A mechanism for early branching in lung morphogenesis

The lung is a highly branched fluid-filled structure, that develops by repeated dichotomous branching of a single bud off the foregut, of epithelium invaginating into mesenchyme. Incorporating the known stress response of developing lung tissues, we model the developing embryonic lung in fluid mechanical terms. We suggest that the repeated branching of the early embryonic lung can be understood as the natural physical consequence of the interactions of two or more plastic substances with surface tension between them. The model makes qualitative and quantitative predictions, as well as suggesting an explanation for such observed phenomena as the asymmetric second branching of the embryonic bronchi.     

Hair morphogenesis inAcetabularia mediterranea: Temperature-dependent spacing and models of morphogen waves

Summary Whorls of sterile hairs inA. mediterranea show, at the moment of first appearance of hair initials, a spacing independent of number of hairs in the whorl but dependent on temperature. By changing the temperature at various times before appearance of hair initials, the pattern-forming event can be located at about 3–4 hours before initials become visible.The temperature dependence of spacing is like that of a chemical rate parameter: In (spacing)versus 1/T is linear. This suggests that the spacing is controlled by kinetic rather than structural factors, and correlates well with reaction-diffusion theory.Mathematical analysis and computer simulation have been used to show that the observed sequence of tip-flattening followed by whorl initiation can be interpreted in terms of published models for generation of dissipative structures by reaction and diffusion, and that at least two sequential processes must occur, the first of which shifts growth activity from extremity to circumference of the growing tip, permitting the second to operate around the circumference.Submitted to workshop on Morphogenesis inAcetabularia, Berlin (West), September 1980.     

Involvement of Wnt-5a in chondrogenic pattern formation in the chick limb bud

Members of the Wnt family are known to play diverse roles in the organogenesis of vertebrates. The full-coding sequences of chicken Wnt-5a were identified and the role it plays in limb development was examined by comparing its expression pattern with that of two other Wnt members, Wnt-4 and Wnt-11, and by misexpressing it with a retrovirus vector in the limb bud. Wnt-5a expression is detected in the limb-forming region at stage 14, and in the apical ectodermal ridge and distal mesenchyme of the limb bud. The signal was graded along the proximal-distal axis at stages 20-28 and also along the anterior-posterior axis during early stages. It disappeared in the cartilage-forming region after stage 26, and was restricted to the region surrounding the phalanges at stage 34. Wnt-4 and Wnt-11, other members of the Wnt-5a-subclass, were expressed with a distinct spatiotemporal pattern during the later phase. Wnt-4 was expressed in the articular structure and Wnt-11 was expressed in the dorsal and ventral mesenchyme adjacent to the ectoderm. Wnt-5a expression was partially reduced after apical ectodermal ridge removal, whereas Wnt-11 expression was down-regulated by dorsal ectoderm removal. Therefore, expression of these Wnt was differentially regulated by the ectodermal signal. Misexpression of Wnt-5a in the limb bud with the retrovirus resulted in truncation of long bones predominantly in the zeugopod because of retarded chondrogenic differentiation. Distal elements, such as the phalanges and metacarpals, were not significantly reduced in size. These results suggest that Wnt-5a is involved in pattern formation along the proximal-distal axis by regulation of chondrogenic differentiation.     

Computational and mathematical models of chondrogenesis in vertebrate limbs

The production of cartilage (chondrogenic patterning) in the limb is one of the best‐studied examples of the emergence of form in developmental biology. At the core of the theoretical study is an effort to understand the mechanism that establishes the characteristic distribution of cartilage in the embryonic limb, which defines the future sites and shapes of bones that will be present in the mature limb. This review article gives an overview of the history and current state of a rich literature of mathematical and computational models that seek to contribute to this problem. We describe models for the mechanisms of limb growth and shaping via interaction with various chemical fields, as well as models addressing the intrinsic self‐organization capabilities of the embryonic mesenchymal tissue, such as reaction‐diffusion and mechanochemical models. We discuss the contributions of these models to the current understanding of chondrogenesis in vertebrate limbs, as well as their relation to the varied conceptual models that have been proposed by experimentalists. Birth Defects Research (Part C) 96:176–192, 2012. © 2012 Wiley Periodicals, Inc.     

Cell division and morphogenesis in angiosperm embryogenesis

Angiosperm embryogenesis generates the basic body organization of flowering plants. The underlying processes of pattern formation, which establishes the diversity of position-dependent cell fates, and morphogenesis, which brings about the shape of the embryo, may not only involve intercellular communication and controlled cell expansion but also non-random cell divisions. Genetic analysis ofArabidopsisembryogenesis which displays a large invariant pattern of cell divisions suggests that unequal cell divisions segregate cell fates and are thus involved in pattern formation whereas other oriented cell divisions and differential mitotic rates reflect patterning and rather play a role in morphogenesis.     

Analytical treatment of pattern formation in the Gierer-Meinhardt model of morphogenesis

Summary We first perform a linear stability analysis of the Gierer-Meinhardt model to determine the critical parameters where the homogeneous distribution of activator and inhibitor concentrations becomes unstable. There are two kinds of instabilities, namely, one leading to spatial patterns and another one leading to temporal oscillations. Focussing our attention on spatial pattern formation we solve the corresponding nonlinear equations by means of our previously introduced method of generalized Ginzburg-Landau equations. We explicitly consider the two-dimensional case and find both rolls and hexagon-like structures. The impact of different boundary conditions on the resulting patterns is also discussed. The occurrence of the new patterns has all the features of nonequilibrium phase transitions.     

The role of trans-membrane signal transduction in turing-type cellular pattern formation

The Turing mechanism (Phil. Trans. R. Soc. B 237 (1952) 37) for the production of a broken spatial symmetry in an initially homogeneous system of reacting and diffusing substances has attracted much interest as a potential model for certain aspects of morphogenesis (Models of Biological Pattern Formation, Academic Press, London, 1982; Nature 376 (1995) 765) such as pre-patterning in the embryo. The two features necessary for the formation of Turing patterns are short-range autocatalysis and long-range inhibition (Kybernetik 12 (1972) 30) which usually only occur when the diffusion rate of the inhibitor is significantly greater than that of the activator. This observation has sometimes been used to cast doubt on applicability of the Turing mechanism to cellular patterning since many messenger molecules that diffuse between cells do so at more-or-less similar rates. Here we show that Turing-type patterns will be able to robustly form under a wide variety of realistic physiological conditions though plausible mechanisms of intra-cellular chemical communication without relying on differences in diffusion rates. In the mechanism we propose, reactions occur within cells. Signal transduction leads to the production of messenger molecules, which diffuse between cells at approximately equal rates, coupling the reactions occurring in different cells. These mechanisms also suggest how this process can be controlled in a rather precise way by the genetic machinery of the cell.     

基于模型的景观格局与生态过程研究

景观格局与生态过程关系的研究是景观生态学的主要特色和理论核心之一。模型可以充分利用实验和观测数据并综合不同时间和空间尺度上的信息提炼规律或揭示内在机制,模拟景观格局与生态过程的动态与相互关系,成为景观生态学研究的有力工具。结合研究实例,总结了基于模型的景观格局研究、生态过程研究和格局-过程关系研究的发展现状和薄弱环节,同时探讨了通过构建耦合模型研究格局-过程相互关系的途径。总结了景观模型研究亟待发展的领域与发展趋势。     

Cell cycle,morphogenesis, and ultrastructure in the pseudoheliozoan clathrulina elegans

Summary The development of the sessile pseudoheliozoan Clathrulina elegans Cienkowski (Desmothoraca, Rhizopoda, Protozoa) was followed by light and electron microscopy. The cell cycle comprises a heliozoan-like stage sitting in an organic perforated capsule, an amoeboid resp. biflagellate stage ensuring dispersal, and an encysted stage. Special reference is given to the morphogenetic processes during the flagellate-to-heliozoan transformation. The differentiation of the stalk is described in detail and a hypothesis of the morphogenesis of the capsule is presented. Granules in the filopods displaying a jerky movement, are identified as a hitherto underscribed type of haptocyst-like organelles. These kinetocysts are shown to be a useful marker for studying the turnover of the plasma membrane at organelle level. Evidence is presented that in the flagellate stage a surplus of plasma membrane is stored in numerous lacunae thus facilitating the rapid transformation into the heliozoan stage with its comparatively large surface area. The morphogenetic significance of microtubules during the formation of the stalk, the latter being an asymmetric extracellular secretion product, is elucidated. The role of microtubule nucleation sites, the precisely timed assembly and disassembly of microtubules and other factors which probably control development are discussed to some extent.The author thanks Mrs. G. Borges and Mrs. B. Gauss for excellent technical assistance. This investigation was supported by the Deutsche Forschungsgemeinschaft.     

干旱半干旱区斑块状植被格局形成模拟研究进展

斑块状植被格局是世界上干旱半干旱区常见的景观类型,它们的形成、组成结构和演替过程研究,对于揭示区域生态系统变化的关键过程具有重要意义。鉴于基于地面调查和遥感技术的方法难以全面刻画斑块状植被格局的形成过程及机制,借助于模型模拟成为解决这一问题的有效方法。自20世纪90年代初至今,斑块状植被格局形成的连续和离散模拟研究不断涌现,然而,连续模拟侧重于植被格局形成的一般机理,缺乏与现实格局的对比和验证,离散模拟单元选择与规则制定等仍需不断研究。在简要回顾斑块状格局形成的反馈机制基础上,重点综述了斑块状植被格局形成的连续和离散模拟的最新研究进展,并指出了现有研究的不足。干旱半干旱区小尺度上植物和水的反馈作用决定了大尺度的斑块状植被格局,充分揭示植被-土壤水分相互作用机理是模型模拟研究的关键,放牧强度和降水格局等外部环境对干旱半干旱区斑块状植被格局特征具有重要影响。在未来研究中,应加强模型模拟结果与实际观测的植被格局比较和验证,重视局域环境条件、生态系统功能在模型中的表达,构建综合连续和离散模型各自优点的混合模型,注重斑块状植被格局形成过程中的标准子模型及模型开发和集成平台的研发,同时强调面向格局...     

Structural evidence for electromagnetic resonance in plant morphogenesis

How a homogeneous collective of cells consistently and precisely establishes long-range tissue patterns remains a question of active research. This work explores the hypothesis of plant organs as resonators for electromagnetic radiation. Long-range structural patterns in the developing ovaries and male flower buds of cucurbit plants (zucchini, acorn, and butternut squash), in addition to mature cucurbit fruits (acorn, butternut, and zucchini squash; watermelon, and cucumber), were investigated. A finite element analysis (FEA) model was used to determine resonant EM modes for models with similar geometric and electrical parameters to those of developing organs. Main features of the developing ovaries (i.e. shape of placental lines, ovum location, definition of distinct tissue regions), male flower buds (i.e. early pollen tube features), and mature fruits (i.e. septa placement, seed location, endocarp and mesocarp) showed distinct correlations with electric and magnetic field components of electromagnetic resonant modes. On account of shared pattern signatures in developing organs and the EM resonant modes supported by a modelled structure with similar geometric and electrical properties to those of cucurbit organs, experimental investigations are warranted. The concept of a developing organ as an EM dielectric resonator may extend to a variety of morphogenetic phenomena in a number of living systems.     

Expression of pattern in plants: combining molecular and calculus-based biophysical paradigms

Pattern formation in plant meristems occurs across a broad scale. At the topographical level (large scale), tissue folding in the meristem is responsible for the initiation of new organs in specific phyllotactic patterns and also determines organ shape. At the cellular level (small scale), oriented cell division and microtubule-based cellulose reinforcement control cell pattern and growth direction. I argue here that structural specification at each scale is highly efficient if the pertinent gene activity is manifested in two complementary biophysical categories. At large scale, one category is the tendency of the formative tissue to fold with a certain spatial periodicity determined by its material properties (e.g., bending stiffness from cellulose content). This latent tendency is formalized in a differential equation for physical buckling. The second category at this scale comprises boundary conditions that specify how the latent tendency is manifested as topography: whether tissue humps occur as whorls or Fibonacci spirals. This versatile combinatorial format accounts for the relative stability of alternative organ patterning as well as alternative organ shaping (e.g., stamens vs. carpels). It also accounts for the structural shifts seen in normal development and after mutation or chemical/physical intervention. At small scale, the latent differential activity is the tendency for groups of dividing cells to co-align their cytoskeletons. The curvature of the surface opposes this tendency. The least curved part of a new primordium is its quasicylindrical midportion. There, by aligning microtubules and cellulose coherently around the organ, a new growth direction is set. Thus large-scale buckling produces curvature variation, which, in turn, affects the localization and orientation of the cytoskeleton. This scheme for the coherent production of diverse geometrical features, involving calculus at two structural levels, is supported by complex organogenetic responses to simple physical intervention. Also, many morphological alternatives, wild type vs. mutant, reflect single changes in parameters in this differential-integral format.     

Formation of spacing pattern and morphogenesis of chick feather buds is regulated by cytoskeletal structures

Chick feather buds develop sequentially in a hexagonal array. Each feather bud develops with anterior posterior polarity, which is thought to develop in response to signals derived from specialized regions of mesenchymal condensation and epithelial thickening. These developmental processes are performed by cellular mechanisms, such as cell proliferation and migration, which occur during chick feather bud development. In order to understand the mechanisms regulating the formation of mesenchymal condensation and their role in feather bud development, we explanted chick dorsal skin at stage HH29+ with cytochalasin D, which inhibits cytoskeletal formation. We show that the aggregation of mesenchymal cells can be prevented by cytochalasin D treatment in a concentration-dependent manner. Subsequently, cytochalasin D disrupts the spacing pattern and inhibits feather bud axis formation as well. In addition, expression patterns of Bmp-4 and Msx-2, key molecules for early feather bud development, were disturbed by cytochalasin D treatment. Our results fully indicate that both the cytoskeletal structure and cell activity via gene regulation are of fundamental importance in mesenchymal condensation leading to proper morphogenesis of feather bud and spacing pattern formation.     

Spatial patterns for an interaction-diffusion equation in morphogenesis

Summary A certain interaction-diffusion equation occurring in morphogenesis is considered. This equation is proposed by Gierer and Meinhardt, which is introduced by Child's gradient theory and Turing's idea about diffusion driven instability. It is shown that slightly asymmetric gradients in the tissue produce stable striking patterns depending on its asymmetry, starting from uniform distribution of morphogens. The tool is the perturbed bifurcation theory. Moreover, from a mathematical point of view, the global existence of steady state solutions with respect to some parameters is discussed.     

Neural networks with constrained inputs as models for pattern formation in primate visual cortex

We present a neural network model for the formation of ocular dominance stripes on primate visual cortex and examine the generic phase behavior and dynamics of the model. The dynamical equation of ocular dominance development can be identified with a class of Langevin equations with a nonconserved order parameter. We first set up and examine an Ising model with long-range interactions in an external field, which is equivalent to the model described by the Langevin equation. We use both mean-field theory and Monte-Carlo simulations to study the equilibrium phase diagram of this equivalent Ising model. The phase diagram comprises three phases: a striped phase, a hexagonal bubble phase, and a uniform paramagnetic phase. We then examine the dynamics of the striped phase by solving the Langevin equation both numerically and by singular perturbation theory. Finally, we compare the results of the model with physiological data. The typical striped structure of the ocular dominance columns corresponds to the zero-field configurations of the model. Monocular deprivation can be simulated by allowing the system to evolve in the absence of an external field at early times and then continuing the simulation in the presence of an external field. The physical and physiological applications of our model are discussed in the conclusion.     

On the evolution of morphogenetic models: mechano-chemical interactions and an integrated view of cell differentiation, growth, pattern formation and morphogenesis

In the 1950s, embryology was conceptualized as four relatively independent problems: cell differentiation, growth, pattern formation and morphogenesis. The mechanisms underlying the first three traditionally have been viewed as being chemical in nature, whereas those underlying morphogenesis have usually been discussed in terms of mechanics. Often, morphogenesis and its mechanical processes have been regarded as subordinate to chemical ones. However, a growing body of evidence indicates that the biomechanics of cells and tissues affect in striking ways those phenomena often thought of as mainly under the control of cell-cell signalling. This accumulation of data has led to a revival of the mechano-transduction concept in particular, and of complexity in general, causing us now to consider whether we should retain the traditional conceptualization of development. The researchers' semantic preferences for the terms 'patterning', 'pattern formation' or 'morphogenesis' can be used to describe three main 'schools of thought' which emerged in the late 1970s. In the 'molecular school', the term patterning is deeply tied to the positional information concept. In the 'chemical school', the term 'pattern formation' regularly implies reaction-diffusion models. In the 'mechanical school', the term 'morphogenesis' is more frequently used in relation to mechanical instabilities. Major differences among these three schools pertain to the concept of self-organization, and models can be classified as morphostatic or morphodynamic. Various examples illustrate the distorted picture that arises from the distinction among differentiation, growth, pattern formation and morphogenesis, based on the idea that the underlying mechanisms are respectively chemical or mechanical. Emerging quantitative approaches integrate the concepts and methods of complex sciences and emphasize the interplay between hierarchical levels of organization via mechano-chemical interactions. They draw upon recent improvements in mathematical and numerical morphogenetic models and upon considerable progress in collecting new quantitative data. This review highlights a variety of such models, which exhibit important advances, such as hybrid, stochastic and multiscale simulations.     

Models for contact-mediated pattern formation: cells that form parallel arrays

Kinetic continuum models are derived for cells that crawl over a 2D substrate, undergo random reorientation, and turn in response to contact with a neighbor. The integro-partial differential equations account for changes in the distribution of orientations in the population. It is found that behavior depends on parameters such as total mass, random motility, adherence, and sloughing rates, as well as on broad aspects of the contact response. Linear stability analysis, and numerical, and cellular automata simulations reveal that as parameters are varied, a bifurcation leads to loss of stability of a uniform (isotropic) steady state, in favor of an (anisotropic) patterned state in which cells are aligned in parallel arrays.     

Cell sorting by differential cell motility: a model for pattern formation in Dictyostelium

In the slug stage of the cellular slime mold Dictyostelium discoideum, prespore cells and four types of prestalk cells show a well-defined spatial distribution in a migrating slug. We have developed a continuous mathematical model for the distribution pattern of these cell types based on the balance of force in individual cells. In the model, cell types are assumed to have different properties in cell motility, i.e. different motive force, the rate of resistance against cell movement, and diffusion coefficient. Analysis of the stationary solution of the model shows that combination of these parameters and slug speed determines the three-dimensional shape of a slug and cell distribution pattern within it. Based on experimental data of slug motive force and velocity measurements, appropriate sets of parameters were chosen so that the cell-type distribution at stationary state matches the distribution in real slugs. With these parameters, we performed numerical calculation of the model in two-dimensional space using a moving particle method. The results reproduced many of the basic features of slug morphogenesis, i.e. cell sorting, translocation of the prestalk region, elongation of the slug, and its steady migration.