Mechanism Of Pattern Formation Research Articles

Leopards and giants, tigers and woolly bears: casting a broader net in exploring heparin effects on Lepidoptera wing patterns

Background: Studies of heparin effects on Lepidoptera wing patterns have been restricted to a small number of species. I report observations from experiments on a broader range of taxa, including first results from swallowtails, tiger moths and microlepidoptera. Methods: Heparin injections were made in prepupal and early pupal stages of the following species representing several Lepidoptera lineages: Junonia coenia, Agraulis vanillae, Asterocampa clyton (Nymphalidae); Heraclides cresphontes, Pterourus troilus, Eurytides marcellus (Papilionidae); Hypercompe scribonia, Estigmene acrea, Hyphantria cunea (Erebidae); and Glyphodes sibillalis (Crambidae). Heparin-induced changes in wing pattern are illustrated, and advantages of using prepupal vs. pupal stages for this type of pharmacological manipulation of wing patterns are discussed. Results: In buckeyes, heparin-induced changes consisted of loss of orange parafocal elements as marginal and submarginal bands shifted basally. In gulf fritillaries, changes in black and silver markings were similar to those found in wild aberrant individuals. In tawny emperor, intermediate and extreme levels of transformation were achieved, pointing to homology of this species’ unusual eyespots to those of other nymphalids. In swallowtails, heparin-induced changes were much more restricted and proved harder to achieve, possibly indicating higher levels of stability and compartmentalization of wing patterns in this butterfly family. In tiger moths, elongation of black markings occurred so that normally distinct spots sometimes merged; in leopard moth, these changes were restricted to areas adjacent to discal spot. In pyraloid moth, changes were mostly restricted to expansion of wing marginal bands and hindwing border. Conclusions: Variation in wing pattern response to heparin found between different species and families in this study warrants further taxonomic widening of exploration of wing pattern formation mechanisms in Lepidoptera. While there are many similarities, there also seem to be very significant differences in the ways wing patterns are formed in different families of butterflies and moths.

Designing Stationary Reaction-Diffusion Patterns in pH Self-Activated Systems.

Since Alan Turing's 1952 pioneering work, reaction-diffusion (RD) processes are regarded as prototype mechanisms for pattern formation in living systems. Though suspected in many aspects of morphogenetic development, pure RD patterns have not yet been demonstrated in living organisms. The first observations of an autonomous development of stationary chemical patterns were made in the early 1990s. In this Account, we discuss the recent developments for producing stationary pH RD patterns in open spatial reactors. The theoretical analysis of the early experiments anticipated the possibility of finding Turing patterns in a wide range of oscillatory reactions if one could control the kinetic and diffusional rate of some key species. However, no experimentally effective method to produce stationary Turing patterns was attained before 2009, and the number of systems stagnated at two until then. The two precursor reaction systems benefited from unplanned favorable chemical properties of the RD media. Theoretical studies point out that appropriate diffusion rate differences are necessary to produce stationary patterns since a competition between an effective short distance self-activation and a long distance inhibitory process is required. This differential diffusion would naturally lead to differential exchange rates between the RD system and its feed environment, an aspect somewhat overlooked in theoretical and in primal experimental approaches. Our pattern design method takes this aspect into account. A slower diffusion of a self-activated species (here, protons), produced in the RD part of the spatial reactor, generates the accumulation of this species compared to the other species. This accumulation has to be at least partly compensated by an independent scavenging reaction. The above requirement naturally brought us to focus on two-substrate pH oscillatory reactions. Stationary RD patterns are now well documented in six pH driven reaction systems. Furthermore, the coupling with a pH dependent metal ion complexing agent led to stationary patterns in calcium ion concentration. Our effective semiempirical design method does not require a detailed knowledge of the reaction kinetics; thus it is applicable to a broad spectrum of reactions and even to synthetic biological systems. It is based on simple dynamic arguments and on general topological characteristics of a nonequilibrium phase diagram. We first illustrate our method with numerical simulations, based on a realistic but idealized general model of the two-substrate pH-oscillator reaction family, and provide a refined view of the topology of the resulting phase diagrams. Then, we exemplify its effectiveness by observations made in distinct pH self-activated systems. Analogies and differences between experiments and the model calculations are pointed out. Besides standard hexagonal arrays of spots and parallel stripes, hitherto undocumented dynamic phenomena, such as randomly blinking areas and complex dynamic and stationary filamentous structures, were observed. The main challenge, to find low-mobility complexing agents that would selectively and reversibly bind a species controlling the self-activatory kinetic path of the reaction, was readily overcome in multiple ways by anions of weak acids: not only by polymeric substances but in some cases by a pH color indicator or even smaller molecules, depending on their proton binding affinity.

Numerical simulation and experimental investigation of band patterns in bobbin tool friction stir welding of aluminum alloy

A coupled Eulerian-Lagrangian (CEL) model was developed to investigate the formation mechanism of band pattern (BP) during bobbin tool friction stir welding (BTFSW) process. The Johnson-Cook constitutive model which combines the strain rate and temperature effects in the material flow stress was used. The workpiece was modeled by the Eulerian formulation, while the tool was characterized by the Lagrangian formulation. The numerical analysis results agree well with experimental observations. The band structures with various sizes were discovered in the BP zone. Both the experimental and numerical analysis results indicate the BP zone forms on the advancing side of the joint. This is because the converged material flow is produced by both shoulders while being driven by the probe. The peak temperature, along the thickness of the BP zone, increased at the beginning followed by a decrease further away from the upper surface. The peak temperature obtained near the lower surface is slightly higher than that near the upper surface.

First-order reversal curve (FORC) diagrams of nanomagnets with cubic magnetocrystalline anisotropy: A numerical approach

First-order reversal curve (FORC) diagrams are increasingly used as a material’s magnetic domain state fingerprint. FORC diagrams of noninteracting dispersions of single-domain (SD) particles with uniaxial magnetocrystalline anisotropy (MCA) are well studied. However, a large class of materials possess a cubic MCA, for which the FORC diagram properties of noninteracting SD particle dispersions are less understood. A coherent rotation model was implemented to study the FORC diagram properties of noninteracting ensembles of SD particles with positive and negative MCA constants. The pattern formation mechanism is identified and related to the irreversible events the individual particles undergo. Our results support the utility of FORC diagrams for the identification of noninteracting to weakly-interacting SD particles with cubic MCA.

Behavioral and social mechanisms behind pattern formation: an experimental study of animal movement

ContextAlthough animal movement behaviors are influenced by spatial heterogeneity, such behaviors can also generate spatial heterogeneity via interactions with the emergent spatial structure and other individuals (i.e., the social landscape).ObjectiveElucidate the behavioral and ecological mechanisms of pattern formation in a homogeneous resource landscape.MethodsWe analyzed the movement pathways and space-use patterns of the lesser grain borer (Rhyzopertha dominica) within homogeneous resource landscapes (wheat kernels). Experimental trials consisted of individual beetles foraging alone or paired with a member of the same or different sex.ResultsWe identified two sources of pattern formation: (1) beetles were attracted to areas where they or another beetle had previously fed, leading to increased patchiness via positive reinforcement; and (2) the presence of conspecifics affected whether and at what scales patchiness occurred. Solitary males had lower rates of movement and less tortuous pathways than solitary females, but both sexes generated fine-scale patchiness in the resource distribution. Patchy resource landscapes were also generated by male–female pairs, but not by same-sex pairings. Paired females in particular exhibited significantly greater daily net displacements and more random space use than solitary females.ConclusionsPattern formation is a complex process, even in a relatively simple, homogeneous resource landscape. In particular, patterns created by individuals when foraging alone versus in pairs underscores how social interactions can fundamentally alter the resultant pattern of heterogeneity that emerges in resource landscapes.

Competition and partnership between conformity and payoff-based imitations in social dilemmas

Learning from a partner who collects a higher payoff is a frequently used working hypothesis in evolutionary game theory. One of the alternative dynamical rules is when the focal player prefers to follow the strategy choice of the majority in the local neighborhood, which is often called a conformity-driven strategy update. In this work we assume that both strategy learning methods are present and compete for space within the framework of a coevolutionary model. Our results reveal that the presence of a payoff-driven strategy learning method becomes exclusive for high sucker’s payoff and/or high temptation values that represent a snowdrift game dilemma situation. In general, however, the competition of the mentioned strategy learning methods could be useful to enlarge the parameter space where only cooperators prevail. The success of cooperation is based on the enforced coordination of cooperator players which reveals the benefit of the latter strategy. Interestingly, the payoff-based and the conformity-based cooperator players can form an effective alliance against defectors that can also extend the parameter space of full cooperator solution in the stag-hunt game region. Our work highlights that the coevolution of strategies and individual features such as the learning method can provide a novel type of pattern formation mechanism that cannot be observed in a static model, and hence remains hidden in traditional models.

Turing patterns in a predator–prey model with seasonality

Many ecological systems show striking non-homogeneous population distributions. Diffusion-driven instabilities are commonly studied as mechanisms of pattern formation in many fields of biology but only rarely in ecology, in part because some of the conditions seem quite restrictive for ecological systems. Seasonal variation is ubiquitous in temperate ecosystems, yet its effect on pattern formation has not yet been explored. We formulate and analyze an impulsive reaction-diffusion system for a resource and its consumer in a two-season environment. While the resource grows throughout the 'summer' season, the consumer reproduces only once per year. We derive conditions for diffusion-driven instability in the system, and we show that pattern formation is possible with a Beddington-DeAngelis functional response. More importantly, we find that a low overwinter survival probability for the resource enhances the propensity for pattern formation: diffusion-driven instability occurs even when the diffusion rates of prey and predator are comparable (although not when they are equal).

Curvature-driven spatial patterns in growing 3D domains: A mechanochemical model for phyllotaxis.

Here we discuss the formation of phyllotactic patterns in the shoot apical meristem (SAM) of plants, where the spatial distribution of the phytohormone auxin determines phyllotaxis in a domain that is growing and changing in time. We assume that the concentration of auxin modifies the mechanical properties of the domain and that the mechanical stress field in the SAM orients the flux of auxin. To study this problem we propose a mechanism for pattern formation in growing domains with variable curvature. The dynamics of chemicals is modeled by a reaction-diffusion system that produces a three dimensional pattern of chemical concentrations that changes the stress field in the domain while growing. The growth process is modeled by a phase-field order parameter which determines the location of the boundaries of the domain. This field is coupled to the chemical concentration through a curvature term that affects the local mechanical stress in the domain. The local stress changes in turn modify the chemical patterns. Our model constitutes a useful and novel approach in theoretical biology, as many developmental processes in organisms seem to be affected by the changes of curvature, size, mechanical stress and other physical aspects. Several patterns seen in many plants are reproduced under certain conditions by our model.

Mechanism of the growth pattern formation and three-dimensional morphological transition of hcp magnesium alloy dendrite

Based on an anisotropy function with the anisotropic strength determined via atomistic calculations, the mechanism of the three-dimensional (3D) growth pattern formation of magnesium alloy dendrite is investigated by performing phase-field simulations with the parallel adaptive-mesh-refinement algorithm. It is found that the 3D morphological transition of the $\ensuremath{\alpha}$-Mg dendrite is dependent on the growth parameters, including the partition coefficient, the anisotropic strength, and the supercooling during solidification. The $\ensuremath{\alpha}$-Mg dendrite exhibits growth tendency along both the basal and nonbasal directions, but the dendritic growth tendency along the basal direction is weaker. Consequently, the 3D morphology of the $\ensuremath{\alpha}$-Mg dendrite would transform from an 18-primary-branch pattern to a 12-primary-branch pattern if the local growth driving force on the basal plane is insufficient. During dendrite growth, the solute concentration increases as the distance from the dendritic nucleus center increases, and reaches the local maximum at the solid/liquid interface, beyond which it decreases before reaching a constant value. The simulation results agree well with those found in experiments and the existing solidification theory.

Stiff-response-induced instability for chemotactic bacteria and flux-limited Keller–Segel equation

Collective motion of chemotactic bacteria such as Escherichia coli relies, at the individual level, on a continuous reorientation by runs and tumbles. It has been established that the length of run is decided by a stiff response to a temporal sensing of chemical cues along the pathway.We describe a novel mechanism for pattern formation stemming from the stiffness of chemotactic response relying on a kinetic chemotaxis model which includes a recently discovered formalism for the bacterial chemotaxis. We prove instability both for a microscopic description in the space-velocity space and for the macroscopic equation, a flux-limited Keller–Segel equation, which has attracted much attention recently.A remarkable property is that the unstable frequencies remain bounded, as it is the case in Turing instability. Numerical illustrations based on a powerful Monte Carlo method show that the stationary homogeneous state of population density is destabilized and periodic patterns are generated in realistic ranges of parameters. These theoretical developments are in accordance with several biological observations.

Stochastic Turing patterns in a synthetic bacterial population

The origin of biological morphology and form is one of the deepest problems in science, underlying our understanding of development and the functioning of living systems. In 1952, Alan Turing showed that chemical morphogenesis could arise from a linear instability of a spatially uniform state, giving rise to periodic pattern formation in reaction-diffusion systems but only those with a rapidly diffusing inhibitor and a slowly diffusing activator. These conditions are disappointingly hard to achieve in nature, and the role of Turing instabilities in biological pattern formation has been called into question. Recently, the theory was extended to include noisy activator-inhibitor birth and death processes. Surprisingly, this stochastic Turing theory predicts the existence of patterns over a wide range of parameters, in particular with no severe requirement on the ratio of activator-inhibitor diffusion coefficients. To explore whether this mechanism is viable in practice, we have genetically engineered a synthetic bacterial population in which the signaling molecules form a stochastic activator-inhibitor system. The synthetic pattern-forming gene circuit destabilizes an initially homogenous lawn of genetically engineered bacteria, producing disordered patterns with tunable features on a spatial scale much larger than that of a single cell. Spatial correlations of the experimental patterns agree quantitatively with the signature predicted by theory. These results show that Turing-type pattern-forming mechanisms, if driven by stochasticity, can potentially underlie a broad range of biological patterns. These findings provide the groundwork for a unified picture of biological morphogenesis, arising from a combination of stochastic gene expression and dynamical instabilities.

Spatio-temporal pattern formation in predator-prey systems with fitness taxis

We pose a spatial predator–prey model in which the movement of animals is not purely diffusive, but also contains a drift term in the direction of higher specific growth rates. We refer to this as fitness taxis. We conduct a linear stability analysis of the resulting coupled reaction–advection–diffusion equations and derive conditions under which spatial patterns form. We find that for some parameters the problem is ill posed and short waves grow with unbounded speeds. To eliminate this, we introduce spatial kernels in the model, yielding coupled integro-differential equations, and conduct a similar stability analysis for this system. Through numerical simulation, we find that a variety of patterns can emerge, including stationary spatial patterns, standing and travelling waves, and seemingly chaotic spatio-temporal patterns. We argue that fitness taxis represents a simple and generic extension of diffusive motion, is ecologically plausible, and provides an alternative mechanism for formation of patterns in spatially explicit ecosystem models, with emphasis on non-stationary spatio-temporal dynamics.

Nutrient-limited growth with non-linear cell diffusion as a mechanism for floral pattern formation in yeast biofilms

Previous experiments have shown that mature yeast mat biofilms develop a floral morphology, characterised by the formation of petal-like structures. In this work, we investigate the hypothesis that nutrient-limited growth is the mechanism by which these floral patterns form. To do this, we use a combination of experiments and mathematical analysis. In mat formation experiments of the yeast species Saccharomyces cerevisiae, we observe that mats expand radially at a roughly constant speed, and eventually undergo a transition from circular to floral morphology. To determine the extent to which nutrient-limited growth can explain these features, we adopt a previously proposed mathematical model for yeast growth. The model consists of a coupled system of reaction–diffusion equations for the yeast cell density and nutrient concentration, with a non-linear, degenerate diffusion term for cell spread. Using geometric singular perturbation theory and numerics, we show that the model admits travelling wave solutions in one dimension, which enables us to infer the diffusion ratio from experimental data. We then use a linear stability analysis to show that two-dimensional planar travelling wave solutions for feasible experimental parameters are linearly unstable to non-planar perturbations. This provides a potential mechanism by which petals can form, and allows us to predict the characteristic petal width. There is good agreement between these predictions, numerical solutions to the model, and experimental data. We therefore conclude that the non-linear cell diffusion mechanism provides a possible explanation for pattern formation in yeast mat biofilms, without the need to invoke other mechanisms such as flow of extracellular fluid, cell adhesion, or changes to cellular shape or behaviour.

Electric Field Induced Pattern Formation on PMMA and ITO Layers

This letter reports on electric field induced pattern formation on a spin‐coated PMMA layer. The PMMA layer is coated onto p‐type silicon substrate using a spin coater at 3000 rpm. A perpendicular electric field is produced by applying a potential difference between the PMMA film and a parallel plate ITO conductor with water trapped between them. Different patterns are formed on PMMA and ITO layers depending upon the strength of electric field and time duration. The formed patterns are studied by scanning electron microscopy and atomic force microscopy. Mechanism of pattern formation and examination of formed pattern are discussed in this report.

Coexistence and Pattern Formation in Bacterial Mixtures with Contact-Dependent Killing

Multistrain microbial communities often exhibit complex spatial organization that emerges because of the interplay of various cooperative and competitive interaction mechanisms. One strong competitive mechanism is contact-dependent neighbor killing enabled by the type VI secretion system. It has been previously shown that contact-dependent killing can result in bistability of bacterial mixtures so that only one strain survives and displaces the other. However, it remains unclear whether stable coexistence is possible in such mixtures. Using a population dynamics model for two interacting bacterial strains, we found that coexistence can be made possible by the interplay of contact-dependent killing and long-range growth inhibition, leading to the formation of various cellular patterns. These patterns emerge in a much broader parameter range than that required for the linear Turing-like instability, suggesting this may be a robust mechanism for pattern formation.

Dimensionless analysis on liquid-liquid flow patterns and scaling law on slug hydrodynamics in cross-junction microchannels

Liquid-liquid flow patterns and slug hydrodynamics were experimentally studied in non-circular glass microchannels with water-butanol, water-toluene, water–oil and water-hexane systems, considering various hydraulic diameters (600 µm, 400 µm, 200 µm), inlet junctions (crossed, T) and aspect ratios (0.5, 1). The aqueous phase was the continuous phase due to the hydrophilic microchannel walls and the organic phase was the dispersed phase. Three main flow patterns were observed, i.e., annular flow, slug flow and droplet flow. The mechanism of flow pattern formation was explained by a force analysis, based on which, a dimensionless analysis regarding Weber number and Reynolds number was performed to develop general flow pattern transition criteria. Additionally, slug velocities and slug length were investigated. A new scaling law was proposed to predict the slug length and it showed a good agreement with the experimental results. A linear relationship between the slug velocity and the bulk velocity of the two phases was obtained.

Pattern Formation through Temporal Fractional Derivatives

It is well known that temporal first-derivative reaction-diffusion systems can produce various fascinating Turing patterns. However, it has been found that many physical, chemical and biological systems are well described by temporal fractional-derivative reaction-diffusion equations. Naturally arises an issue whether and how spatial patterns form for such a kind of systems. To address this issue clearly, we consider a classical prey-predator diffusive model with the Holling II functional response, where temporal fractional derivatives are introduced according to the memory character of prey’s and predator’s behaviors. In this paper, we show that this fractional-derivative system can form steadily spatial patterns even though its first-derivative counterpart can’t exhibit any steady pattern. This result implies that the temporal fractional derivatives can induce spatial patterns, which enriches the current mechanisms of pattern formation.

Comparative Analysis of WUSCHEL-Related Homeobox Genes Revealed Their Parent-of-Origin and Cell Type-Specific Expression Pattern During Early Embryogenesis in Tobacco.

WUSCHEL-related homeobox (WOX) gene is a plant-specific clade of homeobox transcription factors. Increasing evidences reveal that WOXs play critical roles in early embryogenesis, which involves zygote development, initiation of zygote division, and apical or basal cell lineage establishment. However, how WOXs regulate these developmental events remains largely unknown, and even detailed expression pattern in gametes and early proembryos is not yet available. Here, 13 WOX family genes were identified in Nicotiana tabacum genome. Comparative analysis of 13 WOX family genes with their homologs in Arabidopsis thaliana reveals relatively conserved expression pattern of WUS and WOX5 in shoot/root apical meristem. Whereas variations were also found, e.g., lacking homolog of WOX8 (a marker for suspensor cell) in tobacco genome and the expression of WOX2/WOX9 in both apical cell and basal cell. Transient transcriptional activity analysis revealed that WOXs in WUS clade have repressive activities for their target's transcription, whereas WOXs in ancient and intermediate clade have activation activities, giving a molecular basis for the phylogenetic classification of tobacco WOXs into three major clades. Expression pattern analysis revealed that some WOXs (e.g., WOX 13a) expressed in both male and female gametes and some WOXs (e.g., WOX 11 and WOX 13b) displayed the characteristics of parent-of-origin genes. Interestingly, some WOXs (e.g., WOX2 and WOX9), which are essential for early embryo patterning, were de novo transcribed in zygote, indicating relevant mechanism for embryo pattern formation is only established in zygote right after fertilization and not carried in by gametes. We also found that most WOXs displayed a stage-specific and cell type-specific expression pattern. Taken together, this work provides a detailed landscape of WOXs in tobacco during fertilization and early embryogenesis, which will facilitate the understanding of their specific roles in these critical developmental processes of embryogenesis.

Deformation patterning in finite-strain crystal plasticity by spectral homogenization with application to magnesium

Complex microstructural patterns arise as energy minimizers in systems having non-convex energy landscapes such as those associated with phase transformations, deformation twinning, or finite-strain crystal plasticity. The prediction of such patterns at the microscale along with the resulting, effective material response at the macroscale is key to understanding a wide range of mechanical phenomena and has classically been dealt with by simplifying energy relaxation theory or by expensive finite element calculations. Here, we discuss a stabilized Fourier spectral technique for the homogenized response at the level of a representative volume element (RVE). We show that the FFT-based method admits sufficiently high resolution suitable to predict the emergence of energy-minimizing microstructures and the resulting effective response by computing the approximated quasiconvex energy hull. We test the method in the classical single-slip problem in single- and bicrystals. Especially the latter goes beyond the scope of traditional finite element and analytical relaxation treatments and hints at mechanisms of pattern formation in polycrystals. We also demonstrate that the chosen spectral finite-difference approximation, important for removing ringing artifacts in the presence of high contrasts, adds a natural regularization to the non-convex minimization. Finally, the technique is applied to polycrystalline pure magnesium, where we account for the competition between dislocation-mediated plasticity and deformation twinning. These inelastic deformation mechanisms result in complex texture evolution paths at the polycrystalline mesoscale and are simulated within RVEs of varying grain size and texture by a constitutive crystal plasticity model with an effective, volume fraction-based description of twinning.

Dissolution behavior of negative-type photoresists for display manufacture studied by quartz crystal microbalance method

Photoresists have been widely used as patterning materials for electronic devices such as displays and semiconductors. Understanding pattern formation mechanisms is essential for the efficient development of resist materials. In particular, the dissolution mechanism of resist materials is an important process in pattern formation. In this study, the dissolution mechanisms of negative-type resists for display manufacture were investigated using a quartz crystal microbalance (QCM) method. The changes in frequency during development were measured for polymer and resist films. The observed major trend was as follows. The development type changed from an insoluble state to a peeling type and a dissolution type with Case II diffusion with an increase in the acid value of the polymers. The characteristics of the dissolution with Case II diffusion are the formation of a transient swelling layer (dissolution front) and steady-state front motion (linear weight loss). For the dissolution with Case II diffusion, the dissolution time and the original thickness of the transient swelling layer decreased with an increase in the acid value of the polymers.