Mollusc Shell Pigmentation: Cellular Automaton Simulations and Evidence for Undecidability

Kusch, Ingo; Markus, Mario

doi:10.1006/jtbi.1996.0029

Cited by 33 publications

(16 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Early attempts to reproduce shell patterns used cellular automata models, in which arbitrary rules determine the pigmentation of cells on a grid (22)(23)(24). Although they can reproduce some observed patterns, these models have shed little light on how such patterns actually arise in the animal.…”

mentioning

confidence: 99%

The neural origins of shell structure and pattern in aquatic mollusks

Boettiger

Ermentrout

Oster

2009

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

We present a model to explain how the neurosecretory system of aquatic mollusks generates their diversity of shell structures and pigmentation patterns. The anatomical and physiological basis of this model sets it apart from other models used to explain shape and pattern. The model reproduces most known shell shapes and patterns and accurately predicts how the pattern alters in response to environmental disruption and subsequent repair. Finally, we connect the model to a larger class of neural models. neurosecretory ͉ mathematical model ͉ bifurcation S eashells display a remarkable variety of ornate pigmentation patterns. Accumulating evidence now indicates clearly that shell growth and patterning are under neural control and that shell growth and pigmentation is a neurosecretory phenomenon. Most of this evidence has been gained by detailed studies of the mantle, a tongue-like protrusion of the mollusk that wraps around the edge of the shell and deposits new shell material and pigment at the shell's growing edge (see Fig. 1 A and B) (1, 2). The shell itself is composed of crystal structures of calcium carbonate interspersed with associated proteins and other organic compounds, some of which are pigmented and arrayed in intricate patterns (3,4). This hard shell is covered by a thin organic layer of proteinaceous secretions, believed to function in regulating calcium crystallization (5). Early EM studies of the mantle recorded an extensive distribution of nerve fibers among the secretory cells (1, 6, 7). These fibers were later shown to have active synapses with secretory gland cells and synaptic inputs from other sensory organs in the mantle. From this evidence, it was proposed that neural-stimulated secretion controls shell growth (4, 7). The original evidence from gastropods has been extended to other mollusk taxa, including bivalves (8) and cephalopods, where improved experimental methods confirm clearly the role of neural control (9, 10). Neural recordings and neural cell ablation experiments have further verified the role of neural control in shell growth and repair (6,11,12).This experimental data on mollusk shell construction and pigmentation allow us to formulate a new neural network model and develop a unified explanation for the generation of both shell shapes and patterns. Unlike the purely geometric representations proposed earlier to model shell shape (13-18), our model links shape generation directly to the dynamics of the underlying neural network. Recent experimental work describes how differential growth patterns can lead to shell-like structures (19-21) but does not explain the biological origin or mechanism of these growth patterns. The neural model presented here closes this gap by explaining how the mantle neural net can encode the appropriate information required for shell growth as well as pigment deposition.Early attempts to reproduce shell patterns used cellular automata models, in which arbitrary rules determine the pigmentation of cells on a grid (22-24). Although they can reproduce som...

show abstract

mentioning

confidence: 99%

The neural origins of shell structure and pattern in aquatic mollusks

Boettiger

Ermentrout

Oster

2009

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

show abstract

“…The presence of tubules in different states of secretion (empty, accumulating, or secreting) and the variation of pigment observed within the tubules of a single mantle suggests that pigment secretion operates in a modular fashion, i.e., that regulatory elements are acting on an entire tubule, rather than on individual cells. The regulatory mechanism for shell pigmentation is largely thought to be based upon reaction-diffusion events [1,6,7], however it has also been proposed that the stimulus could be neural in nature [5,9]. As both neural and hormonal stimuli are known to induce vesicle release, we investigated innervation within this region of the mantle.…”

Section: Localisation Of Pigment Within the Tubules Maps To Shell Pigmentioning

confidence: 99%

“…This tractability led to mollusc shell pigmentation being used as one of the first models to explore the potential roles of reaction-diffusion mechanisms in morphogenesis [1]. Although such mechanisms have since been shown to perform key roles during the development of various model species such as Drosophila, chicken, and zebrafish [2], interpretation of the mechanisms underlying molluscan shell pigmentation is mostly limited to mathematical modeling of hypothetical signaling events [3][4][5][6][7][8][9]. These models assume that pigmentation is controlled by localised excitation and lateral inhibition operating along a 'line' of cells (the mantle edge), however it is not known whether the cells involved in pigment secretion are organized in this manner.…”

Section: Introductionmentioning

confidence: 99%

Control of shell pigmentation by secretory tubules in the abalone mantle

et al. 2014

View full text Add to dashboard Cite

Background: Molluscan shells exhibit a wide diversity of pigmentation patterns and are often used as models for understanding the mechanisms underlying biological pattern formation. Numerous mathematical models have been put forward to describe these patterns, but all rely on assumptions regarding the nature of the pigments and the cells from which they are secreted. We investigated pigmentation and cellular morphology of the mantle (shell-secreting organ) of the tropical abalone, Haliotis asinina, as a crucial step towards understanding the molecular mechanisms of shell patterning in this gastropod mollusc.

show abstract

“…• This simplicity of implementation and complexity of behaviour means that CA can be better suited for modelling complex systems than traditional approaches. For example, for modelling shell patterns, CA were found to avoid the considerable numerical problems inherent with partial differential equation based models, and were also substantially faster to compute [Kusch and Markus (1996)]. …”

Section: Introductionmentioning

confidence: 99%

Cellular Automata as a Tool for Image Processing

Rosin

Sun

2011

Emerging Topics in Computer Vision and Its Applications

View full text Add to dashboard Cite

An overview is given on the use of cellular automata for image processing. We first consider the number of patterns that can exist in a neighbourhood, allowing for invariance to certain transformation. These patterns correspond to possible rules, and several schemes are described for automatically learning an appropriate rule set from training data. Two alternative schemes are given for coping with gray level (rather than binary) images without incurring a huge explosion in the number of possible rules. Finally, examples are provided of training various types of cellular automata with various rule identification schemes to perform several image processing tasks.

show abstract

Mollusc Shell Pigmentation: Cellular Automaton Simulations and Evidence for Undecidability

Cited by 33 publications

References 0 publications

The neural origins of shell structure and pattern in aquatic mollusks

The neural origins of shell structure and pattern in aquatic mollusks

Control of shell pigmentation by secretory tubules in the abalone mantle

Cellular Automata as a Tool for Image Processing

Contact Info

Product

Resources

About