growth processes in macromolecular crystallization · where v＝4.8×10－9 is the speciˆc volumes...

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University of California, Irvine Dept. of Molecular Biology and Biochemistry 560 Steinhaus Hall Irvine, CA 92697–3900, USA(E-mail: amalkin＠uci.edu)

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J. Jpn. Soc. Microgravity Appl. Vol. 19 No. 1 2002 (9–13)

Special Issue: ICCG–13(Original Article)

Growth Processes in Macromolecular Crystallization

A. J. MALKIN, M. PLOMP and A. McPHERSON

Abstract

In situ atomic force microscopy (AFM) was utilized to study growth processes of several macromolecular crystals.Correlation between crystal structure, surface morphology, and growth mechanisms of faces of macromolecularcrystals that have screw axes perpendicular to them was demonstrated. Thus the s001tfaces of orthorhombic cata-lase, ribosomal 50 s subunit, trigonal trypsin, and tetragonal Bence-Jones protein (BJP) crystals grow by successivedeposition of n alternating, symmetry-related layers with a thickness of d00n＝1Wn `c`. For crystallization of glucoseisomerase crystals from the supersaturation dependencies of tangential step rates and critical step lengths kineticcoe‹cient of steps and the free energy of the step edge were estimated respectively. Incorporation of the individualvirions into the step edge on the surface of Cucumber Mosaic Virus (CMV) crystals was visualized and attachmentfrequencies and probabilities were estimated.

1. Introduction

Currently, a limited understanding of the mechan-isms operative in crystallization, and their impact onthe solid-state properties of macromolecular crystals,restricts a broader application of X-ray diŠractionanalysis in biotechnology. Despite much recentprogress in the physical analyses of macromolecularcrystallization1–12), important questions remain largelyunanswered, particularly about the development ofsurface morphology and kinetics of growth.

Here we present the results of in situ AFM studies ofcorrelations between surface morphologies and crystalsymmetry during the growth of s001tfaces of cata-lase, ribosomal 50 s subunit, trypsin and Bence-Jonesprotein crystals having respectively two-, three-, orfour-fold screw axes perpendicular to these faces. Wealso describe here the results of studies of growth ki-netics for glucose isomerase crystals, which alloweddetermination of the kinetic coe‹cient of steps and thefree energy of the step edge. Finally incorporation ofthe individual virions into the step edge on the surfaceof Cucumber Mosaic Virus (CMV) crystals was visual-ized and attachment frequencies and probabilities wereestimated.

2. Experimental Section

We examined growth processes of macromolecularcrystal in situ using Nanoscope IIIa AFM (DigitalInstruments, Santa Barbara, CA, USA), operated intapping mode under controlled supersaturation condi-tions, at 259C, according to established methods5).Crystallization conditions for each macromolecule as

well as relevant molecular and crystallization proper-ties are presented elsewhere13–15).

3. Results and Discussion

3.1 Correlation between crystal symmetry andgrowth mechanisms

Growth of the s001tfaces of catalase, trigonal tryp-sin and Ben-Jones protein (BJP) crystals proceeds ex-clusively by two-dimensional nucleation and layer-by-layer step advancement. Generally, crystal faces indirection (hkl) are expected to grow with layers ofthickness dhkl. However, the Bravais Friedel DonnayHarker (BFDH) criterion16) contains exemptions forstructures with centered cells, glide planes and screwaxes, which all lead to reduced growth layer thickness.Indeed orthorhombic catalase, trigonal trypsin andtetragonal BJP all follow the exemption rule which im-plies that the existence of a screw axis in a crystal struc-ture leads to the formation of reduced growth layersdnhnknl on the face (hkl ) perpendicular to that axis. Inthe case of screw axes perpendicular to s001t, growthlayers have a thickness of d00n. From symmetry con-siderations, the unit cell should be divided into two e-quivalent layers for 21, 42 and 63 screw axes (n＝2),three equivalent layers for 31, 32, 62 and 64 (n＝3) fourlayers for 41 and 43 (n＝4) and six layers for 61 and 65

(n＝6).In case of catalase crystals the step height of the

nuclei is equal to 11.5±0.2 nm, which corresponds tohalf of the unit cell dimension d002 along c. Each suc-cessive layer derived from a 2D island is related by a1809, 2–fold rotation to the preceding layer (Fig.1a–c). The anisotropic shape of the nuclei is due to the

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Fig. 1 A sequence of 25×25 mm2 in situ AFM images takenat: (a) 0; (b) 11; and (c) 30 min showing nucleation ofsymmetry-related 2D nuclei on the (001) face of or-thorhombic catalase crystal. (d) 5×5 mm2 image show-ing symmetry-related 2D nuclei (indicated by diŠerent-ly coloured ellipses) on the (001) faces of trigonal tryp-sin crystal.

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A. J. MALKIN, et al.

J. Jpn. Soc. Microgravity Appl. Vol. 19 No. 1 2002

strong anisotropy in the step advancement rates indiŠerent crystallographic directions17). The formationof two alternating growth layers on the s001tface ofcatalase crystals is caused by the presence of the 21

screw axis in the structure perpendicular to this face.This screw axis divides the unit cell in two symmetri-cally equivalent layers rotated by 1809, which indeedshould lead to the observed equivalent but rotatedhalf-layers. Since there are four molecules in the unitcell, there are potentially three ways to distribute theminto two equivalent half-layers. By analyzing thestrength of interactions between the four molecules themost likely distribution was determined17).

The shape of 2D nuclei on the s001tface of trigonaltrypsin resembles an elongated ellipse. The elongationis in the direction parallel to the crystal edges, i.e.along〈100〉directions, with an average widthWlengthanisotropy ratio of 1:4 (Fig. 1d). The shape of thenuclei forming each successive growth layer of thick-ness 3.2±0.5 nm is related by a counterclockwise rota-tion of 1209with respect to the shape of the initiatingnuclei of the preceding layer. This observed 3–foldsymmetric growth behavior of the trigonal s001tfacecan be explained by the presence of the 31 screw axisparallel to c in the P3121 crystal structure (note that, incase of a 32 axis, the new layers would have a clockwiserotation). The six molecules in the unit cell with aheight of c＝10.9 nm can, in accordance with the space

group symmetry, be sorted into three groups consist-ing of two molecules each, that are mutually related bya 3–fold screw axis. This results in three triad-relatedgrowth layers within a unit cell, each with a height ofd003＝1W3 `c`＝3.6 nm, which corresponds well to theexperimentally observed growth steps of height 3.2±0.5 nm.

Similar to the case for catalase crystals, the trigonaltrypsin unit cell permits multiple divisions of the sixmolecules into three equivalent layers. On the basis ofthe bond strengths between the molecules, again themost probably distribution was selected14). Also, theshape of the 2D nuclei was predicted on the basis ofthe bond structure. This predicted shape correlateswell with those experimentally observed14).

In case of growth of the s001tface of tetragonalBJP crystals, symmetry-related layers produced exclu-sively by 2D nucleation were again encountered. Theshape of newly formed 2D nuclei resembled half el-lipses, somewhat similar to the ones described abovefor crystallization of catalase. However, in case of theBJP crystallization, four subsequent growth layerswere distinguished. These were related by a rotation of909clockwise for each subsequent layer (Fig. 2). Thestep height of the nuclei was 4.6±0.2 nm. This cor-responds well to d004＝4.49 nm. These observations in-dicate that the observed symmetry-related layers arecaused by the presence of the 43 screw axis (if therewere a 43 screw axis, successive layers would exhibit a909counterclockwise rotation).

In the case of a growth spiral originating from ascrew dislocation, the origin of each new growth layeris pinned to exactly the same point (i.e. the dislocationoutcrop), and therefore successive symmetry-relatedlayers demonstrating rotated step velocity anisotropycan be signiˆcantly restrained. For crystal faces withrelatively low anisotropy it is still possible for disloca-tion spirals to grow, and they will develop growthpatterns with multiple (e.g. double for 21 or triple for31) growth steps. In growth directions where smalland large step velocities of subsequent layers change,the pairing of steps will alternate. This leads to the for-mation of ``zig-zag'' patterns known as `step interlac-ing'18,19). In the case of macromolecular crystals, inter-lacing at a spiral was observed for the s001tface of aribosomal 50 s subunit crystal (Fig. 3) with spacegroup C2221 (which has a 21 screw axis perpendicularto the s001tface). The greater anisotropy of thegrowth layers, the more severe the steps restrain oneanother. Eventually, this can lead to `self-inhibition'of growth spirals, as was shown for the case of Pnmabarite s001t, having screw axes parallel to c20). In thiscase, the growth rate of the spirals was so reduced (be-cause of step hindrance) that 2D nucleation alone de-termined the growth rate of the face.

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Fig. 2 A sequence of 2×2 mm2 in situ AFM images taken at:(a) 0; (b) 11; and (c) 25 and (d) 32 min showing nuclea-tion of symmetry-related 2D nuclei (indicated by half-ellipses) on the (001) face of tetragonal Bence-Jonesprotein.

Fig. 3 (a) In situ AFM 60×60 mm2 image showing a disloca-tion spiral on the s001tface of ribosomal 50 s subunitcrystal. (b) In situ AFM 25×25 mm2 image showingstep interlacing on the s001tface of a ribosomal 50 ssubunit crystal growth steps.

Fig. 4 (a) Supersaturation dependencies of tangential step growth rates in diŠerent crystallographic directions. –〈010〉; ;–〈100〉; ＋–〈1̃00〉and o–〈01̃0〉. Insert: In situ AFM 11×11 mm2 image showing growth steps advancing around the stacking fault on thesurface of glucose isomerase crystal. Arrows indicate advancing steps segments. (b) Dependence of step critical length on super-saturation for 1,〈01̃0〉; 2,〈100〉.

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3.2 Growth Step Kinetics of Glucose Isomerase Crys-talsGrowth steps on the (001) face of orthorombic glu-

cose isomerase crystals were generated by 2D nuclei.The step height of 10±0.3 nm is equal to the unit cellparameter along c. In several experiments we observedon a surface the combination of a stacking fault with

dislocation sources, which resulted in rotation of twogrowth steps around the stacking fault (insert in Fig.4a). This allowed us to measure the supersaturationdependencies of tangential step rates for four or-thogonal crystallographic directions (Fig. 4a) using thestacking fault as a reference point.

The tangential step rate, v is given by21):

[＝Vb(c－ce) (1)

where V＝4.8×10－9 is the speciˆc volumes of glucoseisomerase tetramers in the crystal, c and ce＝2.1×1015

cm－3 are initial and equilibrium concentrations ofprotein respectively, and b is the step kineticcoe‹cient22). From the linear portion of [(c–ce) depen-dencies for (c–ce)À1014 cm－3 (Fig. 4a), the kineticcoe‹cient b for glucose isomerase crystallization was

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Fig. 5 In situ AFM images of an advancing growth step onthe (001) face of a CMV crystal. Newly incorporatedvirions are indicated with ＋. AFM images are 670 by670 nm in (a–c), and 560 by 560 nm in (d).

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A. J. MALKIN, et al.


estimated to be 4.7×10－4 cmWsec, 5.2×10－4 cmWsec,4.4×10－4 cmWsec and 5.4×10－4 cmWsec for crystallo-graphic directions〈010〉,〈1̃00〉,〈01̃0〉and〈100〉respectively. Similar values for the kinetic coe‹cientwere found for the crystallization of several other mac-romolecules14,23–26). The lower values of b for macro-molecular crystallization compared with inorganiccrystallization22) has been attributed to the necessity ofthe pre-kink selection of the proper orientation of anincoming macromolecule for incorporation into thegrowth step9). At lower supersaturation a non-lineardependency of tangential step rate was observed(Fig. 4a), presumably due to the in‰uence of impuri-ties, a phenomenon well documented for a number ofother macromolecular and inorganic crystals27).

Growth steps advance (Fig. 4b) only when theirlength L exceeds a critical value, Lc

21), Critical lengthLc is related to the free energy of the step edge a by21):

Lc＝2VaWkTs (2)

where k is Boltzmann's constant and T is temperature.Supersaturation dependence of step critical length, Lc,was measured as the average of growth step length im-mediately before and after the growth step started toadvance (Fig. 4b). From the slope of Lc (1Ws) depen-dencies, according to (2), surface free energies of thestep edge a were estimated to be 0.5 ergWcm2 and 0.37ergWcm2 for〈01̃0〉and〈100〉crystallographic direc-tions respectively. Surface free energies of the stepedge were measured for several macromolecular crys-tals and varied in the range of 0.3–5 ergWcm2 14).3.3 Incorporation of CMV virions into CMV crys-

tals: Attachment Frequencies and ProbabilitiesIn addition to measuring step kinetics, AFM also al-

lows to monitor incorporation of individual macro-molecules into the step edge. Because of their relativelylarge sizes, CMV virions can be seen by AFM to incor-porate into growth steps as individuals, thus allowingmeasurement of attachment frequencies under con-trolled supersaturation conditions. From attachmentfrequencies, attachment probabilities can be estimat-ed.

In the case of inorganic crystals grown from solu-tion, solvatation and desolvatation processes typicallyexhibit relatively high activation energies21), while theentropic activation barrier can be relatively low. Thecorresponding steric factor, which is the probability ofa particle having the proper spatial orientation, is closeto unity. In the crystallization of complex macro-molecules, the necessity of desolvatation is likely lessimportant than in the crystallization of inorganicmolecules. However, macromolecules in an arbitraryorientation cannot join a growth site. Thus the entrop-ic activation barrier must play an important role. Pre-kink selection would be expected for the approachingmacromolecule to assume an acceptable orientation

for incorporation into the growth step. In CMV crys-tals, icosahedral virions are connected in the surfacelayer through hexameric capsomers, hence there are 60identical orientations for correct incorporation, farmore than for most proteins. This, given the weak andimprecise nature of bonding between virions in the(001) plane, should result in relatively high attachmentprobabilities.

As seen in Fig. 5, advancement of growth steps pro-ceeds by one-dimensional nucleation of kinks9),formed by single or multiple virions, with subsequentlateral extension of molecular rows by addition ofvirions into kinks. Similar mechanisms of step advan-cement have previously been described for other mac-romolecular crystals5,8,9). Under the supersaturationconditions here (¿0.1 mgWml CMV), the attachmentfrequency of virus particles was found to be ¿2.3×10－2 virionsWsec. There was no detachment of any vi-rus particle, either at supersaturated or equilibriumconditions, hence, thermal energy is insu‹cient to dis-place a particle from the step edge.

In these experiments the concentration of virions insolution was c＝7×1012 cm－3, corresponding to anaverage distance between virions of L＝5×10－5 cm.Assuming that growth proceeds by direct incorpora-tion of virions from the bulk solution into the stepedge21), and that the concentration of virions at thecrystalline interface is zero, then the diŠusive ‰ux canbe estimated as J＝D(C－C0)WL＝2.2×1010 s－1cm－2.D＝1.6×10－7 cm2Ws is the diŠusivity of CMV deter-

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mined from light scattering experiments. From this, vi-rus particles encounter a kink having a size of approxi-mately 30×30 nm with a frequency of approximately¿0.2 s－1. Using the attachment frequencies of 2.3×10－2 s－1 measured from AFM (Fig. 4), the attachmentprobability is ¿10－2. Thus, approximately one out ofevery 100 CMV virions that approach the step edge in-corporates into the step.

This probability of attachment can be related inlarge part to pre-kink selection of proper molecularorientation for incorporation into the growth step. Forhigh symmetry particles, as might be expected, pre-kink selection of the proper molecular orientation isconsiderably less than for most macromolecules. In-deed, from the same calculation using AFM data forstep advancement in thaumatin crystallization27), theattachment probability of those protein molecules,which can have only one correct molecular orientationfor incorporation into the crystal, was estimated to be¿5×10－4.

Acknowledgments

We wish to thank A. Greenwood, R. Lucas, and J.Zhou for technical assistance, N. Ban, B. Freeborn forproviding ribosomal 50S subunit and Yu. G. Kuznet-sov, S. B. Larson, M. Plomp and P. Vekilov for dis-cussions. The National Aeronautics and Space Ad-ministration supported this research.

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(Received Nov. 7, 2001Accepted for publication Nov. 27, 2001)

growth processes in macromolecular crystallization · where v＝4.8×10－9 is the speciˆc volumes...

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