A singular dispersion relation arising in a caricature of a model for morphogenesis

In 1983 Oster et al. proposed a model for morphogenesis consisting of a system of partial differential equations in which the dispersion relation for the problem linearised about the zero solution has a singularity. That is, the initial growth rate of a small perturbation of wave number k from the zero solution tends to positive or negative infinity as k tends to some critical value k _c from above or below respectively. We consider here as a caricature of the model a single partial differential equation with a similar dispersion relation in a bounded one-dimensional domain. The wave number, or equivalently the domain size, may be thought of as a bifurcation parameter. For the Neumann problem a phenomenon arises in which, as the domain size l increases past a critical value l _l ,the linear stability of the n-th mode jumps from one solution to a remote solution. That is, for l _n the trivial solution is unstable and a certain non-trivial solution is stable to perturbations of mode n, whereas for l>l _n the opposite is true. For the Dirichlet or the Robin problem a linear stability change in the trivial solution occurs, but no corresponding change in any other solution has been found. The corresponding initial boundary value problems are then considered. An asymptotic analysis is performed in the weakly nonlinear limit in the particular case in which only one mode is unstable and gives an asymptotic solution for two classes of nonlinearity, one symmetric and the other asymmetric about u=0. A development of the method of harmonic balance is then used to obtain approximate solutions in the strongly nonlinear case and when more than one mode may be unstable.     

Spatio-temporal patterns in a mechanical model for mesenchymal morphogenesis

We present an in-depth study of spatio-temporal patterns in a simplified version of a mechanical model for pattern formation in mesenchymal morphogenesis. We briefly motivate the derivation of the model and show how to choose realistic boundary conditions to make the system well-posed. We firstly consider one-dimensional patterns and carry out a nonlinear perturbation analysis for the case where the uniform steady state is linearly unstable to a single mode. In two-dimensions, we show that if the displacement field in the model is represented as a sum of orthogonal parts, then the model can be decomposed into two sub-models, only one of which is capable of generating pattern. We thus focus on this particular sub-model. We present a nonlinear analysis of spatio-temporal patterns exhibited by the sub-model on a square domain and discuss mode interaction. Our analysis shows that when a two-dimensional mode number admits two or more degenerate mode pairs, the solution of the full nonlinear system of partial differential equations is a mixed mode solution in which all the degenerate mode pairs are represented in a frequency locked oscillation.     

Superposition optics and the time of flight in onitine dung beetles

Dung beetles fly to fresh dung, with vision essential for flight navigation. The daily period of flight varies among different species: some beetles fly only in sunlight, others only when ambient light levels change rapidly during dusk or dawn and others in the constant dark of night. Measurements of the optical properties of the lenses, eye geometry and photoreceptor dimensions were used in a computer ray-tracing model to determine the optical performance of the superposition eyes of nine species of onitine dung beetles. Eye sensitivity to light is determined mainly by body size, by the refractive-index parameters and size of the crystalline cones, and by the photoreceptor dimensions. Based on the optics of the ommatidial lenses and absorption of light in the retina, the most sensitive eyes, found in the crepuscular-nocturnal beetles, are 85 times or nearly two log units more sensitive than the eyes of the diurnal beetles. Three possible criteria are considered to determine the best position for the retina: maximum amount of light absorbed in the target rhabdom; maximum amount of light falling on the target rhabdom (best focus); and maximum resolution. The structure and physiological optics of the superposition compound eyes of an onitine dung beetle are matched to the range of light intensities at which it flies. Accepted: 4 February 1998     

The plant cell body: a cytoskeletal tool for cellular development and morphogenesis

Summary Certain aspects of cellular behaviour in relation to growth and development of plants can be understood in terms of the cell body concept proposed by Daniel Mazia in 1993. During the interphase of the mitotic cell cycle, the plant cell body is held to consist of a nucleus and a perinuclear microtubule-organizing centre from which microtubules radiate into the cytoplasm. During mitosis and cytokinesis in meristematic cells, and also during the period of growth in post-mitotic cells immediately beyond the meristem, the plant cell body undergoes various characteristic morphological transformations, many of which are proposed as being related to changing structural connections with the actin-based component of the cytoskeleton and with specialized, plasma-membrane-associated sites at the cell periphery. In post-mitotic cells, these transformations of the plant cell body coincide with, and probably provide conditions for, the various pathways of development which such cells follow. They are also responsible, for the acquisition of new cellular polarities. Events in which the plant cell body participates include the formation of a mitotic spindle, phragmoplast, and new cell division wall, the rearrangement of a diffuse type of cell wall growth into tip growth (as occurs, e.g., during the initiation and subsequent development of root hairs), and the growth and division that occurs in reactivated vacuolate cells. If more evidence can be marshalled in support of the existence and properties of the plant cell body, then this concept could prove useful in interpreting the cytological bases of a range of developmental events in plants.Abbreviations CMT cortical microtubule - EMT endoplasmic microtubule - ER endoplasmic reticulum - MF microfilament - MT microtubule - MTOC microtubule-organizing centre - PPB preprophase band (of microtubules) - QC quiescent centre - VSC vesicle supply centre     

Free energy transduction in a chemical motor model

Motor enzymes catalyse chemical reactions, like the hydrolysis of ATP, and in the process they also perform work. Recent studies indicate that motor enzymes perform work with specific biochemical steps in their catalysed reactions, challenging the classical view that work can only be performed within a biochemical state. To address these studies an alternative class of models, often referred to as chemical motor models, has emerged in which motors perform work with biochemical transitions. In this paper, I develop a novel, self-consistent framework for chemical motor models, which accommodates multiple pathways for free energy transfer, predicts rich behaviors from the simplest multi-motor systems, and provides important new insights into muscle and motor function.     

The lateral line of zebrafish: a model system for the analysis of morphogenesis and neural development in vertebrates

The lateral line of the zebrafish has many of the advantages that made the sensory organs of Drosophila a very productive model system: 1) it comprises a set of discrete sense organs (neuromasts) arranged in a defined, species-specific pattern, such that each organ can be individually recognized; 2) the neuromasts are superficial and easy to visualize, and the innervating neurons are easy to label; 3) the sensory projection is simple yet reproducibly organized. Here we describe some of the tools that can be used to investigate the development of this system, and we illustrate their usefulness with specific examples. We conclude that the lateral line is uniquely suited among vertebrate sensory systems for a molecular, cellular and genetic analysis of pattern formation and of neural development.     

A three-dimensional in vitro ovarian cancer coculture model using a high-throughput cell patterning platform

In vitro 3D cancer models that provide a more accurate representation of disease in vivo are urgently needed to improve our understanding of cancer pathology and to develop better cancer therapies. However, development of 3D models that are based on manual ejection of cells from micropipettes suffer from inherent limitations such as poor control over cell density, limited repeatability, low throughput, and, in the case of coculture models, lack of reproducible control over spatial distance between cell types (e.g., cancer and stromal cells). In this study, we build on a recently introduced 3D model in which human ovarian cancer (OVCAR-5) cells overlaid on Matrigel^™ spontaneously form multicellular acini. We introduce a high-throughput automated cell printing system to bioprint a 3D coculture model using cancer cells and normal fi broblasts micropatterned on Matrigel^™. Two cell types were patterned within a spatially controlled microenvironment (e.g., cell density, cell-cell distance) in a high-throughput and reproducible manner; both cell types remained viable during printing and continued to proliferate following patterning. This approach enables the miniaturization of an established macro-scale 3D culture model and would allow systematic investigation into the multiple unknown regulatory feedback mechanisms between tumor and stromal cells and provide a tool for high-throughput drug screening.     

PlexinD1 deficiency induces defects in axial skeletal morphogenesis

Axial patterning in embryonic skeletogenesis associates with coordinated programming of somitogenesis and angiogenesis. As seen in endochondral bone formation, skeletogenesis is closely related to angiogenesis during development. PlexinD1 is a member of plexin family, is expressed in central nervous system and endothelium, and plays a role in blood vessel patterning and endothelium positioning during embryonic development. Here, we examined the effects of PlexinD1 deficiency on skeletogenesis. Three-dimensional micro CT examination revealed that PlexinD1 deficiency resulted in axial skeletal patterning defects including malformation in vertebral body and rib bone shape. Histological examination of the vertebral bodies and long bones showed that PlexinD1 deficiency altered the development of cartilage. PlexinD1 deficiency did not affect the levels of von Willebrand factor staining in relatively large vessels not attached but close to the vertebral body of mice. However, PlexinD1 deficiency reduced the von Willebrand factor (vWf) staining in most of the microvasculatures attached to the vertebral bone. PlexinD1 was expressed in osteoblastic cells and bone tissues of newborn and adult mice. As most of the homozygous knockout mice did not survive, we examined the role of PlexinD1 in bone formation in heterozygous adult mice subjected to bone marrow ablation. However, PlexinD1 heterozygous knockout did not reveal defects in new bone formation. In conclusion, PlexinD1 is involved in the patterning of axial skeletogenesis.     

四川无尾两栖类的繁殖模式

依据Duellman和Trueb(1986)的定义,对四川无尾两栖动物的繁殖模式多样性进行了研究。研究结果如下:(1)73种四川无尾类可以划分为2类共5种繁殖模式。水内产卵是比较原始的一类繁殖模式,又分2种:静水产卵(模式1)和流水产卵(模式2),68种(93%)是在水内产卵;水外产卵是较进化的一类繁殖模式,又分3种:卵产在近水塘的泥窝中(模式12),卵泡产在近水域的土穴中(模式21)和卵泡产在近水域的树上或灌丛上(模式23),仅5种(7%)在水外产卵。(2)模式1、12、21、23的两栖动物,雌雄性的体型较模式2的物种为小,产卵的数量大,但卵径较小;蝌蚪的生态表型均可归入静水型,共同特点是蝌蚪体型小,在静水中觅食,生长发育快。模式2的两栖动物,雌雄性的体型较大,产卵的数量少,而卵径较大;蝌蚪的生态表型可归入流水型,特点是蝌蚪体型大,在流水中觅食,生长发育慢。(3)水内产卵的两栖动物的窝卵能量投入方式可以分为两种:静水产卵(模式1)的物种通过增加卵的数量来增加投入,接近于r-选择物种;流水产卵(模式2)的物种通过增大卵径来增加投入,接近于k-选择物种;是两种适应不同环境条件的的繁殖策略。     

Nonlinear pattern selection in a mechanical model for morphogenesis

We present a numerical study of the nonlinear mechanical model for morphogenesis proposed by Oster et al. (1983) with the aim of establishing the pattern forming capability of the model. We present a technique for mode selection based on linear analysis and show that, in many cases, it is a reliable predictor for nonlinear mode selection. In order to determine the set of model parameters that can generate a particular pattern we develop a technique based on nonlinear least square fitting to a dispersion relation. As an application we present a scenario for sequential pattern formation of dermal aggregations in chick embryos which leads to the hexagonal array of cell aggregations observed in feather germ formation in vivo.     

Vezatin, a protein associated to adherens junctions, is required for mouse blastocyst morphogenesis

Cell-cell interactions play a major role during preimplantation development of the mouse embryo. The formation of adherens junctions is a major feature of compaction, the first morphogenetic event that takes place at the 8-cell stage. Then, during the following two cell cycles, tight junctions form, and the outer layer of cells differentiate into a functional epithelium, leading to the formation of the blastocoel cavity. Until now, E-cadherin was the only transmembrane molecule localized in adherens junctions and required for early development. Vezatin is a transmembrane protein of adherens junctions, interacting with the E-cadherin-catenins complex. Here, we show that vezatin is expressed very early during mouse preimplantation development. It co-localizes with E-cadherin throughout development, being found all around the cell cortex before compaction and basolaterally in adherens junctions thereafter. In addition, vezatin is also detected in nuclei during most of the cell cycle. Finally, using a morpholino-oligonucleotide approach to inhibit vezatin function during preimplantation development, we observed that inhibition of vezatin synthesis leads to a cell cycle arrest with limited cell-cell interactions. This phenotype can be rescued when mRNAs coding for vezatin missing the 5'UTR are co-injected with the anti-vezatin morpholino-oligonucleotide. Cells derived from blastomeres injected with morpholino-oligonucleotide had a reduced amount of vezatin concomitantly with a decrease in the quantity of E-cadherin and beta-catenin localized in the areas of intercellular contact. Shift in E-cadherin cortical distribution was correlated with a strong decrease in E-cadherin mRNA and protein contents. Altogether, these observations demonstrate that vezatin is required for morphogenesis of the preimplantation mouse embryo.     

A new pencil beam model for photon dose calculations in heterogeneous media

The pencil beam method is commonly used for dose calculations in intensity-modulated radiation therapy (IMRT). In this study, we have proposed a novel pencil model for calculating photon dose distributions in heterogeneous media. To avoid any oblique kernel-related bias and reduce computation time, dose distributions were computed in a spherical coordinate system based on the pencil kernels of different distances from source to surface (DSS). We employed two different dose calculation methods: the superposition method and the fast Fourier transform convolution (FFTC) method. In order to render the superposition method more accurate, we scaled the depth-directed component by moving the position of the entry point and altering the DSS value for a given beamlet. The lateral components were thus directly corrected by the density scaling method along the spherical shell without taking the densities from the previous layers into account. Significant computation time could be saved by performing the FFTC calculations on each spherical shell, disregarding density changes in the lateral direction. The proposed methods were tested on several phantoms, including lung- and bone-type heterogeneities. We compared them with Monte Carlo (MC) simulation for several field sizes with 6 MV photon beams. Our results revealed mean absolute deviations <1% for the proposed superposition method. Compared to the AAA algorithm, this method improved dose calculation accuracy by at least 0.3% in heterogeneous phantoms. The FFTC method was approximately 40 times faster than the superposition method. However, compared with MC, mean absolute deviations were <3% for the FFTC method.     

Spatial and spatio-temporal patterns in a cell-haptotaxis model

We investigate a cell-haptotaxis model for the generation of spatial and spatio-temporal patterns in one dimension. We analyse the steady state problem for specific boundary conditions and show the existence of spatially hetero-geneous steady states. A linear analysis shows that stability is lost through a Hopf bifurcation. We carry out a nonlinear multi-time scale perturbation procedure to study the evolution of the resulting spatio-temporal patterns. We also analyse the model in a parameter domain wherein it exhibits a singular dispersion relation.     

Spectral broadening of the Soret band in myoglobin: an interpretation by the full spectrum of low-frequency modes from a normal modes analysis

In this work the temperature dependence of the Soret band line shape in carbon-monoxy myoglobin is re-analyzed by using both the full correlator approach in the time domain and the frequency domain approach. The new analyses exploit the full density of vibrational states of carbon-monoxy myoglobin available from normal modes analysis, and avoid the artificial division of the entire set of vibrational modes coupled to the Soret transition into "high-frequency" and "low-frequency" subsets; the frequency domain analysis, however, makes use of the so-called short-times approximation, while the time domain one avoids it. Time domain and frequency domain analyses give very similar results, thus supporting the applicability of the short-times approximation to the analysis of hemeprotein spectra; in particular, they clearly indicate the presence of spectral heterogeneity in the Soret band of carbon-monoxy myoglobin. The analyses also show that a temperature dependence of the Gaussian width parameter steeper than the hyperbolic cotangent law predicted by the Einstein harmonic oscillator and/or a temperature dependence of inhomogeneous broadening are not sufficient to obtain quantitative information on the magnitude of an-harmonic contributions to the iron-heme plane motion. However, the dependence of the previous two quantities may be used to obtain semiquantitative information on the overall coupling of the Soret transition to the low-frequency modes and therefore on the dynamic properties of the heme pocket in different states of the protein.     

Superposition of impulse activity in a rapidly-adapting afferent unit model

Mechanosensory afferent units consist of a parent axon, the peripheral axonal arborization, and the branch terminal mechanoreceptors. The present work uses a mathematical model to describe the contribution of a given number of rapidly-adapting mechanoreceptors to the impulse pattern of their parent axon. In the model impulses initiated by any driven mechanoreceptor instantaneously propagate orthodromically and antidromically. The model also incorporates the axonal absolute refractory period as well as ortho-and antidromically elicited recovery cycles. In separate computations, periodic or random (Poisson process) trains of short-duration stimuli at constant amplitude are delivered to a given number (N=2–30) of co-innervated mechanoreceptors. The superposition of component impulse trains always departs from the theoretical ideal (Poisson process). Such departures are attributable to: (i) the number of driven mechanoreceptors, when N is small, (ii) axonal absolute refractory period, during maximal amplitude stimulation, and (iii) antidromic recovery cycles as well as absolute refractoriness, during submaximal-amplitude stimulation. Computations reveal that this instantaneous reset model results in the elimination of information extracted by driven mechanoreceptors. Model predictions with Poisson stimulation at varied amplitudes are compared to G-hair afferent unit responses to analogous stimulation. Qualitatively opposite results with respect to parent axonal impulse patterns imply that the axonal arborization is not simply a substrate for impulse propagation from branch terminals to parent axon.     

E-cadherin is required for intestinal morphogenesis in the mouse

E-cadherin, the primary epithelial adherens junction protein, has been implicated as playing a critical role in nucleating formation of adherens junctions, tight junctions, and desmosomes. In addition to its role in maintaining structural tissue integrity, E-cadherin has also been suggested as an important modulator of cell signaling via interactions with its cytoplasmic binding partners, catenins, as well as with growth factor receptors. Therefore, we proposed that loss of E-cadherin from the developing mouse intestinal epithelium would disrupt intestinal epithelial morphogenesis and function. To test this hypothesis, we used a conditional knockout approach to eliminate E-cadherin specifically in the intestinal epithelium during embryonic development. We found that E-cadherin conditional knockout mice failed to survive, dying within the first 24 hours of birth. Examination of intestinal architecture at E18.5 demonstrated severe disruption to intestinal morphogenesis in animals lacking E-cadherin in the epithelium of the small intestine. We observed changes in epithelial cell shape as well as in the morphology of villi. Although junctional complexes were evident, junctions were abnormal, and barrier function was compromised in E-cadherin mutant intestine. We also identified changes in the epithelial cell populations present in E-cadherin conditional knockout animals. The number of proliferating cells was increased, whereas the number of enterocytes was decreased. Although Wnt/β-catenin target mRNAs were more abundant in mutants compared with controls, the amount of nuclear activated β-catenin protein was dramatically lower in mutants compared with controls. In summary, our data demonstrate that E-cadherin is essential for intestinal epithelial morphogenesis and homeostasis during embryonic development.     

Myosin VI plays a role in cell-cell adhesion during epithelial morphogenesis

Myosin VI is an unconventional Myosin that has been implicated in vesicle transport and membrane trafficking. We isolated lethal mutants of Myosin VI, which lack protein once maternal supplies have been utilised during embryogenesis. Dorsal closure, where there is a ring of Myosin VI at the edge of the migrating epithelial sheet, is often abnormal. The sheet of migrating cells is irregular, rather than a smooth epithelium and cells begin to detach. Some embryos hatch into larvae, containing detached cells loose in the haemolymph. Myosin VI is crucial for correct cell morphology and maintenance of adhesive cellular contacts within epithelial cell layers.     

The integration of cell proliferation and growth in leaf morphogenesis

A number of recent publications have assessed the outcome on leaf development of targeted manipulation of cell proliferation. The results of these investigations have awakened interest in the long-standing debate in plant biology on the precise role of cell division in morphogenesis. Does cell proliferation drive morphogenesis (cell theory) or is it subservient to a mechanism which acts at the whole organ level to regulate morphogenesis (organismal theory)? In this review, the central role of growth processes (distinct from cell proliferation) in morphogenesis is highlighted and the limitations in our understanding of the basic mechanisms of plant growth control are highlighted. Finally, an attempt is made to demonstrate how sequential local co-ordination of growth might provide an interpretation of some of the recent observations on cell proliferation and leaf morphogenesis.