Transport‐Limited Growth of Coccolith Crystals

Biogenic crystals present a variety of complex morphologies that form with exquisite fidelity. In the case of the intricate morphologies of coccoliths, calcite crystals produced by marine algae, only a single set of crystallographic facets is utilized. It is unclear which growth process can merge this simple crystallographic habit with the species‐specific architectures. Here, a suite of state‐of‐the‐art electron microscopies is used to follow both the growth trajectories of the crystals ex situ, and the cellular environment in situ, in the species Emiliania huxleyi. It is shown that crystal growth alternates between a space filling and a skeletonized growth mode, where the crystals elongate via their stable crystallographic facets, but the final morphology is a manifestation of growth arrest. This process is reminiscent of the balance between reaction‐limited and transport‐limited growth regimes underlying snowflake formation. It is suggested that localized ion transport regulates the kinetic instabilities that are required for transport‐limited growth, leading to reproducible morphologies.


Introduction
The shapes of crystals are often related to their lattice symmetry, with known examples that include the cubes of halite (rock salt) or the hexagons of ice crystals.[3][4][5][6] This is because snowflake growth is limited by diffusion of water vapor, [5] enabling delicate differences in environmental conditions to be expressed in the crystal growth process.The fact that such diffusion-limited growth is sensitive to external conditions gives rise to nearly infinite shapes that emerge from a single crystalline material, [5] but makes control over the process difficult to accomplish.Biologically formed crystals seem to break the dichotomy that exists between simpleand-reproducible and complex-and-variable morphologies.13][14][15][16] Coccoliths are a benchmark for the ability of organisms to control complex crystal growth.These calcite (CaCO 3 ) multi-crystal arrays are formed intracellularly by a group of unicellular algae called coccolithophores. [17]Each coccolith forms inside a dedicated organelle, the coccolith vesicle, via a sequential process.First, an organic oval scale, the base plate, is produced.Then crystals nucleate and grow at specific locations along the periphery of the base plate, until the coccolith is complete.[19][20] Even though this general process is shared by all coccolith-producing cells, each species regulates crystallization to yield a specific morphological outcome (Figure 1).Some coccoliths are made strictly of simple rhombohedra, the most stable habit of calcite (Figure 1A).These coccoliths grow in a spacious coccolith vesicle that resembles conditions in bulk solution. [21]On the other hand, some coccoliths have far more complicated architectures, made of an alternating arrangement of two differently oriented crystal units on the periphery of the base plate.These two crystal types are called Runits, for crystals with their c-axis directed roughly radially to the coccolith plane, and V-units, for crystals with a c-axis roughly vertical to the coccolith plane.[24][25] It was thought that the complex crystal morphologies of coccoliths are the result of "tailored" interactions between biological macromolecules and specific crystallographic facets that yield regulated growth. [8,17,26,27]However, advanced imaging modalities revealed that the calcite crystals grow solely through anisotropic growth of their rhombohedral facets. [25]In the species Pleurochrysis carterae, the anisotropy in growth was proposed to originate from the confined environment within the coccolith vesicle. [24]In this species, the membranes of the coccolith vesicle are positioned only tens of nanometers away from the growing crystals, and sometimes seemed to mold some parts of the crystal morphology.However, membrane molding alone cannot account for the many morphological traits that are tightly related to calcite crystallography. [20]These observations indicate a growth mechanism that involves a directional process that is crystallographic but not dependent on modified crystal facets.We therefore speculated that a transport-limited growth regime could be responsible for the intricate morphologies of coccolith crystals.Transport-limited growth includes distinct processes; diffusion-limited growth is only one of them, in which a single crystallographic facet can experience different chemical conditions due to the limited transport of the building blocks.How this can be accommodated in a cellular environment is yet to be explored.
Here, we used 3D imaging to investigate both the developing crystals and their cellular environment.We study a model coccolith, made by the species Emiliania huxleyi, which is characterized by delicate crystals with well-defined architectural motifs. [28]The results demonstrate a crystal growth process in which the coccolith vesicle controls the macroscopic architectural motifs, yet the fine morphological details are a manifestation of a transportlimited growth regime.

Results and Discussion
The coccoliths of E. huxleyi have a characteristic ultrastructure that consists of two shields, proximal and distal, connected by a stem (Figure 1C).Differing from similar species such as Calcidiscus leptoporus, E. huxleyi coccoliths are made of dominant Runits, whereas the V-units remain undeveloped and engulfed between adjacent R-units (Figure 1D). [22]In addition, the coccoliths of E. huxleyi have no clear crystallographic surfaces and their overall shape is delicate, especially the distal shield that appears as straight individual spokes that terminate in a T-shaped "hammerhead" (Figure 1C). [20,28]These characteristics have led to contradicting reports on the role of crystallographic facets in crystal morphology, stemming from the difficulties in assigning 3D orientations to minuscule crystal facets with 2D imaging tools. [27,29]n order to provide high-resolution 3D data on growth motifs of developing E. huxleyi coccoliths, we chose two main approaches to examine crystal morphogenesis: (i) ex situ analysis of extracted coccoliths, which allows full-volume morphological characterization; (ii) in situ analysis of developing coccoliths within cells, which provides information about the architecture of their native intracellular environment.
We extracted developing intracellular coccoliths from E. huxleyi cells, using a modification of a previously described method. [25]Since coccolith formation is not synchronized between different cells, the extracted coccoliths were at different stages of the formation process.Various extracted coccoliths were imaged in 2D with a scanning electron microscope (SEM), and in 3D with high-resolution tomography in a scanning transmissionelectron microscope (STEM) using the high angle annular darkfield (HAADF) detector (Figure 2; Figure S1, Supporting Information).We analyzed the morphological evolution of crystals from various stages present in each sample, using the same approach used to investigate C. leptoporus. [25]This showed similar results, namely, that the crystals grow anisotropically while presenting only the stable {104} facets of the calcite rhombohedron (Figure 2A,B; see Figure S2, Supporting Information for extended morphological analysis of the 3D datasets).Interestingly, the development of the distal shield spokes shows a modified route of morphological evolution.The spokes elongate by a directional growth that is not filling all the spaces between the crystals, whereby only the growth fronts at the tips of the elements appear faceted and crystallographic (Figure 2A-C, Movies S1-S5, Supporting Information).The fact that the crystallographic facets at the growth front expand significantly only in the main elongation direction yields a skeletonized crystalline element that presents a degenerated crystallographic habit.The curved surfaces that prevail behind the growth front are non-crystallographic, and their rounded morphology dominates the mature coccolith.
In addition to a qualitative description of morphological evolution, the 3D data of the thin and elongated R-units enabled analysis of their growth directions (Figure 2B-D).Initially, the Runits elongate along the tangent of the coccolith circumference, leading to parallelogram-shaped facets (Stage 1).As the crystals thicken, non-crystallographic surfaces emerge in the middle of crystallographic facets, creating concave areas that give rise to the "splitting" of the shields (Stage 2).29] However, the development of the distal shield element is more complex, starting with an elongated rod that extends from a crystallographic apex pointing toward a direction close to one of the a-axes (Stage 2).A unique aspect of the growing rods is that the growth is no longer space filling, leading to the formation of gaps between neighboring spokes (Stage 2, 3).At a certain point, growth switches direction to the crystallographic c-axis, forming the prominent section of the distal shield elements (Stage 3).Approaching completion, the distal shield elements change growth direction back to a tangential growth and to a spacefilling regime again, where the crystals grow until they meet their neighbors, leading to the development of their characteristic "hammerhead" morphology (Stage 4, 5).These observations show that the anisotropy in crystal growth alternates between different preferred directions during crystallization (Figure 2D).Yet, at all of these stages, crystal growth utilizes calcite crystallography (growth from apexes of the {104} rhombohedron and along primary crystallographic directions).Such crystallographic growth directions, that do not manifest in crystallographic surfaces upon coccolith maturation, explain why characterizing morphogenesis can be so elusive.
To elucidate the cellular environment that underlies coccolith development, we imaged intracellular coccoliths in situ at near-native state conditions using cryogenic electron tomography (cryo-ET).We vitrified actively calcifying E. huxleyi cells by plunging them into liquid ethane and used cryo-focused ion beam (cryo-FIB) milling to generate ≈200 nm thin lamellae that span the cell width (Figure 3A).The cryo-ET data show the intracellular organization, including the nucleus, chloroplasts, and internal membrane systems (Figure 3B).The coccolith vesicle is situated close to the nuclear envelope and is connected to a labyrinthine membrane structure known as the reticular body. [18,30]Inside the coccolith vesicle, the base plate is observed as a thin organic sheet, on the periphery of which the crystals develop (Figure 3C).Interestingly, in contrast to coccolith formation in P. carterae, which is characterized by the presence of dense Ca-loaded particles in the coccolith vesicle, [24,31] no such dense phases are observed within the coccolith vesicle or the reticular body of E. huxleyi.The fenestrated lumen of the reticular body is connected at multiple places to the central area of the coccolith vesicle (Figure S3, Supporting Information). [32]These observations suggest that the transport of calcium and carbonate building blocks for the coccolith is mostly done in a soluble state, either via short-range transmembrane transport from the cytoplasm, or long-range diffusion path through the reticular body lumen.
We acquired tomograms of growing crystals at various developmental stages, allowing the visualization of their intracellular 3D environment (Figure 4A,B; Figure S4 and Movies S6-S11, Supporting Information).Crystal morphologies determined from the cryo-ET data correspond to the observations of the extracted crystals in Figure 2.This reinforces the observation that crystallographic facets are characteristic of the initial growth stages and the growing tips of the shield elements, whereas the mature surfaces show a smooth, yet not flat, topography.The data also qualitatively show that non-crystallographic surfaces are tightly bound by the coccolith vesicle membrane, suggesting that membrane confinement is associated with noncrystallographic growth arrest.We quantified and mapped the distances between each vertex on the crystal surface and the nearest point on its enveloping membranes (Figure 4C,D; Figure S5, Supporting Information).These distance maps show that in the initial stages, where the crystals present predominantly crystallographic facets, the membrane is located ≈40-80 nm away from the crystals.However, as the crystals grow, the appearance of non-crystallographic surfaces (initially the stem region, followed by the distal and proximal sides of both shields) is associated with membrane confinement that is less than 20 nm.This is evident by the orange-green colors that dominate the distance maps at the early stages, which transition into green-blue colors in the mature stages.Because the crystals are constantly growing, we do not think that the membrane is approaching or adhering to the crystals, providing an active barrier to their further growth.Rather, we suggest that it is the crystals themselves that cease from growing -when nearing the membrane at specific locations that do not provide the needed building blocks for growth.Importantly, at the stages of stem formation and shield expansion, where only the apexes of the elements continue to elongate, their growing fronts maintain a more spacious distance of ≈40 nm from the vesicle membrane, in accordance with the presence of crystallographic facets at these locations.Although active membrane shaping is inherent to crystal morphogenesis, [33] it should be noted that no cytoskeleton filaments were associated with the vesicle (Figures S3 and S4, Supporting Information).The observed architectures suggest a link between the vesicle membrane proximity to the crystals and their ability to grow.This can be reasoned by a scenario where only close to the growing tips of the crystals, there are conditions that support crystal growth (i.e., supply of ions and a supersaturated environment that creates crystallization pressure).In this scenario, the membrane that surrounds other locations of the crystals acts as a non-permeable barrier for the crystal building blocks, resulting in a passive cessation of growth.
The presented analyses of developing E. huxleyi coccoliths provide a basis to interpret their nanoscale morphology and mechanism of crystallization.An important observation is that all crystallographic facets belong to the {104} family, similar to recent observations in P. carterae and C. leptoporus. [24,25]This consensus brings up the question of how species-specific coccolith morphologies are controlled.In other words, if the underlying crystallographic habit is identical, what regulates the various and nuanced morphologies of the crystals?One important mechanism is membrane confinement, which manifests in many locations of coccolith architecture.For example, the curved surfaces that separate the two shields mirror the shape of the coccolith vesicle membrane in all examined species. [19,24]Nevertheless, we propose that morphological regulation is not achieved only by external membrane molding with direct contact to the crystals, but rather by controlling the conditions at which different modes of crystallographic growth occur inside the coccolith vesicle.
The proposed morphogenesis mechanism suggests a dynamic continuum between reaction-limited and transportlimited growth regimes.This is analogous to the importance of the growth regime in shaping snowflakes (ice crystals), [2,5] even though the physical mechanisms, i.e., diffusion limitation versus transport limitation, are very different.In reaction-limited conditions within a coccolith vesicle, growth is space filling, and the crystals grow by {104} facets until reaching a neighboring crystal (as is the case for C. leptoporus). [25]In transport-limited growth conditions within a coccolith vesicle, which is analogous to diffusion-limited growth in the sense that the formation of new crystallographic layers is faster than their lateral expansion, the crystals grow via the addition of layers to crystallographic facets; but these fail to complete (fill space), resulting in a skeletonized  element.This mode of growth can explain how the E. huxleyi elements always show crystallographic facets in their growing fronts, but the final morphology is dominated by the effects of growth-cessation behind this front, giving rise to the curved morphology.
Currently, it is impossible to measure concentration gradients inside the coccolith vesicle and directly determine the nanoenvironment of crystallization.Nevertheless, our data provide several lines of evidence supporting a transport-limited growth regime in E. huxleyi coccoliths: 1) The gaps between the shield elements.The cryo-ET data clearly show that there is no membrane barrier between the neighboring crystals (Figure 4 stage 6, Figure 5A; Figure S4, Supporting Information), therefore these gaps are not the result of membrane molding.[36][37] In some E. huxleyi strains no gaps are present within the shields, while in others, gaps appear in both shields (Figure 5B,C; Figure S6, Supporting Information).This suggests that the biological control over this trait is indirect and can be executed by controlling the growth regime.3) The elongation of the distal shield elements from an apex of the underlying rhombohedral shape is reminiscent of transport-limited regime, which is characterized by growth at apexes that are the preferred sites for transport-derived instabilities (Figure 2 stage 2). [5]4) The mature surfaces of the crystals are curved but the growth directions are crystallographic, [29] again reminiscent of transport-limited growth regime.
The proposed transport-limited growth mechanism can be explained by spatial and temporal heterogeneities in the transport of ions into the coccolith vesicle, which affects ion availability to the crystals.Initially, the environment inside the coccolith vesi-cle allows space-filling growth that is anisotropic, with a preferred growth direction tangential to the coccolith circumference.In the following stages, the coccolith vesicle expands concurrently with the growth of the crystals.At locations where ions are supplied, the crystals grow, and the consequent crystallization pressure pushes the membrane away, predominantly at the expanding fronts of the crystals.Yet, as ion supply is exhausted behind these fronts, growth is slowed to a halt and the membrane remains to envelop the crystal surface.We hypothesize that transmembrane transport of at least some of the crystal building blocks (for example, influx of carbonate, bicarbonate, calcium, and∖or outflux of protons), is localized to specific areas at the coccolith vesicle membrane.This is in line with previous observations of heterogeneous cytoplasmic calcium levels in other microalgae, [38] which may arise from specific localization of membrane proteins driven by biophysical traits such as membrane curvature. [39]imilar mechanisms may be responsible for site-specific switch between reaction-and transport-limited regimes in the coccolith vesicle (Figure 5D,E).This scenario is by no means conclusive, but we think it can inspire future research by taking into account such a crystal growth process.For example, other organisms, such as echinoderms, that shape their crystals primarily via molding of an amorphous precursor phase also demonstrate shapes that are related to their crystallography. [7,16,40]It will be interesting to explore whether a crosstalk between the crystallographic driving forces in their nanoenvironment and precursor phase mineralization can explain some of the morphological traits.
To conclude, our observations show that nuanced morphological control of E. huxleyi coccoliths is not reliant on intricate crystallographic faceting, but rather, on a manifestation of growth-arrest behind a prevailing growth front.Such crystallographic growth, via the stable rhombohedral facets of calcite, is becoming the rule in our understanding of coccolith formation.This brings forward an interesting hypothesis that intra-and interspecies similarities and differences in coccolith morphologies are rooted in controlling two properties of the growth environment -the preferred directions by which the crystals elongate, and the degree by which this growth is space filling.Both these properties can be sensitive to initial crystal orientations, leaving the key unanswered question of nucleation control.We propose that an environment within the coccolith vesicle that can balance reaction-limited and transport-limited growth can explain these morphological traits (Figure 5E).Such an environment can conceivably be the result of membrane-mediated fluxes that can be regulated both in their magnitude and in their spatial distribution on the membrane surface.

Figure 1 .
Figure 1.Diversity in coccolith morphologies and surface-types.A-C) Left, SEM images of cells encapsulated by a coccolith shell from the species Calyptrosphaera sp.(A), Calcidiscus leptoporus (B), and Emiliania huxleyi (C); Right, corresponding SEM images of individual coccoliths, with single units artificially colored to emphasize the different surface-types of mature crystals (green, crystallographic; purple, non-crystallographic).The distal and proximal shields, as well as the connecting stem region, are denoted.White scale bars, 500 nm.D) A schematic cross-section across a mature E. huxleyi coccolith, highlighting the dominant R-units (blue) that make up the structure, and the degenerate V-units (orange); red arrows denote respective c-axes directions.

Figure 2 .
Figure 2.Forming crystals present crystallographic growth fronts and alternating growth directions.A) SEM images of extracted intracellular coccoliths from five stages ranging from early to mature, viewed distally.Crystallographic facets (green arrowheads) dominate the early crystals and appear at the growing fronts of the crystals yet disappear and give-way to non-crystallographic surfaces (purple arrowheads) during maturation.Stem region and distal shield formation (stages 2 and 3, respectively) extend via the corners of meeting {104} facets.Shields are denoted by arrowheads (white, distal; yellow, proximal).Scale bars, 200 nm.B) 3D volume rendering of the STEM tomography data of coccoliths from stages similar to those in (A), with a highlighted R-unit (colored).In stage 2, two units were segmented to demonstrate the corner growth better.Black arrows point to corners that will elongate.C) 3D surface rendering of individual crystals from (B), viewed with the c-axis (red arrows) parallel to page.In stage 2, the units are also observed parallel to the stem, showing the vertical growth through a corner.See also Movies S1-S5 (Supporting Information).D) Schematic model of the evolving crystals, showing three interlocked R-units, viewed distally (top) and slightly tilted (bottom).Crystallographic direction of the c-axis (red arrows) and one a-axis (blue arrows), as well as crystallographic growth fronts (green) and curved surfaces (purple), are highlighted for a single unit.Black arrows show how the dominant growth direction alternates between tangential, a-axis, and c-axis.

Figure 3 .
Figure 3.The intracellular environment of growing coccoliths inside E. huxleyi cells.A) A schematic illustration of a FIB-milled E. huxleyi cell, and the resulting cell-spanning lamella used for imaging.B) Low magnification cryo-TEM image of a whole cell in a lamella, with a mature extracellular coccolith (area highlighted in blue and enlarged in the inset at the bottom right) and a forming intracellular coccolith (area highlighted in yellow).C) A slice through the reconstructed cryo-ET dataset collected at the area highlighted in yellow in (B).In (B) and (C), artificial coloring highlights major ultrastructural elements.

Figure 4 .
Figure 4.The coccolith vesicle membrane is closest to curved surfaces while maintaining distance from crystallographic growth fronts.A) Slices through the reconstructed cryo-ET datasets of developing crystals in situ, ranging from early to mature, viewed along the base plate periphery.Artificial colors highlight relevant structures: crystals (blue, R∖orange, V) vesicle membrane (green), base plate (pink).Scale bars, 100 nm.See also Movies S6-S11, Supporting Information.B) Surface rendering of the datasets in (A).C) Analyses of distances from points on the crystal surfaces to their closest point on the membrane surface.Magnification of the distal shield shows that the growing tip is more distant from the membrane relative to other surfaces that face the membrane.D) Distributions of distances from the analyses in (C) along the different stages.Numbering corresponds to that indicated in A.

Figure 5 .
Figure 5.A balance between reaction-and transport-limited growth controls morphogenesis in E. huxleyi.A) Surface rendering of coccolith vesicle membrane (cyan) and crystals (blue), viewed parallel to the stem and across the shields.Gaps are visible between the elements (black arrows), with no membrane delimiting lateral growth.Inset shows a slice from the reconstructed dataset.Scale bar, 100 nm.B) SEM image of a proximal shield with gaps (black arrows) between shield elements.C) SEM image of a distal shield, showing a filled morphology (i.e., no gaps).Artificial light blue coloring highlights an individual element, and dashed lines indicate borders between neighboring crystals.D) SEM images of developing distal shield elements with a "skeletonized" morphology.Artificial dark blue coloring shows skeletonized growth, while light blue indicates growth that is space filling (forming the hammerhead).Dashed lines show the would-be meeting borders.Scale bars in (B)-(D), 200 nm.E) Suggested model for crystal morphogenesis in E. huxleyi distal shield: Transport-limited growth results in skeletonized elongation (dark blue), while reaction-limited growth, results in a space filling morphology (light blue).Putative ion transporters (purple) can facilitate the fluxes of building blocks (blue gradient emanating from transporters) that dictate the growth regime.Red arrow indicates c-axis.