Edited by H. Eugene Stanley, Boston University, Boston, MA, and approved May 1, 2009 (received for review January 27, 2009)
Nacre is an exquisitely structured biocomposite of the calcium carbonate mineral aragonite with small amounts of proteins and the polysaccharide chitin. For many years, it has been the subject of research, not just because of its beauty, but also to discover how nature can produce such a superior product with excellent mechanical properties from such relatively weak raw materials. Four decades ago, Wada [Wada K (1966) Spiral growth of nacre. Nature 211:1427] proposed that the spiral patterns in nacre could be explained by using the theory Frank [Frank F (1949) The influence of dislocations on crystal growth. Discuss Faraday Soc 5:48–54] had put forward of the growth of crystals by means of screw dislocations. Frank's mechanism of crystal growth has been amply confirmed by experimental observations of screw dislocations in crystals, but it is a growth mechanism for a single crystal, with growth fronts of molecules. However, the growth fronts composed of many tablets of crystalline aragonite visible in micrographs of nacre are not a molecular-scale but a mesoscale phenomenon, so it has not been evident how the Frank mechanism might be of relevance. Here, we demonstrate that nacre growth is organized around a liquid-crystal core of chitin crystallites, a skeleton that the other components of nacre subsequently flesh out in a process of hierarchical self-assembly. We establish that spiral and target patterns can arise in a liquid crystal formed layer by layer through the Burton–Cabrera–Frank [Burton W, Cabrera N, Frank F (1951) The growth of crystals and the equilibrium structure of their surfaces. Philos Trans R Soc London Ser A 243:299–358] dynamics, and furthermore that this layer growth mechanism is an instance of an important class of physical systems termed excitable media. Artificial liquid crystals grown in this way may have many technological applications.
The splendor of a pearl extends even to under a microscope; with magnification, one can see that the nacreous surfaces of bivalve mollusks—clams, mussels, oysters, scallops, and so on—are made up of a striking arrangement of spiral, target, and labyrinthine patterns (1); see Fig. 1. Nacre, or mother of pearl, is the iridescent material that forms an inner layer of the shells of numerous species of mollusks as well as the pearls that many of those same species produce. The structure of nacre is often likened to a brick wall, and indeed, it is composed of bricks of aragonite tablets (≈95%) and mortar of organic so-called interlamellar membranes (polysaccharide and protein, ≈5%), but it is a brick wall built in a peculiar fashion, because first, the mortar is put in place, and then the bricks grow within it. (See Fig. 2 for a sketch of bivalve molluscan anatomy and nacre structure.) From an examination of the extrapallial space of the bivalve mollusk, the narrow liquid-filled cavity between the soft tissues and the shell of the organism, it is seen that the first visible feature in nacre growth is the formation of a new interlamellar membrane in the fluid (2–4). In Fig. 3A, we show this process occurring in a transmission electron micrograph section through the growth front of bivalve nacre that displays the hard shell below and the soft body of the organism, the mantle, above the liquid-filled extrapallial space. The membrane in its moment of formation is spaced some 100 nm above an earlier-formed one below it; there is not space between the membrane and the microvilli of the mantle cells above for any additional membrane to form. We must follow it back some 20 μm to find the front where the process of mineralization is seen to commence, and by this stage, its spacing from the membrane beneath has increased to ≈500 nm. The core of these membranes is composed of rod-shaped crystallites of the polysaccharide chitin in its β-polymorph (5). This chitin must be secreted into the extrapallial liquid together with the mineral and protein components of nacre; it is thought—although not yet confirmed—that similar mechanisms are responsible for chitin as for cellulose crystallite formation, wherein rosette structures in the cellular membrane extrude polymer chains from closely packed pores, whence they immediately crystallize by interchain hydrogen bonding into long thin needle crystallites (6). In the case of nacre, these crystallites of β-chitin are known to be some 20–30 nm in diameter and up to hundreds of nanometers in length, consisting of hundreds of chitin polymers (7).
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.
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.
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.
Interlamellar membrane formation is then necessarily a process of self-assembly within the extrapallial fluid; to use our brick-wall analogy, it is as if one empties clay, lime, sand, and water into a tub and finds that sheets of mortar form spontaneously within it. What prompts chitin crystallites to self-assemble into sheets? α-Chitin crystallites of similar dimensions to the β-chitin crystallites of mollusks have been studied in vitro. When dispersed in a colloidal aqueous suspension, they form a so-called cholesteric liquid-crystalline phase in which the crystallites are parallel to the plane of the layers, and the crystallites in each layer are twisted with respect to those in the neighboring layers, with an interlayer spacing of 60–120 nm (8), comparable with the 100 nm seen here. Similar preparations using β-chitin crystallites from a cephalopod mollusk (Todarodes pacificus squid pen) (9) and from a vestimentiferan tube worm (Riftia pachyptila tubes) (10) indicate that these too form a liquid-crystal phase in aqueous suspension. Birefringence was observed at rest between cross-polarizers for dispersions of >0.1% β-chitin, and at 0.3% consistency, they formed hard gels (9). (Note that we are concerned not with a molecular liquid crystal of chitin polymers but with a colloidal or supramolecular one of chitin crystallites.) In laboratory experiments, the liquid-crystalline structure is allowed to come to equilibrium by waiting from a few days up to a year (8). In the mollusk in vivo, on the other hand, a fresh layer of nacre is laid down every 1–24 h, so the system does not have time to arrive at equilibrium, and the liquid-crystalline ordering of β-chitin is only partial. It comprises a lamellar structure, but within the layers there is disorder, with the crystallites forming a felt-like mesh, like a logjam on a lake, as seen in the plan view of Fig. 3B. Simulations of the dynamics of the formation of a cholesteric phase of a liquid crystal confirm that there is an initial orientation of the material into layers followed by its alignment within and between layers (11). The evidence leads us to conclude that, in Fig. 3, we are observing the rod-shaped crystallites of β-chitin being compelled by their mutual interactions, self-organizing in the extrapallial space into a liquid crystal.
Artificial liquid crystals are formed by altering a global variable—be it temperature, concentration, electric field, etc.—that causes the whole of a domain to crystallize, forming many layers at once. We perceive from Fig. 3 that mollusks, on the other hand, perform liquid crystallization in quite a different manner: layer by layer. The narrowness of the molluscan extrapallial space implies that, as chitin crystallites are secreted into the extrapallial fluid, they can only self-assemble through their mutual interactions into 1 new liquid-crystal layer. The continual secretion of material from the mantle cells maintains the extrapallial space approximately constant in depth, so that at any time 1 fresh layer of the liquid crystal is being deposited, and in this way, in time, the mollusk builds a liquid crystal within an expanding domain. This is concurrently transformed with the addition of proteins and aragonite into the solid biocomposite that is nacre; a process that we analyze in depth in ref. 2. Here, we concentrate on understanding the mode of liquid-crystal construction used by the mollusk, in which it is built up layer by layer. This method is unique in terms of artificial liquid crystals, but is the manner in which solid crystals generally grow, and this connection allows us to comprehend the spiral and target patterns on the surface of nacre.
Layer or tangential growth of a solid crystal, analyzed by Burton, Cabrera, and Frank (12), involves 2 processes: on one hand, the addition of material at the edges of 2-dimensional islands on the surface of the crystal together with the occasional nucleation of a fresh island atop an earlier one and, on the other, the continual accretion of material at the edges of a helical ramp on the surface of the crystal, termed a screw dislocation (13). [Tangential growth as a whole was examined by Burton, Cabrera, and Frank (12); Frank's contribution was the analysis of screw dislocations (14)]. These 2 processes produce characteristic target and spiral patterns seen at the molecular scale in solid crystals (15). These same patterns are visible in the conspicuous features of the surface of nacre at the mesoscale in Fig. 1. In that figure, the patterns are arrangements of aragonite tablets in mineralized nacre. However, as we see in Fig. 3A, in growing nacre, interlamellar membranes extend ahead of these mineralization fronts; the latter follow the geometry laid down by the former. This is evidenced by the forms of tablets that grow at the centers of the screw dislocations in the membranes, which mold themselves to the spiral, as shown in Fig. 1F. Thus, the spirals and target patterns are in fact laid down in the interlamellar membranes, and we must establish that growth of an interlamellar membrane as a liquid crystal layer by layer can give rise to this geometry of spirals and target patterns.
We formulate a minimal model containing the fundamental physics of liquid crystallization. Growth proceeds by the incorporation of individual growth units, which are the chitin crystallites that compose the liquid crystal. Because this is an essentially discrete process, we employ a discrete coupled map lattice, or lattice Boltzmann model, with a square lattice of discrete space and time but continuous state variables, that puts nucleation and growth on an equal footing. The surface is divided into a randomized grid of cells, as introduced by Markus and Hess (16), to avoid anisotropic growth. Each cell has a growth height H(i, j), initially zero, updated at the end of each iteration of the growth. The surface is scanned on each iteration, and in each cell, there may occur either nucleation, growth, or neither as a function of the relative height of the nearest neighbors. The neighbors to each cell are assigned by proximity, defining a circle of radius R around the cell.
The essential physics we wish to capture in our model is that a fresh growth unit is incorporated into the growing surface most probably at a site where it is more strongly bound by virtue of having most neighbors. Such sites are so-called kinks: concavities at the base of steps on the surface. Thus, there is no probability of a growth unit settling above a step, because it will slide down to occupy a more favorable site below; there is a rather low probability of a growth unit settling on a flat surface and a very high probability of it occupying a site at the base of a step. This physics we can model by setting a low probability of addition of material, which is termed nucleation, at any point over the surface that is not elevated above its neighbors, together with a certainty of the addition of material, which is termed growth, at the kinks of steps.
The condition for nucleation is that the cell should not stick out far above its neighbors, that the surface be sufficiently smooth. The cell in question should have height comparable with that of its neighbors with a difference not more than ΔhN. If so, there is a small probability PN of nucleating a fresh growth surface. Nucleation is a fundamentally stochastic process, and this is reflected in the model. If nucleation takes place, and a new growth unit is incorporated, the growth surface increases in height by 1 plus or minus a small random factor α:
The condition for growth is that the cell must be at the edge of a growth front; i.e., must have neighbors higher by at least ΔhG. If so, a growth unit is incorporated: The growth height is increased by the mean of the higher neighbors ±α, and a growth front extends:
where (k, l) are the coordinates for each higher neighbor, and n is the total number of higher neighbors, which depends on R. This part of the model is deterministic except for the parameter α, which adds a certain amount of noise so that the growth surfaces are not completely flat and defect free.
In this way, as a growth front grows out, its height may vary, and if it encounters another front of different height, following the rules above, defects may be spontaneously incorporated into the growth. Two growth fronts that meet may join seamlessly with each other, terminating growth; they may completely overlap each other, forming an edge dislocation; or they may overlap along part of the edge and join along the rest, nucleating a spiral defect as growth continues. All of these behaviors are comparable in the model—Fig. 4—with nacre itself (Fig. 1).
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, ΔhN = 0.1, PN = 10-3, ΔhG = 0.8, R = 10. (B) Colliding growth fronts and spiral—see Fig. 1C—after (i) 300 and (ii) 310 iterations; parameters α = 0.06, ΔhN = 0.06, PN = 5 × 10−6, ΔhG = 0.6, R = 4. (C) Paired spirals—see Fig. 1 D and E—after (i) 230 and (ii) 250 iterations; parameters α = 0.08, ΔhN = 0.09, PN = 10-4, ΔhG = 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.
In our model the set of parameters comprises:
α Stochastic term, typically ±0.05–0.1, that varies the height of the growth cell on nucleation and growth, otherwise renormalized to be unity. This term is responsible for defects. Physically this growth-height variation is related to the fact that the growth units in the case of nacre are nonidentical; they are rods of differing lengths. An additional factor in the appearance of height variations leading to defects in all layer growth is the presence of impurities.
ΔhN Threshold of elevation with respect to the neighbors below which a cell's neighborhood is considered sufficiently flat for nucleation of a fresh layer to occur. A larger value of ΔhN implies that more nucleation will take place, typically set similar in magnitude to α.
PN Probability of nucleation occurring in a given cell in which, according to ΔhN, it may occur; typical value 10−3 to 10−6. PN in combination with ΔhN determine the frequency of nucleation. If PN is zero, screw dislocations leading to spiral growth are the only growth mechanism; if PN is large, the surface is rough.
ΔhG Threshold of difference in height with the neighbors for there to be an active neighbor. There must be at least 1 active neighbor for a site to be a kink and so to have growth in a cell. Physically, this parameter in combination with α determines the frequency of screw dislocations. Typical values to produce spiral growth are 0.4–0.8. If ΔhG is large, spiral growth is suppressed and growth proceeds by layers. If ΔhG is small, growth fronts that encounter one another cross to produce edge dislocations.
R Radius of the circle of neighbors, typically set between 3 and 10. The model begins with a randomized grid (16): A point is set at random within each cell at the beginning of the simulation. Subsequently the neighbors of the cell are sought by tracing a circle of radius R about this point. Owing to the initial random positioning of the center of the circle, this procedure produces a varying number of neighbors per cell. As with α, the randomization introduced with the grid here is related to the nonidentical nature of the chitin crystallites that are the growth units for the nacre. A larger radius R implies wider terraces between growth steps. This is physically related to the surface diffusion of the growth units. If we look at nacre from different species, we indeed find that some have steeper, narrower terraces, and others have shallower, wider ones.
In Fig. 4, we display the evolution in time of 3 different scenarios in our model, to be compared with the various phenomena in nacre of Fig. 1. In each case, the simulation began at time 0 with a flat surface of zero height. In Fig. 4A, we show the evolution of target patterns; we see the system after 87 and 93 iterations. Each terrace expands laterally, and, once the uppermost terrace has expanded sufficiently, a fresh terrace nucleates on it. This is similar to what is seen in Fig. 1B in nacre and corresponds to island growth, the first process of Burton–Cabrera–Frank (12). In Fig. 4B, we show, after 300 and 310 iterations, colliding growth fronts and an evolving spiral similar to those seen in nacre in Fig. 1C. As the spiral rotates and grows out, it meets other growth fronts coming from the top right. The fronts of the same height annihilate each other by joining seamlessly as they meet. Last, in Fig. 4C, we show, after 230 and 250 iterations, paired spirals similar to those in the nacre of Fig. 1 D and E. Fig. 4 B and C corresponds to spiral growth, which is the second process of Burton–Cabrera–Frank. Those in Fig. 4B are single screw dislocations, whereas the paired spirals in Fig. 4C are Frank–Read sources (26).
These time evolutions can be seen in nacre samples by looking down through the nacre layers, as the third dimension of space—into the material—is equivalent to time. However, although that procedure takes us back in time, it does not indicate which events are coeval, as the model does. From our model, we can see that Wada (1) was correct in noting the parallel between nacre growth and the Burton–Cabrera– Frank (12) dynamics [in fact, Wada (1) singled out the spiral growth mechanism that was Frank's contribution (14)] of layer growth, albeit, for a liquid crystal rather than the solid crystal Wada had envisaged.
From our model of layer growth, we can comprehend why these spiral and target patterns, familiar from such diverse instances as the Belousov–Zhabotinsky reaction in chemistry and ventricular fibrillation of the heart in biology, appear in nacre: All of these systems are describable in physical terms as excitable media (17). Excitable media form a rather general class of systems in which there are elements that are quiescent until excited into an active state by some stimulus, after which, they are unresponsive to further stimuli during some refractory period before returning to their initial quiescent, excitable state. This very simple physics is sufficient to produce complex spatiotemporal patterns of targets and spirals, which is why these patterns are observed so generally in many different fields. Here, the excitable paradigm holds too, and we can describe the growth of nacre as an excitable medium: A point on the surface of the last-formed layer is quiescent, but receptive to the nucleation of a new layer above it, given a large enough perturbation, that is to say, a fluctuation that concentrates sufficient material nearby to nucleate a new surface. The edges of layers, the kinks of steps, where new material is incorporated, are active, whereas just after a new layer has formed, there is a refractory period in which another new layer cannot be formed at that point, because material is preferentially incorporated at the growing edge of the layer nearby. Thus, the growth dynamics of our model of the formation of interlamellar membranes of nacre corresponds to an excitable medium.
The growth model we put forward here is for the formation of a liquid crystal of chitin that is the first component of nacre to be laid down. But nacre—by which we mean the completed product: mother of pearl, or a pearl itself—is no longer a liquid crystal but a complex solid. Some of the complexity of the series of processes the liquid crystal then undergoes to become nacre, we lay out in ref. 2. The problem of supramolecular assembly in biology—how does an organism assemble itself: After the cells make the molecules that are to form part of the structure, how do they form into tissue; flesh and bone?—is, as yet in general, unsolved. Nacre is of particular interest and is by far the most intensively studied nonhuman organomineral biocomposite. It lies at the intersection of 2 groups of supramolecular biological structures: fibrous composites and biominerals. It is of interest not just because it is beautiful, but also because it is strong: with just 5 percent polysaccharide and protein, its work of fracture is up to 3,000 times higher than that of inorganic aragonite (18). The importance of fluid dynamics in the organization of supramolecular biological structures, both in transporting materials and in their self-assembly, is beginning to be recognized (19). Such is the case with biomineralization processes such as bone and fish otolith formation, and it is likely that further examples will come to light as our knowledge of the so-called “soft chemistry” involved in biological mineral deposition improves. The extrapallial liquid is fundamental in the formation of nacre, and it is probable that we shall, in future, find that there are active fluid dynamical processes involved in the transport of chitin crystallites, proteins, and mineral to produce nacre.
Nacre is secreted by some species of 4 classes in the phylum Mollusca: Bivalvia, Gastropoda, Cephalopoda, and, to a minor extent, Tryblidiida. Although the material has many points in common between the classes—hence its general classification as nacre—at the level of details, there are important differences. In the present case, we have concentrated on bivalve nacre. The other large class of nacre-secreting mollusks, the gastropods, possesses an additional feature not present in bivalves, the surface membrane, interposed between the mantle and the shell. This organizes the mineralization of gastropod nacre so that it grows in towers, rather than in the fronts of bivalve nacre (20). Nonetheless, gastropod interlamellar membranes have a similar geometry to those in the bivalves, and screw and edge dislocations are noted in gastropod nacre (2); they are simply not so clearly visible at the growth surface as in bivalves, on account of gastropod mineralization being in towers rather than fronts that follow the leading edges of the membranes as in bivalves. It seems likely that our liquid-crystal growth model, possibly with some variations, should be applicable in gastropods too.
Today, layer-by-layer growth of materials is of great technological interest; but the synthetic process used is often a rather primitive one consisting of building up layers by dipping the material into first one component then another to produce a corresponding layering of so-called artificial nacre (21). Nature, on the other hand, is more sophisticated in using a self-organized system of liquid crystallization to assemble nacre layer by layer. Liquid crystals have long been surmised to play an important role in the organization of biological tissues (22–24); yet, without a model for their formation, a key section of the argument that biological systems make use of liquid crystals for the self-organization of supramolecular structure has been lacking (25). Here, we have shown how such a biological liquid crystal may be constructed and that this self-assembly is occurring through an unfamiliar process—unfamiliar, that is, to humans, because mollusks have been using it since the Cambrian—of liquid crystallization layer by layer. It may be of advantage in many technological applications to follow nature's way.
Shells of living specimens of Pteria avicula, Pteria hirundo, and Anodonta cygnea were fixed with 2.5% glutaraldehyde in a 0.1 M cacodylate buffer. After CO2 critical-point drying samples were observed intact with a Leo Gemini 1530 field emission scanning electron microscope.
We had access to original material of Pinctada radiata of the late H. Nakahara. This was prepared at Meikai University (Chiba, Japan) by M. Kakei according to the protocol described in ref. 4. We used a Philips CM20 transmission electron microscope.
We thank Prof. M. Kakei (Meikai University, Chiba, Japan) for providing material of Prof. H. Nakahara. This work was supported by Research Projects CGL2007-60549 and CGL2008-06245-CO2-01 (Ministerio de Educacíon y Ciencia) and Research Group RNM190 (Junta de Andalucía).
Author contributions: J.H.E.C., A.G.C., and C.I.S.-D. designed research; A.G.C. and B.E. performed research; C.I.S.-D. analyzed data; and J.H.E.C. and C.I.S.-D. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/cgi/content/full/0900867106/DCSupplemental.
