Spatial patterns in the fruiting bodies of the cellular slime mold Polysphondylium pallidum

During morphogenesis in the slime mold Polysphondylium pallidum cell masses are periodically pinched off from the base of the developing sorogen. These masses round up and differentiate into secondary sorogens, which become radially ordered arrays of secondary fruiting bodies called whorls. Here we describe the morphogenesis of P. pallidum and characterize the spacing of whorls along the central stalk of the fruiting body and the spacing of sorocarps within whorls. We find both are highly regular. We propose that the linear spacing of whorls can be accounted for satisfactorily by a model that views the periodic release of cell masses from the base of the developing sorogen as the consequence of an imbalance between forces that orient amoebae toward the tip of the culminating sorogen, and cohesive forces between randomly moving cells in the basal region of the sorogen, which act as a retarding force. The orderly arrangement of fruiting bodies within whorls can be explained most easily by models that employ short-range activation and lateral inhibition.     

Spatial heterogeneity in three species,plant-parasite-hyperparasite,systems

This paper addresses the question of how heterogeneity may evolve due to interactions between the dynamics and movement of three-species systems involving hosts, parasites and hyperparasites in homogeneous environments. The models are motivated by the spread of soil-borne parasites within plant populations, where the hyperparasite is used as a biological control agent but where patchiness in the distribution of the parasite occurs, even when environmental conditions are apparently homogeneous. However, the models are introduced in generic form as three-species reaction-diffusion systems so that they have broad applicability to a range of ecological systems. We establish necessary criteria for the occurrence of population-driven patterning via diffusion-driven instability. Sufficient conditions are obtained for restricted cases with no host movement. The criteria are similar to those for the well-documented two-species reaction-diffusion system, although more possibilities arise for spatial patterning with three species. In particular, temporally varying patterns, that may be responsible for the apparent drifting of hot-spots of disease and periodic occurrence of disease at a given location, are possible when three species interact. We propose that the criteria can be used to screen population interactions, to distinguish those that cannot cause patterning from those that may give rise to population-driven patterning. This establishes a basic dynamical ''landscape'' against which other perturbations, including environmentally driven variations, can be analysed and distinguished from population-driven patterns. By applying the theory to a specific model example for host-parasite-hyperparasite interactions both with and without host movement, we show directly how the evolution of spatial pattern is related to biologically meaningful parameters. In particular, we demonstrate that when there is strong density dependence limiting host growth, the pattern is stable over time, whereas with less stable underlying host growth, the pattern varies with time.     

Whorl morphogenesis in the dasycladalean algae: the pattern formation viewpoint

The dasycladalean algae produce diverse whorled structures, among which the best known are the vegetative and reproductive whorls of Acetabularia acetabulum. In this paper, we review the literature pertaining to the origin of these structures. The question is addressed in terms of the necessary pattern-forming events and the possible mechanisms involved, an outlook we call the pattern formation viewpoint. The pattern-forming events involved in the morphogenesis of the vegetative and reproductive whorls of Acetabularia have been used to define five and six morphogenetic stages, respectively. We discuss three published mechanisms which account, at least in part, for the pattern-forming events. The mechanisms are mechanical buckling of the cell wall, reaction-diffusion of morphogen molecules along the cell membrane, and mechanochemical interactions between Ca2+ ions and the cytoskeleton in the cytosol. The numerous differences between these mechanisms provide experimental grounds to test their validity. To date, the results of these experiments point towards reaction diffusion as the most likely patterning mechanism. Finally, we consider the evolutionary origin of the vegetative and reproductive whorls and provide mechanistic explanations for some of the major evolutionary advances.     

A novel role of BELL1-like homeobox genes, PENNYWISE and POUND-FOOLISH, in floral patterning

Flowers are determinate shoots comprised of perianth and reproductive organs displayed in a whorled phyllotactic pattern. Floral organ identity genes display region-specific expression patterns in the developing flower. In Arabidopsis, floral organ identity genes are activated by LEAFY (LFY), which functions with region-specific co-regulators, UNUSUAL FLORAL ORGANS (UFO) and WUSCHEL (WUS), to up-regulate homeotic genes in specific whorls of the flower. PENNYWISE (PNY) and POUND-FOOLISH (PNF) are redundant functioning BELL1-like homeodomain proteins that are expressed in shoot and floral meristems. During flower development, PNY functions with a co-repressor complex to down-regulate the homeotic gene, AGAMOUS (AG), in the outer whorls of the flower. However, the function of PNY as well as PNF in regulating floral organ identity in the central whorls of the flower is not known. In this report, we show that combining mutations in PNY and PNF enhance the floral patterning phenotypes of weak and strong alleles of lfy, indicating that these BELL1-like homeodomain proteins play a role in the specification of petals, stamens and carpels during flower development. Expression studies show that PNY and PNF positively regulate the homeotic genes, APETALA3 and AG, in the inner whorls of the flower. Moreover, PNY and PNF function in parallel with LFY, UFO and WUS to regulate homeotic gene expression. Since PNY and PNF interact with the KNOTTED1-like homeodomain proteins, SHOOTMERISTEMLESS (STM) and KNOTTED-LIKE from ARABIDOPSIS THALIANA2 (KNAT2) that regulate floral development, we propose that PNY/PNF-STM and PNY/PNF-KNAT2 complexes function in the inner whorls to regulate flower patterning events.     

HyAlx, an aristaless-related gene, is involved in tentacle formation in hydra

Developmental gradients are known to play important roles in axial patterning in hydra. Current efforts are directed toward elucidating the molecular basis of these gradients. We report the isolation and characterization of HyAlx, an aristaless-related gene in hydra. The expression patterns of the gene in adult hydra, as well as during bud formation, head regeneration and the formation of ectopic head structures along the body column, indicate the gene plays a role in the specification of tissue for tentacle formation. The use of RNAi provides more direct evidence for this conclusion. The different patterns of HyAlx expression during head regeneration and bud formation also provide support for a recent version of a reaction-diffusion model for axial patterning in hydra.     

Spots and stripes: Pleomorphic patterning of stem cells via p-ERK-dependent cell chemotaxis shown by feather morphogenesis and mathematical simulation

A key issue in stem cell biology is the differentiation of homogeneous stem cells towards different fates which are also organized into desired configurations. Little is known about the mechanisms underlying the process of periodic patterning. Feather explants offer a fundamental and testable model in which multi-potential cells are organized into hexagonally arranged primordia and the spacing between primordia. Previous work explored roles of a Turing reaction-diffusion mechanism in establishing chemical patterns. Here we show that a continuum of feather patterns, ranging from stripes to spots, can be obtained when the level of p-ERK activity is adjusted with chemical inhibitors. The patterns are dose-dependent, tissue stage-dependent, and irreversible. Analyses show that ERK activity-dependent mesenchymal cell chemotaxis is essential for converting micro-signaling centers into stable feather primordia. A mathematical model based on short-range activation, long-range inhibition, and cell chemotaxis is developed and shown to simulate observed experimental results. This generic cell behavior model can be applied to model stem cell patterning behavior at large.     

Spatial patterning in Polysphondylium: monoclonal antibodies specific for whorl prepatterns

In this report we describe three monoclonal antibodies which detect prepatterning events preceding the appearance of visible tips in Polysphondylium pallidum whorls. A spatial and temporal analysis of the antigens against which these antibodies are directed reveals that the radial distribution of arms within whorls has its origins in an initial global amplification of tip-specific antigens over the surface of very early whorl masses. This two-dimensional distribution becomes restricted with time to a single dimension, a smooth distribution of antigen in a band about the equator of the whorl mass. This equatorial distribution breaks up into patches which eventually become visible tips. These results reveal that a spatial pattern can arise from a smooth prepattern, and grow through a series of intermediates characteristic of the symmetry breaking model first described by A. Turing (1952).     

On the orientation of stripes in fish skin patterning

This paper is focused on the study of the stripes orientation in the fish skin patterns. Based on microscopic observations of the pigment cells behavior at the embryonic stage, the key aspects of the pigmentation process are implemented in an experimental reaction-diffusion system. The experiment consists of a photosensitive Turing pattern of stripes growing directionally in one direction with controlled velocity. Different growth velocities of the system rearrange the stripes in the same three possible orientations observed in the skin of the colored fishes: parallel, oblique, and perpendicular. Our results suggest that the spreading velocity of the pigment cells in the fish dermis selects the orientation in the patterning processes.     

Interactions between Shh, Sostdc1 and Wnt signaling and a new feedback loop for spatial patterning of the teeth

Each vertebrate species displays specific tooth patterns in each quadrant of the jaw: the mouse has one incisor and three molars, which develop at precise locations and at different times. The reason why multiple teeth form in the jaw of vertebrates and the way in which they develop separately from each other have been extensively studied, but the genetic mechanism governing the spatial patterning of teeth still remains to be elucidated. Sonic hedgehog (Shh) is one of the key signaling molecules involved in the spatial patterning of teeth and other ectodermal organs such as hair, vibrissae and feathers. Sostdc1, a secreted inhibitor of the Wnt and Bmp pathways, also regulates the spatial patterning of teeth and hair. Here, by utilizing maternal transfer of 5E1 (an anti-Shh antibody) to mouse embryos through the placenta, we show that Sostdc1 is downstream of Shh signaling and suggest a Wnt-Shh-Sostdc1 negative feedback loop as a pivotal mechanism controlling the spatial patterning of teeth. Furthermore, we propose a new reaction-diffusion model in which Wnt, Shh and Sostdc1 act as the activator, mediator and inhibitor, respectively, and confirm that such interactions can generate the tooth pattern of a wild-type mouse and can explain the various tooth patterns produced experimentally.     

A Developmental Model for Branching Morphogenesis of Lake Cress Compound Leaf

Lake cress, Rorippa aquatica (Brassicaceae), is a semi-aquatic plant that exhibits a variety of leaf shapes, from simple leaves to highly branched compound leaves, depending on the environment. Leaf shape can vary within a single plant, suggesting that the variation can be explained by a simple model. In order to simulate the branched structure in the compound leaves of R. aquatica, we implemented reaction-diffusion (RD) patterning onto a theoretical framework that had been developed for serration distribution in the leaves of Arabidopsis thaliana, with the modification of the one-dimensional reaction-diffusion domain being deformed with the spatial periodicity of the RD pattern while expanding. This simple method using an iterative pattern could create regular and nested branching patterns. Subsequently, we verified the plausibility of our theoretical model by comparing it with the experimentally observed branching patterns. The results suggested that our model successfully predicted both the qualitative and quantitative aspects of the timing and positioning of branching in growing R. aquatica leaves.     

Why the leopard got its spots: relating pattern development to ecology in felids

A complete explanation of the diversity of animal colour patterns requires an understanding of both the developmental mechanisms generating them and their adaptive value. However, only two previous studies, which involved computer-generated evolving prey, have attempted to make this link. This study examines variation in the camouflage patterns displayed on the flanks of many felids. After controlling for the effects of shared ancestry using a fully resolved molecular phylogeny, this study shows how phenotypes from plausible felid coat pattern generation mechanisms relate to ecology. We found that likelihood of patterning and pattern attributes, such as complexity and irregularity, were related to felids' habitats, arboreality and nocturnality. Our analysis also indicates that disruptive selection is a likely explanation for the prevalence of melanistic forms in Felidae. Furthermore, we show that there is little phylogenetic signal in the visual appearance of felid patterning, indicating that camouflage adapts to ecology over relatively short time scales. Our method could be applied to any taxon with colour patterns that can reasonably be matched to reaction-diffusion and similar models, where the kinetics of the reaction between two or more initially randomly dispersed morphogens determines the outcome of pattern development.     

Computational biology: Turing’s lessons in simplicity

Biophysical modeling of development started with Alan Turing. His two-morphogen reaction-diffusion model was a radical but powerful simplification. Despite its apparent limitations, the model captured real developmental processes that only recently have been validated at the molecular level in many systems. The precision and robustness of reaction-diffusion patterning, despite boundary condition-dependence, remain active areas of investigation in developmental biology.     

A Modified Consumer Inkjet for Spatiotemporal Control of Gene Expression

This paper presents a low-cost inkjet dosing system capable of continuous, two-dimensional spatiotemporal regulation of gene expression via delivery of diffusible regulators to a custom-mounted gel culture of E. coli. A consumer-grade, inkjet printer was adapted for chemical printing; E. coli cultures were grown on 750 µm thick agar embedded in micro-wells machined into commercial compact discs. Spatio-temporal regulation of the lac operon was demonstrated via the printing of patterns of lactose and glucose directly into the cultures; X-Gal blue patterns were used for visual feedback. We demonstrate how the bistable nature of the lac operon''s feedback, when perturbed by patterning lactose (inducer) and glucose (inhibitor), can lead to coordination of cell expression patterns across a field in ways that mimic motifs seen in developmental biology. Examples of this include sharp boundaries and the generation of traveling waves of mRNA expression. To our knowledge, this is the first demonstration of reaction-diffusion effects in the well-studied lac operon. A finite element reaction-diffusion model of the lac operon is also presented which predicts pattern formation with good fidelity.     

Continuous growth-line sequences in gastropod shells

Studies of gastropod shell growth at the level of fine growth layers are scarce, because coiling of gastropod shells hinders the observation of continuous growth series spanning across whorls. We propose here a new method to obtain continuous growth patterns of gastropod shells over whorls with Terebralia palustris (L.) as an example. Comparison of vertical and horizontal sections of the shell of this species reveals that growth patterns can be observed continuously for several whorls on the vertical section of the columella. In addition, an obvious tidal growth pattern preserved in this species enables us to trace its growth with a precision of 12.4 h and indicates that it takes about two years for a shell to grow from 3 cm to 9.5 cm in height and add 5 complete whorls.     

A model of primitive streak initiation in the chick embryo

Initiation of the primitive streak in avian embryos provides a well-studied example of a pattern-forming event that displays a striking capacity for regulation. The mechanisms underlying the regulative properties are, however, poorly understood and are not easily accounted for by traditional models of pattern formation, such as reaction-diffusion models. In this paper, we propose a new activator-inhibitor model for streak initiation. We show that the model is consistent with experimental observations, both in its pattern-forming properties and in its ability to form these patterns on the correct time-scales for biologically realistic parameter values. A key component of the model is a travelling wave of inhibition. We present a mathematical analysis of the speed of such waves in both diffusive and juxtacrine relay systems. We use the streak initiation model to make testable predictions. By varying parameters of the model, two very different types of patterning can be obtained, suggesting that our model may be applicable to other processes in addition to streak initiation.