Anterior-posterior pattern formation: an evolutionary perspective on genes specifying terminal domains

The Drosophila anterior-posterior pattern genes of the terminal class, particularly the tailless gene, affect structures derived from the acron and the tail region of the embryo. These domains correspond in position and function to asegmental domains at the termini of annelids and more primitive insect embryos. This suggests that terminal genes in Drosophila may have originated in an ancestor common to both annelids and arthropods, and thus that the specification of termini in these metameric organisms is an ancient, evolutionarily conserved process.     

Morphogenetic pattern formation during ascidian notochord formation is regulative and highly robust.

The ascidian notochord forms through simultaneous invagination and convergent extension of a monolayer epithelial plate. Here we combine micromanipulation with time lapse and confocal microscopy to examine how notochord-intrinsic morphogenetic behaviors and interactions with surrounding tissues, determine these global patterns of movement. We show that notochord rudiments isolated at the 64-cell stage divide and become motile with normal timing; but, in the absence of interactions with non-notochordal tissues, they neither invaginate nor converge and extend. We find that notochord formation is robust in the sense that no particular neighboring tissue is required for notochord formation. Basal contact with either neural plate or anterior endoderm/lateral mesenchyme or posterior mesoderm are each alone sufficient to ensure that the notochord plate forms and extends a cylindrical rod. Surprisingly, the axis of convergent extension depends on the specific tissues that contact the notochord, as do other patterns of cell shape change, movement and tissue deformation that accompany notochord formation. We characterize one case in detail, namely, embryos lacking neural plates, in which a normal notochord forms but by an entirely different trajectory. Our results show ascidian notochord formation to be regulative in a fashion and to a degree never before appreciated. They suggest this regulative behavior depends on a complex interplay between morphogenetic tendencies intrinsic to the notochord plate and instructive and permissive interactions with surrounding tissues. We discuss mechanisms that could account for these data and what they imply about notochord morphogenesis and its evolution within the chordate phylum.     

Travelling lipid domains in a dynamic model for protein-induced pattern formation in biomembranes

Cell membranes are composed of a mixture of lipids. Many biological processes require the formation of spatial domains in the lipid distribution of the plasma membrane. We have developed a mathematical model that describes the dynamic spatial distribution of acidic lipids in response to the presence of GMC proteins and regulating enzymes. The model encompasses diffusion of lipids and GMC proteins, electrostatic attraction between acidic lipids and GMC proteins as well as the kinetics of membrane attachment/detachment of GMC proteins. If the lipid-protein interaction is strong enough, phase separation occurs in the membrane as a result of free energy minimization and protein/lipid domains are formed. The picture is changed if a constant activity of enzymes is included into the model. We chose the myristoyl-electrostatic switch as a regulatory module. It consists of a protein kinase C that phosphorylates and removes the GMC proteins from the membrane and a phosphatase that dephosphorylates the proteins and enables them to rebind to the membrane. For sufficiently high enzymatic activity, the phase separation is replaced by travelling domains of acidic lipids and proteins. The latter active process is typical for nonequilibrium systems. It allows for a faster restructuring and polarization of the membrane since it acts on a larger length scale than the passive phase separation. The travelling domains can be pinned by spatial gradients in the activity; thus the membrane is able to detect spatial clues and can adapt its polarity dynamically to changes in the environment.     

Biological action at a distance: Correlated pattern formation in adjacent tessellation domains without communication

Tessellations emerge in many natural systems, and the constituent domains often contain regular patterns, raising the intriguing possibility that pattern formation within adjacent domains might be correlated by the geometry, without the direct exchange of information between parts comprising either domain. We confirm this paradoxical effect, by simulating pattern formation via reaction-diffusion in domains whose boundary shapes tessellate, and showing that correlations between adjacent patterns are strong compared to controls that self-organize in domains with equivalent sizes but unrelated shapes. The effect holds in systems with linear and non-linear diffusive terms, and for boundary shapes derived from regular and irregular tessellations. Based on the prediction that correlations between adjacent patterns should be bimodally distributed, we develop methods for testing whether a given set of domain boundaries constrained pattern formation within those domains. We then confirm such a prediction by analysing the development of ‘subbarrel’ patterns, which are thought to emerge via reaction-diffusion, and whose enclosing borders form a Voronoi tessellation on the surface of the rodent somatosensory cortex. In more general terms, this result demonstrates how causal links can be established between the dynamical processes through which biological patterns emerge and the constraints that shape them.     

A bifurcation analysis of pattern formation in a diffusion governed morphogenetic field

Summary We discuss from an analytical point of view the mechanism of pre-pattern formation in a diffusion governed morphogenetic field. The model here considered is a normalized form of one of the models, proposed by Gierer and Meinhardt, based on the general principle of lateral inhibition. The results, obtained in the framework of bifurcation theory, shows that there is a spontaneous formation of a gradient both for activator and inhibitor concentrations if the ratio between the mean squares of the diffusion ranges of inhibitor and activator is greater than a well defined critical value.     

Endosymbionts: factors on egg pattern formation

Elimination of the intracellular symbionts of Euscelis plebejus either by X-ray irradiation of the posterior pole of the freshly laid egg or by interruption of egg infection by application of tetracycline or lysozyme to female leafhoppers leads to the production of embryos without abdomens, ‘head-embryos’.Homogenates of symbiont-free eggs and symbiont-containing eggs in the state of invagination have a pH of 7·5±0·2 and 7·0±0·2 and an osmotic pressure (pO) of 8·3±0·2 and 7·8±0·2, respectively. The presence of symbionts leads to a decrease of both the pH and pO.These data indicate that the correct formation of the posterior gradient, necessary for normal abdomen development, is dependent on the presence of endosymbionts at the posterior pole. It is possible that the symbionts change the pH and pO of the posterior gradient. These results are consistent with a hypothetical model of early differentiation of the Euscelis egg.     

Mode-doubling and tripling in reaction-diffusion patterns on growing domains: A piecewise linear model

 Reaction-diffusion equations are ubiquitous as models of biological pattern formation. In a recent paper [4] we have shown that incorporation of domain growth in a reaction-diffusion model generates a sequence of quasi-steady patterns and can provide a mechanism for increased reliability of pattern selection. In this paper we analyse the model to examine the transitions between patterns in the sequence. Introducing a piecewise linear approximation we find closed form approximate solutions for steady-state patterns by exploiting a small parameter, the ratio of diffusivities, in a singular perturbation expansion. We consider the existence of these steady-state solutions as a parameter related to the domain length is varied and predict the point at which the solution ceases to exist, which we identify with the onset of transition between patterns for the sequence generated on the growing domain. Applying these results to the model in one spatial dimension we are able to predict the mechanism and timing of transitions between quasi-steady patterns in the sequence. We also highlight a novel sequence behaviour, mode-tripling, which is a consequence of a symmetry in the reaction term of the reaction-diffusion system. Received: 19 December 2000 / Revised version: 24 May 2001 / Published online: 7 December 2001     

Dynamic regulation of growing domains for elongating and branching morphogenesis in plants

With their continuous growth, understanding how plant shapes form is fundamentally linked to understanding how growth rates are controlled across different regions of the plant. Much of a plant's architecture is generated in shoots and roots, where fast growth in tips contrasts with slow growth in supporting stalks. Shapes can be determined by where the boundaries between fast- and slow-growing regions are positioned, determining whether tips elongate, branch, or cease to grow. Across plants, there is a diversity in the cell wall chemistry through which growth operates. However, prototypical morphologies, such as tip growth and branching, suggest there are common dynamic constraints in localizing chemical growth catalysts. We have used Turing-type reaction-diffusion mechanisms to model this spatial localization and the resulting growth trajectories, characterizing the chemistry-growth feedback necessary for maintaining tip growth and for inducing branching. The mechanism defining the boundaries between fast- and slow-growing regions not only affects tip shape, it must be able to form new boundaries when the pattern-forming dynamics break symmetry, for instance in the branching of a tip. In previous work, we used an arbitrary concentration threshold to switch between two dynamic regimes of the growth catalyst in order to define growth boundaries. Here, we present a chemical dynamic basis for this threshold, in which feedback between two pattern-forming mechanisms controls the extent of the regions in which fast growth occurs. This provides a general self-contained mechanism for growth control in plant morphogenesis (not relying on external cues) which can account for both simple tip extension and symmetry-breaking branching phenomena.     

Pigmentation pattern formation on snakes

We consider a cell-chemotaxis model mechanism for generating some of the common, simple and complex, patterns found on the skin of snakes. By investigating the pattern generation potential of the model we show that many of the more complex patterns might result from growth of the integument during the pattern formation process. We suggest that many of the diverse elaborate patterns on snakes, and other species, can be generated by a single mechanism if the time scale of the pattern process is commensurate with the time scale associated with significant embryonic growth.     

Problems and paradigms: Morphogens and pattern formation

Morphogen gradient theories have enjoyed considerable popularity since the beginning of this century, but conclusive evidence for a role of morphogens in controlling multicellular development has been elusive. Recently, work on three secreted signalling proteins, Activin in Xenopus, and Wingless and Dpp in Drosophila, has stongly suggested that these proteins function as morphogens. In order to define a factor as a morphogen, it is necessary to show firstly, that it has a direct effect on target cells and secondly, that it affects the development of target cells in a concentration-dependent manner. With these criteria in mind, the evidence available for a variety of proposed morphogens is discussed. While the evidence is not conclusive in most of the cases considered, there is a strong case in favour of the three proteins mentioned above, which suggests that morphogens are potentially of general importance in controlling the development of multicellular organisms.     

Advances in pattern formation: Signaling and transcription

The 49(th) Annual Drosophila Research Conference was held in the sunny confines of San Diego. As usual, large numbers of Drosophila scientists working in fields as different as immunology and evolution descended on the venue. The meeting showed that the fly community is still vibrant and diverse even with the funding crunch at the NIH and the renewed rumors that Drosophila may have outlived its usefulness. This short review will focus on one session of platform presentations detailing the recent advances in the field of pattern formation. This session offered a variety of topics reviewing the formation of pattern in various tissues through diverse mechanisms. I will focus on early embryonic patterning through pair-rule genes, specificity of FGF signaling, and tissue regeneration.     

One-dimensional daisyworld: spatial interactions and pattern formation

The zero-dimensional daisyworld model of Watson and Lovelock (1983) demonstrates that life can unconsciously regulate a global environment. Here that model is extended to one dimension, incorporating a distribution of incoming solar radiation and diffusion of heat consistent with a spherical planet. Global regulatory properties of the original model are retained. The daisy populations are initially restricted to hospitable regions of the surface but exert both global and local feedback to increase this habitable area, eventually colonizing the whole surface. The introduction of heat diffusion destabilizes the coexistence equilibrium of the two daisy types. In response, a striped pattern consisting of blocks of all black or all white daisies emerges. There are two mechanisms behind this pattern formation. Both are connected to the stability of the system and an overview of the mathematics involved is presented. Numerical experiments show that this pattern is globally determined. Perturbations in one region have an impact over the whole surface but the regulatory properties of the system are not compromised by transient perturbations. The relevance of these results to the Earth and the wider climate modelling field is discussed.     

Cell adhesiveness and affinity for limb pattern formation

Stage-dependent cell sorting in vitro is an intriguing property that mesenchymal cells of a chick limb bud have. We previously proposed that N-cadherin, a cell adhesion molecule, is involved in the sorting process and is likely to be a component of the mechanism of proximal-distal patterning in the developing limb (Yajima et al., (1999) Dev. Dynam. 216:274-284). Here, we present more direct evidence that N-cadherin is one of the molecules responsible for regulation of stage-dependent cell sorting in vitro. Our results suggest that N-cadherin, which accumulates in the distal region of the chick limb bud as limb development proceeds, is related to the positional identity that gives rise to the different shapes and numbers of cartilaginous elements along the proximal-distal axis. In this article we also give insights into positional identity which is mediated by Hoxgenes and cell surface property during limb development.     

Limb development: an international model for vertebrate pattern formation

Limb development is an excellent model for studying how patterns of differentiated cells and tissues are generated in vertebrate embryos. The cell interactions that mediate patterning have been discovered and, more recently, some of the molecules involved in these interactions have been identified. This has provided a direct link to genetics and thus to genes that cause human congenital limb defects.     

Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains

By using asymptotic theory, we generalise the Turing diffusively-driven instability conditions for reaction-diffusion systems with slow, isotropic domain growth. There are two fundamental biological differences between the Turing conditions on fixed and growing domains, namely: (i) we need not enforce cross nor pure kinetic conditions and (ii) the restriction to activator-inhibitor kinetics to induce pattern formation on a growing biological system is no longer a requirement. Our theoretical findings are confirmed and reinforced by numerical simulations for the special cases of isotropic linear, exponential and logistic growth profiles. In particular we illustrate an example of a reaction-diffusion system which cannot exhibit a diffusively-driven instability on a fixed domain but is unstable in the presence of slow growth.