Morphogenesis of Biomineralized Calcitic Prismatic Tissue in

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Morphogenesis of Biomineralized Calcitic Prismatic Tissue in Mollusca Fully Described by Classical Hierarchical Grain Boundary Motion Dana Zöllner,† Elke Reich,‡ and Igor Zlotnikov*,‡ †

Institute for Structural Physics, TU Dresden, Dresden, 01062 Germany B CUBE - Center for Molecular Bioengineering, TU Dresden, Dresden, 01307 Germany

‡

S Supporting Information *

ABSTRACT: Biomineralization of complex composite architectures comprising the shells of molluscs is known to proceed via self-assembly and in accordance with thermodynamic boundary conditions set by an organic macromolecular framework that is regulated by the organism. Hence, theoretically, the formation of these ultrastructures can be reproduced using the analytical backbone of various physical theories that are commonly employed to express crystal growth of man-made materials. Using a two-dimensional Monte Carlo Potts model simulation, we quantitatively describe and fully predict the structural evolution of the prismatic assembly in the shell of Pinctada nigra. The model, based on hierarchical motion of different types of grain boundaries that are involved in structural formation, has the capacity to describe the morphogenesis of various other biogenic and synthetic polycrystalline composite systems.

B

Calcium carbonate (CaCO3) is one of the most abundant and well-studied minerals in nature and is used by molluscs to form their protective outer shells. The latter consist of a variety of composite ultrastructures arranged in layers that lay parallel to the outer surface of the shell. Each ultrastructure has a welldefined morphology: it is made of mineral blocks with a distinctive shape and a CaCO3 polymorph (calcite or aragonite) held together by an intercrystalline organic matrix.6 These structures are commonly used as a model system to study the process of biomineral formation and are a paradigm of biologically controlled extracellular biomineralization.7,8 Here, the growth proceeds in an extracellular cavity, the extrapallial space, in a framework of proteins and polysaccharides that are secreted by the cellular component, the epithelial cells of the mantle, prior to mineral deposition. Interestingly, it was previously argued that, in most cases, the cells are not directly involved in the process of mineral deposition, but choreograph it indirectly by producing the necessary chemical and physical environment in which a specific ultrastructure is self-assembled.9,10 In other words, the cells form thermodynamic boundary conditions, which regulate spontaneous ultrastructural morphogenesis of shell layers. This assertion is fundamental as it suggests that quantitative analytical framework describing the process of shell biominer-

iomineralization is the process by which living organisms form composite mineral-organic tissues. In most cases, these biogenic structures perform a multiplicity of tasks, ranging from providing the animals with strength and structural support to magnetic and optical functionalities.1 These capabilities stem from complex three-dimensional hierarchical arrangement of the tissues, from the nanoscale to the macroscale, optimized throughout hundreds of millions of years of evolution.2 Interestingly, having formed under biological regulation, the mineral units, comprising the biocomposite architectures, exhibit crystallographic and morphological properties that are significantly different from their abiotic counterparts.3 Whereas pure and thermodynamically stable geological or synthetic mineral crystals have well-defined and flat facets that are a consequence of their internal atomic organization and lattice plane energies,4 the biogenic crystals exhibit a large variety of unique morphologies. Therefore, understanding the process of biomineralization has major implications not only in the fields of life and earth sciences, but also in physics and chemistry of materials and, in turn, in functional materials design. In recent decades, substantial effort has been directed into studying and mimicking the process of mineral formation in nature.5 However, despite the significant progress made in describing key mechanisms involved in biomineralization, very little is known about mechanisms that control the form of individual mineral units comprising the biocomposites and determining the morphology of the entire mineral-organic assembly. © XXXX American Chemical Society

Received: July 12, 2017 Revised: August 1, 2017 Published: August 29, 2017 A

DOI: 10.1021/acs.cgd.7b00965 Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

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Figure 1. Structural characterization of the prismatic layer in P. nigra. (a) Representative fractured surface of the entire shell obtained by scanning electron microscopy (SEM). (b) Representative SEM image of a polished prismatic structure prepared in parallel to the growth direction of the layer. (c) Crystallographic orientation image of an area marked in (b), obtained by electron back scattered diffraction (EBSD). (d) Representative SEM image of a polished prismatic structure prepared perpendicularly to the growth direction of the layer. (e) Crystallographic orientation image of an area marked in (d), obtained by EBSD. (f) Representative 3D tomographic reconstruction of a segment of the prismatic structured. z denotes the growth direction of the layer.

by an organic phase, approximately 1−2 μm in thickness (dark areas in Figure 1b and d). The growth of the prismatic layer is known to proceed in a unidirectional manner, from the periostracum toward the inner part of the shell, reminiscent of a columnar growth of synthetic thin films obtained by various deposition technologies.15−17 In a way, the entire history of structural evolution of the layer is preserved along the prismatic assembly and the different cross sections, perpendicular to the growth direction (Figure 1d), represent the different temporal stages of its growth. Indeed, recent studies of the prismatic architecture in the shells of a variety of organisms, among them the noble pen shell Pinna nobilis, showed that its formation can be linked to classical physical models that are commonly used to describe grain growth and coarsening of man-made materials.9,10 In fact, cross sections of the prismatic structure in P. nobilis exhibit an almost perfect honeycomb morphology demonstrating a textbook example of a classical coarsening behavior where the driving force is the reduction in the mineral-organic boundary area. However, in the case of P. nigra, these sections show substantial irregularities (Figure 1d). In many cases, the organic boundaries are not straight, showing a wavy conformation, and the triple-junctions seem to be far from an energetic equilibrium, having an angle that is significantly different from the expected 120° between the three arms of the junction. Crystallographic properties of the calcitic units in the prismatic structure of bivalves were previously studied using a variety of X-ray- and electron-based diffraction techniques.18−20 It was shown that while the prismatic blocks in the majority of bivalves show diffraction patterns characteristic of a singlecrystalline unit, the prisms in the genus Pinctada (e.g., Pinctada margaritifera and Pinctada fucata) are divided into subprismatic domains. These domains are also clearly visible in electron back scattered diffraction (EBSD) maps, in Figure 1c and e, obtained

alization can be developed. Consequently, it might be used to express the process of shell formation in time and in space and, most importantly, to provide insights into synthetic routes toward novel bioinspired composite materials design. However, we are still far from a comprehensive analytical model able to describe the morphogenesis of shell ultrastructures or even to determine the forces and thermodynamic constraints that govern the shape evolution of the constituting mineral building blocks. In this work, we present a Monte Carlo Potts model developed for (but not limited to) simulating the structural evolution of the prismatic layer in the shell of the bivalve Pinctada nigra (P. nigra). Originally, the Potts model was established to recreate the coarsening of polycrystalline metals and alloys during thermal treatment (i.e., grain growth) in 2D.11 Based on the principle of reducing the Gibbs free energy of a system, the algorithm of the model is capable to predict the decrease of the total grain boundary area of that system and thus, the morphology of the structure as a function of time.12 Classically, assuming the existence of one type of boundary, the only two parameters required to perform the simulation are its surface energy and mobility. In recent years, the algorithm was extended to include, among others, the effect of subgrain boundaries on structural evolution of composite systems having a complex relationship between a variety of physical parameters.13,14 However, so far, the model was never used to simulate the structural evolution of naturally occurring mineralized composites. Like the majority of other bivalves, the shell of P. nigra consists of two mineralized ultrastructures: the inner aragonitic nacreous layer and the outer calcitic prismatic layer, which is covered by an organic film, known as the periostracum (Figure 1a). The prismatic layer consists of elongated columnar mineral units (bright areas in Figure 1b and d) that are glued together B



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Figure 2. Comparison of experimental and simulated behavior of main prismsfirst hierarchical level. (a) Initial distribution of grain boundaries used in the simulation. Blue lines represent the main mineral−organic interfaces obtained by microtomography experiment. Red lines represent the mineral−mineral secondary boundaries introduced artificially. (b) and (c) Simulated and experimental boundary distribution at z = 129.8 μm, respectively. (d) Simulated and experimental average main prism area as a function of the growth direction, z. The curves represent linear leastsquares fits to the data specified in the graph. (e) Simulated and experimental scaled prism radius distribution at z = 129.8 μm. The curves represents a fit of a normal distribution function to the simulated data. (f) Simulated and experimental rate of prism area change as a function of the number of neighboring prisms, n, averaged for each value of n. The curves represent linear least-squares fits to the data specified in the graph.

from the shell of P. nigra. They run parallel to the long axis of the main columnar units and essentially, form a hierarchical prismatic ultrastructure with two types of grain boundaries. These are the main mineral-organic boundaries, having a surface energy γm and mobility mm (first hierarchical level), that define the main prisms and the secondary calcite−calcite subboundaries with a surface energy γsb and mobility msb (second hierarchical level). The interplay between these thermodynamic parameters is in the core of the developed model and is shown here to be a key factor in the morphogenesis of the prismatic architecture. Experimental data on the spatial arrangement of the prismatic layer was obtained using phase contrast synchrotron-based microtomography imaging at beamline ID19 of the European Synchrotron Radiation Facility (ESRF). In Figure 1f, a representative 3D reconstruction obtained from the microtomography data is presented. Using a voxel size of 0.649 μm, the organic interprismatic matrix and the shape of all the individual main prisms were clearly resolved. To gain information on the structural evolution of the prismatic layer (such as prisms morphology, size and their distribution), spatial data from a total width of 272.58 μm were taken from the main body of the prismatic region and analyzed every 20 steps perpendicular to the growth direction, z, corresponding to an interval of 12.98 μm (Figure 1f). To reveal the mineral-organic grain boundary distribution, each 2D section was binarized. An example of such a cross-section, obtained at z = 0, representing

the initial configuration of the prismatic morphology, is presented in Figure 2a (blue lines). This section was also used as the input for the starting main grain boundary distribution in our Potts model adaptation. Since the subboundaries could not be resolved during the microtomography experiment, they were introduced artificially at random locations based on an estimated average density of five domains per prism (red lines in Figure 2a). It is important to note that, during simulation, the time parameter, t, was substituted with the direction of growth, z. Here we assume a linear relationship between the two and, essentially, reduce the three-dimensional prismatic growth in space into a two-dimensional temporal problem.9,10 A detailed description of the simulation procedure, as well as simulation parameters selection, is presented in Supporting Information. An example of the morphology of the prismatic structure, as simulated using the Potts model and as measured employing the tomography experiment, at z = 129.8 μm (after ten steps), is presented in Figure 2b and c, respectively. Similar sections, throughout the entire main body of the prismatic ultrastructure, were further statistically analyzed. According to the classical theory of coarsening of polycrystalline materials that contain only one type of boundary, the average prism area is expected to increase as a linear function of time.21 Here, the slope essentially depends on the energy and the mobility of the boundary, while, statistically, the structure itself remains selfsimilar. The latter describes the fact that if rescaled by the C



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Figure 3. Behavior of the subprismatic structuresecond hierarchical level. (a) Temporal change of a six-edged main prism divided into ten subprisms. (b) Average subprism area as a function of the growth direction, z. The curve represents linear least-squares fit to the data. (c) Scaled subprism radius distribution at z = 129.8 μm. The curve represents a fit of a Rayleigh distribution function. (d) Rate of subprism area change as a function of the number of neighboring prisms, n, averaged for each value of n. The curve represents linear least-squares fit to the data.

average size, different growth stages should yield the same size distribution and topology. Astonishingly, this exact behavior can be observed in the present case for the main prismatic structure (first hierarchical level). The average prism area, ⟨A⟩(z), increases linearly with the measured growth direction z (Figure 2d). Moreover, prism radius distribution f(x), where x is the scaled size, e.g., single prism radius divided by the average radius of the entire ensemble, is indeed self-similar. A representative distribution is presented in Figure 2e. Furthermore, the growth rates of individual prisms are also consistent with considerations of ideal coarsening from an average point of view. To show this, the rate of area change dA/ dz was calculated for all main prisms as a function of their respective number of sides, n. The classical von NeumannMullins-law predicts dA/dt ∝ n − nc, where nc = 6.22,23 Even though it has been recently revealed24,25 that this holds only for an ideal situation, where regular grains are subjected to an ideal coarsening in a constant environment, in the present work a linear relation between the average rate of prism area change and the number of sides was still obtained (Figure 2f). Most significantly, in all three analyses, almost identical behavior is observed when comparing the experimental data and Potts simulations of the hierarchical structure. However, when comparing the experimental data to Potts simulations of ideal coarsening (not containing the subprismatic boundaries), clear differences in the growth kinetics and topology of the structure were obtained. First, the absence of sub-boundaries is reflected in a significant increase in the growth rate of the average main prism area. A slope of 4.9448 for the ideal case, in comparison to 1.6818 in the hierarchical boundary structure, is obtained (Figure 2d)nearly a 3-fold increase in coarsening rate. This is accompanied by more than a 3-fold increase in the growth rate of individual prisms (Figure 2f). Second, broadening of prism size distribution is obtained (Figure 2e). Hence, there are clear differences in prismatic ultrastructure formation from a quantitative point of view. The sub-boundaries seem to play a

major role in structural evolution of the mineralized layer by inhibiting main boundary motion and thus, reducing the average main prism size and narrowing its distribution. In principle, the subprismatic structure in P. nigra is an array of grains with mixed boundary conditions (Figure 2a). Their coarsening is the result of a complex interplay between two different kinds of boundaries: those with higher energy and mobility that in general move faster than the boundaries with lower energy and mobility. The latter exert a drag effect on the adjoining fast boundaries resulting in a variety of nonclassical main prism morphologies, as well as deviation from classical kinetics (Figure S1 in Supporting Information). For example, during Potts simulation of an individual six-edged prism embedded in an idealized neighborhood, which should allow for an ideal growth in the form of the von Neumann-Mullinslaw, one would expect no growth. Nevertheless, introducing sub-boundaries to the interior of the prism results in the formation of a drag effect that is directed to the center of the main prism causing its shrinkage (Figure 3a). A key benefit of the Potts simulation is the capability to study the kinetics of the intricate subprismatic morphology, which is not accessible experimentally. Examples of a possible analysis are presented in Figure 3b,c,d. Astonishingly, in comparison to the main prismatic structure, the average subprism area still shows a classical linear dependency on the direction of growth, z (Figure 3b); nevertheless, the subprismatic structure exhibits a completely different size distribution (in the form of a Rayleigh distribution function (Figure 3c) and a unique growth kinetics of individual subprisms (Figure 3d). In the latter, a deviation from the classical von Neumann-Mullins-law is evident. Here, the critical number of sides, nc, is close to 7 and the shrinkage of the subprisms is significantly inhibited. This means that while more subprisms are shrinking, the kinetics of the process is restrained as it is also demonstrated by the Rayleigh distribution function. D



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(9) Bayerlein, B.; Zaslansky, P.; Dauphin, Y.; Rack, A.; Fratzl, P.; Zlotnikov, I. Nat. Mater. 2014, 13, 1102−1107. (10) Zlotnikov, I.; Schoeppler, V. Adv. Funct. Mater. 2017, 27, 1700506. (11) Srolovitz, D. J.; Anderson, M. P.; Grest, G. S.; Sahni, P. S. Acta Metall. 1984, 32, 793−802. (12) Zöllner, D. In Reference Module in Materials Science and Materials Engineering; 2016. (13) Park, C.-S.; Na, T.-W.; Park, H.-K.; Lee, B.-J.; Han, C.-H.; Hwang, N.-M. Scr. Mater. 2012, 66, 398−401. (14) Zöllner, D.; Skrotzki, W. IOP Conf. Ser.: Mater. Sci. Eng. 2017, 194, 12049. (15) Thompson, C. V. Annu. Rev. Mater. Sci. 1990, 20, 245−268. (16) Kaiser, N. Appl. Opt. 2002, 41, 3053−3060. (17) Barranco, A.; Borras, A.; Gonzalez-Elipe, A. R.; Palmero, A. Prog. Mater. Sci. 2016, 76, 59−153. (18) Checa, A. G.; Bonarski, J. T.; Willinger, M. G.; Faryna, M.; Berent, K.; Kania, B.; González-Segura, A.; Pina, C. M.; Pospiech, J.; Morawiec, A. J. R. Soc., Interface 2013, 10, 20130425. (19) Olson, I. C.; Metzler, R. A.; Tamura, N.; Kunz, M.; Killian, C. E.; Gilbert, P. U. P. A. J. Struct. Biol. 2013, 183, 180−190. (20) Okumura, T.; Suzuki, M.; Nagasawa, H.; Kogure, T. Micron 2010, 41, 821−826. (21) Burke, J.; Turnbull, D. Prog. Met. Phys. 1952, 3, 220. (22) von Neumann, J. Metal interfaces, Herring, C., Ed.; American Society of Metals: Cleveland, 1952. (23) Mullins, W. W. J. Appl. Phys. 1956, 27, 900. (24) Zöllner, D. Comput. Mater. Sci. 2017, 137, 67−74. (25) Zöllner, D. Comput. Mater. Sci. 2014, 86, 99−107.

In summary, we provide an analytical approach, borrowed from classical physics of materials, for a quantitative study of hierarchical biocomposite architectures formed by a living organism. By using the Monte Carlo Potts simulation technique, we are not only able to describe the growth of a simple prismatic morphology, like the one in P. nobilis,9 but also to fully predict the formation of the complex two-level hierarchical prismatic ultrastructure in P. nigra. This outcome is consistent with our assertions that shell biomineralization is in fact a spontaneous process that proceeds without the direct intervention of the cellular component. The main benefits of the method are the capacity to estimate the relationship between different thermodynamic parameters that govern the structural evolution of the biological architecture and evaluate the effect of structural hierarchy on its morphogenesis, which are experimentally not yet accessible. The presented framework offers a new tool for the study of biomineralization that has the capacity to provide significant insights into bottom-up synthesis of functional composite structures beyond the living tissue.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.7b00965. Methods, detailed description of the Monte Carlo Potts simulation procedure, and detailed analysis of EBSD maps (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +49 351 463 43090. Fax: +49 351 463 40322. ORCID

Igor Zlotnikov: 0000-0003-2388-9028 Author Contributions

I.Z. conceived the study and designed the experiments. performed the simulations and analyzed the data. performed the electron microscopy. The manuscript written through contributions of all authors. All authors given approval to the final version of the manuscript.

D.Z. E.R. was have

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS I.Z. acknowledges the financial support provided by Bundesministerium für Bildung und Forschung (BMBF) through grant 03Z22EN11. D.Z. acknowledges the financial support provided by the Dresden Fellowship Program. We acknowledge the European Synchrotron Radiation Facility for beamtime allocation on beamline ID19.

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REFERENCES

(1) Mann, S. Biomineralization; Oxford University Press: New York, 2001. (2) Fratzl, P.; Weinkamer, R. Prog. Mater. Sci. 2007, 52, 1263−1334. (3) Weiner, S.; Dove, P. M. Rev. Mineral. Geochem. 2003, 54, 1−29. (4) Hartman, P.; Perdok, W. G. Acta Crystallogr. 1955, 8, 49−52. (5) Meldrum, F. C.; Cölfen, H. Chem. Rev. 2008, 108, 4332−4432. (6) Currey, J. D.; Taylor, J. D. J. Zool. 1974, 173, 395−406. (7) Marin, F. Front. Biosci., Scholar Ed. 2012, S4, 1099. (8) Crenshaw, M. A. Mechanisms of shell formation and dissolution, Rhoads, D. C.; Lutz, R. A., Eds.; Plenum Press: New York, 1980. E


Morphogenesis of Biomineralized Calcitic Prismatic Tissue in

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