An interplay of geometry and signaling enables robust lung branching morphogenesis

Mechanism of branching morphogenesis inspired by diatom silica formation

The silica-based cell walls of diatoms are prime examples of genetically controlled, species-specific mineral architectures. The physical principles underlying morphogenesis of their hierarchically structured silica patterns are not understood, yet such insight could indicate novel routes toward synthesizing functional inorganic materials. Recent advances in imaging nascent diatom silica allow rationalizing possible mechanisms of their pattern formation. Here, we combine theory and experiments on the model diatom Thalassiosira pseudonana to put forward a minimal model of branched rib patterns-a fundamental feature of the silica cell wall. We quantitatively recapitulate the time course of rib pattern morphogenesis by accounting for silica biochemistry with autocatalytic formation of diffusible silica precursors followed by conversion into solid silica. We propose that silica deposition releases an inhibitor that slows down up-stream precursor conversion, thereby implementing a self-replicating reaction-diffusion system different from a classical Turing mechanism. The proposed mechanism highlights the role of geometrical cues for guided self-organization, rationalizing the instructive role for the single initial pattern seed known as the primary silicification site. The mechanism of branching morphogenesis that we characterize here is possibly generic and may apply also in other biological systems.

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.

ERK-mediated curvature feedback regulates branching morphogenesis in lung epithelial tissue

Intricate branching patterns emerge in internal organs due to the recurrent occurrence of simple deformations in epithelial tissues. During murine lung development, epithelial cells in distal tips of the single tube require fibroblast growth factor (FGF) signals emanating from their surrounding mesenchyme to form repetitive tip bifurcations. However, it remains unknown how the cells employ FGF signaling to convert their behaviors to achieve the recursive branching processes. Here, we show a mechano-chemical regulatory system underlying lung branching morphogenesis, orchestrated by extracellular signal-regulated kinase (ERK) as a downstream driver of FGF signaling. We found that tissue-scale curvature regulated ERK activity in the lung epithelium using two-photon live cell imaging and mechanical perturbations. ERK activation occurs specifically in epithelial tissues exhibiting positive curvature, regardless of whether the change in curvature was attributable to morphogenesis or perturbations. Moreover, ERK activation accelerates actin polymerization preferentially at the apical side of cells, mechanically contributing to the extension of the apical membrane, culminating in a reduction of epithelial tissue curvature. These results indicate the existence of a negative feedback loop between tissue curvature and ERK activity that transcends spatial scales. Our mathematical model confirms that this regulatory mechanism is sufficient to generate the recursive branching processes. Taken together, we propose that ERK orchestrates a curvature feedback loop pivotal to the self-organized patterning of tissues.

Geometric effects position renal vesicles during kidney development

During kidney development, reciprocal signaling between the epithelium and the mesenchyme coordinates nephrogenesis with branching morphogenesis of the collecting ducts. The mechanism that positions the renal vesicles, and thus the nephrons, relative to the branching ureteric buds has remained elusive. By combining computational modeling and experiments, we show that geometric effects concentrate the key regulator, WNT9b, at the junctions between parent and daughter branches where renal vesicles emerge, even when uniformly expressed in the ureteric epithelium. This curvature effect might be a general paradigm to create non-uniform signaling in development.

Inflationary theory of branching morphogenesis in the mouse salivary gland

The mechanisms that regulate the patterning of branched epithelia remain a subject of long-standing debate. Recently, it has been proposed that the statistical organization of multiple ductal tissues can be explained through a local self-organizing principle based on the branching-annihilating random walk (BARW) in which proliferating tips drive a process of ductal elongation and stochastic bifurcation that terminates when tips encounter maturing ducts. Here, applied to mouse salivary gland, we show the BARW model struggles to explain the large-scale organization of tissue. Instead, we propose that the gland develops as a tip-driven branching-delayed random walk (BDRW). In this framework, a generalization of the BARW, tips inhibited through steric interaction with proximate ducts may continue their branching program as constraints become alleviated through the persistent expansion of the surrounding tissue. This inflationary BDRW model presents a general paradigm for branching morphogenesis when the ductal epithelium grows cooperatively with the domain into which it expands.

A Guide Toward Multi-scale and Quantitative Branching Analysis in the Mammary Gland

The mammary gland consists of a bilayered epithelial structure with an extensively branched morphology. The majority of this epithelial tree is laid down during puberty, during which actively proliferating terminal end buds repeatedly elongate and bifurcate to form the basic structure of the ductal tree. Mammary ducts consist of a basal and luminal cell layer with a multitude of identified sub-lineages within both layers. The understanding of how these different cell lineages are cooperatively driving branching morphogenesis is a problem of crossing multiple scales, as this requires information on the macroscopic branched structure of the gland, as well as data on single-cell dynamics driving the morphogenic program. Here we describe a method to combine genetic lineage tracing with whole-gland branching analysis. Quantitative data on the global organ structure can be used to derive a model for mammary gland branching morphogenesis and provide a backbone on which the dynamics of individual cell lineages can be simulated and compared to lineage-tracing approaches. Eventually, these quantitative models and experiments allow to understand the couplings between the macroscopic shape of the mammary gland and the underlying single-cell dynamics driving branching morphogenesis.

Simple Models of Lung Development

Models are essential to further our understanding of lung development and regeneration and to facilitate identification and testing of potential treatments for lung diseases. A wide variety of rodent and human models are available that recapitulate one or more stages of lung development. This chapter describes the existing 'simple' in vitro, in silico and ex vivo models of lung development. We define which stage(s) of development each model recapitulates and highlight their pros and cons.

The present and future of Turing models in developmental biology

The Turing model (or reaction-diffusion model), first published in 1952, is a mathematical model that can account for autonomy in the morphogenesis of organisms. Although initially controversial, the model has gradually gained wider acceptance among experimental embryologists due to the accumulation of experimental data to support it. More recently, this model and others based on it have been used not only to explain biological phenomena conceptually but also as working hypotheses for molecular-level experiments and as internal components of more-complex 3D models. In this Spotlight, I will provide a personal perspective from an experimental biologist on some of the recent developments of the Turing model.

How to build an epithelial tree

Nature has evolved a variety of mechanisms to build epithelial trees of diverse architectures within different organs and across species. Epithelial trees are elaborated through branch initiation and extension, and their morphogenesis ends with branch termination. Each of these steps of the branching process can be driven by the actions of epithelial cells themselves (epithelial-intrinsic mechanisms) or by the cells of their surrounding tissues (epithelial-extrinsic mechanisms). Here, we describe examples of how these mechanisms drive each stage of branching morphogenesis, drawing primarily from studies of the lung, kidney, salivary gland, mammary gland, and pancreas, all of which contain epithelial trees that form through collective cell behaviors. Much of our understanding of epithelial branching comes from experiments using mice, but we also include examples here from avian and reptilian models. Throughout, we highlight how distinct mechanisms are employed in different organs and species to build epithelial trees. We also highlight how similar morphogenetic motifs are used to carry out conserved developmental programs or repurposed to support novel ones. Understanding the unique strategies used by nature to build branched epithelia from across the tree of life can help to inspire creative solutions to problems in tissue engineering and regenerative medicine.

Tracheal Ring Formation

The trachea is a long tube that enables air passage between the larynx and the bronchi. C-shaped cartilage rings on the ventral side stabilise the structure. On its esophagus-facing dorsal side, deformable smooth muscle facilitates the passage of food in the esophagus. While the symmetry break along the dorsal-ventral axis is well understood, the molecular mechanism that results in the periodic Sox9 expression pattern that translates into the cartilage rings has remained elusive. Here, we review the molecular regulatory interactions that have been elucidated, and discuss possible patterning mechanisms. Understanding the principles of self-organisation is important, both to define biomedical interventions and to enable tissue engineering.

Patterning the embryonic pulmonary mesenchyme

Smooth muscle guides the morphogenesis of several epithelia during organogenesis, including the mammalian airways. However, it remains unclear how airway smooth muscle differentiation is spatiotemporally patterned and whether it originates from transcriptionally distinct mesenchymal progenitors. Using single-cell RNA-sequencing of embryonic mouse lungs, we show that the pulmonary mesenchyme contains a continuum of cell identities, but no transcriptionally distinct progenitors. Transcriptional variability correlates with spatially distinct sub-epithelial and sub-mesothelial mesenchymal compartments that are regulated by Wnt signaling. Live-imaging and tension-sensors reveal compartment-specific migratory behaviors and cortical forces and show that sub-epithelial mesenchyme contributes to airway smooth muscle. Reconstructing differentiation trajectories reveals early activation of cytoskeletal and Wnt signaling genes. Consistently, Wnt activation induces the earliest stages of smooth muscle differentiation and local accumulation of mesenchymal F-actin, which influences epithelial morphology. Our single-cell approach uncovers the principles of pulmonary mesenchymal patterning and identifies a morphogenetically active mesenchymal layer that sculpts the airway epithelium.

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The embryonic lung mesenchyme is organized into spatially distinct compartments

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Migratory behaviors and cortical forces differ between compartments

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Diffusion analysis recapitulates airway smooth muscle differentiation

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The early stages of smooth muscle differentiation influence airway branching

Pattern formation features might explain homoplasy: fertile surfaces in higher fungi as an example

Fungi show a high degree of morphological convergence. Regarded for a long time as an obstacle for phylogenetic studies, homoplasy has also been proposed as a source of information about underlying morphogenetic patterning mechanisms. The "local-activation and long-range inhibition principle" (LALIP), underlying the famous reaction-diffusion model proposed by Alan Turing in 1952, appears to be one of the universal phenomena that can explain the ontogenetic origin of seriate patterns in living organisms. Reproductive structures of fungi in the class Agaricomycetes show a highly periodic structure resulting in, for example, poroid, odontoid, lamellate or labyrinthic hymenophores. In this paper, we claim that self-organized patterns might underlie the basic ontogenetic processes of these structures. Simulations based on LALIP-driven models and covering a wide range of parameters show an absolute mutual correspondence with the morphospace explored by extant agaricomycetes. This could not only explain geometric particularities but could also account for the limited possibilities displayed by hymenial configurations, thus making homoplasy a direct consequence of the limited morphospace resulting from the proposed patterning dynamics.

Alveologenesis: What Governs Secondary Septa Formation

The simplification of alveoli leads to various lung pathologies such as bronchopulmonary dysplasia and emphysema. Deep insight into the process of emergence of the secondary septa during development and regeneration after pneumonectomy, and into the contribution of the drivers of alveologenesis and neo-alveolarization is required in an efficient search for therapeutic approaches. In this review, we describe the formation of the gas exchange units of the lung as a multifactorial process, which includes changes in the actomyosin cytoskeleton of alveocytes and myofibroblasts, elastogenesis, retinoic acid signaling, and the contribution of alveolar mesenchymal cells in secondary septation. Knowledge of the mechanistic context of alveologenesis remains incomplete. The characterization of the mechanisms that govern the emergence and depletion of αSMA will allow for an understanding of how the niche of fibroblasts is changing. Taking into account the intense studies that have been performed on the pool of lung mesenchymal cells, we present data on the typing of interstitial fibroblasts and their role in the formation and maintenance of alveoli. On the whole, when identifying cell subpopulations in lung mesenchyme, one has to consider the developmental context, the changing cellular functions, and the lability of gene signatures.

Organoid models: assessing lung cell fate decisions and disease responses

Organoids can be derived from various cell types in the lung, and they provide a reproducible and tractable model for understanding the complex signals driving cell fate decisions in a regenerative context. In this review, we provide a retrospective account of organoid methodologies and outline new opportunities for optimizing these methods to further explore emerging concepts in lung biology. Moreover, we examine the benefits of integrating organoid assays with in vivo modeling to explore how the various niches and compartments in the respiratory system respond to both acute and chronic lung disease. The strategic implementation and improvement of organoid techniques will provide exciting new opportunities to understand and identify new therapeutic approaches to ameliorate lung disease states.

A review of regulated self-organizing approaches for tissue regeneration

Tissue and organ regeneration is the dynamic process by which a population of cells rearranges into a specific form with specific functions. Traditional tissue regeneration utilizes tissue grafting, cell implantation, and structured scaffolds to achieve clinical efficacy. However, tissue grafting methods face a shortage of donor tissue, while cell implantation may involve leakage of the implanted cells without a supportive 3D matrix. Cell migration, proliferation, and differentiation in structured scaffolds may disorganize and frustrate the artificially pre-designed structures, and sometimes involve immunogenic reactions. To overcome this limitation, the self-organizing properties and innate regenerative capability of tissue/organism formation in the absence of guidance by structured scaffolds has been investigated. This review emphasizes the growing subfield of the regulated self-organizing approach for neotissue formation and describes advances in the subfield using diverse, cutting-edge, inter-disciplinarity technologies. We cohesively summarize the directed self-organization of cells in the micro-engineered cell-ECM system and 3D/4D cell printing. Mathematical modeling of cellular self-organization is also discussed for providing rational guidance to intractable problems in tissue regeneration. It is envisioned that future self-organization approaches integrating biomathematics, micro-nano engineering, and gene circuits developed from synthetic biology will continue to work in concert with self-organizing morphogenesis to enhance rational control during self-organizing in tissue and organ regeneration.

Organ-Specific Branching Morphogenesis

A common developmental process, called branching morphogenesis, generates the epithelial trees in a variety of organs, including the lungs, kidneys, and glands. How branching morphogenesis can create epithelial architectures of very different shapes and functions remains elusive. In this review, we compare branching morphogenesis and its regulation in lungs and kidneys and discuss the role of signaling pathways, the mesenchyme, the extracellular matrix, and the cytoskeleton as potential organ-specific determinants of branch position, orientation, and shape. Identifying the determinants of branch and organ shape and their adaptation in different organs may reveal how a highly conserved developmental process can be adapted to different structural and functional frameworks and should provide important insights into epithelial morphogenesis and developmental disorders.

Defective mesothelium and limited physical space are drivers of dysregulated lung development in a genetic model of congenital diaphragmatic hernia

Congenital diaphragmatic hernia (CDH) is a developmental disorder associated with diaphragm defects and lung hypoplasia. The etiology of CDH is complex and its clinical presentation is variable. We investigated the role of the pulmonary mesothelium in dysregulated lung growth noted in the Wt1 knockout mouse model of CDH. Loss of WT1 leads to intrafetal effusions, altered lung growth, and branching defects prior to normal closure of the diaphragm. We found significant differences in key genes; however, when Wt1 null lungs were cultured ex vivo, growth and branching were indistinguishable from wild-type littermates. Micro-CT imaging of embryos in situ within the uterus revealed a near absence of space in the dorsal chest cavity, but no difference in total chest cavity volume in Wt1 null embryos, indicating a redistribution of pleural space. The altered space and normal ex vivo growth suggest that physical constraints are contributing to the CDH lung phenotype observed in this mouse model. These studies emphasize the importance of examining the mesothelium and chest cavity as a whole, rather than focusing on single organs in isolation to understand early CDH etiology.

The biomechanical basis of biased epithelial tube elongation in lung and kidney development

During lung development, epithelial branches expand preferentially in a longitudinal direction. This bias in outgrowth has been linked to a bias in cell shape and in the cell division plane. How this bias arises is unknown. Here, we show that biased epithelial outgrowth occurs independent of the surrounding mesenchyme, of preferential turnover of the extracellular matrix at the bud tips and of FGF signalling. There is also no evidence for actin-rich filopodia at the bud tips. Rather, we find epithelial tubes to be collapsed during early lung and kidney development, and we observe fluid flow in the narrow tubes. By simulating the measured fluid flow inside segmented narrow epithelial tubes, we show that the shear stress levels on the apical surface are sufficient to explain the reported bias in cell shape and outgrowth. We use a cell-based vertex model to confirm that apical shear forces, unlike constricting forces, can give rise to both the observed bias in cell shapes and tube elongation. We conclude that shear stress may be a more general driver of biased tube elongation beyond its established role in angiogenesis. This article has an associated 'The people behind the papers' interview.

The control of lung branching morphogenesis

Branching morphogenesis generates epithelial trees which facilitate gas exchange, filtering, as well as secretion processes with their large surface to volume ratio. In this review, we focus on the developmental mechanisms that control the early stages of lung branching morphogenesis. Lung branching morphogenesis involves the stereotypic, recurrent definition of new branch points, subsequent epithelial budding, and lung tube elongation. We discuss current models and experimental evidence for each of these steps. Finally, we discuss the role of the mesenchyme in determining the organ-specific shape.

Fgf10/Fgfr2b Signaling Orchestrates the Symphony of Molecular, Cellular, and Physical Processes Required for Harmonious Airway Branching Morphogenesis

Airway branching morphogenesis depends on the intricate orchestration of numerous biological and physical factors connected across different spatial scales. One of the key regulatory pathways controlling airway branching is fibroblast growth factor 10 (Fgf10) signaling via its epithelial fibroblast growth factor receptor 2b (Fgfr2b). Fine reviews have been published on the molecular mechanisms, in general, involved in branching morphogenesis, including those mechanisms, in particular, connected to Fgf10/Fgfr2b signaling. However, a comprehensive review looking at all the major biological and physical factors involved in branching, at the different scales at which branching operates, and the known role of Fgf10/Fgfr2b therein, is missing. In the current review, we attempt to summarize the existing literature on airway branching morphogenesis by taking a broad approach. We focus on the biophysical and mechanical forces directly shaping epithelial bud initiation, branch elongation, and branch tip bifurcation. We then shift focus to more passive means by which branching proceeds, via extracellular matrix remodeling and the influence of the other pulmonary arborized networks: the vasculature and nerves. We end the review by briefly discussing work in computational modeling of airway branching. Throughout, we emphasize the known or speculative effects of Fgfr2b signaling at each point of discussion. It is our aim to promote an understanding of branching morphogenesis that captures the multi-scalar biological and physical nature of the phenomenon, and the interdisciplinary approach to its study.

Of mitogens and morphogens: modelling Sonic Hedgehog mechanisms in vertebrate development

Sonic Hedgehog (Shh) Is a critical protein in vertebrate development, orchestrating patterning and growth in many developing systems. First described as a classic morphogen that patterns tissues through a spatial concentration gradient, subsequent studies have revealed a more complex mechanism, in which Shh can also regulate proliferation and differentiation. While the mechanism of action of Shh as a morphogen is well understood, it remains less clear how Shh might integrate patterning, proliferation and differentiation in a given tissue, to ultimately direct its morphogenesis. In tandem with experimental studies, mathematical modelling can help gain mechanistic insights into these processes and bridge the gap between Shh-regulated patterning and growth, by integrating these processes into a common theoretical framework. Here, we briefly review the roles of Shh in vertebrate development, focusing on its functions as a morphogen, mitogen and regulator of differentiation. We then discuss the contributions that modelling has made to our understanding of the action of Shh and highlight current challenges in using mathematical models in a quantitative and predictive way. This article is part of a discussion meeting issue 'Contemporary morphogenesis'.

Branching morphogenesis as a driver of renal development

Branching morphogenesis is an integral developmental mechanism central to the formation of a range of organs including the kidney, lung, pancreas and mammary gland. The ramified networks of epithelial tubules it establishes are critical for the processes of secretion, excretion and exchange mediated by these tissues. In the kidney, branching serves to establish the collecting duct system that transports urine from the nephrons into the renal pelvis, ureter and finally the bladder. Generally speaking, the formation of these networks in different organs begins with the specification and differentiation of simple bud-like organ anlage, which then undergo a process of elaboration, typically by bifurcation. This process is often governed by the interaction of progenitor cells at the tips of the epithelia with neighboring mesenchymal cell populations which direct the branching process and which often themselves differentiate to form part of the adult organ. In the kidney, the tips of ureteric bud elaborate through a dynamic cell signaling relationship with overlying nephron progenitor cell populations. These cells sequentially commit to differentiation and the resulting nephrons reintegrate with the ureteric epithelium as development progresses. This review will describe recent advances in understanding the how the elaboration of the ureteric bud is patterned and consider the extent to which this process is shared with other organs.

Space colonization by branching trachea explains the morphospace of a simple respiratory organ

Branching morphogenesis helps increase the efficiency of gas and liquid transport in many animal organs. Studies in several model organisms have highlighted the molecular and cellular complexity behind branching morphogenesis. To understand this complexity, computational models have been developed with the goal of identifying the "major rules" that globally explain the branching patterns. These models also guide further experimental exploration of the biological processes that execute and maintain these rules. In this paper we introduce the tracheal gills of mayfly (Ephemeroptera) larvae as a model system to study the generation of branched respiratory patterns. First, we describe the gills of the mayfly Cloeon dipterum, and quantitatively characterize the geometry of its branching trachea. We next extend this characterization to those of related species to generate the morphospace of branching patterns. Then, we show how an algorithm based on the "space colonization" concept (SCA) can generate this branching morphospace via growth towards a hypothetical attractor molecule (M). SCA differs from other branch-generating algorithms in that the geometry generated depends to a great extent on its perception of the "external" space available for branching, uses few rules and, importantly, can be easily translated into a realistic "biological patterning algorithm". We identified a gene in the C. dipterum genome (Cd-bnl) that is orthologous to the fibroblast growth factor branchless (bnl), which stimulates growth and branching of embryonic trachea in Drosophila. In C. dipterum, this gene is expressed in the gill margins and areas of finer tracheolar branching from thicker trachea. Thus, Cd-bnl may perform the function of M in our model. Finally, we discuss this general mechanism in the context of other branching pattern-generating algorithms.

Branching morphogenesis

Over the past 5 years, several studies have begun to uncover the links between the classical signal transduction pathways and the physical mechanisms that are used to sculpt branched tissues. These advances have been made, in part, thanks to innovations in live imaging and reporter animals. With modern research tools, our conceptual models of branching morphogenesis are rapidly evolving, and the differences in branching mechanisms between each organ are becoming increasingly apparent. Here, we highlight four branched epithelia that develop at different spatial scales, within different surrounding tissues and via divergent physical mechanisms. Each of these organs has evolved to employ unique branching strategies to achieve a specialized final architecture.

Mechanobiology of vertebrate gut morphogenesis

Approximately a century after D'Arcy Thompson's On Growth and Form, there continues to be widespread interest in the biophysical and mathematical basis of morphogenesis. Particularly over the past 20 years, this interest has led to great advances in our understanding of a broad range of processes in embryonic development through a quantitative, mechanically driven framework. Nowhere in vertebrate development is this more apparent than the development of endodermally derived organs. Here, we discuss recent advances in the study of gut development that have emerged primarily from mechanobiology-motivated approaches that span from gut tube morphogenesis and later organogenesis of the respiratory and gastrointestinal systems.

Lung regeneration: a tale of mice and men

The respiratory system is the main site of gas exchange with the external environment in complex terrestrial animals. Within the trachea and lungs are multiple different tissue niches each consisting of a myriad of cells types with critical roles in air conduction, gas exchange, providing important niche specific cell-cell interactions, connection to the cardiovascular system, and immune surveillance. How the respiratory system responds to external insults and executes the appropriate regenerative response remains challenging to study given the plethora of cell and tissue interactions for this to occur properly. This review will examine the various cell types and tissue niches found within the respiratory system and provide a comparison between mouse and human lungs and trachea to highlight important similarities and differences. Defining the critical gaps in knowledge in human lung and tracheal regeneration is critical for future development of therapies directed towards respiratory diseases.

Cell-based simulations of biased epithelial lung growth

During morphogenesis, epithelial tubes elongate. In the case of the mammalian lung, biased elongation has been linked to a bias in cell shape and cell division, but it has remained unclear whether a bias in cell shape along the axis of outgrowth is sufficient for biased outgrowth and how it arises. Here, we use our 2D cell-based tissue simulation software [Formula: see text] to investigate the conditions for biased epithelial outgrowth. We show that the observed bias in cell shape and cell division can result in the observed bias in outgrowth only in the case of strong cortical tension, and comparison to biological data suggests that the cortical tension in epithelia is likely sufficient. We explore mechanisms that may result in the observed bias in cell division and cell shapes. To this end, we test the possibility that the surrounding tissue or extracellular matrix acts as a mechanical constraint that biases growth in the longitudinal direction. While external compressive forces can result in the observed bias in outgrowth, we find that they do not result in the observed bias in cell shapes. We conclude that other mechanisms must exist that generate the bias in lung epithelial outgrowth.

Design Principles of Branching Morphogenesis in Filamentous Organisms

The radiation of life on Earth was accompanied by the diversification of multicellular body plans in the eukaryotic kingdoms Animalia, Plantae, Fungi and Chromista. Branching forms are ubiquitous in nature and evolved repeatedly in the above lineages. The developmental and genetic basis of branch formation is well studied in the three-dimensional shoot and root systems of land plants, and in animal organs such as the lung, kidney, mammary gland, vasculature, etc. Notably, recent thought-provoking studies combining experimental analysis and computational modeling of branching patterns in whole animal organs have identified global patterning rules and proposed unifying principles of branching morphogenesis. Filamentous branching forms represent one of the simplest expressions of the multicellular body plan and constitute a key step in the evolution of morphological complexity. Similarities between simple and complex branching forms distantly related in evolution are compelling, raising the question whether shared mechanisms underlie their development. Here, we focus on filamentous branching organisms that represent major study models from three distinct eukaryotic kingdoms, including the moss Physcomitrella patens (Plantae), the brown alga Ectocarpus sp. (Chromista), and the ascomycetes Neurospora crassa and Aspergillus nidulans (Fungi), and bring to light developmental regulatory mechanisms and design principles common to these lineages. Throughout the review we explore how the regulatory mechanisms of branching morphogenesis identified in other models, and in particular animal organs, may inform our thinking on filamentous systems and thereby advance our understanding of the diverse strategies deployed across the eukaryotic tree of life to evolve similar forms.

Morphogenesis software based on epigenetic code concept

The process of morphogenesis is an evolution of shape of an organism together with the differentiation of its parts. This process encompasses numerous biological processes ranging from embryogenesis to regeneration following crisis such as amputation or transplantation. A fundamental theoretical question is where exactly do these instructions for (re-)construction reside and how are they implemented?

We have recently proposed a set of concepts, aiming to respond to these questions and to provide an appropriate mathematical formalization of the geometry of morphogenesis [1]. First, we consider a possibility that the evolution of shape is determined by epigenetic information, responsible for realization of different types of cell events. Second, we suggest a set of rules for converting this epigenetic information into instructive signals for cell event for each cell, as well as for transforming it after each cell event. Next we give notions of cell state, determined by its epigenetic array, and cell event, which is a change of cell state, and formalize development as a graph (tree) of cell states connected by 5 types of cell events, corresponding to the processes of cell division, cell growth, cell death, cell movement and cell differentiation.

Here we present a Morphogenesis software capable to simulate an evolution of a 3D embryo starting from zygote, following a set of rules, based on our theoretical assumptions, and thus to provide a proof-of-concept of the hypothesis of epigenetic code regulation. The software creates a developing embryo and a corresponding graph of cell events according to the zygotic epigenetic spectrum and chosen parameters of the developmental rules. Variation of rules influencing the resulting shape of an embryo may help elucidating the principal laws underlying pattern formation.

Inductive signals in branching morphogenesis - lessons from mammary and salivary glands

Branching morphogenesis is a fundamental developmental program that generates large epithelial surfaces in a limited three-dimensional space. It is regulated by inductive tissue interactions whose effects are mediated by soluble signaling molecules, and cell-cell and cell-extracellular matrix interactions. Here, we will review recent studies on inductive signaling interactions governing branching morphogenesis in light of phenotypes of mouse mutants and ex vivo organ culture studies with emphasis on developing mammary and salivary glands. We will highlight advances in understanding how cell fate decisions are intimately linked with branching morphogenesis. We will also discuss novel insights into the molecular control of cellular mechanisms driving the formation of these arborized ductal structures and reflect upon how distinct spatial patterns are generated.

Cellular crosstalk in the development and regeneration of the respiratory system

The respiratory system, including the peripheral lungs, large airways and trachea, is one of the most recently evolved adaptations to terrestrial life. To support the exchange of respiratory gases, the respiratory system is interconnected with the cardiovascular system, and this interconnective nature requires a complex interplay between a myriad of cell types. Until recently, this complexity has hampered our understanding of how the respiratory system develops and responds to postnatal injury to maintain homeostasis. The advent of new single-cell sequencing technologies, developments in cellular and tissue imaging and advances in cell lineage tracing have begun to fill this gap. The view that emerges from these studies is that cellular and functional heterogeneity of the respiratory system is even greater than expected and also highly adaptive. In this Review, we explore the cellular crosstalk that coordinates the development and regeneration of the respiratory system. We discuss both the classic cell and developmental biology studies and recent single-cell analysis to provide an integrated understanding of the cellular niches that control how the respiratory system develops, interacts with the external environment and responds to injury.

Image-based modeling of kidney branching morphogenesis reveals GDNF-RET based Turing-type mechanism and pattern-modulating WNT11 feedback

Branching patterns and regulatory networks differ between branched organs. It has remained unclear whether a common regulatory mechanism exists and how organ-specific patterns can emerge. Of all previously proposed signalling-based mechanisms, only a ligand-receptor-based Turing mechanism based on FGF10 and SHH quantitatively recapitulates the lung branching patterns. We now show that a GDNF-dependent ligand-receptor-based Turing mechanism quantitatively recapitulates branching of cultured wildtype and mutant ureteric buds, and achieves similar branching patterns when directing domain outgrowth in silico. We further predict and confirm experimentally that the kidney-specific positive feedback between WNT11 and GDNF permits the dense packing of ureteric tips. We conclude that the ligand-receptor based Turing mechanism presents a common regulatory mechanism for lungs and kidneys, despite the differences in the molecular implementation. Given its flexibility and robustness, we expect that the ligand-receptor-based Turing mechanism constitutes a likely general mechanism to guide branching morphogenesis and other symmetry breaks during organogenesis.

Many organs develop through branching morphogenesis, but whether the underlying mechanisms are shared is unknown. Here, the authors show that a ligand-receptor based Turing mechanisms, similar to that observed in lung development, likely underlies branching morphogenesis of the kidney.

Mechanistic description of spatial processes using integrative modelling of noise-corrupted imaging data

Spatial patterns are ubiquitous on the subcellular, cellular and tissue level, and can be studied using imaging techniques such as light and fluorescence microscopy. Imaging data provide quantitative information about biological systems; however, mechanisms causing spatial patterning often remain elusive. In recent years, spatio-temporal mathematical modelling has helped to overcome this problem. Yet, outliers and structured noise limit modelling of whole imaging data, and models often consider spatial summary statistics. Here, we introduce an integrated data-driven modelling approach that can cope with measurement artefacts and whole imaging data. Our approach combines mechanistic models of the biological processes with robust statistical models of the measurement process. The parameters of the integrated model are calibrated using a maximum-likelihood approach. We used this integrated modelling approach to study in vivo gradients of the chemokine (C-C motif) ligand 21 (CCL21). CCL21 gradients guide dendritic cells and are important in the adaptive immune response. Using artificial data, we verified that the integrated modelling approach provides reliable parameter estimates in the presence of measurement noise and that bias and variance of these estimates are reduced compared to conventional approaches. The application to experimental data allowed the parametrization and subsequent refinement of the model using additional mechanisms. Among other results, model-based hypothesis testing predicted lymphatic vessel-dependent concentration of heparan sulfate, the binding partner of CCL21. The selected model provided an accurate description of the experimental data and was partially validated using published data. Our findings demonstrate that integrated statistical modelling of whole imaging data is computationally feasible and can provide novel biological insights.

Mathematical Approaches of Branching Morphogenesis

Many organs require a high surface to volume ratio to properly function. Lungs and kidneys, for example, achieve this by creating highly branched tubular structures during a developmental process called branching morphogenesis. The genes that control lung and kidney branching share a similar network structure that is based on ligand-receptor reciprocal signalling interactions between the epithelium and the surrounding mesenchyme. Nevertheless, the temporal and spatial development of the branched epithelial trees differs, resulting in organs of distinct shape and size. In the embryonic lung, branching morphogenesis highly depends on FGF10 signalling, whereas GDNF is the driving morphogen in the kidney. Knockout of Fgf10 and Gdnf leads to lung and kidney agenesis, respectively. However, FGF10 plays a significant role during kidney branching and both the FGF10 and GDNF pathway converge on the transcription factors ETV4/5. Although the involved signalling proteins have been defined, the underlying mechanism that controls lung and kidney branching morphogenesis is still elusive. A wide range of modelling approaches exists that differ not only in the mathematical framework (e.g., stochastic or deterministic) but also in the spatial scale (e.g., cell or tissue level). Due to advancing imaging techniques, image-based modelling approaches have proven to be a valuable method for investigating the control of branching events with respect to organ-specific properties. Here, we review several mathematical models on lung and kidney branching morphogenesis and suggest that a ligand-receptor-based Turing model represents a potential candidate for a general but also adaptive mechanism to control branching morphogenesis during development.

Synthetic mammalian pattern formation driven by differential diffusivity of Nodal and Lefty

A synthetic mammalian reaction-diffusion pattern has yet to be created, and Nodal-Lefty signaling has been proposed to meet conditions for pattern formation: Nodal is a short-range activator whereas Lefty is a long-range inhibitor. However, this pattern forming possibility has never been directly tested, and the underlying mechanisms of differential diffusivity of Nodal and Lefty remain unclear. Here, through a combination of synthetic and theoretical approaches, we show that a reconstituted Nodal-Lefty network in mammalian cells spontaneously gives rise to a pattern. Surprisingly, extracellular Nodal is confined underneath the cells, resulting in a narrow distribution compared with Lefty. The short-range distribution requires the finger 1 domain of Nodal, and transplantation of the finger 1 domain into Lefty shortens the distribution of Lefty, successfully preventing pattern formation. These results indicate that the differences in localization and domain structures between Nodal and Lefty, combined with the activator-inhibitor topology, are sufficient for reaction-diffusion patterning.

Nodal-Lefty signaling combines a short-range activator and a long-range inhibitor for axis formation and left-right patterning. Here the authors reconstitute a synthetic biology activator-inhibitor circuit of Nodal-Lefty to drive pattern formation in mammalian cells.

Spontaneous calcium activity in metanephric mesenchymal cells regulates branching morphogenesis in the embryonic kidney

The central role of calcium signaling during development of early vertebrates is well documented, but little is known about its role in mammalian embryogenesis. We have used immunofluorescence and time-lapse calcium imaging of cultured explanted embryonic rat kidneys to study the role of calcium signaling for branching morphogenesis. In mesenchymal cells, we recorded spontaneous calcium activity that was characterized by irregular calcium transients. The calcium signals were dependent on release of calcium from intracellular stores in the endoplasmic reticulum. Down-regulation of the calcium activity, both by blocking the sarco-endoplasmic reticulum Ca²⁺-ATPase and by chelating cytosolic calcium, resulted in retardation of branching morphogenesis and a reduced formation of primitive nephrons but had no effect on cell proliferation. We propose that spontaneous calcium activity contributes with a stochastic factor to the self-organizing process that controls branching morphogenesis, a major determinant of the ultimate number of nephrons in the kidney.-Fontana, J. M., Khodus, G. R., Unnersjö-Jess, D., Blom, H., Aperia, A., Brismar, H. Spontaneous calcium activity in metanephric mesenchymal cells regulates branching morphogenesis in the embryonic kidney.

A general framework dedicated to computational morphogenesis Part I - Constitutive equations

In order to understand living organisms, considerable experimental efforts and resources have been devoted to correlate genes and their expressions with cell, tissue, organ and whole organisms' phenotypes. This data driven approach to knowledge discovery has led to many breakthrough in our understanding of healthy and diseased states, and is paving the way to improve the diagnosis and treatment of diseases. Complementary to this data-driven approach, computational models of biological systems based on first principles have been developed in order to deepen our understanding of the multi-scale dynamics that drives normal and pathological biological functions. In this paper we describe the biological, physical and mathematical concepts that led to the design of a Computational Morphogenesis (CM) platform baptized Generic Modeling and Simulating Platform (GMSP). Its role is to generate realistic 3D multi-scale biological tissues from virtual stem cells and the intended target applications include in virtuo studies of normal and abnormal tissue (re)generation as well as the development of complex diseases such as carcinogenesis. At all space-scales of interest, biological agents interact with each other via biochemical, bioelectrical, and mechanical fields that operate in concert during embryogenesis, growth and adult life. The spatio-temporal dependencies of these fields can be modeled by physics-based constitutive equations that we propose to examine in relation to the landmark biological events that occur during embryogenesis.

Voltage-dependent Ca2+ channels promote branching morphogenesis of salivary glands by patterning differential growth

Branching morphogenesis is a crucial part of early developmental processes in diverse organs, but the detailed mechanism of this morphogenic event remains to be elucidated. Here we introduce an unknown mechanism leading to branching morphogenesis using mouse embryonic organotypic cultures with time-lapse live imaging. We found spatially expressed L-type voltage-dependent Ca²⁺ channels (VDCCs) in the peripheral layers of developing epithelial buds and identified the VDCCs as a core signaling mediator for patterning branching architecture. In this process, differential growth in peripheral layers by VDCC-induced ERK activity promoted cleft formation through an epithelial buckling-folding mechanism. Our findings reveal an unexpected role of VDCCs in developmental processes, and address a fundamental question regarding the initial process of branching morphogenesis.

Turing Instability-Driven Biofabrication of Branching Tissue Structures: A Dynamic Simulation and Analysis Based on the Reaction⁻Diffusion Mechanism †

Four-dimensional (4D) biofabrication techniques aim to dynamically produce and control three-dimensional (3D) biological structures that would transform their shapes or functionalities with time, when a stimulus is imposed or cell post-printing self-assembly occurs. The evolution of 3D branching patterns via self-assembly of cells is critical for the 4D biofabrication of artificial organs or tissues with branched geometry. However, it is still unclear how the formation and evolution of these branching patterns are biologically encoded. Here, we study the biofabrication of lung branching structures utilizing a simulation model based on Turing instability that raises a dynamic reaction⁻diffusion (RD) process of the biomolecules and cells. The simulation model incorporates partial differential equations of four variables, describing the tempo-spatial distribution of the variables in 3D over time. The simulation results present the formation and evolution process of 3D branching patterns over time and also interpret both the behaviors of side-branching and tip-splitting as the stalk grows and the fabrication style under an external concentration gradient of morphogen, through 3D visualization. This provides a theoretical framework for rationally guiding the 4D biofabrication of lung airway grafts via cellular self-organization, which would potentially reduce the complexity of future experimental research and number of trials.

Tissue geometry may govern lung branching mode selection

Lung branching morphogenesis proceeds in three stereotyped modes (domain, planar, and orthogonal branching). Much is known about the molecular players, including growth factors such as fibroblast growth factor 10 but it is unknown how these signals could actuate the different branching patterns. With the aim of identifying mechanisms that may determine the different branching modes, we developed a computational model of the epithelial lung bud and its surrounding mesenchyme. We studied transport of morphogens and localization of morphogen flux at lobe surfaces and lobe edges. We find that a single simple mechanism is theoretically capable of directing an epithelial tubule to elongate, bend, flatten, or bifurcate, depending solely on geometric ratios of the tissues in the vicinity of a growing tubule tip. Furthermore, the same simple mechanism is capable of generating orthogonal or planar branching, depending only on the same geometric ratios.

Branching morphogenesis in the developing kidney is governed by rules that pattern the ureteric tree

Metanephric kidney development is orchestrated by the iterative branching morphogenesis of the ureteric bud. We describe an underlying patterning associated with the ramification of this structure and show that this pattern is conserved between developing kidneys, in different parts of the organ and across developmental time. This regularity is associated with a highly reproducible branching asymmetry that is consistent with locally operative growth mechanisms. We then develop a class of tip state models to represent elaboration of the ureteric tree and describe rules for 'half-delay' branching morphogenesis that describe almost perfectly the patterning of this structure. Spatial analysis suggests that the observed asymmetry may arise from mutual suppression of bifurcation, but not extension, between the growing ureteric tips, and demonstrates that disruption of patterning occurs in mouse mutants in which the distribution of tips on the surface of the kidney is altered. These findings demonstrate that kidney development occurs by way of a highly conserved reiterative pattern of asymmetric bifurcation that is governed by intrinsic and locally operative mechanisms.

Symmetry-breaking in branching epithelia: cells on micro-patterns under flow challenge the hypothesis of positive feedback by a secreted autocrine inhibitor of motility

Branching morphogenesis of epithelia involves division of cells into leader (tip) and follower (stalk) cells. Published work on cell lines in culture has suggested that symmetry-breaking takes place via a secreted autocrine inhibitor of motility, the inhibitor accumulating more in concave regions of the culture boundary, slowing advance of cells there, and less in convex areas, allowing advance and a further exaggeration of the concave/convex difference. Here we test this hypothesis using a two-dimensional culture system that includes strong flow conditions to remove accumulating diffusible secretions. We find that, while motility does indeed follow boundary curvature in this system, flow makes no difference: this challenges the hypothesis of control by a diffusible secreted autocrine inhibitor.

Emerging technologies for prediction of drug candidate efficacy in the preclinical pipeline

The pharmaceutical industry is tackling increasingly complex multifactorial diseases, resulting in increases in research & development (R&D) costs and reductions in the success rates for drug candidates during Phase 2 and 3 clinical trials, with a lack of efficacy being the primary reason for drug candidate failure. This implies that the predictive power of current preclinical assays for drug candidate efficacy is suboptimal and, therefore, that alternatives should be developed. Here, I review emerging in vitro, imaging, and in silico technologies and discuss their potential contribution to drug efficacy assessment. Importantly, these technologies are complimentary and can be bundled into the preclinical platform. In particular, patient-on-a-chip recapitulates both human genetics and physiology. The response of a patient-on-a-chip to drug candidate treatment is monitored with light-sheet fluorescent microscopy and fed into the image-analysis pipeline to reconstruct an image-based systems-level model for disease pathophysiology and drug candidate mode of action. Thus, such models could be useful tools for assessing drug candidate efficacy and safety in humans.

Visualizing Morphogenesis with the Processing Programming Language

We used Processing, a visual artists' programming language developed at MIT Media Lab, to simulate cellular mechanisms of morphogenesis - the generation of form and shape in embryonic tissues. Based on observations of in vivo time-lapse image sequences, we created animations of neural cell motility responsible for elongating the spinal cord, and of optic axon branching dynamics that establish primary visual connectivity. These visual models underscore the significance of the computational decomposition of cellular dynamics underlying morphogenesis.

Computational models of airway branching morphogenesis

The bronchial network of the mammalian lung consists of millions of dichotomous branches arranged in a highly complex, space-filling tree. Recent computational models of branching morphogenesis in the lung have helped uncover the biological mechanisms that construct this ramified architecture. In this review, we focus on three different theoretical approaches - geometric modeling, reaction-diffusion modeling, and continuum mechanical modeling - and discuss how, taken together, these models have identified the geometric principles necessary to build an efficient bronchial network, as well as the patterning mechanisms that specify airway geometry in the developing embryo. We emphasize models that are integrated with biological experiments and suggest how recent progress in computational modeling has advanced our understanding of airway branching morphogenesis.