Spiral and target patterns in bivalve nacre manifest a natural excitable medium from layer growth of a biological liquid crystal

Julyan H. E. Cartwright; Antonio G. Checa; Bruno Escribano; C. Ignacio Sainz-Díaz

doi:10.1073/pnas.0900867106

New Research In

Edited by H. Eugene Stanley, Boston University, Boston, MA, and approved May 1, 2009 (received for review January 27, 2009)

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Fig. 1.
Scanning electron micrographs of the growth surface of bivalve nacre. (A) General view of labyrinthine patterning. (B) Target patterns. (C) Colliding growth fronts and spiral. (D and E) Paired spirals. (F) The aragonite tablet at the center of a spiral follows its structure. A–D are Pteria avicula; E and F are Pteria hirundo. In all these images, we see only the mineralized portion of the nacre, consisting of aragonite tablets. The interlamellar membranes atop the uppermost mineral layer are generally lost as the soft tissue is removed, unless the sample is especially prepared to preserve soft tissue as well as biomineral, as in Fig. 3A.
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Fig. 2.
Sketch of bivalve molluscan anatomy indicates the position of the liquid-filled interlamellar space between the mineralized shell and the mantle part of the soft body of the organism and illustrates with successive amplifications the brick and mortar structure of nacre. The growth surface, on which the patterns in Fig. 1 are observed, is between the mantle and the shell; i.e., into the page.
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Fig. 3.
Cross-sectional and surface views of the interlamellar membranes of bivalves. (A) Transmission electron micrographs show the interlamellar membranes being laid down before mineralization in Pinctada radiata; the orientation of the sample is as in Fig. 2. The blowups provide more detail of the membranes and show that the initial spacing of ≈100 nm when a fresh layer is laid down gradually increases to ≈500 nm in mineralized nacre over a distance of some 20 μm. We have surmised elsewhere (2) that this increase in layer spacing accompanies the coating of the chitin liquid-crystal layers with proteins before mineralization and is likely caused by an additional repulsion term in the force balance between membranes introduced by the electrostatic charges on the amphiphilic structure of the mature membrane. This change in the force balance from the original cholesteric liquid crystal to the mature membrane covered with protein would serve to repel the membrane from its neighboring interlamellar membrane (2). (B) Scanning electron micrograph of the interlamellar membrane of Anodonta cygnea shows its logjam structure when viewed from above. When interpreting this image, one must bear in mind various points. This is a completed interlamellar membrane seen in plan view; we are not just looking at chitin, but at the result of a later stage of nacre formation in which the chitin has become coated with protein. This stabilizes the layer, which is why we are able to see it in this micrograph, for which the sample has inevitably been subjected to drying, which must disintegrate the uncoated initial state of the chitin layer.
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Fig. 4.
Our model of liquid-crystal layer growth reproduces the features seen in micrographs of nacre growth and shows—what cannot be seen in nacre samples—how they evolve in time. (A) Target patterns—see Fig. 1B—after (i) 87 and (ii) 93 iterations; parameters α = 0.08, Δh_N = 0.1, P_N = 10-3, Δh_G = 0.8, R = 10. (B) Colliding growth fronts and spiral—see Fig. 1C—after (i) 300 and (ii) 310 iterations; parameters α = 0.06, Δh_N = 0.06, P_N = 5 × 10⁻⁶, Δh_G = 0.6, R = 4. (C) Paired spirals—see Fig. 1 D and E—after (i) 230 and (ii) 250 iterations; parameters α = 0.08, Δh_N = 0.09, P_N = 10-4, Δh_G = 0.8, R = 5. The color scheme is shown alongside each subfigure; lighter is higher. These 3 cases can be found in supporting information (SI) Movie S1, Movie S2, and Movie S3.