DOI: 10.1021/cg1002989
Growth Rate Dispersion in Protein Crystal Growth
2010, Vol. 10 3164–3168
Russell A. Judge,*,† Elizabeth L. Forsythe,‡ and Marc L. Pusey# †
Structural Biology Department, 100 Abbott Park Road, Abbott Park, Illinois 60064, Nektar Therapeutics, 490 Discovery Drive, Huntsville, Alabama 35806, and # iXpressGenes Inc., 601 Genome Way, Huntsville, Alabama 35806 ‡
Received March 5, 2010; Revised Manuscript Received May 21, 2010
ABSTRACT: Like many small molecule materials, tetragonal lysozyme crystals exhibit growth rate dispersion. To investigate this phenomenon further, the growth rate dispersion of the (110) and (101) crystal faces was determined as a function of sodium chloride concentration, temperature, and solution pH. Under the conditions investigated, the growth rate dispersion follows the constant crystal growth model, in which each individual crystal is assumed to have a unique, constant growth rate. While the growth rate dispersion of the (110) face seems independent of the solution conditions, for the (101) face it was observed to vary systematically with temperature and pH. The greater susceptibility of the (101) face to the causes of growth rate dispersion was interpreted in light of a model proposed to explain the differing growth mechanisms of each face. Overall, the magnitude of crystal growth rate dispersion observed for lysozyme is similar to that reported for some small organic molecules.
Introduction
Experimental Methods
Growth rate dispersion describes the phenomenon where crystals of the same material under the same solution conditions grow at different rates. It has been reported for a number of inorganic and organic small molecule materials, for crystals generated by both primary and secondary nucleation.1-6 Growth rate dispersion broadens the crystal size distribution and hence affects the product quality of industrial crystallizers.1,2,4,5,7,8 For individual crystals, growth rate dispersion has also been linked to internal crystal lattice strain and crystal diffraction quality, with the more strained crystals exhibiting slower growth rates, while less strained crystals grow faster.9,10 While there are a number of reports for small molecule materials, reports of growth rate dispersion for protein crystals are limited. Schlichtkrull (1967)11 grew insulin crystals in a stirred batch crystallizer and reported that the insulin face growth rate was independent of crystal size or choice of crystal. In the bulk crystallization of ovalbumin, negligible growth rate dispersion was observed.12 The first report of growth rate dispersion for a protein was that of lysozyme. Cherdrungsi (1999) measured tetragonal lysozyme crystal growth rates in a batch stirred crystallizer and reported significant growth rate dispersion, with crystal growth rates varying by a factor of 8.13 In this case, the crystal size was measured as a volume equivalent size distribution. The crystallizer was operated at 5% (w/v) NaCl, pH 4.0, 22 °C, with growth rate dispersion measured at buffer concentrations of 0.1, 0.3, and 0.6 M sodium acetate. The growth rate dispersion was observed to be independent of the sodium acetate buffer concentration. To further explore the growth rate dispersion of tetragonal lysozyme over a wider range of solution conditions, we examined crystal growth rate data measured for both the (110) and (101) crystal faces as a function of NaCl concentration, temperature, and solution pH.
Extensive crystal growth rate data for tetragonal lysozyme was collected in the Biophysics laboratory at the Marshall Space Flight Center, Huntsville, AL, USA. Data for both the (110) and (101) face growth rates at multiple lysozyme solution concentrations were obtained as a function of temperature (4, 9, 12, 14, 18, 20, 22 °C), NaCl concentration (2% (w/v), 2.5% (w/v), 3% (w/v), 5% (w/v), 7% (w/v)) and pH (4.0, 4.2, 4.4, 4.6, 4.8, 5.0, 5.2, 5.4). The buffer used for these experiments was 0.1 M sodium acetate. Most of the data were collected at 5% (w/v) NaCl. While some of the data have yet to be published, a significant proportion has already been presented in a series of research papers.14-19 The methods for generating and measuring the lysozyme crystal growth rates have been reported previously.17 In brief, commercial hen egg-white lysozyme (Sigma Chemicals, St. Louis, MO, three times crystallized, dialyzed, and lyophilized) was dissolved in and dialyzed against 0.1 M sodium phosphate, 1% (w/v) NaC1, pH 6.4. The protein was further purified by cation-exchange chromatography, and the eluted protein was recrystallized overnight in 10% (w/v) NaCl at 4 °C. The crystalline precipitate was recovered, dissolved in 0.1 M sodium acetate buffer which was then titrated to the desired pH by the addition of dilute acetic acid, extensively dialyzed against 0.1 M sodium acetate buffer at the same pH, and concentrated as required for use in the crystallization experiments. Lysozyme concentrations were determined by UV absorbance using an A (l%, 281.5 nm) = 26.4.20 Crystal face growth measurements were made using a computer-controlled video microscope system.21 Crystals were nucleated in situ on the glass growth cell walls by primary nucleation. The growth cell which has an approximate volume of 250 μL was jacketed and temperature controlled via a water bath. Crystals growing in the cell were observed through a video microscope. Crystal locations were identified within the cell using PC-controlled translation stages for X, Y, and Z axes of motion. Multiple suitably aligned crystals in the size range of 10-50 μm were selected for data collection during the programmed measurement cycle. Growth solution at a given protein concentration was freshly prepared prior to each run by mixing equal quantities of buffered protein and salt solutions, which were then injected into the observation chamber. Crystal growth over time was then recorded for the preselected crystals. After the experiment, the crystals were dissolved. Fresh crystals were nucleated within the growth cell immediately before the next growth experiment. This provided a new population of crystals
*To whom correspondence should be addressed. Phone: 847-935-1343. Fax: 847-938-1083. E-mail:
[email protected]. pubs.acs.org/crystal
Published on Web 06/09/2010
r 2010 American Chemical Society
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Figure 1. Lysozyme (110) face growth rates (18 °C, pH 4.0, 5% (w/v) NaCl, 19.4 mg/mL lysozyme). The different symbols represent the growth of individual crystals over time. within the size range of 10-50 μm for each experiment. All growth rates were obtained in the absence of imposed solution flow. These extensive growth rate data were mined to recover data sets that were amenable for growth rate dispersion analysis. Growth rate data sets at the same solution conditions were only considered if they contained growth rate data for at least 6-10 crystals or more. Some data sets contained data for up to 17 crystals. While more crystal data points per data set would provide a more accurate value of the growth rate standard deviation, these data sets were sufficient to enable comparison between solution conditions. In general, (110) face growth rate data sets were more abundant than that of the (101) face.
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Figure 2. Plot of the growth rate standard deviation against the mean growth rate for both the (110) (b) and (101) (O) lysozyme crystal faces at 22 °C, pH 4.0, and 5% (w/v) NaCl. Each point represents growth rate data obtained at a specific value of supersaturation. The slope of the line represents the coefficient of variation, CVG. The linear regression correlation coefficient (r2) was 0.98 for the (110) and 0.99 for the (101) crystal face data sets.
Results Tetragonal lysozyme face growth rates exhibit growth rate dispersion. Figure 1 illustrates the growth of the (110) face over time for four individual crystals. The variation in the slope of the lines, the variation in growth rate, is far larger than the scatter of measurements for individual crystals around the line fitted to determine their growth rate. The face growth rates display a good linear fit for each crystal indicating that these lysozyme crystals are following the constant crystal growth model. This model implies that each individual crystal has an inherent constant growth rate different from the inherent constant grow rate of other crystals growing under the same solution conditions.5 In displaying growth rate dispersion results, some prior investigators have calculated (for a given set of solution conditions) the growth rate variance, σG2 and the mean growth rate, G. For citric acid monohydrate,22 sucrose,4 and fructose,5 the growth rate variance was found to increase with increases in the mean growth rate. This was also observed for both the lysozyme (110) and (101) faces in this study. In an analysis of the growth rate dispersion of fructose crystals however, Johns et al. (1990)6 replotted the data obtained by Shiau and Berglund (1987),5 plotting the standard deviation of the growth rates, σG, against the mean growth rate, G, and obtained a good linear fit. A linear relation is expected from the constant crystal growth model.6 The slope of this line is defined as the coefficient of variation, CVG (which is dimensionless). In order to compare the growth rate dispersion of lysozyme for crystal growth rate data obtained at different solution conditions, the coefficient of variation, CVG, was therefore calculated. A lysozyme crystal growth rate experiment set, in which the face growth rates are measured at multiple lysozyme concentrations with the pH, temperature,
Figure 3. Growth rate dispersion of the (110) face as a function of precipitant concentration at pH 4.0.
and NaCl concentration being held constant (hence growth rate dispersion over a range of supersaturation values), provides one value of the coefficient of variation. An example is illustrated in Figure 2, in which the growth rate standard deviation is plotted against the mean growth rate for both the (110) and (101) crystal faces for a crystallization experiment conducted at 5% (w/v) NaCl, pH 4.0, and 22 °C. In this example and in the other growth conditions where data were available, there was a good linear fit for both crystal faces. At this specific condition, the coefficient of variation for the (101) face is approximately two times greater than that observed for the (110) face. In general for the conditions investigated in this study, greater growth rate dispersion was observed for the (101) face in comparison to the (110) face. In Figure 3, the coefficient of variation is plotted against precipitant concentration for the (110) face at pH 4.0 for two temperatures, 18 and 22 °C. In this case, there was insufficient data for the (101) face growth rates to afford a comparison. Error bars are estimated from duplicate data sets at 18 °C. The data show no significant effect of precipitant concentration on the growth rate dispersion at these temperatures.
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Figure 4. Effect of temperature on the growth rate dispersion of the (110) face at 5% (w/v) NaCl.
Figure 5. Effect of temperature on the growth rate dispersion of the (101) face at 5% (w/v) NaCl, pH 4.0.
The effect of temperature on the growth rate dispersion of the (110) face at 5% (w/v) NaCl for pH 4.0 and 5.0, over the temperature range of 4-22 °C is illustrated in Figure 4. No significant effect of temperature was observed at these values of pH. There is however a potential effect of pH with observation of consistently lower values of the coefficient of variation at pH 5.0. Figure 5 illustrates the same experimental conditions for the (101) face. Here the data show a significant effect of temperature with a minimum observed around 14 °C. The effect of pH on the growth rate dispersion of the (110) face is illustrated in Figure 6. There is no effect at 22 °C. While there is a possible increase in the coefficient of variation at 14 °C at the lower pH values (pH 4.0 and 4.2), it generally appears independent of pH over the rest of the pH range. There were insufficient data at 4 °C to test if there is an effect of pH with temperature. A trend with pH is far more pronounced for the (101) face as the coefficient of variation values are high at pH 4.0 and consistently decline with increasing pH (Figure 7). In fact, the highest value of the coefficient of variation measured in this study is for the (101) face at pH 4.0 and 22 °C (0.33). In general, there is little effect of NaCl concentration or temperature on the growth rate dispersion of the (110) face, although there is a marginal effect of pH. Overall, coefficient
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Figure 6. Effect of pH on the growth rate dispersion of the (110) face at 5% (w/v) NaCl.
Figure 7. Effect of pH on the growth rate dispersion of the (101) face at 5% (w/v) NaCl and 22 °C.
of variation values for this face ranged from 0.05 to approximately 0.2. The (101) face in comparison showed a strong effect of temperature and pH on the growth rate dispersion, with values of the coefficient of variation ranging from 0.05 to 0.33. The most pronounced effect in terms of the range of growth rate dispersion was that of pH. The (101) face is therefore more susceptible to growth rate dispersion with varying solution conditions than is the (110) face. Discussion In describing growth rate dispersion, two models are generally referred to, the constant crystal growth model and the random fluctuation model.5,7,8 In the constant crystal growth model, each individual crystal has an inherent constant growth rate different from the inherent constant grow rate of other crystals growing under the same solution conditions. In the random fluctuation model, surface dislocation density and hence intrinsic growth rate of individual crystals can change as the crystal grows. For the face growth rates reported in this study, a constant crystal growth was observed. This is commonly reported however for small crystals, viewed over a short growth time, growing in nonflow growth cells.8 It is possible that if crystal growth had been observed over a far longer growth time that random fluctuation may have been observed for the same crystals.23
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Table 1. Growth Rate Dispersion of Lysozyme Compared to That of Some Small Molecule Materialsa crystallization system
CVG
lysozyme fructoseb citric acid monohydratec
0.20 ( 0.05 0.23 ( 0.03 0.35 ( 0.08
a Note for citric acid monohydrate, growth rate data was re-plotted as the standard deviation of the growth rate against the mean growth rate to obtain a value of the coefficient of variation. b Ref 6. c Refs 3 and 22.
In terms of the magnitude of the growth rate dispersion, the coefficient of variation for the lysozyme face growth rates in this study ranged from 0.05 to 0.33. For comparison to other studies, growth rates observed at the condition giving the highest growth rate dispersion (22 °C, 5% (w/v) sodium chloride, 0.1 M sodium acetate pH 4.0) were converted to growth rates based on equivalent circular diameter and volume equivalent diameter. The growth rate dispersion expressed in terms of equivalent circular diameter permitted comparison with growth rate dispersion reported for the small organic molecules, fructose6 and citric acid monohydrate.3,22 These studies were also performed in batch, nonflow growth cells with measurements made on individual crystals. While this is a limited comparison of crystallization systems, it is apparent that the growth rate dispersion of lysozyme is of the same order of magnitude as that observed for these materials (Table 1). Conversion to volume equivalent size24 permitted comparison at the same experimental conditions (22 °C, 5% (w/v) sodium chloride, 0.1 M sodium acetate pH 4.0) to the growth rate dispersion reported for lysozyme measured in a bulk, batch, stirred crystallizer.13 For the nonflow growth cell, the coefficient of variation was 0.22 ( 0.05. For the stirred crystallizer, it was 0.32 ( 0.05, approximately 1.5 times that of the nonflow cell. It is unclear how stirring may effect protein crystal growth rate dispersion. Protein crystals are fragile, and it is conceivable that in a stirred environment, the solution flow and crystal collisions with vessel walls, the impeller, or other crystals could increase defects and therefore increase growth rate dispersion. Overall for lysozyme face growth rates, the crystallization temperature and pH were observed to influence the magnitude of the growth rate dispersion. Trends in growth rate dispersion with solution conditions are not unusual. For example, in the fructose-ethanol-water system6 variation in crystal sizes was reported to decrease (indicating more uniform growth) with increasing ethanol content. Looking however at specific crystal faces, the lysozyme (110) face growth rate dispersion seems to be largely independent of growth conditions while the (101) face exhibits variation with solution conditions and greater growth rate dispersion overall. Differences in the magnitude of growth rate dispersion on different crystal faces have previously been reported for small molecule materials.25 It has been postulated that this might be due to a varying susceptibility of the growth mechanisms on particular crystal faces to the causes of growth rate dispersion. Growth rate dispersion is often linked to lattice strain or dislocation type and density, with the slower growing crystals exhibiting more strain.4,7,9,10,25,26 Lysozyme crystal growth is dominated by surface integration kinetics.27 Under this growth regime, dislocation density variation can occur and can be influenced by the crystal growth mechanism of specific faces. In lysozyme crystal growth experiments under solution flow, different characteristics of growth deceleration and
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cessation were observed for the (110) and (101) faces. This was assumed to be due to the character of the structural defects that form growth step sources, which depend on the crystallographic orientation of each facet.28 In this respect, Nadarajah et al.29 used lysozyme crystal face growth rate data from a nonflow growth cell (the same data accessed for this study) in combination with an analysis of the intermolecular crystal packing to generate a model for lysozyme crystal growth for the (110) face. Li et al.30 performed a similar analysis for the (101) face. In these models, the growth unit in the crystallization process was determined to be at least a tetramer corresponding to four molecules making up a single turn of a helix centered about the 43 axis. Crystal growth then proceeds by addition of tetramers to the (101) face along this crystallographic axis, creating a jagged steplike structured surface, while tetramers or larger growth units can add with the crystallographic axis of the tetramer parallel to the relatively smooth (110) face. With this growth model, it is therefore more likely that the (101) face is more easily poisoned and strained by misaligned lysozyme molecules or other macromolecular impurities, giving rise to macrosteps consisting of multiple growth layers. Such macrosteps have experimentally been observed. In crystal growth rate measurements with pH, Forsythe et al. report significant variation for the (101) face growth rates at pH 4.0. Upon further investigation using time lapse video, initially only the (110) face was observed to be growing, and then macrosteps were seen to form and move rapidly across the (101) face.17 Incorporation of impurities is another significant source of lattice strain.25 In a previous study, we investigated the effect of egg white proteins (conalbumin, ovalbumin, and avidin) as impurities on lysozyme crystal face growth rates.31 The experiments were conducted at 5% (w/v) NaCl, 0.1 M sodium acetate buffer pH 4.0 and 18 °C. For ovalbumin and avidin, there was no effect of impurity concentration on crystal face growth rates. For conalbumin however there was no effect on the (110) face but there was an effect on the (101) face. This impurity both slowed the average growth rate and appeared to increase the variation in growth rates. The covalently bound lysozyme dimer is another native impurity that can affect lysozyme crystal growth. In atomic force microscopy experiments,32,33 the dimer was observed to roughen the surface of the (101) face in comparison to that grown with purified solutions, while the (110) face was unaffected. Increasing concentrations of lysozyme dimer have also been observed to degrade crystal diffraction quality.32,34 In both these instances where an impurity effect has been reported, it has preferentially affected the (101) face. In each case however identifiable quantities of the impurity (>5% (w/v)) were necessary to observe the effect. The lysozyme used in the face growth rate measurements reported in this study was highly purified and no impurity proteins were identified by SDS-PAGE gel analysis.17 While it cannot be ruled out that impurities were present below detection limits,28 it seems more likely that the growth rate dispersion observed in this study was due to misaligned native lysozyme molecules to which the (101) face is more susceptible,30 the susceptibility of which varies with solution conditions. Whether caused by misaligned native molecules, impurities, or mechanical stress, lattice strain is often cited as a cause of growth rate dispersion. In research with sodium chlorate, Cunningham et al.9 reported a relationship between the growth rate of individual crystals (grown under the same solution conditions) and the strain, measured as the mosaicity
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of the crystal in X-ray diffraction experiments. Faster growing crystals had less strain (lower mosaicity), while the slower growing crystals had higher strain (higher mosaicity). The growth rate dispersion is therefore caused by an uneven distribution of strain within a population of crystals, with the least strained or more perfect crystals growing at the faster rates and the crystals with more strain showing degraded growth rates. A low value of the coefficient of variation would therefore indicate a more uniform growth rate from a population of least strained crystals. With this in mind, knowledge of the growth rate dispersion characteristics of a crystallization system can be used to guide crystallization operations. In the case of an industrial crystallizer, the growth rate dispersion must be taken into account in order to effectively predict the product crystal size distribution. In the case of crystal growth for structure determination, crystal diffraction quality is paramount. Under conditions where the growth rate dispersion is high, if direct observation of a growing population of crystals is possible, the faster growing crystals should provide the better quality diffraction data. If direct observation of the experiment is not possible, as is often the case, then many crystals should be sampled as a distribution of crystal quality is expected. Alternatively, crystallization conditions that provide for minimal growth rate dispersion should overall provide less variation in crystal quality and give the experimenter a better chance of getting good diffracting crystals. In the case of tetragonal lysozyme, as reported in this study, the (101) face exhibited higher growth rate dispersion than the (110) face. Conditions therefore that provide for minimal growth rate dispersion (5% (w/v) NaCl, 12-14 °C and higher pH values such as 0.1 M sodium acetate buffer pH 5.2) in combination with moderate to high supersaturations that promote the growth of the (110) face in preference to the (101) face are more likely therefore, with respect to growth rate dispersion, to provide better quality crystals. This report, however, has focused on describing the observed growth rate dispersion and variation of growth rate dispersion with solution conditions for the protein lysozyme. X-ray diffraction experiments in combination with growth rate dispersion measurements, currently beyond the scope of this study, are needed to confirm the effect of growth rate dispersion on protein crystal quality. Conclusions Under the solution conditions examined in this study, lysozyme crystals exhibit growth rate dispersion, the magnitude of which is similar to that reported for small molecule materials. The growth rate dispersion was found to vary with solution conditions, in which the (101) face exhibited a greater degree and variability of growth rate dispersion than the (110) face. This increased susceptibility of the (101) face to the causes of growth rate dispersion is due to the differing crystal growth mechanisms of each face.
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Acknowledgment. This work was funded by NASA Research Grant NCC8-66. We thank Prof. E. T. White for useful discussions.
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