Pattern formation of the 'Tilapia mark' in the tilapia fish, Oreochromis mossambicus

The dorsal fin of the larval and juvenile Oreochromis mossambicus exhibits a unique black spot known as the ' Tilapia mark'. We traced its development and found that it occupied a specific position in the dorsal fin bounded by rays 15 and 20. Ablation experiments carried out on the larval dorsal fin showed that this spot region constituted a developmental positional field. This positional field in the fin could regenerate and re-establish the spot pattern despite repeated perturbation. The re-establishment of spot was not simply due to fin injury since ablation of the non-spotted region of the dorsal and the tail fin did not result in aggregation of melanophores. We propose that that' Tilapia mark' is a result of positional information in operation.     

Interactions between the Foot and the Head Patterning Systems in Hydra vulgaris

The Cnidarian, hydra, is an appealing model system for studying the basic processes underlying pattern formation. Classical studies have elucidated much basic information regarding the role of development gradients, and theoretical models have been quite successful at describing experimental results. However, most experiments and computer simulations have dealt with isolated patterning events such as the dynamics of head regeneration. More global events such as interactions among the head, bud, and foot patterning systems have not been extensively addressed. The characterization of monoclonal antibodies with position-specific labeling patterns and the recent cloning and characterization of genes expressed in position-specific manners now provide the tools for investigating global interactions between patterning systems. In particular, changes in the axial positional value gradient may be monitored in response to experimental perturbation. Rather than studying isolated patterning events, this approach allows us to study patterning over the entire animal. The studies reported here focus on interactions between the foot and the head patterning systems in Hydra vulgaris following induction of a foot in close proximity to a head, axial grafting of a foot closer to the head, or doubling the amount of basal tissue by lateral grafting of an additional peduncle-foot onto host animals. Resulting positional value changes as monitored by antigen (TS19) and gene (ks1 and CnNK-2) expression were assessed in the foot, head, and intervening tissue. The results of the experiments indicate that positional values changed rapidly, in a matter of hours, and that there were reciprocal interactions between the foot and the head patterning systems. Theoretical interpretations of the results in the form of computer simulations based on the reaction-diffusion model are presented and predict many, but not all, of the experimental observations. Since the lateral grafting experiment cannot, at present, be simulated, it is discussed in light of what has been learned from the axial grafting experiments and their simulations.     

Chemical morphogenesis: Turing patterns in an experimental chemical system

Patterns resulting from the sole interplay between reaction and diffusion are probably involved in certain stages of morphogenesis in biological systems, as initially proposed by Alan Turing. Self-organization phenomena of this type can only develop in nonlinear systems (i.e. involving positive and negative feedback loops) maintained far from equilibrium. We present Turing patterns experimentally observed in a chemical system. An oscillating chemical reaction, the CIMA reaction, is operated in an open spatial reactor designed in order to obtain a pure reaction-diffusion system. The two types of Turing patterns observed, hexagonal arrays of spots and parallel stripes, are characterized by an intrinsic wavelength. We identify the origin of the necessary difference of diffusivity between activator and inhibitor. We also describe a pattern growth mechanism by spot splitting that recalls cell division.     

Maintenance of heterocyst patterning in a filamentous cyanobacterium

In the absence of sufficient combined nitrogen, some filamentous cyanobacteria differentiate nitrogen-fixing heterocysts at approximately every 10th cell position. As cells between heterocysts grow and divide, this initial pattern is maintained by the differentiation of a single cell approximately midway between existing heterocysts. This paper introduces a mathematical model for the maintenance of the periodic pattern of heterocysts differentiated by Anabaena sp. strain PCC 7120 based on the current experimental knowledge of the system. The model equations describe a non-diffusing activator (HetR) and two inhibitors (PatS and HetN) that undergo diffusion in a growing one-dimensional domain. The inhibitors in this model have distinct diffusion rates and temporal expression patterns. These unique aspects of the model reflect recent experimental findings regarding the molecular interactions that regulate patterning in Anabaena. Output from the model is in good agreement with both the temporal and spatial characteristics of the pattern maintenance process observed experimentally.     

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.     

Forging patterns and making waves from biology to geology: a commentary on Turing (1952) ‘The chemical basis of morphogenesis’

Alan Turing was neither a biologist nor a chemist, and yet the paper he published in 1952, ‘The chemical basis of morphogenesis’, on the spontaneous formation of patterns in systems undergoing reaction and diffusion of their ingredients has had a substantial impact on both fields, as well as in other areas as disparate as geomorphology and criminology. Motivated by the question of how a spherical embryo becomes a decidedly non-spherical organism such as a human being, Turing devised a mathematical model that explained how random fluctuations can drive the emergence of pattern and structure from initial uniformity. The spontaneous appearance of pattern and form in a system far away from its equilibrium state occurs in many types of natural process, and in some artificial ones too. It is often driven by very general mechanisms, of which Turing''s model supplies one of the most versatile. For that reason, these patterns show striking similarities in systems that seem superficially to share nothing in common, such as the stripes of sand ripples and of pigmentation on a zebra skin. New examples of ‘Turing patterns'' in biology and beyond are still being discovered today. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.     

Reaction–diffusion wave model for self-assembled network formation of poly(dA)·poly(dT) DNA on mica and HOPG surfaces

Deoxyribonucleic acid (DNA) is a vital molecule for life since it contains genetic information. However, DNA has recently been reported to have unique properties that make it suitable for bionanoelectronic applications, such as the possibility of electrical conductivity and self-organisation. Self-assembled DNA network structures have been observed on several substrates, but the detailed self-assembly mechanism has yet to be determined. The present study investigates self-assembled structures of DNA both theoretically and experimentally. We developed a reaction–diffusion model and used it to investigate pattern formations observed by atomic force microscopy. The computational results qualitatively replicate the network patterns of DNA molecules based on a quantitative agreement with the surface size and timescale. The model can account for the effect of the DNA concentration on pattern formation. Furthermore, peculiar geometric patterns are simulated for mica and highly oriented pyrolytic graphite surfaces.     

About the equilibrium shape of fibred structures, and biological shapes

Biological morphogenesis has often been modeled with reaction-diffusion models [A.M. Turing, The chemical basis of morphogenesis, Phil. Trans. R. Soc. Lond. B 237 (1952) 37-72]. The interplay of bio-chemical fields is supposed to generate shapes by positional information carried by the values in the field. However, the structure of the biological tissue at the microscopic scale is absent from these models. We show that the fibred nature of biological tissue induces specific morphogenic properties. Fibred shapes can be calculated from physical principles borrowed from the theory of crystallogenesis. These give an intuitive insight into the shape of fruits or vegetables, buds and pins in botany, fingers, muscles, insects abdomen and heart in the animal realm, and also into other fibred structures such as the mitotic spindle. We predict the existence of bumps, apices or cusps at poles of fibred structures. An extrapolation to out-of-equilibrium growth predicts that these structures grow forward in the direction of the cusp, and that fibred organs should have a regular branching ordering. However, our model does not take into account the elasto-plastic properties, or the composite nature of the living material.     

The Role of Complex Formation and Deleterious Mutations for the Stability of RNA-Like Replicator Systems

In the RNA world hypothesis, RNA(-like) self-replicators are suggested as the central player of prebiotic evolution. However, there is a serious problem in the evolution of complexity in such replicators, i.e., the problem of parasites. Parasites, which are replicated by catalytic replicators (catalysts), but do not replicate the others, can destroy a whole replicator system by exploitation. Recently, a theoretical study underlined complex formation between replicators--an often neglected but realistic process--as a stabilizing factor in a replicator system by demonstrating that complex formation can shift the viable range of diffusion intensity to higher values. In the current study, we extend the previous study of complex formation. Firstly, by investigating a well-mixed replicator system, we establish that complex formation gives parasites an implicit advantage over catalysts, which makes the system significantly more vulnerable to parasites. Secondly, by investigating a spatially extended replicator system, we show that the formation of traveling wave patterns plays a crucial role in the stability of the system against parasites, and that because of this the effect of complex formation is not straightforward; i.e., whether complex formation stabilizes or destabilizes the spatial system is a complex function of other parameters. We give a detailed analysis of the spatial system by considering the pattern dynamics of waves. Furthermore, we investigate the effect of deleterious mutations. Surprisingly, high mutation rates can weaken the exploitation of the catalyst by the parasite.     

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.