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Results for “Spatial pattern formation”

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PubMed1998

Pattern Formation and the Spatial Scale of Interaction between Predators and Their Prey.

We study interactions of predators and prey that are characterized by a scale difference in their use of space. Prey are assumed to occupy patches, forming a metapopulation with low migration among patches. Predators are homogeneously distributed over these patches, due to broad-scale foraging behavior or long-range juvenile dispersal. The predator population thus exerts a globally uniform predation pressure on the prey subpopulations. Under these conditions a nonlinear predator functional response depending on local prey density leads to multiple equilibria that can occur for the same parameter values. These equilibria differ in the fraction of prey patches that are (nearly) empty. Equilibria with a larger fraction of empty prey patches are more stable. The system tends to approach equilibria with a sufficiently high number of empty prey patches, so that local and global population dynamics are stable. If unstable dynamics are observed at all, the fluctuations in local prey density exhibit predictable characteristics. Our main conclusion is that a nonlinear functional response of the predator to local prey density can induce the formation of static patterns in prey density and, hence, lead to stable local and global dynamics. It is shown that these results are sufficiently general to carry over to situations in which prey migration between patches does occur or the spatial domain occupied by the prey population is continuous instead of subdivided into patches. Copyright 1998 Academic Press.

Journal Article↗

PubMed2002

Theory of electrochemical pattern formation.

The spatial coupling in electrochemical systems is mediated by ion migration under the influence of the electric field. Since field effects spread very rapidly, every point of an electrode can communicate with every other one practically instantaneously through migration coupling. Based on mathematical potential theory we present the derivation of a generally applicable reaction-migration equation, which describes the coupling via an integral over the whole electrode area. The corresponding coupling function depends only on the geometry of the electrode setup and has been computed for commonly used electrode shapes (such as ring, disk, ribbon or rectangle). The pattern formation observed in electrochemical systems in the bistable, excitable and oscillatory regime can be reproduced in computer simulations, and the types of patterns occurring under different geometries can be rationalized. (c) 2002 American Institute of Physics.

Journal Article↗

PubMed2003

Pattern selection in a cooperative biochemical in vitro amplification system: the role of parasites.

Previously, numerical simulations have shown that evolving systems can be stabilized against emerging parasites by pattern formation in spatially extended flow reactors. Hence, it can be argued that pattern formation is a prerequisite for any experimental investigation of the biochemical evolution of cooperative function. Here, we study a model of an experimental biochemical system for the cooperative in vitro amplification of DNA strands and show that emerging parasites can induce a complex pattern formation even when no pattern formation occurs without parasites. In an adiabatic approximation where the cooperative amplification reaction is assumed to adapt fast to slowly emerging parasites, the parasite concentration itself acts as a Steuer parameter for the selection of various complex patterns. Without such an adiabatic approximation only transient patterns emerge. As any species can grow for very low concentrations, the parasite is able to infect the entire reactor and the system is finally diluted out. In the experimental biochemical system, however, the species are individual molecules and the growth of spatially separated, non-infected regions becomes feasible. Hence a cutoff threshold for the minimal concentration is applied. In these simulations the otherwise lethal infection by parasites induces the formation of spatiotemporal spirals, and this spatial structure help the host and parasitoid species to survive together. These theoretical results describe an inherent property of cooperative reactions and have an important impact on experimental investigations on the molecular evolution and complex function in spatially extended reactors. Since the formation of the complex pattern is restricted either to a rather large cutoff value or a special choice of the kinetic parameters, we, however, conclude that the persistence of evolving cooperative amplification is not possible in a simple reaction-diffusion reactor. Experimental set-ups with patchy environments, e.g. biomolecular amplification in coupled microstructured flow chambers or in microemulsion, are eligible candidates for the observation of such a self-organized pattern selection.

Animals↗

PubMed2006

Spatial growth and pattern formation in the small intestine microvascular bed from larval to adult Xenopus laevis: a scanning electron microscope study of microvascular corrosion casts.

The microvascular anatomy of the small intestine of metamorphosing tadpoles of the South African Clawed Toad, Xenopus laevis (Daudin) is studied from developmental stages 55 to 65 and in adults by scanning electron microscopy (SEM) of vascular corrosion casts (VCCs) and light microscopy. Up to stage 62, VCCs reveal a dense two-dimensional vascular network ensheating the intestinal tube, whose proximal portion forms a clockwise spiralling outer and its distal portion an anti-clockwise spiralling inner coil. Vessels of the intestinal network impose flat and run circularly to slightly obliquely. Locally, dense capillary plexus with small "holes" indicating ongoing intussusceptive microvascular growth (IMG) and vessel maturation, are present. The typhlosole, an invagination along the proximal portion of the small intestine, reveals a dense capillary bed with locally ongoing IMG. VCCs of stages 62/63 for the first time reveal a three-dimensional vascular bed with longitudinal intestinal folds of varying size and heights greatly enlarging the luminal exchange area of the intestinal tube. From stage 65 onwards, longitudinal intestinal folds undulate and, though smaller in size and less mature as indicated in VCCs by the presence of wider, sinus-like vessels with small "holes" interposed between, closely resemble the intestinal folds present in the small intestine of adult Xenopus. Our data suggest that maturation of the vascular pattern in the small intestine of X. laevis tadpoles takes place successively after stages 62-63, and growth during this period is preferentially by intussusception.

Age Factors↗

PubMed2003

One-dimensional daisyworld: spatial interactions and pattern formation.

The zero-dimensional daisyworld model of Watson and Lovelock (1983) demonstrates that life can unconsciously regulate a global environment. Here that model is extended to one dimension, incorporating a distribution of incoming solar radiation and diffusion of heat consistent with a spherical planet. Global regulatory properties of the original model are retained. The daisy populations are initially restricted to hospitable regions of the surface but exert both global and local feedback to increase this habitable area, eventually colonizing the whole surface. The introduction of heat diffusion destabilizes the coexistence equilibrium of the two daisy types. In response, a striped pattern consisting of blocks of all black or all white daisies emerges. There are two mechanisms behind this pattern formation. Both are connected to the stability of the system and an overview of the mathematics involved is presented. Numerical experiments show that this pattern is globally determined. Perturbations in one region have an impact over the whole surface but the regulatory properties of the system are not compromised by transient perturbations. The relevance of these results to the Earth and the wider climate modelling field is discussed.

Climate↗

PubMed1988

A pattern formation mechanism to control spatial organization in the embryo of Drosophila melanogaster.

It is known that cells are already committed to a particular segment at the cellular blastoderm stage during embryogenesis of Drosophila melanogaster. Recently, several segmentation genes have been observed to be expressed in a sequence of banded spatial patterns in the syncytial blastoderm, prior to the formation of the cellular blastoderm. It is demonstrated in this paper that a two component reaction-diffusion (RD) system with net production functions which are antisymmetric with respect to the uniform steady-state values, is capable of producing a sequence of seven spatial patterns in the syncytial blastoderm. The sequence of patterns obtained exhibit a strong preference for banded or striped patterns. The first pattern is a simple anteroposterior gradient while the second is a gradient in the dorsoventral direction. The next five patterns are a sequence of banded patterns which exhibit frequency doubling, i.e. the number of bands in each pattern tend to be double the number in the previous pattern. The predicted pattern sequence is comparable to that observed in the expression of some segmentation genes. It is suggested that a pattern formation mechanism based on such an RD system may exist in the embryo where it produces a sequence of prepatterns to regulate the expression of various segmentation genes leading ultimately to a segmented embryo. There is sufficient spatial information in the sequence of banded prepatterns for the segments to be unique.

Animals↗

PubMed2003

Stabilizing Turing patterns with subdiffusion in systems with low particle numbers.

The role of subdiffusion in the formation of spatial Turing patterns with particle number fluctuations is studied. It is demonstrated for a generic activator-inhibitor system that for normal diffusion the particle number fluctuations stabilize the homogenous steady state in a regime where the mean-field analysis already predicts stable spatial patterns. In contrast, pattern formation is stabilized considerably even for very low particle numbers when the activator moves subdiffusively while the inhibitor diffuses normally. In particular, this also holds true when the subdiffusive activator spreads faster than the inhibitor on small time scales. Possible applications to pattern formation in cell biology are discussed.

Journal Article↗

PubMed2000

Spontaneous pattern formation in driven nonlinear lattices

We demonstrate the spontaneous formation of spatial patterns in a damped, ac-driven cubic Klein-Gordon lattice. These patterns are composed of arrays of intrinsic localized modes characteristic for nonlinear lattices. We analyze the modulation instability leading to this spontaneous pattern formation. Our calculation of the modulational instability is applicable in one- and two-dimensional lattices; however, in the analyses of the emerging patterns we concentrate particularly on the two-dimensional case.

Journal Article↗

PubMed1980

Temporal and spatial patterns of Purkinje cell formation in the mouse cerebellum.

In an attempt to determine the time of origin and the final localization of Purkinje cells in the cerebellum, pregnant mice were injected with tritiated thymidine successively, four to six times daily, beginning on either day 10, 11, 12, 12.5, 13, or 14 of gestation, considering 6 a.m. on the day when vaginal plugs were found as day 0. Offspring were killed at 30 days of age, and serial sagittal sections of the cerebellum were prepared for autoradiography. Labeled and unlabeled Purkinje cells in the various regions of the cerebellum were counted, and unlabeled ones were considered to be formed earlier than the initiation of the injections. In the medial level of the vermis, the majority of the Purkinje cell population was formed on day 12 of gestation and a few on day 13, whereas the cells in the paravermian and hemispheric portions were formed on days 11 and 12. Thus, a slight lateromedial gradient of the time of Purkinje cell origin was demonstrated. Purkinje cells that were formed after day 12.5 were distributed more in the vermis than in the hemisphere, more in the ventral region of the vermis (lingula, ventral lobule of lobulus centralis, and nodulus) than in the dorsal region (culmen, declive, tuber, pyramis, and uvula), and deep in the vermian fissures, rather than on the surface of the lobules. These findings suggest that postnatally, early maturing regions of the cerebellum may have received many of the later formed Purkinje cells.

Animals↗

PubMed1984

Appearance of distinct types of proteoglycan in a well-defined temporal and spatial pattern during early cartilage formation in the chick limb.

Our recent studies have shown that chick embryo epiphyseal cartilage synthesizes three distinct species of proteoglycan (PG-H, PG-Lb, and PG-Lt) which are analogous in having glycosaminoglycan side chains of the chondroitin (dermatan) sulfate type but different from one another in regard to the structure of core protein. In the present report, the expression of PG-H and PG-Lb has been studied in developing chick hind limbs (stages 19-33), using antibodies specific for these substances in indirect immunofluorescence. At the onset of cartilage morphogenesis (stage 24), PG-H became recognizable in the cartilage primordia, whereas a parallel section stained for PG-Lb showed no reaction. The first evidence of PG-Lb appearance was seen in a stage 28 cartilage (e.g., tibia) in which the cells in the middiaphysis became elongated in a direction perpendicular to the long axis of the cartilage. The PG-Lb fluorescence was confined to the zone of these flattened, disc-like cells, whereas the fluorescence for PG-H was uniformly distributed throughout the cartilage. With further development of cartilage (stage 29 approximately), the zone of flattened cells spread proximally and distally, and simultaneously large hypertrophied cells appeared at the diaphyseal region. During these zonal changes of cell morphology, the PG-Lb fluorescence remained restricted to the zone of flattened cells. Parallel sections stained for PG-H, in contrast, showed an evenly distributed pattern of the PG-H fluorescence throughout the cartilage. The results indicate that the appearance of PG-Lb is closely associated with the zonal changes of cell shape and orientation along the proximal-distal axis of the developing limb cartilage, and further suggest that the flattened chondrocytes in this particular zone have undergone additional changes in gene expression to form an extracellular matrix of still another chemical property.

Animals↗

PubMed2004

Control of Turing pattern by weak spatial perturbation.

The control of Turing pattern formation by weak spatial perturbation is investigated. The weak spatial perturbation added before Turing pattern stabilization is found to show prominent spatial orientation effect. The control process of perturbation to Turing patterns is tracked. The effect of perturbation factors, such as amplitude and imposing time are also discussed.

Journal Article↗

PubMedDate not supplied

Effects of retinoids on chick face development.

Local application of retinoic acid to chick embryos produces severe bilateral clefting of the primary palate but does not affect the lower beak. This paper reviews what is known about the basis and specificity of this retinoid-induced defect by examining three major developmental processes: morphogenesis, cell differentiation, and pattern formation. The conclusion reached is that neither cytotoxicity nor cartilage inhibition is the basis of the specific retinoid-induced defect. Retinoid treatment interferes with reciprocal epithelial-mesenchymal interactions in the upper beak. These interactions are involved in linking pattern formation--the spatial ordering of cell differentiation--to morphogenesis and outgrowth. These results suggest that retinoids are interfering with the process of pattern formation in the upper beak, a conclusion that is supported by the similarities between retinoid effects on face and limb development. Thus, it appears that retinoids may be acting as general signaling molecules throughout the developing embryo. In the lower beak, pattern-forming cues may occur earlier in development. Alternatively, the cells may be unresponsive to retinoids. The molecular basis for the specificity of the facial defect--as well as for the action of retinoids on developing systems--is discussed with reference to recent advances in molecular biology.

Animals↗

PubMed2006

Geometrically repatterned immunological synapses uncover formation mechanisms.

The interaction of T cells and antigen-presenting cells is central to adaptive immunity and involves the formation of immunological synapses in many cases. The surface molecules of the cells form a characteristic spatial pattern whose formation mechanisms and function are largely unknown. We perform computer simulations of recent experiments on geometrically repatterned immunological synapses and explain the emerging structure as well as the formation dynamics. Only the combination of in vitro experiments and computer simulations has the potential to pinpoint the kind of interactions involved. The presented simulations make clear predictions for the structure of the immunological synapse and elucidate the role of a self-organizing attraction between complexes of T cell receptor and peptide-MHC molecule, versus a centrally directed motion of these complexes.

Antigen-Presenting Cells↗

PubMed2003

Cell behavior and cell-cell communication during fruiting body morphogenesis in Myxococcus xanthus.

Formation of spatial patterns of cells from a mass of initially identical cells is a recurring theme in developmental biology. The dynamics that direct pattern formation in biological systems often involve morphogenetic cell movements. An example is fruiting body formation in the gliding bacterium Myxococcus xanthus in which an unstructured population of identical cells rearranges into an asymmetric, stable pattern of multicellular fruiting bodies in response to starvation. Fruiting body formation depends on changes in organized cell movements from swarming to aggregation. The aggregation process is induced and orchestrated by the cell-surface associated 17 kDa C-signal protein. C-signal transmission depends on direct contact between cells. Evidence suggests that C-signal transmission is geometrically constrained to cell ends and that productive C-signal transmission only occurs when cells engage in end-to-end contacts. Here, we review recent progress in the understanding of the pattern formation process that leads to fruiting body formation. Gliding motility in M. xanthus involves two polarly localized gliding machines, the S-machine depends on type IV pili and the A-machine seems to involve a slime extrusion mechanism. Using time-lapse video microscopy the gliding motility parameters controlled by the C-signal have been identified. The C-signal induces cells to move with increased gliding speeds, in longer gliding intervals and with decreased stop and reversal frequencies. The combined effect of the C-signal dependent changes in gliding motility behaviour is an increase in the net-distance travelled by a cell per minute. The identification of the motility parameters controlled by the C-signal in combination with the contact-dependent C-signal transmission mechanism have allowed the generation of a qualitative model for C-signal induced aggregation. In this model, the directive properties of the C-signal are a direct consequence of the contact-dependent signal-transmission mechanism, which is a local event involving direct contact between cells that results in a global organization of cells. This pattern formation process does not depend on a diffusible substance. Rather it depends on a cell-surface associated signal to direct the cells appropriately.

Bacterial Proteins↗

PubMed2004

Stripe patterns in two-dimensional systems with core-corona molecular architecture.

The behavior of a two-dimensional system of particles interacting through a potential consisting of a hard core surrounded by a soft repulsive corona is investigated at several densities and temperatures. We find that the competition between hard and soft repulsions gives origin to the spontaneous formation of spatial patterns resembling stripe textures. The effect of varying the hard and soft core radii ratio as well as that of adding an attractive component to the interparticle interaction is studied. The model investigated is relevant for macromolecular topologies possessing two intrinsic length scales.

Journal Article↗

PubMed2000

Thoracic skeletal defects in myogenin- and MRF4-deficient mice correlate with early defects in myotome and intercostal musculature.

Myogenin and MRF4 are skeletal muscle-specific bHLH transcription factors critical for muscle development. In addition to a variety of skeletal muscle defects, embryos homozygous for mutations in myogenin or MRF4 display phenotypes in the thoracic skeleton, including rib fusions and sternal defects. These skeletal defects are likely to be secondary because myogenin and MRF4 are not expressed in the rib cartilage or sternum. In this study, the requirement for myogenin and MRF4 in thoracic skeletal development was further examined. When a hypomorphic allele of myogenin and an MRF4-null mutation were placed together, the severity of the thoracic skeletal defects was greatly increased and included extensive rib cartilage fusion and fused sternebrae. Additionally, new rib defects were observed in myogenin/MRF4 compound mutants, including a failure of the rib cartilage to contact the sternum. These results suggested that myogenin and MRF4 share overlapping functions in thoracic skeletal formation. Spatial expression patterns of skeletal muscle-specific markers in myogenin- and MRF4-mutant embryos revealed early skeletal muscle defects not previously reported. MRF4-/- mice displayed abnormal intercostal muscle morphology, including bifurcation and fusion of adjacent intercostals. myogenin/MRF4-mutant combinations displayed ventral myotome defects, including a failure to express normal levels of myf5. The results suggested that the early muscle defects observed in myogenin and MRF4 mutants may cause subsequent thoracic skeletal defects, and that myogenin and MRF4 have overlapping functions in ventral myotome differentiation and intercostal muscle morphogenesis.

Alleles↗

PubMed2005

Turing instability in pioneer/climax species interactions.

Systems of pioneer and climax species are used to model interactions of species whose reproductive capacity is sensitive to population density in their shared ecosystem. Intraspecies interaction coefficients can be adjusted so that spatially homogeneous solutions are stable to small perturbations. In a reaction-diffusion pioneer/climax model we will determine the critical value of the diffusion rate of the climax species, below which the equilibrium solution is unstable to non-homogeneous perturbations. For diffusion rates smaller than this critical value, an equilibrium solution remains stable to spatially homogeneous perturbations but is unstable to non-homogeneous perturbations. A Turing (diffusional) bifurcation leads to the formation of spatial patterns in species' densities. Forcing, interpreted as stocking or harvesting of the species, can reverse the bifurcation and establish equilibrium solutions which are stable to small perturbations. The implicit function theorem is used to determine whether stocking or harvesting of one of the species in the model is the appropriate remedy for diffusional instability. The use of stocking or harvesting by a natural resource manager thus influences the long-term dynamics and spatial distribution of species in a pioneer/climax ecosystem.

Algorithms↗

PubMed1990

Prediction of apical thrombus formation in acute myocardial infarction based on left ventricular spatial flow pattern.

The predictive value of the left ventricular spatial flow pattern for thrombus formation was determined in 62 patients with acute myocardial infarction. A normal flow pattern by pulsed Doppler echocardiography was characterized by 1) simultaneous onset of blood motion at the mitral valve and apical level, and 2) a discontinuous Doppler signal along the lateral wall and interventricular septum. The flow pattern was assessed by these criteria, within 24 h after the onset of complaints and after 6 and 12 weeks. In 46 of the 62 patients, a normal flow pattern was found at the first examination; none of these 46 patients developed a thrombus during the study period. An abnormal flow pattern was seen at the first examination in 16 patients; this pattern normalized during follow-up in 6 patients, none of whom developed a thrombus. In the other 10 patients the abnormal flow pattern persisted, and 7 of these developed a thrombus. These findings suggest that a normal left ventricular flow pattern in the setting of acute myocardial infarction is not associated with subsequent thrombus formation. This observation may be of importance if anticoagulation is considered.

Aged↗