Precision of morphogen gradients in neural tube development

Additive manufacturing in spatial patterning for spinal cord injury treatment

Combinatorial treatments integrating cells and biomolecules within scaffolds have been investigated to address the multifactorial nature of spinal cord injury (SCI). Current regenerative treatments have been ineffective as they do not consider the spatial positions of various cell types to effectively form functional neural pathways. Emulating the complex heterogeneity of cells in the native spinal cord requires translating the existing biological understanding of spatial patterning in neural development, as well as the influence of biomolecule and mechanical patterning on regional specification and axonal regeneration, to engineer a scaffold for spinal cord regeneration. This review explores the potential of 3D bioprinting to precisely control material, cell and drug patterns in scaffolds, achieving spatial phenotype specification and providing axonal guidance to form appropriate connections. We also discuss the application of extrusion-based and digital light processing bioprinting in integrating mechanical, chemical and biological cues within a scaffold to advance spatially patterned 3D bioprinted scaffold, as well as current challenges and future perspectives in these bioengineering strategies.

Geometric influences on the regional organization of the mammalian brain

The mammalian brain is comprised of anatomically and functionally distinct regions. Substantial work over the past century has pursued the generation of ever-more accurate maps of regional boundaries, using either expert judgement or data-driven clustering of functional, connectional, and/or architectonic properties. However, these approaches are often purely descriptive, have limited generalizability, and do not elucidate the underlying generative mechanisms that shape the regional organization of the brain. Here, we develop a novel approach that leverages a simple, hierarchical principle for generating a multiscale parcellation of any brain structure in any mammalian species using only its geometry. We show that this approach yields regions at any resolution scale that are more homogeneous than those defined in nearly all existing benchmark brain parcellations in use today across hundreds of anatomical, functional, cellular, and molecular brain properties measured in humans, macaques, marmosets, and mice. We additionally show how our method can be generalized to previously unstudied mammalian species for which no parcellations exist. Finally, we demonstrate how our approach captures the essence of a simple, hierarchical reaction-diffusion mechanism, in which the geometry of a brain structure shapes the spatial expression of putative patterning molecules linked to the formation of distinct regions through development. Our findings point to a highly conserved and universal influence of geometry on the regional organization of the mammalian brain.

Responses of organ precursors to correct and incorrect inductive signals

During embryonic development, the inductive molecules produced by local origins normally arrive at their target tissues in a nondirectional, diffusion manner. The target organ precursor cells must correctly interpret these inductive signals to ensure proper specification/differentiation, which is dependent on two prerequisites: (i) obtaining cell-intrinsic competence; and (ii) receiving correct inductive signals while resisting incorrect ones. Gain of intrinsic competence could avoid a large number of misinductions because the incompetent cells are nonresponsive to inductive signals. However, in cases of different precursor cells with similar competence and located in close proximity, resistance to incorrect inductive signals is essential for accurate determination of cell fate. Here we outline the mechanisms of how organ precursors respond to correct and incorrect inductive signals.

Learning a conserved mechanism for early neuroectoderm morphogenesis

Morphogenesis is the process whereby the body of an organism develops its target shape. The morphogen BMP is known to play a conserved role across bilaterian organisms in determining the dorsoventral (DV) axis. Yet, how BMP governs the spatio-temporal dynamics of cytoskeletal proteins driving morphogenetic flow remains an open question. Here, we use machine learning to mine a morphodynamic atlas of Drosophila development, and construct a mathematical model capable of predicting the coupled dynamics of myosin, E-cadherin, and morphogenetic flow. Mutant analysis shows that BMP sets the initial condition of this dynamical system according to the following signaling cascade: BMP establishes DV pair-rule-gene patterns that set-up an E-cadherin gradient which in turn creates a myosin gradient in the opposite direction through mechanochemical feedbacks. Using neural tube organoids, we argue that BMP, and the signaling cascade it triggers, prime the conserved dynamics of neuroectoderm morphogenesis from fly to humans.

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.

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.

Early radial positional information in the cochlea is optimized by a precise linear BMP gradient and enhanced by SOX2

Positional information encoded in signaling molecules is essential for early patterning in the prosensory domain of the developing cochlea. The sensory epithelium, the organ of Corti, contains an exquisite repeating pattern of hair cells and supporting cells. This requires precision in the morphogen signals that set the initial radial compartment boundaries, but this has not been investigated. To measure gradient formation and morphogenetic precision in developing cochlea, we developed a quantitative image analysis procedure measuring SOX2 and pSMAD1/5/9 profiles in mouse embryos at embryonic day (E)12.5, E13.5, and E14.5. Intriguingly, we found that the pSMAD1/5/9 profile forms a linear gradient up to the medial ~ 75% of the PSD from the pSMAD1/5/9 peak in the lateral edge during E12.5 and E13.5. This is a surprising activity readout for a diffusive BMP4 ligand secreted from a tightly constrained lateral region since morphogens typically form exponential or power-law gradient shapes. This is meaningful for gradient interpretation because while linear profiles offer the theoretically highest information content and distributed precision for patterning, a linear morphogen gradient has not yet been observed. Furthermore, this is unique to the cochlear epithelium as the pSMAD1/5/9 gradient is exponential in the surrounding mesenchyme. In addition to the information-optimized linear profile, we found that while pSMAD1/5/9 is stable during this timeframe, an accompanying gradient of SOX2 shifts dynamically. Last, through joint decoding maps of pSMAD1/5/9 and SOX2, we see that there is a high-fidelity mapping between signaling activity and position in the regions that will become Kölliker's organ and the organ of Corti. Mapping is ambiguous in the prosensory domain precursory to the outer sulcus. Altogether, this research provides new insights into the precision of early morphogenetic patterning cues in the radial cochlea prosensory domain.

The impact of cell size on morphogen gradient precision

Tissue patterning during embryonic development is remarkably precise. Here, we numerically determine the impact of the cell diameter, gradient length and the morphogen source on the variability of morphogen gradients. We show that the positional error increases with the gradient length relative to the size of the morphogen source, and with the square root of the cell diameter and the readout position. We provide theoretical explanations for these relationships, and show that they enable high patterning precision over developmental time for readouts that scale with expanding tissue domains, as observed in the Drosophila wing disc. Our analysis suggests that epithelial tissues generally achieve higher patterning precision with small cross-sectional cell areas. An extensive survey of measured apical cell areas shows that they are indeed small in developing tissues that are patterned by morphogen gradients. Enhanced precision may thus have led to the emergence of pseudostratification in epithelia, a phenomenon for which the evolutionary benefit had so far remained elusive.

Patterning precision under non-linear morphogen decay and molecular noise

Morphogen gradients can instruct cells about their position in a patterned tissue. Non-linear morphogen decay has been suggested to increase gradient precision by reducing the sensitivity to variability in the morphogen source. Here, we use cell-based simulations to quantitatively compare the positional error of gradients for linear and non-linear morphogen decay. While we confirm that non-linear decay reduces the positional error close to the source, the reduction is very small for physiological noise levels. Far from the source, the positional error is much larger for non-linear decay in tissues that pose a flux barrier to the morphogen at the boundary. In light of this new data, a physiological role of morphogen decay dynamics in patterning precision appears unlikely.

Gradient to sectioning CUBE workflow for the generation and imaging of organoids with localized differentiation

Advancements in organoid culture have led to various in vitro mini-organs that mimic native tissues in many ways. Yet, the bottleneck remains to generate complex organoids with body axis patterning, as well as keeping the orientation of organoids during post-experiment analysis processes. Here, we present a workflow for culturing organoids with morphogen gradient using a CUBE culture device, followed by sectioning samples with the CUBE to retain information on gradient direction. We show that hiPSC spheroids cultured with two separated differentiation media on opposing ends of the CUBE resulted in localized expressions of the respective differentiation markers, in contrast to homogeneous distribution of markers in controls. We also describe the processes for cryo and paraffin sectioning of spheroids in CUBE to retain gradient orientation information. This workflow from gradient culture to sectioning with CUBE can provide researchers with a convenient tool to generate increasingly complex organoids and study their developmental processes in vitro.

Mechanisms of robustness in gene regulatory networks involved in neural development

The functions of living organisms are affected by different kinds of perturbation, both internal and external, which in many cases have functional effects and phenotypic impact. The effects of these perturbations become particularly relevant for multicellular organisms with complex body patterns and cell type heterogeneity, where transcriptional programs controlled by gene regulatory networks determine, for example, the cell fate during embryonic development. Therefore, an essential aspect of development in these organisms is the ability to maintain the functionality of their genetic developmental programs even in the presence of genetic variation, changing environmental conditions and biochemical noise, a property commonly termed robustness. We discuss the implication of different molecular mechanisms of robustness involved in neurodevelopment, which is characterized by the interplay of many developmental programs at a molecular, cellular and systemic level. We specifically focus on processes affecting the function of gene regulatory networks, encompassing transcriptional regulatory elements and post-transcriptional processes such as miRNA-based regulation, but also higher order regulatory organization, such as gene network topology. We also present cases where impairment of robustness mechanisms can be associated with neurodevelopmental disorders, as well as reasons why understanding these mechanisms should represent an important part of the study of gene regulatory networks driving neural development.

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.

Morphogen-directed cell fate boundaries: slow passage through bifurcation and the role of folded saddles

One of the fundamental mechanisms in embryogenesis is the process by which cells differentiate and create tissues and structures important for functioning as a multicellular organism. Morphogenesis involves diffusive process of chemical signalling involving morphogens that pre-pattern the tissue. These morphogens influence cell fate through a highly nonlinear process of transcriptional signalling. In this paper, we consider this multiscale process in an idealised model for a growing domain. We focus on intracellular processes that lead to robust differentiation into two cell lineages through interaction of a single morphogen species with a cell fate variable that undergoes a bifurcation from monostability to bistability. In particular, we investigate conditions that result in successful and robust pattern formation into two well-separated domains, as well as conditions where this fails and produces a pinned boundary wave where only one part of the domain grows. We show that successful and unsuccessful patterning scenarios can be characterised in terms of presence or absence of a folded saddle singularity for a system with two slow variables and one fast variable; this models the interaction of slow morphogen diffusion, slow parameter drift through bifurcation and fast transcription dynamics. We illustrate how this approach can successfully model acquisition of three cell fates to produce three-domain "French flag" patterning, as well as for a more realistic model of the cell fate dynamics in terms of two mutually inhibiting transcription factors.

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.

Collective gradient sensing with limited positional information

Eukaryotic cells sense chemical gradients to decide where and when to move. Clusters of cells can sense gradients more accurately than individual cells by integrating measurements of the concentration made across the cluster. Is this gradient-sensing accuracy impeded when cells have limited knowledge of their position within the cluster, i.e., limited positional information? We apply maximum likelihood estimation to study gradient-sensing accuracy of a cluster of cells with finite positional information. If cells must estimate their location within the cluster, this lowers the accuracy of collective gradient sensing. We compare our results with a tug-of-war model where cells respond to the gradient by polarizing away from their neighbors without relying on their positional information. As the cell positional uncertainty increases, there is a trade-off where the tug-of-war model responds more accurately to the chemical gradient. However, for sufficiently large cell clusters or sufficiently shallow chemical gradients, the tug-of-war model will always be suboptimal to one that integrates information from all cells, even if positional uncertainty is high.