Molecular mechanisms of microheterogeneity-induced defect formation in ferritin crystallization

Molecular Mechanisms of Microheterogeneity-InducedDefect Formation in Ferritin CrystallizationS.-T. Yau,2 † Bill R. Thomas,2,3 Oleg Galkin,2 Olga Gliko,2 and Peter G. Vekilov1,2*1Department of Chemistry, University of Alabama in Huntsville, Huntsville, Alabama2Center for Microgravity and Materials Research, University of Alabama in Huntsville, Huntsville, Alabama3Universities Space Research Association, Marshal Space Flight Center, Huntsville, Alabama

ABSTRACT We apply in situ atomic force mi-croscopy to the crystallization of ferritins fromsolutions containing '5% (w/w) of their inherentmolecular dimers. Molecular resolution imagingshows that the dimers consist of two bound mono-mers. The constituent monomers are likely partiallydenatured, resulting in increased hydrophobicity ofthe dimer surface. Correspondingly, the dimersstrongly adsorb on the crystal surface. The ad-sorbed dimers hinder step growth and on incorpora-tion by the crystal initiate stacks of up to 10 tripleand single vacancies in the subsequent crystal lay-ers. The molecules around the vacancies are shiftedby '0.1 molecular dimensions from their crystallo-graphic positions. The shifts strain the lattice and,as a consequence, at crystal sizes > 200 mm, theaccumulated strain is resolved by a plastic deforma-tion whereupon the crystal breaks into mosaicblocks 20–50 mm in size. The critical size for theonset of mosaicity is similar for ferritin and apofer-ritin and close to the value for a third protein,lysozyme; it also agrees with theoretical predic-tions. Trapped microcrystals in ferritin and apofer-ritin induce strain with a characteristic length scaleequal to that of a single point defect, and, as aconsequence, trapping does not contribute to themosaicity. The sequence of undesired phenomenathat include heterogeneity generation, adsorption,incorporation, and the resulting lattice strain andmosaicity in this and other proteins systems, couldbe avoided by improved methods to separate similarproteins species (microheterogeneity) or by increas-ing the biochemical stability of the macromoleculesagainst oligomerization. Proteins 2001;43:343–352.© 2001 Wiley-Liss, Inc.

INTRODUCTION

X-ray crystallography is the major method of structuralmolecular biology, including many of the structural andfunctional genomics projects currently underway.1 Al-though many proteins can be relatively easily enticed toyield crystals of size and perfection sufficient for theplanned structure studies, the crystallization of someproteins with important biological functions is still a majorhurdle in structural investigations.2 Incorporation of impu-rities (other proteins or macromolecules or modifications ofthe native protein) having sizes similar to those of thecrystallizing proteins has been identified as a major factor

of protein crystal imperfection.3–6 Recent evidence sug-gests that other proteins are more readily removable onpurification,7,8 and even at high levels in the solution theirincorporation into the crystals may be low.9 Thus, in manycases, the impurity species responsible for the deteriora-tion of the crystal quality are non-dissociable aggregates(oligomers, clusters) of native protein molecules.10,11

Although the mechanisms leading to relatively perfectprotein crystals have been studied in great detail at boththe mesoscopic12–14 and the molecular level,15–19 only afew of the processes leading to defects have been moni-tored.20–22 The goal of the work presented here is to studyat the molecular level the processes that accompanycrystallization and involve a molecular dimer of the se-lected protein system: adsorption at the growth interface,incorporation as the growing step, resulting defects, andassociated lattice strain and potential plastic deformationssuch as mosaicity.

We use atomic force microscopy imaging at molecularand submolecular resolution as recently applied to investi-gation of crystallization mechanisms.18,19,23 We work withferritin, a major iron storage protein in the cytosol, andapoferritin consisting of the ferritin protein shell sans theiron core.24,25 On the molecular level, the structures andprocesses observed with the two proteins are very similar.Previous studies have shown that for both proteins, spe-cies with molecular masses double that of the nativeproteins are the major contaminant.8 The levels of theseimpurities can be brought down to at most '5%; over 30days or more, the dimers are regenerated. Thus, it wasfound that after storage for a year at 5°C, the dimerconcentration reached as high as 40% (w/w) (B.R.T.,unpublished observations). A static and dynamic light-scattering investigation revealed that the likely shape ofthe dimer is of two bound monomer spheres.26 The samestudy found that dimer molecules attract in a solution in

Grant sponsor: National Heart, Lung, and Blood Institute, NationalInstitutes of Health; Grant number: HL 58038; Grant sponsor: Lifeand Microgravity Sciences and Applications Division of NASA; Grantnumbers: NAG8-1354 and 97 HEDS 02-50.

*S.-T. Yau’s present address is Albany Institute for Materials,University at Albany-SUNY, ESTM, Albany, NY 12203.

Correspondence to: Peter G. Vekilov, Department of Chemistry,University of Alabama in Huntsville, Von Braun Research Hall D-9,Huntsville, AL 35899. E-mail: [email protected]

Received 4 August 2000; Accepted 26 January 2001

Published online 00 Month 2001

PROTEINS: Structure, Function, and Genetics 43:343–352 (2001)

© 2001 WILEY-LISS, INC.

which the monomers strongly repel, suggesting a partialunfolding of the monomers on dimerization that exposesthe attractive hydrophobic residues.26

MATERIALS AND METHODS

The ferritin and apoferritin were purified from commer-cial preparations (Sigma, St. Louis, MO) as described inRef. 8. In both preparations, the concentrations of thepredominant contaminants, the respective moleculardimers, were brought down from '50 to '5% (w/w dryprotein). Quantifications of the relative amounts of dimersand monomers in the crystals or in the surroundingsolutions were conducted by gel electrophoresis with silverstaining using a PhastGel Unit (Pharmacia, Piscatway,NJ) and gel-filtration fast protein liquid chromatographyusing Pharmacia Biotech Superose 6 HR 10/30 column.For details about these techniques, see Refs. 7–9 and 27.

Crystallizing solutions containing 0.02–1 mg z mL21

protein, 2.5% CdSO4 precipitant in a 0.05 M acetate bufferwere prepared as described in Refs. 8 and 26. The supersatu-ration of the solution with respect to the crystalline phasewas determined for apoferritin as s [ Dm/kBT 5 ln(g C/geCe),where C and Ce 5 23 mg z mL21 are the actual andequilibrium protein concentrations.19,23 As shown in Ref.19, at these low protein concentrations, the activity coeffi-cients g and ge ' 1. Tests for ferritin revealed similarvalues for Ce and g, used for estimates of the supersatura-tion in solution of this protein.

Atomic force microscopy (AFM) imaging of the crystalli-zation processes was conducted in tapping mode28,29 byusing Nanoscope IIIa from Digital Instruments (SantaBarbara, CA). We used room temperature stabilized to23.0 6 0.3°C as in Ref. 18 and 23; for calibration, tests, anddetermination of the maximum resolution of the method of16 Å, see Ref. 19. As in these previous studies, we used thestandard SiN tips, and the tapping drive frequency wasadjusted in the range 25–31 kHz to the resonance value forspecific tip used. The AFM imaging parameters wereselected such that the imaging does not affect either thesurface structure even at the molecular level or theprocesses of molecular incorporation. However, as shownbelow, impact of the AFM tip significantly reduces theconcentrations of the adsorbed heterogeneities.

Optical microscopy characterization of the grown crys-tals was conducted in situ by using microscopes Leica MZ 8or Leica MZ 9.5. The crystals were illuminated from theside with a He-Ne laser with a 638-nm wavelength and20-mW power. Such illumination enhances the contrast offeatures perpendicular to the horizontal top crystal face.The images were captured by a digital camera, either Sony3CCD CatsEye DKC-5000 or Kodak MegaPlus 1.6i, andthe contrast was further enhanced by using MicrosoftPhoto Editor 3.01.

RESULTS AND DISCUSSIONCharacterization of the Crystal Surface DuringGrowth

Ferritin and apoferritin crystallize in a face-centeredcubic (fcc) lattice with space group F432.30,31 The crystal

habit is dominated by the octahedral [111] faces, character-ized with hexagonal coordination of the constituent mol-ecules. These faces grow by the spreading of layers gener-ated by surface nucleation similar to many other proteins.32

Three steps terminating such layers and the terracesbetween them are seen in Figure 1. This figure alsoillustrates the three common types of defects: single-molecular-site vacancies, triple vacancies (trivacancies),and trivacancies containing a species to be identifiedbelow. These defects exist for unlimited time in the topsurface layer of both ferritin and apoferritin crystals underall studied growth conditions, at supersaturations as highas 3.8 and at conditions close to equilibrium. Sometimes,clusters of four or five vacancies exist for a few minutesafter a growing layer surrounds an underlying defect.They turn into trivacancies by incorporating one or twomolecules. Figure 1 also shows '20 unknown heterogene-ities adsorbed on the surface. The acts of adsorption arerandom events, independent of the terrace age. Adsorptionon a fresh surface may occur after ,1 s; for instance, aheterogeneity molecule is present close to the edge of step2 in Figure 1 where the surface age is '1 s.

The identification of the heterogeneities, the correlationbetween these formations and the defects, and the conse-quences for the crystal perfection are the subject of thediscussion below.

Identification of the Adsorbed HeterogeneityMolecules

Because the molecular dimer is the predominant impu-rity present in solutions of both ferritin and apoferritin8

and it is the impurity preferentially incorporated into therespective crystals,9 we suspect that the adsorbed hetero-geneities are these dimers. However, the image of anadsorbed cluster is a convolution of the cluster shape andits molecular vibrations, with effects due to multiple AFMtips, and this precludes unambiguous AFM identification.Monitoring a step approach and incorporating the clusterin Figure 2 removes these obscuring effects—Figure 2band c show that the heterogeneities are molecular dimers,in this case of apoferritin, shaped as two bound monomerspheres and seen by electron microscopy.33 This shapeagrees with the result of a combined light-scattering andchromatography characterization of the crystallizing solu-tion in our laboratory.26 The dimers in Figure 2 occupythree, rather than two monomer lattice sites; for a discus-sion of this phenomenon, see below. Numerous otherimage sequences with the two proteins showed that (i)detachments of the heterogeneities are extremely rare andthat most adsorbed dimers get incorporated into thecrystal and (ii) although the two-sphere shape was notalways apparent, the incorporated heterogeneity mol-ecules always displace three monomer molecules form thelattice. On the basis of these considerations, we concludethat all heterogeneities that adsorb on the surface and areseen in Figure 1 are the molecular dimers of, respectively,ferritin or apoferritin.

344 S.-T. YAU ET AL.

Surface Concentration of the Dimer

From Figure 1, the dimer surface concentration is 22dimers z mm22 5 2.2 3 109 dimers cm22. A 10-nm-thicklayer above the crystal would have dimer concentration2.2 3 1015 dimer molecules cm23. This is 100–1,000-foldhigher than typical dimer concentrations in the bulksolution: 5% w/w of the dimer corresponds to 2.5 dimermolecule/100 monomer molecules or 3 3 1012 dimer mol-ecules z cm23 in a 0.1 mg z mL21 solution. Note, however,that the surface concentration of the dimmers is likelyreduced by the interactions with the AFM tip during

imaging; we notice that after imaging for times of the orderof 0.5 h, this concentration is reduced about twofold. Thefollowing considerations suggest that even stronger reduc-tion of the surface concentration due to tip impact mayoccur immediately on the commencement of imaging and,hence, remain undetected.

We use the fact discussed above that most adsorbeddimers are incorporated into the crystals. We determinedthe relative amount of dimers incorporated into the crys-tals by dissolving the crystals and quantifying the mono-mer and dimer concentrations in the resulting solution asdiscussed in Materials and Methods. The found dimersegregation coefficient was between 2.5 and 4, Ref. 9, i.e.,there is that-fold more dimers per monomer molecule inthe crystals than in the solution. One square micrometer ofthe top crystal layer contains '12,000 monomers thatoccupy triangles of 13 nm on a side. Hence, because alladsorbed dimers are incorporated, the expected surfacedimer concentration would be .750 mm22. Thus, even inthe gentler tapping mode, atomic force imaging cannot beused to determine the surface concentration of the ad-sorbed dimers.

There are two possible selection criteria that determineif an adsorbed heterogeneity molecule will be removed bythe AFM tip or will stay and be incorporated as we watchit. (i) There are two dimer populations, and only one ofthem, namely, the two sphere-shaped dimer, is sufficientlystrongly adsorbed. (ii) All dimers are identical, but we onlysee those adsorbed at special surface sites; the reasons forthe strong adsorption at these sites cannot be identified bythe techniques used in this study. In view of the light-scattering and gel electrophoresis results in Refs. 8 and 26that show that in ferritin and apoferritin solutions there isa single dimer population with the same shape as the onerevealed by AFM, we conclude that possibility (i) is un-likely. Then, (ii) acts and the AFM observations of thedimer incorporation and its consequences for the crystalquality are relevant to the understanding of the crystalliza-tion and crystal perfection of these proteins.

Fig. 1. In situ atomic force microscopy images of a ferritin surfacecrystal growing from a solution containing 1 mg mL21 ferritin in 2.5%CdSO4 and 0.05 M acetate buffer with pH 4.5. Note the growth steps withadsorbed impurity clusters and related point defects on the terracesbetween the steps.

Fig. 2. Incorporation of a cluster, indicated by arrows, by a step on the surface of an apoferritin crystal growing from a 0.12 mg mL21 solution: a: Thecluster adsorbed on the crystal surface in front of the step. b,c: The step incorporates the cluster, and its shape is deconvoluted from vibration andmultiple-tip effects to allow identification as a ferritin dimer.

MICROHETEROGENEITIES AND DEFECTS 345

Surface Properties and Formation Mechanisms ofthe Dimer

Figure 2c shows that (i) on incorporation, the dimersoccupy three, rather than two, monomer lattice sites.Furthermore, as shown in Refs. 26 and 34 (ii) in theabsence Cd21, the overall interactions between the nativemonomers are repulsive and should preclude dimer forma-tion; whereas (iii) the dimers are present in the initialsolution before the addition of the CdSO4 precipitant.

These observations suggest that the arrangement of thetwo monomers in the dimer is different from that betweentwo neighboring monomers in the lattice, and only mono-mers that have undergone a partial unfolding, e.g., arearrangement of the 24 subunits, or opening of the loopregions in the peptide chain to reveal the hydrophobicregions of the helices, can partake into the formation ofdimers. This unfolding only slightly changes the shape andsize of the constituent monomers (strong changes would bedetectable by the light-scattering technique) and exposes

groups that locally increase the attraction between themonomers. Still, the changes are sufficient to precludeincorporation of the dimers in the ferritin and apoferritincrystal lattices as integral components and to result in thedisplacement of three monomers seen in Figures 1 and 2.The increased hydrophobicity of the dimer surface under-lies the attraction between the dimers under conditionswhere the monomers strongly repel.26 The exposed attrac-tive contact sites are the likely cause for the increasedattraction of the dimers to a monomer crystal surface andfor the preferential adsorption of the dimers on the crystalsurface. Furthermore, note that because the dimers arenot generated by addition of Cd21 ions to the solution, theyare not a preliminary step in the ferritin and apoferritincrystal nucleation or growth.

Dimer Incorporation by the Growing Steps

A possible mode of the effects of impurity molecules onthe spreading of layers during growth of various materials

Fig. 3. Creation and evolution of defects on an apoferritin crystal at supersaturation s 5 1.6. a–e: Interactions between advancing step andtrivacancies with a cluster, vacancy, and two clusters, C1 and C2. f: A new step is stopped by trivacancies with clusters, empty trivacancies, and singlevacancies; a trivacancy is created in the new layer on top of the one first seen in (b) after a shift of the view field.


has been postulated by Cabrera and Vermileya.35 Accord-ing to this mechanism, impurities that are strongly ad-sorbed on the terraces between steps should impede theiradvancement. The characteristic capillary length—theradius of the two-dimensional critical nucleus—is theparameter that determines the velocity of the steps squeez-ing between the impurity stoppers.36,37 This mechanismhas been supported by indirect evidence form crystalliza-tion experiments with various materials,38,39 includingproteins40,41; however, because imaging of individual ad-sorbed molecules on the surface of a growing crystal wasnot possible, direct visualization of the action of thismechanism and possible deviations from the originalpostulate was lacking.

In Figure 3, we monitor the interactions between twoadvancing steps and the surface defects and adsorbeddimers. Figure 3a shows two clusters adsorbed on thelower terrace. This lower terrace also contains a trivacancywith an incorporated dimer and a vacancy. Figure 3b and cshows that the growth steps are retarded not only byadsorbed dimers as in Figure 3d but by the trivacancy aswell. Other similar sequences show retardation by singlevacancies and trivacancies.

With all four types of stoppers, a channel with thestopper at the far end forms as shown in Figure 3b for thedimer-containing trivacancy. This channel does not closeuntil a certain critical number n* of molecules in the stepsforming the channel is reached. For this and other series ofimages at s 5 1.6, the value of n* that occurred mostfrequently was 4. At s 5 1.1 the most frequently occurringn* increased to 6, i.e., n* roughly scales with 1/s. Thisseems to suggest that the short steps are retained because

of capillarity factors, as suggested by the theory.35 To testthis hypothesis, we recall that at the scales of a fewmolecules as here, the excess capillary energy correspondsto energy of the unsaturated bonds of the molecules at theend of the channel. Detailed analyses lead to the discreteform of the Gibbs-Thomson relation42–44

Dm 5 f/n*,

where f 5 3.2kBT is the free energy of the bond between twomolecules in the crystal18; its entropy components stem fromthe release of solvent molecules on crystallization.19 Substi-tuting the values of n* in Eq. (1) and using the above f, weget Dm values about half of the values at which the respectiven* were found. This suggests another deviation from theclassical Cabrera-Vermileya theory: that the elastic strainfield around defect,5 discussed below, may also affect thebehavior of the steps around the cluster.

Formation and Replication of Defects

Steps longer than n* are not hindered by the Gibbs-Thomson factors and the elastic barriers and move to closethe channel in Figure 3c. However, the elastic field doesnot allow molecules to attach on top of the trivacancy withthe cluster, and an empty trivacancy is created in the nextlayer, Figure 3c–e. Cluster C2 is pushed away by the step.The vacancy next to it in Figure 3a, after some configura-tional variations in Figures 3b–d, is replicated in theadvancing layer, Figure 3f. Figure 3f also shows that thethird layer is retarded by all the defects in the second layerand the trivacancy in the second layer in Figure 3b is alsoreplicated in the third layer.

Thus, Figure 3 illustrates the series of transformations:adsorbed cluster3 trivacancy with a cluster3 trivacancyin subsequent crystal layers. In numerous similar imagesequences, we found that both empty and cluster-contain-ing trivacancies may produce single vacancies and trivacan-cies, and single vacancies often replicate in the next layer.A column of vacancies may be terminated by the incorpora-tion of a molecule. The resulting average length of thesecigar-shaped cavities is about five crystal layers. Note thatwe never saw point defects that were not initiated by acluster adsorbed on the crystal surface. Unlike Schottkyand Frenkel defects,45,46 none of the defects observed hereare equilibrium defects induced by the thermal vibrationsof the lattice molecules, and their lattice sites have neverbeen occupied by apoferritin monomer molecules. Becausethey are bound to the incorporated cluster, these defectshave zero translational mobility.

Consequences for Crystal Quality: Lattice Strainand Mosaicity

The strain caused by the various defects in a stack isevidenced in Figure 4 by the '1–2-nm displacements ofthe molecules around the defects from their crystallo-graphic positions (intermolecular distance is '13 nm).With nine lattice monomers in the layer around a triva-cancy, average height of defect stack of five layers, and onedimer molecule per 10 or 20 monomers, the strain should

Fig. 4. Lattice strain in an apoferritin crystal introduced by dimermolecules. Arrows indicate monomers around the three types of pointdefects that are shifted from their crystallographic positions.


affect all lattice sites and have noticeable contribution tothe background X-ray scattering.

Even stronger effects on the crystal quality and utilityfor diffraction studies arise because of the impurity-induced strain. Mosaicity is one of them, and a mechanismleading to it and based on impurity-induced strain issummarized below. The elastic energy of a strained crystalincreases as the crystal grows proportionally to L,3 L beingthe crystal size. On the other hand, the emergence ofunstrained blocks separated by a dislocation networkwould minimize the crystal’s energy with the grain bound-ary energy 'L.2 The balance between the elastic strainand the interblock surface energy determines the criticalsize for the onset of mosaicity.6,47

Indeed, mosaic blocks '20–50-mm wide were observedfor ferritin and apoferritin crystals larger than '200 mmgrowing from solutions 2–3 months old in which theconcentration of the dimers is higher.8 Growth steps wereconfined within the individual blocks, and the growth ofeach block was independent from the others. Similarly,independent growth of blocks of a satellite tobacco mosaiccrystal was reported in Ref. 20.

Other Sources of Mosaicity

Arguments have been put forth that crystals’ qualityand utility for diffraction studies is only affected byshort-scale molecular disorder and not by mosaicity andblock structures.48 There are examples in which heavilymosaic crystals diffract to high resolution.49 On the otherhand, the diffraction resolution is determined by thesignal-to-noise ratio of high-index reflections. Becausehigh-index crystal planes have low molecular density,larger areas of rotationally and translationally alignedmolecules are needed to enhance the intensity of thereflections from these planes. Hence, crystal imperfectionson the scale of microns could affect the diffraction resolu-tion obtainable from a crystal.50 Mosaicity, striae, andblock structures often lead to broader or split diffractionspots and, hence, lower accuracy of the structure determi-nation.51–53 However, if the crystal consists of a few largeblocks, the beam in X-ray diffraction experiments can befocused on only one of these blocks, and high-resolutionstructure determinations can still be achieved.49,54 Hence,studies of mosaicity and the molecular mechanisms lead-ing to it are relevant to the understanding of the factorsunderlying crystal perfection.

Figure 5 illustrates the incorporation of a formation thathas landed on the growing crystal surface of an apoferritincrystal in Figure 5a. Besides this formation, heterogene-ities, likely the apoferritin molecular dimer discussedabove, are also adsorbed on the surface. Their surfaceconcentration is roughly equal to the one in Figure 1.Zooming in, we find in Figure 5b that the formation is anapparently perfect microcrystal consisting of three layers—the section in Figure 5c was taken after the incoming layervisible in Figure 5a surrounded the microcrystal—withabout 60 molecules in each layer. On landing, the micro-crystal may have covered an adsorbed heterogeneity clus-

ter, and this could explain its inclination with respect tothe surface in Figure 5c.

After '15 min, new crystal layers reach the microcrystaland surround it (Fig. 5d and e). Judging from the orienta-tion of the {110} molecular rows in the microcrystal and thelarge crystals in Figures 5b, d, and e, the two crystals arein registry. Still, the tilt seen in Figure 5c leads to a farfrom perfect fit between the microcrystal and the surround-ing material—a boundary with a thickness comparablewith the molecular size obtains in Figures 5d and e. Inanalogy to the strain caused by a single vacancy in Figure4, we can expect this boundary to induce significant strainin the lattice of the large crystal. Unfortunately, thedetrimental effects for the crystal quality from the incorpo-ration of the microcrystal are not limited to this boundaryand the strain associated with it. Figure 5e–i shows thateven after the microcrystal is covered with new layers, acluster of vacancies forms all the way up to the 5th layerabove it. This vacancy cluster is due to the strain caused bythe trapped microcrystal in the layers above it. It is quitesurprising that the strain field around a microcrystal hasthe same characteristic length scale as the strain fieldaround a single heterogeneity molecule or a vacancy in thelattice. As a result, the perturbation in the lattice due tothe trapping of larger objects is localized around theseobjects.

There are numerous observations of the incorporation ofmicrocrystals in protein crystals in literature.17,20,21,32,55–57

The novel insight, contributed by the molecular resolutionimages in Figure 5, consists in the finding that evenmicrocrystals that seem well aligned with the underlyinglattice cause significant lattice strain and that the strainfield stretches to about five molecular dimensions aroundthe trapped microcrystal.

Can Trapping of Microcrystal Be Avoided?

Obviously, if the growth conditions are chosen so that nonucleation of microcrystals occurs, there will be no trap-ping. However, often, as in the cases of ferritin andapoferritin, the growth conditions change during growthdue to, e.g., solution depletion, and may pass thorough aset inductive of nucleation. As a second line of defense, ithas been argued that in a reduced gravity environment, forinstance aboard a spacecraft, the microcrystals will not ofsediment on the growing crystal.58

Other than sedimentation driven by Earth’s gravity, amicrocrystal may reach the surface of a growing largercrystal by Brownian diffusion. Let us consider these twotransport pathways. The velocity of sedimentation v of aparticle of radius r with density r1 falling in a liquid withviscosity h and density r2 is v 5 2r2(r1 2 r2)g/9h, where g isthe free fall acceleration. This velocity is determined by thebalance of the buoyancy, (4/3)pr3(r1 2 r2)g, and the viscous,6phrv, forces.59,60 For the microcrystal in Figure 5, r ' 130nm, and assuming density difference between crystal andsolution similar to that of lysozyme r1 2 r2 ' 0.3 g z cm23,61

we get v 5 1.2 3 1026 cm s21. If the microcrystals form at aheight of '100 mm, they would take more than 2 h to reachthe surface. The corresponding characteristic Brownian diffu-


sion time t to reach the substrate for a cluster formed at adistance x 5 100 mm from the surface can be evaluated fromEinstein’s relation x2 5 2D t. A lower estimate for clusterdiffusivity D can be obtained form the diffusivity of singleapoferritin molecules, 3.2 3 1027 cm2/s26,34 using Stokes lowand assuming that the microcrystal behaves like a particlewith 10 molecules at an edge: D ' 3.2 3 1028 cm2/s.Substituting, t ' 1,500 s ' 25 min. Hence, Browniandiffusion is a more efficient method of transfer of microcrys-tals to the surface of a large crystal than sedimentation, andeven in the absence of gravity, microcrystals can still reachthe surface and get trapped.

Is There a Critical Size for the Onset of Mosaicity?

To further explore the above AFM observation of theonset of a mosaic block structures in ferritin and apofer-ritin crystals .200 mm, we grew numerous crystals of thetwo proteins under careful microscopic observation. Typi-cally, crystals ,200–300 mm appeared perfect without any

visible boundaries or any other defects; an example isshown in Figure 6a. As they grew larger, one and thenmore boundaries appeared, separating the crystal intotwo, three, etc., blocks as in Figure 6b. The sizes of theseblocs varied between 20 and '100 mm. If older solutionsthat contain higher levels of the dimer are used, the size atwhich the crystal breaks into individual domains shiftsdownward.

Figure 6b also shows the trapping of a few 10–15-mmcrystals and smaller objects. Because the strain filedaround the trapped crystals and objects is short ranged,and there is relatively few of them, we conclude that theircontribution to the overall strain in the crystal is insignifi-cant. Furthermore, although we did not carry out X-raycharacterization of the grown crystals, we offer that be-cause the trapped crystal and objects occupy a smallfraction of the total volume of the large crystal, diffractionfrom them is a minor contribution to the mosaicity of thediffraction pattern.

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 onthe 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 thelayers on top of the incorporated microcrystal.


These observations of the onset of mosaicity show that(i) there is critical size, below which even defect-richcrystal will not be mosaic; (ii) trapping of smaller crystalsdoes not significantly contribute to the mosaicity; and (iii)mosaicity is primarily due to the accumulation of strainassociated with the incorporation of the ferritin and apofer-ritin molecular dimers into the lattice.

Theoretical predictions of the critical size for the onset ofmosaicity due to the elastic strain associated with theincorporated impurity molecules have only been per-formed for the protein lysozyme. By using a recentlydetermined Young modulus for lysozyme crystals (AHolmes, private communication), the critical size wasevaluated to be in the range 100–500 mm.6 As with ferritinand apoferritin, the typical impurities for this protein arecovalently bound dimers at '1–2% of the dry proteinmass.7,27 They cannot be fully removed, recur after purifi-cation, and readily incorporate into crystals. For evidencefor impurity-induced mosaicity with this protein, we moni-tored the growth and dissolution of lysozyme crystals. Ifthe crystals were grown at high supersaturations (C/Ce '25) from solutions with impurity contents at the high endof the above range, the crystals exhibited the ratherirregular morphology depicted in Figure 7a. The sequencein Figure 7 shows subsequent stages dissolution of acrystal grown at supersaturation C/Ce 5 38 from a solu-tion containing 1.5% (w/w dry protein mass) of the ly-sozyme dimer. Dissolution of the heavily mosaic crystal,Figure 7a, reveals that below '170 mm, Figure 7c, thecrystal consists of a single block. This is the critical size forthe onset of mosaicity, within the range of the theoreticalestimates in Ref. 6. Crystals grown from solutions contain-ing lower impurity amounts did not reveal such mosaicstructure. This allows us to correlate the mosaicity with

this protein to the lattice strain introduced by the impurityincorporation.

Because this critical size for the onset of this type ofmosaicity for ferritin and apoferritin is '200 mm, in therange expected and shown for lysozyme, we may concludethat the Young modulus of these two crystals is close anddoes not differ much from the one for lysozyme.

The existence of a critical size for the onset of mosaicitysuggests that in some cases smaller crystal may be moresuitable for diffraction studies than larger crystals. On theother hand, for other proteins, the critical size may be toosmall for practical use of subcritical crystals. Note that theperfect faceting of a crystal, such as the one in Figure 6b,does not indicate the lack of mosaicity. High-magnificationoptical observations with specialized techniques are re-quired to see the block structure.

CONCLUSIONS

We have applied atomic force microscopy to monitorwith molecular resolution the growth of ferritin and apofer-ritin crystals from solutions containing '5% (w/w) of amicroheterogeneity—the molecular dimer of the respec-tive protein. Our observations indicate that:

● For both ferritin and apoferritin, the dimer has theshape of two bound monomer spheres. The contactbetween the two monomer molecules in the dimer isdifferent from those in the crystal lattice. The likelycause for the dimerization is the partial denaturation ofthe monomer molecules exposing hydrophobic sidechains to the surface.

● Because of this increased hydrophobicity, the dimeradsorbs on the surface of the growing crystals at concen-trations hugely exceeding those in the solution bulk.Higher dimer concentrations in the solution result inhigher surface concentrations. The characteristic dimeradsorption times are significantly shorter than thetypical times between subsequent growth steps, i.e.,dimer adsorption is not a function of the rate of growthof the crystal.

● Most of the adsorbed dimers are incorporated by thegrowing steps. Because of the dimer shape, each dimerdisplaces three monomers in the crystal lattice. Themonomers around the created defect are shifted fromtheir crystallographic positions by '0.1 molecular di-mensions, i.e., by '1.3 nm. The resulting lattice strainprecludes molecules from the top crystal layer form,taking the site above the incorporated dimer. As aresult, a column of vacancies forms that may be up to5–10 layers high.

● The monomer molecules around the stacked vacanciesare shifted from their crystallographic positions, similarto the monomer molecule surrounding the incorporateddimer. The accumulated strain is resolved for crystallarger than '200 mm by a plastic deformation where-upon the crystal breaks into mosaic blocks 20–100 mmin size.

● The critical size for the onset of mosaicity of '200 mm issimilar for ferritin, apoferritin, and lysozyme. This

Fig. 6. Optical micrograph of a ferritin crystal. a: Typical crystalsmaller than '300 mm—no defects or block boundaries are discernible.b: Typical crystal larger than '300 mm—black arrow indicates a blockboundary, and white arrows indicate incorporated crystals and micro-scopic objects.


value is within the range predicted by a theory based onthe balance between elastic strain due to impurityincorporation and energy of the surface created betweenthe mosaic blocks. The similarity between the threeproteins suggests that their Young moduli have similarvalues.

● Trapping of smaller crystals and microcrystals inducesstrain with a characteristic length scale equal to that ofa single point defect, and, as a consequence, trappingdoes not contribute to the mosaicity in ferritin andapoferritin crystals.

These results suggest that the above sequence of phenom-ena detrimental for the quality of the protein crystals inthis and other systems could be avoided by improvedmethods to separate similar proteins species, includingmicroheterogeneity, or by increasing the biochemical sta-bility of the macromolecules against oligomerization.

ACKNOWLEDGMENTS

We thank A.A. Chernov and D.N. Petsev for referencesand discussions.

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Molecular mechanisms of microheterogeneity-induced defect formation in ferritin crystallization