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.     

Cell-Based Multi-Parametric Model of Cleft Progression during Submandibular Salivary Gland Branching Morphogenesis

Cleft formation during submandibular salivary gland branching morphogenesis is the critical step initiating the growth and development of the complex adult organ. Previous experimental studies indicated requirements for several epithelial cellular processes, such as proliferation, migration, cell-cell adhesion, cell-extracellular matrix (matrix) adhesion, and cellular contraction in cleft formation; however, the relative contribution of each of these processes is not fully understood since it is not possible to experimentally manipulate each factor independently. We present here a comprehensive analysis of several cellular parameters regulating cleft progression during branching morphogenesis in the epithelial tissue of an early embryonic salivary gland at a local scale using an on lattice Monte-Carlo simulation model, the Glazier-Graner-Hogeweg model. We utilized measurements from time-lapse images of mouse submandibular gland organ explants to construct a temporally and spatially relevant cell-based 2D model. Our model simulates the effect of cellular proliferation, actomyosin contractility, cell-cell and cell-matrix adhesions on cleft progression, and it was used to test specific hypotheses regarding the function of these parameters in branching morphogenesis. We use innovative features capturing several aspects of cleft morphology and quantitatively analyze clefts formed during functional modification of the cellular parameters. Our simulations predict that a low epithelial mitosis rate and moderate level of actomyosin contractility in the cleft cells promote cleft progression. Raising or lowering levels of contractility and mitosis rate resulted in non-progressive clefts. We also show that lowered cell-cell adhesion in the cleft region and increased cleft cell-matrix adhesions are required for cleft progression. Using a classifier-based analysis, the relative importance of these four contributing cellular factors for effective cleft progression was determined as follows: cleft cell contractility, cleft region cell-cell adhesion strength, epithelial cell mitosis rate, and cell-matrix adhesion strength.     

胚胎肾分支形态发生调控因素

胚胎肾发育最初阶段是中肾导管尾端在胶质细胞源性神经营养因子诱导下向背侧长出输尿管芽,而后成纤维细胞生长因子、肝细胞生长因子、骨形成蛋白、基质金属蛋白酶、整合素和粘附分子相继表达,作用于输尿管芽和间充质细胞,诱导分支形态发生,包括输尿管芽向间充质侵入、延伸以及间充质细胞向上皮转化。上述这些分子在功能上存在部分重叠与拮抗,维持细胞增殖和分化的平衡,从而保证输尿管芽形成正常的分支结构。本文对肾脏发育时期分支形态发生的调控因素进行综述。     

A Compartmental Model for Activity-Dependent Dendritic Spine Branching

Dendritic spines are small, mushroom-like protrusions from the arbor of a neuron in the central nervous system. Interdependent changes in the morphology, biochemistry, and activity of spines have been associated with learning and memory. Moreover, post-mortem cortices from patients with Alzheimer’s or Parkinson’s disease exhibit biochemical and physical alterations within their dendritic arbors and a reduction in the number of dendritic spines. For over a decade, experimentalists have observed perforations in postsynaptic densities on dendritic spines after induction of long-term potentiation, a sustained enhancement of response to a brief electrical or chemical stimulus, associated with learning and memory. In more recent work, some suggest that activity-dependent intraspine calcium may regulate the surface area of the spine head, and reorganization of postsynaptic densities on the surface. In this paper, we develop a model of a dendritic spine with the ability to partition its transmission and receptor zones, as well as the entire spine head. Simulations are initially performed with fixed parameters for morphology to study electrical properties and identify parameters that increase efficacy of the synaptic connection. Equations are then introduced to incorporate calcium as a second messenger in regulating continuous changes in morphology. In the model, activity affects compartmental calcium, which regulates spine head morphology. Conversely, spine head morphology affects the level of local activity, whether the spines are modeled with passive membrane properties, or excitable membrane using Hodgkin–Huxley kinetics. Results indicate that merely separating the postsynaptic receptors on the surface of the spine may add to the diversity of circuitry, but does not change the efficacy of the synapse. However, when the surface area of the spine is a dynamic variable, efficacy of the synapse may vary continuously over time.     

A Model for Leaf Growth

A model for leaf growth is constructed. The state of the leafat any time is defined by eight variables; five of these definethe ‘chemical’state of the leaf (labile carbohydrate,labile nitrogen, degradable structure, non-degradable structureand tissue water), the other three define its physical state(volume, area and thickness). The main assumption of the modelis that the rate of synthesis of non-degradable structural material(cell walls) is a function of the rate of water uptake (andthence expansion) of the leaf tissues. The rate of water uptakeis assumed to depend upon the amount of osmotically active solutein the leaf, and to be opposed by elastic and inelastic forcesin the leaf tissues, which increase with leaf size. The model simulates a number of the observed features of leafgrowth. For example, it qualitatively describes the observedchanges in leaf thickness and rate of photosynthesis per unitleaf area with different growth light levels. The model canalso be used to describe changes in metabolic activity duringontogenesis of a leaf. leaf growth, mechanistic model, photosynthesis, water uptake     

小鼠胎肺分支形态发生的分子机制

哺乳动物在早期胚胎发育过程中,肺发育经历了气管分支的形态发生、树样结构上皮管道的形成,并伴随着血管的发育而发生的气体通路和肺泡的分化等过程.肺发生涉及到许多复杂的分子机制.肺形态学的变化受到一系列持家基因、激素、核转录因子、生长因子及其他因素的综合调控.目前已经发现决定肺分支形态发生的许多重要因子.本文根据目前最新研究进展,阐述了小鼠胚胎肺在分支形态发生过程中,上皮与间充质之间诱导的信号通路之间的相互作用及其对呼吸树形态建成的调控机制.     

Whole-mount Immunohistochemical Analysis for Embryonic Limb Skin Vasculature: a Model System to Study Vascular Branching Morphogenesis in Embryo

Whole-mount immunohistochemical analysis for imaging the entire vasculature is pivotal for understanding the cellular mechanisms of branching morphogenesis. We have developed the limb skin vasculature model to study vascular development in which a pre-existing primitive capillary plexus is reorganized into a hierarchically branched vascular network. Whole-mount confocal microscopy with multiple labelling allows for robust imaging of intact blood vessels as well as their cellular components including endothelial cells, pericytes and smooth muscle cells, using specific fluorescent markers. Advances in this limb skin vasculature model with genetic studies have improved understanding molecular mechanisms of vascular development and patterning. The limb skin vasculature model has been used to study how peripheral nerves provide a spatial template for the differentiation and patterning of arteries. This video article describes a simple and robust protocol to stain intact blood vessels with vascular specific antibodies and fluorescent secondary antibodies, which is applicable for vascularized embryonic organs where we are able to follow the process of vascular development.Download video file.^{(59M, mov)}     

Morphogenesis of Simple and Compound Leaves: A Critical Review

The leaves of seed plants evolved from a primitive shoot system and are generated as determinate dorsiventral appendages at the flanks of radial indeterminate shoots. The remarkable variation of leaves has remained a constant source of fascination, and their developmental versatility has provided an advantageous platform to study genetic regulation of subtle, and sometimes transient, morphological changes. Here, we describe how eudicot plants recruited conserved shoot meristematic factors to regulate growth of the basic simple leaf blade and how subsets of these factors are subsequently re-employed to promote and maintain further organogenic potential. By comparing tractable genetic programs of species with different leaf types and evaluating the pros and cons of phylogenetic experimental procedures, we suggest that simple and compound leaves, and, by the same token, leaflets and serrations, are regulated by distinct ontogenetic programs. Finally, florigen, in its capacity as a general growth regulator, is presented as a new upper-tier systemic modulator in the patterning of compound leaves.     

Morphogenesis in Kyoto: A Confluence of Cell and Developmental Biology

Understanding morphogenesis is the ultimate multidisciplinary (ad)venture. Three-dimensional tissues are generated from the actions of genes, biochemical pathways, and cells that form multicellular networks and interact with their biomechanical environment. A comprehensive explanation of morphogenetic processes must encompass these different levels of analysis. A recent meeting in Kyoto on “Building the Body Plan: How Cell Adhesion, Signaling, and Cytoskeletal Regulation Shape Morphogenesis” highlighted recent advances in tackling this challenging problem.     

TheAfGene Regulates Timing and Direction of Major Developmental Events during Leaf Morphogenesis in Garden Pea (Pisum sativum)

The wildtype leaf of the garden pea possesses proximal pairsof leaflets and distal pairs of tendrils in the blade region.Theafila (af) mutation causes leaflets to be replaced by compound(branched) tendrils. We characterized the morphological variationin leaf form along the plant axis and leaf development in earlyand late postembryonic leaves onafilaplants to infer the roleof theAfgene. Leaf forms are more diverse early in shoot ontogenyonafilaplants.Afinfluences pinna length and pinna branchingin addition to pinna type. Pinna initiation in the proximalregion ofafilaleaf primordia is basipetal and delayed comparedto wildtype plants. In addition, pinna development in the proximalregion ofafilaleaves occurs for a longer period of time thanon wildtype leaf primordia. Therefore,Afregulates the timingand direction of leaf developmental processes in the proximalregion of the leaf, but has little effect on the distal region.These data support the heterochronic model of pea leaf morphogenesisproposed by Luet al. (International Journal of Plant Science157:311–355, 1996).Copyright 1999 Annals of Botany Company. afila,Fabaceae, garden pea, heterochrony, leaf morphogenesis,Pisum sativum.     

Deterministic and Stochastic Rules of Branching Govern Dendrite Morphogenesis of Sensory Neurons

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Spatial Restriction of FGF Signaling by a Matrix Metalloprotease Controls Branching Morphogenesis

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Highlights? Drosophila Matrix Metalloprotease (Mmp) inhibits FGF signaling ? An FGF – MMP feedback loop regulates branching morphogenesis ? Mmp2 spatially regulates FGF signaling in epithelia     

A Model for Leaf Expansion in Cucumber

A mechanistic model of leaf growth and expansion is described.This involves photosynthesis, the synthesis and degradationof enzymatic machinery from carbon and nitrogen substrates,the import or export of these substrates, and finally, the synthesisof primary and secondary cell wall material. The latter is treatedusing a novel approach to give a natural limit to cell and leafexpansion, depending upon the relative amounts of primary andsecondary wall material, which determine wall extensibility.Solutions are obtained to the model, which involves five statevariables and 27 parameters, and the results are compared withand fitted to an extensive set of experimental data on the firstleaf of the cucumber plant. leaf expansion, model, cucumber     

The Role of Colony Size on Tunnel Branching Morphogenesis in Ant Nests

Many ant species excavate nests that are made up of chambers and interconnecting tunnels. There is a general trend of an increase in nest complexity with increasing population size. This complexity reflects a higher ramification and anastomosis of tunnels that can be estimated by the meshedness coefficient of the tunnelling networks. It has long been observed that meshedness increases with colony size within and across species, but no explanation has been provided so far. Since colony size is a strong factor controlling collective digging, a high value of the meshedness could simply be a side effect of a larger number of workers. To test this hypothesis, we study the digging dynamics in different group size of ants Messor sancta. We build a model of collective digging that is calibrated from the experimental data. Model''s predictions successfully reproduce the topological properties of tunnelling networks observed in experiments, including the increase of the meshedness with group size. We then use the model to investigate situations in which collective digging progresses outward from a centre corresponding to the way tunnelling behaviour occurs in field conditions. Our model predicts that, when all other parameters are kept constant, an increase of the number of workers leads to a higher value of the meshedness and a transition from tree-like structures to highly meshed networks. Therefore we conclude that colony size is a key factor determining tunnelling network complexity in ant colonies.