Two-stage Turing model for generating pigment patterns on the leopard and the jaguar

Liu, R. T.; Liaw, Sy-Sang; Maini, Philip K.

doi:10.1103/physreve.74.011914

Cited by 68 publications

(55 citation statements)

References 28 publications

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“…These include the effects of different boundary conditions and extra sources and sinks of chemical stimuli [30], and the coupling of different reaction-diffusion (RD) processes. For example, the output of one patterning process P-A may be used as the input pattern (concentration profile) for a separate process P-B.…”

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confidence: 99%

Characteristics of Pattern Formation and Evolution in Approximations of Physarum Transport Networks

Jones

2010

Artificial Life

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Most studies of pattern formation place particular emphasis on its role in the development of complex multicellular body plans. In simpler organisms, however, pattern formation is intrinsic to growth and behavior. Inspired by one such organism, the true slime mold Physarum polycephalum, we present examples of complex emergent pattern formation and evolution formed by a population of simple particle-like agents. Using simple local behaviors based on chemotaxis, the mobile agent population spontaneously forms complex and dynamic transport networks. By adjusting simple model parameters, maps of characteristic patterning are obtained. Certain areas of the parameter mapping yield particularly complex long term behaviors, including the circular contraction of network lacunae and bifurcation of network paths to maintain network connectivity. We demonstrate the formation of irregular spots and labyrinthine and reticulated patterns by chemoattraction. Other Turing-like patterning schemes were obtained by using chemorepulsion behaviors, including the self-organization of regular periodic arrays of spots, and striped patterns. We show that complex pattern types can be produced without resorting to the hierarchical coupling of reaction-diffusion mechanisms. We also present network behaviors arising from simple pre-patterning cues, giving simple examples of how the emergent pattern formation processes evolve into networks with functional and quasi-physical properties including tensionlike effects, network minimization behavior, and repair to network damage. The results are interpreted in relation to classical theories of biological pattern formation in natural systems, and we suggest mechanisms by which emergent pattern formation processes may be used as a method for spatially represented unconventional computation.

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confidence: 99%

Characteristics of Pattern Formation and Evolution in Approximations of Physarum Transport Networks

Jones

2010

Artificial Life

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“…A classic, but still extremely important example of wave propagation is the action potential in neurons (Hodgkin and Huxley, 1952a;Hodgkin and Huxley, 1952b). The development of pigment spots on the skins of animals or fish has been suggested to occur via a Turing instability (Kondo, 2002;Kondo and Asai, 1995;Liu et al, 2006). Although the actual molecules and detailed mechanism involved in pigment pattern formation are not yet known, this "Turing mechanism" is certainly more plausible than the mechanism suggested by Rudyard Kipling for development of the spots on a leopard (Kipling, 1996).…”

Section: Introductionmentioning

confidence: 89%

Pattern formation mechanisms in reaction-diffusion systems

Vanag¹,

Epstein²

2009

Int. J. Dev. Biol.

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In systems undergoing chemical reaction and diffusion, a remarkable variety of spatially structured patterns, stationary or moving, local or global, can arise, many of them reminiscent of forms and phenomena seen in living systems. Chemical systems offer the advantage that one can often control the parameters that determine the patterns formed and can thereby probe fundamental issues about pattern formation, with possible insights into biologically relevant phenomena. We present experimental examples and discuss several mechanisms by which such spatiotemporal structure may arise, classifying the mechanisms according to the type of instability that results in pattern formation. In some systems, the pattern that emerges depends not only on the chemical and physical parameters but also on the initial state of the system. Interactions between instabilities can result in particularly complex patterns.

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“…Hence the patterns (inhomogeneous steady state) can appear or disappear by tuning the thickness. This might be a plausible reason for different patterns on leopards and jaguars [7] as they grow in size or rather as the skin thickness increases.…”

Section: Discussionmentioning

confidence: 99%

“…Since then many models [2,3] have been proposed to mimic the complex pattern formation in biological systems. Turing-like R-D equations are routinely used in trying to understand the skin patterns of animals [2]; for example in fish [4], mammals [5], snakes [6] leopards [7] and many others. There have also been attempts to study changes in the pigmentation patterns on leopards and jaguars as they grow in size [7].…”

Section: Introductionmentioning

confidence: 99%

Stability of patterns on thin curved surfaces

Nampoothiri

2016

Phys. Rev. E

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We consider reaction-diffusion equations on a thick curved surface and obtain a set of effective R-D equation to O( 2 ), where is the surface thickness. We observe that the R-D systems on these curved surfaces can have space-dependent reaction kinetics. Further, we use linear stability analysis to study the Schnakenberg model on spherical and cylindrical geometries. The dependence of steady state on the thickness is determined for both cases, and we find that a change in the thickness can stabilize the unstable patterns, and vice versa. The combined effect of thickness and curvature can play an important role in the rearrangement of spatial patterns on thick curved surfaces.

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Two-stage Turing model for generating pigment patterns on the leopard and the jaguar

Cited by 68 publications

References 28 publications

Characteristics of Pattern Formation and Evolution in Approximations of Physarum Transport Networks

Characteristics of Pattern Formation and Evolution in Approximations of Physarum Transport Networks

Pattern formation mechanisms in reaction-diffusion systems

Stability of patterns on thin curved surfaces

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