of mammalian development that define the body axes and first stages of fate assignment. Well-engineered synthetic systems provide an unparalleled assay to disentangle and quantify the contributions of individual tissues as well as the molecular components driving embryogenesis. Experiments using a mixture of mouse embryonic and extra-embryonic stem cell lines show a surprising degree of self-organization akin to certain milestones in the development of intact mouse embryos. To further advance the field and extend the mouse results to human, it is crucial to develop a better control of the assembly process as well as to establish a deeper understanding of the developmental state and potency of cells used in experiments at each step of the process. We review recent advances in the derivation of embryonic and extraembryonic stem cells, and we highlight recent efforts in reconstructing the structural and signaling aspects of embryogenesis in three-dimensional tissue cultures.

Mapping cell migrations and fates in a gastruloid model to the human primitive streak.

Although fate maps of early embryos exist for nearly all model organisms, a fate map of the gastrulating human embryo remains elusive. Here, we use human gastruloids to piece together a rudimentary fate map for the human primitive streak (PS). This is possible because differing levels of BMP, WNT and NODAL lead to self-organization of gastruloids into homogenous subpopulations of endoderm and mesoderm, and comparative analysis of these gastruloids, together with the fate map of the mouse embryo, allows the organization of these subpopulations along an anterior-posterior axis. We also developed a novel cell tracking technique that detected robust fate-dependent cell migrations in our gastruloids comparable with those found in the mouse embryo. Taken together, our fate map and recording of cell migrations provides a first coarse view of what the human PS may resemble in vivo.

A 3D model of a human epiblast reveals BMP4-driven symmetry breaking.

Breaking the anterior-posterior symmetry in mammals occurs at gastrulation. Much of the signalling network underlying this process has been elucidated in the mouse; however, there is no direct molecular evidence of events driving axis formation in humans. Here, we use human embryonic stem cells to generate an in vitro three-dimensional model of a human epiblast whose size, cell polarity and gene expression are similar to a day 10 human epiblast. A defined dose of BMP4 spontaneously breaks axial symmetry, and induces markers of the primitive streak and epithelial-to-mesenchymal transition. We show that WNT signalling and its inhibitor DKK1 play key roles in this process downstream of BMP4. Our work demonstrates that a model human epiblast can break axial symmetry despite the absence of asymmetry in the initial signal and of extra-embryonic tissues or maternal cues. Our three-dimensional model is an assay for the molecular events underlying human axial symmetry breaking.

Self-organization of stem cells into embryos: A window on early mammalian development.

Embryonic development is orchestrated by robust and complex regulatory mechanisms acting at different scales of organization. In vivo studies are particularly challenging for mammals after implantation, owing to the small size and inaccessibility of the embryo. The generation of stem cell models of the embryo represents a powerful system with which to dissect this complexity. Control of geometry, modulation of the physical environment, and priming with chemical signals reveal the intrinsic capacity of embryonic stem cells to make patterns. Adding the stem cells for the extraembryonic lineages generates three-dimensional models that are more autonomous from the environment and recapitulate many features of the pre- and postimplantation mouse embryo, including gastrulation. Here, we review the principles of self-organization and how they set cells in motion to create an embryo.

A wave of WNT signaling balanced by secreted inhibitors controls primitive streak formation in micropattern colonies of human embryonic stem cells.

Long-range signaling by morphogens and their inhibitors define embryonic patterning yet quantitative data and models are rare, especially in humans. Here, we use a human embryonic stem cell micropattern system to model formation of the primitive streak (PS) by WNT. In the pluripotent state, E-cadherin (E-CAD) transduces boundary forces to focus WNT signaling to the colony border. Following application of WNT ligand, E-CAD mediates a front or wave of epithelial-to-mesenchymal (EMT) conversion analogous to PS extension in an embryo. By knocking out the secreted WNT inhibitors active in our system, we show that DKK1 alone controls the extent and duration of patterning. The NODAL inhibitor cerberus 1 acts downstream of WNT to refine the endoderm versus mesoderm fate choice. Our EMT wave is a generic property of a bistable system with diffusion and we present a single quantitative model that describes both the wave and our knockout data.

WNT signaling memory is required for ACTIVIN to function as a morphogen in human gastruloids.

Self-organization of discrete fates in human gastruloids is mediated by a hierarchy of signaling pathways. How these pathways are integrated in time, and whether cells maintain a memory of their signaling history remains obscure. Here, we dissect the temporal integration of two key pathways, WNT and ACTIVIN, which along with BMP control gastrulation. CRISPR/Cas9-engineered live reporters of SMAD1, 2 and 4 demonstrate that in contrast to the stable signaling by SMAD1, signaling and transcriptional response by SMAD2 is transient, and while necessary for pluripotency, it is insufficient for differentiation. Pre-exposure to WNT, however, endows cells with the competence to respond to graded levels of ACTIVIN, which induces differentiation without changing SMAD2 dynamics. This cellular memory of WNT signaling is necessary for ACTIVIN morphogen activity. A re-evaluation of the evidence gathered over decades in model systems, re-enforces our conclusions and points to an evolutionarily conserved mechanism.

Modeling Mammalian Gastrulation With Embryonic Stem Cells.

Understanding cell fate patterning and morphogenesis in the mammalian embryo remains a formidable challenge. Recently, in vivo models based on embryonic stem cells (ESCs) have emerged as complementary methods to quantitatively dissect the physical and molecular processes that shape the embryo. Here we review recent developments in using ESCs to create both two- and three-dimensional culture models that shed light on mammalian gastrulation.

Micropattern differentiation of mouse pluripotent stem cells recapitulates embryo regionalized cell fate patterning.

During gastrulation epiblast cells exit pluripotency as they specify and spatially arrange the three germ layers of the embryo. Similarly, human pluripotent stem cells (PSCs) undergo spatially organized fate specification on micropatterned surfaces. Since in vivo validation is not possible for the human, we developed a mouse PSC micropattern system and, with direct comparisons to mouse embryos, reveal the robust specification of distinct regional identities. BMP, WNT, ACTIVIN and FGF directed mouse epiblast-like cells to undergo an epithelial-to-mesenchymal transition and radially pattern posterior mesoderm fates. Conversely, WNT, ACTIVIN and FGF patterned anterior identities, including definitive endoderm. By contrast, epiblast stem cells, a developmentally advanced state, only specified anterior identities, but without patterning. The mouse micropattern system offers a robust scalable method to generate regionalized cell types present in vivo, resolve how signals promote distinct identities and generate patterns, and compare mechanisms operating in vivo and in vitro and across species.

Gene-free methodology for cell fate dynamics during development.

Models of cell function that assign a variable to each gene frequently lead to systems of equations with many parameters whose behavior is obscure. Geometric models reduce dynamics to intuitive pictorial elements that provide compact representations for sparse in vivo data and transparent descriptions of developmental transitions. To illustrate, a geometric model fit to vulval development in Caenorhabditis elegans, implies a phase diagram where cell-fate choices are displayed in a plane defined by EGF and Notch signaling levels. This diagram defines allowable and forbidden cell-fate transitions as EGF or Notch levels change, and explains surprising observations previously attributed to context-dependent action of these signals. The diagram also reveals the existence of special points at which minor changes in signal levels lead to strong epistatic interactions between EGF and Notch. Our model correctly predicts experiments near these points and suggests specific timed perturbations in signals that can lead to additional unexpected outcomes.

A Geometric Model of Stripe Refinement.

Organizing data about patterning and morphogenesis into a coherent framework remains a challenge in developmental biology. Reporting in Science, Corson et al. (2017) apply innovative analysis to an old problem of bristle patterns in Drosophila, reducing the nonlinear interactions among tens of cells to a succinct model with quantitative predictions.