Crystal Growth with Macromolecular Additives - Chemical Reviews

Review pubs.acs.org/CR

Crystal Growth with Macromolecular Additives Alexander G. Shtukenberg,* Michael D. Ward, and Bart Kahr Department of Chemistry and Molecular Design Institute, New York University, 100 Washington Square East, New York City, New York 10003, United States ABSTRACT: Interactions of macromolecules with growing crystalline surfaces play an important role in biomineralization, determine survival of some organisms at low temperatures, and offer a range of potential industrial applications. The current understanding of crystal growth processes in the presence of macromolecules, including peptides and proteins, is reviewed, with a focus on interactions between macromolecules and surfaces of crystalline materials, macromolecule adsorption on different types of crystal surfaces, crystallization kinetics in the presence of macromolecular additives, macromolecule incorporation, and defect generation. Throughout, special attention is paid to the selectivity of macromolecule adsorption on, and incorporation within, crystal surfaces. The special role played by the size and complexity of macromolecules as compared to other crystallization additives is emphasized.

CONTENTS 1. Introduction 1.1. Motivation and Aim 1.2. Context 2. Adsorption 2.1. Kinetics 2.2. Crystal Types 2.2.1. Salts 2.2.2. Ice 2.2.3. Molecular Crystals 2.3. Macromolecular Synergies 3. Crystallization Kinetics 3.1. Growth Parameters 3.2. Influence of Additives 3.2.1. Cabrera−Vermilyea (C−V) Model 3.2.2. Bliznakov−Chernov (B−C) Model 3.2.3. Shift of Phase Equilibria 3.2.4. Surfactants 3.3. Growth Inhibition 3.3.1. Morphology Evolution 3.3.2. Step Pinning 3.3.3. Hillock Modifications 3.3.4. Combinations of Inhibitors 3.4. Growth Acceleration 3.5. Time Dependence 3.6. Macromolecule Size 3.7. Case Study: Calcium Oxalate Monohydrate 4. Incorporation 4.1. Individual Macromolecules 4.1.1. Concentration 4.1.2. Selectivity 4.2. Macromolecular Aggregates 4.3. Internal Stresses and Growth Defects 5. Summary and Outlook Author Information © 2017 American Chemical Society

Corresponding Author ORCID Notes Biographies Acknowledgments List of Symbols List of Abbreviations References

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1. INTRODUCTION 1.1. Motivation and Aim

Cod fisheries have sustained North Americans for millenia but have collapsed spectacularly in recent decades;1 only the most polar cod thrives today. Boreogadus saida, navigating the frigid Barents Sea, is likely headed for a Russian table in a harvest of prudently managed fish stocks. This meal is not only dependent on international fishing treaties; it also depends, in more ways than one, on the specific interactions of proteins and crystals. Cod antifreeze proteins protect the fish from ocean temperatures that can fall below 0 °C, while cod otoliths, organs for navigation made of calcium carbonate, are grown in processes that are mediated by proteins (Figure 1). Without the capacity to grow some crystals and prevent the growth of others, processes invariably involving proteins, the arctic cod would lose its way while freezing through and through. The role of proteins and other macromolecules in the growth of crystals, wherever they are found, is the focus of this Review. Additives and unintended impurities, whether proteins or not, affect crystal morphology as well as polymorphism. They sometimes inhibit growth and nucleation or promote them. Received: May 22, 2017 Published: November 22, 2017 14042

DOI: 10.1021/acs.chemrev.7b00285 Chem. Rev. 2017, 117, 14042−14090

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additives (ions, small molecules),6,7 and kinetic analyses can illuminate mechanisms of growth inhibition by these additives.2,8−12 The role of peptides, proteins, polysaccharides, and other large molecules in crystal growth is more complex, however, and less well understood. This knowledge gap was made vivid some years ago when we observed that the basal plane of α-lactose monohydrate (ALM), and occasionally certain steps decorating hillocks on the basal plane of ALM, would overgrow a variety of globular proteins (Figure 2).14,15 Moreover, a wide range of proteins were incorporated by the same crystal face, confronting us with a molecular recognition process that was both promiscuous (most proteins did it) and specific (only one (hkl) surface was involved). This was a supramolecular “lock and key” conundrum. All keys will not open any one lock, and no one key will open all. To understand this supramolecular chemistry, it was clear that we needed to become stronger students of the macromolecule/crystal literature. This body of knowledge17−24 has largely focused on two distinct classes of materials: (i) ice inhibition by antifreeze proteins and (ii) biominerals (calcium salts, especially calcite, calcium oxalates, and apatite) interacting

Figure 1. (A) Structure of cod AFGP. (B) Northeast Arctic cod calcium carbonate (aragonite) otolith. Reproduced with permission from ref 13. Copyright 2001 Elsevier B.V.

They also regulate the formation of defects and imperfections, and affect the chemical and physical properties of crystals and crystal aggregates.2−5 Stereochemical insights into mechanisms of crystal/additive interactions have emerged for simple

Figure 2. Micrographs of ALM crystals containing various macromolecules. In all cases, characteristic fluorescence from the (010) growth sector is observed. Reproduced with permission from refs 15 and ref 16. Copyright 2001 Elsevier B.V. and 2016 American Chemical Society. 14043


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Table 1. Growing Crystals Perturbed by Macromolecular Additives compound, formula

space group

importance for science and technology

Calcium Salts calcite, CaCO3 hydroxyapatite (ApOH), Ca5(PO4)3(OH)2

R3c̅ P63/m

fluorapatite (ApF), Ca5(PO4)3F2

P63/m

octacalcium phosphate, Ca8H2(PO4)6·5H2O calcium oxalate monohydrate (COM), CaC2O4·H2O calcium oxalate dihydrate (COD), CaC2O4·2H2O brushite, CaHPO4·2H2O gypsum, CaSO4·2H2O calcium tartrate trihydrate, CaC4H4O6·3H2O calcium tartrate tetrahydrate, CaC4H4O6·4H2O calcium fumarate trihydrate, CaC4H2O4·3H2O calcium malonate dihydrate, CaC3H2O4·2H2O calcium maleate monohydrate, CaC4H2O4·H2O calcium bis-p-nitrophenylphosphate calcium diphenylphosphate calcium phenylphsphate calcium dibenzylphosphate Other Ionic Compounds zinc oxide, ZnO sodium urate monohydrate, NaC5H3N4O3·H2O Molecular Crystals ice, H2O α-lactose monohydrate (ALM), C12H22O11·H2O L-cystine, C6H12N2O4S2 uric acid, C5H4N4O3 cholesterol monohydrate 1,4-dinitrobenzene, C6H4N2O4 L-Leu-L-Leu-L-Tyr peptide 2,4-dihydroxybenzoic acid hemihydrate, C7H6O4· 0.5H2O 2,5-dihydroxybenzoic acid, C7H6O4 succinic acid, C4H6O4 sinapic acid, C11H12O5 paclitaxel, C47H51NO14 tetrahydrofuran (THF), (CH2)4O·17H2O Macromolecular Crystals lysozyme ferritin glucose isomerase Bence−Jones protein

P1̅ P21/c I4/m Cc C2/c P21/c P212121 Pna21 n/d n/d Pna21 P21/n C2/c P1̅

biomineral, main component of marine skeletons and otoliths biomineral, main component of teeth and bones; major component of salivary stones biomineral, main component of fish teeth; model system for study of biomineralizaiton pathological biomineral; important for bone growth pathological biomineral, major component of kidney stones; plant biomineral pathological biomineral, major component of kidney stones; plant biomineral pathological biomineral, major component of a variety of pathological stones biomineral model system for study of cell adhesion model system for study of crystal−protein interaction model system for study of crystal−protein interaction model system for study of crystal−protein interaction model system for study of crystal−protein interaction model system for study of crystal−protein interaction model system for study of crystal−protein interaction model system for study of crystal−protein interaction model system for study of crystal−protein interaction

P63mc P1̅

technologically important crystal pathological biomineral crystallizing in joints

P63/mmc P21 P6122 P21/a P1 P21/n P21 P1̅

solid form of water, most important biological agent potential host for storage of protein drugs pathological biomineral, major component of kidney stones pathological biomineral, major component of kidney stones model system for study of antibody recognition model system for study of antibody recognition model system for study of antibody recognition host for MALDI TOF mass spectrometry

P21/c P21/c P21/n P21 Fd3̅m

host for MALDI host for MALDI host for MALDI antimitotic drug model system to

P43212 and P21 F432 I222 n/d

most studied model protein model protein model protein model protein

a

Na 80 80 15 5 70 10 4 1 3 8 3 2 2 1 1 1 1 5 2

TOF mass spectrometry TOF mass spectrometry TOF mass spectrometry

150 4 1 2 5 5 2 1 6 1 2 1 2

study gas hydrates

10 2 1 1

Approximate number of publications discussing interactions between macromolecules and growing crystals. n/d, not determined.

and 2,5-dihydroxybenzoic acid, as well as other substances listed in Table 1. This Review follows the path of the additive from the growth medium to the crystal interior. The first section is devoted to adsorption of macromolecules, with particular attention to selectivity of adsorption among crystal surfaces. This is followed by the analysis of adsorbate/crystal interactions and their effects on crystallization kinetics. Finally, the effect of additive incorporation and defect generation is considered. Throughout, we have replotted primary data in varied units from different publications on the same graphs for ease of comparison. Does increasing complexity of macromolecular additives lead to richer growth behavior? Is there anything fundamentally new for which we must account to control and understand crystallization in the presence of biopolymers? Answering this question constitutes our principal aim here. We limit our

with acidic proteins. Although these two classes of proteins are quite distinct, they may or may not instruct us about the role of macromolecules in the crystallization of other materials. Indeed, the influence of macromolecular additives on crystal growth has been investigated for more than 30 crystalline phases (Table 1), not all of which fall into the two aforementioned categories. Herein, we attempt to embrace all crystal-additive systems under the same umbrella, regardless of the field of inquiry. In so doing, we aim to draw out the most general principles underlying macromolecule/crystal interactions that might otherwise be masked when examining a single system, or even a single class of macromolecules (MMs) or crystals. Evans has compared biomineralization and ice inhibition using this approach, a rare synthesis of many data.25 We expand here on his holistic approach by including ALM, zinc oxide, L-cystine, 14044


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were carried out by Rainey.34 Of course, neither Harting nor Rainey understood the compositions of the mixtures they were concocting. By the early 1960s, researchers had come to suspect that antifreeze substances circulated in the blood sera of fish adapted to cold water.35 At decade’s end, researchers zeroed in on glycoproteins agents in the blood of polar fishes.36 A prerequisite for study of the interactions of proteins and crystals was advances in analytical chemistry, the isolation of minor components of crystals and crystallizing solutions, and assays of their influences, without which this branch of supramolecular chemistry would have been impossible. For example, the first direct evidence of ice binding by a protein was the observation of surface-enhanced second harmonic generation.37 Recognition of protein interactions with growing biominerals likewise began to emerge in the early 1960s. The proteinaceous organic matrix extracted from the nacre layer in mollusk shells was shown to be responsible for growing aragonite, a less stable polymorph of calcium carbonate than calcite, but a frequent component of biominerals.38 Lowenstam recognized the intimate biological control of goethite in gastropods39 and magnetite in chitons.40 Many dozens of biominerals have since been identified.41,42 Emerging areas of science also rely on macromolecule−crystal interactions. These include mixed crystal growth for the kinetic stabilization of biomolecules and macromolecular mass spectrometry (sections 2.2.3 and 4.1).

purview to the growth of single crystals of microscopic size or greater (>1 μm). We do not consider nucleation and polymorph control, nor do we consider the interaction of macromolecules with static crystalline surfaces. Instead, we eschew the literature on growth in the absence of well-defined facets as well as well-defined surfaces in the absence of growth. While it is clear that macromolecules can affect nucleation by concentrating crystallization components, and they can elicit startlingly complex polycrystalline morphologies, these topics fall outside the scope of this Review.26 In most cases, we consider crystallization from the melt (ice) and aqueous solutions (all other materials) under ambient pressure and temperatures approximately ranging from −10 to + 60 °C. Growth is presumed to proceed by step flow over flat surfaces (layer-by-layer growth; Figure 3).3 Growth of rough

2. ADSORPTION The promotion or inhibition of the adsorption of proteins, peptides, and other biopolymers on solid surfaces is significant for the compatibility of medical implants, and for the functions of sensors, activators, and other components at biological/ electronic junctions. Adsorption is common on surfaces that are growing as well as those that are not. Common features of protein adsorption on solid surfaces include the following:43−46 (i) Adsorption, generally decreases with increasing temperatures. (ii) Adsorption is greatest near the isoelectric point. (iii) Higher ionic strength favors adsorption to like-charged substrates and diminishes adsorption to oppositely charged substrates. (iv) High ionic strength promotes protein aggregation. (v) Proteins are distinguished by their multiple modes of adsorption on most any surface. Hydrophobic interactions favor adsorption of hydrophobic residues on noncharged surfaces; yet adsorption through binding of charged residues favors surfaces decorated with ionic charge. Additionally, adsorption will always be preferred for surfaces with high energy as compared to surfaces of low energy. (vi) Small, rigid proteins such as lysozyme (so-called “hard” proteins) maintain their structure and conformation in the adsorbed state, whereas larger and softer proteins like albumin and transferrin (“soft” proteins) undergo conformational changes upon adsorption. These features collectively set a rather low threshold for biopolymer adsorption. Proteins are sticky, and they often coat material interfaces in circumstances where such fouling is not wanted. Growing crystalline surfaces are distinguished from static surfaces in two important ways: (i) a growing crystal surface is exposed to the growth medium for a short time, often preventing the absorbate from reaching an equilibrium surface coverage and complicating crystallization via feedback between

Figure 3. A crystalline surface growing by step flow with strongly (green ellipses) and weakly (red ellipses) adsorbed macromolecules. Note that the total surface coverage θ is defined by all adsorbed MMs, whereas the crystallization kinetics and incorporation are controlled only by the strongly adsorbed MMs. h, d, and p are the step height, terrace width, and surface slope, respectively.

surfaces is not considered because it is less common and there are little data. Steps on flat surfaces are created via the screw dislocation mechanism as well as 2D nucleation, crystal edges, and various imperfections. Despite their possible importance, we do not consider herein nonclassical crystallization and 3D nucleation4,27 due to a lack of reliable information. The effect of additives (mostly not macromolecules) on nonclassical crystallization has been summarized recently.28 1.2. Context

Appreciation of crystals is part of human history. Proteins, on the other hand, were not identified as monodisperse chemical entities, as opposed to colloidal mixtures, until the ultracentrifugation of Svedberg in the 1930s.29 Likewise, the marriage of proteins and other macromolecules with crystals is an entirely new field. Nonetheless, the idea that living systems beget crystals is ancient. Legend has it that cruciform twins of staurolite result from the crystallization of the Earthbound tears of fairies, to the extent we concede that fairies are living systems, released when the sprites learned of the suffering of the Savior.30 On a more contemporary note, Ozin31 and Ball32 have highlighted the strange effects of biological fluids on growing crystals, as described in the work of Harting.33 Even Harting had antecedents; similar investigations 14045


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Table 2. Characteristic Adsorption Times of Macromolecular Additives τ0, min

additive, cad Host Crystal: Calcium Oxalate Monohydrate osteopontin (OPN), 5−10 mg/mL OPN, 5 mg/mL (D3S)6D3 peptide, 2−10 nM phosphorylated OPN peptide, 75 ng/mL Host Crystal: Hydroxyapatite OPN, 5 mg/mL Host Crystal: Ice AFP I, 0.25−1 mg/mL AFP I, 0.25−1 mg/mL AFGP, 0.6 mg/mL AFGP, 0.67−2 mg/mL GFP-TmAFP, 2−4 μM GFP-CfAFP, 4 μM GFP-AFP III, 0.8−7.5 μM GFP-MpAFP, 2.4 μM carboxylated ε-poly-L-lysine, 20−150 mg/mL Host Crystal: Lysozyme ovalbumin lysozyme dimer, 0.5%; 18 kDa polypeptide, 1.0%; 39 kDa polypeptide, {010}

75,76

0 36c

5.1 44 44

0.01−0.1 0.04−0.2 0.1−0.2

{100} > {010} {100} > other faces {100} > {121}̅ ≈ {010} (milk OPN)d{100} ≈ {121}̅ > {010} (bone OPN)d

76 55,84 99

44 44 68

5−5.5 nM 1−25 nM 0.01−0.1 0.012− 0.37 0.015− 0.45 0.02−0.65

32

44

42

80

albumin, BSA, HSA

41, 39

58, 60

66.5, 66.4 ∼46

∼1

> > > > >

ref

{100} > {010} {100} > {010}

38

{100} {100} {100} {100} {100}

{121̅} > {010}e {010} {121}̅ > {010}d [001] > {010} {010}

2.8 8.3, 12

OPN OPN Tamm−Horsfall protein, THP human transferrin, Tf

chondroitin sulfate A, ChS

cad, μM 0.5−20 0.3, 2 0.06−2.8 1.2−12 0.002− 0.085 0.29−3.64 0.01−4

89−95 86,96 81 82,83 51,52,97,98

{010} ≫ {100} slight inhibition or acceleration

93 91,98 98

{100} > other faces

88

{100} > other faces

88

{100} > other faces

88

#D, #E, #p: Number of Asp, Glu, and phosphorylated residues. bNumber of non-Asp carboxylate groups. cData for human milk OPN. Different OPN types contain slightly different numbers of Asp and Glu residues and phosphorylation sites. Number of phosphorylated residues usually smaller than the number of possible phosphorylation sites. dIn original publications probably as a result of error index {121} was instead of {121̅}. eHere, and throughout, COM indices refer to the P21/c setting with a = 6.290 Å, b = 14.5803 Å, c = 10.116 Å, and β = 109.46°.101 Some authors use the alternative P21/n setting of the same crystal structure with a = 9.976 Å, b = 14.588 Å, c = 6.291 Å, and β = 107.05°.102 Figure 4 shows relationships between the two settings.100,103 a

peptides and proteins. Electrostatic forces, however, are nondirectional, and stereochemistry may also play a role. Addadi and Weiner first argued for strong stereochemical control governing the binding of Asp-rich, mollusk (Mytilus californianus) protein to calcite, calcium fumarate trihydrate (CFT), calcium maleate monohydrate (CMM), calcium malonate dihydrate (CMD), and calcium tartrate tetrahydrate (CTT).67,68 They observed morphological changes for CFT, CMM, and CMD, but not CTT. The most strongly inhibited faces were those with carboxylate groups protruding nearly perpendicular from the exposed crystal surfaces, which was regarded as an optimum condition for the formation of Ca2+ bridges between the crystal surface and anionic residues of a calcium-loaded protein. CTT, however, did not express faces decorated with a large carboxylate surface density. The (0001) face of calcite, with carbonate groups parallel to the surface, was regarded as ideal for binding through the Ca2+ bridge. Neither charge density nor the spacing of the Ca 2+ ions on corresponding faces were found to correlate with habit modification, which is usually a direct consequence of faceselective growth inhibition by strongly bound adsorbates. Mollusk shell proteins were reported to inhibit the growth of calcium bis-p-nitrophenylphosphate, calcium diphenylphosphate, calcium phenylphosphate, and calcium dibenzylphosphate69 primarily by binding to exposed rows of calcium ions and phosphate groups containing two oxygen atoms projecting from the surface, as in hydroxyapatite (ApOH) {100}. Morphology changes of octacalcium phosphate crystals by several acidic and phosphorylated proteins were explained likewise.70

decreased. Recovery of the original step velocity after introduction of peptide-free COM solution exceeded the time needed for the growth of one COM monolayer.53 The same delay was observed for the growth of L-cystine with chondroitin sulfate A (ChS), apotransferrin, and Tamm−Horsfall protein (THP).54 Moreover, these MM additives also can increase terrace width on {0001} of L-cystine without the involvement of step pinning. Such behavior is consistent with simultaneous weak and strong adsorption of the MMs54 (Figure 3), wherein weak adsorbates affect kinetic parameters but neither pin steps nor become overgrown, and strong adsorbates behave as immobile “stoppers” that are eventually consumed by the crystal. The maximum surface coverage in this case can be significant (θmax, total → 1), but the surface coverage by strongly adsorbed MMs, which dominates control of the growth process, can be substantially smaller (θmax, actual ≪ 1), providing an opportunity for the surface to be covered with a small fraction of irreversibly bound MMs. Collectively, these reports illustrate that adsorption of MMs is likely to be more complicated than that of small molecules and not appropriately described by the Langmuir model. It is known that multistep protein adsorption even on static crystalline surfaces can be characterized by complex kinetics46,47 so that adsorption on dynamic surfaces should be even more complicated. 2.2. Crystal Types

2.2.1. Salts. Arguably, protein-growing crystal interactions have been investigated most thoroughly in the context of biomineralization. Binding to calcium salts such as apatite or calcite (Table 1) is mainly controlled by electrostatic interactions between calcium cations and anionic residues of 14047


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Figure 4. (A) COM morphology. Black and blue indices and crystallographic axes are given in the P21/c101 and P21/n102 setting, respectively. Schematics of growth hillocks on {010} and {100} are shown in gray. (B,D,F) COM viewed normal to the growth faces {100}, {121̅}, and {010}, respectively. Atom coloring: white (C), red (O), magenta (Ca), and black (H). (C,E,G) Growth hillocks on growth faces {100}, {121̅}, and {010}, respectively. Adapted with permission from ref 76. Copyright 2004 American Chemical Society.

residue spacings. Instead, the key features were found to be “the lack of folded structure in the crystal-binding region of the protein and the electrostatic potential difference between this region and the crystal face.”71 Here, the protein is behaving like a flexible polyelectrolyte. Indeed, polyE, polyD, and polyAA lacking secondary structure not only adsorb to the faces of COM but significantly and differently affect crystallization kinetics of these faces.75,76 Biomineral proteins such as OPN, sialoprotein, dentin phosphoprotein, and acidic proteins from mollusk shells adopt extended structures or “random coils” in solution.25,71 Molecular dynamics simulations have shown that there are many OPN peptide conformations on ApOH surfaces that lead to strong adsorption.77 Finally, a strong correlation between calcium densities on faces of calcium oxalates and their inhibition by acidic peptides (see below) argues for the

These investigations led to the conclusion that stereochemical control requires71 (i) a protein with a crystal-binding region characterized by charged groups protruding perpendicular to a planar surface (a typical example is the β-sheet motif); (ii) commensurate oppositely charged groups on a protein surface and an opposing crystal surface; and (iii) crystal faces that expose anionic groups with orientations that optimize the coordination of the cations shared with the protein. Later, however, it was determined that crystal-binding protein domains often do not contain β-pleated sheet conformations and/or optimal orientations of crystal anionic groups,72−74 suggesting that conditions (i) and (iii) were not necessary. More recent studies have revealed that the crystal surfaces require neither specific orientations of cationic groups, nor special, rigid, protein conformations, nor matching of charged 14048


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and {010} were found to be −193 and −(145−157) kJ/mol, respectively, suggesting stronger binding to {100}.86 In accord with experiment, simulations suggested stronger binding of the 86 D-Asp6 peptide than the L form to {010}. Molecular dynamic simulations predicted that binding of chondroitin sulfate, a urinary MM, decreased in the order {010} > {100} ≫ {121}̅ ,87 consistent with experimental data on growth inhibition by chondroitin sulfate.88 Calcium oxalate dihydrate (COD) is also found in kidney stones, although not as often as COM. The acidic OPN 86−93 peptide (DDLDDDDD) slowed the normal growth rate of COD {110} faces and was incorporated into the crystal, but its effect on growth rate of {101} was not significant.104 These observations were consistent with the higher Ca2+ surface density on {110}, as well as simulations that suggested stronger binding of this peptide to {110} (−98.0 kJ/mol) as compared to {101} (−10.5 kJ/mol). AFM tips decorated with carboxylate and amidinium groups adhered more strongly to COD {100} than to COD {101}, consistent with the stronger interaction of poly(acrylate) with the more Ca2+-rich {100} as compared to {101} (Figure 5).105 Collectively, these observations indicate that the {101} faces, with the lowest Ca2+ surface density, exhibit the weakest affinity for MM adsorbates. Hydroxyapatite (ApOH), a major component of bones and teeth with a complex variable composition, crystallizes pathologically as salivary and kidney stones. Investigations of ApOH interactions with MMs using microscopy have been limited by the small size of ApOH crystals. Most of our knowledge comes from bulk crystallizations, solid-state nuclear magnetic resonance (ssNMR), and computation. Equilibrium binding constants (K) measured using the constant composition method reveal that small molecules and short peptides are much more weakly adsorbed than proteins (Table 4). Growth inhibition, which is largely controlled by strongly bound additives, is not necessarily correlated with the magnitude of K, which reflects total surface coverage but does not distinguish between weakly and strongly bound adsorbates (Figure 3). For example, the K values of D6, SDESDE, and pSDEpSDE peptides on ApOH crystals are similar, but growth inhibition decreased in the order pSDEpSDE ≫ D6 > SDESDE. These differences are also consistent with calculated binding energies and desorption measurements, which supported strong binding of D6 and pSDEpSDE as compared to SDESDE.106 The conformations of macromolecules adsorbed on ApOH have been analyzed by CD spectroscopy for γ-carboxyglutamic acid-rich 36-residue synthetic peptide JAK1,119 by FTIR spectroscopy for Pro-rich protein,120 by ssNMR for Leu-rich amelogenin,121 and computationally using molecular dynamics for OPN related peptides77 and fibronectin.122 Statherin, a small protein with 43 amino acid residues (DpSpSEEKFLRR IGRFGYGYGP YQPVPEQPLY PQPYQPQYQQ YTF) that inhibits nucleation and growth of ApOH in saliva and serves as a lubricant at the enamel surfaces, was investigated most exhaustively.123 The acidic N-termini of statherin peptides containing two phosphorylated residues and three acidic residues were found to be primarily responsible for binding to ApOH by analyzing crystal growth inhibition, peptide adsorption, and ssNMR.115,124−126 The remaining segments of the protein are regarded as weakly bound.123,127 Statherin and its N-terminal peptide D1-G15 have similar adsorption constants K, and removing the N-terminal fragment reduced K (Table 4) as well as growth inhibition.115

electrostatic nature of interactions. The primary role of electrostatics, absent secondary structures, was revealed by simulations of phosphorylated peptides (e.g., pSpSpSEE) common to many proteins involved in ApOH biomineralization.78 Although the interaction between calcium salts and acidic proteins can be satisfactorily explained by electrostatic interactions between positively charged crystal surfaces and flexible anionic polyelectrolytes, the role of stereochemistry remains an open question. Calcium oxalate monohydrate (COM) is a major component of kidney stones.79 MMs are believed to be involved in all stages of stone formation.80 Asp- and Glu-rich anionic proteins, such as OPN (Table 3), adsorb to COM surfaces, inhibit crystallization (section 3.7), and become overgrown (section 4.1). Adsorption to faces decreases in the order {100} > {121̅} > {010} (Table 3).81−84 (Note: The crystal structure of COM has been reported in two crystallographic settings; for consistency, we use the P21/c setting; see footnote d in Table 3.) This ranking can be explained by the Ca2+ surface density on exposed faces, which can be described as truncations of the bulk crystal at the corresponding planes (Figure 4). Even if the COM surface is terminated by an emergent oxalate dianion and Ca2+ layer, the surface remains positively charged because one −COO− group is not exposed. The surface density of Ca2+ sites (which is equivalent to the density of oxalate sites) decreases in the order {100} > {121̅} > {010}, suggesting that {100} possessed more binding sites for Asp and Glu residues. Chemical force spectroscopy performed with AFM tips functionalized with carboxylate and amidinium groups corroborated this trend in binding site density for the three COM faces as well as the {100} and {101} faces of calcium oxalate dihydrate, COD (Figure 5).85 This ranking of adhesion

Figure 5. Dependence of the mean adhesion force on the surface concentration of Ca2+ (and C2O42− ions) on prominent COM and COD faces. Triangles and squares correspond to Au:S(CH2)10COO− and Au:S(CH2)2NHC(NH2+)NH2 functionalized AFM tips. Adapted with permission from ref 85. Copyright 2005 American Society of Nephrology.

forces, which is expected to be important in crystal−crystal aggregation and attachment to epithelial cells, provided a plausible explanation for the difference between the two compounds in the pathogenesis of kidney stones, where COM is much more commonly observed. Molecular dynamics simulations suggested that adsorption of a phosphorylated 65−80 peptide of rat bone OPN (pSHDHMDDDDDDDDDGD) on COM decreased in the order {100} > {121̅} > {010}, in agreement with electrostatic arguments.81 The binding energies of Asp6 peptides to {100} 14049


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Table 4. Adsorption of Various Additives onto ApOH Crystals additive Small Molecules citrate phosphocitrate L-aspartic acid L-glutamic acid L-serine phospho-L-serine Peptides peptide D6 peptide SDESDE peptide pSDEpSDE Mdm2 cysteine-rich peptide, 48 residues Saliva Proteins and Their Fragments cystatins statherin statherin peptide, residues D1−G15 statherin peptide, residues E5−G15 statherin peptide, residues G19−F43 proline-rich protein deposphorylated proline-rich protein dentin phosphophoryn deposphorylated dentin phosphophoryn Other Proteins albumin osteopontin

K, L/mmola

ref

130 270 0.2 0.2 317b 3.7−5.0

107 107 108,109 109 108 108,110

6.3 25 25 2580

106 106 106 111

420−455 700−1130 910 230 30 20200 1800 8640 4800

112 112−115 115 115 115 116 116 117 117

2280 1087

117 118

Figure 6. Model of statherin adsorption onto ApOH {001}. Upper panel: top view. The lower panel (side view) shows shape complementarity and charge distribution of statherin. Atom colors: green (Ca), orange (P), white (H), wine red (O of phosphate group), red (O of hydroxyl group). Reproduced with permission from ref 134. Copyright 2007 American Chemical Society.

thermal hysteresis ΔTd, can be as large as several degrees, and is used as a metric for freeze resistance and freeze tolerance in organisms. AFPs are responsible for the ability of bacteria to adhere to ice.23 The structures of active AF(G)Ps are varied, complicating structure activity correlations (Table 5, Figures 7 and 8).21,23,24,135−137 AF(G)Ps have been found in a variety of organisms, including diatoms,138−140 mushrooms,141 plants (Table 5),142 bacteria (Table 5),143 and fungi (Table 5). AF(G)Ps from polar fish were discovered first. They exhibit modest antifreeze activity with ΔTd ≈ 1.5 °C at cad = 3 mM,22 whereas ΔTd can reach 6.4 °C for insect and bacteria AFPs with cad as low as 0.003 mM.144 Antifreeze activity also was discovered recently in synthetic MMs,145 including peptides65 and peptoids.146 In the presence of adsorbates, a growing ice surface may be decorated with steps, in which the adsorbate forms a “fence” of pinning sites. Some have posited a two-dimensional “stones on a pillow” model (Figure 9).22 Thermal hysteresis observed for ice is linked to the Gibbs−Thompson effect associated with increased curvature of steps on ice surface. The curvature forms as the ice surface attempts to percolate between the arrays of strongly adsorbed AF(G)P molecules.22,212 The increased curvature raises the solid−liquid interfacial energy, which is directly proportional to the melting point depression. Most data fit the Cabrera−Vermilyea (C−V) step pinning mechanism (section 3.2.1; Figure 9), although alternatives have been proposed.213 In the framework of the C−V model, this leads to a doubled value of ΔTd as compared to the value predicted for the growth by flat faces. Ice crystals in the presence of AF(G)Ps adopt polygonal morphologies, consistent with layer-by-layer growth by advancement of steps, and the classic C−V approach with step pinning seems most appropriate. Comparing antifreeze activities of different AF(G)Ps is not straightforward because ΔTd depends on concentration cad (Figure 8). Luckily, in most cases, and, especially, at low

a

Adsorption constant, K, from the Langmuir isotherm. bUnusually high adsorption constant is associated with small surface coverage indicating selective adsorption on specific defects.

Ab initio simulations and ssNMR indicated that the conformation of statherin adsorbed onto the ApOH surface was comparable to that in trifluoroethanol/water mixtures.73,128,129 Simulations of statherin adsorption on ApOH {001}128 predicted that the N-terminal α-helix binds strongly to the surface and the residues near the surface were identified, in accord with ssNMR data (Figure 6).127,130−132 These residues bind to the surface via H-bonding, van der Waals attraction, electrostatic interaction, and geometric complementarity (Figure 6).130−132 Isothermal titration calorimetry gave a small enthalpy of adsorption (∼13 kJ/mol) at low protein coverage that decreases to zero at θ ≈ 0.25.113 Nevertheless, there must be an entropic contribution due to expulsion of water and ions from the crystal surface.73 Calorimetry and ssNMR133 were consistent with more than one adsorption mode for statherin mutants due to conformational heterogeneity of the protein and/or heterogeneities on the ApOH surface, facts that argue against strict stereochemical control.114 Positively charged residues (K6, R9, R10, R13) were reported to be particularly important for reducing protein−protein charge repulsion and for providing higher surface coverage.114 2.2.2. Ice. Among the crystals discussed here (Table 1), ice is unique in that it usually crystallizes from the melt and at high homological temperatures, when most faces are thermally roughened. Ice growth is inhibited by small concentrations of antifreeze proteins (AFPs) and antifreeze glycoproteins (AFGPs, or AF(G)Ps taken together) that induce large noncolligative freezing point depressions. Melting points, however, exhibit only minor changes by comparison. The difference between freezing and melting points, the so-called 14050


14051

a

Mw, kDa

23 12

grass Lolium perenne

25, dimers in solution 28

23.5

∼1500; fragment studied: 34 26

6.5 and 15.7

3.5 and 8.3

13

8.4 9−12

7, dimer 14 12.3 1.2−33.7

3.3−5 up to 16.7 14−24

psychrophile Antarctomyces psychrotrophicus snow mold fungus Typhula ishikariensis

Arctic yeast Leucosporidium

Antarctic bacterium Flavobacterium frigoris Antarctic bacterium Colwellia

Antarctic bacteriumMarinomonas primoryensis

inchworm larvae of the pale beauty geometer moth, Campaea perlata snow flea, Hypogastrum harveyi

Tenebrio molitor beetle Choristoneura fumiferana moth, spruce budworm Rhagium inquisitor longhorn beetle

winter flounder, shorthorn sculpin, yellow-tail flounder, and Alaskan plaice sea raven, rainbow and Japanese smelt, Atlantic herring, longsnout poacher ocean pout, eel pout longhorn sculpin cod fish and synthetic

source

162−166

C-type lectin fold of mixed α, β, and loop structure; can be Ca2+ dependent or independent globular protein containing short β-strands probably helix bundle structure; 17% Gln tripeptide (Ala-Ala-Thr)n, n = 2−52 with disaccharide attached to Thr forms left-handed helix with disaccharide residues on the same side

193

left-handed superhelix representing β-sandwich of two parallel 6- and 7stranded β-sheets containing Thr-X-Thr-X-Thr-X-Thr β-helical structure containing Thr-X-Thr-X-Thr-X-Thr-X-Thr, most X = Ala 6 and 12−13 left-handed polyproline type II helices stacked in two antiparallel groups; Gly 45%; Gly-Gly-X or Gly-X-X motif

1.5

0.5−27 {0001},{101̅0}, dipyramid

{0001} and prism

207−209 210

right-handed β-helix; no clear motif left-handed β-helix 14 aa repeats containing Asn-X-Val-X-Gly

dipyramids

∼2

207

203−206

right-handed β-helix; no clear motif

preferentially {0001} and {101̅0}

1−22

n/d

201,202

right-handed β-helix; no clear motif

multiple orientations

n/d

137,200

1100− 9000 390

right-handed β-helix containing Thr-Ala/Gly-X-Thr/Asn

194−197

144

185−188 188−192

right-handed β-helix with 12−13 aa repeats containing Thr-Cys-Thr left-handed β-helix with 15 aa repeats containing Thr-X-Thr

167−174 175,176 177−184

60,147−161

ref

α-helical Ala-rich; contain 11aa repeats Thr-X2-Asx-X7, most X = Ala

structure

198,199

all orientations

all orientations

n/d

all orientations

n/d {0001} and {1010̅ }

dipyramids {2021̅ } {101̅0} and {0001}; low concn of high Mw {41−50}; synthetic, low Mw dipyramid

dipyramids or {0001} and prism

{202̅1}, rare {21̅1̅0}

binding faces

right-handed Ca2+ bound β-helix with 19aa repeats and Thr-X-Asn motif

840

87 and 1720

1000− 1750 46700

560−1040 80−950

1.2−3.4 0.7 4 × 10−4 to 21b

0.2−0.6 up to 1330 0.3−7.6

Ka, L/mola

Apparent adsorption constant, Ka, was estimated from eq 5. bΔTd and Ka strongly depend on Mw. See Figure 28.

TisAFP Plants LpAFP

AnpAFP

ColAFP Fungi LeAFP

FfAFP

Bacteria MpAFP

sfAFP

iwAFP

RiAFP

Insects TmAFP CfAFP

AFP III AFP IV AFGP

AFP II

Fish AFP I

type

Table 5. Antifreeze Proteins and Glycoproteins

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Figure 7. Molecular structures of typical AFPs. AFP I (pdb code 1WFA);155 hyp AFP I (pdb code 2KE2);161 AFP II (pdb code 2AFP);162 AFP III (pdb code 1MSI);169 TmAFP (pdb code 1EZG);187 RiAFP (pdb code 4DT5);193 MpAFP (pdb code 3P4G);199 LeAFP (pdb code 3UYU);204 FfAFP (pdb code 4NU2);137 ColAFP (pdb code 3WP9);202 TisAFP (pdb code 3VN3);208 sfAFP (pdb code 2PNE);197 LpAFP (pdb code 3ULT).210 The variety of structures perform one and the same function, to decrease freezing temperature, thus illustrating convergent evolution.137 Structure of CfAFP is shown in Figure 11. See also Figure 3 in ref 136, Figure 3 in ref 23, and Table 1 in ref 24.

underestimation of K include the following: (i) θeq is not achieved because of insufficient time and (ii) the adsorption/ inhibition model assumes a single infinite surface, but thermal hysteresis is measured for a whole crystal, which has multiple faces, edges, and corners. These complications are considered below and in section 3.3.2. Although some argue that AF(G)Ps bind weakly (reversibly),214,215 recent studies suggest that adsorption is strong and virtually irreversible.48,63,174 Experimental determinations (Table 7), however, afford θ < 0.25. Small surface coverage can be explained by surface exposure times much shorter than the characteristic adsorption time, τs ≪ τ0, as confirmed by low rates of AF(G)P adsorption (Table 2).48,59,170 Moreover, the maximum surface coverage may be less than unity (θmax < 1) if an antifreeze protein molecule is encumbered by conjugation with inactive components such as green fluorescent protein (GFP), which is often used to measure adsorption quantitatively. The effect of exposure time was recently illustrated by comparing antifreeze activity measured using nanoliter cryoscopy (a common technique to measure ΔTd) and sonocrystallization.216,217 These investigations showed that Ka values obtained from eq 5 are substantially smaller than the actual K and can be used only for comparing relative values of ΔTd measured for different AF(G)Ps using an identical protocol. At low supercoolings (ΔT < 0.4 °C), ice forms thin circular disks with large {0001} faces. The circular shape is a consequence of thermal roughening that obviates surface energy anisotropy associated with peripheral crystal planes

AF(G)P concentration, ΔTd ∝ cad (see section 3.3.2). More explicitly, antifreeze activity of different additives can be compared using the apparent adsorption constant, Ka, calculated from eq 5, which was deduced from the C−V model described later (eq 17) and Henry’s adsorption isotherm (eq 4), assuming the contact area of the adsorbed molecule is Lad2 = Lad,minLad,max. The maximum and minimum sizes of the molecule Lad,max and Lad,min were estimated from structural data in Table 5. The numerical factor 2460 in eq 5 is expressed in K2 nm2, calculated with Tm = 273.15 K, heat of fusion divided by molecular volume Λ/ω = 3.3 × 109 erg/cm3, and surface energy γ = 30 erg/cm2. The terms cad is expressed in mol/L, Lad is in nm, and ΔTd is in kelvin. ⎛ ΔT Λ ⎞2 Lad,minLad,max ΔTd2Lad,minLad,max Ka = ⎜ d ⎟ ≈ cad 2460cad ⎝ 2γωTm ⎠

(5)

−4

The calculated values of Ka ranged from 4 × 10 to 5 × 104 L/mol (Table 5). An accurate determination of the adsorption constant K was performed only for dipyramidal faces exposed to GFP-AFP III,48 where Langmuir-type adsorption kinetics (eq 2) were observed with k+ = 0.008(1) μM−1 s−1. Although irreversible adsorption was claimed (k− = 0), a better fit to the data was achieved with k+ = 0.007 μM−1 s−1 and k− = 0.005 s−1, corresponding to K = 1.4 × 106 L/mol. This value is near that reported for some of the strongly adsorbing proteins in Table 4, but much larger than Ka’s deduced from the thermal hysteresis in Table 5. For AFP III, Ka = 1.2 L/mol, or 6 orders of magnitude less than K. Possible reasons for the substantial 14052


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Figure 9. Growth inhibition by immobile stoppers (black balls). (A− D) Step propagation in the frame of the classical Cabrera−Vermilyea model for layer-by-layer growth on flat surfaces. See section 3.2.1 for more details. (E−H) “Stone on a pillow” model for atomically rough curved surfaces.

IV)152,166,169,173,176 (Figure 10A,B,D−F) as well as for fungi AnpAFP.207 This was also confirmed by the luminescence distributed around growing ice crystals for GFP-AFP III,219 fish AFGPs,183 some insect,190 plant,210 fungi,208 and sometimes fish type II164 AFPs that exhibit preferred adsorption on the basal face {0001} and prismatic faces (usually {101̅0} but also {21̅1̅0} and higher index) (Figure 10G−I). Hyperactive fish,161 insect,193,210 and bacterial199 AFPs adsorb to all faces (Figure 10J−L). Adsorption to {0001} faces was directly detected in situ by fluorescence microscopy for GFP-TmAFP,48 GFPCfAFP, GFP-RiAFP, and GFP-MpAFP.64 Growth morphologies observed in the presence of various proteins are summarized in Table 5.220 When supercooling exceeds ΔTd (i.e., by lowering the temperature below the hysteretic freezing point), crystals begin to grow. Growth becomes fast and dendrites are observed, behavior described as “bursting”. Fish AF(G)Ps that adsorb to the {202̅1} cause growth bursts at the apexes along the [0001] direction.22,154,221 Moreover, at the tips of ice crystals formed in the presence of fish AFPs, often there are very small {0001} faces, which do not adsorb fish AFPs. ΔTd increases as the size of the {0001} faces decreases, as measured by the temperature at which bursting is observed.219 Although the reason for this behavior is not understood, it was suggested that small faces limit formation of new growth steps. When the crystal was blocked in the [0001] direction by container walls, ΔTd increased significantly (from 0.05 to 0.09 to 0.08−0.22 °C; AFP III, cad = 1−8 μM).219 Hyperactive insect and bacteria

Figure 8. Dependence of thermal hysteresis, ΔTd, on antifreeze concentration, cad. (A) Fish antifreeze proteins: (★) AFP I from winter flounder;151 (magenta ⬠) Ca2+ independent AFP II from longsnout poacher;166 (●) synthetic AFP III;168 AFP IV from longhorn sculpin;175 from Antarctic and saffron cod (▼) AFGP 7.9 kDa, (▲) 10.5 kDa AFGP, and (◆) 28.8 kDa AFGP.181 (B) Hyperactive antifreeze proteins: (★) insect common yellow mealworm beetle TmAFP;185 insect spruce budworm (●) 9 kD CfAFP and (■) 12 kDa CfAFP;191 (◆) AFP I from winter flounder;60 (▲) RiAFP from longhorn beetle;211 (magenta ■) LpAFP from freeze-tolerant grass;210 (aqua ⬠) FfAFP from Antarctic bacterium;137 (▼) sfAFP from snow flea;196 (+) bacterium ColAFP.202 (C) Fungi and diatom antifreeze proteins. (▲) LeAFP from Arctic yeast;137 (■) TisAFP from snow mold fungus;207,209 (●) NagAFP from Antarctic sea ice diatom209 (point ΔTd = 3.1 °C at cad = 1.49 mM was cropped to avoid significant compressing of the scale).

(Figure 10C). At larger supercoolings, ice crystals become morphologically unstable and exhibit highly branched dendritic morphologies. AF(G)Ps adsorb to specific crystal planes, which can stabilize certain polygonal morphologies, however. Preferential adsorption can be established by growing singlecrystal ice hemispheres in the presence of protein and then subliming the external layer of ice. During sublimation, the ice surface becomes mirror smooth except for areas where protein was incorporated (Figure 10A,B).152,218 Alternatively, protein binding sites have been visualized directly by fluorescence (Figure 10D,E,G,H,J,K). Adsorption to dipyramidal faces {h0h̅1} (mostly h = 2) is typical for fish AFPs (types I− 14053


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observations suggest that crystal faces are still within the thermal hysteresis gap but crystallization starts at faces, edges, and apexes, which have less uniform protein coverage and more sources of new growth layers. Investigations aimed at understanding adsorption at the molecular level were first performed for the α-helical AFP I from a winter flounder isoform that included the 37-residue sequence DTASDAAAAAALTAANAKAAAELTAANAAAAAAATAR. Eleven amino acids form an α-helix, exposing hydrophobic, hydrophilic, and Thr-Asx surfaces (Asx = aspartic acid or asparagine). Originally, adsorption of AFP was thought to be driven by formation of hydrogen bonds between ice and residues of the Thr-Asx side,155,159,160,180 supported by an apparent commensurate relationship between Thr residue spacing (16.5 Å), three α-helix complete turns (16.2 Å), and the ⟨011̅2⟩ direction in the {202̅1} plane (16.7 Å),152 consistent with Monte Carlo simulated annealing and energy minimization in vacuum.222,223 Experiments with mutants, however, suggested that adsorption is not related to hydrogen-bonding sites on the Thr-Asx side.151,157,224,225 The replacement of the four Thr residues with Ser, which eliminates methyl groups while leaving hydroxyl hydrogen-bonding groups intact, severely compromised antifreeze activity,157 whereas replacement of Thr with Val (replacing −OH with −CH3) only slightly decreased antifreeze activity.156,226 Increasing hydrophobicity by replacement of Ala with Leu (isopropyls replacing methyls) on the hydrophobic side reduced antifreeze activity.151 These observations suggested a significant role for van der Waals and hydrophobic interactions,151,156,157,225 which was corroborated afterward by computation.227−232 A Monte Carlo energy minimization of AFP adsorption along ⟨011̅2⟩ in {202̅1}229 performed in vacuum suggested binding via formation of hydrogen bonds with the Thr-Asx side of AFP. Simulations in water, however, showed AFP binding via Thr methyl groups on the hydrophobic side. Thr hydroxyl groups and the hydrophilic side chains of Asx were now exposed to the solution. Subsequently, the recognition of the importance of hydrophobic interactions was confirmed by comparing antifreeze activities for mutants, docking, and molecular dynamics simulations, as well as the analysis of complementarity of the AFP putative ice binding site and the ice surface166 for AFP III,233 CfAFP,189,192 TmAFP,234 RiAFP,193 iwAFP,144 sfAFP,196 FfAFP,137 LeAFP,137,204 TisAFP,208 and ColAFP.202

Figure 10. (A−K) Single-crystal ice hemispheres with AFP. [0001] parallel (A,D,G,J) and perpendicular (B,E,H,K) to the plane of the hemisphere. All hemispheres are about 5 cm in diameter. (C,F,I,L) Typical morphologies of ice crystals grown at small supercooling without antifreezes (C) and with AFP I (F), LpAFP (I), and MpAFPsegment IV (L). (C,F,I,L) reprinted with permission from refs 151, 169, 199, and 210, respectively. Copyright 1996 Nature Publishing Group, 1999 Wiley-VCH, 2012 Elsevier B.V., and 2011 National Academy of Sciences, respectively. (A,B) Etching pattern obtained with winder flounder AFP I. Reproduced with permission from ref 152. Copyright 1991 Elsevier Ltd. (D,E) Fluorescence of tetramethylrhodamine labeled AFP I. Reproduced with permission from ref 199. (G,H) Fluorescence of GFP labeled LpAFP. Reproduced with permission from ref 210. Copyright 2012 Elsevier B.V. (J,K) Fluorescence of GFP labeled MpAFP-segment IV. Reproduced with permission from ref 199. Copyright 2011 National Academy of Sciences.

AFPs adsorbed to the {0001} and prismatic planes result in bursting only in directions perpendicular to [0001].221 These

Figure 11. Complementarity between CfAFP and {101̅0} (A,B) and {0001} (C) ice surfaces. Reproduced with permission from ref 190. Copyright 2000 Nature Publishing Group. 14054


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The topography of AFPs may play an important role in ice crystallization. β-Solenoid AFPs from insects, bacteria, fungi, and plants (Table 5) express flat patches rich in Thr, Val, and Ala. The spacing between β-strands (4.5−4.75 Å) is commensurate, or nearly so, with the lattice parameter a = 4.52 Å that defines the periodicity on the {101̅0} and {0001} planes. The spacing between ice-binding residues in TmAFP, CfAFP, and MpAFP varies from 7.35 to 7.45 Å, comparable with the periodicity along [0001] (c = 7.36 Å), which resides in the {101̅0} planes, and comparable with the 7.8 Å periodicity along [112̅ 0 ] in the {0001} planes (Figure 11). A commensurate relationship does not appear to be critical for FfAFP, LpAFP, and RiAFP, indicating that an epitaxial match is not a prerequisite for strong adsorption of an AFP to an ice surface. Comparison of antifreeze activities with areas of ice binding sites on the surfaces of β-solenoid AFPs (Figure 12)

Figure 13. Oxygen density profiles, ρ0(z) [g/cm3] perpendicular to ice−water interface simulated using molecular dynamics for (a) basal {0001}, (b) prism {1010̅ }, (c) dipyramidal {2021̅ }, and (d) prism {21̅1̅0} faces. The bulk-ice structure is gradually replaced with the bulk-water structure as z coordinate increases. Reproduced with permission from ref 238. Copyright 2002 The Royal Society of Chemistry.

surrounding the ice binding site for RiAFP,193 LpAFP,210 MpAFP (Figure 14),198,199 hyperactive fish AFP I,161 and AFP III.244 These findings have suggested an anchored “clathrate” mechanism243 in which an AFP molecule preorders water molecules around the ice binding site to form an ice-like motif, which serves as a crystalline bridge between the AFP molecule and bulk ice. The absence of ice-like ordering around other areas of the AFP surface prevents the AFP molecules from becoming overgrown, however. Collectively, the investigations of ice growth in the presence of antifreeze proteins suggest that activity is favored by the following characteristics: (i) Ice binding that relies on hydrophobic character, contributing to an entropic gain for ice−AFP binding. (ii) An ice binding site with a shape complementary with the ice surface, wherein the binding site is flat and the spacing between ice binding residues matches lattice spacings on the relevant ice surfaces. (iii) Ice binding sites that are partially hydrophilic, enabling formation of hydrogen bonds that organize water molecules on the protein surface. Threonine is a strong candidate in this respect, but amino acid residues with nonpolar side chains such as Ala and Val may be suitable due to the proximity of carboxylate groups with the protein backbone. (iv) Nonbinding hydrophilic surfaces in the AFP that provide aqueous solubility, inhibit protein aggregation, and suppress incorporation by disrupting ice-like water around the AFP molecule so that overgrowth on the exposed surface of the protein is unfavorable. (v) An AFP sufficiently rigid so as to complement the ice surface with minimal requirement for structural changes. The associated entropic penalty is minimized. 2.2.3. Molecular Crystals. The sections above illustrate that protein−crystal interactions can be described as two extremes, one in which adsorption does not rely on welldefined secondary structure, as reported for calcium salts with flexible polyelectrolytes, and the other in which adsorption invokes well-defined secondary structure (e.g., α-helices and βsheets), as reported for ice. This distinction was highlighted in the review by Evans cited in the Introduction.25 Organic molecular crystals exhibit a wide range of intermolecular interactions. For example, adsorption of proteins

Figure 12. Apparent adsorption constants (eq 5) as a function of ice binding site area for a series of β-solenoid AFPs. Sequence below AFP abbreviation denotes ice-binding motif; symbol “---” means the absence of a clear motif. The binding site areas were from ref 193 for TmAFP, smaller CfAFP, LpAFP, MpAFP, RiAFP, and from ref 137 for FfAFP and LeAFP. The binding site areas for ColAFP, TisAFP, iwAFP, and larger CfAFP isoform were estimated from data in refs 144, 191, 202, and 208, respectively. Red ▲ are AFPs with TXT binding motifs. The ■ are AFPs with similar 1°, 2°, and 3° structures. LpAFP and MpAFP are outliers.

suggests that (i) antifreeze activity increases with increasing area of ice binding site for AFPs having ice binding sites with similar structures; for example, insect AFPs with threonine-aathreonine (TXT) ice binding motifs; (ii) repetitive binding motifs exhibit more pronounced antifreeze activity due to higher Ka values as compared to less regular motifs; and (iii) antifreeze activity is sensitive to fine differences in protein structure; proteins FfAFP, ColAFP, TisAFP, and LeAFP are characterized by similar 1°, 2°, and 3° structures (Figure 7), but exhibit different activities. A strict, supramolecular interpretation of AF(G)P inhibition may prove to be a fool’s errand because the ice−water interface is not well-defined as it gradually transforms to water over 10− 20 Å235−238 (Figure 13). This complication has inspired analyses of water ordering around AFPs rather than direct AFP binding.239−243 Simulations have revealed that the water structure surrounding ice binding sites of AFP I,230,241 AFP III,239,240,242 CfAFP,243 and RiAFP193 adopts an ice-like order, whereas other sides of AFP molecules are solvated by disordered water. Attempts to understand the now familiar SSSS, VVVV, and AAAA activities in terms of water ordering241 have confirmed, by X-ray diffraction, structured water 14055


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Figure 14. Ordered surface waters on the ice binding site of MpAFP molecule as revealed from single-crystal X-ray diffraction analysis. (A and B) Two sections of MpAFP freely exposed to solvent in the unit cell. (C) Ordered surface waters hydrogen bonded to the ice binding site. (D) Asp residues on the ice binding site mimic surface waters and also assist in the coordination of two water molecules. (E and F) The organized surface waters make an excellent three-dimensional match to both the basal {0001} (E) and the prism {101̅0} (F) planes of ice. Red circles = oxygen of water molecules in bulk ice structure; cyan circles = oxygen of water molecules bound to MpAFP molecule; green circles = Ca2+ ions. Reproduced with permission from ref 199. Copyright 2011 the authors.

demonstrated a high degree of selectivity and could even distinguish heterochiral surfaces. It is difficult to determine the structures of macromolecular adsorbates on surfaces experimentally.253 Antibodies, however, typically are robust, to the extent that their structure can be expected to remain conserved when binding to a crystal surface, enabling recognition of the crystal surface by a unique and well-defined protein binding site. Antibody 122B1 was reported to bind preferentially to {101}̅ of 1,4-dinitrobenzene.254 Antibody 36A1 binds selectively to the {h01} of cholesterol monohydrate, especially the {301}.255 This was mirrored by its high affinity for monolayers of cholesterol and its enantiomer, ent-cholesterol, at the air−water interface, although the affinity was negligible for monolayers of epicholesterol.256 Antibody 48E selectively bound to the {01̅1} faces of monoclinic crystals of L-Leu-L-Leu-L-Tyr peptide but did not bind to crystals of the enantiomer D-Leu-D-Leu-D-Tyr. Antibody 602E was found to be less selective, binding to all faces except {001} of both L-Leu-L-Leu-L-Tyr and D-Leu-D-Leu257 D-Tyr crystals. Molecular modeling (Figure 15) revealed significant differences among the possible antibody−crystal combinations with respect to the relative contributions of electrostatic interactions and structural complementarity.255,258,259 The binding to, and incorporation of, MMs in molecular crystals is of considerable importance to the characterization of MMs. Matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF-MS) relies on a small quantity of an analyte (e.g., peptides, proteins, polysaccharides, and nucleic acids) adsorbed or incorporated by a suitable crystalline molecular crystal host by precipitation. In a typical measurement, the host is irradiated by a laser, and subsequent energy transfer to the analyte results in the formation of a plume containing ionized, intact MMs for mass analysis.260 Common hosts include nicotinic acid, sinapic acid, 2,5-

on crystals of zwitterionic cystine may be dominated by Coulombic interactions, which can be strong even in the absence of a commensurate protein−crystal interface. The density of NH3+ and COO− groups on {0001} is twice that on {101̅0}, which would be expected to favor greater binding affinity of ionic species for {0001} faces. Indeed, BSA adsorbs on cystine {0001} faces more strongly than on {101̅0}.54 Gold nanoparticles decorated with carboxylate groups exhibited the same selectivity.245 In contrast, gas hydrates, ice-like clathrate structures that crystallize inside wellheads and pipelines, posing serious problems for the petroleum industry, are thought to behave in a manner similar to that of ice crystals with respect to adsorption of antifreeze proteins. This proposition is based on studies of tetrahydrofuran (THF), which is considered to be a mimic for gas hydrates because its crystal structure consists of cages resembling those observed in ice-clathrates. A good mimic for gas hydrates can adsorb a series of antifreeze proteins including AFP III, LpAFP,246 and hyp AFP I.247 The internal clathrate water network of the hyp AFP I, which extends to the protein’s outer surface, resembles the {100} planes of THF, allowing strong adsorption by the mechanism, which is very similar to that established for ice.247 A crystal within an organism may be recognized by the immune system as an antigen, leading to the creation of antibodies. An antibody-binding site, with a typical area of 6−9 nm2, can span several molecules on a crystal surface, suggesting potential for stereospecific interactions with crystal faces. For example, mice have been injected with a suspension of crystals of monosodium urate monohydrate,248 allupurionol, magnesium diurate octahydrate,249 1,4-dinitrobenzene, cholesterol monohydrate, and a simple tripeptide. The antibodies raised against these “crystal antigens” were extracted, purified, and added to solutions of the antigenic crystals.250−252 Some antibodies did not bind to the crystals and some adsorbed nonspecifically to all crystals and surfaces, but some 14056


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Calcite: polysilicic acid,264 nacre-specific proteins,265 the mollusk shell protein asprich,266,267 abalone shell proteins,268 ovalbumin,269,270 and diblock (poly(methacrylic acid)-benzyl methacrylate) copolymer.271 COM: peptides (D3G)6D3 and (D3S)6D3,51,98 OPN,91,98 and THP.98 Tetragonal lysozyme: ovotransferrin, ovalbumin, and lysozyme dimer.66,272 L-Cystine: ChS, apotransferrin, OPN, and human serum albumin (HSA).54 Protein aggregates can achieve sizes ranging from tens of nanometers to several micrometers, though the precise composition is rarely known and aggregates may be admixed with inorganic components such amorphous calcium carbonate.265,266,270 Aggregate surface coverage often grows with time. Aggregation on the surfaces of calcium salts is sufficiently rapid that it can be observed by in situ AFM, which has shown that self-association can be facilitated by a crystal surface. Aggregates also form on lysozyme and L-cystine crystals within a few days, but they appear to form in solution and then deposit on the crystal surface. Aggregate adsorption can be face-specific. Aggregates of OPN or THP were reported to form on COM {100}91,98 with the formation of rippled films upon increased time of exposure to the surface (Figure 16A,B). In contrast, aggregates were not observed on {010}, but at high protein concentration the surface became covered with the uniform layer of adsorbate (Figure 16I,J). Protein aggregates do not appear to interfere with the advancement of steps on key faces of calcite, COM, and lysozyme; for example, OPN aggregates adsorb on COM {100}, but growth steps appear to pass below them (Figure 16C−E), effectively lifting the aggregate layer-by-layer.91 In contrast, protein aggregates became incorporated within Lcystine crystals, as the crystal grows around the bound aggregate until a sufficient number of crystal layers has matched the height of the aggregate and affects overgrowth.54 Cells are highly evolved, complex structures that contain macromolecular aggregates, intracellular and extracellular. Kidney epithelial cells attach to crystals of calcium tartrate triand tetrahydrates,251,273−277 binding to (R,R)-calcium tartrate tetrahydrate in preference to its (S,S) isomer, while adhering to {011} but not {101} (Figure 17).274,275,277 The enantioselectivity was not controlled by fibronectin (the principal extracellular protein involved in cell adhesion), albumin, or the polysaccharide dextran. Hyaluronan, an abundant, ionic polysaccharide produced by cells, exhibits the same enantioselectivity as the epithelial cells.251,277 Cells also interacted selectively with the (R,S)-calcium tartrate trihydrate facets.276 On {100}, which contains bound crystallographic water molecules, the cells were motile, tended to form multicellular aggregates, did not spread, and developed protrusions into the crystals along imperfections. On the hydroxyl-rich {011}, the cells were immobilized and died. In contrast, cells spread rapidly on other {0kl} faces that exposed both hydroxyl and carboxylate groups. COD crystals were observed to nucleate on the surface of cultured renal epithelial cells with the {100} faces contacting the cells.278 This observation is consistent with higher density of positive charges on {100} and thereby stronger attachment to anionic sites on the cell surface. COM,279−285 ApOH,286 and uric acid287 crystals also bind to renal epithelial cells. Calcium salts presumably bind to anionic sites of the cells (glycoproteins

Figure 15. Docking of three antibody binding sites (polar residues are orange, hydrophobic are yellow, aromatic are purple, and backbone is gray) on the surfaces of the respective crystals (green (C), red (O), blue (H2O in (A) and N in (B,C))): (A) 36A1 on the (301) face of cholesterol monohydrate; the molecular step on the crystal has a hydrophilic and a hydrophobic side, matched by the antibody binding site with hydrophilic and hydrophobic groups. (B) 122B1 on 1,4dinitrobenzene (101̅); the aromatic groups exposed edge-on in a stacked herringbone motif with respect to the flat crystal face are well matched by five aromatic side chains and various polar groups of the antibody. (C) 48E1 on (011̅ ) face of L-Leu-L-Leu-L-Tyr peptide; the hydrophobic and hydrophilic groups exposed on the surface along the groove walls and the ridge surface are matched one-to-one by the antibody. Reproduced with permission from ref 252. Copyright 2008 American Chemical Society.

dihydroxybenzoic acid, 3-hydroxypicolinic acid, and succinic acid. There is a debate about whether MMs must be overgrown or merely adsorbed onto MALDI host crystals.261,262 Either circumstance appears to be sufficient for the success of this analytical method.263 2.3. Macromolecular Synergies

Life relies on macromolecular aggregation, and MMs working synergistically can enrich and complicate interactions with growing crystals. Aggregates have been found to affect the growth of calcium salts, molecular crystals, and protein crystals themselves (Figure 16), including the following. 14057


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Figure 16. Deposits on growing crystal surfaces. (A−E) Sequential AFM images showing the effect of 5 nM OPN on growth hillock morphology of COM {100}. Reproduced with permission from ref 91. Copyright 2004 National Academy of Sciences. (C−E) Temporal evolution of step train and protein adsorbates. (F) AFM images of adsorbates on the calcite {101̅4} with 10 μM AP24-N, N-terminal mineral binding domain of nacre-specific protein. Inset shows additive-free surface morphology. Reproduced with permission from ref 265. Copyright 2006 American Chemical Society. (G) Ex situ AFM image of two types of adsorbates (depicted by black and white arrows) on tetragonal lysozyme {011} with other proteins. Inset shows impurity-free surface morphology. Reproduced with permission from ref 66. Copyright 2013 American Chemical Society. (H) SEM of L-cystine with 5 μg/mL ChS. Reproduced with permission from ref 54. Copyright 2016 American Chemical Society. (I−L) AFM images of COM crystals. Reproduced with permission from ref 98. Copyright 2009 Springer. (I,J) {100} face; 1.5 and 4.5 min of exposure to 100 nM THP, respectively. (K,L) {010} face; 1 h exposure to 10 and 75 nM THP. (M) AFM of L-cystine (0001) with HSA aggregates on the surface that become overgrown. Courtesy of T. Mandal.

Table 6. Effect of Additives on Adhesion of Cells to COM, Ap(OH), and Uric Acida half-maximum concentration, μMb additive Anions chondroitin sulfate A heparin polyaspartic acid polyglutamic acid polyvinyl sulfate chondroitin sulfate B dextran sulfate heparan sulfate hyaluronic acid nephrocalcin osteopontin pentosan polysulfate phosphocitrate sodium citrate Tamm−Horsfall protein Cations alcian blue brilliant blue R cationized ferritin cetylpyridinium chloride polyethylenimine Triticum vulgaris lectinc

Figure 17. Scanning electron micrographs of calcium-(R,R)-tartrate tetrahydrate (left) and the (S,S) enantiomorph (right) after incubation with epithelial cells. The respective molecular formulas are below the crystals. Cells adhere rapidly, strongly, and densely only to the crystals of (R,R), and only to {011}. Reproduced with permission from ref 251. Copyright 2003 The Royal Society of Chemistry.

containing sulfate esters, sialic acid, uronic acid, anionic phospholipids, and hyaluronan),280,286,288−290 whereas adhesion of uric acid crystals is believed to be mediated by hydrogen bonds and hydrophobic interactions.287 Adhesion of crystals can be inhibited by polyanions and polycations (Table 6). Polycations block anionic sites of the cells, whereas polyanions adsorb to the crystal surfaces. Consequently, both can play a role in regulating crystal adhesion to cells. Renal cell pretreatment with trypsin, proteinase K, neuraminidase, and wheat germ agglutinin decrease adhesion to COM and ApOH crystals, presumably by blocking anionic sites with specific cations.280,286,287 Biology can intrude upon purely physicochemical mechanisms, as cells can permit feedback. For example, arachidonic acid and prostaglandins can raise intracellular concentrations of secondary messengers in renal cells that can regulate (decrease) adhesion to COM crystals.283

COM

ApOH

uric acid

0.6 0.02 0.1 0.01 0.02 0.1 0.01 0.9 0.05 0.02 0.02 0.02 50 200 NI

15 0.1 0.007 0.1 0.08 1.5 0.2 5.0 0.05 0.08 0.01 0.08 10 100 NI

0.15 0.02 0.01 0.4 0.02 NI NI NI NI NI NI NI NI NI NI

50 90 0.9 15 0.001 100

70 15 0.5 90 0.2 90

9 60 0.6 60 1.0 NI

a

Data from ref 287. NI: no inhibitory activity is detected. Concentration of the additive at which adhesion is 50% of the initial value. cConcentration is expressed in μg/mL.

b

It is now widely appreciated that crystals can grow by the accretion of smaller crystals in near crystallographic register.4 MMs coating a crystal surface can promote aggregation, crystallographic or otherwise, but they can also inhibit crystal aggregation. Aggregation is dependent on MM adsorption but must also account for MM−MM interactions. For example, 14058


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Figure 18. Mechanisms of impurity/additive influence on crystallization kinetics. Black lines show step kinetics of pure materials. Blue and red lines correspond to kinetic perturbations for different types of impurities.

⎛ ⎞ Δμ = ln⎜⎜∏ cimi /KSP⎟⎟ R gT ⎝ i ⎠

aggregation underlies kidney stone formation80 and has been studied intensively in the context of calcium oxalate.56,291,292 As our focus here is on single-crystal growth, we eschew polycrystalline objects.

(7)

and the growth velocity is described by eq 7a: ⎛ ⎞ V = β ⎜⎜∏ cimi − KSP⎟⎟ ⎝ i ⎠

3. CRYSTALLIZATION KINETICS 3.1. Growth Parameters

It has long been established that MM additives inhibit crystallization of calcite, calcium oxalates, and other crystalline phases. The mechanism responsible for the influence of additives on crystal growth can be indicated by the interplay of step propagation velocity and geometric features such terrace width (Figure 3) and surface roughness.19,293 The step velocity, V, which is related to the crystallization driving force by the kinetic coefficient, β, is described by eq 6: c − ceq V = β Δc = β(c − ceq) = β′ ceq (6)

(7a)

where KSP is a solubility product, and ci and mi are the concentrations (activities) and stoichiometric coefficients of all species in the chemical formula, respectively.294,295 In the case of crystallization from stoichiometric solutions, eq 7a is reduced to eq 7b: n V = β(c n − ceq )

(7b)

where n is number of all species in the chemical formula. For practical reasons, typically eq 7c is used:19 ⎞ ⎛⎛ ⎞1/ n ⎜ mi ⎟ 1/ n⎟ ⎜ V = β ⎜∏ ci ⎟ − KSP ⎟ ⎜⎝ ⎠ ⎠ ⎝ i

in which c is the solute concentration and ceq is the equilibrium solubility (zero supersaturation). The term Δc therefore represents the supersaturation. Equation 6 can be replaced with V ≈ β′Δμ/RgT, where Δμ is the difference in chemical potential at concentration c and ceq, β′ = βceq, Rg is the universal gas constant, and T is the absolute temperature. Expressed in this manner, Δμ/RgT = ln(c/ceq). At high driving force for crystallization (c ≫ ceq), ln(c/ceq) is not a good approximation of (c − ceq)/ceq, and it is more appropriate to use eq 6. There are additional complications for ionic compounds, for which the driving force is described by eq 7:

(7c)

which for crystallization from stoichiometric solutions is equivalent to eq 6, and justified when considering crystal growth as a series of consecutive acts of attachment rather than multiparticle coalescence.296,297 The slowest attachment process will define the overall quasi-linear growth kinetics. Terrace width is the distance, d, between consecutive steps (Figure 3). In the spiral dislocation growth mechanism, for steps comprising a circular spiral: 14059


Chemical Reviews d=

sLc = src 2

Review

V = V0 1 −

(8)

where the radius of the critical nucleus can be determined from Gibbs−Thomson law (eq 9): rc =

γω Δμ

dj = Vj∑ i=1

⎡ ⎤ 2c ωγ 2ωγ eq Δcd = cd − ceq = ceq ⎢exp − 1⎥ ≈ R gTLd R gTLd ⎢⎣ ⎥⎦

(9)

Ld = Lad / θ

(10)

Δcd =

2ceqωγ θ R gTLad

∝

cad (16)

The driving force for crystallization from the melt can be expressed as ΛΔT/Tm, where ΔT = Tm − T, Tm is the melting point, T is growth temperature, and Λ is the heat of fusion. The critical supercooling or width of the dead zone is given by eq 17 instead of eq 16. ΔTd =

3.2. Influence of Additives

2γωTm θ ∝ ΛLad

cad

(17)

The shapes of V(Δc) and V(cad) curves can deviate from an ideal behavior predicted by eq 13 due to the simplified character of the C−V formula. More correct theoretical approach proposed by Potapenko303 and recent numerical simulations304 predicted slightly different kinetic behavior (Figure 18) leaving eqs 16 and 17 intact. Further discrepancies can arise due to inadequacy of Henry’s adsorption isotherm, surface energy anisotropy, formation of macrosteps,305 slow impurity adsorption,306,307 and low kink densities on steps,308 among other reasons. Nevertheless, the C−V mechanism is usually accompanied by a dead zone and rough step edges. 3.2.2. Bliznakov−Chernov (B−C) Model.2,3 The B−C model emphasizes kink blocking by adsorbed impurities, rather than C−V step pinning. If an impurity is bound to a kink, it decreases the kinetic coefficient β0 for the attachment to that kink to β∞. The average kinetic coefficient depends on the surface coverage θ, where

3.2.1. Cabrera−Vermilyea (C−V) Model.300 Various mechanisms have been described for the role of additives in growth kinetics (Figure 18).19,301 The widely used Cabrera− Vermilyea (C−V) model assumes that impurity particles (molecules, macromolecules, their aggregates, etc.) adsorb strongly on terraces and, as a consequence, “pin” steps flowing across the terrace. When a step moves between these “stoppers”, its curvature (value inverse to the step radius, κ = 1/r) increases (Figure 9), resulting in a decrease in the effective supersaturation at the step front, δμ, that can be found from the Gibbs−Thomson law (eq 9). The classical consideration is based on the close to equilibrium condition, for which step velocity can be written as eq 11:

(11)

Combining eqs 9 and 11 gives the classical and more useful form, eq 12: ⎛ L ⎞ V = V0⎜1 − c ⎟ Ld ⎠ ⎝

(15)

Application of Henry’s isotherm (eq 4) to eqs 14 and 15 leads to eq 16, another classic prediction of the C−V model.

Terrace width depends not only on all γi but also on the ratio between step velocities for different spiral edges, Vj/Vi. Generally, however, increased step edge energy translates to wider terraces. The normal growth rate perpendicular to the face can be defined by R = pV. The slope of a vicinal hillock slope is p = h/d, where h is a step height (Figure 3). Because p in many cases does not change significantly with supersaturation, normal growth rates are often adequate for determining relative step velocities.

⎛ δμ ⎞ V = β(Δμ − δμ) = V0⎜1 − ⎟ Δμ ⎠ ⎝

(14)

where V0 is the step velocity in the absence of impurity and cd is the solute concentration at which growth resumes. The approximation on the right side of eq 14 can be used for small departures from equilibrium, for which ln(c/ceq) ≈ c/ceq − 1, tantamount to the classic C−V prediction.2,300 We assume that the size of the additive particle, Lad, is much smaller than Ld, so that the distance between stoppers is effectively identical to the distance between their centers. Thus, Ld can be expressed as eq 15:

Lci sin(αi , i − 1) Vi − 1

(13)

The supersaturation, at which growth stops, determines the width of the so-called “dead zone”:

Here, γ is surface energy, ω is molar volume of crystal, and Lc is a critical diameter of 2D nucleus (equal to a doubled radius of the critical nucleus, rc). A shape factor, s, is equal to 4π if the step velocity is assumed to be constant or approximately 19 if the step velocity depends on the step curvature.298 Equation 8 becomes more complex for a polygonal spiral with N edges, requiring eq 10, where Lc is the critical length and where αi,i−1 is the angle between the ith and (i − 1)th edges of a spiral.295,299 Equation 10 is applicable under conditions where the step velocity does not depend on the step length. The proportionality d ∝ γ/Δμ remains valid, however. N

Δcd = β (c − cd)(c − ceq) Δc

β = (1 − θ )β0 + θβ∞

(18)

With eqs 3 and 6, eq 18 can be transformed to eq 19. 1 1 1 = + V0 − V V0 − V∞ (V0 − V∞)Kcad

(12)

Growth stops completely if the effective supersaturation drops to zero, which corresponds to the condition wherein the distance between impurity particles, Ld, is less than the diameter of the critical nucleus Lc. Equation 12 can be generalized to far from equilibrium (eq 13) using eq 6.302

(19)

As additive concentration increases, step velocity gradually decreases from V0 to some steady, but not necessarily zero value. Neither a dead zone nor increased step roughness accompanies this mechanism. Terrace width does not change, but the kinetic coefficient gradually decreases. 14060


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3.2.3. Shift of Phase Equilibria.301,309−311 Every solution composition will correspond to a unique solubility, a unique kinetic coefficient, and a unique surface energy. Typically, these values are not known. Depending on the ratio between solubilities of the major and minor components, the crystal solubility can increase or decrease. If the shift in solubility is not taken into account, the step velocity can become zero at nonzero supersaturation/undersaturation. Correspondingly, an apparent kinetic coefficient, determined from actual step velocity and not corrected supersaturation, will change. 3.2.4. Surfactants. Surfactants301 or additives may alter the adsorption layer on the crystal surface312 as well as solute mobility at and near the crystal surface. This is the least studied growth inhibition mechanism. Growth hillock morphologies, step velocities, and terrace widths can change. Simulations of adsorption/desolvation/attachment processes are providing some insight into this mechanism,313,314 but quantitative analyses are lacking.

bivalve mollusk was reported to affect the morphologies of a variety of calcium salts described above in the context of a strong stereochemical hypothesis (section 2.2.1).67−69 COM {100} are more strongly inhibited with OPN and related peptides than all other faces (Table 3), resulting in thin plates.81,82,99 Tf, ChS, BSA,88 and agar gel exerted a similar effect.353 With these additives, relative development of {100}, {010}, {021}, and {1̅21} faces changes as well.81,88,99 A more pronounced effect of additives on {100} faces appears to be related to higher Ca2+ density on {100} as compared to {010}, {121̅}, and {021} (section 2.2.1). Likewise, {100} and {110} of tetragonal COD have higher Ca2+ density as compared to {101} (section 2.2.1). As a result, COD crystals become elongated along [001] accompanied by the formation of large {110} faces with OPN and its Asp-rich fragment.104 Likewise, poly(acrylic acid), poly(acrylate), poly-L-Glu, and poly-L-Asp promote the development of {100} faces (Figure 19).105,354

3.3. Growth Inhibition

3.3.1. Morphology Evolution. There are many welldocumented examples of growth inhibition by macromolecular additives including decreased precipitate yield of ApOH with the proline-rich salivary protein, statherin, and related peptides, 112,115,116,124,315−319 OPN and related peptides,77,106,320−324 and urinary proteins.111,321,323,325 Octacalcium phosphate precipitation was inhibited with polyAsp and phosphophoryn.326 Brushite was inhibited with alginate and its oligomers;327 its morphology can also be modified by the protein amelogenin.328 COM was inhibited with OPN93 and related peptides,329 Asp-rich peptides,97 albumin,88,330 transferrin,88,331 poly-L-Asp,330 poly-L-Glu,330 chondroitin sulfate,88 prothrombin and its fragments,332 BSA and Se nanoparticles,333 and mutants of protein G.334 A mixture of hyperactive AFPs similar to TmAFP was found to inhibit crystallization of trehalose.335 Identifying the residues and structures responsible for adsorption and inhibition is a foremost challenge. Homologous compositions can exhibit different inhibition activities as for COM inhibition by peptides of equal length Asp18 and Ala18.336 An additional challenge when evaluating the effect of inhibitors using bulk crystallization is the separation of crystal growth inhibition from nucleation inhibition. A review of the literature reveals that investigators can often mistake small, postcritical crystals for nuclei. Nonetheless, it is reasonable to assume that the absence of nucleation in many cases is a consequence of inhibition of incipient, or precritical nuclei that resemble the mature crystal form, particularly where there exist stereospecific interactions with well-defined crystal faces. Additives often have the capacity to inhibit growth on all faces, but the degree of inhibition can vary among the crystal faces. This results in changes in crystal morphology that reflect the anisotropy of inhibition at the microscopic scale. For example, in the presence of acidic peptides,337,338 functionalized and nonfunctionalized α,ω-dicarboxylates,339 acidic proteins and glycoproteins from sea urchin spines and mollusk shells,340−347 lysozyme,348 and diblock (poly(methacrylic acid)-benzyl methacrylate) copolymer, 271 rhombohedral {101̅4} calcite crystals elongate along the [0001] direction, accompanied by the formation of {hki0} faces. Various macromolecules can lead to the formation of {112̅0}, {101̅0}, {2̅ 0 23}, {404̅ 1 }, roughen surfaces, and sometimes {0001}.341,342,348−352 Asp-rich protein extracted from the

Figure 19. SEM images (left), and the corresponding TEM images (right), of thin cuts of COD crystals and aggregates grown from 0.8 mM calcium oxalate solution with increasing polyAA concentrations of 3 (A,B), 7 (C,D), 14 (E,F), 96 (G,H), 200 (I,J), and 225 (K,L) mg/ mL. Reproduced with permission from ref 105. Copyright 2012 WileyVCH.

Growth of {100} faces of octacalcium phosphate crystals, implicated in the genesis of hydroxyapatite, is inhibited in the presence of poly-Glu and Asp-rich mollusk shell protein. In the presence of phosphate-rich proteins, phosphophoryn and phosvitin, growth along {010} is inhibited, however.70 Ice morphology modifications by antifreeze macromolecules have been reported, as was briefly mentioned in section 2.2.2. 14061


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Figure 20. Step velocity as a function of polyE, polyD, and polyAA concentrations for {021} and {121̅} risers on {010} (a,b) and for {001} risers on {100} (c). Supersaturation Δc = 160 μM. Reproduced with permission from ref 76. Copyright 2004 American Chemical Society.

Peptides GLHVMHKVAPPR and GLHVMHKVAPPRGGGC convert [0001] ZnO rods into thin plates.355,356 HSA changes the aspect ratio of sodium urate monohydrate,357,358 a pathological biomineral crystallizing in joints. Fibronectin affects the aspect ratio of calcium fumarate trihydrate.359 Inulin, albumin, amylase, cellulose, and lipase lead to chiral habit modifications of gypsum.360 BSA inhibits growth of {101} of tetragonal lysozyme.361 Monoclonal antibodies to insulin and to the insulin receptor alter the morphology of insulin crystals.362 3.3.2. Step Pinning. The C−V mechanism treats macromolecules as immobile step stoppers. Indeed, in situ AFM observations of calcite crystallization in the presence of shell proteins and their fragments,266−268 Asp-rich peptides,363,364 lysozyme,269 and poly(vinyl alcohol)365 produced step roughening, and in some cases a measurable dead zone. V(cad) dependencies for COM with poly-L-Asp, poly-L-Glu, and polyacrylate (Figure 20)76 reveal C−V behavior illustrated in Figure 18 (section 3.7). COM exhibits significant step edge roughness and a dead zone in certain ranges of cad. Unlike the classical expectation (section 3.2.1), wherein V decreases slowly at low cad followed by a more rapid decrease (Figure 18), the step velocity decreased rapidly at low cad, then decreased more slowly at intermediate cad, then decreased rapidly at high cad. This behavior may reflect macromolecule aggregation at high concentrations. AF(G)Ps lower the freezing temperature of water, leading to a ΔTd that is tantamount to the width of the C−V dead zone (see section 2.2). ΔTd(cad) was analyzed221 for numerous antifreezes (see references in Table 5 and Figure 8, among others)151,157,162,168,181,212,225,366 on the basis of aggregated data. The data reveal that ΔTd(cad) follows the square root law predicted by the C−V mechanism (eq 17).65,160,212 Here, we expanded this analysis for a larger number of AF(G)Ps (Figures 21 and 28b). Agreement between theory and experiment was observed for most AF(G)Ps, consistent with C−V behavior, although hyperactive AFPs fit least well (Figure 21b,c). In some cases, there is a concentration range where ΔT d = 0,60,160,178,198,225 and sometimes ΔTd reaches a plateau at high concentrations.178,212 Such variations can be explained by slow AFP adsorption,48,59,170,367 which is supported indirectly by the observation that fish AF(G)Ps adsorb faster than hyperactive AFPs48 and better fit the ΔTd ∝ cad proportionality predicted by eq 17 (Figure 21). Analysis of growth rate R(ΔT) performed for ice crystallization in the presence of εpoly-L-Lys confirmed C−V behavior as well.65 The C−V mechanism of inhibition of {101̅0} ice surfaces by CfAFP was

Figure 21. Hysteresis activity, ΔTd, as a function of the square root of the additive concentration. (A) Fish AFPs. (B) Hyperactive AFPs. (C) Fungi and diatom AFPs. The proteins and sources of data are the same as in Figure 8.

successfully simulated and visualized using molecular dynamics.368 The greatest difficulty when attempting to verify C−V behavior is obtaining independent measurements of additive 14062


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Table 7. Distances, Ld, between AF(G)Ps Adsorbed on Ice and Values of Thermal Hysteresis, ΔTd antifreeze

Ld, nm

method of Ld determination

ref

θa

ΔTd,calc, °Cb

ΔTd,meas, °C

AFGP, ∼3 kDa, 2 mg/mL AFGP, ∼34 kDa, 2 mg/mL AFP I, 3.2 mg/mL GFP-AFP III, 15 μM GFP-AFGP, 8−17 kDa, 5 μg/mL GFP-TmAFP, 8 μM GFP-TmAFP, 0.4−31.4 μM GFP-AFP III, 1.2−19.8 μM

3.3−5 12−16.5 5 20 16−17 6−18 7.6−35 8.7−24.7

ellipsometry ellipsometry scanning tunneling microscopy fluorescence intensity fluorescence intensity fluorescence intensity fluorescence intensity fluorescence intensity

62 62 154 174 214 63 371 371

0.08−0.13 0.08−0.13 0.03 0.02 0.05−0.06 0.03−0.23 0.01−0.08 0.01−0.07

9.9−15.0 3.0−4.1 5 2.9 2.9−3.1 2.8−8.3 1.4−6.5e 2.0−5.7

0.3c 0.3c 0.45d 0.07 polyD (Figure 20).75,76 Peptide (D3S)6D3 is a more potent inhibitor than (D3G)6D3.51,97 Data show that the situation is more complex. PolyAA, polyD, and polyE with many carboxylates strongly inhibit {100} and {010} (Figure 20) at concentrations in the range 0.04−0.25 μM,76 but BSA, Tf, and ChS inhibit growth of {100} only at concentrations in the range 0.1−0.2 μM (R/R0 ≈ 0.2− 0.3).88 More vexing is the slight acceleration or slight inhibition of growth for {100} and {010} of THP at 10−100 nM (Figure 30).98 The effect of OPN is unsettled. At high concentration (∼0.1−0.2 μM), both faces are strongly inhibited, but {100} more so, and both become rough.84,99 At low concentration, (1−25 nM) {010} is more strongly inhibited than {100}, which appears unaffected (Table 3).91,98 The authors explained this discrepancy as a consequence of relatively weak binding of OPN to steps on {100} with small heights as compared to molecule size. Summarizing data for COM growth kinetics in the presence of MMs, one can conclude: Small molecules (citrate, D−D6 peptides) are adsorbed quickly but weakly. As a result, COM {010}, with a lower affinity for carboxylate groups, is barely inhibited, whereas the step velocity of {100} decreases (Figure 30). This process is accompanied by the formation of a narrow dead zone that widens slightly with increasing cad.89,90 Yet the additive-induced dead zone is sometimes questionable because growth from nominally pure calcium oxalate solutions can also display a dead zone.86 The inhibition occurs mainly via decrease of the kinetic coefficient (Figure 30), suggesting the Bliznakov−Chernov (B−C) kink blocking mechanism (Figure 18). Unlike the C−V step pinning mechanism, B−C invokes weakly adsorbed particles that do not form immobile stoppers, but block kinks temporarily. Although increased step roughening hints at C−V contributions, this aspect of growth kinetics seems to be subordinate. The kinetic data were fitted with a model embodying both mechanisms,86,89,90 but, in fact, the B−C model alone suffices. With longer peptides, adsorption and inhibition are more pronounced, and the inhibition model changes from B−C to C−V. Kinetic data for {100} growth with the (D3S)6D3 peptide demonstrate classic C−V behavior with rough step edges, a dead zone, and minor changes of the kinetic coefficient (Figure

4.1. Individual Macromolecules

4.1.1. Concentration. Incorporation of isolated, nanometer scale objects into growing crystals is primarily driven by their strong adsorption to the crystal surfaces, as illustrated for COM,83,84,418−423 COD,104,105,420,424 calcite,340,341,345,425,426 calcium maleate,340 ice,63,174,180,183,212,427,428 α-lactose monohydrate,14−16,412 L-cystine,54 dihydroxybenzoic acids,261,262,429 succinic acid,430 sinapic acid,431 proteins,361,432−434 and diblock (poly(methacrylic acid)-benzyl methacrylate) copolymer vesicles and “worms”.271 Crystals can occlude not only individual MMs but also functionalized nanoparticles, as demonstrated for magnetite and gold nanoparticles in calcite,435−437 gold nanoparticles in L-cystine,245 and macromolecular aggregates in various host crystals (section 2.3). The quantity of overgrown MMs depends on several adsorption−desorption processes on and near the surface. Advancing growth fronts collide with adsorbed molecules, which are distributed over the crystal surface at an average coverage θ, given by eq 2. These foreign molecules may be trapped by the growing crystal, but during a characteristic time, τ = h/R, where h is height of growth step and R is normal growth rate, they will not be completely occluded. Consequently, at t < τ, foreign molecules can desorb at a rate dθ/dt = −k−1θ, where k−1 is the desorption rate constant of the partially occluded molecule. The volume fraction of molecules 14069


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Table 9. Incorporation of Macromolecular Additives in Crystals macromolecule Host Crystal: Ice AFP III, 7 kDa AFGP, 2.6−3.5 kDa AFGP, 15 kDa AFGP, 3 kDa AFP, 5 kDa AFGP, 3.3 kDa AFP II AFP III, 7 kDa CfAFP, 9 kDa TmAFP, 8.4 kDa dextran, 2 kDa Host Crystal: Tetrahydrofuran AFP III, 7 kDa LpAFP, 12 kDa hyp AFP I, 16.7 kDa Host Crystal: α-Lactose Monohydrate Zn-cytochrome C, 12.5 kDa lysozyme, 14.7 kDa GFP, 27 kDa mCherry-ferritin, 1.1 MDa lectin, 30 kDa Dickerson’s 12-mer oligonucleotide, 4 kDa dextran, 10 kDa ribonuclease, 15.9 kDa ovalbumin, 46 kDa transferrin, 80 kDa fibrinogen, 340 kDa hemoglobin, 64.5 kDa myoglobin, 17 kDa avidin, 68 kDa BSA, 66.5 kDa hemagglutinin, 65 kDa neuraminidase, 49 kDa Host Crystal: 2,5-Dihydroxybenzoic Acid cytochrome C, 12.4 kDa Host Crystal: 2,4-Dihydroxybenzoic Acid cytochrome C, 12.4 kDa Host Crystal: Succinic Acid cytochrome C, 12.4 kDa Host Crystal: Calcium Oxalate Dihydrate polyAA, 5.1 kDa Host Crystal: Calcite sea urchin glycoprotein sea urchin glycoprotein mollusk glycoprotein Host Crystal: Calcium Maleate sea urchin glycoprotein mollusc glycoprotein Host Crystal: Monoclinic Lysozyme avidin, 16.8 kDa ovalbumin, 44 kDa BSA, 66.5 kDa Host Crystal: Tetragonal Lysozyme avidin, 16.8 kDa ovalbumin, 44 kDa BSA, 66.5 kDa

cad, mg/mL

x, 10−6 mol/mol

x, wt %

Kd

ref

0.77 0.001 5 5 5 5 0.16 0.2 0.2 0.07 0.4

0.06 0.1 5.7 7.9 8.2 5.1 0.20 0.48 0.50 0.17 0.02

0.002 0.002 0.48 0.13 0.23 0.09 0.016 0.019 0.025 0.008 0.0002

0.02 0.3 0.89 0.17 0.44 0.30 1.06 0.94 1.25 1.12 0.0055

427 180 212 212 212 212 428 428 428 428 428

0.13 0.22 0.07

2.3 3.8

0.004 0.012

0.31 0.55 0.48

246,247 246 247

0.5a 0.5a 0.04 1.0 0.5a 0.5a 0.5a 0.5a 44 14 0.65 34 18 1.8 4.7 0.03 0.012

1.7 1.8 1.3 0.24c 40 10 14 11 53c 6.3c 4.0c 44c 13 1.8c 13c 2.2c 0.8

0.006 0.007 0.01 0.075 0.28 0.011 0.039 0.049 0.66 0.14 0.37 0.79 0.06 0.034 0.24 0.039 0.011

0.05e 0.06e 1.2 0.24 2.3e 0.1e 0.3e 0.4e 0.056 0.05 1.7 0.14 0.02 0.11 0.22 1.6 3.1

15 15 14−16 16 15 15 15 15 16 16 16 16 16 15,16 16 16 16

b

137c

1.1

0.7

261,262,429

b

66c

0.53

0.3

261

b

31c

0.32

0.3

430

3.5

0.05

105

0.096

1100c

0.008 0.008 0.002

2d 6d 0.75d

0.04 0.11 0.015

0.05e 0.15e 0.075e

345 340,425 340

0.002 0.002

0.09d 0.23d

0.002 0.005

0.01e 0.02e

340 340

31 0.3 1.9

1.87 0.05 0.02

361 361 361

28 40 66

1.61 1.06 1.27

361 361 361

2 2 2

2.7 × 105 10000 4000 2.44 × 105 1.75 × 105 2.95 × 105

3 3 5

a Accurate values not reported. cad range, 0.17−0.83 mg/mL. bValues are not reported. cHere, only the point with largest x is reported. dMw was unknown and assumed to be 20 kDa. eAccurate values cannot be calculated due to insufficient information on additive Mw and/or host/additive concentration in solution.

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Figure 31. Macromolecule incorporation in crystal as a function of solution compositions. Values of distribution coefficient, Kd, estimated from the slopes are indicated. (A) Host, ALM; guests, FITC-BSA, FITC labeled ovalbumin (FITC-Ova), FITC-Tf, FITC-avidin, hemoglobin (Hb), and Oregon green labeled fibrinogen (OG-Fg). The dashed line corresponds to Kd = 1. Reproduced with permission from ref 16. Copyright 2016 American Chemical Society. (B) Host, 2,4-DHB (red ●), 2,5-DHB (▲), succinic acid (blue ▼); guest, cytochrome C. For succinic acid, Kd can be estimated as ∼0.3. Data from refs 261, 429, and 430. (C) Host, COD; guest, polyAA (●). Dots, concentration of polyAA (left y-axis); line, distribution coefficient (right y-axis). Experimental data from ref 105. (D) Host, tetragonal lysozyme; guest, BSA. Ceiling (red ●) and batch (▲) modes correspond to crystallization conditions, for which mass transfer was predominantly driven by diffusion and convection, respectively. Adapted with permission from ref 361. Copyright 2015 American Chemical Society.

in the crystal, Ω, is equal to their surface coverage Ω = exp(−k−1h/R).3 Substituting the expression for θ from eq 2 gives: Ω= ⎡ ⎢1 ⎣

k+cad ⎛ h ⎞ exp⎜ − k −1⎟× ⎝ R ⎠ k − + k+cad ⎛ h ⎞⎤ − exp⎜ − (k+cad + k −)⎟⎥ ⎝ R ⎠⎦

where ωmm and ω are molar volumes of additive and crystal, respectively. Equation 22 contains the factor Lad/h, which accounts for MMs that penetrate several layers. The distribution coefficient also can be defined as the molar fraction of MM in the crystal divided by its molar fraction in the growth medium, Kd = xc/cad, where c is the concentration of the main component (c/cad is expressed in mole fraction). Equation 22 reveals that MM incorporation is possible over a range of growth rates. If the growth rate is low, θ may be maximal but the time available for desorption is long. Conversely, at high growth rates, the MM coverage will tend to be small given the short time a given crystal layer is exposed to the medium. The concentration of the MM in the crystal would be expected to increase with increasing concentration in the growth medium. A high MM concentration in the medium would be expected to slow the growth rate, however (eqs 12−16), resulting in a maximum concentration of occluded MMs when the distance between adsorbates becomes close to the diameter of the critical nucleus Lc (section 3.2.1). The maximum volume fraction, assuming MMs distributed on a surface as a square grid, can be estimated using eq 23:

(21)

A more accurate analysis must account for two complications: (i) MMs are usually thicker than a typical crystal growth layer, n = Lad/h ≥ 1, where Lad/h is rounded to the next largest integer, and (ii) MMs can adsorb onto other MMs already adsorbed. The second correction can be neglected under conditions of nonzero growth rate, which is plausible only at small values of θ. Condition (i) is important, however. Desorption from the i = 1, ...n layer, counting from the surface toward the crystal interior (layer n), can be described by a set of equations dθi/dt = − k−iθi, where k−i are desorption rate constants of partially occluded molecules for the ith layer. The molar fraction of macromolecules in a crystal is given by ⎛ h n ⎞ k+cadLadωmm exp⎜⎜ − ∑ k −i⎟⎟× x= (k+cad + k −)ωh ⎝ R i=1 ⎠ ⎡ ⎛ h ⎞⎤ ⎢1 − exp⎜⎝ − (nk+cad + k −)⎟⎠⎥ ⎣ ⎦ R

⎛ Lad ⎞2 Ω max = ⎜ ⎟ ⎝ Lad + Lc ⎠

(23)

Inspection of eq 23 reveals that Ωmax increases with supersaturation (eq 9) and the size of the MM additive Lad. Using a typical value of Lc = 20 nm, Ωmax = 2.8% for Lad = 4 nm

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protein was x = 2 × 10−4 (Figure 31b), slightly smaller in 2,4DHB (7 × 10−5, Figure 31b), much smaller in 3,4-DHB and 3,5-DHB (x < 10−5), and undetectable in 2,6-DHB.261 The reasons for these disparities are not obvious.261 Additive concentration strongly influences the incorporation of polyAA in COD.105 As the additive concentration cad is increased, the concentration of polyAA in the crystal passes through a maximum and the distribution coefficient decreases monotonically. Such behavior is consistent with a longer time scale available for detachment of adsorbates as the growth rate decreases with increasing cad; that is, the first exponential term in eq 22 tends to zero (Figure 31c). Macromolecular impurities pose a serious problem when growing protein crystals for structure determination as they inhibit crystallization and create defects.433 The distribution coefficients for MMs span a large range. For example, 0.02 ≤ Kd ≤ 4 for lysozyme and ferritin (Table 9, Figure 31d).361,434 MM incorporation can be minimized in several ways: (i) Increased supersaturation can be used to reduce MMs incorporation.66 (ii) Incorporation of MM additives into lysozyme and ferritin was found to depend strongly on position of crystals in the mother liquor, implicating mass transport effects (Figure 31d).361,434,440 Distribution coefficients for ovalbumin and BSA were larger for crystals formed at the upper part of a growth vessel (ceiling mode; mass transfer is predominantly controlled by diffusion), whereas avidin exhibited larger Kd when lysozyme crystallized at the bottom (batch mode; mass transfer is predominantly controlled by convection).361 (iii) Distribution coefficients for ribonuclease, insulin, cytochrome C, myoglobin, and ovalbumin in lysozyme (Kd = 0.16, 0.017, 0.01, 0.052, and 0.97, respectively) as well as in ferritin (Kd = 0.1, 0.02, 0.02, 0.006, and 20 nm.16 The reason for the absence of further incorporation of protein by ALM is not apparent. The distribution coefficient decreases slightly as the growth temperature increases in the range 4 ≤ T ≤ 36 °C, it is not sensitive to supersaturation, and it decreases with increasing salt concentration in the growth medium. Cytochrome C was incorporated measurably in dihydroxybenzoic acid (DHB) crystals, some of which were used for MALDI mass spectrometry. In 2,5-DHB, the mole fraction of 14072


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more protein than subsectors formed by steps running parallel to [001] (Figure 33). Such selectivity is hard to rationalize given that all faces on an ALM crystal expose hydroxyl groups. This is the motivating problem that was expressed in the introduction. Ice preferentially captures two types of AF(G)Ps into the dominant facets ({202̅1}, {21̅1̅0}, and {101̅0}) when these proteins are present (section 2.2.2, Figure 10).152,180 BSA is preferentially overgrown in L-cystine {0001} growth sectors.54 Myoglobin, as well as BSA and lysozyme, was reported to be incorporated only into the {103}̅ growth sectors of sinapic acid, albeit detected indirectly by staining with a chromophore that could color the protein in the crystal,431 or just the crystal itself.443 Fluorescently labeled cytochrome C, BSA, lysozyme, and myoglobin preferentially incorporate into {103̅} and {021} growth sectors of sinapic acid and phthalic acid, respectively.441 Impurities are preferentially incorporated into {101} growth sectors and into sectoral zoning boundaries of tetragonal lysozyme, and these are believed to be mainly macromolecular impurities.433 In sum, strong adsorption generally leads to growth inhibition and MM incorporation as observed for COM, COD, sinapic acid, and ice. Incorporation may not be accompanied by growth inhibition if the additive concentration is too low to provide sufficient surface coverage to pin steps, as observed for ALM and L-cystine. Selective adsorption detected by fluorescence is not always followed by overgrowth and incorporation,55,82,88 most likely reflecting weak adsorption.

Figure 33. Sector- and subsector zoning in the distribution of proteins in ALM crystals. (a) Fluorescence of FITC-avidin. Crystal 1 is viewed along b; crystals 2 and 3 are viewed approximately along c; crystals 4− 6 are viewed approximately along a. (b) Morphology of ALM. The green area corresponds to the subsectors with predominant incorporation of proteins.

4.2. Macromolecular Aggregates

Adsorption remains important for the incorporation of particles of any size, but large macromolecular aggregates can be overgrown in crystals even in the absence of adsorption. Examples of adsorption-independent incorporation include crystal growth from hydrogels and hydrogel-like organic matrices,417 wherein macromolecular aggregates evolve into gel-forming fibers. Calcites grown from agarose,444−446 gelatin,447−449 and agarose-gelatin448 hydrogels have been well studied. Other examples include fluorapatite crystallizing

faces are substantially enriched in MMs as compared to {101} (Figure 19).104,105 ALM can incorporate various globular proteins (Table 9) but only in the basal (010) growth sector (Figure 2).14,15 Even within the (010) sector, protein incorporation often is inhomogeneous. Subsectors formed growth steps running parallel to [100] that adsorb and overgrow several times

Figure 34. (A) Tomographic reconstruction of 3D agarose gel network inside a calcite crystal obtained from a series of high-angle annular dark-field scanning TEM images. Bounding box has dimensions 1453 nm × 975 nm × 220 nm. Reproduced with permission from ref 446. Copyright 2009 American Association for the Advancement of Science. (B and C) Fluorapatite grown from gelatin. (B) TEM image showing spatial distribution of collage fibrils. Yellow lines indicate the borders between the distinct areas 1−3 with different orientations of the microfibrils: (1) parallel to the c-axis; (2) bent microfibrils following the direction of the edges between basal and prism faces; and (3) perpendicular to the prism faces. (C) Simulated 3D fibril pattern. Green and violet surfaces correspond to yellow lines in (B). Reproduced with permission from ref 452. Copyright 2010 Wiley-VCH. 14073


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from gelatin,450−455 several proteins (lysozyme, ferritin, and thaumatin) crystallizing from agarose and silica gels,456,457 as well as calcium tartrate tetrahydrate and α-glycine crystals forming from agarose gel.458 Proteins overgrown in calcium oxalate crystals formed in human urine are probably incorporated as macromolecular aggregates.424,459 Calcite438,439,460−464 and zinc oxide465,466 crystals with embedded nano- and microscale macromolecular particles have been reported. Removal of the organic matter afforded porous calcite and zinc oxide crystals. The volume fraction of incorporated MMs can be as large as 50%. Calcite and flourapatite crystallized from gels can contain up to 2.5 wt % or ca. 8 vol % of the gel matrix. The distribution of gel fibrils in crystals can be complex. Agarose gel fibrils in calcite crystals form a random 3D network (Figure 34A),417,446 whereas gelatin fibrils within a fluorapatite crystal tend to be oriented perpendicular to the growth front (Figure 34B,C).452,453,455 Substantial MM incorporation occurs during bone, teeth, and shell formation,4,448,467−469 but the additional complexities in vivo are beyond the scope of this Review. Incorporation occurs if forces pressing particles into surfaces (hydrodynamic forces, gravity, or external forces) overcome crystallization pressure and so-called disjoining forces. These forces increase with growth rate but in different ways assuming the existence of the critical normal growth rate, Rc, above which foreign particles, as studied for solidifying melts, become overgrown in the crystal.512,513 Incorporation of particles from solution is more complex and less well studied, but the basic forces are comparable.3 Numerical estimates and data for crystallization from melts show that incorporation of particles smaller than 1 μm requires very fast growth (Rc > 10 μm/s ≈ 1 m/day). Such growth rates, several orders of magnitude greater than typical growth rates of crystals with macromolecular additives, make incorporation of isolated nanoscale macromolecular aggregates virtually impossible. A different situation emerges if particles are pressed into the crystal surface by additional forces such as gel network resistance. Gel incorporation is determined by the balance between the gel strength and crystallization pressure.3,417,445,470,471 Crystallization pressure was calculated using eq 24, where Δμ is the driving force for crystallization and ω is molecular volume of the crystallizing material. Π = Δμ/ω

illustrated in the recent study of incorporation of carboxylated micelles by the growing calcite surface.473 4.3. Internal Stresses and Growth Defects

Foreign particles inside a crystal are a source of additional internal stress and imperfections. Additive-driven formation of stresses, their relaxation paths, and mechanisms of defect generation are poorly understood for most solution grown crystals, whether a continuous series of solid solutions,474,475 classical anomalous ionic mixed crystals,415 or proteins.476,477 Little is known about defects in crystals grown in the presence of macromolecular additives. Nonadsorbing macromolecular aggregates occluded by growing crystals do not interact directly with the crystal structure and should not produce significant internal stresses. Indeed, several protein crystals growing in gels do not exhibit gross imperfections as compared to solution-grown crystals as analyzed by single-crystal X-ray diffraction.456,478,479 A strong interaction between a host crystal and occluded MMs is expected to produce lattice strain manifest as changes in lattice constants. This has been demonstrated in greatest detail for calcium carbonate minerals using high-resolution X-ray powder diffraction.480 Lattice constants in various biogenic aragonites differ when compared to geological control samples, up to 0.2%.481−483 The a and c lattice constants of calcitic prisms obtained from shells and synthetic calcites, grown in the presence of proteins extracted from shells, increased 0.05− 0.08% and 0.02−0.1%, respectively, with respect to pure calcite.484 Heat treatment that decomposes the organic component usually returns the lattice constants to their native values, consistent with a direct relationship between adsorption of macromolecules and lattice constants. Likewise, synthetic calcite grown with a perlucin-GFP conjugate showed a and c increases of 0.015% and 0.08%, respectively.426 Calcite incorporates Asp, Glu, and Cys in concentrations up to 0.8 mol % leading to c increase of up to 0.23%.485 As compared to pure zinc oxide crystals, crystals with poly(styrene-acrylic acid) latex microspheres showed a and c decreases of 0.15% and 0.08%, respectively.466 Several amino acids have been reported to increase ZnO lattice constants, some of them anisotropically.486 This suggests that peptides and proteins also can be incorporated into ZnO crystals and affect its structure. Embedded macromolecules can also disrupt long-range periodicity of the crystal lattice with formation of individual dislocations and dislocation ensembles. Depending on the distribution of dislocations, this will result in the reduction of coherency domain sizes and/or the increase of microstrains and domain misorientation angles (crystal mosaicity). Pure synthetic calcite crystals were shown to have the largest domain sizes and smallest crystal mosaicity as compared to biogenic and synthetic calcite grown with MMs from biominerals.345,425,426,487−489 Both parameters show orientational dependence. In synthetic calcite crystals grown with 0.04 wt % of protein extracted from the sea urchin spines, the coherence length decreased by approximately 16% perpendicular to {0001}, 42% perpendicular to {101̅4} and {202̅4̅}, 51% perpendicular to {112̅0}, and 60% perpendicular to {101̅0}.345 This indicates that {hki0} ̅ are most affected by protein incorporation and agree with preferential inhibition of faces parallel to or approximately parallel to [0001]345 (section 3.3.1). Mature sea urchin spine coherence domains are similar to synthetic calcite, but young spines show more or less isotropic coherence length increases by 40−50%. Calcite

(24)

The crystallization pressure calculated for lysozyme and ferritin crystals grown from agarose gels was found to be significantly higher than the gel strength.457 This suggested that gels have to be fractured but not incorporated into crystals. In disagreement with the theory, however, gel incorporation was significant with almost no cracks in the gel medium around crystals. In another example, the amount of gel incorporating into calcite was shown to increase with concentration of Ca2+ ions in the gel and decrease with the gel strength.417,445 Increasing [Ca2+] has a stronger effect on the growth rate (R ∝ [Ca2+]) than on crystallization pressure (Π ∝ ln([Ca2+])), and it is reasonable to assume that higher [Ca2+] will promote incorporation of gel. The qualitative agreement with the theory again disagrees with numerical estimates. In such cases, crystallization pressure Π = 107−109 Pa should exceed the gel strength

Crystal Growth with Macromolecular Additives - Chemical Reviews

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