Pattern Formation Process Research Articles

Spatial dynamics of ecological public goods

The production, consumption, and exploitation of common resources ranging from extracellular products in microorganisms to global issues of climate change refer to public goods interactions. Individuals can cooperate and sustain common resources at some cost or defect and exploit the resources without contributing. This generates a conflict of interest, which characterizes social dilemmas: Individual selection favors defectors, but for the community, it is best if everybody cooperates. Traditional models of public goods do not take into account that benefits of the common resource enable cooperators to maintain higher population densities. This leads to a natural feedback between population dynamics and interaction group sizes as captured by "ecological public goods." Here, we show that the spatial evolutionary dynamics of ecological public goods in "selection-diffusion" systems promotes cooperation based on different types of pattern formation processes. In spatial settings, individuals can migrate (diffuse) to populate new territories. Slow diffusion of cooperators fosters aggregation in highly productive patches (activation), whereas fast diffusion enables defectors to readily locate and exploit these patches (inhibition). These antagonistic forces promote coexistence of cooperators and defectors in static or dynamic patterns, including spatial chaos of ever-changing configurations. The local environment of cooperators and defectors is shaped by the production or consumption of common resources. Hence, diffusion-induced self-organization into spatial patterns not only enhances cooperation but also provides simple mechanisms for the spontaneous generation of habitat diversity, which denotes a crucial determinant of the viability of ecological systems.

Highly ordered nanopatterns on Ge and Si surfaces by ion beam sputtering

The bombardment of surfaces with low-energy ion beams leads to material erosion and canbe accompanied by changes in the topography. Under certain conditions this surfaceerosion can result in well-ordered nanostructures. Here an overview of the patternformation on Si and Ge surfaces under low-energy ion beam erosion at room temperaturewill be given. In particular, the formation of ripple and dot patterns, and theinfluence of different process parameters on their formation, ordering, shape and typewill be discussed. Furthermore, the internal ion beam parameters inherent tobroad beam ion sources are considered as an additional degree of freedom forcontrolling the pattern formation process. In this context: (i) formation of ripples atnear-normal ion incidence, (ii) formation of dots at oblique ion incidence without samplerotation, (iii) transition between patterns, (iv) formation of ripples with differentorientations and (v) long range ordered dot patterns will be presented and discussed.

Inhibition of stored Ca2+ release disrupts convergence‐related cell movements in the lateral intermediate mesoderm resulting in abnormal positioning and morphology of the pronephric anlagen in intact zebrafish embryos

Ca(2+) is a highly versatile intra- and intercellular signal that has been reported to regulate a variety of different pattern-forming processes during early development. To investigate the potential role of Ca(2+) signaling in regulating convergence-related cell movements, and the positioning and morphology of the pronephric anlagen, we treated zebrafish embryos from 11.5 h postfertilization (hpf; i.e. just before the pronephric anlagen are morphologically distinguishable in the lateral intermediate mesoderm; LIM) to 16 hpf, with a variety of membrane permeable pharmacological reagents known to modulate [Ca(2+)](i). The effect of these treatments on pronephric anlagen positioning and morphology was determined in both fixed and live embryos via in situ hybridization using the pronephic-specific probes, cdh17, pax2.1 and sim1, and confocal imaging of BODIPY FL C(5)-ceramide-labeled embryos, respectively. We report that Ca(2+) released from intracellular stores via inositol 1,4,5-trisphosphate receptors plays a significant role in the positioning and morphology of the pronephric anlagen, but does not affect the fate determination of the LIM cells that form these primordia. Our data suggest that when Ca(2+) release is inhibited, the resulting effects on the pronephric anlagen are a consequence of the disruption of normal convergence-related movements of LIM cells toward the embryonic midline.

Axial and radial segregation of granular mixtures in a rotating spherical container

We report the formation of axial segregation patterns of bidisperse granular mixtures of glass beads in a spherical container which is rotated about a central axis. When the rotation axis is horizontal, three distinct segregation bands are formed for a broad range of geometrical and dynamical parameters. We find two distinct regimes: at low fill levels the small size beads of the mixture are collected at the poles and the large size beads in a central band. At high fill levels the pole regions are occupied by large beads, while the small beads form the central band. The critical fill level for this structural transition decreases with increasing container size. For a container with 37 mm inner diameter, containing a mixture of 0.5 and 1.5 mm beads, the transition occurs between 40% and 50% fill level. When the rotation axis is tilted, the band positions are shifted and two-band structures are formed with the smaller particles at the lower pole. In our experiments the granulate is submersed in water; this allows NMR imaging of the complete three-dimensional band structures. We compare the observed segregation structures to those in cylindrical mixers and propose a model for the qualitative explanation of the pattern formation process.

Automation of pattern recognition and fractal-geometry-based pattern quantification, exemplified by mineral-phase distribution patterns in igneous rocks

This study analyses the possibility of accurate quantification of automatically digitized mineral-phase distribution patterns in igneous rocks. Based on their colour contrast, different minerals were manually and automatically digitized on micro to macro scales. Depending on the digitized mineral phase, the accuracy of the automated digitizing procedure varies. Quantification of mineral distribution patterns was performed by box-counting. The results do not depend greatly on the pattern's pixel density and are similar to each other, even if automatic recording is performed at reduced precision in comparison to manual recording. Consequently, box-counting measurement of automatically recorded mineral distribution patterns (i) leads to fast and accurate pattern quantification, (ii) allows analysis of various phase distribution patterns from micro to macro scales, and (iii) forms an excellent basis for receiving information on pattern-forming processes, which is not available otherwise.

Entropy driven mechanism for ordering, phase separation and pattern formation processes in stochastic systems

Entropy driven mechanism for ordering, phase separation and pattern formation processes in stochastic systems

Induced pluripotent stem cells: how to deal with the developmental potential

Recent developments in research on embryonic stem cells and induced pluripotent stem cells suggest that potentiality of cells should be a new focus in stem cell research ethics and policy. Successful reconstitution of viable embryos from induced pluripotent stem cells using tetraploid complementation has been reported and indicates a way for direct cloning of individuals from these cells. This together with recent observations on gastrulation and pattern formation processes in cultures of embryonic stem cells has considerable ethical relevance after the advent and worldwide spread of induced pluripotent stem cell technology. Available knowledge of the molecular basis of mammalian embryology now makes it possible to envisage ways to deal technically with the ethical dilemma of stem cell potentiality.

Hierarchical pattern of microfibrils in a 3D fluorapatite–gelatine nanocomposite: simulation of a bio-related structure building process

The shape development of a biomimetic fluorapatite-gelatine nanocomposite on the mum scale is characterised by a fractal mechanism with the origin being intrinsically coded in a (central) elongated hexagonal-prismatic seed. The 3D superstructure of the seed is distinctively overlaid by a pattern consisting of gelatine microfibrils. The orientation of the microfibrils is assumed to be controlled by an intrinsic electrical field generated by the nanocomposite during development and growth of the seed. In order to confirm this assumption and to get more detailed information on orientational relations of the complex nanocomposite we simulated the pattern formation process up to the microm scale. The results from experimental studies and simulation results on an atomistic level support a model scenario wherein the elementary building blocks for the aggregation are represented by elongated hexagonal-prismatic objects (A-units), with the embedded collagen triple-helices in their centers. The interactions of the A-units are consequently modelled by three contributions: the crystal energy part (originating from the pair-wise interactions of the "apatite shells" of the prismatic units), the electrostatic interaction (originating from the unit charges located at the ends of the collagen triple helices), and the interaction energy of the A-units mediated by the solvent. The next level of complexity is related to the fact that micro fibrils were found in the fluorapatite-gelatine nanocomposites. They consist of bundles of triple helical protein molecules, which are embedded within the 3D-hexagonal prismatic arrangement of the A-units. In our approach we consider the microfibrils as chains of flexible dipoles with effective dipole moments. The crystal growth processes is modelled as an energetically controlled stepwise association of elementary building blocks of different kind on a 3D-grid. The remarkable and excellent qualitative agreement between the simulated fibril patterns and the observations made by SEM and TEM support the concept of an intrinsic electric field driven morphogenesis of the fluorapatite-gelatine nanocomposite. The simulated fibril pattern also bears the chance to make fresh attempts in order to find explanations for experimental observations which are not understood up to now.

In vitroVasculogenesis Models Revisited - Measurement of VEGF Diffusion in Matrigel

The circulatory system is one of the first to function during development. The earliest event in the system's development is vasculogenesis, whereby vascular progeniter cells form clus- ters called blood islands, which later fuse to form capillary networks. There exists a very good in vitro system that mimics this process. When HUVECs (Human Umbilical Vein Endothelial Cells) are cultured on Matrigel, they spontaneously form a capillary network structure. Two theoretical models have been proposed to explain the pattern formation of this in vitro system. Both models utilize chemotaxis to generate spatial instability, and one model specifies VEGF as the chemoat- tractant. However, there are several unknown factors concerning the experimental model. First, the pattern formation process occurs at the interface between the liquid medium and Matrigel, and it is unclear whether diffusion in the liquid or gel is critical. Second, the diffusion coefficient of VEGF, which determines the spatial scale of the capillary structure, has not been properly mea- sured. In the present study, we modified the experimental system to clarify the effect of diffusion in Matrigel, and experimentally measured the diffusion coefficient of VEGF in this system. The relationship with the spatial scale of the pattern generated is discussed.

Parametric dependence studies on cracking of clay

We have studied the shrinkage-crack patterns formed in the process of drying of clay/water slurries employing simple laboratory experiments. Both isotropic and directional drying was studied. The objective has been to examine the correlation between the solvent, materials parameters and the crack patterns. Attempt is made to fit the observations to specific models. The dynamics of the pattern formation process and the geometric properties of the crack patterns are found to be in conformity with the hydrodynamic model by Lee and Routh [W.P. Lee, A.F. Routh, Langmuir 20 (2004) 9887].

Growth of twin-free heteroepitaxial diamond on Ir/YSZ/Si(111)

Heteroepitaxial nucleation and growth of twin-free diamond on Ir(111) is reported. The bias enhanced nucleation (BEN) technique was applied in a microwave plasma chemical vapor deposition setup to induce diamond nucleation on the new multilayer stack Ir/YSZ/Si(111). We demonstrate that the gathering of the diamond nuclei in so-called “domains,” a pattern formation process unique for diamond nucleation on iridium, is also present on Ir(111). The 1–2 nm thick carbon layer deposited by BEN does not show any crystalline diamond structures in electron diffraction and high resolution lattice imaging microscopy. In contrast, x-ray photoelectron diffraction (XPD) measurements yield C 1s diffractograms with clear threefold symmetry. The main features are comparable to measurements on diamond (111) single crystal surfaces. The weaker fine structure in the XPD patterns of the BEN layers is attributed to some disorder due to the harsh ion bombardment. However, this ion bombardment did not induce any measurable amount of twinning as deduced from the threefold symmetry. After 3 h diamond growth, the signal due to twins in the x-ray diffraction pole figures is still below the noise level of ∼1%. Negligible twinning and the low mosaic spread of 0.96° (tilt) and 1.85° (twist) indicate that these films mark a breakthrough toward heteroepitaxial diamond films with (111) orientation. They provide interesting growth substrates, e.g., for phosphorous doped diamond or for the formation of heterojunction devices by deposition of wurtzite-type wide band gap semiconductor materials.

Nanopatterning of Transition Metal Surfaces via Electrochemical Dimple Array Formation

Nanoscale surface patterning is of great importance for applications ranging from catalysts to biomaterials. We show the formation of ordered nanoscale dimple arrays on titanium, tungsten, and zirconium during electropolishing, demonstrating versatility of a process previously only reported for tantalum. This is a rare example of an electrochemical pattern formation process that can be translated to other materials. The dimpled surfaces have been characterized with scanning electron microscopy, transmission electron microscopy, atomic force microscopy, and X-ray photoelectron spectroscopy, and electrochemical conditions were optimized for each material. While conditions for titanium and tungsten resemble those for tantalum, zirconium requires a different type of electrolyte. Given the appropriate electropolishing chemistry, formation of these patterns should be possible on any metal surface. The process is very robust on homogeneous surfaces, but sensitive to inhomogeneities in chemical composition, such as in the case of differentially etched alloys. An alternative process for some materials such as platinum is the coating of a dimpled substrate with a thin film of the required material.

Crystal Structure and NMR Binding Reveal That Two Small Molecule Antagonists Target the High Affinity Ephrin-binding Channel of the EphA4 Receptor

The Eph receptor tyrosine kinases regulate a variety of physiological and pathological processes not only during development but also in adult organs, and therefore they represent a promising class of drug targets. The EphA4 receptor plays important roles in the inhibition of the regeneration of injured axons, synaptic plasticity, platelet aggregation, and likely in certain types of cancer. Here we report the first crystal structure of the EphA4 ligand-binding domain, which adopts the same jellyroll beta-sandwich architecture as shown previously for EphB2 and EphB4. The similarity with EphB receptors is high in the core beta-stranded regions, whereas large variations exist in the loops, particularly the D-E and J-K loops, which form the high affinity ephrin binding channel. We also used isothermal titration calorimetry, NMR spectroscopy, and computational docking to characterize the binding to EphA4 of two small molecules, 4- and 5-(2,5 dimethyl-pyrrol-1-yl)-2-hydroxybenzoic acid which antagonize ephrin-induced effects in EphA4-expressing cells. We show that the two molecules bind to the EphA4 ligand-binding domain with K(d) values of 20.4 and 26.4 microm, respectively. NMR heteronuclear single quantum coherence titrations revealed that upon binding, both molecules significantly perturb EphA4 residues Ile(31)-Met(32) in the D-E loop, Gln(43) in the E beta-strand, and Ile(131)-Gly(132) in the J-K loop. Molecular docking shows that they can occupy a cavity in the high affinity ephrin binding channel of EphA4 in a similar manner, by interacting mainly with the EphA4 residues in the E strand and D-E and J-K loops. However, many of the interactions observed in Eph receptor-ephrin complexes are absent, which is consistent with the small size of the two molecules and may account for their relatively weak binding affinity. Thus, our studies provide the first published structure of the ligand-binding domain of an EphA receptor of the A subclass. Furthermore, the results demonstrate that the high affinity ephrin binding channel of the Eph receptors is amenable to targeting with small molecule antagonists and suggest avenues for further optimization.

Predicting spiral wave patterns from cell properties in a model of biological self-organization

In many biological systems, biological variability (i.e., systematic differences between the system components) can be expected to outrank statistical fluctuations in the shaping of self-organized patterns. In principle, the distribution of single-element properties should thus allow predicting features of such patterns. For a mathematical model of a paradigmatic and well-studied pattern formation process, spiral waves of cAMP signaling in colonies of the slime mold Dictyostelium discoideum, we explore this possibility and observe a pronounced anticorrelation between spiral waves and cell properties (namely, the firing rate) and particularly a clustering of spiral wave tips in regions devoid of spontaneously firing (pacemaker) cells. Furthermore, we observe local inhomogeneities in the distribution of spiral chiralities, again induced by the pacemaker distribution. We show that these findings can be explained by a simple geometrical model of spiral wave generation.

Retinal pigment epithelial cells promote spatial reorganization and differentiation of retina photoreceptors

Retina differentiation involves the acquisition of a precise layered arrangement, with RPE cells in the first layer in intimate contact with photoreceptors in the second layer. Here, we developed an in vitro coculture model, to test the hypothesis that RPE cells play a pivotal role in organizing the spatial structure of the retina. We cocultured rat retinal neurons with ARPE-19 epithelial cells under various experimental conditions. Strikingly, when seeded over RPE cells, photoreceptors attached to their apical surfaces and proceeded with their development, including the increased synthesis of rhodopsin. Conversely, when we seeded RPE cells over neurons, the RPE cells rapidly detached photoreceptors from their substrata and positioned themselves underneath, thus restoring the normal in vivo arrangement. Treatment with the metalloproteinase inhibitor TIMP-1 blocked this reorganization, suggesting the involvement of metalloproteinases in this process. Reorganization was highly selective for photoreceptors because 98% of photoreceptors but very few amacrine neurons were found to redistribute on top of RPE cells. Interestingly, RPE cells were much more efficient than other epithelial or nonepithelial cells in promoting this reorganization. RPE cells also promoted the growth of photoreceptor axons away from them. An additional factor that contributed to the distal arrangement of photoreceptor axons was the migration of photoreceptor cell bodies along their own neurites toward the RPE cells. Our results demonstrate that RPE and photoreceptor cells interact in vitro in very specific ways. They also show that in vitro studies may provide important insights into the process of pattern formation in the retina.

The Evolving Complexity of the Auxin Pathway

The plant hormone and signaling molecule auxin is a key player during pattern formation, organogenesis, and various physiological processes. Recent discoveries in auxin biology point toward an auxin pathway with a higher complexity than previously anticipated. This prompted us to review this

Symmetries, non-Euclidean metrics, and patterns in a Swift–Hohenberg model of the visual cortex

The aim of this work is to investigate the effect of the shift-twist symmetry on pattern formation processes in the visual cortex. First, we describe a generic set of Riemannian metrics of the feature space of orientation preference that obeys properties of the shift-twist, translation, and reflection symmetries. Second, these metrics are embedded in a modified Swift-Hohenberg model. As a result we get a pattern formation process that resembles the pattern formation process in the visual cortex. We focus on the final stable patterns that are regular and periodic. In a third step we analyze the influences on pattern formation using weakly nonlinear theory and mode analysis. We compare the results of the present approach with earlier models.

Quantum pattern formation dynamics of photoinduced nucleation

We study the dynamics of quantum pattern formation processes in molecular crystals which is concomitant with photoinduced nucleation. Since the nucleation process in coherent regime is driven by the nonadiabatic transition in each molecule followed by the propagation of phonons, it is necessary to take into account the quantum nature of both electrons and phonons in order to pursue the dynamics of the system. Therefore, we employ a model of localized electrons coupled with a quantized phonon mode and solve the time-dependent Schr\odinger equation numerically. We found that there is a minimal size of clusters of excited molecules which triggers the photoinduced nucleation process; i.e., nucleation does not take place unless sufficient photoexcitation energy is concentrated within a narrow area of the system. We show that this result means that the spatial distribution of photoexcited molecules plays an important role in the nonlinearity of the dynamics and also in the optical properties observed in experiments. We calculate the conversion ratio, the rate of cluster formation, and correlation functions to reveal the dynamical properties of the pattern formation process; the initial dynamics of the photoinduced structural change is discussed from the viewpoint of pattern formation.

Studying the effect of cell division on expression patterns of the segment polarity genes.

The segment polarity gene family, and its gene regulatory network, is at the basis of Drosophila embryonic development. The network's capacity for generating and robustly maintaining a specific gene expression pattern has been investigated through mathematical modelling. The models have provided several useful insights by suggesting essential network links, or uncovering the importance of the relative time scales of different biological processes in the formation of the segment polarity genes' expression patterns. But the developmental pattern formation process raises many other questions. Two of these questions are analysed here: the dependence of the signalling protein sloppy paired on the segment polarity genes and the effect of cell division on the segment polarity genes' expression patterns. This study suggests that cell division increases the robustness of the segment polarity network with respect to perturbations in biological processes.

Modeling of Branching Patterns in Plants

A major determinant of plant architecture is the arrangement of branches around the stem, known as phyllotaxis. However, the specific form of branching conditions is not known. Here we discuss this question and suggest a branching model which seems to be in agreement with biological observations.Recently, a number of models connected with the genetic network or molecular biology regulation of the processes of pattern formation appeared. Most of these models consider the plant hormone, auxin, transport and distribution in the apical meristem as the main factors for pattern formation and phyllotaxis. However, all these models do not take into consideration the whole plant morphogenesis, concentrating on the events in the shoot or root apex. On the other hand, other approaches for modeling phyllotaxis, where the whole plant is considered, usually are mostly phenomenological, and due to it, do not describe the details of plant growth and branching mechanism. In this work, we develop a mathematical model and study pattern formation of the whole, though simplified, plant organism where the main physiological factors of plant growth and development are taken into consideration. We model a growing plant as a system of intervals, which we will consider as branches. We assume that the number and location of the branches are not given a priori, but appear and grow according to certain rules, elucidated by the application of mathematical modeling. Four variables are included in our model: concentrations of the plant hormones auxin and cytokinin, proliferation and growth factor, and nutrients-we observe a wide variety of plant forms and study more specifically the involvement of each variable in the branching process. Analysis of the numerical simulations shows that the process of pattern formation in plants depends on the interaction of all these variables. While concentrations of auxin and cytokinin determine the appearance of a new bud, its growth is determined by the concentrations of nutrients and proliferation factors. Possible mechanisms of apical domination in the frame of our model are discussed.