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Scientific analysis often relies on the ability to make accurate predictions of a system’s dynamics. Mechanistic models, parameterized by a number of unknown parameters, are often used for this purpose. Accurate estimation of the model state and parameters prior to prediction is necessary, but may be complicated by issues such as noisy data and uncertainty in parameters and initial conditions. At the other end of the spectrum exist nonparametric methods, which rely solely on data to build their predictions. While these nonparametric methods do not require a model of the system, their performance is strongly influenced by the amount and noisiness of the data. In this article, we consider a hybrid approach to modeling and prediction which merges recent advancements in nonparametric analysis with standard parametric methods. The general idea is to replace a subset of a mechanistic model’s equations with their corresponding nonparametric representations, resulting in a hybrid modeling and prediction scheme. Overall, we find that this hybrid approach allows for more robust parameter estimation and improved short-term prediction in situations where there is a large uncertainty in model parameters. We demonstrate these advantages in the classical Lorenz-63 chaotic system and in networks of Hindmarsh-Rose neurons before application to experimentally collected structured population data. [ABSTRACT FROM AUTHOR]

During the solidification of two-component solutions a two-phase mushy layer often forms consisting of solid dendritic crystals and solution in thermal equilibrium. Here, we extend previous weakly nonlinear analyses of convection in mushy layers to the derivation and study of a pattern equation by including a continuous spectrum of horizontal wave vectors in the development. The resulting equation is of the Swift-Hohenberg form with an additional quadratic term that destroys the up-down symmetry of the pattern as in other studies of non-Boussinesq convective pattern formation. In this case, the loss of symmetry is rooted in a non-Boussinesq dependence of the permeability on the solid-fraction of the mushy layer. We also study the motion of localized chimney structures that results from their interactions in a simplified one-dimensional approximation of the full pattern equation. [ABSTRACT FROM AUTHOR]

This paper shows the effects of optimal control techniques on pattern formation in a three-dimensional Rayleigh–Bénard problem with nonhomogeneous heating from below. In particular, we consider a cylindrical domain with a heating profile at the bottom localized around the origin. An axisymmetric basic state appears as soon a nonzero horizontal temperature gradient is imposed. The basic state may bifurcate to different solutions as spiral waves, stationary patterns, etc., depending on the vertical and lateral temperature gradients and on the shape of the heating function. An optimal control problem that determines the thermal boundary condition minimizing the enstrophy is proposed. The control boundary condition obtained changes the leading mode in the bifurcation and allows to eliminate the instabilities for some values of the parameters. [ABSTRACT FROM AUTHOR]

The temporal and stationary behavior of protein modification cascades has been extensively studied, yet little is known about the spatial aspects of signal propagation. We have previously shown that the spatial separation of opposing enzymes, such as a kinase and a phosphatase, creates signaling activity gradients. Here we show under what conditions signals stall in the space or robustly propagate through spatially distributed signaling cascades. Robust signal propagation results in activity gradients with long plateaus, which abruptly decay at successive spatial locations. We derive an approximate analytical solution that relates the maximal amplitude and propagation length of each activation profile with the cascade level, protein diffusivity, and the ratio of the opposing enzyme activities. The control of the spatial signal propagation appears to be very different from the control of transient temporal responses for spatially homogenous cascades. For spatially distributed cascades where activating and deactivating enzymes operate far from saturation, the ratio of the opposing enzyme activities is shown to be a key parameter controlling signal propagation. The signaling gradients characteristic for robust signal propagation exemplify a pattern formation mechanism that generates precise spatial guidance for multiple cellular processes and conveys information about the cell size to the nucleus. [ABSTRACT FROM AUTHOR]

Abstract: Pigment patterns in the integument have long-attracted attention from both scientists and non-scientists alike since their natural attractiveness combines with their excellence as models for the general problem of pattern formation. Pigment cells are formed from the neural crest and must migrate to reach their final locations. In this review, we focus on our current understanding of mechanisms underlying the control of pigment cell migration and patterning in diverse vertebrates. The model systems discussed here – chick, mouse, and zebrafish – each provide unique insights into the major morphogenetic events driving pigment pattern formation. In birds and mammals, melanoblasts must be specified before they can migrate on the dorsolateral pathway. Transmembrane receptors involved in guiding them onto this route include EphB2 and Ednrb2 in chick, and Kit in mouse. Terminal migration depends, in part, upon extracellular matrix reorganization by ADAMTS20. Invasion of the ectoderm, especially into the feather germ and hair follicles, requires specific signals that are beginning to be characterized. We summarize our current understanding of the mechanisms regulating melanoblast number and organization in the epidermis. We note the apparent differences in pigment pattern formation in poikilothermic vertebrates when compared with birds and mammals. With more pigment cell types, migration pathways are more complex and largely unexplored; nevertheless, a role for Kit signaling in melanophore migration is clear and indicates that at least some patterning mechanisms may be highly conserved. We summarize the multiple factors thought to contribute to zebrafish embryonic pigment pattern formation, highlighting a recent study identifying Sdf1a as one factor crucial for regulation of melanophore positioning. Finally, we discuss the mechanisms generating a second, metamorphic pigment pattern in adult fish, emphasizing recent studies strengthening the evidence that undifferentiated progenitor cells play a major role in generating adult pigment cells. [Copyright &y& Elsevier]

Abstract: Viscous flow of the resin in nano-imprinting lithography has been investigated. Flow behavior of the thermoplastic polymer was analyzed experimentally as well as numerically. Effects of process variables such as the temperature and the pressure and the stamp geometry on the filling pattern were studied. In order to observe the effect of stamp geometry, three different types of geometries were considered. Experiments were performed using polymethylmethacrylate (PMMA) sheets. Filled patterns were observed using a scanning electron microscopy (SEM). Fixed grid method along with the finite element method was used for numerical analysis. Numerical results exhibited a similar tendency as the experimental observation. [Copyright &y& Elsevier]

Abstract: Numerical and analytical techniques are used to investigate the effects of quenched disorder of small-world networks on the phase ordering dynamics of lamellar patterns as modeled by the Swift–Hohenberg equation. Morphologies for small and large values of the network randomness are quite different. It is found that addition of shortcuts to an underlying regular lattice makes the growth of domains evolving from random initial conditions much slower at late times. As the randomness increases, the evolution is eventually frozen. [Copyright &y& Elsevier]

Abstract: The scale of landscape pattern formation of an ecological community may provide clues as to the processes influencing its spatial and temporal dynamics. We conducted an examination of the spatial organization of an annual seagrass (Halophila decipiens) in an open ocean setting at two spatial scales and growing seasons to identify the relative influence of external (hurricanes) versus internal (clonal growth) factors. Visual surveys of seagrass cover were conducted over 2 years within three replicate 1km2 study areas each separated by ∼25km in an inshore–offshore transect along the southwest coast of Florida at depths between ∼10 and 30m. A towed video sled allowed observations of seagrass cover of 1m2 areas approximately every 6m over thousands of meters of evenly spaced transects within the study areas (coarse scale). The towed video revealed that 17.5% of the seafloor was disturbed irrespective of location or sample time. Randomly selected 10×10m quadrats within the larger, 1km2 study areas were completely surveyed for seagrass cover by divers at 0.625m2 resolution (fine scale). The coarse-scale observations were tested using both conventional geostatistics and an application of a time-series technique (Runs test) for scale of seagrass cover contiguity. Fine-scale observations were examined using conventional geostatistics and a least squares approach (cumulative logistic). The coarse-scale observations revealed little scale dependency and indicated that the structure was organized at spatial extents finer than our sample spacing; the cumulative logistic technique revealed potential fine-scale patterns not otherwise discerned. In contrast, surveys of the 10×10m quadrats detected strong scale dependency with multiple small gaps, indicating scale-dependent patterns arising from processes operating at extents generally <14m. Between June and October 1999, a Category I hurricane passed over the study area, rearranging large areas of sand that uncovered some rocky hard bottom areas, while covering others; by the next growing season the newly covered areas were vegetated with Halophila decipiens that likely arose from transported seeds. Spatial analysis revealed that the storm led to a shift to greater frequency of H. decipiens, but lower density coverage. Seagrass density remained substantially depressed in all areas a full year following the storm. The short life history of H. decipiens and the apparent existence of a moveable seed bank means that spatial organization of this community is dictated first by large-scale dispersal of plant propagules (hundreds of meters) and then within a growing season, by clonal organization of the seagrass operating over very small distances (m). The two techniques (semivariance and Runs test) led to similar conclusions regarding the organizational scales of seagrass landscape pattern. As with terrestrial examples, this study demonstrates the importance of selecting the appropriate scale for detection of landscape pattern and processes influencing population ecology of a seagrass ecosystem. [Copyright &y& Elsevier]

Abstract: The mechanisms governing pattern formation and selection are important scientific issues for non-equilibrium interfacial growth. In this article, an experimental study of electrochemical deposition was carried out in an ultra-thin layer of CuSO4 solution. Using an unique experimental setup, the convectional interferences in the deposit growth process are effectively restrained. Subjected to different growth driving forces (deposition current), the deposits aggregating in the forms of microcrystalline and nanocrystalline Cu and Cu2O exhibit film and branching morphologies respectively. In particular, the lower the driving force, the larger the width of the deposit and meanwhile the probability of forming film like or finger like morphology becomes great. Whereas in case of high driving force, the deposits turn to be tenuous and appear in quasi-linear filaments arrays due to the growth competition between the adjacent branches. Based on the morphological analysis of deposits, the processes of the nucleation and aggregation for the microcrystallines were deduced. In addition, the effects of electrical migration and diffusion of the Cu2+ cations in the growth front were discussed. [Copyright &y& Elsevier]

Abstract: In systems with moving contacts, as e.g. automotive vehicles on dirt-roads, friction brakes, and of course railway vehicles moving on railway tracks, spatially periodic wear patterns may appear on the contact partners’ surfaces. There is general agreement that the patterns are related to structural resonances. Using simple models with a moving point contact and an idealized wear model the present work first reviews some of the present understanding of wear-pattern generation. Then additional intuitively accessible explanations for the phenomena observed are developed and the effect of randomly specified relative velocities on the wavelength selection process is investigated. For this purpose the stability analysis of the surface evolution equation is pursued with the full, as well as with a reduced system, and a simple linear approach to deal with distributions of relative velocities is introduced. For fixed relative velocity the analysis yields an intuitively accessible picture of wear-pattern appearance or evanescence, as well as of wear-pattern motion. Based on these results it is shown, how dominant wavelengths are selected as a consequence of randomly distributed relative velocities. [Copyright &y& Elsevier]

Abstract: A 25-ha broad-leaved Korean pine (Pinus koraiensis) mixed forest plot was established on Changbai Mountain, PR China, in 2004 in order to gain insights into the processes driving regeneration and succession of the forest. All trees at least 1cm in diameter at breast height were mapped and identified to species. In this study, the spatial distribution patterns and spatial associations of four dominant tree species among different tree height classes were analyzed by a point pattern analysis method, which was the O-ring statistic. We found that: (1) P. koraiensis was a discontinuously regenerating population, while Tilia amurensis and Quercus mongolica were continuously regenerating populations, and Fraxinus mandshurica might be a declining population. (2) Intra- and interspecies spatial associations of varied with species, tree height, and scales. P. koraiensis and T. amurensis at the lower height classes showed positive association to most species at the upper height class at almost all scales, suggesting that they have broad niches and grow well under the canopy of other species. Q. mongolica at the lower height classes showed spatial independence at smaller scales and negative association at larger scales to non-conspecific adults, suggesting that spatial heterogeneity may be important to generate patterns. (3) Scale is an important factor for pattern formation, and different species showed different distribution patterns and spatial associations at different scales. [Copyright &y& Elsevier]

Abstract: The differential susceptibility of inbred mouse strains to teratogen-induced malformations can serve as a model to assess the molecular pathogenesis of dysmorphology. Using such a model, the teratogenic effect of cadmium chloride (CdCl2), which results in limb reduction deformities in the C57BL/6N mouse strain, but not in the SWV strain, was found to correlate with reduction of the expression domains of Fgf8/4 (fibroblast growth factor-8 and -4) in the apical ectodermal ridge (AER) and Shh (sonic hedgehog) in the posterior mesenchyme, as well as reduction of MAPK/Erk1/2 (the mitogen-activated protein kinase/extracellular regulated kinase 1/2) phosphorylation (pErk1/2) in the mesenchyme throughout the limb bud. The pattern of pErk1/2 reduction did not consistently reflect the pattern of Fgf8/4 reduction suggesting that CdCl2 might affect pErk1/2 through an Fgf-independent pathway. Other potential downstream mediators of the Fgf pathway including Mkp3 and Fgf10 as well as pMek (phosphorylated MAPK/Erk1/2 kinase) were not different in limb buds between the two strains at the studied time points. The effect of CdCl2 on skeletogenesis was traced in time to the early stages of pre-chondrogenic condensation as determined by the Sox9 expression domain. The data of the present study indicate that a differential strain response to CdCl2-induced forelimb digital loss may be due to a polymorphic interference with the Fgf/Shh positive feedback loop and Erk1/2 phosphorylation. [Copyright &y& Elsevier]

Abstract: The bone morphogenetic protein (BMP) pathway has been shown to play an important role in the establishment of the dorsoventral axis during development in both vertebrate and invertebrate species. In an attempt to unravel the role of BMPs in pattern formation during planarian regeneration, we studied this signaling pathway in Schmidtea mediterranea. Here, we functionally characterize planarian homologues of two key elements of the pathway: Smed-BMP and Smed-Smad1. Whole-mount in situ hybridization showed that Smed-BMP is expressed at the planarian dorsal midline, suggesting a role in dorsoventral patterning, while Smed-Smad1 is widely expressed throughout the mesenchyme and in the central nervous system. RNA interference (RNAi) knockdowns of Smed-BMP or Smed-Smad1 led to the disappearance of dorsal markers along with the ectopic expression of ventral markers on the dorsal side of the treated animals. In almost all cases, a duplicated central nervous system differentiated dorsally after Smed-BMP or Smed-Smad1 RNAi. These defects were observed not only during regeneration but also in intact non-regenerating animals. Our results suggest that the BMP signaling pathway is conserved in planarians and that it plays a key role in the regeneration and maintenance of the dorsoventral axis. [Copyright &y& Elsevier]

We establish the global existence of classical solutions to a generalized chemotaxis model, which includes the volume filling effect expressed through a nonlinear squeezing probability. This novel choice of squeezing probability reflects the elastic properties of cells. Necessary and sufficient conditions for spatial pattern formation are given and the underlying bifurcations are analyzed. In numerical simulations, the complex dynamics of merging and emerging patterns are shown for zero cell kinetics and nonzero cell kinetics, respectively. We conclude that the emerging process of pattern formation is due to cell growth. [ABSTRACT FROM AUTHOR]

Abstract: The objective of this paper is to investigate the effect of prey-taxis on predator–prey models with Paramecium aurelia as the prey and Didinium nasutum as its predator. The logistic Lotka–Volterra predator–prey models with prey-taxis are solved numerically with four different response functions, two initial conditions and one data set. Routh–Hurwitz’s stability conditions are used to obtain the bifurcation values of the taxis coefficients for each model. We show that both response functions and initial conditions play important roles in the pattern formation. When the value of the taxis coefficient becomes considerably higher than the bifurcation value, chaotic dynamics develop. As diffusion in predator velocity is incorporated into the system, the system returns to a cyclic pattern. [Copyright &y& Elsevier]

A central question of ecology is what determines the presence and abundance of species at different locations. In cases of ecological pattern formation, population sizes are largely determined by spatially distributed interactions and may have very little to do with the habitat template. We find pattern formation in a single-species metapopulation model with quasi-local competition, but only if the populations have (at least) two age or stage classes. Quasi-local competition is modeled using an explicit resource competition model with fast resource dynamics, and assuming that adults, but not juveniles, spend a fraction of their foraging time in habitat patches adjacent to their home patch. Pattern formation occurs if one stage class depletes the common resource but the shortage of resource affects mostly the other stage. When the two stages are spatially separated due to quasi-local competition, this results in competitive exclusion between the populations. We find deep similarity between spatial pattern formation and population cycles due to competitive exclusion between cohorts of biennial species, and discuss the differences between the present mechanism and established ways of pattern formation such as diffusive instability and distributed competition with local Allee-effects. [ABSTRACT FROM AUTHOR]

Abstract: We describe here our recent work on spontaneous regular motion of liquid droplet powered by the chemical Marangoni effect under spatially symmetric conditions. It is shown that a spontaneously crawling oil droplet on a glass substrate with a nonequilibrium chemical condition of cationic surfactant exhibits regular rhythmic motion in a quasi-one-dimensional vessel, whereas irregular motion is induced in a two-dimensionally isotropic environment. Such behavior of a droplet demonstrates that spontaneous regular motion can be generated under fluctuating conditions by imposing an appropriate geometry. As another system, we introduce alcohol droplet moving spontaneously on water surface. The droplet spontaneously forms a specific morphology depending on its volume, causing specific mode of translational motion. An alcohol droplet with a smaller volume floating on water surface moves irregularly. On the other hand, a droplet with a larger volume undergoes vectorial motion accompanied by deformation into an asymmetric shape. This result suggests a scenario on the emergence of regular motion coupled with geometrical pattern formation under far-from-equilibrium conditions. [Copyright &y& Elsevier]

During bouts of evolutionary diversification, such as adaptive radiations, the emerging species cluster around different locations in phenotype space. How such multimodal patterns in phenotype space can emerge from a single ancestral species is a fundamental question in biology. Frequency-dependent competition is one potential mechanism for such pattern formation, as has previously been shown in models based on the theory of adaptive dynamics. Here, we demonstrate that also in models similar to those used in quantitative genetics, phenotype distributions can split into multiple modes under the force of frequency-dependent competition. In sexual populations, this requires assortative mating, and we show that the multimodal splitting of initially unimodal distributions occurs over a range of assortment parameters. In addition, assortative mating can be favoured evolutionarily even if it incurs costs, because it provides a means of alleviating the effects of frequency dependence. Our results reveal that models at both ends of the spectrum between essentially monomorphic (adaptive dynamics) and fully polymorphic (quantitative genetics) yield similar results. This underscores that frequency-dependent selection is a strong agent of pattern formation in phenotype distributions, potentially resulting in adaptive speciation. [ABSTRACT FROM AUTHOR]

Most theories of phyllotaxis are based on the idea that the formation of new primordia is inhibited by the proximity of older primordia. Several mechanisms that could result in such an inhibition have been proposed, including mechanical interactions, diffusion of a chemical inhibitor, and signaling by actively transported substances. Despite the apparent diversity of these mechanisms, their pattern-generation properties can be captured in a unified manner by inhibition fields surrounding the existing primordia. In this paper, we introduce a class of fields that depend on both the spatial distribution and the age of previously formed primordia. Using current techniques to create geometrically realistic, growing apex surfaces, we show that such fields can robustly generate a wide range of spiral, multijugate, and whorled phyllotactic patterns and their transitions. The mathematical form of the inhibition fields suggests research directions for future studies of phyllotactic patterning mechanisms. [ABSTRACT FROM AUTHOR]

Abstract: We have studied the role the canonical Wnt pathway plays in hydroid pattern formation during embryonic development and metamorphosis. Transcripts of Wnt and Tcf were asymmetrically deposited in the oocyte and subsequent developmental stages, marking the sites of first cleavage, posterior larval pole and the upcoming head of the metamorphosed polyp. To address the function of these genes, we activated downstream events of the Wnt pathway by pharmacologically blocking GSK-3β. These treatments rendered the polar expression of Tcf ubiquitous and induced development of ectopic axes that contained head structures. These results allow concluding that Wnt signaling controls axis formation and regional tissue fates along it, determining one single axis terminus from which later the mouth and hypostome develop. Our data also indicate Wnt functions in axis formation and axial patterning as in higher metazoans, and thus point to an ancestral role of Wnt signaling in these processes in animal evolution. [Copyright &y& Elsevier]

We report on a phenomenon of ring pattern formation of nanoparticles in small ink-jetted droplets (30−60 m diameter) of water-based suspensions on substrate, which occurs in several seconds, unlike 10 min and more in most previous works. The phenomenon may open the way for new applications connected with rapid creation of desired structures. In addition, we report here a method for the study of the relative motion of the solvent and pigments in suspension droplets by coloring the solvent with soluble dye and using spectral imaging techniques. [ABSTRACT FROM AUTHOR]

Abstract: To illustrate the interplay between grazers and grass, we present a novel Monte Carlo model including grass-island growth, consumption of grass by grazers, and birth, migration and death of grazers. The rates of the former and three latter processes are assumed to depend on the environment so that the conventional mean-field approximation does not hold (in particular, the model takes into account that grass grows on the grass-island boundaries, and grazers are mobile and prefer to stay on the areas covered by grass). Due to the feedback between various processes, as expected, the model predicts stable regimes and irregular oscillations of the area of the grass islands and grazer population. The patterns observed are however different compared to those predicted by conventional Monte Carlo prey–predator models. Specifically, there is no tendency for grazers and grass to segregate. The mean-field version of the model is briefly discussed as well. [Copyright &y& Elsevier]

Abstract: Fungiform papillae are epithelial specializations that develop in a linear pattern on the anterior mammalian tongue and differentiate to eventually contain taste buds. Little is known about morphogenetic and pattern regulation of these crucial taste organs. We used embryonic rat tongue, organ cultures to test roles for bone morphogenetic proteins, BMP2, 4 and 7, and antagonists noggin and follistatin, in development of papillae from a stage before morphological initiation (E13) or from a stage after the pre-papilla placodes have formed (E14). BMPs and noggin proteins become progressively restricted to papilla locations during tongue development. In E13 cultures, exogenous BMPs or noggin induce increased numbers of fungiform papillae, in a concentration-dependent manner, compared to standard tongue cultures; BMPs, but not noggin, lead to a decreased tongue size at this stage. In E14 cultures, however, exogenous BMP2, 4 or 7 each inhibits papilla formation so that there is a decrease in papilla number. Noggin substantially increases number of papillae in E14 cultures. Using beads for a highly localized protein delivery, papillae are inhibited in the surround of BMP-soaked beads and induced in large clusters around noggin-soaked beads. Follistatin, presented in culture medium or by bead, does not alter papilla formation or number. In all fungiform papillae that form under various culture conditions, the molecular marker, sonic hedgehog, is within each papilla. However, the BMP inhibitory effect on papillae is not prevented by disrupting sonic hedgehog signaling through addition of cyclopamine to cultures. BMPs and noggin alter cell proliferation in tongue epithelium in opposite ways, demonstrated with Ki67 immunostaining. We propose that the BMPs and noggin, colocalized within papilla placodes and the fungiform papillae per se, have opposing inhibitory and activating or inducing roles in papilla development in linear patterns. We present a model for these effects. [Copyright &y& Elsevier]

Abstract: The generation of vascular pattern formation in plants is an interesting process of pattern formation in organisms. It is well known that the plant hormone auxin is involved in plant vascular differentiation and that the PIN1 protein, an auxin efflux carrier, localizes to one side of the cell membrane. Several hypotheses have been proposed to explain the formation of leaf venation. One is the canalization hypothesis that is based on the assumption that a positive feedback regulation exists between the flow of a signal molecule and the capacity of its flow. Here, we attempted to integrate the canalization hypothesis and experimental data. We investigated models of the positive feedback regulation between the auxin flow and PIN1 localization. Model 1, with conserved PIN1 amount in each cell, can generate a branching pattern similar to that of plant leaf venation. We introduced the diffusible enhancer “e” into the model as unknown factor. The obtained patterns show a quasi-periodic distribution of auxin flow paths, when the model dynamics includes domain growth. In order to understand the early initiation process that generates an inhomogeneity from an almost homogeneous distribution, we introduced model 2, a simplified version of model 1. Model 2 can generate inhomogeneity with a parameter dependency similar to that of model 1. To analyse parameter condition required for pattern development, approximated equations are obtained from model 2. The isocline analysis of the equations without spatial structure shows that the inhomogeneous distribution occurs from an almost homogeneous distribution. This parameter condition for generating inhomogeneity is consistent with the results of models 1 and 2. [Copyright &y& Elsevier]

Oscillations and pattern formation driven by a surface reconstruction are studied for the catalytic reduction of NO by CO on Pt(100) single-crystal surfaces through dynamic Monte Carlo simulations at low pressure and relatively high temperatures conditions. This study incorporates recent experimental evidence obtained for the same reaction on a Rh(111) surface, which modifies the reaction scheme used in previous approaches. The main consequence of such experimental evidence is that the production of N2occurs through two parallel mechanisms:  (a) the classical N N recombination step; (b) the formation and subsequent decay of an (N−NO) intermediate species as the fastest pathway. Moreover, different factors influencing the NO dissociation rate, the key step in the whole reaction, such as the availability of neighboring vacant sites, the formation of N-islands, and the presence of other NO and CO adsorbed species in the neighborhood, are also taken into account and their effects discussed. Sustained, modulated, irregular, and damped oscillations are observed in our analysis as well as the formation of cellular structures and turbulent patterns. The effect and the importance of each elementary reaction step on the behavior of the system are discussed. [ABSTRACT FROM AUTHOR]

Abstract: To gain an understanding of molecular events that underlie pattern formation in the retina, we evaluated the expression profiles of over 8000 transcripts randomly selected from an embryonic zebrafish library. Detailed analysis of cDNAs that display restricted expression patterns revealed factors that are specifically expressed in single cell classes and are potential regulators of neurogenesis. These cDNAs belong to numerous molecular categories and include cell surface receptors, cytoplasmic enzymes, and transcription factors. To test whether expression patterns that we have uncovered using this approach are indicative of function in neurogenesis, we used morpholino-mediated knockdown approach. The knockdown of soxp, a transcript expressed in the vicinity of the inner plexiform layer, revealed its role in cell type composition of amacrine and ganglion cell layers. Blocking the function of cxcr4b, a chemokine receptor specifically expressed in ganglion cells, suggests a role in ganglion cell survival. These experiments demonstrate that in situ hybridization-based reverse genetic screens can be applied to isolate genetic regulators of neurogenesis. This approach very well complements forward genetic mutagenesis studies previously used to study retinal neurogenesis in zebrafish. [Copyright &y& Elsevier]

Abstract: We are concerned with the following Gierer–Meinhardt model on a bounded domain with smooth boundary which is a biological pattern formation model proposed by A. Gierer and H. Meinhardtwhere , , and are small positive constants. We also consider the so-called shadow system (SS) of (GM) and another reduced equation (RE) which is obtained by taking in (SS). Our framework is a functional space , where . After we see that each of the systems (GM), (SS) and (RE) generates a global semiflow on , and , respectively, we will prove the existence of global attractors , and of (GM), (SS) and (RE), respectively, Moreover, we will prove the upper semicontinuity of at and at . [Copyright &y& Elsevier]

Abstract: The skeletal elements (spicules) of the demosponge Lubomirskia baicalensis were analyzed; they are composed of amorphous, non-crystalline silica, and contain in a central axial canal the axial filament which consists of the enzyme silicatein. The axial filament, that orients the spicule in its longitudinal axis exists also in the center of the spines which decorate the spicule. During growth of the sponge, new serially arranged modules which are formed from longitudinally arranged spicule bundles are added at the tip of the branches. X-ray analysis revealed that these serial modules are separated from each other by septate zones (annuli). We describe that the longitudinal bundles of spicules of a new module originate from the apex of the earlier module from where they protrude. A cross section through the oscular/apical–basal axis shows that the bundle rays are organized in a concentric and radiate pattern. High resolution magnetic resonance microimaging studies showed that the silica spheres of the spicules in the cone region contain high amounts of ‘mobile’ water. We conclude that the radiate accretive growth pattern of sponges is initiated in the apical region (cones) by newly growing spicules which are characterized by high amounts of ‘mobile’ water; subsequently spicule bundles are formed laterally around the cones. [Copyright &y& Elsevier]

Abstract: Radially symmetric pattern formation phenomena were investigated experimentally and numerically in 2D using a new experimental arrangement in a precipitation system. We examined the dependence of the pattern structure and the evolution of the precipitation front on its curvature. Depending on the radius of the reaction medium, two types of precipitation patterns has been observed: (a) pattern with a continuously distributed precipitate and a well detectable precipitation-free domain (Liesegang eyes phenomenon); (b) pattern with a continuous precipitation zone and discrete ring formation. Results of our simulations are in a good agreement with the experimental observations. [Copyright &y& Elsevier]

Abstract: In the paper, we deal with a reaction–diffusion system well known as the Brusselator model and some improved results for the steady states of this model are presented. We first give an a priori estimates (positive upper and lower bounds) of positive steady states. Then, we obtain the non-existence and existence of positive non-constant steady states as the parameters λ, θ and b are varied, which means some certain conditions under which the pattern formation occurs or not. [Copyright &y& Elsevier]

Abstract: This paper summarizes chick/quail transplantation experiments performed in the INSERM U106 by Alvarado-Mallart''s group from 1989 to 2002. First, it will present the various steps leading us to demonstrate that, at stage 10 of Hamburger and Hamilton, the avian neuroepithelium is still competent to change its fate influenced by environmental inductive factors and that these factors emanate from the cerebellar neuroepithelium; then, it will be briefly reported, experiments aimed to characterize the genetic cascade involved in the formation of the midbrain/hindbrain boundary and the specification of the meso-isthmic-cerebellar domain. [Copyright &y& Elsevier]

Abstract: Spatial synchrony, a normal self-organized spatial pattern in the predator–prey and host–parasitoid systems, can increase risk of regional extinction and hence, shrink metapopulation persistence. Coupled patch models, based on a within-patch Ronsenzweig–MacArthur Model, are adopted to investigate the impact of predator pursuit (PP) and prey evasion (PE) on the spatial synchrony and pattern formation in metapopulation framework. PP indicates that predators migrate not only from patches of higher predator density to those of lower predator density but also from patches of lower prey density to those of higher prey density; while, PE describes that prey migrate not only from patches of higher prey density to those of lower prey density but also from patches of higher predator density to those of lower predator density. Results show that either PP or PE can reduce spatial synchrony and result in the improvement of metapopulation persistence. Spatially explicit predator–prey system with local migration but without PP and PE can produce self-organized spatial patterns such as circular waves. The effect of PP and PE on spatial predator–prey system can decrease the spatial synchrony and change the circular waves to spatial chaos; therefore, these factors increase the spatial complexity and improve the metapopulation persistence. [Copyright &y& Elsevier]

Abstract: In the present paper, a description and mathematical analysis of a simple model of nonlinear pattern formation is given. The model is based on the so-called activator-inhibitor system proposed by Thomas. We introduce time delay into the reaction term and focus on its influence on morphogenesis and pattern formation. Numerical simulations are presented and compared for both cases without and with delay. [Copyright &y& Elsevier]

Abstract: Mesenchymal–epithelial interactions are an important source of information for pattern formation during organogenesis. In the developing excretory system, one of the secreted mesenchymal factors thought to play a critical role in patterning the growth and branching of the epithelial ureteric bud is GDNF. We have tested the requirement for GDNF as a paracrine chemoattractive factor by altering its site of expression during excretory system development. Normally, GDNF is secreted by the metanephric mesenchyme and acts via receptors on the Wolffian duct and ureteric bud epithelium. Misexpression of GDNF in the Wolffian duct and ureteric buds resulted in formation of multiple, ectopic buds, which branched independently of the metanephric mesenchyme. This confirmed the ability of GDNF to induce ureter outgrowth and epithelial branching in vivo. However, in mutant mice lacking endogenous GDNF, kidney development was rescued to a substantial degree by GDNF supplied only by the Wolffian duct and ureteric bud. These results indicate that mesenchymal GDNF is not required as a chemoattractive factor to pattern the growth of the ureteric bud within the developing kidney, and that any positional information provided by the mesenchymal expression of GDNF may provide for renal branching morphogenesis is redundant with other signals. [Copyright &y& Elsevier]

The plant hormone auxin is central in patterning die verse plant tissues. The direction of auxin flow and the distribution of auxin within tissues are regulated by auxin efflux transporters that are polarly localized in cells. Feedback regulation between auxin and its transporters establishes homeostatic patterns of auxin accumulation but allows dynamic repatterning in response to developmental or environmental cues. [ABSTRACT FROM AUTHOR]

The morphogenesis of fungiform papillae occurs in a stereotyped pattern on the dorsal surface of the mammalian tongue via epithelial-mesenchymal interactions. These interactions are thought to be achieved via intercellular communication. Gap junctions can be observed in many developing tissues and have been suggested to participate in a variety of functions, including the regulation of cell proliferation, differentiation, and apoptosis. Here, we demonstrate that the expression of Connexin 43 (Cx43), a gap junction protein, is correlated significantly with the development of fungiform papillae, which exhibit a pattern formation and morphogenesis similar to the development of other epithelial appendages. Antisense-oligodeoxynucleotide (AS-ODN) against Cx43 was used to assess the developmental functions of Cx43. The expression patterns of the signaling molecules were disrupted by Cx43 inhibition. Interestingly, the expression patterns ofShh, a key molecule in the determination of the spacing patterns of fungiform papillae, were disturbed after treatment with Cx43 AS-ODN. We have also attempted to determine the functions ofBmp-2by applying NOGGIN protein to tongue cultures. Our results indicate that upstream regulation via Cx43 controls theShhandBmp-2pathways for the morphogenesis and pattern formation of fungiform papillae. [ABSTRACT FROM AUTHOR]

Abstract: We analyzed an embryo mutant apical displacement1 (apd1) that formed an underdeveloped shoot at the apex of the embryo and one or two radicles in the enlarged basal region. At the early embryonic stage, apd1 initiated shoot and radicle in almost normal positions. However, in later stages, reduction of the apical region and enlargement of the basal region became gradually more pronounced. Consequently, a shoot and a radicle were shifted toward the apical position; the second radicle was formed below the first one. The apd1 plant showed pleiotropic phenotypes in shoots and roots: many tillers, narrow leaves, short roots and small inflorescences. In shl1-2 apd1 double mutant, a shoot was deleted, as in shl1-2. In addition, the number of radicles was more than that of apd1. This result suggests that APD1 and SHL1 function redundantly in the regulation of basal region size. Taken together, these results suggest that APD1 gene regulates the development of shoot and the regionalization along apical–basal axis. Moreover, we infer that in rice embryogenesis, sizes of apical and basal regions are under compensatory regulation. [Copyright &y& Elsevier]

Pattern formation is a hallmark of coordinated cell behaviour in both single and multicellular organisms. It typically involves cell-cell communication and intracellular signal processing. Here we show a synthetic multicellular system in which genetically engineered‘receiver’cells are programmed to form ring-like patterns of differentiation based on chemical gradients of an acyl-homoserine lactone (AHL) signal that is synthesized by‘sender’cells. In receiver cells,‘band-detect’gene networks respond to user-defined ranges of AHL concentrations. By fusing different fluorescent proteins as outputs of network variants, an initially undifferentiated‘lawn’of receivers is engineered to form a bullseye pattern around a sender colony. Other patterns, such as ellipses and clovers, are achieved by placing senders in different configurations. Experimental and theoretical analyses reveal which kinetic parameters most significantly affect ring development over time. Construction and study of such synthetic multicellular systems can improve our quantitative understanding of naturally occurring developmental processes and may foster applications in tissue engineering, biomaterial fabrication and biosensing. [ABSTRACT FROM AUTHOR]

Abstract: Many infectious diseases exist in several pathogenic variants, or strains, which interact via cross-immunity. It is observed that strains tend to self-organise into groups, or clusters. The aim of this paper is to investigate cluster formation. Computations demonstrate that clustering is independent of the model used, and is an intrinsic feature of the strain system itself. We observe that an ordered strain system, if it is sufficiently complex, admits several cluster structures of different types. Appearance of a particular cluster structure depends on levels of cross-immunity and, in some cases, on initial conditions. Clusters, once formed, are stable, and behave remarkably regularly (in contrast to the generally chaotic behaviour of the strains themselves). In general, clustering is a type of self-organisation having many features in common with pattern formation. [Copyright &y& Elsevier]

Background: Segmentation of the Drosophila embryo is a classic paradigm for pattern formation during development. The Wnt-1 homolog Wingless (Wg) is a key player in the establishment of a segmentally reiterated pattern of cell type specification. The intrasegmental polarity of this pattern depends on the precise positioning of the Wg signaling source anterior to the Engrailed (En)/Hedgehog (Hh) domain. Proper polarity of epidermal segments requires an asymmetric response to the bidirectional Hh signal: wg is activated in cells anterior to the Hh signaling source and is restricted from cells posterior to this signaling source.Results: Here we report that Midline (Mid) and H15, two highly related T box proteins representing the orthologs of zebrafish hrT and mouse Tbx20, are novel negative regulators of wg transcription and act to break the symmetry of Hh signaling. Loss of mid and H15 results in the symmetric outcome of Hh signaling: the establishment of wg domains anterior and posterior to the signaling source predominantly, but not exclusively, in odd-numbered segments. Accordingly, loss of mid and H15 produces defects that mimic a wg gain-of-function phenotype. Misexpression of mid represses wg and produces a weak/moderate wg loss-of-function phenocopy. Furthermore, we show that loss of mid and H15 results in an anterior expansion of the expression of serrate (ser) in every segment, representing a second instance of target gene repression downstream of Hh signaling in the establishment of segment polarity.Conclusions: The data we present here indicate that mid and H15 are important components in pattern formation in the ventral epidermis. In odd-numbered abdominal segments, Mid/H15 activity plays an important role in restricting the expression of Wg to a single domain. [Copyright &y& Elsevier]

Abstract: A complex process-based model (Delft3D) is used to simulate the formation of channels and shoals in a schematised estuary. The model set-up enables a comparison with results obtained from other studies using idealised models. Initial (one tidal cycle) as well as long-term (up to 300 years) simulations are made. Dominant wavelengths of channel–shoal patterns are investigated together with their dependency on width and depth of the basin and the local maximum velocity. Prevalent wavelengths range between 5 and and increase with increasing width and flow velocity. Initial model results are compared with those of idealised models. The dominant wavelengths are of the same order of magnitude as those found in idealised models and their dependency on width and velocity agrees qualitatively. (Exponential) growth of the perturbations during long-term simulations provides information on the limits of validity of the idealised models. Subsequent pattern formation and changes of dominant wavelengths are attributed to non-linear interactions. Morphological developments during long-term simulations suggest that channel–shoal patterns evolve into a unique morphodynamic equilibrium state, independent of the initial perturbation. [Copyright &y& Elsevier]

Metamorphosis is an organic process of change that is seen in all levels of life. Whether at the individual, the corporate or the global level of human life, the processes of change involve natural periods of chaos and order, times of conflict that underlie the movement toward transformation, and developmental shifts that may be painful as well as pleasurable. This paper addresses these phenomena in relation to current changes going on in our world. [ABSTRACT FROM AUTHOR]

Many of the genes involved in the initial development of the limb in higher vertebrates are also expressed during regeneration of the limb in urodeles such as Notophthalmus viridescens. These similarities have led researchers to conclude that the regeneration process is a recapitulation of development, and that patterning of the regenerate mimics pattern formation in development. However, the developing limb and the regenerating limb do not look similar. In developing urodele forelimbs, digits appear sequentially as outgrowths from the limb palette. In regeneration, all the digits appear at once. In this work, we address the issue of whether regeneration and development are similar by examining growth and apoptosis patterns. In contrast to higher vertebrates, forelimb development in the newt, N. viridescens, does not use interdigital apoptosis as the method of digit separation. During adult forelimb regeneration, apoptosis seems to play an important role in wound healing and again during cartilage to bone turnover in the advanced digits and radius/ulna. However, similar to forelimb development, demarcation of the digits in adult forelimb regeneration does not involve interdigital apoptosis. Outgrowth, rather than regression of the interdigital mesenchyme, leads to the individualization of forelimb digits in both newt development and regeneration. [ABSTRACT FROM AUTHOR]

Turing pattern formation under local feedback is investigated. Simulation results show that local feedback can significantly orient Turing patterns, change the local or global dynamic behavior of the system and even inhibit or induce pattern formation in some conditions. Since a lot of modulating effects in biological systems are realized through local feedback, this work is of practical significance to the investigations of pattern formation in complex biological systems. [Copyright &y& Elsevier]

During C. elegans development, the temporal pattern of many cell lineages is specified by graded activity of the heterochronic gene Lin-14. Here we demonstrate that a temporal gradient in lin-14 protein is generated posttranscriptionally by multiple elements in the lin-14 3'UTR that are regulated by the heterochronic gene Lin-4. The lin-14 3'UTR is both necessary and sufficient to confer lin-4-mediated posttranscriptional temporal regulation. The function of the lin-14 3'UTR is conserved between C. elegans and C. briggsae. Among the conserved sequences are seven elements that are each complementary to the lin-4 RNAs. A reporter gene bearing three of these elements shows partial temporal gradient activity. These data suggest a molecular mechanism for Lin-14p temporal gradient formation: the lin-4 RNAs base pair to sites in the lin-14 3'UTR to form multiple RNA duplexes that down-regulate lin-14 translation. [ABSTRACT FROM AUTHOR]

We have formulated the dynamics and the simulation scheme for large deformation of gels using the stress-diffusion coupling model [Yamaue, T., Taniguchi, T., and Doi, M., 2000, AIP Conference Proceedings , Vol. 519 (AIP), p. 584]. Using this model, we have simulated the deswelling process of 2D slab thermo-responsive gels undergoing spinodal decomposition, in comparison with the conventional collective diffusion model of gel networks. We reproduced the 'plateau period' due to the surface skin formation and the pattern formations in the inner region of gels by the stress-diffusion coupling model. [ABSTRACT FROM AUTHOR]

From time to time, novel ways of interpreting and modifying ageing mechanisms are proposed. Occasionally, these lead to a conceptual dead end, whereas at other times new and vital insights into basic ageing mechanisms are gained. This review concentrates on one such way of interpreting and manipulating ageing processes, based on chaos (dynamical systems) theory. One prediction of this theory is that a wide-ranging loss of physiological complexity from molecular to cellular, and from tissue to organismic levels accompanies ageing and age-related diseases. Although this view has been criticised, and arguments have been put forward to claim that there is also an increase of complexity during ageing and dysfunction, this review holds that the interpretation of ageing as a simplification of physiological dynamical complexity offers clear advantages. Ageing changes can be quantified and the results of treatment monitored. Clinical benefits can be predicted and intervention strategies improved. Two main practical suggestions for achieving successful ageing at the clinical level are examined. First, chaos theory challenges the traditional pharmacological regimes and implies that, for maximum benefit, medication aimed at modifying some of the signs of ageing should be given at irregular, pulsed or multiple intervals, and at constantly changing dosage strengths. Second, for preventing age-related disability, it is necessary to introduce and maintain a multiplicity of external and internal physiological stimuli, such as variable physical and mental exercise regimes. [ABSTRACT FROM AUTHOR]

The self-epitaxial nucleation and growth origin of the formation and transformation of crystalline fractal pattern is identified for the first time. Two universal parameters, so-called relative elemental branching period 〈&ltilde;〉and the anisotropy or structural match parameter m, are introduced to describe the pattern transformation. These two parameters can be predicted according to our model. Fractal patterns arise when 〈&ltilde;〉1. Fractal patterns having a strong anisotropy (m→1) at relatively low surface supersaturations, and a very weak anisotropy (m→-1) at high surface supersaturations. The results are in excellent agreement with the results of NH4Cl crystals grown from different mediums. [Copyright &y& Elsevier]