The Algorithmic Beauty of Sea Shells

Meinhardt, Hans

doi:10.1007/978-3-540-92142-4

Cited by 94 publications

(39 citation statements)

References 75 publications

(94 reference statements)

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“…They posses an extensive fossil record dating back to the early Cambrian (543+ MYA) and comprise more than 200,000 extant species occupying various marine and terrestrial environments from the deep sea to desert habitats [1,2]. Much of this evolutionary success can be attributed to the phenotypic plasticity of the external shell which displays an incredible range of mineralogical textures [3], pigments [4,5] and ornamentations [6]. This phenotypic diversity is underscored by a diversity in the molecular mechanisms responsible for the construction of the adult shell [7-10].…”

Section: Introductionmentioning

confidence: 99%

An ancient process in a modern mollusc: early development of the shell in Lymnaea stagnalis

Hohagen

2013

BMC Dev Biol

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BackgroundThe morphological variety displayed by the molluscan shell underlies much of the evolutionary success of this phylum. However, the broad diversity of shell forms, sizes, ornamentations and functions contrasts with a deep conservation of early cell movements associated with the initiation of shell construction. This process begins during early embryogenesis with a thickening of an ectodermal, ‘dorsal’ (opposite the blastopore) population of cells, which then invaginates into the blastocoel to form the shell gland. The shell gland evaginates to form the shell field, which then expands and further differentiates to eventually become the adult shell-secreting organ commonly known as the mantle. Despite the deep conservation of the early shell forming developmental program across molluscan classes, little is known about the fine-scale cellular or molecular processes that underlie molluscan shell development.ResultsUsing modern imaging techniques we provide here a description of the morphogenesis of a gastropod shell gland and shell field using the pulmonate gastropod Lymnaea stagnalis as a model. We find supporting evidence for a hypothesis of molluscan shell gland specification proposed over 60 years ago, and present histochemical assays that can be used to identify a variety of larval shell stages and distinct cell populations in whole mounts.ConclusionsBy providing a detailed spatial and temporal map of cell movements and differentiation events during early shell development in L. stagnalis we have established a platform for future work aimed at elucidation of the molecular mechanisms and regulatory networks that underlie the evo-devo of the molluscan shell.

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Section: Introductionmentioning

confidence: 99%

An ancient process in a modern mollusc: early development of the shell in Lymnaea stagnalis

Hohagen

2013

BMC Dev Biol

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“…As pointed out by Kondo and Miura (Kondo and Miura, 2010), even if in complex systems the specific mode of transport at the molecular level might not involve free diffusion, diffusion equations often correctly recapitulate the behavior of the system, which justifies the use of such equations as a simple way to model complex patterning phenomena. For more information on simulation models of pattern formation and growth involving diffusion equations, we refer the reader to the classical models of sea shell patterns (Meinhardt, 2009).…”

Section: Model Assumptions and Simplificationsmentioning

confidence: 99%

“…Simulation modeling provides a way to test hypothetical mechanisms of growth and patterning that would otherwise be difficult to comprehend owing to the highly dynamic nature of development in time and space (Baker et al, 2008;Kondo and Miura, 2010;Meinhardt, 2009). In this paper, we use simulation modeling to explore how growth and patterning might be coordinated through the action of morphogens during the development and regeneration of bony fin rays in the zebrafish (Danio rerio), an emerging model system for the study of bone morphogenesis (Akimenko et al, 2003;Iovine, 2007;Poss et al, 2003).…”

Section: Introductionmentioning

confidence: 99%

Morphogen-based simulation model of ray growth and joint patterning during fin development and regeneration

et al. 2012

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SUMMARYThe fact that some organisms are able to regenerate organs of the correct shape and size following amputation is particularly fascinating, but the mechanism by which this occurs remains poorly understood. The zebrafish (Danio rerio) caudal fin has emerged as a model system for the study of bone development and regeneration. The fin comprises 16 to 18 bony rays, each containing multiple joints along its proximodistal axis that give rise to segments. Experimental observations on fin ray growth, regeneration and joint formation have been described, but no unified theory has yet been put forward to explain how growth and joint patterns are controlled. We present a model for the control of fin ray growth during development and regeneration, integrated with a model for joint pattern formation, which is in agreement with published, as well as new, experimental data. We propose that fin ray growth and joint patterning are coordinated through the interaction of three morphogens. When the model is extended to incorporate multiple rays across the fin, it also accounts for how the caudal fin acquires its shape during development, and regains its correct size and shape following amputation.

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“…Turing termed the reactants ''morphogens" and, under the assumption that cells respond to signaling chemicals in a concentration-dependent manner, this model serves to set up a morphogen pre-pattern to determine cell differentiation. This model has been applied to a whole range of patterning phenomena in biology, for example, fish pigmentation patterns [30], shell patterns [36], cartilage formation [37]. The idea of morphogens interacting in this way to form patterns is still controversial, but recent experimental evidence suggests that the Turing model cannot be simply dismissed [48].…”

Section: Introductionmentioning

confidence: 99%

An efficient and robust numerical algorithm for estimating parameters in Turing systems

Garvie

Maini

Trenchea

2010

Journal of Computational Physics

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a b s t r a c tWe present a new algorithm for estimating parameters in reaction-diffusion systems that display pattern formation via the mechanism of diffusion-driven instability. A Modified Discrete Optimal Control Algorithm (MDOCA) is illustrated with the Schnakenberg and Gierer-Meinhardt reaction-diffusion systems using PDE constrained optimization techniques. The MDOCA algorithm is a modification of a standard variable step gradient algorithm that yields a huge saving in computational cost. The results of numerical experiments demonstrate that the algorithm accurately estimated key parameters associated with stationary target functions generated from the models themselves. Furthermore, the robustness of the algorithm was verified by performing experiments with target functions perturbed with various levels of additive noise. The MDOCA algorithm could have important applications in the mathematical modeling of realistic Turing systems when experimental data are available.

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The Algorithmic Beauty of Sea Shells

Cited by 94 publications

References 75 publications

An ancient process in a modern mollusc: early development of the shell in Lymnaea stagnalis

An ancient process in a modern mollusc: early development of the shell in Lymnaea stagnalis

Morphogen-based simulation model of ray growth and joint patterning during fin development and regeneration

An efficient and robust numerical algorithm for estimating parameters in Turing systems

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