Precision of tissue patterning is controlled by dynamical properties of gene regulatory networks

Target gene responses differ when transcription factor levels are acutely decreased by nuclear export versus degradation

Defining the time of action for morphogens requires tools capable of temporally controlled perturbations. To study how the transcription factor Dorsal affects patterning of the Drosophila embryonic dorsal-ventral axis, we used two light-inducible tags that result in either nuclear export or degradation of Dorsal when exposed to blue light. Nuclear export of Dorsal results in loss of expression for the high threshold, ventrally-expressed target gene snail (sna) but retention of the low threshold, laterally-expressed target gene short-gastrulation (sog). In contrast, degradation of Dorsal results in retention of sna, loss of sog, and lower nuclear levels than when Dorsal is exported from the nucleus. To elucidate how nuclear export results in loss of sna but degradation does not, we investigated Dorsal kinetics using photobleaching and found it reenters the nucleus even under conditions of blue-light when export is favored. The associated kinetics of being imported and exported continuously are likely responsible for loss of sna but, alternatively, can support sog. Collectively, our results show that this dynamic patterning process is influenced by both Dorsal concentration and nuclear retention.

How do stochastic processes and genetic threshold effects explain incomplete penetrance and inform causal disease mechanisms?

Incomplete penetrance is the rule rather than the exception in Mendelian disease. In syndromic monogenic disorders, phenotypic variability can be viewed as the combination of incomplete penetrance for each of multiple independent clinical features. Within genetically identical individuals, such as isogenic model organisms, stochastic variation at molecular and cellular levels is the primary cause of incomplete penetrance according to a genetic threshold model. By defining specific probability distributions of causal biological readouts and genetic liability values, stochasticity and incomplete penetrance provide information about threshold values in biological systems. Ascertainment of threshold values has been achieved by simultaneous scoring of relatively simple phenotypes and quantitation of molecular readouts at the level of single cells. However, this is much more challenging for complex morphological phenotypes using experimental and reductionist approaches alone, where cause and effect are separated temporally and across multiple biological modes and scales. Here I consider how causal inference, which integrates observational data with high confidence causal models, might be used to quantify the relative contribution of different sources of stochastic variation to phenotypic diversity. Collectively, these approaches could inform disease mechanisms, improve predictions of clinical outcomes and prioritize gene therapy targets across modes and scales of gene function. This article is part of a discussion meeting issue 'Causes and consequences of stochastic processes in development and disease'.

From signalling to form: the coordination of neural tube patterning

The development of the vertebrate spinal cord involves the formation of the neural tube and the generation of multiple distinct cell types. The process starts during gastrulation, combining axial elongation with specification of neural cells and the formation of the neuroepithelium. Tissue movements produce the neural tube which is then exposed to signals that provide patterning information to neural progenitors. The intracellular response to these signals, via a gene regulatory network, governs the spatial and temporal differentiation of progenitors into specific cell types, facilitating the assembly of functional neuronal circuits. The interplay between the gene regulatory network, cell movement, and tissue mechanics generates the conserved neural tube pattern observed across species. In this review we offer an overview of the molecular and cellular processes governing the formation and patterning of the neural tube, highlighting how the remarkable complexity and precision of vertebrate nervous system arises. We argue that a multidisciplinary and multiscale understanding of the neural tube development, paired with the study of species-specific strategies, will be crucial to tackle the open questions.

Enhanced production of mesencephalic dopaminergic neurons from lineage-restricted human undifferentiated stem cells

Current differentiation protocols for generating mesencephalic dopaminergic (mesDA) neurons from human pluripotent stem cells result in grafts containing only a small proportion of mesDA neurons when transplanted in vivo. In this study, we develop lineage-restricted undifferentiated stem cells (LR-USCs) from pluripotent stem cells, which enhances their potential for differentiating into caudal midbrain floor plate progenitors and mesDA neurons. Using a ventral midbrain protocol, 69% of LR-USCs become bona fide caudal midbrain floor plate progenitors, compared to only 25% of human embryonic stem cells (hESCs). Importantly, LR-USCs generate significantly more mesDA neurons under midbrain and hindbrain conditions in vitro and in vivo. We demonstrate that midbrain-patterned LR-USC progenitors transplanted into 6-hydroxydopamine-lesioned rats restore function in a clinically relevant non-pharmacological behavioral test, whereas midbrain-patterned hESC-derived progenitors do not. This strategy demonstrates how lineage restriction can prevent the development of undesirable lineages and enhance the conditions necessary for mesDA neuron generation.

Optimal control of gene regulatory networks for morphogen-driven tissue patterning

The generation of distinct cell types in developing tissues depends on establishing spatial patterns of gene expression. Often, this is directed by spatially graded chemical signals-known as morphogens. In the "French Flag model," morphogen concentration instructs cells to acquire specific fates. How this mechanism produces timely and organized cell-fate decisions, despite the presence of changing morphogen levels, molecular noise, and individual variability, is unclear. Moreover, feedback is present at various levels in developing tissues, breaking the link between morphogen concentration, signaling activity, and position. Here, we develop an alternative framework using optimal control theory to tackle the problem of morphogen-driven patterning: intracellular signaling is derived as the control strategy that guides cells to the correct fate while minimizing a combination of signaling levels and time. This approach recovers experimentally observed properties of patterning strategies and offers insight into design principles that produce timely, precise, and reproducible morphogen patterning.

2D effects enhance precision of gradient-based tissue patterning

Robust embryonic development requires pattern formation with high spatial accuracy. In epithelial tissues that are patterned by morphogen gradients, the emerging patterns achieve levels of precision that have recently been explained by a simple one-dimensional reaction-diffusion model with kinetic noise. Here, we show that patterning precision is even greater if transverse diffusion effects are at play in such tissues. The positional error, a measure for spatial patterning accuracy, decreases in wider tissues but then saturates beyond a width of about ten cells. This demonstrates that the precision of gradient-based patterning in two- or higher-dimensional systems can be even greater than predicted by 1D models, and further attests to the potential of noisy morphogen gradients for high-precision tissue patterning.

The σB alternative sigma factor circuit modulates noise to generate different types of pulsing dynamics

Single-cell approaches are revealing a high degree of heterogeneity, or noise, in gene expression in isogenic bacteria. How gene circuits modulate this noise in gene expression to generate robust output dynamics is unclear. Here we use the Bacillus subtilis alternative sigma factor σB as a model system for understanding the role of noise in generating circuit output dynamics. σB controls the general stress response in B. subtilis and is activated by a range of energy and environmental stresses. Recent single-cell studies have revealed that the circuit can generate two distinct outputs, stochastic pulsing and a single pulse response, but the conditions under which each response is generated are under debate. We implement a stochastic mathematical model of the σB circuit to investigate this and find that the system's core circuit can generate both response types. This is despite one response (stochastic pulsing) being stochastic in nature, and the other (single response pulse) being deterministic. We demonstrate that the main determinant for whichever response is generated is the degree with which the input pathway activates the core circuit, although the noise properties of the input pathway also biases the system towards one or the other type of output. Thus, our work shows how stochastic modelling can reveal the mechanisms behind non-intuitive gene circuit output dynamics.

Selection and Validation of Optimal RT-qPCR Reference Genes for the Normalization of Gene Expression under Different Experimental Conditions in Lindera megaphylla

Lindera megaphylla, a broad-leaved evergreen that is used as a landscape ornamental plant and medicinal plant, is an ecologically important and dominant tree species. However, little is known about the molecular mechanisms of its growth, development, and metabolism. The selection of suitable reference genes is critical for molecular biological analyses. To date, no research on reference genes as a foundation for gene expression analysis has been undertaken in L. megaphylla. In this study, 14 candidate genes were selected from the transcriptome database of L. megaphylla for RT-qPCR assay under different conditions. Results showed that helicase-15 and UBC28 were most stable in different tissues of seedlings and adult trees. For different leaf developmental stages, the best combination of reference genes was ACT7 and UBC36. UBC36 and TCTP were the best under cold treatment, while PAB2 and CYP20-2 were the best under heat treatment. Finally, a RT-qPCR assay of LmNAC83 and LmERF60 genes were used to further verify the reliability of selected reference genes above. This work is the first to select and evaluate the stability of reference genes for the normalization of gene expression analysis in L. megaphylla and will provide an important foundation for future genetic studies of this species.

Inertial effect of cell state velocity on the quiescence-proliferation fate decision in breast cancer

Energy landscapes can provide intuitive depictions of population heterogeneity and dynamics. However, it is unclear whether individual cell behavior, hypothesized to be determined by initial position and noise, is faithfully recapitulated. Using the p21-/Cdk2-dependent quiescence-proliferation decision in breast cancer dormancy as a testbed, we examined single-cell dynamics on the landscape when perturbed by hypoxia, a dormancy-inducing stress. Combining trajectory-based energy landscape generation with single-cell time-lapse microscopy, we found that initial position on a p21/Cdk2 landscape did not fully explain the observed cell-fate heterogeneity under hypoxia. Instead, cells with higher cell state velocities prior to hypoxia, influenced by epigenetic parameters, tended to remain proliferative under hypoxia. Thus, the fate decision on this landscape is significantly influenced by "inertia", a velocity-dependent ability to resist directional changes despite reshaping of the underlying landscape, superseding positional effects. Such inertial effects may markedly influence cell-fate trajectories in tumors and other dynamically changing microenvironments.

Stability of Pattern Formation in Systems with Dynamic Source Regions

We explain the principles of gene expression pattern stabilization in systems of interacting, diffusible morphogens, with dynamically established source regions. Using a reaction-diffusion model with a step-function production term, we identify the phase transition between low-precision indeterminate patterning and the phase in which a traveling, well-defined contact zone between two domains is formed. Our model analytically explains single- and two-gene domain dynamics and provides pattern stability conditions for all possible two-gene regulatory network motifs.

Specialized cells that sense tissue mechanics to regulate Drosophila morphogenesis

Shaping of developing organs requires dynamic regulation of force and resistance to achieve precise outcomes, but how organs monitor tissue mechanical properties is poorly understood. We show that in developing Drosophila follicles (egg chambers), a single pair of cells performs such monitoring to drive organ shaping. These anterior polar cells secrete a matrix metalloproteinase (MMP) that specifies the appropriate degree of tissue elongation, rather than hyper- or hypo-elongated organs. MMP production is negatively regulated by basement membrane (BM) mechanical properties, which are sensed through focal adhesion signaling and autonomous contractile activity; MMP then reciprocally regulates BM remodeling, particularly at the anterior region. Changing BM properties at remote locations alone is sufficient to induce a remodeling response in polar cells. We propose that this small group of cells senses both local and distant stiffness cues to produce factors that pattern the organ's BM mechanics, ensuring proper tissue shape and reproductive success.

Precision of morphogen-driven tissue patterning during development is enhanced through contact-mediated cellular interactions

Cells in developing embryos reliably differentiate to attain location-specific fates, despite fluctuations in morphogen concentrations that provide positional information and in molecular processes that interpret it. We show that local contact-mediated cell-cell interactions utilize inherent asymmetry in the response of patterning genes to the global morphogen signal yielding a bimodal response. This results in robust developmental outcomes with a consistent identity for the dominant gene at each cell, substantially reducing the uncertainty in the location of boundaries between distinct fates.

Establishing Hedgehog Gradients during Neural Development

A morphogen is a signaling molecule that induces specific cellular responses depending on its local concentration. The concept of morphogenic gradients has been a central paradigm of developmental biology for decades. Sonic Hedgehog (Shh) is one of the most important morphogens that displays pleiotropic functions during embryonic development, ranging from neuronal patterning to axon guidance. It is commonly accepted that Shh is distributed in a gradient in several tissues from different origins during development; however, how these gradients are formed and maintained at the cellular and molecular levels is still the center of a great deal of research. In this review, we first explored all of the different sources of Shh during the development of the nervous system. Then, we detailed how these sources can distribute Shh in the surrounding tissues via a variety of mechanisms. Finally, we addressed how disrupting Shh distribution and gradients can induce severe neurodevelopmental disorders and cancers. Although the concept of gradient has been central in the field of neurodevelopment since the fifties, we also describe how contemporary leading-edge techniques, such as organoids, can revisit this classical model.

Characterization of larval shell formation and CgPOU2F1, CgSox5, and CgPax6 gene expression during shell morphogenesis in Crassostrea gigas

Shell formation is a dynamic process involving organic matrix secretion and calcification. In this study, we characterized shell morphogenesis during larval development in Crassostrea gigas. Using scanning electron microscopy (SEM) and fluorescence staining, we demonstrated that shell field, the first morphologically distinguishable shell-forming tissue, became visible soon after enlargement of the blastopore at the anterior end of the trochophore. Shell organic matrix namely protein polysaccharides and calcified structure appeared as a slit at the dorsal side of the embryo. The early shell field began to extend along the dorsal side of the trochophore larvae, and became a saddle shaped shell field that gave rise to the prodissoconch I embryonic shell in the early D-shaped larvae. Subsequently, prodissoconch II shell was formed in the late D-shaped larvae with a characteristic appearance of growth lines. To identify gene expression markers for studying shell formation, we isolated three potential larval shell formation genes CgPOU2F1, CgSox5, and CgPax6 and analyzed their expression during shell morphogenesis. The three potential shell formation genes possessed a similar pattern of expression. Their expression was detected in the shell gland and shell field regions in early D-shaped larvae, hereafter, their expression was detected at the larval mantle edge in the calcified shell stages. Together, these studies provide knowledge of shell morphogenesis in pacific oyster and molecular markers for studying the molecular regulation of biomineralization and shell formation.

Nodal signaling establishes a competency window for stochastic cell fate switching

Specification of the germ layers by Nodal signaling has long been regarded as an archetype of how graded morphogens induce different cell fates. However, this deterministic model cannot explain why only a subset of cells at the early zebrafish embryo margin adopt the endodermal fate, whereas their immediate neighbours, experiencing a similar signaling environment, become mesoderm. Combining pharmacology, quantitative imaging and single cell transcriptomics, we demonstrate that sustained Nodal signaling establishes a bipotential progenitor state from which cells can switch to an endodermal fate or differentiate into mesoderm. Switching is a random event, the likelihood of which is modulated by Fgf signaling. This inherently imprecise mechanism nevertheless leads to robust endoderm formation because of buffering at later stages. Thus, in contrast to previous deterministic models of morphogen action, Nodal signaling establishes a temporal window when cells are competent to undergo a stochastic cell fate switch, rather than determining fate itself.

Robust boundary formation in a morphogen gradient via cell-cell signaling

Establishing sharp and correctly positioned boundaries in spatial gene expression patterns is a central task in both developmental and synthetic biology. We consider situations where a global morphogen gradient provides positional information to cells but is insufficient to ensure the required boundary precision, due to different types of noise in the system. In a conceptual model, we quantitatively compare three mechanisms, which combine the global signal with local signaling between neighboring cells, to enhance the boundary formation process. These mechanisms differ with respect to the way in which they combine the signals by following either an AND, an OR, or a SUM rule. Within our model, we analyze the dynamics of the boundary formation process, and the fuzziness of the resulting boundary. Furthermore, we consider the tunability of the boundary position and its scaling with system size. We find that all three mechanisms produce less fuzzy boundaries than the purely gradient-based reference mechanism, even in the regime of high noise in the local signals relative to the noise in the global signal. Among the three mechanisms, the SUM rule produces the most accurate boundary. However, in contrast to the other two mechanisms, it requires noise to exit metastable states and rapidly reach the stable boundary pattern.

Relationship between epithelial organization and morphogen interpretation

Despite molecular noise and genetic differences between individuals, developmental outcomes are remarkably constant. Decades of research has focused on the underlying mechanisms that ensure this precision and robustness. Recent quantifications of chemical gradients and epithelial cell shapes provide novel insights into the basis of precise development. In this review, we argue that these two aspects may be linked in epithelial morphogenesis.

Precision of morphogen gradients in neural tube development

Morphogen gradients encode positional information during development. How high patterning precision is achieved despite natural variation in both the morphogen gradients and in the readout process, is still largely elusive. Here, we show that the positional error of gradients in the mouse neural tube has previously been overestimated, and that the reported accuracy of the central progenitor domain boundaries in the mouse neural tube can be achieved with a single gradient, rather than requiring the simultaneous readout of opposing gradients. Consistently and independently, numerical simulations based on measured molecular noise levels likewise result in lower gradient variabilities than reported. Finally, we show that the patterning mechanism yields progenitor cell numbers with even greater precision than boundary positions, as gradient amplitude changes do not affect interior progenitor domain sizes. We conclude that single gradients can yield the observed developmental precision, which provides prospects for tissue engineering.

A theoretical understanding of mammalian preimplantation development

The blastocyst has long been a hallmark system of study in developmental biology due to its importance in mammalian development and clinical relevance for assisted reproductive technologies. In recent years, the blastocyst is emerging as a system of study for mathematical modelling. In this review, we compile, to our knowledge, all models describing preimplantation development. Coupled with experiments, these models have provided insight regarding the morphogenesis and cell-fate specification throughout preimplantation development. In the case of cell-fate specification, theoretical models have provided mechanisms explaining how proportion of cell types are established and maintained when confronted to perturbations. For cell-shape based models, they have described quantitatively how mechanical forces sculpt the blastocyst and even predicted how morphogenesis could be manipulated. As theoretical biology develops, we believe the next critical stage in modelling involves an integration of cell fate and mechanics to provide integrative models of development at distinct spatiotemporal scales. We discuss how, building on a balanced base of mechanical and chemical models, the preimplantation embryo will play a key role in integrating these two faces of the same coin.

The developmental hourglass model is applicable to the spinal cord based on single-cell transcriptomes and non-conserved cis-regulatory elements

The developmental hourglass model predicts that embryonic morphology is most conserved at the mid‐embryonic stage and diverges at the early and late stages. To date, this model has been verified by examining the anatomical features or gene expression profiles at the whole embryonic level. Here, by data mining approach utilizing multiple genomic and transcriptomic datasets from different species in combination, and by experimental validation, we demonstrate that the hourglass model is also applicable to a reduced element, the spinal cord. In the middle of spinal cord development, dorsoventrally arrayed neuronal progenitor domains are established, which are conserved among vertebrates. By comparing the publicly available single‐cell transcriptome datasets of mice and zebrafish, we found that ventral subpopulations of post‐mitotic spinal neurons display divergent molecular profiles. We also detected the non‐conservation of cis‐regulatory elements located around the progenitor fate determinants, indicating that the cis‐regulatory elements contributing to the progenitor specification are evolvable. These results demonstrate that, despite the conservation of the progenitor domains, the processes before and after the progenitor domain specification diverged. This study will be helpful to understand the molecular basis of the developmental hourglass model.

Multiple morphogens and rapid elongation promote segmental patterning during development

The vertebrate hindbrain is segmented into rhombomeres (r) initially defined by distinct domains of gene expression. Previous studies have shown that noise-induced gene regulation and cell sorting are critical for the sharpening of rhombomere boundaries, which start out rough in the forming neural plate (NP) and sharpen over time. However, the mechanisms controlling simultaneous formation of multiple rhombomeres and accuracy in their sizes are unclear. We have developed a stochastic multiscale cell-based model that explicitly incorporates dynamic morphogenetic changes (i.e. convergent-extension of the NP), multiple morphogens, and gene regulatory networks to investigate the formation of rhombomeres and their corresponding boundaries in the zebrafish hindbrain. During pattern initiation, the short-range signal, fibroblast growth factor (FGF), works together with the longer-range morphogen, retinoic acid (RA), to specify all of these boundaries and maintain accurately sized segments with sharp boundaries. At later stages of patterning, we show a nonlinear change in the shape of rhombomeres with rapid left-right narrowing of the NP followed by slower dynamics. Rapid initial convergence improves boundary sharpness and segment size by regulating cell sorting and cell fate both independently and coordinately. Overall, multiple morphogens and tissue dynamics synergize to regulate the sizes and boundaries of multiple segments during development.

In segmental pattern formation, chemical gradients control gene expression in a concentration-dependent manner to specify distinct gene expression domains. Despite the stochasticity inherent to such biological processes, precise and accurate borders form between segmental gene expression domains. Previous work has revealed synergy between gene regulation and cell sorting in sharpening borders that are initially rough. However, it is still poorly understood how size and boundary sharpness of multiple segments are regulated in a tissue that changes dramatically in its morphology as the embryo develops. Here we develop a stochastic multiscale cell-base model to investigate these questions. Two novel strategies synergize to promote accurate segment formation, a combination of long- and short-range morphogens plus rapid tissue convergence, with one responsible for pattern initiation and the other enabling pattern refinement.

Contact-mediated cellular communication supplements positional information to regulate spatial patterning during development

Development in multicellular organisms is marked by a high degree of spatial organization of the cells attaining distinct fates in the embryo. Recent experiments showing that suppression of intercellular interactions can alter the spatial patterns arising during development suggest that cell fates cannot be determined by the exclusive regulation of differential gene expression by morphogen gradients (the conventional view encapsulated in the French flag model). Using a mathematical model that describes the receptor-ligand interaction between cells in close physical proximity, we show that such intercellular signaling can regulate the process of selective gene expression within each cell, allowing information from the cellular neighborhood to influence the process by which the thresholds of morphogen concentration that dictate cell fates adaptively emerge. This results in local modulations of the positional cues provided by the global field set up by the morphogen, allowing interaction-mediated self-organized pattern formation to complement boundary-organized mechanisms in the context of development.

Dynamical modules in metabolism, cell and developmental biology

Modularity is an essential feature of any adaptive complex system. Phenotypic traits are modules in the sense that they have a distinguishable structure or function, which can vary (quasi-)independently from its context. Since all phenotypic traits are the product of some underlying regulatory dynamics, the generative processes that constitute the genotype-phenotype map must also be functionally modular. Traditionally, modular processes have been identified as structural modules in regulatory networks. However, structure only constrains, but does not determine, the dynamics of a process. Here, we propose an alternative approach that decomposes the behaviour of a complex regulatory system into elementary activity-functions. Modular activities can occur in networks that show no structural modularity, making dynamical modularity more widely applicable than structural decomposition. Furthermore, the behaviour of a regulatory system closely mirrors its functional contribution to the outcome of a process, which makes dynamical modularity particularly suited for functional decomposition. We illustrate our approach with numerous examples from the study of metabolism, cellular processes, as well as development and pattern formation. We argue that dynamical modules provide a shared conceptual foundation for developmental and evolutionary biology, and serve as the foundation for a new account of process homology, which is presented in a separate contribution by DiFrisco and Jaeger to this focus issue.

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.