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Results for “Spatial pattern formation”

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PubMed1996

The large-scale vortex structures in plasma-like media and the electric explosion of conductors.

Formation of large-scale hydrodynamic convective patterns in plasma-like current-carrying media is considered. This process is shown to be described by the same equations, as Benard rolls, except that a temperature field must be replaced by a magnetic field. A simple low-mode model of spatial pattern formation for a case of cylindrical liquid-metal conductor with current is proposed and investigated. Nonlinear interaction of perturbations of the magnetic field and the velocity field results in an increase of effective conductor resistance even when transport coefficients are constant. In our opinion, it is this instability, that is of first importance at the initial stages of the electric explosion of conductors. In particular, it leads to conductor stratification and electric current interruption. (c) 1996 American Institute of Physics.

Journal Article↗

PubMed1974

Models for positional information and positional differentiation.

It is commonly thought that the formation of patterns in developing organisms is due to the existence of a gradient of a morphogen that determines the fate of cells as a function of position in the organism. A model is presented based on a molecular mechanism where the gradient is established by the active transport of a morphogen between source and sink. The cellular differentiation and the subsequent spatial pattern formation results from the interaction of this morphogen with the genetic regulatory mechanisms of cells. Some properties of the model are given and discussed in relation to grafting experiments in hydra.

Animals↗

PubMed2001

Hippocampal mossy fibers induce assembly and clustering of PSD95-containing postsynaptic densities independent of glutamate receptor activation.

Factors that regulate the formation, spatial patterning, and maturation of CNS synapses are poorly understood. We used organotypic hippocampal slice cultures derived from developing (P5-P7) rat to test whether synaptic activity regulates the development and organization of postsynaptic structures at mossy fiber (MF) giant synapses. Antibodies to a prominent postsynaptic density (PSD) scaffold protein, PSD95, identified large (>1 microm) and irregularly shaped PSD assemblies that codistributed with synapsin-I or metabotropic glutamate receptor 7b (mGluR7b) -immunolabeled MF terminals in area CA3. To investigate the spatial organization of synaptic PSDs on individual pyramidal cells, neurons in slice cultures were transfected with a vector encoding a GFP-PSD95 fusion protein. Confocal three-dimensional reconstructions revealed clusters of PSDs along proximal dendrites of transfected pyramidal neurons in area CA3, but not in CA1. Clusters averaged 7.6 microm in length (range, 2.2-29 microm) and contained up to 35 individual PSDs (mean, 8.3). PSD clusters failed to form when slices were cultured without MFs, indicating that MFs induce cluster assembly. Chronic blockade of N-methyl-D-apartate- and AMPA/kainate-type glutamate receptors did not disrupt MF targeting or de novo formation of PSD clusters with a normal distribution on target cells. Additionally, glutamate receptor blockers did not alter the ultrastructural development of MF giant synapses containing multiple puncta adherens-like junctions and asymmetric synaptic junctions at dendritic shaft and spine domains, respectively. The results indicate that MF axons can induce the assembly and clustering of PSD95-containing postsynaptic complexes, displaying a normal subcellular and tissue distribution, by mechanisms that are independent of ionotropic glutamate receptor activation.

Animals↗

PubMed2005

Molecular organization and signal transduction at intermembrane junctions.

Surfaces create an environment in which multiple forces conspire together to yield a wealth of complex chemical processes. This is especially true of cell membranes, whose fluidity and flexibility enables responsive feedback with surface chemical interactions in ways not generally seen with inorganic materials. Spatial pattern formation of cell-surface proteins at intermembrane junctions provides many beautiful examples of these phenomena, and is also emerging as a functional aspect of intercellular signaling. Correspondingly, the study of interactions of cell-membrane surfaces is attracting significant attention from cell biologists and physical chemists alike. This convergence is fueled be recent, exquisite observations of protein pattern formation events within living immunological synapses along with parallel advances in membrane reconstitution, manipulation, and imaging technologies.

Animals↗

PubMed2006

Chemical waves.

In our paper we try to describe the basic concepts of chemical waves and spatial pattern formation in a simple way. We pay particular attention to self-organisation phenomena in extended excitable systems. These result in the appearance of travelling waves, spiral waves, target patterns, Turing structures or more complicated structures called scroll waves, which are three-dimensional systems. We describe the most famous oscillating reaction, the Belousov-Zhabotinsky (BZ) reaction, in greater detail. This is because it is of great interest in both physical chemistry and in studies on the evolution and sustenance of self-organising biological systems.

Journal Article↗

PubMed2003

Oscillations and patterns in spatially discrete models for developmental intercellular signalling.

We extend previous models for nearest neighbour ligand-receptor binding to include both lateral induction and inhibition of ligand and receptor production, and different geometries (strings of cells and hexagonal arrays, in addition to square arrays). We demonstrate the possibility of lateral inhibition giving patterns with a characteristic length scale of many cell diameters, when receptor production is included. In contrast, lateral induction combined with inhibition of receptor synthesis cannot give rise to a patterning instability under any circumstances. Interesting new dynamics include the analytical prediction and consequent numerical observation of spatiotemporal oscillations, this depends crucially on the production terms and on the relationship between the decay rates of ligand and free receptor. Our approach allows for a detailed comparison with the model for Delta-Notch interactions of Collier et al. [4], and we find that a formal reduction may be made only when the ligand receptor binding kinetics are very slow. Without such very slow receptor kinetics, spatial pattern formation via lateral inhibition in hexagonal cellular arrays requires significant activation of receptor production, a feature that is not apparent from previous analyses.

Algorithms↗

PubMed2006

From biochemistry to morphogenesis in myxobacteria.

Many aspects of metazoan morphogenesis find parallels in the communal behavior of microorganisms. The cellular slime mold D. discoideum has long provided a metaphor for multicellular embryogenesis. However, the spatial patterns in D.d. colonies are generated by an intercellular communication system based on diffusible morphogens, whereas the interactions between embryonic cells are more often mediated by direct cell contact. For this reason, the myxobacteria have emerged as a contending system in which to study spatial pattern formation, for their colony strutures rival those of D.d. in complexity, yet communication between cells in a colony is carried out by direct cell contacts. Here I sketch some of the progress my laboratory has made in modeling the life cycle of these organisms.

Animals↗

PubMed2005

Advances in synthetic biology: on the path from prototypes to applications.

Synthetic biology combines knowledge from various disciplines including molecular biology, engineering, mathematics and physics to design and build novel proteins, genetic circuits and metabolic networks. Early efforts aimed at altering the behavior of individual elements have now evolved to focus on the construction of complex networks in single-cell and multicellular systems. Recent achievements include the development of sophisticated non-native behaviors such as bi-stability, oscillations, proteins customized for biosensing, optimized drug synthesis and programmed spatial pattern formation. The de novo construction of such systems offers valuable quantitative insight into naturally occurring information processing activities. Furthermore, as the techniques for system design, synthesis and optimization mature, we will witness a rapid growth in the capabilities of synthetic systems with a wide-range of applications.

Gene Expression Regulation↗

PubMed1997

A molecular predator and its prey: coupled isothermal amplification of nucleic acids.

BACKGROUND: A novel approach to the study of in vitro evolution is provided by the investigation of continuous, functionally coupled, amplifying systems. To date, in vitro evolution experiments have focused on issues of mutation and selection. Our work contributes to the new field of in vitro molecular ecology studies in which detailed information about the relationship between sequence changes and molecular interactions is obtained. Predator-prey systems are interesting in this context both in terms of evolutionary limits and in terms of the potential kinetic properties of oscillation and spatial pattern formation. Such molecular predator-prey models can be extended to a further negative-interaction mode, viral-host molecular evolution. RESULTS: A simple, nonfunctional predator-prey system based on the self-sustained sequence replication reaction is proposed. Coupling within the system is achieved using the single-stranded DNA intermediate of one cycle, the prey cycle, as primer for the second one, the predator cycle. Hybridization by complementary base pairing is the second order reaction step underlying the predation. Single steps of the whole reaction system have been investigated by radiolabeling. Each isolated subsystem operates according to the proposed reaction scheme, and evidence for an efficient coupling of both subsystems according to the proposed mechanism was found. CONCLUSIONS: Simple, interacting model systems based on nucleic acids can be designed and constructed for the study of coevolution. The results of studies such as the one described here will provide a basis for the construction of coupled systems of ribozymes, from which point the engineering of catalytic units for applications in biotechnology is feasible.

Base Sequence↗

PubMed1980

Complete reversal of antero-posterior polarity in a centrifuged insect embryo.

Spatial pattern formation during embryogenesis is ascribed to differential gene expression, which in turn is thought to result in part from interactions of nuclei with cytoplasmic determinants. In the chironomid midge Smittia, and probably in other dipterans as well, blastoderm cells seem to make an early decision as to whether they contribute to cephalic and thoracic or to abdominal (and possibly thoracic) structures. Inactivation or translocation of cytoplasmic components involved in this antero-posterior decision could conceivably lead to duplications of head and thorax, or abdomen, or to complete but inverted embryos forming the head posteriorly and the abdomen anteriorly in the egg. Whereas the former two malformations have been described, completely inverted embryos are reported for the first time, to our knowledge, in this letter. Reversal of partial germ bands has previously been observed following combined ligation and cytoplasmic translocation in eggs of the leaf hopper, Euscelis plebejus.

Animals↗

PubMed2002

From atomistic lattice-gas models for surface reactions to hydrodynamic reaction-diffusion equations.

Atomistic lattice-gas models for surface reactions can accurately describe spatial correlations and ordering in chemisorbed layers due to adspecies interactions or due to limited mobility of some adspecies. The primary challenge in such modeling is to describe spatiotemporal behavior in the physically relevant "hydrodynamic" regime of rapid diffusion of (at least some) reactant adspecies. For such models, we discuss the development of exact reaction-diffusion equations (RDEs) describing mesoscale spatial pattern formation in surface reactions. Formulation and implementation of these RDEs requires detailed analysis of chemical diffusion in mixed reactant adlayers, as well as development of novel hybrid and parallel simulation techniques. (c) 2002 American Institute of Physics.

Journal Article↗

PubMed2004

Emergent trade-offs and selection for outbreak frequency in spatial epidemics.

Nonspatial theory on pathogen evolution generally predicts selection for maximal number of secondary infections, constrained only by supposed physiological trade-offs between pathogen infectiousness and virulence. Spread of diseases in human populations can, however, exhibit large scale patterns, underlining the need for spatially explicit approaches to pathogen evolution. Here, we show, in a spatial model where all pathogen traits are allowed to evolve independently, that evolutionary trajectories follow a single relationship between transmission and clearance. This trade-off relation is an emergent system property, as opposed to being a property of pathogen physiology, and maximizes outbreak frequency instead of the number of secondary infections. We conclude that spatial pattern formation in contact networks can act to link infectiousness and clearance during pathogen evolution in the absence of any physiological trade-off. Selection for outbreak frequency offers an explanation for the evolution of pathogens that cause mild but frequent infections.

Biological Evolution↗

PubMed2006

Environmental variability and the initiation of dispersal: turbulence strongly increases seed release.

Dispersal is a critical process in ecology. It is an important biological driver of, for example, invasions, metapopulation dynamics, spatial pattern formation and pathogen movement. Much is known about the effect of environmental variability, including turbulence, on dispersal of diaspores. Here, we document experimentally the strong but under-explored influence of turbulence on the initiation of dispersal. Flower heads of two thistle species (Carduus nutans and Carduus acanthoides) with ripe seeds were exposed to series of laminar and turbulent air flows of increasing velocity in a wind tunnel. Seed release increased with wind speeds for both laminar and turbulent flows for both species. However, far more seeds were released, at significantly lower wind speeds, during turbulent flows. These results strongly suggest a need for more quantitative studies of abscission in the field, as well as dispersal models that incorporate variability in the diaspore release phase.

Carduus↗

PubMed1998

Evolving reaction-diffusion ecosystems with self-assembling structures in thin films.

Recently, new types of coupled isothermal polynucleotide amplification reactions for the investigation of in vitro evolution have been established that are based on the multi-enzyme 3SR reaction. Microstructured thin-film open bioreactors have been constructed in our laboratory to run these reactions spatially resolved in flow experiments. Artificial DNA/RNA chemistries close to the in vitro biochemistry of these systems have been developed, which we have studied in computer simulations in configurable hardware (NGEN). These artificial chemistries are described on the level of individual polynucleotide molecules, each with a defined sequence, and their complexes. The key feature of spatial pattern formation provides a weak stabilization of cooperative catalytic properties of the evolving molecules. Of great interest is the step to include extended self-assembly processes of flexible structures-allowing the additional stabilization of cooperation through semipermeable, flexible, self-organizing membrane boundaries. We show how programmable matter simulations of experimentally relevant molecular in vitro evolution can be extended to include the influence of self-assembling flexible membranes.

Bioreactors↗

PubMed1979

The glycolytic oscillator.

The glycolytic oscillator, mainly studied in yeast, is described with respect to its overall dynamic and biochemical properties and the kinetics of its master enzyme phosphofructokinase. Biochemical and kinetic analyses are complemented by analysis of mathematical models. In addition to the discussion of structure and function of the glycolytic oscillator under homogeneous spatial conditions, recent theoretical and biochemical experiments demonstrating spatial pattern formation are also discussed, followed by a presentation of physiological viewpoints.

Adenine Nucleotides↗

PubMed2005

Diffusion and scaling during early embryonic pattern formation.

Development of spatial patterns in multicellular organisms depends on gradients in the concentration of signaling molecules that control gene expression. In the Drosophila embryo, Bicoid (Bcd) morphogen controls cell fate along 70% of the anteroposterior axis but is translated from mRNA localized at the anterior pole. Gradients of Bcd and other morphogens are thought to arise through diffusion, but this basic assumption has never been rigorously tested in living embryos. Furthermore, because diffusion sets a relationship between length and time scales, it is hard to see how patterns of gene expression established by diffusion would scale proportionately as egg size changes during evolution. Here, we show that the motion of inert molecules through the embryo is well described by the diffusion equation on the relevant length and time scales, and that effective diffusion constants are essentially the same in closely related dipteran species with embryos of very different size. Nonetheless, patterns of gene expression in these different species scale with egg length. We show that this scaling can be traced back to scaling of the Bcd gradient itself. Our results, together with constraints imposed by the time scales of development, suggest that the mechanism for scaling is a species-specific adaptation of the Bcd lifetime.

Animals↗

PubMed2004

Pattern formation capacity of spatially extended systems.

We analyze a class of spatially extended systems which are capable of generating many complicated patterns. These systems are given by the Ginzburg-Landau equation coupled with a system of two linear equations and describe nonlinear media with localized defects. We find a connection between these systems and spin-glass systems. We show that the system is capable to produce many patterns and describe patterning algorithms.

Journal Article↗

PubMed2001

Turing pattern formation induced by spatially correlated noise.

The effect of spatially correlated noise on Turing structures is analyzed both experimentally and numerically. Using the photosensitive character of the chlorine dioxide-iodine-malonic acid reaction-diffusion system, spatial randomness is introduced in the system. In the presence of noise, Turing patterns appear and are stable at levels of average illumination that would be more than sufficient to suppress pattern formation in the case of homogeneous illumination.

Journal Article↗