Crystal growth as an excitable medium

Cartwright, Julyan H. E.; Checa, António; Escribano, Bruno; Sainz‐Díaz, C. Ignacio

doi:10.1098/rsta.2011.0600

Cited by 13 publications

(15 citation statements)

References 25 publications

(39 reference statements)

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“…Therefore, it is plausible that the patterns observed during the formation of nacre are also the result of a reaction‐diffusion self‐assembly process. Or as was claimed by Cartwright et al, the physics of crystal growth can be set within the framework of the BZ reaction in 3D. However, it is important to note that while the contrast seen in the original BZ patterns in Figures i,j was attained due to differences in chemical composition, the contrast obtained in nacre, in Figures f,h, is merely the consequence of the imaging method in scanning electron microscopy.…”

Section: Evidence Of Spontaneous Growthmentioning

confidence: 73%

“…Wada was also the first to make the analogy to the BCF model emphasizing that the spiral pattern can be well explained by Frank's screw dislocation theory describing the spiral growth of single crystals. This line of thought was investigated further much later by Cartwright, Checa and colleagues in a series of studies . They proposed a simplistic mathematical treatment to model the morphogenesis of the patterns observed in the growth front of nacre inspired by the BCF model.…”

Section: Evidence Of Spontaneous Growthmentioning

confidence: 99%

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Thermodynamic Aspects of Molluscan Shell Ultrastructural Morphogenesis

Zlotnikov

Schoeppler

2017

Adv Funct Materials

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Over the years, molluscan shells have become an exemplar model system to study the process of mineral formation by living organisms, the process of biomineralization. Typically, the shells consist of a number of mineralized ultrastructural motifs, each exhibiting a specific mineral-organic composite architecture. These are made of calcium carbonate building blocks having a well-defined three-dimensional morphology that is significantly different from the shape of inorganically formed counterparts. Shell ultrastructures are known to form via a biologically controlled extracellular mineralization pathway in which the organism has no direct control over mineral formation. The cellular tissue, responsible for shell biomineralization, forms an organic framework and sets-up the physical conditions necessary for the deposition of a specific morphology, whereas the growth of the mineral part of the shell proceeds spontaneously via the process of self-assembly. In this feature article, the ability to employ thermodynamic models from classical materials science to describe the process of self-assembly and structural evolution of a variety of shell architectures is reviewed. Having the potential to offer an analytical framework to express ultrastructure formation in time and in space, these models not only provide a deeper insight into shell biomineralization, but also suggest tools for novel composite materials design.

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Section: Evidence Of Spontaneous Growthmentioning

confidence: 73%

Section: Evidence Of Spontaneous Growthmentioning

confidence: 99%

Thermodynamic Aspects of Molluscan Shell Ultrastructural Morphogenesis

Zlotnikov

Schoeppler

2017

Adv Funct Materials

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“…During a time step, nucleation has a probability of 1 to occur at all the cells where the condition (2.2) is satisfied. In previous work with a numerical model of this type, we had a nucleation probability, a small number, typically 10 −3 , so that nucleation would be a rare event [15,16]. In the present case, we have removed this parameter, with the objective to have a more elegant model; to eliminate as much complexity as possible while still being able to reproduce all the patterns observed.…”

Section: Modelmentioning

confidence: 99%

“…Common to these varied systems is that they are excitable media: they all have a threshold in some parameter, below which the system returns quickly to its resting state, but above which it undertakes a large excursion before doing so, and then has a refractory period during which the system is unresponsive to further perturbations. Some of us developed a model of Burton–Cabrera–Frank dynamics as an excitable system, and showed that it could be applied both to crystal growth [15] and to liquid crystals growing layer by layer as they do in the formation of the mother-of-pearl produced by molluscs [16]. In the present work, we show that a version of this coupled-map lattice excitable medium model explains how the complex structures seen in Tetragonula combs emerge from simple behavioural rules.…”

Section: Introductionmentioning

confidence: 99%

The beeTetragonulabuilds its comb like a crystal

Cardoso

Cartwright

Checa

et al. 2020

J. R. Soc. Interface.

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Stingless bees of the genus Tetragonula construct a brood comb with a spiral or a target pattern architecture in three dimensions. Crystals possess these same patterns on the molecular scale. Here, we show that the same excitable-medium dynamics governs both crystal nucleation and growth and comb construction in Tetragonula , so that a minimal coupled-map lattice model based on crystal growth explains how these bees produce the structures seen in their bee combs.

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“…To give just one example of the power of such a comprehensive understanding, excitability [23] is a general mechanism that produces spiral and target patterns at various scales in a great variety of natural systems in physics, chemistry, biology and beyond, from the Belousov-Zhabotinsky reaction [28][29][30][31] to the myocardial tissue of the heart undergoing ventricular fibrillation. It turns out that the Burton-Cabrera-Frank mechanism of crystal growth [32] is one more instance of an excitable medium [33]; this mechanism of excitability functions in the self-assembly of crystals themselves, and hence the spiral and target patterns characteristic of excitable media appear at the molecular scale on the faces of growing crystals.…”

Section: (A) Generalized Crystallographymentioning

confidence: 99%

Beyond crystals: the dialectic of materials and information

Cartwright

Mackay

2012

Phil. Trans. R. Soc. A.

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We argue for a convergence of crystallography, materials science and biology, that will come about through asking materials questions about biology and biological questions about materials, illuminated by considerations of information. The complex structures now being studied in biology and produced in nanotechnology have outstripped the framework of classical crystallography, and a variety of organizing concepts are now taking shape into a more modern and dynamic science of structure, form and function. Absolute stability and equilibrium are replaced by metastable structures existing in a flux of energy-carrying information and moving within an energy landscape of complex topology. Structures give place to processes and processes to systems. The fundamental level is that of atoms. As smaller and smaller groups of atoms are used for their physical properties, quantum effects become important; already we see quantum computation taking shape. Concepts move towards those in life with the emergence of specifically informational structures. We now see the possibility of the artificial construction of a synthetic living system, different from biological life, but having many or all of the same properties. Interactions are essentially nonlinear and collective. Structures begin to have an evolutionary history with episodes of symbiosis. Underlying all the structures are constraints of time and space. Through hierarchization, a more general principle than the periodicity of crystals, structures may be found within structures on different scales. We must integrate unifying concepts from dynamical systems and information theory to form a coherent language and science of shape and structure beyond crystals. To this end, we discuss the idea of categorizing structures based on information according to the algorithmic complexity of their assembly.

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Crystal growth as an excitable medium

Cited by 13 publications

References 25 publications

Thermodynamic Aspects of Molluscan Shell Ultrastructural Morphogenesis

Thermodynamic Aspects of Molluscan Shell Ultrastructural Morphogenesis

The beeTetragonulabuilds its comb like a crystal

Beyond crystals: the dialectic of materials and information

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