The control of branching morphogenesis

Collective Cell Migration in Development

Collective cell migration is a key process in developmental biology, facilitating the bulk movement of cells in the morphogenesis of animal tissues. Predictive understanding in this field remains challenging due to the complexity of many interacting cells, their signalling, and microenvironmental factors - all of which can give rise to non-intuitive emergent behaviours. In this chapter we discuss biological examples of collective cell migration from a range of model systems, developmental stages, and spatial scales: border cell migration and haemocyte dispersal in Drosophila, gastrulation, neural crest migration, lateral line formation in zebrafish, and branching morphogenesis; as well as examples of developmental defects and similarities to metastatic invasion in cancer. These examples will be used to illustrate principles that we propose to be important: heterogeneity of cell states, substrate-free migration, contact-inhibition of locomotion, confinement and repulsive cues, cell-induced (or self-generated) gradients, stochastic group decisions, tissue mechanics, and reprogramming of cell behaviours. Understanding how such principles play a common, overarching role across multiple biological systems may lead towards a more integrative understanding of the causes and function of collective cell migration in developmental biology, and to potential strategies for the repair of developmental defects, the prevention and control of cancer, and advances in tissue engineering.

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.

Statistical theory of branching morphogenesis

Branching morphogenesis remains a subject of abiding interest. Although much is known about the gene regulatory programs and signaling pathways that operate at the cellular scale, it has remained unclear how the macroscopic features of branched organs, including their size, network topology and spatial patterning, are encoded. Lately, it has been proposed that, these features can be explained quantitatively in several organs within a single unifying framework. Based on large-scale organ reconstructions and cell lineage tracing, it has been argued that morphogenesis follows from the collective dynamics of sublineage-restricted self-renewing progenitor cells, localized at ductal tips, that act cooperatively to drive a serial process of ductal elongation and stochastic tip bifurcation. By correlating differentiation or cell cycle exit with proximity to maturing ducts, this dynamic results in the specification of a complex network of defined density and statistical organization. These results suggest that, for several mammalian tissues, branched epithelial structures develop as a self-organized process, reliant upon a strikingly simple, but generic, set of local rules, without recourse to a rigid and deterministic sequence of genetically programmed events. Here, we review the basis of these findings and discuss their implications.

Recent advances in branching mechanisms underlying neuronal morphogenesis

Proper neuronal wiring is central to all bodily functions, sensory perception, cognition, memory, and learning. Establishment of a functional neuronal circuit is a highly regulated and dynamic process involving axonal and dendritic branching and navigation toward appropriate targets and connection partners. This intricate circuitry includes axo-dendritic synapse formation, synaptic connections formed with effector cells, and extensive dendritic arborization that function to receive and transmit mechanical and chemical sensory inputs. Such complexity is primarily achieved by extensive axonal and dendritic branch formation and pruning. Fundamental to neuronal branching are cytoskeletal dynamics and plasma membrane expansion, both of which are regulated via numerous extracellular and intracellular signaling mechanisms and molecules. This review focuses on recent advances in understanding the biology of neuronal branching.

A review of inflammatory mechanism in airway diseases

BACKGROUND

Inflammation in the lung is the body's natural response to injury. It acts to remove harmful stimuli such as pathogens, irritants, and damaged cells and initiate the healing process. Acute and chronic pulmonary inflammation are seen in different respiratory diseases such as; acute respiratory distress syndrome, chronic obstructive pulmonary disease (COPD), asthma, and cystic fibrosis (CF).

FINDINGS

In this review, we found that inflammatory response in COPD is determined by the activation of epithelial cells and macrophages in the respiratory tract. Epithelial cells and macrophages discharge transforming growth factor-β (TGF-β), which trigger fibroblast proliferation and tissue remodeling. Asthma leads to airway hyper-responsiveness, obstruction, mucus hyper-production, and airway-wall remodeling. Cytokines, allergens, chemokines, and infectious agents are the main stimuli that activate signaling pathways in epithelial cells in asthma. Mutation of the CF transmembrane conductance regulator (CFTR) gene results in CF. Mutations in CFTR influence the lung epithelial innate immune function that leads to exaggerated and ineffective airway inflammation that fails to abolish pulmonary pathogens. We present mechanistic computational models (based on ordinary differential equations, partial differential equations and agent-based models) that have been applied in studying the complex physiological and pathological mechanisms of chronic inflammation in different airway diseases.

CONCLUSION

The scope of the present review is to explore the inflammatory mechanism in airway diseases and highlight the influence of aging on airways' inflammation mechanism. The main goal of this review is to encourage research collaborations between experimentalist and modelers to promote our understanding of the physiological and pathological mechanisms that control inflammation in different airway diseases.

Information Thermodynamics of Turing Patterns

We set up a rigorous thermodynamic description of reaction-diffusion systems driven out of equilibrium by time-dependent space-distributed chemostats. Building on the assumption of local equilibrium, nonequilibrium thermodynamic potentials are constructed exploiting the symmetries of the chemical network topology. It is shown that the canonical (resp. semigrand canonical) nonequilibrium free energy works as a Lyapunov function in the relaxation to equilibrium of a closed (resp. open) system, and its variation provides the minimum amount of work needed to manipulate the species concentrations. The theory is used to study analytically the Turing pattern formation in a prototypical reaction-diffusion system, the one-dimensional Brusselator model, and to classify it as a genuine thermodynamic nonequilibrium phase transition.

Development of the human prostate

This paper provides a detailed compilation of human prostatic development that includes human fetal prostatic gross anatomy, histology, and ontogeny of selected epithelial and mesenchymal differentiation markers and signaling molecules throughout the stages of human prostatic development: (a) pre-bud urogenital sinus (UGS), (b) emergence of solid prostatic epithelial buds from urogenital sinus epithelium (UGE), (c) bud elongation and branching, (d) canalization of the solid epithelial cords, (e) differentiation of luminal and basal epithelial cells, and (f) secretory cytodifferentiation. Additionally, we describe the use of xenografts to assess the actions of androgens and estrogens on human fetal prostatic development. In this regard, we report a new model of de novo DHT-induction of prostatic development from xenografts of human fetal female urethras, which emphasizes the utility of the xenograft approach for investigation of initiation of human prostatic development. These studies raise the possibility of molecular mechanistic studies on human prostatic development through the use of tissue recombinants composed of mutant mouse UGM combined with human fetal prostatic epithelium. Our compilation of human prostatic developmental processes is likely to advance our understanding of the pathogenesis of benign prostatic hyperplasia and prostate cancer as the neoformation of ductal-acinar architecture during normal development is shared during the pathogenesis of benign prostatic hyperplasia and prostate cancer.

3D culture models for studying branching morphogenesis in the mammary gland and mammalian lung

The intricate architecture of branched tissues and organs has fascinated scientists and engineers for centuries. Yet-despite their ubiquity-the biophysical and biochemical mechanisms by which tissues and organs undergo branching morphogenesis remain unclear. With the advent of three-dimensional (3D) culture models, an increasingly powerful and diverse set of tools are available for investigating the development and remodeling of branched tissues and organs. In this review, we discuss the application of 3D culture models for studying branching morphogenesis of the mammary gland and the mammalian lung in the context of normal development and disease. While current 3D culture models lack the cellular and molecular complexity observed in vivo, we emphasize how these models can be used to answer targeted questions about branching morphogenesis. We highlight the specific advantages and limitations of using 3D culture models to study the dynamics and mechanisms of branching in the mammary gland and mammalian lung. Finally, we discuss potential directions for future research and propose strategies for engineering the next generation of 3D culture models for studying tissue morphogenesis.

Defining Lineage Potential and Fate Behavior of Precursors during Pancreas Development

Pancreas development involves a coordinated process in which an early phase of cell segregation is followed by a longer phase of lineage restriction, expansion, and tissue remodeling. By combining clonal tracing and whole-mount reconstruction with proliferation kinetics and single-cell transcriptional profiling, we define the functional basis of pancreas morphogenesis. We show that the large-scale organization of mouse pancreas can be traced to the activity of self-renewing precursors positioned at the termini of growing ducts, which act collectively to drive serial rounds of stochastic ductal bifurcation balanced by termination. During this phase of branching morphogenesis, multipotent precursors become progressively fate-restricted, giving rise to self-renewing acinar-committed precursors that are conveyed with growing ducts, as well as ductal progenitors that expand the trailing ducts and give rise to delaminating endocrine cells. These findings define quantitatively how the functional behavior and lineage progression of precursor pools determine the large-scale patterning of pancreatic sub-compartments.

Bayesian inference of agent-based models: a tool for studying kidney branching morphogenesis

The adult mammalian kidney has a complex, highly-branched collecting duct epithelium that arises as a ureteric bud sidebranch from an epithelial tube known as the nephric duct. Subsequent branching of the ureteric bud to form the collecting duct tree is regulated by subcellular interactions between the epithelium and a population of mesenchymal cells that surround the tips of outgrowing branches. The mesenchymal cells produce glial cell-line derived neurotrophic factor (GDNF), that binds with RET receptors on the surface of the epithelial cells to stimulate several subcellular pathways in the epithelium. Such interactions are known to be a prerequisite for normal branching development, although competing theories exist for their role in morphogenesis. Here we introduce the first agent-based model of ex vivo kidney uretic branching. Through comparison with experimental data, we show that growth factor-regulated growth mechanisms can explain early epithelial cell branching, but only if epithelial cell division depends in a switch-like way on the local growth factor concentration; cell division occurring only if the driving growth factor level exceeds a threshold. We also show how a recently-developed method, "Approximate Approximate Bayesian Computation", can be used to infer key model parameters, and reveal the dependency between the parameters controlling a growth factor-dependent growth switch. These results are consistent with a requirement for signals controlling proliferation and chemotaxis, both of which are previously identified roles for GDNF.

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.

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.

Simulation of Morphogen and Tissue Dynamics

Morphogenesis, the process by which an adult organism emerges from a single cell, has fascinated humans for a long time. Modeling this process can provide novel insights into development and the principles that orchestrate the developmental processes. This chapter focuses on the mathematical description and numerical simulation of developmental processes. In particular, we discuss the mathematical representation of morphogen and tissue dynamics on static and growing domains, as well as the corresponding tissue mechanics. In addition, we give an overview of numerical methods that are routinely used to solve the resulting systems of partial differential equations. These include the finite element method and the Lattice Boltzmann method for the discretization as well as the arbitrary Lagrangian-Eulerian method and the Diffuse-Domain method to numerically treat deforming domains.

A Unifying Theory of Branching Morphogenesis

The morphogenesis of branched organs remains a subject of abiding interest. Although much is known about the underlying signaling pathways, it remains unclear how macroscopic features of branched organs, including their size, network topology, and spatial patterning, are encoded. Here, we show that, in mouse mammary gland, kidney, and human prostate, these features can be explained quantitatively within a single unifying framework of branching and annihilating random walks. Based on quantitative analyses of large-scale organ reconstructions and proliferation kinetics measurements, we propose that morphogenesis follows from the proliferative activity of equipotent tips that stochastically branch and randomly explore their environment but compete neutrally for space, becoming proliferatively inactive when in proximity with neighboring ducts. These results show that complex branched epithelial structures develop as a self-organized process, reliant upon a strikingly simple but generic rule, without recourse to a rigid and deterministic sequence of genetically programmed events.

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Branching morphogenesis follows conserved statistical rules in multiple organs

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Ductal tips grow and branch as default state and stop dividing in high-density regions

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Model reproduces quantitatively organ properties in a parameter-free manner

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Shows that complex organ formation proceeds in a stochastic, self-organized manner

Cellular heterogeneity in the ureteric progenitor niche and distinct profiles of branching morphogenesis in organ development

Branching morphogenesis creates arborized epithelial networks. In the mammalian kidney, an epithelial progenitor pool at ureteric branch tips (UBTs) creates the urine-transporting collecting system. Using region-specific mouse reporter strains, we performed an RNA-seq screen, identifying tip- and stalk-enriched gene sets in the developing collecting duct system. Detailed in situ hybridization studies of tip-enriched predictions identified UBT-enriched gene sets conserved between the mouse and human kidney. Comparative spatial analysis of their UBT niche expression highlighted distinct patterns of gene expression revealing novel molecular heterogeneity within the UBT progenitor population. To identify kidney-specific and shared programs of branching morphogenesis, comparative expression studies on the developing mouse lung were combined with in silico analysis of the developing mouse salivary gland. These studies highlight a shared gene set with multi-organ tip enrichment and a gene set specific to UBTs. This comprehensive analysis extends our current understanding of the ureteric branch tip niche.

RETRACTED: Btbd7 is essential for region-specific epithelial cell dynamics and branching morphogenesis in vivo

Branching morphogenesis of developing organs requires coordinated but poorly understood changes in epithelial cell-cell adhesion and cell motility. We report that Btbd7 is a crucial regulator of branching morphogenesis in vivo. Btbd7 levels are elevated in peripheral cells of branching epithelial end buds, where it enhances cell motility and cell-cell adhesion dynamics. Genetic ablation of Btbd7 in mice disrupts branching morphogenesis of salivary gland, lung and kidney. Btbd7 knockout results in more tightly packed outer bud cells, which display stronger E-cadherin localization, reduced cell motility and decreased dynamics of transient cell separations associated with cleft formation; inner bud cells remain unaffected. Mechanistic analyses using in vitro MDCK cells to mimic outer bud cell behavior establish that Btbd7 promotes loss of E-cadherin from cell-cell adhesions with enhanced migration and transient cell separation. Btbd7 can enhance E-cadherin ubiquitination, internalization, and degradation in MDCK and peripheral bud cells for regulating cell dynamics. These studies show how a specific regulatory molecule, Btbd7, can function at a local region of developing organs to regulate dynamics of cell adhesion and motility during epithelial branching morphogenesis.

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.

Patterned cell and matrix dynamics in branching morphogenesis

Many embryonic organs undergo branching morphogenesis to maximize their functional epithelial surface area. Branching morphogenesis requires the coordinated interplay of multiple types of cells with the extracellular matrix (ECM). During branching morphogenesis, new branches form by "budding" or "clefting." Cell migration, proliferation, rearrangement, deformation, and ECM dynamics have varied roles in driving budding versus clefting in different organs. Elongation of the newly formed branch and final maturation of the tip involve cellular mechanisms that include cell elongation, intercalation, convergent extension, proliferation, and differentiation. New methodologies such as high-resolution live imaging, tension sensors, and force-mapping techniques are providing exciting new opportunities for future research into branching morphogenesis.

Fuzzy-Logic Based Detection and Characterization of Junctions and Terminations in Fluorescence Microscopy Images of Neurons

Digital reconstruction of neuronal cell morphology is an important step toward understanding the functionality of neuronal networks. Neurons are tree-like structures whose description depends critically on the junctions and terminations, collectively called critical points, making the correct localization and identification of these points a crucial task in the reconstruction process. Here we present a fully automatic method for the integrated detection and characterization of both types of critical points in fluorescence microscopy images of neurons. In view of the majority of our current studies, which are based on cultured neurons, we describe and evaluate the method for application to two-dimensional (2D) images. The method relies on directional filtering and angular profile analysis to extract essential features about the main streamlines at any location in an image, and employs fuzzy logic with carefully designed rules to reason about the feature values in order to make well-informed decisions about the presence of a critical point and its type. Experiments on simulated as well as real images of neurons demonstrate the detection performance of our method. A comparison with the output of two existing neuron reconstruction methods reveals that our method achieves substantially higher detection rates and could provide beneficial information to the reconstruction process.

Intraspecific scaling laws are preserved in ventricular hypertrophy but not in heart failure

It is scientifically and clinically important to understand the structure-function scaling of coronary arterial trees in compensatory (e.g., left and right ventricular hypertrophy, LVH and RVH) and decompensatory vascular remodeling (e.g., congestive heart failure, CHF). This study hypothesizes that intraspecific scaling power laws of vascular trees are preserved in hypertrophic hearts but not in CHF swine hearts. To test the hypothesis, we carried out the scaling analysis based on morphometry and hemodynamics of coronary arterial trees in moderate LVH, severe RVH, and CHF compared with age-matched respective control hearts. The scaling exponents of volume-diameter, length-volume, and flow-diameter power laws in control hearts were consistent with the theoretical predictions (i.e., 3, 7/9, and 7/3, respectively), which remained unchanged in LVH and RVH hearts. The scaling exponents were also preserved with an increase of body weight during normal growth of control animals. In contrast, CHF increased the exponents of volume-diameter and flow-diameter scaling laws to 4.25 ± 1.50 and 3.15 ± 1.49, respectively, in the epicardial arterial trees. This study validates the predictive utility of the scaling laws to diagnose vascular structure and function in CHF hearts to identify the borderline between compensatory and decompensatory remodeling.

A new mechanism for spatial pattern formation via lateral and protrusion-mediated lateral signalling

Tissue organization and patterning are critical during development when genetically identical cells take on different fates. Lateral signalling plays an important role in this process by helping to generate self-organized spatial patterns in an otherwise uniform collection of cells. Recent data suggest that lateral signalling can be mediated both by junctional contacts between neighbouring cells and via cellular protrusions that allow non-neighbouring cells to interact with one another at a distance. However, it remains unclear precisely how signalling mediated by these distinct types of cell-cell contact can physically contribute to the generation of complex patterns without the assistance of diffusible morphogens or pre-patterns. To explore this question, in this work we develop a model of lateral signalling based on a single receptor/ligand pair as exemplified by Notch and Delta. We show that allowing the signalling kinetics to differ at junctional versus protrusion-mediated contacts, an assumption inspired by recent data which show that the cleavage of Notch in several systems requires both Delta binding and the application of mechanical force, permits individual cells to act to promote both lateral activation and lateral inhibition. Strikingly, under this model, in which Delta can sequester Notch, a variety of patterns resembling those typical of reaction-diffusion systems is observed, together with more unusual patterns that arise when we consider changes in signalling kinetics, and in the length and distribution of protrusions. Importantly, these patterns are self-organizing-so that local interactions drive tissue-scale patterning. Together, these data show that protrusions can, in principle, generate different types of patterns in addition to contributing to long-range signalling and to pattern refinement.

Modeling mammary organogenesis from biological first principles: Cells and their physical constraints

In multicellular organisms, relations among parts and between parts and the whole are contextual and interdependent. These organisms and their cells are ontogenetically linked: an organism starts as a cell that divides producing non-identical cells, which organize in tri-dimensional patterns. These association patterns and cells types change as tissues and organs are formed. This contextuality and circularity makes it difficult to establish detailed cause and effect relationships. Here we propose an approach to overcome these intrinsic difficulties by combining the use of two models; 1) an experimental one that employs 3D culture technology to obtain the structures of the mammary gland, namely, ducts and acini, and 2) a mathematical model based on biological principles. The typical approach for mathematical modeling in biology is to apply mathematical tools and concepts developed originally in physics or computer sciences. Instead, we propose to construct a mathematical model based on proper biological principles. Specifically, we use principles identified as fundamental for the elaboration of a theory of organisms, namely i) the default state of cell proliferation with variation and motility and ii) the principle of organization by closure of constraints. This model has a biological component, the cells, and a physical component, a matrix which contains collagen fibers. Cells display agency and move and proliferate unless constrained; they exert mechanical forces that i) act on collagen fibers and ii) on other cells. As fibers organize, they constrain the cells on their ability to move and to proliferate. The model exhibits a circularity that can be interpreted in terms of closure of constraints. Implementing the mathematical model shows that constraints to the default state are sufficient to explain ductal and acinar formation, and points to a target of future research, namely, to inhibitors of cell proliferation and motility generated by the epithelial cells. The success of this model suggests a step-wise approach whereby additional constraints imposed by the tissue and the organism could be examined in silico and rigorously tested by in vitro and in vivo experiments, in accordance with the organicist perspective we embrace.

ESE-1 in Early Development: Approaches for the Future

E26 transformation-specific (Ets) family of transcription factors are characterized by the presence of Ets-DNA binding domain and have been found to be highly involved in hematopoiesis and various tissue differentiation. ESE-1, or Elf3 in mice, is a member of epithelium-specific Ets sub-family which is most prominently expressed in epithelial tissues such as the gut, mammary gland, and lung. The role of ESE-1 during embryogenesis had long been alluded from 30% fetal lethality in homozygous knockout mice and its high expression in preimplantation mouse embryos, but there has been no in-depth of analysis of ESE-1 function in early development. With improved proteomics, gene editing tools and increasing knowledge of ESE-1 function in adult tissues, we hereby propose future research directions for the study of ESE-1 in embryogenesis, including studying its regulation at the protein level and at the protein family level, as well as better defining the developmental phase under investigation. Understanding the role of ESE-1 in early development will provide new insights into its involvement in tissue regeneration and cancer, as well as how it functions with other Ets factors as a protein family.

Mathematical study on robust tissue pattern formation in growing epididymal tubule

Tissue pattern formation during development is a reproducible morphogenetic process organized by a series of kinetic cellular activities, leading to the building of functional and stable organs. Recent studies focusing on mechanical aspects have revealed physical mechanisms on how the cellular activities contribute to the formation of reproducible tissue patterns; however, the understanding for what factors achieve the reproducibility of such patterning and how it occurs is far from complete. Here, I focus on a tube pattern formation during murine epididymal development, and show that two factors influencing physical design for the patterning, the proliferative zone within the tubule and the viscosity of tissues surrounding to the tubule, control the reproducibility of epididymal tubule pattern, using a mathematical model based on experimental data. Extensive numerical simulation of the simple mathematical model revealed that a spatially localized proliferative zone within the tubule, observed in experiments, results in more reproducible tubule pattern. Moreover, I found that the viscosity of tissues surrounding to the tubule imposes a trade-off regarding pattern reproducibility and spatial accuracy relating to the region where the tubule pattern is formed. This indicates an existence of optimality in material properties of tissues for the robust patterning of epididymal tubule. The results obtained by numerical analysis based on experimental observations provide a general insight on how physical design realizes robust tissue pattern formation.

A Geometrically-Constrained Mathematical Model of Mammary Gland Ductal Elongation Reveals Novel Cellular Dynamics within the Terminal End Bud

Mathematics is often used to model biological systems. In mammary gland development, mathematical modeling has been limited to acinar and branching morphogenesis and breast cancer, without reference to normal duct formation. We present a model of ductal elongation that exploits the geometrically-constrained shape of the terminal end bud (TEB), the growing tip of the duct, and incorporates morphometrics, region-specific proliferation and apoptosis rates. Iterative model refinement and behavior analysis, compared with biological data, indicated that the traditional metric of nipple to the ductal front distance, or percent fat pad filled to evaluate ductal elongation rate can be misleading, as it disregards branching events that can reduce its magnitude. Further, model driven investigations of the fates of specific TEB cell types confirmed migration of cap cells into the body cell layer, but showed their subsequent preferential elimination by apoptosis, thus minimizing their contribution to the luminal lineage and the mature duct.

Our paper describes a mathematical model of mammary ductal elongation during pubertal development. We make several conclusions that will be of interest to scientists studying mammary gland biology, epithelial tube formation, and branching morphogenesis. First, our model indicates that a common measurement of developmental outgrowth (‘percent fat pad filled’) underestimates the total growth and leads to mischaracterization of mutant phenotypes. Second, we show that cap cells, a population enriched with putative mammary stem cells, do not contribute to the luminal lineage as previously hypothesized. Further, we find that a high percentage of proliferation in these cells is not used productively to actually form the mammary duct. We believe our model has future application to other branching organs and also for the modeling of disease states in the breast.

Geranylgeranyl Diphosphate Synthase Modulates Fetal Lung Branching Morphogenesis Possibly through Controlling K-Ras Prenylation

G proteins play essential roles in regulating fetal lung development, and any defects in their expression or function (eg, activation or posttranslational modification) can lead to lung developmental malformation. Geranylgeranyl diphosphate synthase (GGPPS) can modulate protein prenylation that is required for protein membrane-anchoring and activation. Here, we report that GGPPS regulates fetal lung branching morphogenesis possibly through controlling K-Ras prenylation during fetal lung development. GGPPS was continuously expressed in lung epithelium throughout whole fetal lung development. Specific deletion of geranylgeranyl diphosphate synthase 1 (Ggps1) in lung epithelium during fetal lung development resulted in neonatal respiratory distress syndrome-like disease. The knockout mice died at postnatal day 1 of respiratory failure, and the lungs showed compensatory pneumonectasis, pulmonary atelectasis, and hyaline membranes. Subsequently, we proved that lung malformations in Ggps1-deficient mice resulted from the failure of fetal lung branching morphogenesis. Further investigation revealed Ggps1 deletion blocked K-Ras geranylgeranylation and extracellular signal-related kinase 1 or 2/mitogen-activated protein kinase signaling, which in turn disturbed fibroblast growth factor 10 regulation on fetal lung branching morphogenesis. Collectively, our data suggest that GGPPS is essential for maintaining fetal lung branching morphogenesis, which is possibly through regulating K-Ras prenylation.

Spatiotemporal patterns of sortilin and SorCS2 localization during organ development

BACKGROUND

Sortilin and SorCS2 are part of the Vps10p receptor family. They have both been studied in nervous tissue with several important functions revealed, while their expression and possible functions in developing peripheral tissue remain poorly understood. Here we deliver a thorough characterization of the prenatal localization of sortilin and SorCS2 in mouse peripheral tissue.

RESULTS

Sortilin is highly expressed in epithelial tissues of the developing lung, nasal cavity, kidney, pancreas, salivary gland and developing intrahepatic bile ducts. Furthermore tissues such as the thyroid gland, developing cartilage and ossifying bone also show high expression of sortilin together with cell types such as megakaryocytes in the liver. SorCS2 is primarily expressed in mesodermally derived tissues such as striated muscle, adipose tissue, ossifying bone and general connective tissue throughout the body, as well as in lung epithelia. Furthermore, the adrenal gland and liver show high expression of SorCS2 in embryos 13.5 days old.

CONCLUSIONS

The possible functions relating to the expression patterns of Sortilin and SorCS2 in development are numerous and hopefully this paper will help to generate new hypotheses to further our understanding of the Vps10p receptor family.

Short-range growth inhibitory signals from the epithelium can drive non-stereotypic branching in the pancreas

Many organs such as the vasculature, kidney, lungs, pancreas and several other glands form ramified networks of tubes that either maximize exchange surfaces between two compartments or minimize the volume of an organ dedicated to the production and local delivery of a cell-derived product. The structure of these tubular networks can be stereotyped, as in the lungs, or stochastic with large variations between individuals, as in the pancreas. The principles driving stereotyped branching have attracted much attention and several models have been proposed and refined. Here we focus on the pancreas, as a model of non-stereotyped branching. In many ramified tubular organs, an important role of the mesenchyme as a source of branching signals has been proposed, including in the pancreas. However, our previous work has shown that in the absence of mesenchyme, epithelial cells seeded in vitro in Matrigel form heavily branched organoids. Here we experimentally show that pancreatic organoids grow primarily at the tips. Furthermore, in contrast to classical 'depletion of activator' mechanisms, organoids growing in close vicinity seem not to affect each other's growth before they get in contact. We recapitulate these observations in an in silico model of branching assuming a 'local inhibitor' is secreted by the epithelium. Remarkably this simple mechanism is sufficient to generate branched organoids similar to those observed in vitro, including their transition from filled spheres to a tree like structure. Quantifying the similarity between in silico and in vitro development through a normalized surface to volume ratio, our in silico model predicts that inhibition is likely to be cooperative and that the diffusing inhibitor decays within a length scale of 10-20 μm.

FGF-Regulated ETV Transcription Factors Control FGF-SHH Feedback Loop in Lung Branching

The mammalian lung forms its elaborate tree-like structure following a largely stereotypical branching sequence. While a number of genes have been identified to play essential roles in lung branching, what coordinates the choice between branch growth and new branch formation has not been elucidated. Here we show that loss of FGF-activated transcription factor genes, Etv4 and Etv5 (collectively Etv), led to prolonged branch tip growth and delayed new branch formation. Unexpectedly, this phenotype is more similar to mutants with increased rather than decreased FGF activity. Indeed, an increased Fgf10 expression is observed, and reducing Fgf10 dosage can attenuate the Etv mutant phenotype. Further evidence indicates that ETV inhibits Fgf10 via directly promoting Shh expression. SHH in turn inhibits local Fgf10 expression and redirects growth, thereby initiating new branches. Together, our findings establish ETV as a key node in the FGF-ETV-SHH inhibitory feedback loop that dictates branching periodicity.

Beyond cell proliferation in avian facial morphogenesis

The upper jaw in vertebrates forms from several prominences that arise around the stomodeum or primitive mouth. These prominences undergo coordinated growth and morphogenesis to fuse and form the face. Undirected, regionalized cell proliferation is thought to be the driving force behind the morphogenesis of the facial prominences. However, recent findings suggest that directed cell behaviors in the mesenchyme (e.g., directed cell division, directed cell movement, convergent extension) might be required for successful face formation. Here we discuss the evidence for this view and how directed behaviors may interact with the basement membrane to regulate morphogenesis of the facial region. We believe that future research in these largely unexplored areas could significantly impact our understanding of facial morphogenesis.

Growth, ageing and scaling laws of coronary arterial trees

Despite the well-known design principles of vascular systems, it is unclear whether the vascular arterial tree obeys some scaling constraints during normal growth and ageing in a given species. Based on the micro-computed tomography measurements of coronary arterial trees in mice at different ages (one week to more than eight months), we show a constant exponent of 3/4, but age-dependent scaling coefficients in a length-volume scaling law (Lc=K(length-volume) · Vc³/⁴; Lc is the crown length, Vc is the crown volume, K(length-volume) is the age-dependent scaling coefficient) during normal growth and ageing. The constant 3/4 exponent represents the self-similar fractal-like branching pattern (i.e. basic mechanism to regulate the development of vascular trees within a species), whereas the age-dependent scaling coefficients characterize the structural growth or resorption of vascular trees during normal growth or ageing, respectively. This study enhances the understanding of age-associated changes in vascular structure and function.

A global sensitivity analysis approach for morphogenesis models

BACKGROUND

Morphogenesis is a developmental process in which cells organize into shapes and patterns. Complex, non-linear and multi-factorial models with images as output are commonly used to study morphogenesis. It is difficult to understand the relation between the uncertainty in the input and the output of such 'black-box' models, giving rise to the need for sensitivity analysis tools. In this paper, we introduce a workflow for a global sensitivity analysis approach to study the impact of single parameters and the interactions between them on the output of morphogenesis models.

RESULTS

To demonstrate the workflow, we used a published, well-studied model of vascular morphogenesis. The parameters of this cellular Potts model (CPM) represent cell properties and behaviors that drive the mechanisms of angiogenic sprouting. The global sensitivity analysis correctly identified the dominant parameters in the model, consistent with previous studies. Additionally, the analysis provided information on the relative impact of single parameters and of interactions between them. This is very relevant because interactions of parameters impede the experimental verification of the predicted effect of single parameters. The parameter interactions, although of low impact, provided also new insights in the mechanisms of in silico sprouting. Finally, the analysis indicated that the model could be reduced by one parameter.

CONCLUSIONS

We propose global sensitivity analysis as an alternative approach to study the mechanisms of morphogenesis. Comparison of the ranking of the impact of the model parameters to knowledge derived from experimental data and from manipulation experiments can help to falsify models and to find the operand mechanisms in morphogenesis. The workflow is applicable to all 'black-box' models, including high-throughput in vitro models in which output measures are affected by a set of experimental perturbations.

Tissue patterning and cellular mechanics

In development, cells organize into biological tissues through cell growth, migration, and differentiation. Globally, this process is dictated by a genetically encoded program in which secreted morphogens and cell-cell interactions prompt the adoption of unique cell fates. Yet, at its lowest level, development is achieved through the modification of cell-cell adhesion and actomyosin-based contractility, which set the level of tension within cells and dictate how they pack together into tissues. The regulation of tension within individual cells and across large groups of cells is a major driving force of tissue organization and the basis of all cell shape change and cell movement in development.

Transcriptomic analyses of regenerating adult feathers in chicken

Background

Feathers have diverse forms with hierarchical branching patterns and are an excellent model for studying the development and evolution of morphological traits. The complex structure of feathers allows for various types of morphological changes to occur. The genetic basis of the structural differences between different parts of a feather and between different types of feather is a fundamental question in the study of feather diversity, yet there is only limited relevant information for gene expression during feather development.

Results

We conducted transcriptomic analysis of five zones of feather morphologies from two feather types at different times during their regeneration after plucking. The expression profiles of genes associated with the development of feather structure were examined. We compared the gene expression patterns in different types of feathers and different portions of a feather and identified morphotype-specific gene expression patterns. Many candidate genes were identified for growth control, morphogenesis, or the differentiation of specific structures of different feather types.

Conclusion

This study laid the ground work for studying the evolutionary origin and diversification of feathers as abundant data were produced for the study of feather morphogenesis. It significantly increased our understanding of the complex molecular and cellular events in feather development processes and provided a foundation for future studies on the development of other skin appendages.

Electronic supplementary material

The online version of this article (doi:10.1186/s12864-015-1966-6) contains supplementary material, which is available to authorized users.

Quantifying stretch and secretion in the embryonic lung: Implications for morphogenesis

Branching in the embryonic lung is controlled by a variety of morphogens. Mechanics is also believed to play a significant role in lung branching. The relative roles and interactions of these two broad factors are challenging to determine. We considered three hypotheses for explaining why tracheal occlusion triples branching with no overall increase in size. Both hypotheses are based on tracheal occlusion blocking the exit of secretions. (H1) Increased lumen pressure stretches tissues; stretch receptors at shoulders of growing tips increase local rate of branching. (H2) Blocking exit of secretions blocks advective transport of morphogens, leading to (H2a) increased overall concentration of morphogens or (H2b) increased flux of morphogens at specific locations. We constructed and analyzed computational models of tissue stretch and solute transport in a 3D lung geometry. Observed tissue stresses and stretches were predominantly in locations unrelated to subsequent branch locations, suggesting that tissue stretch (H1) is not the mechanism of enhancement of branching. Morphogen concentration in the mesenchyme (H2a) increased with tracheal occlusion, consistent with previously reported results. Morphogen flux at the epithelial surface (H2b) completely changed its distribution pattern when the trachea was occluded, tripling the number of locations at which it was elevated. Our results are consistent with the hypothesis that tracheal occlusion blocks outflow of secretions, leading to a higher number of high-flux locations at branching tips, in turn leading to a large increase in number of branching locations.

Lung cancer-a fractal viewpoint

Fractals are mathematical constructs that show self-similarity over a range of scales and non-integer (fractal) dimensions. Owing to these properties, fractal geometry can be used to efficiently estimate the geometrical complexity, and the irregularity of shapes and patterns observed in lung tumour growth (over space or time), whereas the use of traditional Euclidean geometry in such calculations is more challenging. The application of fractal analysis in biomedical imaging and time series has shown considerable promise for measuring processes as varied as heart and respiratory rates, neuronal cell characterization, and vascular development. Despite the advantages of fractal mathematics and numerous studies demonstrating its applicability to lung cancer research, many researchers and clinicians remain unaware of its potential. Therefore, this Review aims to introduce the fundamental basis of fractals and to illustrate how analysis of fractal dimension (FD) and associated measurements, such as lacunarity (texture) can be performed. We describe the fractal nature of the lung and explain why this organ is particularly suited to fractal analysis. Studies that have used fractal analyses to quantify changes in nuclear and chromatin FD in primary and metastatic tumour cells, and clinical imaging studies that correlated changes in the FD of tumours on CT and/or PET images with tumour growth and treatment responses are reviewed. Moreover, the potential use of these techniques in the diagnosis and therapeutic management of lung cancer are discussed.

Algorithmically generated rodent hepatic vascular trees in arbitrary detail

Physiologically realistic geometric models of the vasculature in the liver are indispensable for modelling hepatic blood flow, the main connection between the liver and the organism. Current in vivo imaging techniques do not provide sufficiently detailed vascular trees for many simulation applications, so it is necessary to use algorithmic refinement methods. The method of Constrained Constructive Optimization (CCO) (Schreiner et al., 2006) is well suited for this purpose. Its results after calibration have been previously compared to experimentally acquired human vascular trees (Schwen and Preusser, 2012). The goal of this paper is to extend this calibration to the case of rodents (mice and rats), the most commonly used animal models in liver research. Based on in vivo and ex vivo micro-CT scans of rodent livers and their vasculature, we performed an analysis of various geometric features of the vascular trees. Starting from pruned versions of the original vascular trees, we applied the CCO procedure and compared these algorithmic results to the original vascular trees using a suitable similarity measure. The calibration of the postprocessing improved the algorithmic results compared to those obtained using standard CCO. In terms of angular features, the average similarity increased from 0.27 to 0.61, improving the total similarity from 0.28 to 0.40. Finally, we applied the calibrated algorithm to refine measured vascular trees to the (higher) level of detail desired for specific applications. Having successfully adapted the CCO algorithm to the rodent model organism, the resulting individual-specific refined hepatic vascular trees can now be used for advanced modeling involving, e.g., detailed blood flow simulations.

An interplay of geometry and signaling enables robust lung branching morphogenesis

Early branching events during lung development are stereotyped. Although key regulatory components have been defined, the branching mechanism remains elusive. We have now used a developmental series of 3D geometric datasets of mouse embryonic lungs as well as time-lapse movies of cultured lungs to obtain physiological geometries and displacement fields. We find that only a ligand-receptor-based Turing model in combination with a particular geometry effect that arises from the distinct expression domains of ligands and receptors successfully predicts the embryonic areas of outgrowth and supports robust branch outgrowth. The geometry effect alone does not support bifurcating outgrowth, while the Turing mechanism alone is not robust to noisy initial conditions. The negative feedback between the individual Turing modules formed by fibroblast growth factor 10 (FGF10) and sonic hedgehog (SHH) enlarges the parameter space for which the embryonic growth field is reproduced. We therefore propose that a signaling mechanism based on FGF10 and SHH directs outgrowth of the lung bud via a ligand-receptor-based Turing mechanism and a geometry effect.

Functional Role of the microRNA-200 Family in Breast Morphogenesis and Neoplasia

Branching epithelial morphogenesis is closely linked to epithelial-to-mesenchymal transition (EMT), a process important in normal development and cancer progression. The miR-200 family regulates epithelial morphogenesis and EMT through a negative feedback loop with the ZEB1 and ZEB2 transcription factors. miR-200 inhibits expression of ZEB1/2 mRNA, which in turn can down-regulate the miR-200 family that further results in down-regulation of E-cadherin and induction of a mesenchymal phenotype. Recent studies show that the expression of miR-200 genes is high during late pregnancy and lactation, thereby indicating that these miRs are important for breast epithelial morphogenesis and differentiation. miR-200 genes have been studied intensively in relation to breast cancer progression and metastasis, where it has been shown that miR-200 members are down-regulated in basal-like breast cancer where the EMT phenotype is prominent. There is growing evidence that the miR-200 family is up-regulated in distal breast metastasis indicating that these miRs are important for colonization of metastatic breast cancer cells through induction of mesenchymal to epithelial transition. The dual role of miR-200 in primary and metastatic breast cancer is of interest for future therapeutic interventions, making it important to understand its role and interacting partners in more detail.

Cellular and physical mechanisms of branching morphogenesis

Branching morphogenesis is the developmental program that builds the ramified epithelial trees of various organs, including the airways of the lung, the collecting ducts of the kidney, and the ducts of the mammary and salivary glands. Even though the final geometries of epithelial trees are distinct, the molecular signaling pathways that control branching morphogenesis appear to be conserved across organs and species. However, despite this molecular homology, recent advances in cell lineage analysis and real-time imaging have uncovered surprising differences in the mechanisms that build these diverse tissues. Here, we review these studies and discuss the cellular and physical mechanisms that can contribute to branching morphogenesis.

Feedback, receptor clustering, and receptor restriction to single cells yield large Turing spaces for ligand-receptor-based Turing models

Turing mechanisms can yield a large variety of patterns from noisy, homogenous initial conditions and have been proposed as patterning mechanism for many developmental processes. However, the molecular components that give rise to Turing patterns have remained elusive, and the small size of the parameter space that permits Turing patterns to emerge makes it difficult to explain how Turing patterns could evolve. We have recently shown that Turing patterns can be obtained with a single ligand if the ligand-receptor interaction is taken into account. Here we show that the general properties of ligand-receptor systems result in very large Turing spaces. Thus, the restriction of receptors to single cells, negative feedbacks, regulatory interactions among different ligand-receptor systems, and the clustering of receptors on the cell surface all greatly enlarge the Turing space. We further show that the feedbacks that occur in the FGF10-SHH network that controls lung branching morphogenesis are sufficient to result in large Turing spaces. We conclude that the cellular restriction of receptors provides a mechanism to sufficiently increase the size of the Turing space to make the evolution of Turing patterns likely. Additional feedbacks may then have further enlarged the Turing space. Given their robustness and flexibility, we propose that receptor-ligand-based Turing mechanisms present a general mechanism for patterning in biology.