Hierarchical patterning modes orchestrate hair follicle morphogenesis

Unraveling biochemical spatial patterns: Machine learning approaches to the inverse problem of stationary Turing patterns

The diffusion-driven Turing instability is a potential mechanism for spatial pattern formation in numerous biological and chemical systems. However, engineering these patterns and demonstrating that they are produced by this mechanism is challenging. To address this, we aim to solve the inverse problem in artificial and experimental Turing patterns. This task is challenging since patterns are often corrupted by noise and slight changes in initial conditions can lead to different patterns. We used both least squares to explore the problem and physics-informed neural networks to build a noise-robust method. We elucidate the functionality of our network in scenarios mimicking biological noise levels and showcase its application using an experimentally obtained chemical pattern. The findings reveal the significant promise of machine learning in steering the creation of synthetic patterns in bioengineering, thereby advancing our grasp of morphological intricacies within biological systems while acknowledging existing limitations.

Patterning and folding of intestinal villi by active mesenchymal dewetting

Tissue folds are structural motifs critical to organ function. In the intestine, bending of a flat epithelium into a periodic pattern of folds gives rise to villi, finger-like protrusions that enable nutrient absorption. However, the molecular and mechanical processes driving villus morphogenesis remain unclear. Here, we identify an active mechanical mechanism that simultaneously patterns and folds the intestinal epithelium to initiate villus formation. At the cellular level, we find that PDGFRA+ subepithelial mesenchymal cells generate myosin II-dependent forces sufficient to produce patterned curvature in neighboring tissue interfaces. This symmetry-breaking process requires altered cell and extracellular matrix interactions that are enabled by matrix metalloproteinase-mediated tissue fluidization. Computational models, together with in vitro and in vivo experiments, revealed that these cellular features manifest at the tissue level as differences in interfacial tensions that promote mesenchymal aggregation and interface bending through a process analogous to the active dewetting of a thin liquid film.

The development of hair follicles and nail

The hair follicle and nail unit develop and regenerate through epithelial-mesenchymal interactions. Here, we review some of the key signals and molecular interactions that regulate mammalian hair follicle and nail formation during embryonic development and how these interactions are reutilized to promote their regeneration during adult homeostasis and in response to skin wounding. Finally, we highlight the role of some of these signals in mediating human hair follicle and nail conditions.

Twist2 contributes to skin regeneration and hair follicle formation in mouse fetuses

Unlike adult mammalian wounds, early embryonic mouse skin wounds completely regenerate and heal without scars. Analysis of the underlying molecular mechanism will provide insights into scarless wound healing. Twist2 is an important regulator of hair follicle formation and biological patterning; however, it is unclear whether it plays a role in skin or skin appendage regeneration. Here, we aimed to elucidate Twist2 expression and its role in fetal wound healing. ICR mouse fetuses were surgically wounded on embryonic day 13 (E13), E15, and E17, and Twist2 expression in tissue samples from these fetuses was evaluated via in situ hybridization, immunohistochemistry, and reverse transcription-quantitative polymerase chain reaction. Twist2 expression was upregulated in the dermis of E13 wound margins but downregulated in E15 and E17 wounds. Twist2 knockdown on E13 left visible marks at the wound site, inhibited regeneration, and resulted in defective follicle formation. Twist2-knockdown dermal fibroblasts lacked the ability to undifferentiate. Furthermore, Twist2 hetero knockout mice (Twist + /-) formed visible scars, even on E13, when all skin structures should regenerate. Thus, Twist2 expression correlated with skin texture formation and hair follicle defects in late mouse embryos. These findings may help develop a therapeutic strategy to reduce scarring and promote hair follicle regeneration.

Modelling Human Hair Follicles-Lessons from Animal Models and Beyond

The hair follicle is a specialized appendage of the skin that is critical for multiple functions, including thermoregulation, immune surveillance, and sebum production. Mammals are born with a fixed number of hair follicles that develop embryonically. Postnatally, these hair follicles undergo regenerative cycles of regression and growth that recapitulate many of the embryonic signaling pathways. Furthermore, hair cycles have a direct impact on skin regeneration in homeostasis, cutaneous wound healing, and disease conditions such as alopecia. Here, we review the current knowledge of hair follicle formation during embryonic development and the post-natal hair cycle, with an emphasis on the molecular signaling pathways underlying these processes. We then discuss efforts to capitalize on the field's understanding of in vivo mechanisms to bioengineer hair follicles or hair-bearing skin in vitro and how such models may be further improved to develop strategies for hair regeneration.

Mechanical state transitions in the regulation of tissue form and function

From embryonic development, postnatal growth and adult homeostasis to reparative and disease states, cells and tissues undergo constant changes in genome activity, cell fate, proliferation, movement, metabolism and growth. Importantly, these biological state transitions are coupled to changes in the mechanical and material properties of cells and tissues, termed mechanical state transitions. These mechanical states share features with physical states of matter, liquids and solids. Tissues can switch between mechanical states by changing behavioural dynamics or connectivity between cells. Conversely, these changes in tissue mechanical properties are known to control cell and tissue function, most importantly the ability of cells to move or tissues to deform. Thus, tissue mechanical state transitions are implicated in transmitting information across biological length and time scales, especially during processes of early development, wound healing and diseases such as cancer. This Review will focus on the biological basis of tissue-scale mechanical state transitions, how they emerge from molecular and cellular interactions, and their roles in organismal development, homeostasis, regeneration and disease.

The avian ectodermal default competence to make feathers

Feathers originate as protofeathers before birds, in pterosaurs and basal dinosaurs. What characterizes a feather is not only its outgrowth, but its barb cells differentiation and a set of beta-corneous proteins. Reticula appear concomitantly with feathers, as small bumps on plantar skin, made only of keratins. Avian scales, with their own set of beta-corneous proteins, appear more recently than feathers on the shank, and only in some species. In the chick embryo, when feather placodes form, all the non-feather areas of the integument are already specified. Among them, midventral apterium, cornea, reticula, and scale morphogenesis appear to be driven by negative regulatory mechanisms, which modulate the inherited capacity of the avian ectoderm to form feathers. Successive dermal/epidermal interactions, initiated by the Wnt/β-catenin pathway, and involving principally Eda/Edar, BMP, FGF20 and Shh signaling, are responsible for the formation not only of feather, but also of scale placodes and reticula, with notable differences in the level of Shh, and probably FGF20 expressions. This sequence is a dynamic and labile process, the turning point being the FGF20 expression by the placode. This epidermal signal endows its associated dermis with the memory to aggregate and to stimulate the morphogenesis that follows, involving even a re-initiation of the placode.

Nuclear mechanotransduction on skin stem cell fate regulation

Mammalian skin is a highly dynamic and regenerative organ that has long been recognized as a mechanically active composite of tissues withstanding daily compressive and tensile forces that arise from body movement. Importantly, cell- and tissue-scale mechanical signals are critical regulators of skin morphogenesis and homeostasis. These signals are sensed at the cellular periphery and transduced by mechanosensitive proteins within the plasma membrane to the cytoskeletal networks, and eventually into the nucleus to regulate chromatin organization and gene expression. The role of each of these nodes in producing a coherent mechanoresponse at both cell- and tissue-scales is emerging. Here we focus on the key cytoplasmic and nuclear mechanosensitive structures that are critical for the mammalian skin development and homeostatic maintenance. We propose that the mechanical state of the skin, in particular of its nuclear compartment, is a critical rheostat that fine-tunes developmental and homeostatic processes essential for the proper function of the organ.

Periodic pattern formation during embryonic development

During embryonic development many organs and structures require the formation of series of repeating elements known as periodic patterns. Ranging from the digits of the limb to the feathers of the avian skin, the correct formation of these embryonic patterns is essential for the future form and function of these tissues. However, the mechanisms that produce these patterns are not fully understood due to the existence of several modes of pattern generation which often differ between organs and species. Here, we review the current state of the field and provide a perspective on future approaches to studying this fundamental process of embryonic development.

MDIC3: Matrix decomposition to infer cell-cell communication

Crosstalk among cells is vital for maintaining the biological function and intactness of systems. Most existing methods for investigating cell-cell communications are based on ligand-receptor (L-R) expression, and they focus on the study between two cells. Thus, the final communication inference results are particularly sensitive to the completeness and accuracy of the prior biological knowledge. Because existing L-R research focuses mainly on humans, most existing methods can only examine cell-cell communication for humans. As far as we know, there is currently no effective method to overcome this species limitation. Here, we propose MDIC3 (matrix decomposition to infer cell-cell communication), an unsupervised tool to investigate cell-cell communication in any species, and the results are not limited by specific L-R pairs or signaling pathways. By comparing it with existing methods for the inference of cell-cell communication, MDIC3 obtained better performance in both humans and mice.

Mechanical forces across compartments coordinate cell shape and fate transitions to generate tissue architecture

Morphogenesis and cell state transitions must be coordinated in time and space to produce a functional tissue. An excellent paradigm to understand the coupling of these processes is mammalian hair follicle development, which is initiated by the formation of an epithelial invagination-termed placode-that coincides with the emergence of a designated hair follicle stem cell population. The mechanisms directing the deformation of the epithelium, cell state transitions and physical compartmentalization of the placode are unknown. Here we identify a key role for coordinated mechanical forces stemming from contractile, proliferative and proteolytic activities across the epithelial and mesenchymal compartments in generating the placode structure. A ring of fibroblast cells gradually wraps around the placode cells to generate centripetal contractile forces, which, in collaboration with polarized epithelial myosin activity, promote elongation and local tissue thickening. These mechanical stresses further enhance compartmentalization of Sox9 expression to promote stem cell positioning. Subsequently, proteolytic remodelling locally softens the basement membrane to facilitate a release of pressure on the placode, enabling localized cell divisions, tissue fluidification and epithelial invagination into the underlying mesenchyme. Together, our experiments and modelling identify dynamic cell shape transformations and tissue-scale mechanical cooperation as key factors for orchestrating organ formation.

Generation and characterization of a Dkk4-Cre knock-in mouse line

Ectodermal appendages in mammals, such as teeth, mammary glands, sweat glands and hair follicles, are generated during embryogenesis through a series of mesenchymal-epithelial interactions. Canonical Wnt signaling and its inhibitors are implicated in the early steps of ectodermal appendage development and patterning. To study the activation dynamics of the Wnt target and inhibitor Dickkopf4 (Dkk4) in ectodermal appendages, we used CRSIPR/Cas9 to generate a Dkk4-Cre knock-in mouse (Mus musculus) line, where the Cre recombinase cDNA replaces the expression of endogenous Dkk4. Using Cre reporters, the Dkk4-Cre activity was evident at the prospective sites of ectodermal appendages, overlapping with the Dkk4 mRNA expression. Unexpectedly, a predominantly mesenchymal cell population in the embryo posterior also showed Dkk4-Cre activity. Lineage-tracing suggested that these cells are likely derived from a few Dkk4-Cre-expressing cells in the epiblast at early gastrulation. Finally, our analyses of Dkk4-Cre-expressing cells in developing hair follicle epithelial placodes revealed intra- and inter-placodal cellular heterogeneity, supporting emerging data on the positional and transcriptional cellular variability in placodes. Collectively, we propose the new Dkk4-Cre knock-in mouse line as a suitable model to study Wnt and DKK4 inhibitor dynamics in early mouse development and ectodermal appendage morphogenesis.

Turing Pattern Formation in Reaction-Cross-Diffusion Systems with a Bilayer Geometry

Conditions for self-organisation via Turing's mechanism in biological systems represented by reaction-diffusion or reaction-cross-diffusion models have been extensively studied. Nonetheless, the impact of tissue stratification in such systems is under-explored, despite its ubiquity in the context of a thin epithelium overlying connective tissue, for instance the epidermis and underlying dermal mesenchyme of embryonic skin. In particular, each layer can be subject to extensively different biochemical reactions and transport processes, with chemotaxis - a special case of cross-diffusion - often present in the mesenchyme, contrasting the solely molecular transport typically found in the epidermal layer. We study Turing patterning conditions for a class of reaction-cross-diffusion systems in bilayered regions, with a thin upper layer and coupled by a linear transport law. In particular, the role of differential transport through the interface is explored together with the presence of asymmetry between the homogeneous equilibria of the two layers. A linear stability analysis is carried out around a spatially homogeneous equilibrium state in the asymptotic limit of weak and strong coupling strengths, where quantitative approximations of the bifurcation curve can be computed. Our theoretical findings, for an arbitrary number of reacting species, reveal quantitative Turing conditions, highlighting when the coupling mechanism between the layered regions can either trigger patterning or stabilize a spatially homogeneous equilibrium regardless of the independent patterning state of each layer. We support our theoretical results through direct numerical simulations, and provide an open source code to explore such systems further.

Novel Aspects in Pattern Formation Arise from Coupling Turing Reaction-Diffusion and Chemotaxis

Recent experimental studies on primary hair follicle formation and feather bud morphogenesis indicate a coupling between Turing-type diffusion driven instability and chemotactic patterning. Inspired by these findings we develop and analyse a mathematical model that couples chemotaxis to a reaction-diffusion system exhibiting diffusion-driven (Turing) instability. While both systems, reaction-diffusion systems and chemotaxis, can independently generate spatial patterns, we were interested in how the coupling impacts the stability of the system, parameter region for patterning, pattern geometry, as well as the dynamics of pattern formation. We conduct a classical linear stability analysis for different model structures, and confirm our results by numerical analysis of the system. Our results show that the coupling generally increases the robustness of the patterning process by enlarging the pattern region in the parameter space. Concerning time scale and pattern regularity, we find that an increase in the chemosensitivity can speed up the patterning process for parameters inside and outside of the Turing space, but generally reduces spatial regularity of the pattern. Interestingly, our analysis indicates that pattern formation can also occur when neither the Turing nor the chemotaxis system can independently generate pattern. On the other hand, for some parameter settings, the coupling of the two processes can extinguish the pattern formation, rather than reinforce it. These theoretical findings can be used to corroborate the biological findings on morphogenesis and guide future experimental studies. From a mathematical point of view, this work sheds a light on coupling classical pattern formation systems from the parameter space perspective.

Mesenchyme governs hair follicle induction

Tissue interactions are essential for guiding organ development and regeneration. Hair follicle formation relies on inductive signalling between two tissues, the embryonic surface epithelium and the adjacent mesenchyme. Although previous research has highlighted the hair-inducing potential of the mesenchymal component of the hair follicle - the dermal papilla and its precursor, the dermal condensate - the source and nature of the primary inductive signal before dermal condensate formation have remained elusive. Here, we performed epithelial-mesenchymal tissue recombination experiments using hair-forming back skin and glabrous plantar skin from mouse embryos to unveil that the back skin mesenchyme is inductive even before dermal condensate formation. Moreover, the naïve, unpatterned mesenchyme was sufficient to trigger hair follicle formation even in the oral epithelium. Building on previous knowledge, we explored the hair-inductive ability of the Wnt agonist R-spondin 1 and a Bmp receptor inhibitor in embryonic skin explants. Although R-spondin 1 instigated precocious placode-specific transcriptional responses, it was insufficient for hair follicle induction, either alone or in combination with Bmp receptor inhibition. Our findings pave the way for identifying the hair follicle-inducing cue.

Cooperation of TGF-β and FGF signalling pathways in skin development

The skin is a multi-layered structure composed of the epidermis, dermis and hypodermis. The epidermis originates entirely from the ectoderm, whereas the dermis originates from various germ layers depending on its anatomical location; thus, there are different developmental patterns of the skin. Although the regulatory mechanisms of epidermal formation are well understood, mechanisms regulating dermis development are not clear owing to the complex origin. It has been shown that several morphogenetic pathways regulate dermis development. Of these, transforming growth factor-β (TGF-β) and fibroblast growth factor (FGF) signalling pathways are the main modulators regulating skin cell induction, fate decision, migration and differentiation. Recently, the successful generation of human skin by modulating TGF-β and FGF signals further demonstrated the irreplaceable roles of these pathways in skin regeneration. This review provides evidence of the role of TGF-β and FGF signalling pathways in the development of different skin layers, especially the disparate dermis of different body regions. This review also provides new perspectives on the distinct developmental patterns of skin and explores new ideas for clinical applications in the future.

Rapid mechanosensitive migration and dispersal of newly divided mesenchymal cells aid their recruitment into dermal condensates

Embryonic mesenchymal cells are dispersed within an extracellular matrix but can coalesce to form condensates with key developmental roles. Cells within condensates undergo fate and morphological changes and induce cell fate changes in nearby epithelia to produce structures including hair follicles, feathers, or intestinal villi. Here, by imaging mouse and chicken embryonic skin, we find that mesenchymal cells undergo much of their dispersal in early interphase, in a stereotyped process of displacement driven by 3 hours of rapid and persistent migration followed by a long period of low motility. The cell division plane and the elevated migration speed and persistence of newly born mesenchymal cells are mechanosensitive, aligning with tissue tension, and are reliant on active WNT secretion. This behaviour disperses mesenchymal cells and allows daughters of recent divisions to travel long distances to enter dermal condensates, demonstrating an unanticipated effect of cell cycle subphase on core mesenchymal behaviour.

Patterning and folding of intestinal villi by active mesenchymal dewetting

Tissue folding generates structural motifs critical to organ function. In the intestine, bending of a flat epithelium into a periodic pattern of folds gives rise to villi, the numerous finger-like protrusions that are essential for nutrient absorption. However, the molecular and mechanical mechanisms driving the initiation and morphogenesis of villi remain a matter of debate. Here, we identify an active mechanical mechanism that simultaneously patterns and folds intestinal villi. We find that PDGFRA+ subepithelial mesenchymal cells generate myosin II-dependent forces sufficient to produce patterned curvature in neighboring tissue interfaces. At the cell-level, this occurs through a process dependent upon matrix metalloproteinase-mediated tissue fluidization and altered cell-ECM adhesion. By combining computational models with in vivo experiments, we reveal these cellular features manifest at the tissue-level as differences in interfacial tensions that promote mesenchymal aggregation and interface bending through a process analogous to the active de-wetting of a thin liquid film.

Evo Devo of the Vertebrates Integument

All living jawed vertebrates possess teeth or did so ancestrally. Integumental surface also includes the cornea. Conversely, no other anatomical feature differentiates the clades so readily as skin appendages do, multicellular glands in amphibians, hair follicle/gland complexes in mammals, feathers in birds, and the different types of scales. Tooth-like scales are characteristic of chondrichthyans, while mineralized dermal scales are characteristic of bony fishes. Corneous epidermal scales might have appeared twice, in squamates, and on feet in avian lineages, but posteriorly to feathers. In contrast to the other skin appendages, the origin of multicellular glands of amphibians has never been addressed. In the seventies, pioneering dermal-epidermal recombination between chick, mouse and lizard embryos showed that: (1) the clade type of the appendage is determined by the epidermis; (2) their morphogenesis requires two groups of dermal messages, first for primordia formation, second for appendage final architecture; (3) the early messages were conserved during amniotes evolution. Molecular biology studies that have identified the involved pathways, extending those data to teeth and dermal scales, suggest that the different vertebrate skin appendages evolved in parallel from a shared placode/dermal cells unit, present in a common toothed ancestor, c.a. 420 mya.

A shark-inspired general model of tooth morphogenesis unveils developmental asymmetries in phenotype transitions

Developmental complexity stemming from the dynamic interplay between genetic and biomechanic factors canalizes the ways genotypes and phenotypes can change in evolution. As a paradigmatic system, we explore how changes in developmental factors generate typical tooth shape transitions. Since tooth development has mainly been researched in mammals, we contribute to a more general understanding by studying the development of tooth diversity in sharks. To this end, we build a general, but realistic, mathematical model of odontogenesis. We show that it reproduces key shark-specific features of tooth development as well as real tooth shape variation in small-spotted catsharks Scyliorhinus canicula. We validate our model by comparison with experiments in vivo. Strikingly, we observe that developmental transitions between tooth shapes tend to be highly degenerate, even for complex phenotypes. We also discover that the sets of developmental parameters involved in tooth shape transitions tend to depend asymmetrically on the direction of that transition. Together, our findings provide a valuable base for furthering our understanding of how developmental changes can lead to both adaptive phenotypic change and trait convergence in complex, phenotypically highly diverse, structures.

The developmental basis of fingerprint pattern formation and variation

Fingerprints are complex and individually unique patterns in the skin. Established prenatally, the molecular and cellular mechanisms that guide fingerprint ridge formation and their intricate arrangements are unknown. Here we show that fingerprint ridges are epithelial structures that undergo a truncated hair follicle developmental program and fail to recruit a mesenchymal condensate. Their spatial pattern is established by a Turing reaction-diffusion system, based on signaling between EDAR, WNT, and antagonistic BMP pathways. These signals resolve epithelial growth into bands of focalized proliferation under a precociously differentiated suprabasal layer. Ridge formation occurs as a set of waves spreading from variable initiation sites defined by the local signaling environments and anatomical intricacies of the digit, with the propagation and meeting of these waves determining the type of pattern that forms. Relying on a dynamic patterning system triggered at spatially distinct sites generates the characteristic types and unending variation of human fingerprint patterns.

Single-cell chromatin landscapes of mouse skin development

The coat of mammals is produced by hair follicles, and hair follicle is an important and complex accessory organ of skin. As a complex physiological regulation process, hair follicle morphogenesis is regulated by a series of signal pathway factors, involves the interaction of multiple cell types and begins in the early embryonic stage. However, its transcriptional regulatory mechanism is unclear. We have therefore utilized single-cell ATAC sequencing to obtain the chromatin accessibility landscapes of 6,928, 6,961 and 7,374 high-quality cells from the dorsal skins of E13.5, E16.5 and P0 mice (Mus musculus), respectively. Based on marker gene activity clustering, we defined 6, 8 and 5 distinct cell types in E13.5, E16.5 and P0 stages, respectively. Furtherly, we integrated the fibroblasts and keratinocytes clusters, performed further analysis and re-clustered. The single cell map of the chromatin open area was drawn from each cell type and the mechanism of cell transcription regulation was explored. Collectively, our data provide a reference for deeply exploring the epigenetic regulation mechanism of mouse hair follicles development.

The origins of skin diversity: lessons from dermal fibroblasts

Skin is largely composed of an epidermis that overlies a supporting dermis. Recent advancements in our understanding of how diverse groups of dermal fibroblasts regulate epidermal and hair follicle growth and differentiation have been fueled by tools capable of resolving molecular heterogeneity at a single-cell level. Fibroblast heterogeneity can be traced back to their developmental origin before their segregation into spatially distinct fibroblast subtypes. The mechanisms that drive this lineage diversification during development are being unraveled, with studies showing that both large- and small-scale positional signals play important roles during dermal development. Here, we first delineate what is known about the origins of the dermis and the central role of Wnt/β-catenin signaling in its specification across anatomical locations. We then discuss how one of the first morphologically recognizable fibroblast subtypes, the hair follicle dermal condensate lineage, emerges. Leveraging the natural variation of skin and its appendages between species and between different anatomical locations, these collective studies have identified shared and divergent factors that contribute to the extraordinary diversity of skin.

The Impact of Phenotypic Heterogeneity on Chemotactic Self-Organisation

The capacity to aggregate through chemosensitive movement forms a paradigm of self-organisation, with examples spanning cellular and animal systems. A basic mechanism assumes a phenotypically homogeneous population that secretes its own attractant, with the well known system introduced more than five decades ago by Keller and Segel proving resolutely popular in modelling studies. The typical assumption of population phenotypic homogeneity, however, often lies at odds with the heterogeneity of natural systems, where populations may comprise distinct phenotypes that vary according to their chemotactic ability, attractant secretion, etc. To initiate an understanding into how this diversity can impact on autoaggregation, we propose a simple extension to the classical Keller and Segel model, in which the population is divided into two distinct phenotypes: those performing chemotaxis and those producing attractant. Using a combination of linear stability analysis and numerical simulations, we demonstrate that switching between these phenotypic states alters the capacity of a population to self-aggregate. Further, we show that switching based on the local environment (population density or chemoattractant level) leads to diverse patterning and provides a route through which a population can effectively curb the size and density of an aggregate. We discuss the results in the context of real world examples of chemotactic aggregation, as well as theoretical aspects of the model such as global existence and blow-up of solutions.

Turing's turtles all the way down: A conserved role of EDAR in the carapacial ridge suggests a deep homology of prepatterns across ectodermal appendages

The scutes of the turtle shell are epidermal shields that begin their formation during the early stages of shell development. Like other skin appendages, turtle scutes are hypothesized to be patterned by reaction-diffusion systems. We have previously established ex vivo and in silico systems to study these mechanisms experimentally and have further shown that mathematical models can explain the dynamics of the induction of turtle scute primordia and the generation of final scute architecture. Using these foundations, we expand our current knowledge and test the roles of ectodysplasin and activin signaling in the development of turtle scutes. We find that these molecules play important roles in the prepatterning of scute primordia along the carapacial ridge and show that blocking Edar signaling may lead to a complete loss of marginal scute primordia. We show that it is possible to reproduce these observations using simple mathematical modeling, thereby suggesting a stabilizing role for ectodysplasin within the reaction-diffusion mechanisms. Finally, we argue that our findings further entrench turtle scutes within a class of developmental systems composed of hierarchically nested reaction-diffusion mechanisms, which is conserved across ectodermal organs.

Identification of key pathways and genes that regulate cashmere development in cashmere goats mediated by exogenous melatonin

The growth of secondary hair follicles in cashmere goats follows a seasonal cycle. Melatonin can regulate the cycle of cashmere growth. In this study, melatonin was implanted into live cashmere goats. After skin samples were collected, transcriptome sequencing and histological section observation were performed, and weighted gene co-expression network analysis (WGCNA) was used to identify key genes and establish an interaction network. A total of 14 co-expression modules were defined by WGCNA, and combined with previous analysis results, it was found that the blue module was related to the cycle of cashmere growth after melatonin implantation. Kyoto Encyclopedia of Genes and Genomes (KEGG) pathway enrichment analysis showed that the first initiation of exogenous melatonin-mediated cashmere development was related mainly to the signaling pathway regulating stem cell pluripotency and to the Hippo, TGF-beta and MAPK signaling pathways. Via combined differential gene expression analyses, 6 hub genes were identified: PDGFRA, WNT5A, PPP2R1A, BMPR2, BMPR1A, and SMAD1. This study provides a foundation for further research on the mechanism by which melatonin regulates cashmere growth.

Homeostases of epidermis and hair follicle, and development of basal cell carcinoma

Hedgehog signaling (Hh) plays a critical role in embryogenesis. On the other hand, its overactivity may cause basal cell carcinoma (BCC), the most common human cancer. Further, epidermal and hair follicle homeostases may have a key role in the development of BCC. This article describes the importance of different signaling pathways in the different stages of the two processes. The description of the homeostases brought up the importance of the Notch signaling along with the sonic hedgehog (Shh) and the Wnt pathways. Loss of the Notch signaling adversely affects the late stages of hair follicle formation and allows the bulge cells in the hair follicles to take the fate of the keratinocytes in the interfollicular epidermis. Further, the loss of Notch activity upregulates the Shh and Wnt activities, adversely affecting the homeostases. Notably, the Notch signaling is suppressed in BCC, and the peripheral BCC cells, which have low Notch activity, show drug resistance in comparison to the interior suprabasal BCC cells, which have high Notch activity.

New developments in the biology of fibroblast growth factors

The fibroblast growth factor (FGF) family is composed of 18 secreted signaling proteins consisting of canonical FGFs and endocrine FGFs that activate four receptor tyrosine kinases (FGFRs 1-4) and four intracellular proteins (intracellular FGFs or iFGFs) that primarily function to regulate the activity of voltage-gated sodium channels and other molecules. The canonical FGFs, endocrine FGFs, and iFGFs have been reviewed extensively by us and others. In this review, we briefly summarize past reviews and then focus on new developments in the FGF field since our last review in 2015. Some of the highlights in the past 6 years include the use of optogenetic tools, viral vectors, and inducible transgenes to experimentally modulate FGF signaling, the clinical use of small molecule FGFR inhibitors, an expanded understanding of endocrine FGF signaling, functions for FGF signaling in stem cell pluripotency and differentiation, roles for FGF signaling in tissue homeostasis and regeneration, a continuing elaboration of mechanisms of FGF signaling in development, and an expanding appreciation of roles for FGF signaling in neuropsychiatric diseases. This article is categorized under: Cardiovascular Diseases > Molecular and Cellular Physiology Neurological Diseases > Molecular and Cellular Physiology Congenital Diseases > Stem Cells and Development Cancer > Stem Cells and Development.

Engineering multiscale structural orders for high-fidelity embryoids and organoids

Embryoids and organoids hold great promise for human biology and medicine. Herein, we discuss conceptual and technological frameworks useful for developing high-fidelity embryoids and organoids that display tissue- and organ-level phenotypes and functions, which are critically needed for decoding developmental programs and improving translational applications. Through dissecting the layers of inputs controlling mammalian embryogenesis, we review recent progress in reconstructing multiscale structural orders in embryoids and organoids. Bioengineering tools useful for multiscale, multimodal structural engineering of tissue- and organ-level cellular organization and microenvironment are also discussed to present integrative, bioengineering-directed approaches to achieve next-generation, high-fidelity embryoids and organoids.

Decomposing a deterministic path to mesenchymal niche formation by two intersecting morphogen gradients

Organ formation requires integrating signals to coordinate proliferation, specify cell fates, and shape tissue. Tracing these events and signals remains a challenge, as intermediate states across many critical transitions are unresolvable over real time and space. Here, we designed a unique computational approach to decompose a non-linear differentiation process into key components to resolve the signals and cell behaviors that drive a rapid transition, using the hair follicle dermal condensate as a model. Combining scRNA sequencing with genetic perturbation, we reveal that proliferative Dkk1+ progenitors transiently amplify to become quiescent dermal condensate cells by the mere spatiotemporal patterning of Wnt/β-catenin and SHH signaling gradients. Together, they deterministically coordinate a rapid transition from proliferation to quiescence, cell fate specification, and morphogenesis. Moreover, genetically repatterning these gradients reproduces these events autonomously in "slow motion" across more intermediates that resolve the process. This analysis unravels two morphogen gradients that intersect to coordinate events of organogenesis.

Emergence of a geometric pattern of cell fates from tissue-scale mechanics in the Drosophila eye

Pattern formation of biological structures involves the arrangement of different types of cells in an ordered spatial configuration. In this study, we investigate the mechanism of patterning the Drosophila eye epithelium into a precise triangular grid of photoreceptor clusters called ommatidia. Previous studies had led to a long-standing biochemical model whereby a reaction-diffusion process is templated by recently formed ommatidia to propagate a molecular prepattern across the eye. Here, we find that the templating mechanism is instead, mechanochemical in origin; newly born columns of differentiating ommatidia serve as a template to spatially pattern flows that move epithelial cells into position to form each new column of ommatidia. Cell flow is generated by a source and sink, corresponding to narrow zones of cell dilation and contraction respectively, that straddle the growing wavefront of ommatidia. The newly formed lattice grid of ommatidia cells are immobile, deflecting, and focusing the flow of other cells. Thus, the self-organization of a regular pattern of cell fates in an epithelium is mechanically driven.

Modern perspectives on near-equilibrium analysis of Turing systems

In the nearly seven decades since the publication of Alan Turing's work on morphogenesis, enormous progress has been made in understanding both the mathematical and biological aspects of his proposed reaction-diffusion theory. Some of these developments were nascent in Turing's paper, and others have been due to new insights from modern mathematical techniques, advances in numerical simulations and extensive biological experiments. Despite such progress, there are still important gaps between theory and experiment, with many examples of biological patterning where the underlying mechanisms are still unclear. Here, we review modern developments in the mathematical theory pioneered by Turing, showing how his approach has been generalized to a range of settings beyond the classical two-species reaction-diffusion framework, including evolving and complex manifolds, systems heterogeneous in space and time, and more general reaction-transport equations. While substantial progress has been made in understanding these more complicated models, there are many remaining challenges that we highlight throughout. We focus on the mathematical theory, and in particular linear stability analysis of 'trivial' base states. We emphasize important open questions in developing this theory further, and discuss obstacles in using these techniques to understand biological reality. This article is part of the theme issue 'Recent progress and open frontiers in Turing's theory of morphogenesis'.

Systems for intricate patterning of the vertebrate anatomy

Periodic patterns form intricate arrays in the vertebrate anatomy, notably the hair and feather follicles of the skin, but also internally the villi of the gut and the many branches of the lung, kidney, mammary and salivary glands. These tissues are composite structures, being composed of adjoined epithelium and mesenchyme, and the patterns that arise within them require interaction between these two tissue layers. In embryonic development, cells change both their distribution and state in a periodic manner, defining the size and relative positions of these specialized structures. Their placement is determined by simple spacing mechanisms, with substantial evidence pointing to a variety of local enhancement/lateral inhibition systems underlying the breaking of symmetry. The nature of the cellular processes involved, however, has been less clear. While much attention has focused on intercellular soluble signals, such as protein growth factors, experimental evidence has grown for contributions of cell movement or mechanical forces to symmetry breaking. In the mesenchyme, unlike the epithelium, cells may move freely and can self-organize into aggregates by chemotaxis, or through generation and response to mechanical strain on their surrounding matrix. Different modes of self-organization may coexist, either coordinated into a single system or with hierarchical relationships. Consideration of a broad range of distinct biological processes is required to advance understanding of biological pattern formation. This article is part of the theme issue 'Recent progress and open frontiers in Turing's theory of morphogenesis'.

QuickPIV: Efficient 3D particle image velocimetry software applied to quantifying cellular migration during embryogenesis

BACKGROUND

The technical development of imaging techniques in life sciences has enabled the three-dimensional recording of living samples at increasing temporal resolutions. Dynamic 3D data sets of developing organisms allow for time-resolved quantitative analyses of morphogenetic changes in three dimensions, but require efficient and automatable analysis pipelines to tackle the resulting Terabytes of image data. Particle image velocimetry (PIV) is a robust and segmentation-free technique that is suitable for quantifying collective cellular migration on data sets with different labeling schemes. This paper presents the implementation of an efficient 3D PIV package using the Julia programming language-quickPIV. Our software is focused on optimizing CPU performance and ensuring the robustness of the PIV analyses on biological data.

RESULTS

QuickPIV is three times faster than the Python implementation hosted in openPIV, both in 2D and 3D. Our software is also faster than the fastest 2D PIV package in openPIV, written in C++. The accuracy evaluation of our software on synthetic data agrees with the expected accuracies described in the literature. Additionally, by applying quickPIV to three data sets of the embryogenesis of Tribolium castaneum, we obtained vector fields that recapitulate the migration movements of gastrulation, both in nuclear and actin-labeled embryos. We show normalized squared error cross-correlation to be especially accurate in detecting translations in non-segmentable biological image data.

CONCLUSIONS

The presented software addresses the need for a fast and open-source 3D PIV package in biological research. Currently, quickPIV offers efficient 2D and 3D PIV analyses featuring zero-normalized and normalized squared error cross-correlations, sub-pixel/voxel approximation, and multi-pass. Post-processing options include filtering and averaging of the resulting vector fields, extraction of velocity, divergence and collectiveness maps, simulation of pseudo-trajectories, and unit conversion. In addition, our software includes functions to visualize the 3D vector fields in Paraview.

Reaction-diffusion models for morphological patterning of hESCs

In this paper we consider mathematical modeling of the dynamics of self-organized patterning of spatially confined human embryonic stem cells (hESCs) treated with BMP4 (gastruloids) described in recent experimental works (Warmflash in Nat Methods 11:847-854, 2014; Chhabra in PloS Biol 17: 3000498, 2019). In the first part of the paper we use the activator-inhibitor equations of Gierer and Meinhardt to identify 3 reaction-diffusion regimes for each of the three morphogenic proteins, BMP4, Wnt and Nodal, based on the characteristic features of the dynamic patterning. We identify appropriate boundary conditions which correspond to the experimental setup and perform numerical simulations of the reaction-diffusion (RD) systems, using the finite element approximation, to confirm that the RD systems in these regimes produce realistic dynamics of the protein concentrations. In the second part of the paper we use analytic tools to address the questions of the existence and stability of non-homogeneous steady states for the reaction-diffusion systems of the type considered in the first part of the paper.

Systems of pattern formation within developmental biology

Applications of mathematical models to developmental biology have provided helpful insight into various subfields, ranging from the patterning of animal skin to the development of complex organ systems. Systems involved in patterning within morphology present a unique path to explain self-organizing systems. Current efforts show that patterning systems, notably Reaction-Diffusion and specific signaling pathways, provide insight for explaining morphology and could provide novel applications revolving around the formation of biological systems. Furthermore, the application of pattern formation provides a new perspective on understanding developmental biology and pathology research to study molecular mechanisms. The current review is to cover and take a more in-depth overlook at current applications of patterning systems while also building on the principles of patterning of future research in predictive medicine.

Developmental genetics of color pattern establishment in cats

Intricate color patterns are a defining aspect of morphological diversity in the Felidae. We applied morphological and single-cell gene expression analysis to fetal skin of domestic cats to identify when, where, and how, during fetal development, felid color patterns are established. Early in development, we identify stripe-like alterations in epidermal thickness preceded by a gene expression pre-pattern. The secreted Wnt inhibitor encoded by Dickkopf 4 plays a central role in this process, and is mutated in cats with the Ticked pattern type. Our results bring molecular understanding to how the leopard got its spots, suggest that similar mechanisms underlie periodic color pattern and periodic hair follicle spacing, and identify targets for diverse pattern variation in other mammals.

Tracing the origin of hair follicle stem cells

Tissue stem cells are generated from a population of embryonic progenitors through organ-specific morphogenetic events^1,2. Although tissue stem cells are central to organ homeostasis and regeneration, it remains unclear how they are induced during development, mainly because of the lack of markers that exclusively label prospective stem cells. Here we combine marker-independent long-term 3D live imaging and single-cell transcriptomics to capture a dynamic lineage progression and transcriptome changes in the entire epithelium of the mouse hair follicle as it develops. We found that the precursors of different epithelial lineages were aligned in a 2D concentric manner in the basal layer of the hair placode. Each concentric ring acquired unique transcriptomes and extended to form longitudinally aligned, 3D cylindrical compartments. Prospective bulge stem cells were derived from the peripheral ring of the placode basal layer, but not from suprabasal cells (as was previously suggested³). The fate of placode cells is determined by the cell position, rather than by the orientation of cell division. We also identified 13 gene clusters: the ensemble expression dynamics of these clusters drew the entire transcriptional landscape of epithelial lineage diversification, consistent with cell lineage data. Combining these findings with previous work on the development of appendages in insects^4,5, we describe the 'telescope model', a generalized model for the development of ectodermal organs in which 2D concentric zones in the placode telescope out to form 3D longitudinally aligned cylindrical compartments.

Isolating Patterns in Open Reaction-Diffusion Systems

Realistic examples of reaction-diffusion phenomena governing spatial and spatiotemporal pattern formation are rarely isolated systems, either chemically or thermodynamically. However, even formulations of 'open' reaction-diffusion systems often neglect the role of domain boundaries. Most idealizations of closed reaction-diffusion systems employ no-flux boundary conditions, and often patterns will form up to, or along, these boundaries. Motivated by boundaries of patterning fields related to the emergence of spatial form in embryonic development, we propose a set of mixed boundary conditions for a two-species reaction-diffusion system which forms inhomogeneous solutions away from the boundary of the domain for a variety of different reaction kinetics, with a prescribed uniform state near the boundary. We show that these boundary conditions can be derived from a larger heterogeneous field, indicating that these conditions can arise naturally if cell signalling or other properties of the medium vary in space. We explain the basic mechanisms behind this pattern localization and demonstrate that it can capture a large range of localized patterning in one, two, and three dimensions and that this framework can be applied to systems involving more than two species. Furthermore, the boundary conditions proposed lead to more symmetrical patterns on the interior of the domain and plausibly capture more realistic boundaries in developmental systems. Finally, we show that these isolated patterns are more robust to fluctuations in initial conditions and that they allow intriguing possibilities of pattern selection via geometry, distinct from known selection mechanisms.

Inference and analysis of cell-cell communication using CellChat

Understanding global communications among cells requires accurate representation of cell-cell signaling links and effective systems-level analyses of those links. We construct a database of interactions among ligands, receptors and their cofactors that accurately represent known heteromeric molecular complexes. We then develop CellChat, a tool that is able to quantitatively infer and analyze intercellular communication networks from single-cell RNA-sequencing (scRNA-seq) data. CellChat predicts major signaling inputs and outputs for cells and how those cells and signals coordinate for functions using network analysis and pattern recognition approaches. Through manifold learning and quantitative contrasts, CellChat classifies signaling pathways and delineates conserved and context-specific pathways across different datasets. Applying CellChat to mouse and human skin datasets shows its ability to extract complex signaling patterns. Our versatile and easy-to-use toolkit CellChat and a web-based Explorer ( http://www.cellchat.org/ ) will help discover novel intercellular communications and build cell-cell communication atlases in diverse tissues.

Turing Patterning in Stratified Domains

Reaction-diffusion processes across layered media arise in several scientific domains such as pattern-forming E. coli on agar substrates, epidermal-mesenchymal coupling in development, and symmetry-breaking in cell polarization. We develop a modeling framework for bilayer reaction-diffusion systems and relate it to a range of existing models. We derive conditions for diffusion-driven instability of a spatially homogeneous equilibrium analogous to the classical conditions for a Turing instability in the simplest nontrivial setting where one domain has a standard reaction-diffusion system, and the other permits only diffusion. Due to the transverse coupling between these two regions, standard techniques for computing eigenfunctions of the Laplacian cannot be applied, and so we propose an alternative method to compute the dispersion relation directly. We compare instability conditions with full numerical simulations to demonstrate impacts of the geometry and coupling parameters on patterning, and explore various experimentally relevant asymptotic regimes. In the regime where the first domain is suitably thin, we recover a simple modulation of the standard Turing conditions, and find that often the broad impact of the diffusion-only domain is to reduce the ability of the system to form patterns. We also demonstrate complex impacts of this coupling on pattern formation. For instance, we exhibit non-monotonicity of pattern-forming instabilities with respect to geometric and coupling parameters, and highlight an instability from a nontrivial interaction between kinetics in one domain and diffusion in the other. These results are valuable for informing design choices in applications such as synthetic engineering of Turing patterns, but also for understanding the role of stratified media in modulating pattern-forming processes in developmental biology and beyond.

Eckhaus selection: The mechanism of pattern persistence in a reaction-diffusion system

In this work, we show theoretically and numerically that a one-dimensional reaction-diffusion system, near the Turing bifurcation, produces different number of stripes when, in addition to random noise, the Fourier mode of a prepattern used to initialize the system changes. We also show that the Fourier modes that persist are inside the Eckhaus stability regions, while those outside this region follow a wave number selection process not predicted by the linear analysis. To test our results, we use the Brusselator reaction-diffusion system obtaining an excellent agreement between the weakly nonlinear predictions of the real Ginzburg-Landau equations and the numerical solutions near the bifurcation. Although the persistence of patterns is not relevant as a simple generating mechanism of self-organization, it is crucial to understand the formation of patterns that occurs in multiple stages. In this work, we discuss the relevance of our results on the robustness and diversity of solutions in multiple-steps mechanisms of biological pattern formation and auto-organization in growing domains.

Self-organizing hair peg-like structures from dissociated skin progenitor cells: New insights for human hair follicle organoid engineering and Turing patterning in an asymmetric morphogenetic field

Human skin progenitor cells will form new hair follicles, although at a low efficiency, when injected into nude mouse skin. To better study and improve upon this regenerative process, we developed an in vitro system to analyse the morphogenetic cell behaviour in detail and modulate physical-chemical parameters to more effectively generate hair primordia. In this three-dimensional culture, dissociated human neonatal foreskin keratinocytes self-assembled into a planar epidermal layer while fetal scalp dermal cells coalesced into stripes, then large clusters, and finally small clusters resembling dermal condensations. At sites of dermal clustering, subjacent epidermal cells protruded to form hair peg-like structures, molecularly resembling hair pegs within the sequence of follicular development. The hair peg-like structures emerged in a coordinated, formative wave, moving from periphery to centre, suggesting that the droplet culture constitutes a microcosm with an asymmetric morphogenetic field. In vivo, hair follicle populations also form in a progressive wave, implying the summation of local periodic patterning events with an asymmetric global influence. To further understand this global patterning process, we developed a mathematical simulation using Turing activator-inhibitor principles in an asymmetric morphogenetic field. Together, our culture system provides a suitable platform to (a) analyse the self-assembly behaviour of hair progenitor cells into periodically arranged hair primordia and (b) identify parameters that impact the formation of hair primordia in an asymmetric morphogenetic field. This understanding will enhance our future ability to successfully engineer human hair follicle organoids.

An updated classification of hair follicle morphogenesis

Hair follicle (HF) formation in developing embryonic skin requires stepwise signalling between the epithelial epidermis and mesenchymal dermis, and their specialized derivatives, the placode/germ/peg and dermal condensate/papilla, respectively. Classically, distinct stages of HF morphogenesis have been defined, in the mouse model, based on (a) changes in cell morphology and aggregation; (b) expression of few known molecular markers; (c) the extent of follicle downgrowth; and (d) the presence of differentiating cell types. Refined genetic strategies and recent emerging technologies, such as live imaging and transcriptome analyses of isolated cell populations or single cells, have enabled a closer dissection of the signalling requirements at different stages of HF formation, particularly early on. They have also led to the discovery of precursor cells for placode, dermal condensate and future bulge stem cells that, combined with molecular insights into their fate specification and subsequent formation, serve as novel landmarks for early HF morphogenetic events and studies of the signalling networks mediating these processes. In this review, we integrate the emergence of HF precursor cell states and novel molecular markers of fate and formation to update the widely used 20-year-old seminal classification guide of HF morphogenetic stages by Paus et al. We then temporally describe the latest insights into the early cellular and molecular events and signalling requirements for HF morphogenesis in relation to one another in a holistic manner.

Wnt/β-catenin Signaling in Tissue Self-Organization

Across metazoans, animal body structures and tissues exist in robust patterns that arise seemingly out of stochasticity of a few early cells in the embryo. These patterns ensure proper tissue form and function during early embryogenesis, development, homeostasis, and regeneration. Fundamental questions are how these patterns are generated and maintained during tissue homeostasis and regeneration. Though fascinating scientists for generations, these ideas remain poorly understood. Today, it is apparent that the Wnt/β-catenin pathway plays a central role in tissue patterning. Wnt proteins are small diffusible morphogens which are essential for cell type specification and patterning of tissues. In this review, we highlight several mechanisms described where the spatial properties of Wnt/β-catenin signaling are controlled, allowing them to work in combination with other diffusible molecules to control tissue patterning. We discuss examples of this self-patterning behavior during development and adult tissues' maintenance. The combination of new physiological culture systems, mathematical approaches, and synthetic biology will continue to fuel discoveries about how tissues are patterned. These insights are critical for understanding the intricate interplay of core patterning signals and how they become disrupted in disease.

Reconstructed human skin shows epidermal invagination towards integrated neopapillae indicating early hair follicle formation in vitro

Application of reconstructed human Skin (RhS) is a promising approach for the treatment of extensive wounds and for drug efficacy and safety testing. However, incorporating appendages, such as hair follicles, into RhS still remains a challenge. The hair follicle plays a critical role in thermal regulation, dispersion of sweat and sebum, sensory and tactile functions, skin regeneration, and repigmentation. The aim of this study was to determine whether human neopapilla could be incorporated into RhS (differentiated epidermis on fibroblast and endothelial cell populated dermis) and whether the neopapillae maintain their inductive follicular properties in vitro. Neopapillae spheroids, constructed from expanded and self‐aggregating dermal papilla cells, synthesized extracellular matrix typically found in follicular papillae. Compared with dermal fibroblasts, neopapillae showed increased expression of multiple genes (Wnt5a, Wnt10b, and LEF1) known to regulate hair development and also increased secretion of CXCL1, which is a strong keratinocyte chemoattractant. When neopapillae were incorporated into the dermis of RhS, they stimulated epidermal down‐growth resulting in engulfment of the neopapillae sphere. Similar to the native hair follicle, the differentiated invaginating epidermis inner side was keratin 10 positive and the undifferentiated outer side keratin 10 negative. The outer side was keratin 15 positive confirming the undifferentiated nature of these keratinocytes aligning a newly formed collagen IV, laminin V positive basement membrane within the hydrogel. In conclusion, we describe a RhS model containing neopapillae with hair follicle‐inductive properties. Importantly, epidermal invagination occurred to engulf the neopapillae, thus demonstrating in vitro the first steps towards hair follicle morphogenesis in RhS.

Progenitors oppositely polarize WNT activators and inhibitors to orchestrate tissue development

To spatially co-exist and differentially specify fates within developing tissues, morphogenetic cues must be correctly positioned and interpreted. Here, we investigate mouse hair follicle development to understand how morphogens operate within closely spaced, fate-diverging progenitors. Coupling transcriptomics with genetics, we show that emerging hair progenitors produce both WNTs and WNT inhibitors. Surprisingly, however, instead of generating a negative feedback loop, the signals oppositely polarize, establishing sharp boundaries and consequently a short-range morphogen gradient that we show is essential for three-dimensional pattern formation. By establishing a morphogen gradient at the cellular level, signals become constrained. The progenitor preserves its WNT signaling identity and maintains WNT signaling with underlying mesenchymal neighbors, while its overlying epithelial cells become WNT-restricted. The outcome guarantees emergence of adjacent distinct cell types to pattern the tissue.