Branching patterns emerge in a mathematical model of the dynamics of lung development

Front propagation and global bifurcations in a multivariable reaction-diffusion model

We study the existence and stability of propagating fronts in Meinhardt's multivariable reaction-diffusion model of branching in one spatial dimension. We identify a saddle-node-infinite-period bifurcation of fronts that leads to episodic front propagation in the parameter region below propagation failure and show that this state is stable. Stable constant speed fronts exist only above this parameter value. We use numerical continuation to show that propagation failure is a consequence of the presence of a T-point corresponding to the formation of a heteroclinic cycle in a spatial dynamics description. Additional T-points are identified that are responsible for a large multiplicity of different unstable traveling front-peak states. The results indicate that multivariable models may support new types of behavior that are absent from typical two-variable models but may nevertheless be important in developmental processes such as branching and somitogenesis.

Instability mechanisms of repelling peak solutions in a multi-variable activator-inhibitor system

We study the linear stability properties of spatially localized single- and multi-peak states generated in a subcritical Turing bifurcation in the Meinhardt model of branching. In one spatial dimension, these states are organized in a foliated snaking structure owing to peak-peak repulsion but are shown to be all linearly unstable, with the number of unstable modes increasing with the number of peaks present. Despite this, in two spatial dimensions, direct numerical simulations reveal the presence of stable single- and multi-spot states whose properties depend on the repulsion from nearby spots as well as the shape of the domain and the boundary conditions imposed thereon. Front propagation is shown to trigger the growth of new spots while destabilizing others. The results indicate that multi-variable models may support new types of behavior that are absent from typical two-variable models.

Systems of pattern formation within developmental biology

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

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.

Conserved Mechanisms in the Formation of the Airways and Alveoli of the Lung

Branching is an intrinsic property of respiratory epithelium that can be induced and modified by signals emerging from the mesenchyme. However, during stereotypic branching morphogenesis of the airway, the relatively thick upper respiratory epithelium extrudes through a mesenchymal orifice to form a new branch, whereas during alveologenesis the relatively thin lower respiratory epithelium extrudes to form sacs or bubbles. Thus, both branching morphogenesis of the upper airway and alveolarization in the lower airway seem to rely on the same fundamental physical process: epithelial extrusion through an orifice. Here I propose that it is the orientation and relative stiffness of the orifice boundary that determines the stereotypy of upper airway branching as well as the orientation of individual alveolar components of the gas exchange surface. The previously accepted dogma of the process of alveologenesis, largely based on 2D microscopy, is that alveoli arise by erection of finger-like interalveolar septae to form septal clefts that subdivide pre-existing saccules, a process for which the contractile properties of specialized alveolar myofibroblasts are necessary. Here I suggest that airway tip splitting and stereotypical side domain branching are actually conserved processes, but modified somewhat by evolution to achieve both airway tip splitting and side branching of the upper airway epithelium, as well as alveologenesis. Viewed in 3D it is clear that alveolar “septal tips” are in fact ring or purse string structures containing elastin and collagen that only appear as finger like projections in cross section. Therefore, I propose that airway branch orifices as well as alveolar mouth rings serve to delineate and stabilize the budding of both airway and alveolar epithelium, from the tips and sides of upper airways as well as from the sides and tips of alveolar ducts. Certainly, in the case of alveoli arising laterally and with radial symmetry from the sides of alveolar ducts, the mouth of each alveolus remains within the plane of the side of the ductal lumen. This suggests that the thin epithelium lining these lateral alveolar duct buds may extrude or “pop out” from the duct lumen through rings rather like soap or gum bubbles, whereas the thicker upper airway epithelium extrudes through a ring like toothpaste from a tube to form a new branch.

Reaction-Diffusion Model-Based Research on Formation Mechanism of Neuron Dendritic Spine Patterns

The pattern abnormalities of dendritic spine, tiny protrusions on neuron dendrites, have been found related to multiple nervous system diseases, such as Parkinson's disease and schizophrenia. The determination of the factors affecting spine patterns is of vital importance to explore the pathogenesis of these diseases, and further, search the treatment method for them. Although the study of dendritic spines is a hot topic in neuroscience in recent years, there is still a lack of systematic study on the formation mechanism of its pattern. This paper provided a reinterpretation of reaction-diffusion model to simulate the formation process of dendritic spine, and further, study the factors affecting spine patterns. First, all four classic shapes of spines, mushroom-type, stubby-type, thin-type, and branched-type were reproduced using the model. We found that the consumption rate of substrates by the cytoskeleton is a key factor to regulate spine shape. Moreover, we found that the density of spines can be regulated by the amount of an exogenous activator and inhibitor, which is in accordance with the anatomical results found in hippocampal CA1 in SD rats with glioma. Further, we analyzed the inner mechanism of the above model parameters regulating the dendritic spine pattern through Turing instability analysis and drew a conclusion that an exogenous inhibitor and activator changes Turing wavelength through which to regulate spine densities. Finally, we discussed the deep regulation mechanisms of several reported regulators of dendritic spine shape and densities based on our simulation results. Our work might evoke attention to the mathematic model-based pathogenesis research for neuron diseases which are related to the dendritic spine pattern abnormalities and spark inspiration in the treatment research for these diseases.

The nonlinear initiation of side-branching by activator-inhibitor-substrate (Turing) morphogenesis

An understanding of the underlying mechanism of side-branching is paramount in controlling and/or therapeutically treating mammalian organs, such as lungs, kidneys, and glands. Motivated by an activator-inhibitor-substrate approach that is conjectured to dominate the initiation of side-branching in a pulmonary vascular pattern, I demonstrate a distinct transverse front instability in which new fingers grow out of an oscillatory breakup dynamics at the front line without any typical length scale. These two features are attributed to unstable peak solutions in 1D that subcritically emanate from Turing bifurcation and that exhibit repulsive interactions. The results are based on a bifurcation analysis and numerical simulations and provide a potential strategy toward also developing a framework of side-branching for other biological systems, such as plant roots and cellular protrusions.

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.

Wavelength of a Turing-type mechanism regulates the morphogenesis of meshwork patterns

The meshwork pattern is a significant pattern in the development of biological tissues and organs. It is necessary to explore the mathematical mechanism of meshwork pattern formation. In this paper, we found that the meshwork pattern is formed by four kinds of stalk behaviours: stalk extension, tip bifurcation, side branching and tip fusion. The Turing-type pattern underlying the meshwork pattern is a Turing spot pattern, which indicates that the Turing instability of the spot pattern promotes activator peak formation and then guides the formation of meshwork patterns. Then, we found that the Turing wavelength decreased in turn from tip bifurcation to side branching to tip fusion via statistical evaluation. Through the functional relationship between the Turing wavelength and model parameters ([Formula: see text] and [Formula: see text]), we found that parameters [Formula: see text] and [Formula: see text] had monotonic effects on the Turing wavelength and that parameter [Formula: see text] had nonmonotonic effects. Furthermore, we performed simulations of local meshwork pattern formation under variable model parameter values. The simulation results verified the corresponding relationship between the Turing wavelength and stalk behaviours and the functional relationship between the Turing wavelength and model parameters. The simulation results showed that the Turing wavelength regulated the meshwork pattern and that the small Turing wavelength facilitated dense meshwork pattern formation. Our work provides novel insight into and understanding of the formation of meshwork patterns. We believe that studies associated with network morphogenesis can benefit from our work.

The Lung Vasculature: A Driver or Passenger in Lung Branching Morphogenesis?

Multiple cellular, biochemical, and physical factors converge to coordinate organogenesis. During embryonic development, several organs such as the lung, salivary glands, mammary glands, and kidneys undergo rapid, but intricate, iterative branching. This biological process not only determines the overall architecture, size and shape of such organs but is also a pre-requisite for optimal organ function. The lung, in particular, relies on a vast surface area to carry out efficient gas exchange, and it is logical to suggest that airway branching during lung development represents a rate-limiting step in this context. Against this background, the vascular network develops in parallel to the airway tree and reciprocal interaction between these two compartments is critical for their patterning, branching, and co-alignment. In this mini review, we present an overview of the branching process in the developing mouse lung and discuss whether the vasculature plays a leading role in the process of airway epithelial branching.

Mesenchymal proteases and tissue fluidity remodel the extracellular matrix during airway epithelial branching in the embryonic avian lung

Reciprocal epithelial-mesenchymal signaling is essential for morphogenesis, including branching of the lung. In the mouse, mesenchymal cells differentiate into airway smooth muscle that wraps around epithelial branches, but this contractile tissue is absent from the early avian lung. Here, we have found that branching morphogenesis in the embryonic chicken lung requires extracellular matrix (ECM) remodeling driven by reciprocal interactions between the epithelium and mesenchyme. Before branching, the basement membrane wraps the airway epithelium as a spatially uniform sheath. After branch initiation, however, the basement membrane thins at branch tips; this remodeling requires mesenchymal expression of matrix metalloproteinase 2, which is necessary for branch extension but for not branch initiation. As branches extend, tenascin C (TNC) accumulates in the mesenchyme several cell diameters away from the epithelium. Despite its pattern of accumulation, TNC is expressed exclusively by epithelial cells. Branch extension coincides with deformation of adjacent mesenchymal cells, which correlates with an increase in mesenchymal fluidity at branch tips that may transport TNC away from the epithelium. These data reveal novel epithelial-mesenchymal interactions that direct ECM remodeling during airway branching morphogenesis.

Agent-based modeling of morphogenetic systems: Advantages and challenges

The complexity of morphogenesis poses a fundamental challenge to understanding the mechanisms governing the formation of biological patterns and structures. Over the past century, numerous processes have been identified as critically contributing to morphogenetic events, but the interplay between the various components and aspects of pattern formation have been much harder to grasp. The combination of traditional biology with mathematical and computational methods has had a profound effect on our current understanding of morphogenesis and led to significant insights and advancements in the field. In particular, the theoretical concepts of reaction–diffusion systems and positional information, proposed by Alan Turing and Lewis Wolpert, respectively, dramatically influenced our general view of morphogenesis, although typically in isolation from one another. In recent years, agent-based modeling has been emerging as a consolidation and implementation of the two theories within a single framework. Agent-based models (ABMs) are unique in their ability to integrate combinations of heterogeneous processes and investigate their respective dynamics, especially in the context of spatial phenomena. In this review, we highlight the benefits and technical challenges associated with ABMs as tools for examining morphogenetic events. These models display unparalleled flexibility for studying various morphogenetic phenomena at multiple levels and have the important advantage of informing future experimental work, including the targeted engineering of tissues and organs.

Developmental analyses of divarications in leaves of an aquatic fern Microsorum pteropus and its varieties

Plant leaves occur in diverse shapes. Divarication patterns that develop during early growths are one of key factors that determine leaf shapes. We utilized leaves of Microsorum pteropus, a semi-aquatic fern, and closely related varieties to analyze a variation in the divarication patterns. The leaves exhibited three major types of divarication: no lobes, bifurcation, and trifurcation (i.e., monopodial branching). Our investigation of their developmental processes, using time-lapse imaging, revealed localized growths and dissections of blades near each leaf apex. Restricted cell divisions responsible for the apical growths were confirmed using a pulse-chase strategy for EdU labeling assays.

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.

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.

The influence of a high fat diet on bone and soft tissue formation in Matrix Gla Protein knockout mice

Studies suggest bone growth and development are influenced by maternal nutrition, during intrauterine and early postnatal life. This study assessed the role of MGP and a maternal high fat diet on vitamin K-dependent proteins' gene expression and their impact on bone formation. Knockout (KO) offspring were smaller than wild type (WT) littermates, yet possessed the same volume of intrascapular brown adipose tissue. The total proportion of body fat was reduced, but only in animals on a control diet. Lung air volume was observed to be comparable in both KO and WT animals on the same diet. The degree of aortic calcification was reduced in KO animals maintained on a HF diet. KO females on the high fat diet showed reduced cortical bone volume and thickness in the femur and tibia. Gene expression levels of GGCX and VKOR were reduced in control fed KO animals suggesting a potential link between gene expression levels of MGP, GGCX, and VKOR and total volumes of bone, calcified soft tissue, and iBAT; with implications for modulation of body length and mass. Our results confirm the important role for vitamin K in bone and calcified soft tissue, but now extend this role to include iBAT.

Integrating Mechanical Force into Lung Development

In this issue of Developmental Cell, Tang et al. (2018) and Li et al. (2018) combine genetic manipulation, mechanical perturbation, and live imaging to show how mechanical forces and local growth factors intersect to influence epithelial behavior and cell fate specification within the developing lung.

Turing mechanism underlying a branching model for lung morphogenesis

The mammalian lung develops through branching morphogenesis. Two primary forms of branching, which occur in order, in the lung have been identified: tip bifurcation and side branching. However, the mechanisms of lung branching morphogenesis remain to be explored. In our previous study, a biological mechanism was presented for lung branching pattern formation through a branching model. Here, we provide a mathematical mechanism underlying the branching patterns. By decoupling the branching model, we demonstrated the existence of Turing instability. We performed Turing instability analysis to reveal the mathematical mechanism of the branching patterns. Our simulation results show that the Turing patterns underlying the branching patterns are spot patterns that exhibit high local morphogen concentration. The high local morphogen concentration induces the growth of branching. Furthermore, we found that the sparse spot patterns underlie the tip bifurcation patterns, while the dense spot patterns underlies the side branching patterns. The dispersion relation analysis shows that the Turing wavelength affects the branching structure. As the wavelength decreases, the spot patterns change from sparse to dense, the rate of tip bifurcation decreases and side branching eventually occurs instead. In the process of transformation, there may exists hybrid branching that mixes tip bifurcation and side branching. Since experimental studies have reported that branching mode switching from side branching to tip bifurcation in the lung is under genetic control, our simulation results suggest that genes control the switch of the branching mode by regulating the Turing wavelength. Our results provide a novel insight into and understanding of the formation of branching patterns in the lung and other biological systems.

Automated numerical simulation of biological pattern formation based on visual feedback simulation framework

There are various fantastic biological phenomena in biological pattern formation. Mathematical modeling using reaction-diffusion partial differential equation systems is employed to study the mechanism of pattern formation. However, model parameter selection is both difficult and time consuming. In this paper, a visual feedback simulation framework is proposed to calculate the parameters of a mathematical model automatically based on the basic principle of feedback control. In the simulation framework, the simulation results are visualized, and the image features are extracted as the system feedback. Then, the unknown model parameters are obtained by comparing the image features of the simulation image and the target biological pattern. Considering two typical applications, the visual feedback simulation framework is applied to fulfill pattern formation simulations for vascular mesenchymal cells and lung development. In the simulation framework, the spot, stripe, labyrinthine patterns of vascular mesenchymal cells, the normal branching pattern and the branching pattern lacking side branching for lung branching are obtained in a finite number of iterations. The simulation results indicate that it is easy to achieve the simulation targets, especially when the simulation patterns are sensitive to the model parameters. Moreover, this simulation framework can expand to other types of biological pattern formation.

Overview of Lung Development in the Newborn Human

In human neonates rapid adaptation from an aqueous intrauterine environment to permanent air breathing is the rate-limiting step for extrauterine life, failure of which justifies the existence of neonatal intensive care units. The lung develops at about 4-6 weeks' gestation in humans as a ventral outpouching of the primitive foregut into the surrounding ventral mesenchyme, termed the laryngotracheal groove. At its posterior end lie progenitor cells that form a pair of bronchial tubes, from which arise all the distal epithelial structures of the lung. In humans, formation of the distal gas exchange surfaces begins in utero at about 20 weeks' gestation and is substantially established by term. Stereotypic branching of the proximal airway ends relatively early at 16-18 weeks at the bronchoalveolar duct junctions. Distally, about 5 finger-like alveolar ducts arise from each bronchoalveolar duct junction and ramify outwards towards the pleura. The majority of alveolar air sacs arise from the sides of the alveolar ducts and each of these alveoli can have up to 5 daughter alveoli arising from the outer surface as subsequent buds. At the end of each alveolar duct lie the mouths of 5 interconnected alveoli. Each family of alveoli arising from each bronchoalveolar duct junction has a different shape depending upon the limitations imposed by the pleural surface as well as the interstitial fascial planes.

Do Vascular Networks Branch Optimally or Randomly across Spatial Scales?

Modern models that derive allometric relationships between metabolic rate and body mass are based on the architectural design of the cardiovascular system and presume sibling vessels are symmetric in terms of radius, length, flow rate, and pressure. Here, we study the cardiovascular structure of the human head and torso and of a mouse lung based on three-dimensional images processed via our software Angicart. In contrast to modern allometric theories, we find systematic patterns of asymmetry in vascular branching, potentially explaining previously documented mismatches between predictions (power-law or concave curvature) and observed empirical data (convex curvature) for the allometric scaling of metabolic rate. To examine why these systematic asymmetries in vascular branching might arise, we construct a mathematical framework to derive predictions based on local, junction-level optimality principles that have been proposed to be favored in the course of natural selection and development. The two most commonly used principles are material-cost optimizations (construction materials or blood volume) and optimization of efficient flow via minimization of power loss. We show that material-cost optimization solutions match with distributions for asymmetric branching across the whole network but do not match well for individual junctions. Consequently, we also explore random branching that is constrained at scales that range from local (junction-level) to global (whole network). We find that material-cost optimizations are the strongest predictor of vascular branching in the human head and torso, whereas locally or intermediately constrained random branching is comparable to material-cost optimizations for the mouse lung. These differences could be attributable to developmentally-programmed local branching for larger vessels and constrained random branching for smaller vessels.

The architecture of vascular networks must balance complex demands to efficiently deliver oxygen and resources throughout the entire body. These demands constrain the possible forms of vasculature. Because of these constraints and the indispensable role of vasculature for much of life, scientists have sought to identify systematic patterns in the structural properties of vascular networks and whether these patterns can be predicted from models based on biological and physical principles. These studies have been limited by the lack of extensive, detailed data. Using high-quality vascular network data obtained via our software, Angicart, we identify novel, systematic patterns of asymmetry in sizes and branching angles among sibling vessels from mouse lung and human head and torso. To examine what constraints might underlie these patterns, we investigate several explanations, including various types of optimal branching as well as random branching. The optimal branchings were derived locally with respect to constraints on material costs or power loss. For random branching we allowed the degree of randomness to vary from local to global spatial scales. By comparing predictions with real data, our study suggests that a key component in determining vascular branching is material cost with some randomness at local to intermediate spatial scales.

An in vitro-in silico interface platform for spatiotemporal analysis of pattern formation in collective epithelial cells

A multicellular organization is a complex resulting from the coordinated migration of cells to form a specific pattern. The directionality of migration is governed by the mechanical and molecular dynamics of factors secreted from the cells. The mechanism underlying pattern formation is too complex to unveil by culture experiments alone. A mathematical model could provide a powerful tool for elucidating the mechanism of pattern formation by computing the molecular dynamics, which are difficult to visualize by culture experiments. However, there tends to be a gap between mathematical models and experimental research due to incongruity between the idealized conditions of the model and the experimental results. This paper presents an in vitro-in silico interface platform for elucidating the logic of multicellular pattern formation. Two-dimensional collective cell pattern formation was developed using normal human bronchial epithelial cells. Then, geometrical control of collective cells followed by feedback iteration was used to bridge the gap between the mathematical model and in vitro experiments. The mechanisms underlying the pattern formation of bronchial epithelial cells were evaluated using a reaction-diffusion model. The results indicated that differences in the diffusion rates of the activator and inhibitor determine the direction of collective cell migration to form a specific pattern.

Cell-matrix mechanics and pattern formation in inflammatory cardiovascular calcification

Calcific diseases of the cardiovascular system, such as atherosclerotic calcification and calcific aortic valve disease, are widespread and clinically significant, causing substantial morbidity and mortality. Vascular cells, like bone cells, interact with their matrix substrate through molecular signals, and through biomechanical signals, such as traction forces transmitted from cytoskeleton to matrix. The interaction of contractile vascular cells with their matrix may be one of the most important factors controlling pathological mineralisation of the artery wall and cardiac valves. In many respects, the matricrine and matrix mechanical changes in calcific vasculopathy and valvulopathy resemble those occurring in embryonic bone development and normal bone mineralisation. The matrix proteins provide a microenvironment for propagation of crystal growth and provide mechanical cues to the cells that direct differentiation. Small contractions of the cytoskeleton may tug on integrin links to sites on matrix proteins, and thereby sense the stiffness, possibly through deformation of binding proteins causing release of differentiation factors such as products of the members of the transforming growth factor-β superfamily. Inflammation and matrix characteristics are intertwined: inflammation alters the matrix such as through matrix metalloproteinases, while matrix mechanical properties affect cellular sensitivity to inflammatory cytokines. The adhesive properties of the matrix also regulate self-organisation of vascular cells into patterns through reaction-diffusion phenomena and left-right chirality. In this review, we summarise the roles of extracellular matrix proteins and biomechanics in the development of inflammatory cardiovascular calcification.

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.

In vitro reconstruction of branched tubular structures from lung epithelial cells in high cell concentration gradient environment

We have succeeded in developing hollow branching structure in vitro commonly observed in lung airway using primary lung airway epithelial cells. Cell concentration gradient is the key factor that determines production of the branching cellular structures, as optimization of this component removes the need for heterotypic culture. The higher cell concentration leads to the more production of morphogens and increases the growth rate of cells. However, homogeneous high cell concentration does not make a branching structure. Branching requires sufficient space in which cells can grow from a high concentration toward a low concentration. Simulation performed using a reaction-diffusion model revealed that long-range inhibition prevents cells from branching when they are homogeneously spread in culture environments, while short-range activation from neighboring cells leads to positive feedback. Thus, a high cell concentration gradient is required to make branching structures. Spatial distributions of morphogens, such as BMP-4, play important roles in the pattern formation. This simple yet robust system provides an optimal platform for the further study and understanding of branching mechanisms in the lung airway, and will facilitate chemical and genetic studies of lung morphogenesis programs.

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.

Mechanisms of side branching and tip splitting in a model of branching morphogenesis

Recent experimental work in lung morphogenesis has described an elegant pattern of branching phenomena. Two primary forms of branching have been identified: side branching and tip splitting. In our previous study of lung branching morphogenesis, we used a 4 variable partial differential equation (PDE), due to Meinhardt, as our mathematical model to describe the reaction and diffusion of morphogens creating those branched patterns. By altering key parameters in the model, we were able to reproduce all the branching styles and the switch between branching modes. Here, we attempt to explain the branching phenomena described above, as growing out of two fundamental instabilities, one in the longitudinal (growth) direction and the other in the transverse direction. We begin by decoupling the original branching process into two semi-independent sub-processes, 1) a classic activator/inhibitor system along the growing stalk, and 2) the spatial growth of the stalk. We then reduced the full branching model into an activator/inhibitor model that embeds growth of the stalk as a controllable parameter, to explore the mechanisms that determine different branching patterns. We found that, in this model, 1) side branching results from a pattern-formation instability of the activator/inhibitor subsystem in the longitudinal direction. This instability is far from equilibrium, requiring a large inhomogeneity in the initial conditions. It successively creates periodic activator peaks along the growing stalk, each of which later on migrates out and forms a side branch; 2) tip splitting is due to a Turing-style instability along the transversal direction, that creates the spatial splitting of the activator peak into 2 simultaneously-formed peaks at the growing tip, the occurrence of which requires the widening of the growing stalk. Tip splitting is abolished when transversal stalk widening is prevented; 3) when both instabilities are satisfied, tip bifurcation occurs together with side branching.