Molecular Mechanisms of Defect Formation

Molecular Mechanisms of Defect Formation

170 [10] crystals [10] Molecular Mechanisms of Defect Formation By Peter G. Vekilov Introduction The growth of protein crystals, as well as any ot...

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[10] Molecular Mechanisms of Defect Formation By Peter G. Vekilov Introduction

The growth of protein crystals, as well as any other crystal, occurs by the ordered addition of molecules. For a perfect crystal, a huge number of such additions (of the order of 1015 and higher) have to occur in a strictly identical fashion. This large number awards many opportunities for misaligned attachment of single molecules, molecular aggregates (amorphous and crystalline), or other species present in the nutrient medium, as well as for short- and long-term variability of the growth process. As a result, defects ranging in scale from the molecular (mutated and conformationally different molecules, misaligned molecules, and single vacancies) through trapped impurities, clusters and oligomers, dislocations, and twinning planes, to the macroscopic (striations, occlusions, twins, blocks and grains, and zones) are formed. While the mechanisms leading to relatively perfect protein crystals have been studied in great detail at both the mesoscopic1–3 and the molecular level,4–8 only a few of the processes leading to defects have been monitored.9–11 The goal of this chapter is to summarize recent work on the molecular level on the processes that accompany crystallization and lead to defects and associated lattice strain and potential plastic deformations such as mosaicity. One may argue that even if a crystal contains 1% of misplaced molecules, this will result in only a 1% decrease in diffraction intensity or a 1% increase in the background noise. Unfortunately, this is not the case. As discussed in detail below, even for the smallest, molecular level, ‘‘point’’ 1

S. D. Durbin and G. Feher, Annu. Rev. Phys. Chem. 47, 171 (1996). A. J. Malkin, Y. G. Kuznetsov, T. A. Land, J. J. De Yoreo, and A. McPherson, Nat. Struct. Biol. 2, 956 (1996). 3 T. A. Land, J. J. De Yoreo, and J. D. Lee, Surf Sci. 384, 136 (1997). 4 C. M. Yip and M. D. Ward, Biophys. J. 71, 1071 (1996). 5 C. M. Yip, M. R. DePhelippis, B. H. Frank, M. L. Brader, and M. D. Ward, Biophys. J. 75, 1172 (1998). 6 A. J. Malkin, Y. G. Kuznetsov, R. W. Lucas, and A. McPherson, J. Struct. Biol. 127, 35 (1999). 7 S.-T. Yau, B. R. Thomas, and P. G. Vekilov, Phys. Rev. Lett. 85, 353 (2000). 8 S.-T. Yau, D. N. Petsev, B. R. Thomas, and P. G. Vekilov, J. Mol. Biol. 303(5), 667 (2000). 9 A. J. Malkin, Y. G. Kuznetsov, and A. McPherson, J. Struct. Biol. 117, 124 (1996). 10 A. J. Malkin, Y. G. Kuznetsov, and A. McPherson, Proteins Struct. Funct. Genet. 24, 247 (1996). 11 P. G. Vekilov and J. I. D. Alexander, Chem. Rev. 100, 2061 (2000). 2

METHODS IN ENZYMOLOGY, VOL. 368

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defects, it has been shown that (1) they replicate in subsequent layers during growth, (2) they cause strain with the strain field extending to 5 to 10 molecular diameters, and (3) the accumulation of strain leads to mosaicity and block structure. Arguments have been put forth that diffraction resolution is affected only by short-scale molecular disorder and not by mosaicity, striae, zoning, and block structures.12 There are examples in which heavily mosaic crystals diffract to high resolution.13 On the other hand, the diffraction resolution is determined by the signal-to-noise ratio of high-index reflections. Since high-index crystal planes have low molecular density, larger areas of rotationally and translationally aligned molecules are needed to enhance the intensity of the reflections from these planes. Hence, crystal imperfections on the scale of microns, e.g., striae, and even tens and hundreds of microns, e.g., block structures, twins, etc., should affect the diffraction resolution obtainable from a crystal.14 Mosaicity, striae, and block structures often lead to broader or split diffraction spots, and, hence, lower accuracy of the structure determination.15,16 However, if the crystal consists of a few large blocks, the beam in X-ray diffraction experiments can be focused on only one of these blocks, and high-resolution structure determinations can still be achieved.13,17 Correlation between Growth Kinetics and Generation of Defects

The various defects that may be present in a protein crystal, the factors underlying their formation, and the possible changes in crystallization conditions to avoid them are summarized below. Submolecular Level Defects Poor crystal quality has often been attributed to conformational or genetic variability of the protein molecular structure, see, e.g., Puhler et al.18 The way to crystal perfection passes through either structure stabilization by ligands,19 or breaking the protein into smaller domains, e.g., Cohen et al.20 12

A. Shaikevich and Z. Kam, Acta Crystallogr. A 37, 871 (1981). R. Fourme, A. Ducruix, M. Ries-Kaut, and B. Capelle, J. Synchrotron Radiat. 2, 136 (1995). 14 P. G. Vekilov and F. Rosenberger, Phys. Rev. E 57, 6979 (1998). 15 S. Weisgerber and J. R. Helliwell, Acta Crystallogr. D 51, 1099 (1995). 16 E. H. Snell, A. Cassetta, J. R. Helliwell, T. J. Boggon, N. E. Chayen, E. Weckert, K. Hoelzer, K. Schroer, E. J. Gordon, and P. F. Zagalski, Acta Crystallogr. D 53, 231 (1997). 17 A. Guinier, Cryst. Res. Technol. 33, 543 (1998). 18 G. Puhler, S. Weinkauf, L. Bachmann, S. Muller, A. Engel, R. Hegerl, and W. Baumeister, EMBO J. 11, 1607 (1992). 13

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No data exist on the effects of the protein conformational variability on processes of growth and defect formation. This lack of insight stems from the resolution of the techniques used to monitor in situ the growth processes, which is limited to about one-third to one-tenth of the molecular size. However, the results reviewed here, by imaging the evolution of defects on slightly greater lengthscale, allow delineation of the biochemical from the physical causes underlying crystal imperfection. Furthermore, the range of negative consequence due to such submolecular level defects should not be exaggerated. Even rigid and spherical species, such as Si atoms, may fail to produce perfect crystals.21 Rotational and Translational Lattice Defects The rotational orientation of the molecules in the protein crystals may vary. The reason is that the size of the protein molecules is about an order of magnitude larger than the range of interactions between them.22 The strength of these interactions, if recalculated per unit contact area, is also rather low. This is considered to be one of the reasons behind the relatively slow protein crystal growth kinetics, and may also underlie the presence of an imperfection unique for this type of crystal: rotational disorder of the protein macromolecules. This disorder has been studied by electron microscopy of freeze-etched and metal-decorated crystals.23 This technique is based on coating under vacuum of frozen-hydrated protein crystals with a few monolayers of a low melting metal, such as Au or Ag. The distribution of the metal clusters on the surface of the protein is related to the topochemistry of the molecule’s surface.24 This technique was used to study two- and three-dimensional crystals that allow an averaged decoration pattern to be identified18,25,26 as well as noncrystalline specimens.27,28 19

A. McPherson, ‘‘Crystallization of Biological Mechanisms,’’ Cold Spring Harbor Laboratory Press, Cold Spring Harbor, NY, 1999. 20 S. L. Cohen, A. R. Ferre-D’Amare, S. K. Burley, and B. T. Chait, Protein Sci. 4, 1088 (1995). 21 H. J. Queisser and E. E. Haller, Science 281, 945 (1998). 22 A. A. Chernov and H. Komatsu, in ‘‘Science and Technology of Crystal Growth’’ (J. P. van der Eerden and O. S. L. Bruinsma, eds.), p. 329. Kluwer Academic, Dordrecht, 1995. 23 N. Braun, J. Tack, M. Fischer, A. Bacher, L. Bachmann, and S. Weinkauf, J. Cryst. Growth 212, 270 (2000). 24 S. Weinkauf, A. Bacher, W. Baumeister, R. Ladenstein, R. Huber, and L. Bachmann, J. Mol. Biol. 221, 637 (1991). 25 W. Meining, A. Bacher, L. Bachmann, C. Schmid, S. Weinkauf, R. Huber, and H. Nar, J. Mol. Biol. 253, 208 (1995). 26 A. Bacher, S. Weinkauf, L. Bachmann, K. Ritsert, W. Baumeister, R. Huber, and R. Ladenstein, J. Mol. Biol. 225, 1065 (1992). 27 E. Ru¨ benkamp, N. Braun, L. Bachmann, A. Bacher, J. Brandt, W. Baumeister, and S. Weinkauf, Ultramicroscopy 58, 337 (1995). 28 N. Braun, J. Tack, L. Bachmann, and S. Weinkauf, Thin Solid Films 284/285, 703 (1996).

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On the decoration pattern, various features of the packing of the top crystallographic plane can be visualized, including the rotational orientation of the individual molecules.26 When this technique was applied to, among many others, hexagonal crystals of lumazine synthase, it was found that the surface molecules on an undisturbed surface adopted two possible orientations in an alternating manner according to the crystal packing (Fig. 1). Orientational disorder was observed at and around a dislocation, where patches of molecules showed ‘‘wrong’’ orientations.23 Similarly, the molecules on the surface of ferritin crystals seemed to possess no orientational order.

Fig. 1. Silver-decorated (010) face of a lumazine synthase crystal. (A) Distribution of silver spots along the surface, from which the orientation of the individual molecules can be deduced: As shown in (C), in this crystal, molecules take one of two orientations: with the 5-fold axis upward, represented by black circles in (B), or with the 5-fold axis tilted forward, open circles in (B). (B) Schematic illustrating the distribution of the two molecular orientations on the surface. Perfect crystals exhibit alternating ‘‘white’’ and ‘‘black’’ molecular rows; deviations from this pattern indicate molecular disorder. Arrows in (A) and rectangles in (B) highlight locations of accumulated misoriented molecules. By permission from Braun et al.28

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These results on the molecular orientational disorder in protein crystals, although still limited to only a few materials, indicate that even if it were possible to grow the crystals from a perfectly pure solution, defects, and related strain can still be introduced and compromise the crystals’ utility. Another type of point defect are the lattice vacancies or molecules out of their lattice positions. These defects are often caused by the incorporation of impurity particles. We discuss this, together with other undesirable consequences of impurity incorporation, below. However, in small-molecule crystals, there are many instances where these defects are caused by intrinsic instabilities of the growth process on many lengthscales, and their existence cannot be related to an impurity action. We cannot exclude the possibility that point defects unrelated to impurity action may also appear in protein crystals. In analogy to inorganic crystallization, we surmise that they may be caused by insufficient selectivity of the growth process,7 i.e., a molecule attached in a ‘‘wrong’’ orientation or wrong position does not have the chance to detach before being buried by the attachment of the next molecule. Typically, incorrectly oriented attachment is caused by fast growth at high supersaturations. It can be avoided by slower growth at lower supersaturations. Note, however, that slower growth is inductive of higher impurity adsorption29,30 and may lead to a greater number of impurityrelated defects, as shown below. Impurity-Related Defects The impurities are often other proteins from the same tissue source. In many cases, the impurity proteins do not adsorb on the growth interface, and hence do not influence growth and are not incorporated into the crystals. However, there are documented cases in which two protein preparations that differ only by concentrations of the companion proteins exhibit quite different growth rates, and crystal perfection.29,31,32 Often, the impurity species that strongly affect the growth process are oligomers or subunits of the protein of interest. One such case is the growth of the much studied protein lysozyme, inhibited by the covalently bound dimer, which seems to be the product of one of the isolation procedures.

29

P. G. Vekilov and F. Rosenberger, J. Cryst. Growth 158, 540 (1996). P. G. Vekilov, B. R. Thomas, and F. Rosenberger, J. Phys. Chem. 102, 5208 (1998). 31 V. Stojanoff, D. P. Siddons, L. A. Monaco, P. G. Vekilov, and F. Rosenberger, Acta Crystallogr. D 53, 588 (1997). 32 B. R. Thomas, P. G. Vekilov, and F. Rosenberger, Acta Crystallogr. D 52, 776 (1996). 30

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Another example is ferritin and apoferritin, in which, again, the dominant impurity is a molecular dimer that we would like to discuss in more detail below. An obvious way to deal with impurity-generated defects is to purify the solutions used in crystallization. However, the capabilities of the protein purification techniques are limited by the fact that from the viewpoint of their elemental composition, all proteins are very similar.33 As a result, protein purity levels of 99.99% are very rare,32,34 and even these levels are a few orders of magnitude poorer when compared to the purity levels needed for perfect growth of, for instance, semiconductor or nonlinear optical crystals.21,35 Furthermore, purification often entails the loss of a significant fraction of scarce protein preparations. Recent modeling and microgravity crystallization results suggest that further reduction of impurity action by factors of several-fold may be achieved through microgravity growth—by eliminating supply of impurities to the interface via buoyancy-driven convection, these conditions result in lower interfacial concentration of the impurity species.36–38 Adsorption of Heterogeneities on the Growing Surface of Apoferritin Crystals. These studies used the proteins ferritin, a major iron storage protein in the cytosol, and apoferritin, consisting of the ferritin protein shell sans the iron core.39,40 On the molecular level, the structures and processes observed with the two proteins are very similar. Previous studies have shown that for both proteins, species with molecular masses double that of the native proteins are the major contaminant.34 The levels of these impurities can be brought down to at most 5%; over 30 days or more, the dimers are regenerated. Thus, it was found that after storage for a year at  5 the dimer concentration reached as high as 40% (w/w) (B. R. Thomas, unpublished observations). Ferritin and apoferritin crystallize in a face-centered cubic (fcc) lattice with space group F432.41,42 The crystal habit is dominated by the octahedral {111} faces, characterized with hexagonal coordination of the 33

W. F. Patton, J. Chromatogr. 698, 55 (1995). B. R. Thomas, D. Carter, and F. Rosenberger, J. Cryst. Growth 187, 499 (1997). 35 N. P. Zaitseva, J. J. DeYoreo, M. R. Dehaven, R. L. Vital, K. E. Montgomery, M. Richardson, and L. J. Atherton, J. Cryst. Growth 180, 255 (1997). 36 B. R. Thomas, A. A. Chernov, P. G. Vekilov, and D. C. Carter, J. Cryst. Growth 211, 149 (2000). 37 H. Lin, D. N. Petsev, S.-T. Yau, B. R. Thomas, and P. G. Vekilov, Cryst. Growth Des. 1(1), 73 (2001). 38 D. C. Carter, K. Lim, J. X. Ho, B. S. Wright, P. D. Twigg, T. Y. Miller, J. Chapman, K. Keeling, J. Ruble, P. G. Vekilov et al., J. Cryst. Growth 196, 623 (1999). 39 W. H. Massover, Micron 24(4), 389 (1993). 40 P. M. Harrison and P. Arosio, Biochim. Biophys. Acta 1275, 161 (1996). 34

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constituent molecules. These faces grow by the spreading of layers generated by surface nucleation similar to many other proteins.43 Three steps terminating such layers and the terraces between them are seen in Fig. 2. Figure 2 also illustrates the three common types of defects: singlemolecular-site vacancies, triple vacancies (trivacancies), and trivacancies containing a species to be identified below. These defects exist for unlimited time in the top surface layer of both ferritin and apoferritin crystals under all studied growth conditions, at supersaturations as high as 3.8 and at conditions close to equilibrium. Sometimes, clusters of four or five vacancies exist for a few minutes after a growing layer surrounds an underlying defect. They turn into trivacancies by incorporating one or two molecules. Figure 2 also shows about

Fig. 2. In situ atomic force microscopy images of a ferritin surface crystal growing from a solution containing 1 mg ml1 ferritin in 2.5% CdSO4 and 0.05 M acetate buffer with pH 4.5. Note the growth steps with adsorbed impurity clusters and related point defects on the terraces between the steps. 41

D. M. Lawson, P. J. Artymiuk, S. J. Yewdall, J. M. A. Smith, J. C. Livingstone, A. Trefry, A. Luzzago, S. Levi, P. Arosio, G. Cesareni et al., Nature 349, 541 (1991). 42 P. D. Hempstead, S. J. Yewdall, A. R. Fernie, D. M. Lawson, P. J. Artymiuk, D. W. Rice, G. C. Ford, and P. M. Harrison, J. Mol. Biol. 268(2), 424 (1997). 43 A. J. Malkin, Y. G. Kuznetsov, W. Glanz, and A. McPherson, J. Phys. Chem. 100, 11736 (1996).

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20 unknown heterogeneities adsorbed on the surface and this number roughly agrees with other observations under similar conditions. However, when this value was compared with surface concentration of heterogeneities expected from the amount of heterogeneities incorporated into the crystal, it was found that in all likelihood, this surface concentration is strongly reduced by the interactions with the AFM tip during imaging.44 Since the molecular dimer is the predominant impurity present in solutions of both ferritin and apoferritin,34 and it is the impurity preferentially incorporated into the respective crystals,36 we suspect that the adsorbed heterogeneities are these dimers. Indeed, an AFM investigation of the interactions between the adsorbed heterogeneities and the advancing growth steps allowed disconsolation of the shape of the formation from the imaging artifacts, and identification of the heterogeneities as molecular dimers, shaped as two bound monomer spheres.44 This shape agrees with previous electron microscopy observations,45 and with the results of a combined light scattering and chromatography characterization of the crystallizing solution.46 Further monitoring of the growth processes with the two proteins showed that (1) detachments of the dimer molecules are extremely rare and most adsorbed dimers get incorporated into the crystal, and (2) although the two-sphere shape was not always apparent, the incorporated heterogeneity molecules always displace three monomer molecules from the lattice. Based on these considerations, we conclude that all heterogeneities that adsorb on the surface and are seen in Fig. 2 are the molecular dimers of, respectively, ferritin or apoferritin. Surface Properties and Formation Mechanisms of the Dimer. In the studies reviewed here, it was noticed that (1) upon incorporation, the dimers occupy three, rather than two, monomer lattice sites,44 (2) even in the absence Cd2þ or other divalent ions used as precipitant to induce crystallization the overall interactions between the native monomers are repulsive and should preclude dimer formation,47 and (3) the dimers are present in the initial solution prior to the addition of the Cd2þ.46 These observations suggest that the arrangement of the two monomers in the dimer is different from that between two neighboring monomers in the lattice and only monomers that have undergone a partial unfolding, e.g., a rearrangement of the 24 subunits, or opening of the loop regions 44

S.-T. Yau, B. R. Thomas, O. Galkin, O. Gliko, and P. G. Vekilov, Proteins Struct. Funct. Genet. 43, 343 (2001). 45 D. Yang, K. Matsubara, M. Yamaki, S. Ebina, and K. Nagayama, Biochim. Biophys. Acta 1206(2), 173 (1994). 46 D. N. Petsev, B. R. Thomas, S.-T. Yau, and P. G. Vekilov, Biophys. J. 78, 2060 (2000). 47 D. N. Petsev and P. G. Vekilov, Phys. Rev. Lett. 84, 1339 (2000).

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in the peptide chain to reveal the hydrophobic regions of the helices, can partake into the formation of dimers. This unfolding only slightly changes the shape and size of the constituent monomers (strong changes would be detectable by the light scattering technique), and exposes groups that locally increase the attraction between the monomers. Still, the changes are sufficient to preclude incorporation of the dimers in the ferritin and apoferritin crystal lattices as integral components, and to result in the displacement of three monomers. The increased hydrophobicity of the dimer surface underlies the attraction between the dimers under conditions where the monomers strongly repel.46 The exposed attractive contact sites are the likely cause for the increased attraction of the dimers to a monomer crystal surface and for the preferential adsorption of the dimers on the crystal surface. Note that since the dimers are not generated by addition of Cd2þ ions to the solution, they are not a preliminary step in the ferritin and apoferritin crystal nucleation or growth. Dimer Incorporation by the Growing Steps. A possible mode of the effects of impurity molecules on the spreading of layers during growth of various materials has been postulated by Cabrera and Vermileya.48 According to this mechanism, impurities that are strongly adsorbed on the terraces between steps should impede their advancement. The characteristic capillary length—the radius of the two-dimensional critical nucleus—is the parameter that determines the velocity of the steps squeezing between the impurity stoppers.49,50 This mechanism has been supported by indirect evidence from crystallization experiments with various materials,51,52 including proteins,53,54 however, since imaging of individual adsorbed molecules on the surface of a growing crystal was not possible, direct visualization of the action of this mechanism and possible deviations from the original postulate were lacking. In Fig. 3, we monitor the interactions between two advancing steps and the surface defects and adsorbed dimers. Figure 3A shows two clusters adsorbed on the lower terrace. This lower terrace also contains a trivacancy 48

N. Cabrera and D. A. Vermileya, in ‘‘Growth and Perfection of Crystals’’ (R. H. Doremus, B. W. Roberts and D. Turnbul, ed.). John Wiley & Sons, New York, 1958. 49 S. Y. Potapenko, J. Cryst. Growth 133, 141 (1993). 50 V. V. Voronkov and L. N. Rashkovich, J. Cryst. Growth 144, 107 (1994). 51 K. Onuma, K. Tsukamoto and I. Sunagawa, Microgr. Sci. Technol. 2, 62 (1992). 52 A. A. Chernov, ‘‘Modern Crystallography III: Growth of Crystals.’’ Springer-Verlag, Berlin, 1984. 53 P. G. Vekilov, in ‘‘Studies and Concepts in Crystal Growth’’ (H. Komatsu, ed.), p. 25. Pergamon, Oxford, 1993. 54 T. Nakada, G. Sazaki, S. Miyashita, S. D. Durbin, and H. Komatsu, J. Cryst. Growth 196, 503 (1999).

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Fig. 3. Creation and evolution of defects on an apoferritin crystal at supersaturation  ¼ 1.6. (A)–(E) Interactions between advancing step and trivacancies (TV) with a cluster, vacancy, and two clusters, C1 and C2. (F) A new step is stopped by trivacancies with clusters, empty trivacancies, and single vacancies; a trivacancy is created in the new layer on top of the one first seen in (B) after a shift of the view field.

with an incorporated dimer, and a vacancy. Figure 3B and C shows that the growth steps are retarded not only by adsorbed dimers as in Fig. 3D, but by the trivacancy as well. Other similar sequences demonstrate retardation by single vacancies and trivacancies. With all four types of stoppers, a channel with the stopper at the far end forms as shown in Fig. 3B for the dimer-containing trivacancy. This channel does not close until a certain critical number n* of molecules in the steps forming the channel is reached. For this and other series of images at supersaturation,  ¼ 1.6, the value of n* that occurred most frequently was 4. At  ¼ 1.1 the most frequently occurring n* increased to 6, i.e., n* roughly scales with 1/. This appears to suggest that the short steps are retained because of capillarity factors, as suggested by theory. To test this hypothesis, we recall that at the scales of a few molecules as here, the excess capillary energy corresponds to energy of the unsaturated bonds of the molecules at the end of the channel. Detailed analyses lead to the discrete form of the Gibbs–Thomson relation for two-dimensional objects55–57  ¼ =n*

(1)

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where  ¼ 3.2kB T is the free energy of the bond between two molecules in the crystal7; its entropy components stem from the release of solvent molecules upon crystallization.8 Substituting the values of n* in Eq. (1) and using the above , we get  values about half of the values at which the respective n* were found. This suggests a deviation from the classical Cabrera–Vermileya theory: that the elastic strain field around defects, visualized below, may also affect the behavior of the steps around the cluster. Formation and Replication of Defects and Lattice Strain. Steps longer than n* are not hindered by the Gibbs–Thomson factors and move to close the channel in Fig. 3C. However, the elastic field does not allow molecules to attach on top of the trivacancy with the cluster, and an empty trivacancy is created in the next layer, (Fig. 3C–E). Cluster C2 is pushed away by the step. The vacancy next to it in Fig. 3A, after some configurational variations in Fig. 3B–D, is replicated in the advancing layer (Fig. 3F). Figure 3F also shows that the third layer is retarded by all the defects in the second layer and the trivacancy in the second layer in Fig. 3B is also replicated in the third layer. Thus, Fig. 3 illustrates the series of transformations: adsorbed cluster ! trivacancy with a cluster ! trivacancy in subsequent crystal layers. In numerous similar image sequences, we found that both empty and cluster-containing trivacancies may produce single vacancies and trivacancies and single vacancies often replicate in the next layer. A column of vacancies may be terminated by the incorporation of a molecule. The resulting average length of these cigar-shaped cavities is about five crystal layers. Note that we never saw point defects that were not initiated by a cluster adsorbed on the crystal surface. Unlike Schottky and Frenkel defects,21,58 none of the defects observed here is an equilibrium defect induced by the thermal vibrations of the lattice molecules and their lattice sites have never been occupied by apoferritin monomer molecules. Since they are bound to the incorporated cluster, these defects have zero translational mobility. The strain caused by the various defects in a stack is evidenced in Fig. 4 by the 1–2 nm displacements of the molecules around the defects from their crystallographic positions (intermolecular distance is 13 nm). With nine lattice monomers around a trivacancy, the average height of defect stack of five layers, and one dimer molecule per 10 or 20 monomers, the strain should affect all lattice sites and have a noticeable contribution to the background X-ray scattering. 55

I. N. Stranski and R. Kaischew, Z. Phys. Chem. I. N. Stranski and R. Kaischew, Z. Phys. Chem. 57 R. Kaischew and I. N. Stranski, Z. Phys. Chem. 58 C. Kittel, ‘‘Introduction to Solid State Physics.’’ 56

B26, 100 (1934). B26, 114 (1934). B35, 427 (1937). John Wiley & Sons, New York, 1986.

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Fig. 4. Lattice strain in a apoferritin crystal introduced by dimer molecules. Arrows indicate monomers around the three types of point defects that are shifted from their crystallographic positions.

Linear and Planar Defects These are dislocations, twins, sector, grain, and block boundaries. There have been numerous observations of such defects in the AFM literature; for illustrative cases, see Malkin et al.,9 Kuznetsov et al.,59 McPherson et al.,60 and Malkin et al.61; for a recent review, see Mc Person et al.62 Typically, dislocations, twinning, and block structures are the result of accumulation of crystal lattice strain that is resolved in a plastic deformation at a certain critical crystal size.63,64 Sometimes, dislocations may be a side product of the formation of an occlusion.29 Thus, the means to avoid these types of defects are the same as those for the types of defects listed above, namely, to ensure that crystallization proceeds at low to modest supersaturations.

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Y. G. Kuznetsov, A. J. Malkin, and A. McPherson, J. Cryst. Growth 196, 489 (1999). A. McPherson, A. J. Malkin, and Y. G. Kuznetsov, Structure 3, 759 (1995). 61 A. J. Malkin, T. A. Land, Y. U. G. Kuznetsov, A. McPherson, and J. J. DeYoreo, Phys. Rev. Lett. 75(14), 2778 (1995). 62 A. McPherson, A. J. Malkin and Y. G. Kuznetsov, Annu. Rev. Biomol. Struct. 20, 361 (2000). 63 A. A. Chernov, J. Cryst. Growth 196, 524 (1999). 64 F. Rosenberger, P. G. Vekilov, M. Muschol, and B. R. Thomas, J. Cryst. Growth 167, (1996). 60

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Striations, Occlusions These types of defects occur due to unsteady growth rates, either imposed by variations of external conditions,65 or may be intrinsic to the growth process.14,66,67 They can be minimized by maintaining steady external conditions, and adjusting the rate of transport to the growth interface, as suggested by our previous research.14,66,67 Transport rate acceleration can be achieved through forced flow of the solution,30 while transport is slower during, for instance, growth in microgravity.11,68 For a recent review on the mechanisms leading to such defects and for suggested modifications of the crystallization conditions that may help to avoid them, see Vekilov and Alexander.11 Incorporation of Microcrystals Continuing nucleation throughout a crystallization run and poor separation of nucleation and growth9,10,43 can lead to incorporation of microcrystals. In principle, this can be minimized by suppressing the nucleation of the microcrystals.69 In many cases, however, such levels of control of the nucleation process are not available. Figure 5 illustrates the incorporation of a formation that has landed on the growing crystal surface of an apoferritin crystal in Fig. 5A. Besides this formation, heterogeneities, likely the apoferritin molecular dimer discussed above, are also adsorbed on the surface. Zooming in, we find in Fig. 5B that the formation is an apparently perfect microcrystal consisting of three layers—the section in Fig. 5C was taken after the incoming layer visible in Fig. 5A surrounded the microcrystal—with about 60 molecules in each layer. Upon landing, the microcrystal may have covered an adsorbed heterogeneity cluster and this could explain its inclination with respect to the surface in Fig. 5C. After about 15 min new crystal layers reach the microcrystal and surround it (Fig. 5D and E). Judging from the orientation of the {110} molecular rows in the microcrystal and the large crystals in Fig. 5B, D, and E, the two crystals are in registry. Still, the tilt seen in Fig. 5C leads to a far from perfect fit between the microcrystal and the surrounding material— a boundary with a thickness comparable to the molecular size obtained in Fig. 5D and E. In analogy to the strain caused by a single vacancy in Fig. 4, 65

L. A. Monaco, F. Rosenberger, J. Cryst. Growth 129, 465 (1993). P. G. Vekilov, J. I. D. Alexander, and F. Rosenberger, Phys. Rev. E 54, 6650 (1996). 67 P. G. Vekilov and F. Rosenberger, Phys. Rev. Lett. 80, 2654 (1998). 68 P. G. Vekilov, Adv. Space Res. 24, 1231 (1999). 69 O. Galkin and P. G. Vekilov, Proc. Natl. Acad. Sci. USA 97(12), 6277 (2000). 66

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Fig. 5. Incorporation of a microcrystal by a growing apoferritin crystal. (A) A microcrystal, identified by zoom in (B) and indicated by an arrow lands on the surface. (C) Height profile along diagonal in (B) showing the inclination of the microcrystal with respect to the underlying plane of the large crystal. (D)–(I) Stages of the incorporation of the microcrystal; times shown are after the image in (A) was recorded; the Arabic numerals at the bottom of (E)–(I) count the layers on top of the incorporated microcrystal.

we can expect this boundary to induce significant strain in the lattice of the large crystal. Unfortunately, the detrimental effects for the crystal quality from the incorporation of the microcrystal are not limited to this boundary and the strain associated with it. Figure 5E–I shows that even after the microcrystal is covered with new layers, a cluster of vacancies forms all the way up to the fifth layer above it. This vacancy cluster is due to the strain caused by the trapped microcrystal in the layers above it. It is quite surprising that the strain field around a microcrystal has the same characteristic lengthscale as the strain field around a single heterogeneity molecule or a vacancy in the lattice. As a result, the perturbation in the lattice due to the trapping of larger objects is localized around these objects. There are numerous observations of the incorporation of microcrystals in protein crystals in the literature.6,9,10,43,60,62,70 The novel insight

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contributed by the molecular resolution images in Fig. 5 consists in the finding that even microcrystals that appear well aligned with the underlying lattice cause significant lattice strain, and that the strain field stretches to about five molecular dimensions around the trapped microcrystal. Can trapping of microcrystals be avoided? Obviously, if the growth conditions are chosen such that no nucleation of microcrystals occurs, there will be no trapping. However, often, as in the cases of ferritin and apoferritin, the growth conditions change during growth due to, e.g., solution depletion and precipitant segregation at the crystal–solution interface, and may pass thorough a set inductive of nucleation. As a second line of defense, it has been argued that in a microgravity environment, for instance aboard a spacecraft, the microcrystals will not sediment on the growing crystal.71 As shown below, this may not always help. Other than sedimentation driven by Earth’s gravity, a microcrystal may reach the surface of a growing larger crystal by Brownian diffusion. Let us consider these two transport pathways. The velocity of sedimentation  of a particle of radius r with density 1 falling in a liquid with viscosity  and density 2 is  ¼ 2r2 (1  2)g/9, where g is the free fall acceleration. This velocity is determined by the balance of the buoyancy, (4/3)r3 (1  2)g, and the viscous, 6r, forces.72,73 For the microcrystal in Fig. 5, r  130 nm, and assuming density difference between crystal and solution 12  0.3 g cm3,74 we get  ¼ 1.2  106 cm s1. If the microcrystals form at a height of about 100 m, they would take more than 2 hr to reach the surface. The corresponding characteristic Brownian diffusion time to reach the substrate for a cluster formed at a distance x ¼ 100 m from the surface can be evaluated from Einstein’s relation x2 ¼ 2D . A lower estimate for cluster diffusivity D can be obtained from the diffusivity of single apoferritin molecules, 3.2  107 cm2/s46,47 using Stokes low and assuming that the microcrystal behaves like a particle with 10 molecules at an edge: D  3.2  108 cm2/s. Substituting,  1500 s  25 min. Hence, Brownian diffusion is a more efficient method of transfer of microcrystals to the surface of a large crystal than sedimentation, and even in the absence of gravity, microcrystals can still reach the surface and get trapped.

70

A. J. Malkin, Y. G. Kuznetsov, and A. McPherson, J. Cryst. Growth 196, 471 (1999). A. McPherson, A. J. Malkin, Y. G. Kuznetsov, S. Kozselak, M. Wells, G. Jenkins, J. Howard, and G. Lawson, J. Cryst. Growth 196, 572 (1999). 72 P. Atkins, ‘‘Physical Chemistry.’’ Freeman, New York, 1998. 73 E. A. Moelwyn-Hughes, ‘‘Physical Chemistry.’’ Pergamon, London, 1961. 74 L. K. Steinrauf, Acta Crystallogr. 12, 77 (1959). 71

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Mosaicity

Relation between Point Defects, Lattice Strain, and Mosaicity The link between the impurity-induced defects and the strain in the crystal’s lattice is illustrated above by Fig. 4. It has been argued that the lattice strain may accumulate only to a certain level, and if this level is exceeded, a plastic deformation, leading to block structures, etc., may occur.63,75 The elastic energy of a strained crystal increases as the crystal grows proportionally to L3, L being the crystal size. On the other hand, the emergence of unstrained blocks separated by a dislocation network would minimize the crystal’s energy with the grain boundary energy  L2. The balance between the elastic strain and the interblock surface energy determines the critical size for the onset of mosaicity.63,75 Indeed, mosaic blocks 20–50 m wide were observed for ferritin and apoferritin crystals larger than 200 m growing from solutions 2–3 months old in which the concentration of the dimers is higher.34 Growth steps were confined within the individual blocks and the growth of each block was independent of the others. Similarly, independent growth of blocks of a satellite tobacco mosaic crystal were reported by Malkin et al.9 Mosaicity due to Trapped Microcrystals? To further explore the above AFM observation of the onset of mosaic block structures in ferritin and apoferritin crystals larger than 200 m, we grew numerous crystals of the two proteins under careful microscopic observation. Typically, crystals smaller than 200–300 m appeared perfect without any visible boundaries or any other defects; an example is shown in Fig. 6A. As they grew larger, one and then more boundaries appeared, separating the crystal into two, three, etc., blocs as in Fig. 6B. The sizes of these blocs varied between 20 and about 100 m. If older solutions that contain higher levels of the dimer are used, the size at which the crystal breaks into individual domains shifts downward. Figure 6B also shows the trapping of a few 10–15 m crystals and smaller objects. Since the strain filed around the trapped crystals and objects is short-ranged, and there are relatively few of them, we conclude that their contribution to the overall strain in the crystal is insignificant. Furthermore, although we did not carry out X-ray characterization of the grown crystals, we offer that since the trapped crystal and objects occupy a small fraction of the total volume of the large crystal, diffraction from them is a minor contribution to the mosaicity of the diffraction pattern. 75

A. A. Chernov, Acta Crystallogr. A54, 859 (1998).

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Fig. 6. Optical micrograph of a ferritin crystal. (A) Typical crystal smaller than 300 m— no defects or block boundaries are discernible. (B) Typical crystal larger than 300 m—black arrow indicates a block boundary; white arrows indicate incorporated crystals and microscopic objects.

These observations of the onset of mosaicity show that (1) there is a critical size below which even defect-rich crystal will not be mosaic, (2) trapping of smaller crystals does not significantly contribute to the mosaicity, and (3) mosaicity is primarily due to the accumulation of strain associated with the incorporation of the ferritin and apoferritin molecular dimers into the lattice. Critical Size for the Onset of Mosaicity Theoretical predictions of the critical size for the onset of mosaicity due to the elastic strain associated with the incorporated impurity molecules have been performed only for the protein lysozyme. Using a recently determined Young modulus for lysozyme crystals (A. Holmes, private communication), the critical size was evaluated to be in the range 100–500 m.63 As with ferritin and apoferritin, the typical impurities for this protein are covalently bound dimers at  1–2% of the dry protein mass.32,76 They cannot be fully removed, recur after purification, and readily incorporate into crystals. For evidence of impurity-induced mosaicity with this protein, we monitored the growth and dissolution of lysozyme crystals. If the crystals were grown at high supersaturations ( ¼ C/Ce 25) from solutions

76

B. R. Thomas, P. G. Vekilov, and F. Rosenberger, Acta Crystallogr. D 54, 226 (1998).

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with impurity contents at the high end of the above range, the crystals exhibited the rather irregular morphology depicted in Fig. 7A. The sequence in Fig. 7 shows subsequent stages dissolution of a crystal grown at supersaturation C/Ce ¼ 38 from a solution containing 1.5% (w/w dry protein mass) of the lysozyme dimer. Dissolution of the heavily mosaic crystal (Fig. 7A) reveals that below  170 m (Fig. 7C) the crystal consists of a single block. This is the critical size for the onset of mosaicity, within the range of the theoretical estimates by Chernov.63 Crystals grown from solutions containing lower impurity amounts did not reveal such mosaic structure. This allows us to correlate the mosaicity with this protein to the lattice strain introduced by the impurity incorporation. Since the critical size of  200 m for the onset of this type of mosaicity for ferritin and apoferritin is in the range expected and demonstrated for lysozyme, we may conclude that the Young modulus of these two crystals is close and does not differ much from that for lysozyme. The existence of a critical size for the onset of mosaicity suggests that in some cases smaller crystals may be more suitable for diffraction studies than larger crystals. On the other hand, for other proteins, the critical size may be too small for practical use of subcritical crystals. Note that the perfect faceting of a crystal, such as the one in Fig. 6B, does not indicate the lack of mosaicity. High magnification optical observations with specialized techniques are required to see the block structure.

Fig. 7. Determination of the critical size for the onset of mosaicity during growth of a  lysozyme crystal by monitoring the crystal’s dissolution. (A) A crystal grown at T  10 , from a solution with C/Ce ¼ 38 that contains covalently bound dimers at  1.5% of the dry protein mass. (B) Faster dissolution along the block boundaries causes ‘‘hairy’’ morphology. (C) A well-faceted, undeformed crystal emerges when size decreases to  170 m; slow and uniform dissolution indicates lack of block boundaries.

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Acknowledgments My deepest gratitude goes to my colleagues and collaborators, without whom the results reviewed here would never have been obtained: Siu-Tung Yau, Dimiter Petsev, Bill R. Thomas, Oleg Galkin, and Olga Gliko. Most of the work reviewed here was carried out during my tenure at the University of Alabama in Huntsville. I highly appreciate the support that the academic and research units in that institution have given me over the years. Financial support was provided by the National Heart, Lung and Blood Institute, NIH, and by the Office for Biological and Physical Research, NASA.

[11] Cryocooling of Macromolecular Crystals: Optimization Methods By Elspeth F. Garman and Sylvie Doublie´ Introduction

The compelling advantages of collecting macromolecular crystallographic X-ray data at cryotemperatures are now widely recognized, and the technique is currently used substantially more than room temperature data collection, particularly at synchrotrons. The driving force behind this shift has been the significant reduction in X-ray-induced radiation damage suffered by a crystal held at around 100 K during data collection. The energy loss of the X-ray beam by absorption in the crystal produces primary radicals, which in turn give rise to secondary radicals, the diffusion of which is substantially reduced at low temperatures. However, even at 100 K, radiation damage can still be a limiting problem when using X-ray beams from second- and third-generation synchrotrons, particularly on undulator-fed beamlines. An understanding of the processes involved in the damage and possible methods of mitigating it are actively being sought.1–3 A further significant advantage of current cryotechniques is that the predominant mounting method, whereby the crystal is suspended in a solution of cryobuffer by surface tension in a loop4 of thin fiber, often inflicts less mechanical stress on fragile crystals than do conventional capillarymounting methods where the crystal must be inserted into a quartz or glass tube. This enables one to use smaller and thinner crystals for structure 1

Radiation Damage Workshop Reports, J. Synchrotron Radiat. 9, 327–375 (2002). T. Y. Teng and K. Moffat, J. Synchrotron Radiat. 7, 313 (2000). 3 B. L. Hanson, J. M. Harp, K. Kirschbaum, D. A. Parrish, D. T. Timm, A. Howard, A. A. Pinkerton, and G. J. Bunick, J. Cryst. Growth 232, 536 (2001). 4 T. Y. Teng, J. Appl. Crystallogr. 23, 387 (1990). 2

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