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Polyhedral Instability of Glucose Isomerase CrystalsMike Sleutel, Ronnie Willaert, Lode Wyns, and Dominique Maes

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Polyhedral Instability of Glucose Isomerase Crystals

Mike Sleutel,* Ronnie Willaert, Lode Wyns, and Dominique Maes

Structural Biology Brussels, Flanders Institute for Biotechnology (VIB), Vrije UniVersiteit Brussel,Pleinlaan 2, B-1050 Brussels, Belgium

ReceiVed July 8, 2008; ReVised Manuscript ReceiVed September 24, 2008

ABSTRACT: The problem of polyhedral (in)stability for the crystallization of macromolecules is discussed. We present bothqualitative and quantitative data on the transition of face morphology in response to surface concentration gradients for the case ofglucose isomerase. We show that in the absence of convective currents an isotropic protein depletion zone (PDZ) is installed. Themismatch between the spherical shape of the PDZ and the crystal habit leads to the Berg effect which gives rise to a localizationof two-dimensional nucleation near the vertices and a retardation of step advancement at the center of the face. In response to thissupersaturation inconstancy, a stabilizing microcompensation profile is setup that changes the local face kinetic constant . Uponattaining a critical slope, reaches its maximum and the destabilizing mechanism, that is, surface protein concentration gradients,leads to the loss of polyhedral stability. Furthermore, we demonstrate that polyhedral instability is promoted even further by 0.1%agarose.

Introduction

The interplay between surface growth processes and thedistribution of concentration around a growing crystal deter-mines the shape and stability of the crystal habit. When thekinetics of protein attachment onto a growing crystal faceremoves protein more rapidly from the region adjacent to thecrystal face than mass transport can replenish the supply ofgrowth units, a significant concentration gradient is established.In the absence of relatively fast convective currents, an isotropicprotein depletion zone (PDZ) is formed which creates localsolutal conditions that can differ greatly from the bulk composi-tion. The accompanied slow-down of the crystal growth processis considered to promote the growth of high quality crystals.1

Also, a more stable mode of growth is attained.2-4 By removingconvection, spatial irregularities and temporal oscillations insolute transport that cause the formation of defective regionsin the crystal are reduced. However, the effect of ablation ofconvection is system dependent and may either be advantageousor disadvantageous to the crystal quality. For instance, it hasbeen shown that a reduction of the mass transport rate canenhance defect-causing step density and velocity fluctuations5-7

or augment impurity uptake.8-11 Such a mass transport regimethat is governed by diffusion can be attained by working in azero- or microgravity environment,12-14 in gelled solutions15-17

or by lowering the ratio of the buoyancy and viscous forces ofthe system (capillary,18,19 closely spaced glass plates,20-23 highmolecular weight PEGs24).

There is one more case where elimination of convection willnot be beneficial for protein crystallization and ultimately crystalquality, that is, the case of loss of polyhedral stability.25,26 It isa kinetic phenomenon where, due to the specific interplay ofsurface kinetics and mass transfer, the crystal is no longercapable to retain its polyhedral shape and large depressionsdevelop on the habit faces. Since the destabilizing mechanismsscale-up with crystal size and the limiting of nutrient supply,polyhedral stability is expected to occur in the same conditionsrequired for the formation of a depletion zone. The geometryof this metastable halo encircling the crystal does not coincidewith the polyhedral shape of the crystal. Consequently, edges

and vertices of growing crystals are better supplied with nutrientsthan facet centers. This surface concentration inconstancy isreferred to as the Berg effect27 and can have a pronounced effecton surface kinetics and ultimately surface morphology.28

Polyhedral instability is a long standing problem in thecrystallization of small molecules due to their fast incorporationkinetics (for examples, see refs 29-32), and it is important forapplications where large protein crystals are required, forexample, neutron diffraction. Initial reports of polyhedralinstability of protein crystals were made by Nanev et al.33,34

for ferritin, lysozyme, and trypsin. Further steps toward a deeperunderstanding were made by Vivares et al. who studied theconcentration gradients in the vicinity of glucose isomerasecrystals using confocal scanning fluorescence microscopy.24

They achieved ablation of convection through the use of a highmolecular weight PEG (10 kDa) and correlated the polyhedralinstability of crystals to the presence of a depletion zone.However, the insights gained so far have been obtained fromlow resolution mesoscale data. A more detailed understandingof the problem requires microscopic data on both the stabilizingand destabilizing mechanisms.

Hence, in this paper we present for the first time quantitativedata obtained from high resolution noninvasive in situ imagingof the microscopic surface processes during the loss ofpolyhedral stability of glucose isomerase crystals. We begin byaddressing the most prominent destabilizing mechanism, thatis, surface concentration gradients and their effects on surfacekinetics. Next, we discuss the transition from a stable flatinterface to a concave microcompensation profile. In the thirdsection, we present quantitative data on the crystal’s compensa-tion mechanisms and their ultimate failure beyond a criticalpoint, followed by a last section where we ascertain the roleand applicability of the hydrogel agarose as a putative micro-gravity mimic.

Materials and Methods

Crystallization of Glucose Isomerase. Glucose isomerase fromStreptomyces rubiginosus was purchased from Hampton Research(California, USA). The protein solution was dialyzed against 10 mMHepes buffer pH 7.0 and 1 mM MgCl2. Protein concentrations weredetermined by UV absorbance at 280 nm. For the interferometryexperiments, protein crystals were nucleated in situ inside the

* To whom correspondence should be addressed. Tel: +32-2-6291923. Fax:+32-2-6291963. E-mail: mike.sleutel@vub.ac.be.

CRYSTALGROWTH& DESIGN

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10.1021/cg800728x CCC: $40.75 XXXX American Chemical Society

Mach-Zehnder interferometer (MZI) in a Hellma fluorescence cuvette(Jena, Germany) kept at a constant 20 °C using the macrobatch method.Mother liquor consisted of 40 mg/mL glucose isomerase, 100 mMHepes pH 7.0, 200 mM MgCl2, 5% PEG 1000 and 0.1% LM agarose(Hampton) to inhibit convective flows. For the laser confocal micros-copy experiments, crystals were grown at 25 °C in a QS 106 quartzHellma cuvette (0.5-1 mm solution thickness; Jena, Germany) from30 mg/mL glucose isomerase, 100 mM Hepes pH 7.0, 200 mM MgCl2,5% PEG1000, and 0% or 0.1% agarose. For these conditions, the proteincrystallizes exclusively in the orthorhombic form (I222, a ) 94.01 Å,b ) 99.37 Å, c ) 103.01 Å).35

Protein Depletion Zone Characterization. Protein concentrationgradients were measured using a computer controlled MZI-microscopysystem using a quartz fluorescence cuvette as experimental cell withinner dimensions 10 mm × 4 mm × 45 mm (D × W × L) for thegelled solutions. For the nongelled experiments the solution thicknesswas either 0.5 or 1 mm. The experimental cell was placed in theinterferometer in the object beam trajectory and kept at 20 ( 0.1 °Cusing peltier elements in combination with coolant water flows at thesides of the experimental cell. The Mach-Zehnder driven by a 680nm laser diode was used to collect interferograms of the cell. Phaseswere obtained using the phase-shift method. Phase-shifts were inducedby a piezo connected to the object beam mirror. Using the Hariharanalgorithm36 phase interferograms could be reconstructed. Real phasevalues were obtained by subtracting the reference phase field (taken atthe start of the experiment) from each phase map. Phase differencemaps were transformed into concentration difference maps by usingrefractive index versus concentration calibration curves that wedetermined using an Abbe Refractometer model 60/ED. Such aconversion from refractive indices to protein concentrations doeshowever require that the phase difference between two successiveinterferograms is smaller than one corresponding wavelength. Theobtained raw data represents the integration of the protein concentrationalong the optical path, and as such are averaged values.

Crystal Face Imaging Using Laser Confocal Microscopy (LCM)Combined with Differential Interference Contrast Microscopy (DIM).Growing (011) faces of orthorhombic glucose isomerase crystals wereobserved in situ by LCM-DIM.37,38 For this, a D-Eclipse C1 confocalsystem was attached to an inverted Eclipse TE-2000 U opticalmicroscope (Nikon, Brussels). An air objective lens PlanFluor 20×with a numerical aperture of 0.45 and a working distance of 7.6 mmwas used (theoretical lateral resolution 660 nm). The diameter of theconfocal aperture used for the observation was 103 µm. A Nomarskiprism was inserted into the optical path to utilize differential interferencecontrast. Crystals were illuminated with an argon-ion laser with awavelength of 488 nm. Photomicrographs of 512 × 512 pixels wereacquired over a 4 s scan time with a pixel-dwell of 11 µs.

The Accuracy of the Surface Concentration Determination MethodUsing Measured 2D Nucleation Rates and Step Velocities. The surfaceconcentration Csurf is calculated from two-dimensional (2D) nucleationrates using the following expression

Csurf ) exp(( BA- ln J) 1

T2)Ce

with A) ln(ω * ΓZ), B)πκHON2sk-2 (1)

For an explanation of the used symbols, the reader is referred to theResults and Discussion section. The concentration at the edge isconsidered to be the bulk concentration, that is, Csurf (x ) 0) ) Cedge )Cbulk. The relative depletion (RD) in surface concentration is thendefined as RD(x) ) 1 - Csurf(x)/Cbulk. The error of Csurf is the resultantof the propagation of a number of errors associated with bothexperimental parameters (ln J, T, Ce) and coefficients obtained throughfitting (ln(ω*ΓZ), κHON). These uncertainties accumulate into an errorof approximately 40% in the determination of Csurf. However, thecalculation of the relative depletion RD is a little less error sensitive.RD is mostly affected by errors associated with ln J, ln(ω*ΓZ), andκHON. For the determination of the nucleation rates as a function ofsurface coordinate, the total number of nuclei appearing on 2700 µm2

areas 40 µm apart were counted during a measuring period of 20 min.This translates into a maximum relative error of 1.5% and 12% in thedetermination of ln J and Csurf/Cbulk, respectively. The errors in ln(ω*ΓZ)(2.3%) and κHON (5%) propagate into a combined relative error of 23%in RD. RD is much less sensitive to errors associated with the

experimental parameters T and Ce. For example, whereas an uncertaintyof 0.5 K in the temperature leads to a relative error of 10% for Csurf,the quantity RD varies only by 0.3%. An even smaller dependency isobserved for the associated error of 0.05 mg/mL in Ce. All these errorscombined lead to an uncertainty of 36% for crystal 1 in the calculationof RD.

Grashof Number Calculation. The dimensionless Grashof number(Gr) was used to approximate the ratio of the buoyancy to viscousforces in our system. Gr was calculated using the following expression39

Gr)Cprotγgh3ν-2

with γ) 1Fsol

( δFsol

δFprot)) Fprot -Fw

FprotFsoland ν) η

Fsol

where Cprot is the protein concentration, Fprot, Fsol, and Fw are the densityof the protein, the solution and water, respectively, γ is the proteinsolutal expansion coefficient, g is the gravitational acceleration, h isthe characteristic length (solution thickness inside the experimental cell),and ν and η are the kinematic and dynamic viscosity. The used valuesare summarized in Table 1.

Results and Discussion

The Berg Effect Leads to Preferential 2D Nucleation atFacet Edges. The impact of surface concentration gradients onstep generation and advancement can be studied with a numberof imaging techniques. However, since the typical length scaleof the Berg effect is commensurable with crystal size, the classicsurface imaging technique atomic force microscopy (AFM) isless ideal due to its limited surface scanning area. We thereforeemploy the less invasive optical method LCM-DIM which,given the fast scan rates (on average 5 s/image), large scanningarea (mm range), and medium lateral resolution ((0.6 µm), isideal to probe microscopic kinetic surface phenomena.37,38

Crystals were grown in quartz cuvettes with a spacing of 0.5-1mm. With this technique, we observe a clear impact of the Bergeffect on the dominating step source mechanism42 (i.e., 2Dnucleation for supersaturations σ ) ln(C/Ce) < 5.0 at 25 °C)on the (011) face of orthorhombic glucose isomerase crystals.Figure 1a shows the manifestations of the Berg effect on 2Dnucleation kinetics and step density for crystallization in anongelled medium (no agarose present). A clear increase in stepdensity is observed from the crystal edge (left-hand side) towardthe facet center (right-hand side). The reverse trend is visiblewith regard to the presence of 2D islands, that is, the surfacedensity of 2D islands decreases as a function of distance fromthe crystal’s edge. A similar deceleration of kinetics is observedfor the lateral step velocity Vstep.

In a more quantitative approach, time-lapse imaging of thecrystal surface allowed us to determine 2D nucleation rates J(m-2 s-1) as a function of the distance from the edge x (in µm,taken to be zero at the crystal edge). Figure 1b shows an ln Jversus distance from the edge plot obtained for two differentcrystals. A (kinked) linear decrease in nucleation rates isobserved as a function of surface coordinate. We attribute the

Table 1. Data for Gr Calculation

Cprot (g/cm3) 5 × 10-3

Fsol (g/cm3)a 1.12Fprot (g/cm3)b 1.41Fw (g/cm3) 1.00γ (cm3/g) 0.26g (cm/s2) 981h (cm) 0.05 - 0.1η (g/cm s)c 1.20 × 10-2

ν(cm2/s) 1.07 × 10-2

a Calculated for a 100 mM Hepes, 200 mM MgCl2, 5% PEG1000, 5mg/mL glucose isomerase solution. b Taken from ref . c Taken from ref .

B Crystal Growth & Design, Vol. xxx, No. xx, XXXX Sleutel et al.

kink in the plot for crystal 2 to the geometry of the system,that is, the angle and distance between the crystal surface andthe reactor walls and edges. Given the high nucleation rates,the prevailing step generating mechanism is homogeneous 2Dnucleation (HON)42 characterized by a specific edge free energyof κHON ) 6.0 ( 0.3 × 10-13 J/m. Through a model for thesteady-state 2D nucleation rates J derived from classicalnucleation theory43

ln J) ln(ω * ΓZ)-πκHON

2s

k2T2 ln(Csurf/Ce)(2)

where ω* is the frequency of attachment of molecules to thecritical 2D nucleus, Γ is the Zeldovich factor, Z is the steady-state admolecule surface concentration, s is the surface area ofa single molecule in the critical 2D nucleus (9.7 × 10-17 m2),and Csurf and Ce are the protein surface and equilibriumconcentration, respectively, we calculate the local surfacesupersaturation σsurf ) ln(Csurf/Ce). The observed retardation ofkinetics is not a consequence of step diffusion field overlap.AFM experiments42 have shown that no step-step interactionwas observed for distances >75 nm (3-4 lattice parameters),well below the minimum interstep distances for Figure 1, thatis, 2.8 µm. Assuming no significant temperature gradients alongthe surface coordinate and with ln(ω*ΓZ) ) 24.8 ( 0.6 and Ce

) 0.28 mg/mL we obtain the relative surface depletion Csurf/Cbulk where Cbulk is the protein bulk concentration which weequate with Cedge. In reality, most likely Cedge e Cbulk; however,we disregard this inequality since we focus here on thedetermination of relative surface concentration gradients ratherthan absolute gradients. This leads to the Csurf/Cbulk versusdistance from edge plots in Figure 1c. A depletion of ap-proximately 11 ( 4% is measured at ( 250 µm from the crystaledge. A discussion on the error associated with the calculateddepletion can be found in the Materials and Methods section.To summarize, the observed slowing-down of kinetics (dlnJ/dx < 0 and dVstep/dx < 0) along the x-axis is a direct conse-quence of a decreasing protein surface concentration.

Transition from a Stable Flat Interface to the Appearanceof a Central Depressed Area. In the presence of relatively smallsurface concentration gradients (moderate Berg effect), shape

stabilizing factors44 (e.g., anisotropy of face kinetic constant,surface tension and capillarity, nonuniform distribution ofgrowth-retarding impurities, temperature gradients) succeed inpreserving the polyhedral shape of the crystal. However, shape-destabilizing factors (e.g., nonuniformity of (impurity) concen-tration distribution) scale-up with crystal size and can lead tomorphological defects. In the following section we discuss thevarious (micro)structures of the surface in response to super-saturation inhomogeneity while retaining a flat macroscopicinterface. Figure 2a shows one of the “flattest” and most stablemodes of growth, that is, ad random homogeneous multilayer2D nucleation (note that layer-by-layer growth would be flatter)with an average slope of zero. The random nature of this process(average island density is constant as a function of surfacecoordinate) indicates the absence of any significant concentrationgradients on the surface. Any local perturbations in surfaceheight show no temporal stability and fade away. When thecrystal size increases or supply becomes hampered by reactoredge effects, concentration gradients arise that affect both thekinetics and localization of 2D nucleation. Figure 2b illustratesthis phenomenon: step generation becomes limited to specificlocal areas of higher surface concentration leading to theformation of a 2D hillock. In response to the concentrationgradients, the step density increases as a function of distanceto the nucleation center until eventually the interstep distancebecomes smaller than the critical length of a 2D nucleus or thesupersaturation becomes smaller than the critical supersaturationfor 2D nucleation. This effect enhances the “confinement” of2D nucleation and hence step generation to a specific region.While Figure 2b shows straight step trains, Figure 2c showsloss of step straightness at a specific distance from the crystal’sedge. We interpret this step concavity as the result of anonconstant step velocity along the average direction of thesteps. Since we observe this effect for all the face’s edges atspecific edge distances, we attribute the observed concavity tosurface concentration gradients and rule out other step retardingpossibilities such as impurities. However, we do observe theinfluence of impurities in the face’s center under a differentform, namely, through step pinning (will be discussed below).Next, impurity pinning and very high step densities giving rise

Figure 1. (a) Step and 2D island density increase and decrease, respectively, as a function of the distance to the crystal edge (left-hand side) as aconsequence of the Berg effect, that is, nonconstant surface concentration. Nucleation rates (ln J) (b) and relative depletion Csurf/Cbulk (c) as afunction of surface coordinate along the white arrow in (a).

Loss of Polyhedral Stability Crystal Growth & Design, Vol. xxx, No. xx, XXXX C

to diffusion-field overlap in the face’s center can eventually leadto loss of stability of the step trains. This gives rise to the stepbunching and subsequently formation of macrosteps in the centerof the face (Figure 2d). Macrosteps can then lead to an additionalslowing down of step advancement in the central areas of thecrystal face. All these effects combined finally result in theappearance of a singular point/region on the surface where quasi-zero step velocity is reached. Upon reaching this point a cascadeof events enhances the instability even more; that is, step densityincreases further and faster by the arrival of new steps to thenear-zero-velocity region and step advancement slows down dueto step-step interaction. Ultimately, this nonmoving macrostep(shock wave) leads to the formation of a central expandingdepression (Figure 2e). This microscopic transformation is theonset of loss of polyhedral stability. We note that it is a kineticphenomenon and that it can be remedied by decreasing thesupersaturation or increasing material supply through (forced)convection.

The Microscopic Compensation Profile Fails to PreserveMacroscopic Stability. For a moderate Berg effect the crystalremains able to retain its polyhedral facetted shape through theavailable compensation mechanisms. However, in the absenceof convective currents, the concentration difference betweenedge and center Cedge - Ccenter scale-up with26 f l/D andeventually the crystal starts to change its habit, turning into askeleton or dendrite, where f is the face kinetic constant, l isthe crystal size, and the D is the diffusivity. Here, we discussthe most general (albeit limited) factor maintaining the regularpolyhedral shape of a growing crystal,45 that is, the anisotropyof face growth rate V(n) as a function of orientation n. Figure3a shows the microcompensation profile in response to super-saturation inconstancy, that is, a gradual increase in step densitytoward the crystal center leading to a concave surface profile.The local slope p changes from 0.004° to 0.09° between thewhite markers along the dashed white arrow in Figure 3a, withp calculated as the inverse tangent of the ratio of the step heightand the interstep distance. The reverse trend is measured forthe tangential step velocity Vstep (Figure 3b); that is, steps slowdown farther from the edge. The crystal can offset this step

retardation generated by the supersaturation inconstancy byincreasing its local slope p (Figure 3c). The obtained surfacecurvature generates a higher kinetic coefficient in the centralarea compared to the face periphery and is able to counteractthe destabilizing effect of supersaturation surface gradients. Thisis illustrated in Figure 3c, where Vstep × p, which we use as ameasure of the normal growth rate, remains constant over thefirst ( 200 µm along the trajectory indicated by the dashedwhite arrow in Figure 3a. Note the smaller values of Vstep × pclose to the edge. In this region, where 2D nucleation stilloccurs, the face growth rate cannot be approximated with Vstep

× p and the normal growth rate is underestimated. Step densityand velocity measurements become impossible closer to thecenter because here interstep distances become smaller than thelateral resolution of the LCM-DIM technique.

For regions closer to the center an “avalanche like loss ofstability”26 sets in. The increase in f l/D as a result of thecompensation profile leads to an additional rise in Cedge - Ccenter

thereby increasing the demand for an increased surface curva-ture. Eventually, an abrupt decline is reached in the anisotropyof the kinetic constant (expected for larger p) and the kineticcoefficient b(p) attains its maximum (∂b/∂p ) 0). We calculate∂b/∂p using the following relationships:26

pcenter - pedge )1Θ

σedge - σcenter

σedge(3a)

Θ) 1b

(∂b/ ∂ p) with b(p)) (p)√1+ p2 (3b)

where Θ is the anisotropy of the face kinetic coefficient (p).We derive the local slope p(x) from the surface profile (Figure4a) and calculate σ(x) from the step velocity assuming nodiffusion-field overlap using46 Vstep ) Ωstep(C - Ce) with step

) 5 × 10-4 cm/s. The results between 0-200 µm from theedge are summarized in Figure 4b. The decrease in surfacesupersaturation (∼60%) is far more pronounced than in Figure1c. Such significant depletion can arise when the crystal face isin close proximity to the reactor wall, rendering the face’s centerpoorly supplied and enlarging the Berg effect (will be discussed

Figure 2. The violation of the morphological stability of a flat, crystallographic low index face (011) leads to the appearance of a central depressedarea: (a) step generation through 2D nucleation occurs ad random across the entire surface; (b) surface concentration gradients lead to preferential2D nucleation at crystal edges, leading to step trains crossing the vicinal surface; (c) step train velocity becomes nonconstant along the averagedirection of the step resulting in increased step concavity toward the center of the crystal face; (d) loss of stability of semi-equidistant step trainsleads to the coalescing of steps and formation of macrosteps downhill of the nucleation center; (e) step pinning combined with increasing diminishmentof step velocity in the face center lead to a singular critical point where quasi-zero step velocity is reached, creating a depressed valley downhillof the critical point, dashed white line indicates direction of step advancement. Dashed white boxes in zoom-out pictures indicate zoom-in area(a-c). White x’s denote preferential 2D nucleation centers (b-e).

D Crystal Growth & Design, Vol. xxx, No. xx, XXXX Sleutel et al.

below). A steady decrease in both σsurf ) ln(Csurf /Ce) and ∂b/∂p is observed, demonstrating the diminishing strength of thecompensation mechanism at higher slopes. For low stepdensities, the kinetic coefficient increases strongly with increas-ing local slopes. At larger slopes, however, the kinetic coefficientof the face becomes practically independent of the orientation.These data demonstrate that crystals larger than a critical sizewill inevitably lose their polyhedral stability and a centralstarvation flaw will form. When this critical point is reached,the faceted form is no longer capable to remain similar to itself.In practice the depression is offset from the center of the face

and step generation is limited to only a single vertex as opposedto multiple vertices. We believe this to be the result of a nonzeroangle between the average crystal face orientation and the reactorwall.

The low reflectivity and high roughness of the depletiondefects excludes techniques such as AFM and Michelsoninterferometry to visualize starvation flaws. With LCM-DIM,however, direct imaging of these regions is possible. A typicalexample of a starvation flaw is shown in Figure 5. Individualsteps are not discernible, indicating high step densities. Thecone-like structures are areas of strong step pinning, that is, stepretardation by surface adsorbed impurities. These pinning conesare oriented radial with respect to the depression centerindicating that growth occurs toward the depression center. Thedensity of these pinning cones is also far higher than for theflat periphery of the singular face, suggesting a higher surfaceconcentration of growth retarding impurities in the defect. Thismight be due to longer terrace exposure times as a consequenceof slower step advancement. For the specific crystal in Figure3, we can estimate the terrace exposure time τ as a function ofdistance to the edge by calculating the ratio of interstep distanceλ and the step velocity Vstep. As can be clearly seen in Figure3c, τ decreases strongly as a function of edge distance. Wecannot evaluate τ for areas closer to the starvation flaw or thestarvation flaw itself because of too high step densities. Thiswould suggest that a mechanism of enhanced impurity incor-poration due to longer terrace exposure closer to the face centerdoes not apply. A different mechanism of impurity uptake mightbe responsible for the increased step pinning at the center.Because of the rising inclination of the crystal surface towardthe center, the face may decompose into multiple facets withsingular orientations other than the (011) direction. Indeed, twofacets appear to be present in the starvation flaw shown in Figure5. These new faces may incorporate impurities at different ratesthan the (011) face at the periphery. Such face-dependentincorporation of impurities has already been observed formacromolecules (e.g., dimer incorporation into lysozyme crys-tals47), and may be in effect here as well. Or, if the impurity is

Figure 3. (a) The crystal’s microscopic compensation profile in response to supersaturation inconstancy is limited by the maximum of the kineticcoefficient . A clear failing to preserve polyhedral stability results in the formation of a large central circular depression, (inset) zoom-out of theregion presented in (a); (b) tangential step velocity Vstep (b) and local slope p (0) as a function of distance from the edge in the direction indicatedby the dashed white arrow in (a); (c) Vstep × p (b) and terrace exposure time τ (∆) as a function of edge distance.

Figure 4. (a) Surface relief of the compensation profile in Figure 3a;(b) surface supersaturation derived from step velocities as a functionof edge distance, bottom x-axis and right y-axis ((); anisotropy of thekinetic coefficient as a function of local slope p, upper x-axis and lefty-axis (b).

Loss of Polyhedral Stability Crystal Growth & Design, Vol. xxx, No. xx, XXXX E

rejected by the growing crystal, its concentration will be highestat the center of the faces. This would lead to an additionaldistortion of the facet plane.44

Currently, we cannot yet identify the exact mechanism thatenhances the impurity uptake in the starvation flaws. Additionalresearch is required to elucidate this further.

Agarose Enhances Polyhedral Instability. In the previoussections, we discussed crystal growth in nongelled solutionsbetween two glass plates. Here, we study the polyhedral stabilityof crystals in the presence of 0.1% agarose gel. UsingMach-Zehnder interferometry, we determined the phase dif-ference map in the vicinity of the growing crystal. A near-spherical protein depletion zone (PDZ) was observed (Figure6a). This would suggest that crystal growth is diffusion-limited.With D ) 3.5 × 10-7cm2/s, face ) 2 × 10-4 cm/s or 2 ×10-5 cm/s (kinetic roughening and 2D nucleation respectively48),face l/D > 1 for crystals larger than 200 µm, therebydemonstrating that diffusion is indeed the rate-limiting step.Vivares et al.24 concluded that for their conditions glucoseisomerase crystallizes in a mixed regime. However, they usedPEG 10 kDa as a precipitant and at higher concentrations.Hence, no direct comparison with the results in this work canbe made. From the isotropic nature of the concentration gradientsthe presence of the Berg effect becomes readily apparent, thatis, a clear mismatch between the polyhedral crystal shape andthe spherical PDZ. We calculate the protein surface concentra-tion at the edge and the center of the crystal face as a functionof time using the refractive index increment dn/dC ) 0.232mL/g (determined using Abbe refractometer) (Figure 6b). Arelative depletion of roughly 7.5% for Ccenter with respect toCedge is measured. Note that this value represents an averagevalue for the concentration gradient because the concentrationsobtained using MZI are integrated values along the optical path.As such, real surface concentration gradients may be underes-timated using this technique.

Optical imaging in transmission mode showed that crystalsgrowing in 0.1% agarose showed a severe loss of polyhedralstability (Figure 7). At 25 °C, all crystals reaching sizes >1mm displayed deep (∼100 µm) depressions in the faces makingup the habit. An unambiguous exact determination of the criticalstability length was not feasible since it is strongly correlatedto the distance between the crystal face and the reactor walls.Figure 7a does show that it is possible for glucose isomerase toretain a polyhedral shape at crystal sizes of ∼1500 µm whenthe crystal-reactor distance is ( 175 µm with no agarose present.A strong difference in crystal habit at various temperatures (25°C, 15 °C, 4 °C) is observed between gelled and nongelledsolutions. At 25 °C, most crystal faces retained a polyhedralshape in the absence of agarose; however, macrosteps andmother liquor inclusions were frequently observed for largercrystals (>1 mm). Starvation flaws only appeared on the crystalfaces closest to the reactor walls. For crystals grown in gel,these effects were enhanced greatly; that is, deeper and largerstarvation pits not only restricted to a single face appeared. Astrong temperature dependence was found as well, which, giventhe normal solubility dependence on temperature for glucoseisomerase, can be attributed to a higher supersaturation at lowertemperatures, thereby decreasing the critical length for poly-hedral stability. For the agarose-free conditions, the crystal habittransforms gradually toward a dendrite (Figure 7a-c), whereasin the presence of agarose, the habit switches to a skeletal formand no dendritic side branches are formed (Figure 7d-f).Dendrite formation is expected to occur when the characteristiclength of the skeletal side-branches exceeds a critical value,which is determined by the interplay of material supply andincorporation kinetics. From Figure 1c and Figure 6b weconclude that the surface concentration gradients are comparablein systems where buoyancy driven convection is either inhibitedthrough the presence of a hydrogel (e.g., agarose) or partlysuppressed (shallow depletion zones are still observed, seeSupporting Information) through the specific reactor geometrycharacterized by a low Grashof number (here two closely spacedglass plates). This would suggest that agarose not only affects

Figure 5. LCM-DIM image of the central depressed area of a crystalexhibiting loss of polyhedral stability. Severe step pinning suggestshigh density of growth-retarding impurities. Pinning cones are directed(white arrows) at the center of the depression indicating radial growth(image area 450 × 450 µm); (inset) optical macroscopic image of thecrystal.

Figure 6. (a) Isotropic depletion zone encircling a glucose isomerasecrystal growing in 0.1% agarose; (b) ratio of protein concentration atface’s center and edge (Ccenter/Cedge) as a function of time; (c) effect ofthe proximity of the reactor wall on the protein depletion zone; (d)amplification of the Berg effect due to the proximity of the wall: therelative surface depletion (Cedge - Center)/Cedge is larger for the faceclosest to the wall (C-D) than for the opposite face (A-B).

F Crystal Growth & Design, Vol. xxx, No. xx, XXXX Sleutel et al.

protein crystallization at the level of mass transport, butpotentially affects the molecular scale kinetics as well. LCM-DIM imaging of crystals growing in agarose lends credence tothis hypothesis. Figure 8a shows loss of polyhedral stability ofthe (011) face growing in the presence of 0.1% agarose. A veryhigh density of pinned steps can be discerned on the flatperiphery of the central depression. Step pinning through surfaceadsorbed impurities is much more pronounced in 0.1% agarosecompared to nongelled solutions (Figure 3a). We put forth threepossible explanations: (i) there are additional impurities presentin the agarose. For this we tested agarose from two suppliers(Hispanagar and Hampton Research) both of which gave similarresults. (ii) The agarose polymers pierce the surface uponincorporation into the crystal bulk thereby pinning the steps.However, the density of pinned steps is smaller near the outeredges of the singular face. This would exclude the agarosepolymers as pinning agents as they would be incorporatedhomogeneously in the crystal bulk. (iii) If the impurity(responsible for the step pinning in the ungelled solution) isrepelled by the crystal, ablation of convection would generatea local environment that is strongly enriched in impurities. Forthis case, the gel will enlarge any impurity surface concentrationgradients, leading to increased step pinning at the facet center.

The protein sample was analyzed by SDS-PAGE to ascertainthe purity level (Figure 9a). Three bands of different molecularweight were observed. We identify the 87 kDa and the 42 kDabands to be the glucose isomerase dimer and monomer,respectively. The intensity of these 2 bands was >99%,indicating a high level of purity. A third band corresponding to

a molecular weight of 31 kDa could not be identified. Highresolution imaging of pinned steps shows that the pinning agentsare microscopic particles (µm size) adhered to the surface(Figure 9b,c). In Figure 9b we show an example where multiplesteps remain pinned at the same time over a distance of 11 µm.These foreign particles might be composed of aggregates ofthe 31 kDa protein. However, as of yet, the exact identity ofthese pinning agents remains unclear.

Role of the Protein Depletion Zone in Polyhedral Instabil-ity. Next, we tried to ascertain the role of the depletion zone inthese polyhedral instability phenomena. Therefore, we calculatedthe dimensionless Grashof number in order to ascertain therelative role of convection and diffusion in material supply forthe nongelled experiments. For a solution thickness of 0.5 or 1mm, we obtained Gr values of 1.4 and 11.1, respectively. Thiswould suggest a mixed regime; that is, natural convection isnot fully suppressed and it contributes significantly to the overallrate of mass transport. This was verified experimentally usingMach-Zehnder interferometry. Only faint, shallow depletionzones were observed around crystals growing inside theexperimental cells (see Supporting Information). The maximumobserved Cbulk - Csurf was on the order of 1 mg/ml. Typicalvalues for gelled solutions were larger by a factor of 20. Asshown in the previous section, when convection is effectivelysuppressed using 0.1% agarose, clear wide and deep PDZs areformed. This indicates that convection is present in the ungelledsolution and that it prevents formation of a deep PDZ.Nonetheless, Figures 1-5 clearly show that a significant Bergeffect as well as a loss of polyhedral stability are possible inexperimental cells where no clear macroscopic depletion zonesare installed during growth. Vivares et al. concluded that lossof stability is correlated to the presence of a depletion zone.24

Here we propose a slightly different mechanism; that is, PDZformation is not a prerequisite for stability loss but it enhancesone of the destabilizing mechanisms, that is, surface concentra-tion gradients. We also suggest that the distance between thecrystal face and the reactor walls is a key parameter in stability

Figure 7. (a) Crystal habit as a function of temperature: 25 °C (a, d),15 °C (b, e), 4 °C (c, f), and agarose concentration: 0% (a, b, c), 0.1%(d, e, f).

Figure 8. (a) The (011) face growing in the presence of 0.1% agarosewith a central depression showing clear loss of polyhedral stability.The flat periphery of the starvation flaw is strewn with zones of pinning(image width: 610 µm); (b) zoom-in of the region indicated by thewhite dashed rectangle in (a); (c) macroscopic image of the crystalhabit.

Loss of Polyhedral Stability Crystal Growth & Design, Vol. xxx, No. xx, XXXX G

control. To substantiate this claim, we measured the concentra-tion profile surrounding a crystal in close proximity to the reactoredge. We added 0.1% agarose to ensure a diffusive environment(Figure 6c). The distance between the point C and the wall andD and the wall are 200 and 330 µm, respectively. In Figure 6d,the relative surface depletion (Cedge - Center)/Cedge is plottedfor the face closest to the wall (C-D) and the opposite face (A-B). For face A-B, (Cedge - Center)/Cedge reaches a value of 8%(similar to the crystal in Figure 6a). For the face C-D orientedtoward the reactor wall, (Cedge - Center)/Cedge is more thandoubled, that is, 17%. These data show that surface concentra-tion gradients become larger due to edge effects. Although theeffect is not as large as the 60% depletion observed for thecrystal shown in Figure 3, here, however, the crystal was grownin a gelled solution. For a nongelled medium, gradients areexpected to be larger. Convection will still be present at theedges thereby exposing them to a higher concentration and thecenter will experience a strong depletion due to a more limitedmaterial supply (Gr ) 0.2 for h ) 265 µm).

Conclusion

In this paper we have shown for the crystallization of glucoseisomerase:

(1) In the absence of convective currents an isotropic PDZ isinstalled. From an estimation of the relative weights of thekinetics of incorporation and the rate of mass transport weconcluded that crystallization is diffusion-limited.

(2) The influence of the Berg effect on the kinetics of thegrowth of glucose isomerase crystals was quantitativelydetermined.

(3) In response to surface supersaturation inconstancies, astabilizing microcompensation profile is setup that changes thelocal face kinetic constant . Upon attaining a critical slope, reaches its maximum and the destabilizing mechanisms, thatis, surface protein and possibly impurity concentration gradientslead to loss of polyhedral stability.

(4) Polyhedral instability is promoted even further by thepresence of 0.1% agarose.

Hence, we conclude that for the diffusion-limited crystal-lization of glucose isomerase ablation of convection can havea detrimental effect on the polyhedral stability of large crystals.

The loss of stability is of kinetic nature and can be remediedby growing crystals in larger reactors (much larger than crystalsize).

Acknowledgment. We are indebted to G. Nicolis and P.Vekilov for vital critical discussions. The authors wish to thankthe reviewers for valuable comments and suggestions on themanuscript. This work was supported by the Flanders Interuni-versity Institute for Biotechnology (VIB), the Research Councilof the VUB and the Belgian Federal Science Policy Office(DWTC). We thank the European Space Agency for financingin the context of Prodex project AO2004.

Supporting Information Available: MZI phase interferogramdemonstrating the absence of a deep protein depletion zone fornongelled solution for glucose isomerase; glucose isomerase diffusivityas a function of PEG 1000, obtained using DLS. This material isavailable free of charge via the Internet at http://pubs.acs.org.

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Figure 9. (a) SDS-PAGE analysis of glucose isomerase. Three bands of different molecular weight were observed: 87 kDa which corresponds tothe molecular weight of the dimer (86.5 kDa), 42 kDa which matches the monomer (43.3 kDa) and an unknown protein of molecular weight 31kDa; (b) strong step pinning observed on the (011) face growing in a nongelled environment. The pinning agent is a microscopic (foreign) particleadhered to the surface. Multiple steps remain pinned at the same time over a distance of 11 µm; (c) step pinning in the presence of 0.1% agarose.The density of pinned steps is much larger in comparison to the nongelled solution.

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