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Results for “Spatial pattern formation”

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PubMed1994

Chemical turbulence and standing waves in a surface reaction model: The influence of global coupling and wave instabilities.

Among heterogeneously catalyzed chemical reactions, the CO oxidation on the Pt(110) surface under vacuum conditions offers probably the greatest wealth of spontaneous formation of spatial patterns. Spirals, fronts, and solitary pulses were detected at low surface temperatures (T<500 K), in line with the standard phenomenology of bistable, excitable, and oscillatory reaction-diffusion systems. At high temperatures (T greater, similar 540 K), more surprising features like chemical turbulence and standing waves appeared in the experiments. Herein, we study a realistic reaction-diffusion model of this system, with respect to the latter phenomena. In particular, we deal both with the influence of global coupling through the gas phase on the oscillatory reaction and the possibility of wave instabilities under excitable conditions. Gas-phase coupling is shown to either synchronize the oscillations or to yield turbulence and standing structures. The latter findings are closely related to clustering in networks of coupled oscillators and indicate a dominance of the global gas-phase coupling over local coupling via surface diffusion. In the excitable regime wave instabilities in one and two dimensions have been discovered. In one dimension, pulses become unstable due to a vanishing of the refractory zone. In two dimensions, turbulence can also emerge due to spiral breakup, which results from a violation of the dispersion relation.

Journal Article↗
PubMed1996

Catastrophic extinction, noise-stabilized turbulence and unpredictability of competition in a modified Volterra-Lotka model.

Spatial coexistence and competition among species is investigated through a modified Volterra-Lotka model which takes into account sexual breeding. This allows the population specific growth rate to depend on the population density. As a result of this modification the degeneracy inherent in the classical model is eliminated and qualitatively novel regimes are observed, as demonstrated by parametric analysis of the model. In the case where the corresponding parameters of competing species do not differ significantly the model can be reduced to a single Ginzburg-Landau type equation. The spatially distributed model is analyzed both in the absence and in the presence of noise mimicking inherent fluctuations in birth and death rates. It is shown that noise can qualitatively change the behavior of the system. Not only does it induce the formation of spatial patterns, but also switches on endless turbulent-like rearrangement of the system. When initially unpopulated habitat is occupied by competing species even a very low-intensity noise makes the final state of the system totally unpredictable and sensitive to any fluctuations. (c) 1996 American Institute of Physics.

Journal Article↗
PubMed2004

Dynamic phase separation: from coarsening to turbulence via structure formation.

We investigate some new two-dimensional evolution models belonging to the class of convective Cahn-Hilliard models: (i) a local model with a scalar order parameter, (ii) a nonlocal model with a scalar order parameter, and (iii) a model with a vector order parameter. These models are applicable to phase-separating system where concentration gradients cause hydrodynamic motion due to buoyancy or Marangoni effect. The numerical study of the models shows transition from coarsening, typical of Cahn-Hilliard systems, to spatiotemporally irregular behavior (turbulence), typical of the Kuramoto-Sivashinsky equation, which is obtained in the limit of very strong driving. The transition occurs not in a straightforward way, but through the formation of spatial patterns that emerge for intermediate values of the driving intensity. As in driven one-dimensional models studied before, the mere presence of the driving force, however small, breaks the symmetry between the two separating phases, as well as increases the coarsening rate. With increasing driving, coarsening stops. The dynamics is generally irregular at strong driving, but exhibits specific structural features.

Algorithms↗
PubMed1998

Diet-induced diabetes activates an osteogenic gene regulatory program in the aortas of low density lipoprotein receptor-deficient mice.

Vascular calcification is common in people with diabetes and its presence predicts premature mortality. To clarify the underlying mechanisms, we used low density lipoprotein receptor-deficient (LDLR -/-) mice to study vascular calcification in the ascending aorta. LDLR -/- mice on a chow diet did not develop obesity, diabetes, atheroma, or vascular calcification. In contrast, LDLR -/- mice on high fat diets containing cholesterol developed obesity, severe hyperlipidemia, hyperinsulinemic diabetes, and aortic atheroma. A high fat diet without cholesterol also induced obesity and diabetes, but caused only moderate hyperlipidemia and did not result in significant aortic atheroma formation. Regardless of cholesterol content, high fat diets induced mineralization of the proximal aorta (assessed by von Kossa staining) and promoted aortic expression of Msx2 and Msx1, genes encoding homeodomain transcription factors that regulate mineralization and osseous differentiation programs in the developing skull. Osteopontin (Opn), an osteoblast matrix protein gene also expressed by activated macrophages, was up-regulated in the aorta by these high fat diets. In situ hybridization showed that peri-aortic adventitial cells in high fat-fed mice express Msx2. Opn was also detected in this adventitial cell population, but in addition was expressed by aortic vascular smooth muscle cells and macrophages of the intimal atheroma. High fat diets associated with hyperinsulinemic diabetes activate an aortic osteoblast transcriptional regulatory program that is independent of intimal atheroma formation. The spatial pattern of Msx2 and Opn gene expression strongly suggests that vascular calcification, thought to be limited to the media, is an active process that can originate from an osteoprogenitor cell population in the adventitia.

Animals↗
PubMed1975

Properties of surface and junctional membranes of embryonic cells isolated from blastula stages of Xenopus laevis.

1. Some membrane properties of endoderm and mesoderm cells isolated from late blastula stages of Xenopus laevis have been examined using electrophysiological techniques. 2. Cells were isolated by treatment of whole embryos with Ca-free EDTA containing media, or mechanically by micro-dissection, and cultured in Ca-containing Holtfreter solution (60 mM-NaCl) or Ringer solution (120 mM-NaCl). 3. Membrane potentials lay between -6 and -84 mV; specific membrane resistances ranged from 500 to 29,000 omega cm2; there was no difference between EDTA isolated and mechanically isolated cells. 4. Relative and absolute cation and anion conductances varied from cell to cell. Some cells were anion impermeable; the cation conductance ranged from 35 to 300 mumho/cm2. 5. The resting potential of some cells was largely determined by the concentration gradient and membrane permeability of K ions. In other cells the potential was maintained either by some other ion or by an electrogenic pump. [K]i came to approximately 130 mM in Ringer solution (the value pertaining in the intact embryo) and similar to 60 mM in Holtfreter solution. 6. In most pairs and small clumps of cells ionic current spread from one cell to the next; some single cells and groups of cells were uncoupled from their neighbours. 7. The junctional resistance lay between 10(5) and 10(8) omega; it behaved as a linear resistor in most cell pairs studied. In three pairs the intercellular junction showed rectifying properites. 8. By the late blastula stage of development presumptive endoderm and mesoderm cells form a heterogeneous population with widely varying passive membrane properties. The significance of these findings is discussed in relation to current hypotheses for the formation of spatial patterns during differentiation.

Animals↗
PubMed1985

Regional specification of cell-specific gene expression during craniofacial development.

The core problem in craniofacial development is regional specification of cell-specific gene expression. Regional specification is also referred to as pattern formation or spatial organization. During early embryogenesis, regional specification is possibly operant following blastula, and is apparent during gastrulation and thereafter during embryonic and fetal stages of development. Current interdisciplinary approaches toward understanding embryonic development incorporate a number of scientific approaches including those of recombinant DNA technology. Three major advances have significantly enhanced the utility of so-called "genetic engineering," including the discovery of restriction nuclease enzymes that cleave DNA sequences at specific sites; the discovery of DNA ligase enzymes that facilitate ligation and annealing of DNA sequences to one another, so as to facilitate the joining of foreign DNA sequences with host DNA; and the discovery of effective techniques for the introduction of foreign DNA sequences into previously refractory organisms. The present discussion analyzes the problem of regional specification of ameloblast-specific gene expression as a paradigm for utilizing recombinant DNA technology in studies of normal and abnormal craniofacial development.

Animals↗
PubMed1993

Transcriptional regulation and spatial patterning in Drosophila.

Pattern formation in Drosophila is initiated by a small set of asymmetrically distributed maternal transcription factors that act as graded morphogens along the anterior-posterior and the dorsal-ventral axes of the embryo. Recent progress in the field provides first insight into the molecular mechanisms by which long-range positional information in the egg causes a series of localized zygotic transcription factors to position the developmental fate along the blastoderm.

Animals↗
PubMed2006

On the formation mechanisms, spatial resolution and intensity of backscatter Kikuchi patterns.

The present paper is divided into two main sections. In the first, the formation mechanisms of backscatter Kikuchi patterns (BKP) are discussed on the basis of measurements on the sharpness of Kikuchi lines and on the spatial, that means the lateral and depth resolution of the technique. We propose that thermal diffuse scattering is the important incoherent scattering mechanism involved in pattern formation. This mechanism is not considered in the classical description of the origin of backscattered electrons in the scanning electron microscope (SEM) which is why there is in some important points no agreement between classical Monte-Carlo-type electron trajectory simulations and experimental results. We assume that the energy spectrum of the backscattered electrons shows, similar to the spectra in transmission electron microscopy, a sharp zero-loss peak. In the second section, we discuss the intensity of Kikuchi bands in BKP. It is shown that the kinematical theory gives-of course-not the correct intensities, but that these intensities are, on the other hand, not too far off the experimental ones. We subsequently introduce a simple intensity correction procedure that is based on the two-beam dynamical theory, originally proposed by Blackman for transmission electron diffraction patterns. It is shown by examples of diffraction patterns of niobium and silicon that this procedure leads to satisfying results, once two unknown variables (a universal constant and the exit depth of the electrons) have been empirically fit. It is assumed that in the future, this correction will improve the possibilities of phase identification by backscatter Kikuchi diffraction patterns.

Journal Article↗
PubMed1999

Use of developmental marker genes to define temporal and spatial patterns of differentiation during embryoid body formation.

Mouse embryonic stem cells are pluripotent cells that are derived from the inner cell mass of blastocysts. When induced to synchronously enter a program of differentiation in vitro, they form embryoid bodies that contain cells of the mesodermal, hematopoietic, endothelial, muscle, and neuronal lineages. Here, we used a panel of marker genes with early expression within the germ layers (oct-3, Brachyury T, Fgf-5, nodal, and GATA-4) or a variety of lineages (flk-1, Nkx-2.5, EKLF, and Msx3) to determine how progressive differentiation of embryoid bodies in culture correlated with early postimplantation development of mouse embryos. Using RNA in situ hybridization, we found that the temporal and spatial relationships existing between these marker genes in vivo were maintained also in vitro. Studying the onset of marker gene expression allowed us also to determine the time course of differentiation during the formation of embryoid bodies. Thus, stages equivalent to embryogenesis between implantation and the beginning of gastrulation (4.5-6.5 d.p.c.) occur within the first two days of embryoid body differentiation. Between days 3 and 5, embryoid bodies contain cell lineages found in embryos during gastrulation at 6.5 to 7.0 d.p.c., and after day 6 in culture, embryoid bodies are equivalent to early organogenesis-stage embryos (7.5 d.p.c.). In addition, we demonstrate that the panel of developmental markers can be applied in a screen for stage- or lineage-specific genes. Reporter gene expression from entrapment vector insertions can be co-localized with expression of specific markers within the same cell during embryoid body formation as well as during embryogenesis. Our results thus demonstrate the power of embryoid body formation as an in vitro model system to study early lineage determination and organogenesis in mammals, and indicate that they will prove to be useful tools for identifying developmental genes whose expression is restricted to particular lineages.

Animals↗
PubMed2001

Additive noise in noise-induced nonequilibrium transitions.

We study different nonlinear systems which possess noise-induced nonequlibrium transitions and shed light on the role of additive noise in these effects. We find that the influence of additive noise can be very nontrivial: it can induce first- and second-order phase transitions, can change properties of on-off intermittency, or stabilize oscillations. For the Swift-Hohenberg coupling, that is a paradigm in the study of pattern formation, we show that additive noise can cause the formation of ordered spatial patterns in distributed systems. We show also the effect of doubly stochastic resonance, which differs from stochastic resonance, because the influence of noise is twofold: multiplicative noise and coupling induce a bistability of a system, and additive noise changes a response of this noise-induced structure to the periodic driving. Despite the close similarity, we point out several important distinctions between conventional stochastic resonance and doubly stochastic resonance. Finally, we discuss open questions and possible experimental implementations. (c) 2001 American Institute of Physics.

Journal Article↗
PubMed2006

Pattern stabilization through parameter alternation in a nonlinear optical system.

We report the first experimental realization of pattern formation in a spatially extended nonlinear system when the system is alternated between two states, neither of which exhibits patterning. Dynamical equations modeling the system are used for both numerical simulations and a weakly nonlinear analysis of the patterned states. The simulations show excellent agreement with the experiment. The nonlinear analysis provides an explanation of the patterning under alternation and accurately predicts both the observed dependence of the patterning on the frequency of alternation and the measured spatial frequencies of the patterns.

Journal Article↗
PubMed2003

Distinct patterns of hippocampal formation activity associated with different spatial tasks: a Fos imaging study in rats.

Fos levels were measured in rats trained in one of two qualitatively different spatial memory tasks in a water maze. In one task, ( landmark condition) rats found a submerged platform that was always 25 cm south of a visible landmark, the absolute position of the platform and landmark changing after every trial. In the other task ( place condition), rats swam to a platform that remained in the same absolute position on every session, but changed session to session, with this task relying on the memory of allocentric cues. Despite matched swim times, the landmark condition resulted in higher levels of Fos in a wide range of cortical and subcortical sites, including the hippocampus and its connections. Structural equation modelling revealed two different patterns of hippocampal function. In the allocentric place task there was a significant association between Fos activity in the entorhinal cortices and the hippocampus proper, while in the non-allocentric landmark task this relationship was not present, but was replaced by a connection from the entorhinal cortices to the subiculum. Thus, the two different tasks engage two different modes of hippocampal activity as demonstrated by Fos expression.

Animals↗
PubMed2006

Spatial-pattern-induced evolution of a self-replicating loop network.

We study a system of self-replicating loops in which interaction rules between individuals allow competition that leads to the formation of a hypercycle-like network. The main feature of the model is the multiple layers of interaction between loops, which lead to both global spatial patterns and local replication. The network of loops manifests itself as a spiral structure from which new kinds of self-replicating loops emerge at the boundaries between different species. In these regions, larger and more complex self-replicating loops live for longer periods of time, managing to self-replicate in spite of their slower replication. Of particular interest is how micro-scale interactions between replicators lead to macro-scale spatial pattern formation, and how these macro-scale patterns in turn perturb the micro-scale replication dynamics.

Artificial Intelligence↗
PubMed2005

Scattering of traveling spots in dissipative systems.

One of the fundamental questions for self-organization in pattern formation is how spatial periodic structure is spontaneously formed starting from a localized fluctuation. It is known in dissipative systems that splitting dynamics is one of the driving forces to create many particle-like patterns from a single seed. On the way to final state there occur many collisions among them and its scattering manner is crucial to predict whether periodic structure is realized or not. We focus on the colliding dynamics of traveling spots arising in a three-component system and study how the transition of scattering dynamics is brought about. It has been clarified that hidden unstable patterns called "scattors" and their stable and unstable manifolds direct the traffic flow of orbits before and after collisions. The collision process in general can be decomposed into several steps and each step is controlled by such a scattor, in other words, a network among scattors forms the backbone for scattering dynamics. A variety of input-output relations comes from the complexity of the network as well as high Morse indices of the scattor. The change of transition manners is caused by the switching of the network from one structure to another, and such a change is caused by the singularities of scattors. We illustrate a typical example of the change of transition caused by the destabilization of the scattor. A new instability of the scattor brings a new destination for the orbit resulting in a new input-output relation, for instance, Hopf instability for the scattor of peanut type brings an annihilation.

Journal Article↗