Endogenous electromagnetic fields in plant leaves: a new hypothesis for vascular pattern formation

Electromagnetic (EM) phenomena have long been implicated in biological development, but few detailed, practical mechanisms have been put forth to connect electromagnetism with morphogenetic processes. This work describes a new hypothesis for plant leaf veination, whereby an endogenous electric field forming as a result of a coherent Frohlich process, and corresponding to an EM resonant mode of the developing leaf structure, is capable of instigating leaf vascularisation. In order to test the feasibility of this hypothesis, a three-dimensional, EM finite-element model (FEM) of a leaf primordium was constructed to determine if suitable resonant modes were physically possible for geometric and physical parameters similar to those of developing leaf tissue. Using the FEM model, resonant EM modes with patterns of relevance to developing leaf vein modalities were detected. On account of the existence of shared geometric signatures in a leaf's vascular pattern and the electric field component of EM resonant modes supported by a developing leaf structure, further theoretical and experimental investigations are warranted. Significantly, this hypothesis is not limited to leaf vascular patterning, but may be applicable to a variety of morphogenetic phenomena in a number of living systems.     

Structural evidence for electromagnetic resonance in plant morphogenesis

How a homogeneous collective of cells consistently and precisely establishes long-range tissue patterns remains a question of active research. This work explores the hypothesis of plant organs as resonators for electromagnetic radiation. Long-range structural patterns in the developing ovaries and male flower buds of cucurbit plants (zucchini, acorn, and butternut squash), in addition to mature cucurbit fruits (acorn, butternut, and zucchini squash; watermelon, and cucumber), were investigated. A finite element analysis (FEA) model was used to determine resonant EM modes for models with similar geometric and electrical parameters to those of developing organs. Main features of the developing ovaries (i.e. shape of placental lines, ovum location, definition of distinct tissue regions), male flower buds (i.e. early pollen tube features), and mature fruits (i.e. septa placement, seed location, endocarp and mesocarp) showed distinct correlations with electric and magnetic field components of electromagnetic resonant modes. On account of shared pattern signatures in developing organs and the EM resonant modes supported by a modelled structure with similar geometric and electrical properties to those of cucurbit organs, experimental investigations are warranted. The concept of a developing organ as an EM dielectric resonator may extend to a variety of morphogenetic phenomena in a number of living systems.     

How canalization can make loops: a new model of reticulated leaf vascular pattern formation

Formation of the vascular system in plant leaves can be explained by the canalization hypothesis which states that veins are formed in an initially homogeneous field by a self-organizing process between the plant hormone auxin and auxin carrier proteins. Previous models of canalization can generate vein patterns with branching but fail to generate vein patterns with closed loops. However, closed vein loops are commonly observed in plant leaves and are important in making them robust to herbivore attacks and physical damage. Here we propose a new model which generates a vein system with closed loops. We postulate that the "flux bifurcator" level is enhanced in cells with a high auxin flux and that it causes reallocation of auxin carriers toward neighbouring cells also having a high bifurcator level. This causes the auxin flux to bifurcate, allowing vein tips to attach to other veins creating vein loops. We explore several alternative functional forms for the flux bifurcator affecting the reallocation of efflux carriers and examine parameter dependence of the resulting vein pattern.     

Self-organization of the vascular system in plant leaves: inter-dependent dynamics of auxin flux and carrier proteins

The vegetative hormone Auxin is involved in vascular tissues formation throughout the plant. Trans-membrane carrier proteins transporting auxin from cell to cell and distributed asymmetrically around each cell give to auxin a polarized movement in tissues, creating streams of auxin that presume future vascular bundles. According to the canalization hypothesis, auxin transport ability of cells is thought to increase with auxin flux, resulting in the self-enhancement of this flux along auxin paths. In this study we evaluate a series of models based on canalization hypothesis using carrier proteins, under different assumptions concerning auxin flux formation and carrier protein dynamics. Simulations are run on a hexagonal lattice with uniform auxin production. A single cell located in the margin of the lattice indicates the petiole, and acts as an auxin sink. The main results are: (1) We obtain branching auxin distribution patterns. (2) The type of self-enhancement described by the functional form of the carrier proteins regulation responding to the auxin flux intensity in different parts of a cell, has a strong effect on the possibility of generating the branching patterns. For response functions with acceleration in the increase of carrier protein numbers compared to the auxin flux, branching patterns are likely to be generated. For linear or decelerating response functions, no branching patterns are formed. (3) When branching patterns are formed, auxin distribution greatly differs between the case in which the number of carrier proteins in different parts of a cell are regulated independently, and the case in which different parts of a cell compete for a limited number of carrier proteins. In the former case, the auxin level is lower in veins than in the surrounding tissue, while in the latter, the auxin is present in greater abundance in veins. These results suggest that canalization is a good candidate for describing plant vein pattern formation.     

Evolution of a colour pattern: history,development, and selection

Patterns of melanin pigmentation in birds are extremely varied. Nevertheless it is easy to think of many patterns that are never observed, and others that frequently recur in diverse and distantly related species. Using as our model the avian genus Phylloscopus we ask how the restricted range of observed patterns might be attributable to a restricted range of variants produced by developmental perturbations. The patterns we consider consist of unmelanized patches on the wings, crown and rump on otherwise pigmented upperparts. We use reaction-diffusion models to show that gross features of the pattern can be simply predicted from considerations of embryo shape. We suggest that birds are expected to have more patterned heads, because the head region is relatively larger than other regions in the developing embryo. A comparative analysis across many species of birds and a phylogenetic analysis within the genus Phylloscopus show that the component elements of the pattern have repeatedly been lost and gained during evolution. A shift in a threshold reading could explain the appearance and disappearance of the unmelanized patches, perhaps through changes in the sensitivity of melanocytes to epidermal signals. Such threshold shifts would make the transition between patterned and unpatterned forms particularly easy once the patterns have been exposed to selection in some distant ancestor. This partitioning of the roles of selection and development implies that many features of the patterns reflect developmental mechanisms in both immediate and more distant ancestors.     

Involvement of Wnt-5a in chondrogenic pattern formation in the chick limb bud

Members of the Wnt family are known to play diverse roles in the organogenesis of vertebrates. The full-coding sequences of chicken Wnt-5a were identified and the role it plays in limb development was examined by comparing its expression pattern with that of two other Wnt members, Wnt-4 and Wnt-11, and by misexpressing it with a retrovirus vector in the limb bud. Wnt-5a expression is detected in the limb-forming region at stage 14, and in the apical ectodermal ridge and distal mesenchyme of the limb bud. The signal was graded along the proximal-distal axis at stages 20-28 and also along the anterior-posterior axis during early stages. It disappeared in the cartilage-forming region after stage 26, and was restricted to the region surrounding the phalanges at stage 34. Wnt-4 and Wnt-11, other members of the Wnt-5a-subclass, were expressed with a distinct spatiotemporal pattern during the later phase. Wnt-4 was expressed in the articular structure and Wnt-11 was expressed in the dorsal and ventral mesenchyme adjacent to the ectoderm. Wnt-5a expression was partially reduced after apical ectodermal ridge removal, whereas Wnt-11 expression was down-regulated by dorsal ectoderm removal. Therefore, expression of these Wnt was differentially regulated by the ectodermal signal. Misexpression of Wnt-5a in the limb bud with the retrovirus resulted in truncation of long bones predominantly in the zeugopod because of retarded chondrogenic differentiation. Distal elements, such as the phalanges and metacarpals, were not significantly reduced in size. These results suggest that Wnt-5a is involved in pattern formation along the proximal-distal axis by regulation of chondrogenic differentiation.     

Models for contact-mediated pattern formation: cells that form parallel arrays

Kinetic continuum models are derived for cells that crawl over a 2D substrate, undergo random reorientation, and turn in response to contact with a neighbor. The integro-partial differential equations account for changes in the distribution of orientations in the population. It is found that behavior depends on parameters such as total mass, random motility, adherence, and sloughing rates, as well as on broad aspects of the contact response. Linear stability analysis, and numerical, and cellular automata simulations reveal that as parameters are varied, a bifurcation leads to loss of stability of a uniform (isotropic) steady state, in favor of an (anisotropic) patterned state in which cells are aligned in parallel arrays.     

From endogenous to exogenous pattern formation: Invasive plant species changes the spatial distribution of a native ant

Invasive species are a significant threat to global biodiversity, but our understanding of how invasive species impact native communities across space and time remains limited. Based on observations in an old field in Southeast Michigan spanning 35 years, our study documents significant impacts of habitat change, likely driven by the invasion of the shrub, Elaeagnus umbellata, on the nest distribution patterns and population demographics of a native ant species, Formica obscuripes. Landcover change in aerial photographs indicates that E. umbellata expanded aggressively, transforming a large proportion of the original open field into dense shrubland. By comparing the ant's landcover preferences before and after the invasion, we demonstrate that this species experienced a significant unfavorable change in its foraging areas. We also find that shrub landcover significantly moderates aggression between nests, suggesting nests are more related where there is more E. umbellata. This may represent a shift in reproductive strategy from queen flights, reported in the past, to asexual nest budding. Our results suggest that E. umbellata may affect the spatial distribution of F. obscuripes by shifting the drivers of nest pattern formation from an endogenous process (queen flights), which led to a uniform pattern, to a process that is both endogenous (nest budding) and exogenous (loss of preferred habitat), resulting in a significantly different clustered pattern. The number and sizes of F. obscuripes nests in our study site are projected to decrease in the next 40 years, although further study of this population's colony structures is needed to understand the extent of this decrease. Elaeagnus umbellata is a common invasive shrub, and similar impacts on native species might occur in its invasive range, or in areas with similar shrub invasions.     

Global cell sorting in the C. elegans embryo defines a new mechanism for pattern formation

4D microscopic observations of Caenorhabditis elegans development show that the nematode uses an unprecedented strategy for development. The embryo achieves pattern formation by sorting cells, through far-ranging movements, into coherent regions before morphogenesis is initiated. This sorting of cells is coupled to their particular fate. If cell identity is altered by experiment, cells are rerouted to positions appropriate to their new fates even across the whole embryo. This cell behavior defines a new mechanism of pattern formation, a mechanism that is also found in other animals. We call this new mechanism "cell focusing". When the fate of cells is changed, they move to new positions which also affect the shape of the body. Thus, this process is also important for morphogenesis.     

Neural networks with constrained inputs as models for pattern formation in primate visual cortex

We present a neural network model for the formation of ocular dominance stripes on primate visual cortex and examine the generic phase behavior and dynamics of the model. The dynamical equation of ocular dominance development can be identified with a class of Langevin equations with a nonconserved order parameter. We first set up and examine an Ising model with long-range interactions in an external field, which is equivalent to the model described by the Langevin equation. We use both mean-field theory and Monte-Carlo simulations to study the equilibrium phase diagram of this equivalent Ising model. The phase diagram comprises three phases: a striped phase, a hexagonal bubble phase, and a uniform paramagnetic phase. We then examine the dynamics of the striped phase by solving the Langevin equation both numerically and by singular perturbation theory. Finally, we compare the results of the model with physiological data. The typical striped structure of the ocular dominance columns corresponds to the zero-field configurations of the model. Monocular deprivation can be simulated by allowing the system to evolve in the absence of an external field at early times and then continuing the simulation in the presence of an external field. The physical and physiological applications of our model are discussed in the conclusion.     

Polygenic analysis of pattern formation in Drosophila: Specification of campaniform sensilla positions on the wing

This study was designed to measure the degree of correlation between vein formation and the specification of campaniform sensillae positions in the wing of Drosophila melanogaster. The campaniform sensillae are sensory organs placed at various locations on the wing. Those on the third longitudinal vein (L3) were the focus of this analysis. The system of polygenic modifiers of vein length is comparatively simple, as shown in whole chromosome assays of selected lines. This variability provides a sensitive method of altering vein-forming ability and of assessing correlated changes in other parts of the vein pattern. In selection lines of veinlet, sensillae were displaced toward the base of the wing as vein length decreased by distal loss of vein material. Changes in the amount of vein were, however, not directly proportional to changes in sensillae positions. The more distal sensillae were shifted the largest amount. In the mutant tilt, in which reduced L3 vein-forming competence results in subterminal gaps, distal campaniform sensillae were almost completely eliminated. The remaining sensillae were shifted toward the base of the wing where vein formation is normal. The placement of sensillae therefore appears to be sensitive to the same underlying determinants involved in vein-forming competence.     

Travelling waves and pattern formation in a model for fungal development

 Under a variety of conditions, the hyphal density within the expanding outer edge of growing fungal mycelia can be spatially heterogeneous or nearly uniform. We conduct an analysis of a system of reaction-diffusion equations used to model the growth of fungal mycelia and the subsequent development of macroscopic patterns produced by differing hyphal and hence biomass densities. Both local and global results are obtained using analytical and numerical techniques. The emphasis is on qualitative results, including the effects of changes in parameter values on the structure of the solution set. Received 22 November 1995; received in revised form 17 May 1996     

On a simplified model for pattern formation in honey bee colonies

We present a simplified version of a previously presented model (Camazine et al. (1990)) that generates the characteristic pattern of honey, pollen and brood which develops on combs in honey bee colonies. We demonstrate that the formation of a band of pollen surrounding the brood area is dependent on the assumed form of the honey and pollen removal terms, and that a significant pollen band arises as the parameter controlling the rate of pollen input passes through a bifurcation value. The persistence of the pollen band after a temporary increase in pollen input can be predicted from the model. We also determine conditions on the parameters which ensure the accumulation of honey in the periphery and demonstrate that, although there is an important qualitative difference between the simplified and complete models, an analysis of the simplified version helps us understand many biological aspects of the more complex complete model. Corresponding author     

A densitometrical method for the study of pattern formation in a ciliateChilodonella

Summary An easy and sensitive method is reported here for testing the similarities of individual patterns by photographically transforming maps of these patterns to given, deductively chosen conventions involving constant distances between selected reference points. A cumulative map is produced by loading all landmarks from a set of individual maps on to one sheet of paper. The use of various a priori conventions results in variable cumulative maps, which are then optically transformed on an analog digital converter, with additional input for optical picture processing. The densitometrical maps thus obtained may be compared as to the cumulative degree of areas of maximal and minimal density of landmarks. The best conventions are those that yield the map with the most contrast.Maps of spatial patterns of the sites of contractile vacuole pore (CVP) primordia in an early stage of divisional morphogenesis of the ciliateChilodonella steini were compared after four different transformations and adjustments of the same set of individual maps. The best focusing of the sites of CVP differentiation was achieved by use of the postoral axis, defined by the center of the oral apparatus and the posterior end of the cell as the scaling parameter. The composite domain map obtained by optical transformation of this cumulative map could distinguish the specific CVP territories observed in earlier work (Kaczanowska 1981). These results confirm earlier findings that indicated the site of the oral apparatus is an important reference point in CVP primordia positioning. They also strongly suggest the existence of an overriding scaling factor governing the positioning of sites of differentiation in both dimensions of the developmental field. The method of superposition and scaling of pattern maps is generally applicable to situations in which pattern elements appear at discrete points on a flat surface.     

Interplay between activator-inhibitor coupling and cell-matrix adhesion in a cellular automaton model for chondrogenic patterning

We present a stochastic cellular automaton model for the behavior of limb bud precartilage mesenchymal cells undergoing chondrogenic patterning. This "agent-oriented" model represents cells by points on a lattice that obey rules motivated by experimental findings. The "cells" follow these rules as autonomous agents, interacting with other cells and with the microenvironments cell activities produce. The rules include random cell motion, production and lateral deposition of a substrate adhesion molecule (SAM, corresponding to fibronectin), production and release of a diffusible growth factor ("activator," corresponding to TGF-beta) that stimulates production of the SAM, and another diffusible factor ("inhibitor") that suppresses the activity of the activator. We implemented the cellular automaton on a two-dimensional (2D) square lattice to emulate the quasi-2D micromass culture extensively used to study patterning in avian limb bud precartilage cells. We identified parameters that produce nodular patterns that resemble, in size and distribution, cell condensations in leg-cell cultures, thus establishing a correspondence between in vitro and in silico results. We then studied the in vitro and in silico micromass cultures experimentally. We altered the standard in vitro micromass culture by diluting the initial cell density, transiently exposing it to exogenous activator, suppressing the inhibitor, and constitutively activating fibronectin production. We altered the standard in silico micromass culture in each case by changing the corresponding parameter. In vitro and in silico experiments agreed well. We also used the model to test hypotheses for differences in the in vitro patterns of cells derived from chick embryo forelimb and hindlimb. We discuss the applicability of this model to limb development in vivo and to other organ development.     

Pigmentation pattern formation in butterflies: experiments and models

Butterfly pigmentation patterns are one of the most spectacular and vivid examples of pattern formation in biology. They have attracted much attention from experimentalists and theoreticians, who have tried to understand the underlying genetic, chemical and physical processes that lead to patterning. In this paper, we present a brief review of this field by first considering the generation of the localised, eyespot, patterns and then the formation of more globally controlled patterns. We present some new results applied to pattern formation on the wing of the mimetic butterfly Papilio dardanus.     

Expression of form and pattern in plants — a role for biophysical fields

Coordinated or ‘field’ behaviour of cells of a tissue can be treated as an interaction between signals and a responding system. When the response involves the reaction of similar cells to a gradient, the field properties are thought to reside mainly in the signal. It is not generally recognized that initially uniform properties in the responding tissue can contribute to the specification of geometrical detail. One such feature is that a tissue may have an intrinsic wavelength, e.g. for the diameter of a new-forming organ. Another is tensor properties. Both features can greatly expand the role of signals in the expression of pattern.     

COE1, an LRR–RLK responsible for commissural vein pattern formation in rice

Leaf veins have a complex network pattern. Formation of this vein pattern has been widely studied as a model of tissue pattern formation in plants. To understand the molecular mechanism governing the vascular patterning process, we isolated the rice mutant, commissural vein excessive1 (coe1). The coe1 mutants had short commissural vein (CV) intervals and produced clustered CVs. Application of 1‐N‐naphthylphthalamic acid and brefeldin A decreased CV intervals, and application of 1‐naphthaleneacetic acid increased CV intervals in wild‐type rice; however, coe1 mutants were insensitive to these chemicals. COE1 encodes a leucine‐rich repeat receptor‐like kinase, whose amino acid sequence is similar to that of brassinosteroid‐insensitive 1‐associated receptor kinase 1 (BAK1), and which is localized at the plasma membrane. Because of the sequence similarity of COE1 to BAK1, we also examined the involvement of brassinosteroids in CV formation. Brassinolide, an active brassinosteroid, decreased the CV intervals of wild‐type rice, and brassinazole, an inhibitor of brassinosteroid biosynthesis, increased the CV intervals of wild‐type rice, but coe1 mutants showed insensitivity to these chemicals. These results suggest that auxin and brassinosteroids regulate CV intervals in opposite directions, and COE1 may regulate CV intervals downstream of auxin and brassinosteroid signals.     

A model for budding in hydra: pattern formation in concentric rings

Current models of pattern formation in Hydra propose head-and foot-specific morphogens to control the development of the body ends and along the body length axis. In addition, these morphogens are proposed to control a cellular parameter (positional value, source density) which changes gradually along the axis. This gradient determines the tissue polarity and the regional capacity to form a head and a foot, respectively, in transplantation experiments. The current models are very successful in explaining regeneration and transplantation experiments. However, some results obtained render problems, in particular budding, the asexual way of reproduction is not understood. Here an alternative model is presented to overcome these problems. A primary system of interactions controls the positional values. At certain positional values secondary systems become active which initiate the local formation of e.g. mouth, tentacles, and basal disc. (i) A system of autocatalysis and lateral inhibition is suggested to exist as proposed by Gierer and Meinhardt (Kybernetik 12 (1972) 30). (ii) The activator is neither a head nor a foot activator but rather causes an increase of the positional value. (iii) On the other hand, a generation of the activator leads to its loss from cells and therewith to a (local) decrease of the positional value. (iv) An inhibitor is proposed to exist which antagonizes an increase of the positional value. External conditions like the gradient of positional values in the surroundings and interactions with other sites of morphogen production decide whether at a certain site of activator generation the positional value will increase (head formation), decrease (foot formation) or increase in the centre and decrease in the periphery thereby forming concentric rings (bud formation). Computer-simulation experiments show basic features of budding, regeneration and transplantation.