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.

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.

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.

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.

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.

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.

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 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.

Self-organization of the in vitro attached human embryo.

Implantation of the blastocyst is a developmental milestone in mammalian embryonic development. At this time, a coordinated program of lineage diversification, cell-fate specification, and morphogenetic movements establishes the generation of extra-embryonic tissues and the embryo proper, and determines the conditions for successful pregnancy and gastrulation. Despite its basic and clinical importance, this process remains mysterious in humans. Here we report the use of a novel in vitro system to study the post-implantation development of the human embryo. We unveil the self-organizing abilities and autonomy of in vitro attached human embryos. We find human-specific molecular signatures of early cell lineage, timing, and architecture. Embryos display key landmarks of normal development, including epiblast expansion, lineage segregation, bi-laminar disc formation, amniotic and yolk sac cavitation, and trophoblast diversification. Our findings highlight the species-specificity of these developmental events and provide a new understanding of early human embryonic development beyond the blastocyst stage. In addition, our study establishes a new model system relevant to early human pregnancy loss. Finally, our work will also assist in the rational design of differentiation protocols of human embryonic stem cells to specific cell types for disease modelling and cell replacement therapy.

Predicting Ancestral Segmentation Phenotypes from Drosophila to Anopheles Using In Silico Evolution.

Molecular evolution is an established technique for inferring gene homology but regulatory DNA turns over so rapidly that inference of ancestral networks is often impossible. In silico evolution is used to compute the most parsimonious path in regulatory space for anterior-posterior patterning linking two Dipterian species. The expression pattern of gap genes has evolved between Drosophila (fly) and Anopheles (mosquito), yet one of their targets, eve, has remained invariant. Our model predicts that stripe 5 in fly disappears and a new posterior stripe is created in mosquito, thus eve stripe modules 3+7 and 4+6 in fly are homologous to 3+6 and 4+5 in mosquito. We can place Clogmia on this evolutionary pathway and it shares the mosquito homologies. To account for the evolution of the other pair-rule genes in the posterior we have to assume that the ancestral Dipterian utilized a dynamic method to phase those genes in relation to eve.

Temperature compensation and temperature sensation in the circadian clock.

All known circadian clocks have an endogenous period that is remarkably insensitive to temperature, a property known as temperature compensation, while at the same time being readily entrained by a diurnal temperature oscillation. Although temperature compensation and entrainment are defining features of circadian clocks, their mechanisms remain poorly understood. Most models presume that multiple steps in the circadian cycle are temperature-dependent, thus facilitating temperature entrainment, but then insist that the effect of changes around the cycle sums to zero to enforce temperature compensation. An alternative theory proposes that the circadian oscillator evolved from an adaptive temperature sensor: a gene circuit that responds only to temperature changes. This theory implies that temperature changes should linearly rescale the amplitudes of clock component oscillations but leave phase relationships and shapes unchanged. We show using timeless luciferase reporter measurements and Western blots against TIMELESS protein that this prediction is satisfied by the Drosophila circadian clock. We also review evidence for pathways that couple temperature to the circadian clock, and show previously unidentified evidence for coupling between the Drosophila clock and the heat-shock pathway.

A method to recapitulate early embryonic spatial patterning in human embryonic stem cells.

Embryos allocate cells to the three germ layers in a spatially ordered sequence. Human embryonic stem cells (hESCs) can generate the three germ layers in culture; however, differentiation is typically heterogeneous and spatially disordered. We show that geometric confinement is sufficient to trigger self-organized patterning in hESCs. In response to BMP4, colonies reproducibly differentiated to an outer trophectoderm-like ring, an inner ectodermal circle and a ring of mesendoderm expressing primitive-streak markers in between. Fates were defined relative to the boundary with a fixed length scale: small colonies corresponded to the outer layers of larger ones. Inhibitory signals limited the range of BMP4 signaling to the colony edge and induced a gradient of Activin-Nodal signaling that patterned mesendodermal fates. These results demonstrate that the intrinsic tendency of stem cells to make patterns can be harnessed by controlling colony geometries and provide a quantitative assay for studying paracrine signaling in early development.

Decisions on the fly in cellular sensory systems.

Cells send and receive signals through pathways that have been defined in great detail biochemically, and it is often presumed that the signals convey only level information. Cell signaling in the presence of noise is extensively studied but only rarely is the speed required to make a decision considered. However, in the immune system, rapidly developing embryos, and cellular response to stress, fast and accurate actions are required. Statistical theory under the rubric of "exploit-explore" quantifies trade-offs between decision speed and accuracy and supplies rigorous performance bounds and algorithms that realize them. We show that common protein phosphorylation networks can implement optimal decision theory algorithms and speculate that the ubiquitous chemical modifications to receptors during signaling actually perform analog computations. We quantify performance trade-offs when the cellular system has incomplete knowledge of the data model. For the problem of sensing the time when the composition of a ligand mixture changes, we find a nonanalytic dependence on relative concentrations and specify the number of parameters needed for near-optimal performance and how to adjust them. The algorithms specify the minimal computation that has to take place on a single receptor before the information is pooled across the cell.

Phenotypic model for early T-cell activation displaying sensitivity, specificity, and antagonism.

Early T-cell activation is selected by evolution to discriminate a few foreign peptides rapidly from a vast excess of self-peptides, and it is unclear in quantitative terms how this is possible. We show that a generic proofreading cascade supplemented by a single negative feedback mediated by the Src homology 2 domain phosphatase-1 (SHP-1) accounts quantitatively for early T-cell activation, including the effects of antagonists. Modulation of the negative feedback with SHP-1 concentration explains counterintuitive experimental observations, such as the nonmonotonic behavior of receptor activity on agonist concentration, the digital vs. continuous behavior on certain parameters, and the loss of response for high SHP-1 concentration. New experiments validate predictions on the nontrivial joint dependence on binding time and concentration for the relative effect of two antagonists: We explain why strong antagonists behave as partial agonists at low concentration and predict that the relative effect of antagonists can invert as their concentrations are varied. By focusing on the phenotype, our model quantitatively fits a body of experimental data with minimal variables and parameters.

Scaling of BMP gradients in Xenopus embryos.

Metazoan organisms can 'scale', that is, maintain similar proportions regardless of size. Ben-Zvi et al. use experiments in Xenopus to support a quantitative model that explains morphological scaling as the result of scaling of a gradient of bone morphogenetic protein (BMP) signals. We believe that the evidence for scaling in Xenopus is misinterpreted, and that their model for embryonic patterning disagrees with prior data. The experiments they present supporting their model admit alternative interpretations.

Analysis of combinatorial cis-regulation in synthetic and genomic promoters.

Transcription factor binding sites are being discovered at a rapid pace. It is now necessary to turn attention towards understanding how these sites work in combination to influence gene expression. Quantitative models that accurately predict gene expression from promoter sequence will be a crucial part of solving this problem. Here we present such a model, based on the analysis of synthetic promoter libraries in yeast (Saccharomyces cerevisiae). Thermodynamic models based only on the equilibrium binding of transcription factors to DNA and to each other captured a large fraction of the variation in expression in every library. Thermodynamic analysis of these libraries uncovered several phenomena in our system, including cooperativity and the effects of weak binding sites. When applied to the S. cerevisiae genome, a model of repression by Mig1 (which was trained on synthetic promoters) predicts a number of Mig1-regulated genes that lack significant Mig1-binding sites in their promoters. The success of the thermodynamic approach suggests that the information encoded by combinations of cis-regulatory sites is interpreted primarily through simple protein-DNA and protein-protein interactions, with complicated biochemical reactions-such as nucleosome modifications-being downstream events. Quantitative analyses of synthetic promoter libraries will be an important tool in unravelling the rules underlying combinatorial cis-regulation.

Dynamics of TGF-ß signaling reveal adaptive and pulsatile behaviors reflected in the nuclear localization of transcription factor Smad4.

The TGF-ß pathway plays a vital role in development and disease and regulates transcription through a complex composed of receptor-regulated Smads (R-Smads) and Smad4. Extensive biochemical and genetic studies argue that the pathway is activated through R-Smad phosphorylation; however, the dynamics of signaling remain largely unexplored. We monitored signaling and transcriptional dynamics and found that although R-Smads stably translocate to the nucleus under continuous pathway stimulation, transcription of direct targets is transient. Surprisingly, Smad4 nuclear localization is confined to short pulses that coincide with transcriptional activity. Upon perturbation, the dynamics of transcription correlate with Smad4 nuclear localization rather than with R-Smad activity. In Xenopus embryos, Smad4 shows stereotyped, uncorrelated bursts of nuclear localization, but activated R-Smads are uniform. Thus, R-Smads relay graded information about ligand levels that is integrated with intrinsic temporal control reflected in Smad4 into the active signaling complex.

Positive feedback of G1 cyclins ensures coherent cell cycle entry.

In budding yeast, Saccharomyces cerevisiae, the Start checkpoint integrates multiple internal and external signals into an all-or-none decision to enter the cell cycle. Here we show that Start behaves like a switch due to systems-level feedback in the regulatory network. In contrast to current models proposing a linear cascade of Start activation, transcriptional positive feedback of the G1 cyclins Cln1 and Cln2 induces the near-simultaneous expression of the approximately 200-gene G1/S regulon. Nuclear Cln2 drives coherent regulon expression, whereas cytoplasmic Cln2 drives efficient budding. Cells with the CLN1 and CLN2 genes deleted frequently arrest as unbudded cells, incurring a large fluctuation-induced fitness penalty due to both the lack of cytoplasmic Cln2 and insufficient G1/S regulon expression. Thus, positive-feedback-amplified expression of Cln1 and Cln2 simultaneously drives robust budding and rapid, coherent regulon expression. A similar G1/S regulatory network in mammalian cells, comprised of non-orthologous genes, suggests either conservation of regulatory architecture or convergent evolution.

Predicting embryonic patterning using mutual entropy fitness and in silico evolution.

During vertebrate embryogenesis, the expression of Hox genes that define anterior-posterior identity follows general rules: temporal colinearity and posterior prevalence. A mathematical measure for the quality or fitness of the embryonic pattern produced by a gene regulatory network is derived. Using this measure and in silico evolution we derive gene interaction networks for anterior-posterior (AP) patterning under two developmental paradigms. For patterning during growth (paradigm I), which is appropriate for vertebrates and short germ-band insects, the algorithm creates gene expression patterns reminiscent of Hox gene expression. The networks operate through a timer gene, the level of which measures developmental progression (a candidate is the widely conserved posterior morphogen Caudal). The timer gene provides a simple mechanism to coordinate patterning with growth rate. The timer, when expressed as a static spatial gradient, functions as a classical morphogen (paradigm II), providing a natural way to derive the AP patterning, as seen in long germ-band insects that express their Hox genes simultaneously, from the ancestral short germ-band system. Although the biochemistry of Hox regulation in higher vertebrates is complex, the actual spatiotemporal expression phenotype is not, and simple activation and repression by Hill functions suffices in our model. In silico evolution provides a quantitative demonstration that continuous positive selection can generate complex phenotypes from simple components by incremental evolution, as Darwin proposed.

Origin of irreversibility of cell cycle start in budding yeast.

Budding yeast cells irreversibly commit to a new division cycle at a regulatory transition called Start. This essential decision-making step involves the activation of the SBF/MBF transcription factors. SBF/MBF promote expression of the G1 cyclins encoded by CLN1 and CLN2. Cln1,2 can activate their own expression by inactivating the Whi5 repressor of SBF/MBF. The resulting transcriptional positive feedback provides an appealing, but as yet unproven, candidate for generating irreversibility of Start. Here, we investigate the logic of the Start regulatory module by quantitative single-cell time-lapse microscopy, using strains in which expression of key regulators is efficiently controlled by changes of inducers in a microfluidic chamber. We show that Start activation is ultrasensitive to G1 cyclin. In the absence of CLN1,2-dependent positive feedback, we observe that Start transit is reversible, due to reactivation of the Whi5 transcriptional repressor. Introduction of the positive feedback loop makes Whi5 inactivation and Start activation irreversible, which therefore guarantees unidirectional entry into S phase. A simple mathematical model to describe G1 cyclin turn on at Start, entirely constrained by empirically measured parameters, shows that the experimentally measured ultrasensitivity and transcriptional positive feedback are necessary and sufficient dynamical characteristics to make the Start transition a bistable and irreversible switch. Our study thus demonstrates that Start irreversibility is a property that arises from the architecture of the system (Whi5/SBF/Cln2 loop), rather than the consequence of the regulation of a single component (e.g., irreversible protein degradation).