Laser Michelson interferometry investigation of protein crystal growth

Journal of CD,stal Growth 130 (1993) 317-320 North-Holland

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Laser Michelson interferometry investigation of protein crystal growth P e t e r G. Vekilov t, Mitsuo A t a k a ': and T a t s u o K a t s u r a Research Institute for Polymers and Testiles, 1-1-4, Higashi, Tsukuba 305, Japan Received 26 October 1992; manuscript received in final form 4 January 1993

Laser Michelson interferometry was applied to study the elementary growth mechanism of protein crystals. The results for the (101) face of tetragonal lysozyme show that for supersaturations cr higher than 1.6, growth proceeds by two-dimensional nucleation. However, at lower supersaturations growth is governed by dislocation sources. The observed non-linearits, of the step velocity versus supersaturation dependence for supersaturations up to 1.2 is proved to be due to strong impurity effects. At o- < 0.4 the crystal surface is covered with macrosteps. The effective step kinetic coefficient for the studied face is determined:/3 = 2.8 x 10-6 m/s. The applicability of general crystal growth principles and theories to protein crystallization is thus illustrated.

The pursuit of high quality and sufficiently large protein crystals for X-ray structure determination has brought about the understanding that processes on the growing protein crystal surface need to be studied at a mc,lecular level [1,2]. Laser Micheison interferometry [3,4], a real time in-situ quantitative method of kinetic measurements and morphological observations, has shown its great advantages for such studies [5-8]. We applied this method to elucidate some important aspects of protein crystal growth: the role of two-dimensional nucleation and dislocation sources, impurities action leading to crystal poisoning, determination of kinetic parameters, on the example of the (101) face of hen egg-white (HEW) lysozyme tetragonal crystals. The experimental set-up (laser Michelson interferometer attached to an inverted microscope) was principally the same as the one described in ref. [8]. A time-lapse video recording system (Sankei, allowing up to 3 frames per 10 s recording mode) was attached in order to measure the very slow growth kinetics. A specially designed crystallization cell w~s applied, allowing optical t Permanent address: Institute of Physical Chemistry, Bulgarian Academy of Sciences, Sofia 1040, Bulgaria. 2 To whom correspondence should be addressed.

measurements to be carried out in a thermostated solution of a volume of 300 ~1 and less. The crystal ( ~ 1 mm in size) was glued to the crystal holder, the studied face downward. Solutions were prepared from 6 × crystallized lysozyme (Seikagaku) [9] with 3% (w/w) NaCI, pH = 4.6 by HCI, lysoz3,me concentration was C = 2.78% (w/w) in all experiments. The driving force for crystallization was considered to be thermodynamic supersaturation, ,A~x measured in kT units. It was denoted by o-, imposed by undercooling the system and calculated as cr-A~/kT= In[C/S(T)] (T is temperature in kelvins). Solubility S in mol/l was determined from the phase diagrams [10] as S = e x p ( 2 4 . 1 - 9 1 0 0 / T ) . Measurements were performed in the temperature interval 12-22.5°C. The growth morphology was observed both in the real time of the experiment and accelerated. Normal growth rate, growth hillock slope and tangential step velocity were measured from the recorded images ~s has been described before [3,4,8]. In order to clear the crystal surface, after immersing into the solution the crystals were slowly etched through overheating by ~ 3°C for about 2 h. Then the surface was regenerated for 2 days at an undercooling of 5°C (lower undercool-

0022-0248/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved

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P.G Vekilov et al. / Laser Michelson interferometry im;estigation of protein cn'stal growth

Fig. 1. Interference pattern from approximately 1/4 of the (101) iysozyme face showing two major growth hillocks and numerous small ones, covering most of the face. The difference in height between two neighboring interference fringes is 0.229 /~,m [8] (the refractive index of the solution n = 1.384 was measured experimentally, it is mostly determined by the 3% NaCI, when compared with the value of pure lysozyme solution [11]). The edge with the adjacent (110) face is bottom right. Kinetic measurements were performed on the bottom left growth hillock. Bar equals 100 p.m.

ing yielded a rough surface). Usually the surface was covered with numerous growth hillocks, ~ 0.4 /~m high (two interference fringes), that were not suitable for measurements (see fig. 1). Or the average, in 1 out of 4 experiments we had at least one growth hillock with 5-6 interference fringes on which growth kinetics could be measured. Observations of the morphology of the growing crystal surface revealed that in the supersaturation region, 0.4 < cr < 1.6, growth hillocks had the form of circular cones (fig. 1) and existed for unlimited time (measurements were carried out for 4-5 days). Even if they disappeared outside this supersaturation range, on coming back they were formed at the sarr~e places. This means that we are dealing with dislocation growth hillocks and the above stated supersaturation interval is the region of dislocation induced growth of the lysozyme crystals. At o-< 0.4 the growth hillocks were gradually lost and the surface was covered with macrosteps.

At ar > 1.6 the growth hillocks were lost again. The interference pattern was very irregular, the interference fringes were interlaced, moved in all directions, and appeared and disappeared. These observations led us to the conclusion that in this supersaturation region growth proceeds by the polynuclear mode of two-dimensional (2D) nucleation [12-15]. This is in accordance with the results of other authors [1]. Kinetic measurements (dependencies of the hillock slope, normal growth rate and the step velocity on the supersaturation) were performed on one and the same growth hillock for 2 - 3 h each. No change in the kinetic values with time was observed in two 8 h measurements. The hillock slope remained constant in the course of one experiment, the measured values being in the range (1.3-1.5) x 10 -2. Knowing that the free surface energy of the face is of the order of several m J / m 2 [16,1] and following the formalism of ref. [3], the predicted hillock slope is of the order of the measured value. As shown for crystals of low molecular weight substances [8,17], groups of many closely situated dislocations may produce hillocks with constant slope over a wide supersaturation region. Fig. 2 presents the dependence of the normal growth rate R on the supersaturation, measured on a dislocation growth hillock. Our values of R are higher than those obtained by others from crystal sizes [16,18]. This is probably due to the higher purity of our raw material. The curve has a typical S-form. If less measurements were done and if simultaneous in-situ morphological observations were not available, the lower part of the curve could have been misinterpreted as exponential increase typical of the two-dimensional nucleation mechanism. In order to understand what happens at lower supersaturations, we investigated an existing growth hillock at o" = 0.4. The normal growth rate on the growth hillock decreased with tflae (fig. 2, insert). Eventually the hillock disappeared and the face surface became covered with macrosteps moving extremely slowly. This means that nonequilibrium adsorption of impurities (either coming with commercial lysozyme or introduced during preparations for the experiment) on the ter-

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.6 o=-lnlClS(T)] Fig. 2. The dependence of the normal growth rate R on the supersaturation o- for the bottom left dislocation growth hillock in fig. 1. Temperature range is indicated on the upper o" axis. For each point, 8-10 periods between passing interference fringes were measured and hence the mean value and the error range were determined [8]. (o), (o) Measurements taken in two series of supersaturation increase. Insert: Decreasing growth rate at small supersaturations, leading to poisoning of the surface by impurities and formation of macrosteps. 0.8

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teristic adsorption time of the second impurity becomes comparable to the exposure times of the terraces between steps, a non-linear increase of ~' with (r is observed. Furthermore, in the second linear region, growth is fast enough so that only ineffective amounts of impurities can be adsorbed on the surface in the interval between passing steps. Such non-linear increase was observed in previous estimates of the step velocity [1], while a super-quadratic increase of growth rate in the same supersaturation region was recorded by other authors [16,18,1]. Hence, we may conclude that the second impurity is typical for lysozyme, independent of the source of the material. As in the second linear region of the t,(or) curve, for 1.2 _.
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races between steps takes place at this supersaturation: the surface concentration of the impurities increases as the terraces between steps are exposed to impurity adsorption for longer and longer times between passing steps as the growth rate decreases [19]. Fig. 3 presents the dependence of the step velocity c on the supersaturation, corresponding to the normal growth rate curve in fig. 2. The plot consists of two linear parts, connected by a fast increase in the step velocity; for cr < 0.4 the step velocity is practically zero. The behaviour of the step velocity, together with the morphological observations and the normal growth rate measurements, are evidence for the action of two types of impurities [20,21]. One of them, after the Cabrera-Vermilyea stopper mechanism [22], determines the "dead" zone for or _< 0.4. The second impurity decreases the slope of the straight line v(o-) in the first linear region as compared to 1.2 _< ~_< 1.6. When the charac-

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ln[C/S(T)] Fig. 3. The dependence of the tangential velocity of steps t' on the supersaturation tr, corresponding to the normal growth rate measurement in fig. 2. Error range was determined by summing t~e relative errors of normal growth rate and hillock slope determinations. The value of the step kinetic coefficient /3 for the (101) face of tetragonal HEW lysozyme is shown.

320

P. G Vekilov et al. / Laser Michelson

interferometry investigationof protein crystal growth

the crystal, C = 1.12 x 10 24 m -3 is the molecular concentration of the solution), we obtain/3 = (2.8 + 0.2) x 10 -6 m / s . Now we can a-posteriori estimate the significance of transport processes towards steps for the overall growth kinetics. According to refs. [12,8], in the absence of convection, the surface supersaturation tr~ is related to the bulk supersaturation trb as trs =tr b (1 + / 3 p r / D ) -t. Here p is the hillock slope, r is approximately half the crystal size and D = 1.03 × 10 -l° m 2 / s [23] is the diffusion coefficient of lysozyme in the solution. Substituting, we get tr~ = 0.9trb; transport is not a limiting parameter. The correction in /3 that follows from this slight reduction in tr exceeds only slightly the error limits of the /3 determination (fig. 3). These theoretical considerations corroborate our observation that the kinetics results were independent of the crystal size over the range 0.7-1.8 mm. At high growth rates the interval between passing steps becomes shorter than the characteristic adsorption time of impurities. As a consequence the step velocity increases linearly with supersaturation, as shown in fig. 3 in the region 1.2 _< tr _< 1.6, leading to a relatively slow increase in the dislocation governed R(tr) dependence (fig. 2). On the other hand, the growth rate for two-dimensional nucleation increases exponentially with supersaturation, and at tr= 1.6 becomes probably higher than for dislocation governed growth. Under the given conditions, the face grows with the fastest possible growth rate, so for o->_ 1.6 growth proceeds by the 2D nucleation mechanism. This study clearly demonstrates the applicability of crystal growth principles and theories developed for small molecule systems to protein crystallization. More detailed investigations, in particular concerning the separation of the effects of supersaturation and temperature, are now in progress. The authors are grateful to the Institute of Physical Chemistry., Sofia, for technical assistance. One of them (P.G.V.) acknowledges the

financial support of STA of Japan for his stay at RIPT.

References [1] S.D. Durbin and G. Feher, J. Mol. Biol. 212 (1990) 763. [2] L.A. Monaco, F. Rosenberger and N.B. Ming, presented at 10th Intern, Conf. on Crystal Growth (ICCG-10), San Diego, CA, 1992. [3] A,A. Chernov, L.N. Rashkovich and A.A. Mkrtchan, J, Crystal Growth 74 (1986) 101. [4] Yu.G. Kuznetsov, A.A. Chernov, P.G. Vekilov and I.L. Smol'skii, Soviet Phys.-Cryst. 32 (1987) 584, [5] A.A. Chernov and L,N. Rashkovich, J. Crystal Growth 84 (1987) 389. [6] K. Onuma, K. Tsukamoto and I. Sunagawa, J. Crystal Growth 98 (1989) 377. [7] P.G. Vekilov, Yu.G. Kuznetsov and A.A. Chernov, J. Crystal Growth 121 (1992) 643. [8] P.G. Vekilov and Chr. Nanev, J. Crystal Growth 125 (1992) 229. [9] A.V. EIgersma, M. Ataka and T. Katsura, J. Crystal Growth 122 (1992) 31. [10] M. Ataka and M. Asai, J. Crystal Growth 90 (1988) 86. [11] R.S. Feigelson, Report to NASA, NASA #NAG8-489, CMR-88-9 (1988). [12] A.A. Chernov, Modern Crystallography III: Crystal Growth (Springer, Berlin, 1984). [13] W. van Saarloos and G.H. Gilmer, Phys. Rev. B 33 (1986) 4927. [14] A.I. Malkin, A.A. Chernov and I.V. AIcxeev, J. Crystal Growth 97 (1989) 765. [15] W. Obretenov, D. Kashchiev and V. Bostanov, J. Crystal Growth 96 (1989) 843. [16] R.W. Fiddis, R.A. Longman and P.D. Calvert, J. Chem. Soc., Faraday Trans. I, 75 (1979) 2753. [17] P.G. Vekilov and Yu.G. Kuznetsov, J.Crystal Growth 119 (1992) 248. [18] S.D. Durbin and G. Feher, J. Crystal Growth 76 (1986) 583. [19] A.A. Chernov and A.I. Malkin, J. Crystal Growth 92 (1988) 432. [20] L.N. Rashkovich and B.Yu. Shekunov, in: Growth of Crystals, Vol. 18, Ed. E.I. Givargizov (Nauka, Moscow, lOOm p. !24 ~;,, ~ .... ;.,.-) [21] V.V. Voronkov and L.N. Rashkovich, Kristailografiya 37 (3) (1992) 559. [22] N. Cabrera and D.A, Vermilyea, in: Growth and Perfection of Crystals, Eds. R.H. Doremus, B.W. Roberts and D. Turnbull (Wiley, New York, 1958) p. 393. [23] V. Mikol, E. Hirsch and R. Gieg~, J. Mol. Biol. 213 (1990) 187. •

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