CRYSTAL GROWTH & DESIGN
Quantifying Main Trends in Lysozyme Nucleation: The Effect of Precipitant Concentration, Supersaturation, and Impurities
2001 VOL. 1, NO. 4 333-337
Michael W. Burke,† Riccardo Leardi,‡ Russell A. Judge,*,† and Marc L. Pusey† Biophysics SD48, NASA/MSFC, Huntsville, Alabama 35812, and Dipartimento di Chimica e Tecnologie Farmaceutiche e Alimentari, Via Brigata Salerno (ponte), I 16147 Genova, Italy Received February 23, 2001;
Revised Manuscript Received May 18, 2001
ABSTRACT: Full factorial experimental design incorporating multilinear regression analysis of the experimental data allows quick identification of main trends and effects using a limited number of experiments. In this study, we illustrate the usefulness of these techniques in macromolecule crystallization studies, by employing them to identify the effect of precipitant concentration, supersaturation, and the presence of an impurity, the physiological lysozyme dimer, on the nucleation and dimensions of chicken egg white lysozyme crystals. Decreasing precipitant concentration, increasing supersaturation, and increasing impurity were found to increase crystal numbers. The crystal axial ratio decreased with increasing precipitant concentration, independent of impurity. Introduction Factorial experimental design techniques are extremely useful methods for determining important parameters and the magnitude of their effects while using a minimum number of experiments. They provide the largest gain for the least effort. Biological crystal growth is a process involving many parameters, and factorial experimental design would seem to be naturally suited to this field. Despite the power of these techniques, they have been used in only a limited number of biological crystal growth studies.1,2 In a recent study,3 we examined the effect of solution pH, temperature, and initial supersaturation on the final number of lysozyme crystals formed in batch crystallization at 5% (w/v) NaCl. Solution pH was found to have the greatest effect on crystal numbers, with lower crystal numbers being formed at higher pH. Increasing supersaturation also increased crystal numbers, with temperature exhibiting only a small effect. From this study, it became apparent that the best pH (within the experimental parameter ranges examined) for growing a small number of large tetragonal lysozyme crystals was at pH 5.2. On the basis of these findings, in this study we have chosen the localized region of pH 5.2 and 18 °C to investigate the effect of precipitant concentration, supersaturation, and the addition of impurity on lysozyme crystallization. In this case, however, we have used factorial experimental design to elucidate the main trends and interactions between variables, illustrating the application of these techniques to macromolecular crystal growth studies. Experimental Method A replicated, two-level, three-factor, full factorial design experiment was used. The factors examined were precipitant concentration, initial supersaturation, and impurity concentra* To whom correspondence should be addressed. Phone: 256-5442295. Fax: 256-544-6660. E-mail:
[email protected]. † NASA/MSFC. ‡ Dipartimento di Chimica e Tecnologie Farmaceutiche e Alimentari.
Table 1. Replicated, Two-Level, Three-Factor, Full Factorial Experimental Design with Center Pointa precipsuperitant saturation impurity expt % (w/v) ln(c/s) % (w/w) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
3 3 7 7 3 3 7 7 3 3 7 7 3 3 7 7 5 5
2.4 2.4 2.4 2.4 3.0 3.0 3.0 3.0 2.4 2.4 2.4 2.4 3.0 3.0 3.0 3.0 2.7 2.7
0 0 0 0 0 0 0 0 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.45 0.45
X1
X2
X3
-1 -1 +1 +1 -1 -1 +1 +1 -1 -1 +1 +1 -1 -1 +1 +1 0 0
-1 -1 -1 -1 +1 +1 +1 +1 -1 -1 -1 -1 +1 +1 +1 +1 0 0
-1 -1 -1 -1 -1 -1 -1 -1 +1 +1 +1 +1 +1 +1 +1 +1 0 0
log crystal (crystal no. no.) 14.3 14.7 13.9 5.6 189.8 117.0 46.0 49.5 46.3 51.5 22.7 43.1 144.0 146.0 88.7 72.8 55.9 56.9
1.16 1.17 1.14 0.75 2.28 2.07 1.66 1.69 1.67 1.71 1.36 1.63 2.16 2.16 1.95 1.86 1.75 1.76
a Here X , X , and X 1 2 3 represent, respectively, precipitant concentration, initial supersaturation, and impurity.
tion. In accordance with a two-level design, these factors are set at a low and a high level, coded as -1 and +1, respectively. For each factor, the levels chosen were 3 and 7% (w/v) for the precipitant concentration, 2.4 and 3.0 for the supersaturation (with supersaturation expressed as ln(c/s), where c is the initial bulk protein concentration and s is the solubility), and 0 and 0.9% lysozyme dimer (w/w) for the impurity concentration. The 0.9% dimer impurity level is typical for commercial lysozyme preparations.4 The experimental matrix is given in Table 1. In addition to the factorial design, we also added a center point. Center points are used to test the regression model for curvature and therefore validate the linear model with interactions provided by the factorial design.5 Multilinear regression was performed using Matlab (The Mathworks, Natick, MA). Lysozyme was extracted from fresh chicken eggs and purified using a two-step chromatography technique as previously described.6,3 The physiological lysozyme dimer was also recovered as a byproduct of this purification and further purified by cation exchange chromatography as given in Snell et al.7 Lysozyme crystallization was performed using the method of Judge et al.3 Batch crystallization solutions were
10.1021/cg0155088 CCC: $20.00 © 2001 American Chemical Society Published on Web 06/05/2001
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prepared by mixing equal volumes of two times the final concentration of protein and precipitant solutions, both in one times the buffer concentration, and dispensed in 50 µL volumes into 96-well plates (Greiner America Inc., Orlando, FL). Ten wells were used for each experiment, and the results are given as an average over the 10 wells. All experiments were conducted using 0.1 M sodium acetate buffer at pH 5.2 and incubated at 18 °C for one week. The solubility of lysozyme at these conditions, for NaCl concentrations of 3, 5, and 7% (w/ v), are 4.13, 2.13, and 1.58 mg/mL, respectively.8 A low magnification microscope with an attached CCD video camera was used in combination with a computer containing a frame grabber board to record images of each well. Image-Pro Plus 4.0 software (Media Cybernetics L. P., Silver Spring, MD) was used to display the images, manually tag and count crystals, and measure crystal size after calibration with a standard size grid. Where possible, five crystals per well were randomly selected and the distance between parallel {110} faces and between the apexes of the {101} faces were measured using crystals suitably aligned to the optical axis. As only five crystals per well were sized (giving 50 per initial concentration per plate), these measurements constitute an estimate of the crystal size and dimensions. With this method, we typically find an average variation from the mean size of up to ( 8%,3 indicating that not all the crystals were likely to have formed in the well at the same time and may have experienced slightly different supersaturation growth environments. As the variation in crystal size obtained in using this method is small compared to the change in crystal sizes observed when using different precipitant and impurity concentrations, the technique is therefore considered sufficiently accurate for the quantification of these effects.
Burke et al. Table 2. Values of Multilinear Regression Coefficients with Their Corresponding Significance Levels for the Factorial Design to Investigate the Effect of Precipitant, Supersaturation, and Impurity on Final Crystal Numbersa coefficient
coefficient value
significance
b0 b1 b2 b3 b12 b13 b23 b123
1.65 -0.15 0.33 0.16 -0.04 0.03 -0.11 0.03
*** ** *** ** *
a Blank, not statistically significant, * ) p < 0.05, ** ) p < 0.01, *** ) p < 0.001.
Results Crystal Number. Results for the factorial design to investigate the effect of precipitant concentration, supersaturation, and impurity on crystal number are listed in Table 1. For this analysis, a multilinear regression will provide an equation of form,
Figure 1. Contour plot for the effect of precipitant concentration and supersaturation on crystal numbers. Values on the contours represent the log10 (crystal number). The impurity concentration for this plot is set at its midpoint.
Y ) b0 + b1X1 + b2X2 + b3X3 + b12X1X2 + b13X1X3 + b23X2X3 + b123X1X2X3 (1) where b0 is a constant, b1, b2, and b3 are the coefficients for the main effects of the variables X1, X2, and X3, while b12, b13, and b23 are the coefficients for the interactions between pairs of variables and b123 is the coefficient for the interaction of all the variables. The response (Y) is the logarithm (base 10) of the number of crystals. The choice of this transformation is due to the wide range of the number of crystals and to the fact that the experimental error is roughly proportional to the number of crystals. By taking into account the original value, the assumption of homoscedasticity (equal statistical variances) would have been severely violated. The values of the coefficients and their significance are given in Table 2. Examination of Table 2 reveals that b0, the three coefficients of the main effects, and the coefficient of the interaction of supersaturation and impurity are significant. From the nine pairs of experiments, the pure experimental error can be estimated. The pooled standard deviation is 0.13 (9 degrees of freedom). Since t0.05,9 ) 2.26 and n ) 2, the confidence interval of the result of the experiments at the center point is 1.76 ( (2.26 × 0.13/(2)1/2), giving 1.76 ( 0.20. Since the predicted value at the center point is 1.65, then it can be concluded that the difference between the experimental and the pre-
Figure 2. Contour plot for the effect of precipitant concentration and impurity concentration on crystal numbers. Values on the contours represent the log10 (crystal number). The supersaturation for this plot is set at its midpoint.
dicted value is not significant. This means that the model can be accepted. The effects as expressed by Table 2 are illustrated in Figures 1-3. From these figures, it can be seen that increasing supersaturation and impurity concentration increase crystal numbers, while increasing precipitant concentration decreases crystal numbers. Figure 3 also il-
Quantifying Main Trends in Lysozyme Nucleation
Crystal Growth & Design, Vol. 1, No. 4, 2001 335 Table 3. Subset Factorial Design for Analysis of Effects of Precipitant and Impurity Concentration on Crystal Size and Axial Ratioa expt
precipitant impurity % (w/v) % (w/w)
1 2 3 4 9 10 11 12
3 3 7 7 3 3 7 7
0 0 0 0 0.9 0.9 0.9 0.9
X1
X2
-1 -1 +1 +1 -1 -1 +1 +1
-1 -1 -1 -1 +1 +1 +1 +1
crystal size axial ratio (W) µm (L/W) 480 475 611 791 341 325 530 447
2.4 2.2 0.8 0.8 2.1 2.0 0.8 0.7
a Crystal size measurements represent the average of approximately 50 crystals over 10 wells. In this case, X1 and X2 represent precipitant concentration and impurity concentration, respectively.
Figure 3. Contour plot for the effect of supersaturation and impurity concentration on crystal numbers. Values on the contours represent the log10 (crystal number). The precipitant concentration for this plot is set at its midpoint.
Table 4. Values of Multilinear Regression Coefficients with Their Corresponding Significance Levels for the Factorial Design to Investigate the Effect of Precipitant and Impurity Concentration on Final Crystal Size (W) and Axial Ratio (L/W)a W coefficient
coefficient value
b0 b1 b2 b12
500 95 -89 -17
L/W
significance *** * *
coefficient value 1.48 -0.70 -0.08 0.05
significance *** ***
a Blank, not statistically significant, * ) p < 0.05, ** ) p < 0.01, *** ) p < 0.001.
Figure 4. Comparison of crystal numbers for pure solutions predicted using the full factorial design model, with experimental data obtained in a prior study at 5% (w/v) NaCl. The error bars represent 95% confidence limits. All other solution conditions, including pH, incubation time, and temperature, are the same for both studies.
lustrates the interaction between supersaturation and impurity. The effect of supersaturation is greater at lower levels of impurity, while the effect of impurity is greater at lower supersaturation. Comparison of the model generated in this study with experimental data collected over the same supersaturation range using pure solutions with 5% (w/v) NaCl, at the same solution pH and incubation temperature,3 is illustrated in Figure 4. There is generally good agreement between the two studies. Crystal Size and Axial Ratio. Crystallization conditions of 7% (w/v) NaCl and ln(c/s) ) 3.0, both with and without the addition of impurity, produced crystals with very rough surfaces. With these crystals, particular faces could not consistently be identified, and so size data was not collected. In the case of experiment 13 (3% (w/v) NaCl, ln(c/s) ) 3.0 and 0.9% (w/w) impurity), many wells contained crystals that although easily identified tended to cluster together making size measurement difficult. With this in mind, and as the desired region for examination is the condition that provides lower crystal numbers, the analysis on crystal size was
conducted using a subset of the original factorial design. In this case, data at ln(c/s) ) 2.4 only were considered, and the factors of precipitant and impurity concentration were investigated in a two-level, two-factor, full factorial design. The data set for analysis then consisted of experiment numbers 1, 2, 3, 4, 9, 10, 11, and 12. Table 3 shows this subset with the corresponding crystal size information, where (W) is the average distance between parallel {110} faces and (L) refers to the average distance between the apexes of the {101} faces.3 This analysis will therefore provide equations of form,
Y ) b0 + b1X1 + b2X2 + b12X1X2
(2)
where b0 is a constant, b1 and b2 are the coefficients for the main effects of the variables X1 and X2, and b12 is the coefficient for the interaction of the two variables. The coefficients with their significance are listed in Table 4. As adequate material was not available to conduct center point experiments for this subset factorial design, the predictive ability of this model cannot with confidence be confirmed. The data however is instructive in indicating overall trends. Pursuing the analysis in this light, it can be seen that for crystal size the two main effects are statistically significant. Increasing precipitant concentration increases crystal size, while increasing impurity concentration reduces crystal size. For the crystal axial ratio, only the effect of precipitant is accepted as being significant. Increasing precipitant concentration reduces the axial ratio. Discussion As supersaturation is the driving force behind crystallization, it is not surprising to find that crystal
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numbers increase with increasing supersaturation. Similar trends have been reported by other investigations.9,3 Interestingly, for the same value of initial supersaturation, increasing precipitant concentration results in a decrease in crystal numbers. This trend appears to be consistent within both the 3-7% (w/v) NaCl range (presented here) and in the 2.5-4% (w/v) NaCl range,10 despite differences in the crystallization temperature and solution pH used in these two studies. In lysozyme crystal growth rate studies, Forsythe and Pusey11 also report that for the same value of supersaturation, both the {110} and {101} crystal face growth rates decrease with increasing precipitant concentration. Increasing precipitant concentration is therefore interfering or restricting the crystal growth process. Changes in ionic strength may affect the pK values of localized charged groups involved in crystal contact regions. For example, Kuramitsu et al.12 report that increasing ionic strength increases the pK values of the catalytic groups. If these trends are extrapolated to groups in crystal contact regions, changes in charge of these residues may modify the interactions between molecules making it more difficult to form successful contacts. Iyer et al.13 also report that ionic strength can affect intermolecular contact formation and that this may be due to ion binding at crystal contacts. For tetragonal lysozyme crystallization solution conditions, Cl- ions apparently occupy many if not all available positive charged sites on the lysozyme molecule surface.11 As only one Cl- ion binding site is observed in a crystal contact region in the crystal,14,15 the other ions must be removed to form protein-protein molecular interactions. Removing these ions and increasing the number of successful protein-protein interactions may become easier when less Cl- ions are present in solution. Our impurity of choice was the naturally occurring lysozyme dimer, which has the same amino acid composition as the monomer and a reduced activity.16 The reduced activity is postulated to be due to the dimerization causing a steric hindrance between the lysozyme active sites and the bacterial cell wall. While disruptive to crystal X-ray quality and diffraction resolution,7 in the conditions investigated in this study the role of the dimer in nucleation is to increase crystal numbers. This increase in numbers is in contrast to the effect of a manufactured lysozyme dimer, produced by random oxidation of monomeric lysozyme solution, where it was found that crystal numbers decreased with increasing impurity concentration.17 It is interesting to note that the pH was different in these two studies being pH 5.2 and 4.5, respectively. This may indicate that the effect of the dimer is strongly pH dependent. It may also indicate an effect of the conformation of the dimer, as the native dimer formed inside the egg may not be the same as a mixed population of dimers formed by random oxidation. The observed contrast in effect with either pH or conformation makes it impractical to compare these results with other systems. Mullin18 indicates that the effect of impurities is unpredictable with increased nucleation in some cases while in others it is reduced and no general rule can be applied. The impurity also exhibits an interaction effect with supersaturation. For crystal number, this was the only significant interaction effect observed. The presence of
Burke et al.
impurity has a greater effect on increasing crystal numbers at low supersaturation. As the aim of crystal growth for structural studies is to obtain a small number of large crystals, a low supersaturation is usually desirable. This however is the region in which this protein is most susceptible to this particular impurity, and purification of solutions prior to crystallization trials will assist in reproducibility of results. As increasing precipitant concentration significantly reduces the crystal axial ratio, this would indicate a preferential growth of the {110} face. As the impurity does not have a significant effect on the axial ratio, if it acts on crystal growth rates it would seem to act to the same extent on each crystal face. In this instance, the precipitant concentration has a greater effect on the crystal growth processes of the respective crystal faces than does the presence of the impurity. As this work followed on from our previous investigation,3 the combined results indicate that the best conditions, within the range investigated, to grow a small number of large tetragonal lysozyme crystals of suitable habit in batch crystallization, is low supersaturation (ln(c/s) ∼ 2.4), pH 5.2, 18 °C, and NaCl concentration 5-7% (w/v), using high purity protein solution. Conclusions Full factorial experimental design techniques were successfully used to quickly elucidate the effects of supersaturation, precipitant, and impurity concentration on lysozyme crystallization. They also quickly provided an indication of parameter values where optimal crystallization conditions in terms of reduced crystal numbers and large crystals of suitable habit may be found. As macromolecule crystal growth usually involves the use of multiple solution parameters, the use of experimental design techniques should be considered as part of an experimental strategy. Acknowledgment. This work was funded by NASA Grant NCC8-66. M.W.B. and R.A.J. are contracted to NASA through the University of Alabama in Huntsville. Fresh chicken eggs were supplied by Madison County Poultry Farm Inc., Madison, AL 35758. Dr. Charlie Carter, Jr., is thanked for useful discussions. References (1) Carter, C. W., Jr.; Doublie, S.; Coleman, D. E. J. Mol. Biol. 1994, 238, 346-365. (2) Carter, C. W., Jr.; Yin, Y. Acta Crystallogr. 1994, D50, 572590. (3) Judge, R. A.; Jacobs, R. S.; Frazier, T.; Snell, E. H.; Pusey, M. L. Biophysical J. 1999, 77, 1585-1593. (4) Thomas, B. R.; Vekilov, P. G.; Rosenberger, F. Acta Crystallogr. 1996, D52, 776-784. (5) Box, G. E. P.; Hunter, W. G.; Hunter, J. S. Statistics for Experimenters; Wiley/Interscience: New York, 1978; Chapter 15, pp 511-537. (6) Judge, R. A.; Forsythe, E. L.; Pusey, M. L. Biotechnol. Bioeng. 1998, 59, 776-785. (7) Snell, E. H.; Judge, R. A.; Crawford, L.; Forsythe, E. L.; Pusey, M. L.; Sportiello, M.; Todd, P.; Bellamy, H.; Lovelace, J.; Cassanto, J. M.; Borgstahl, G. E. O. Cryst. Growth Des. 2001, 1, 151-158. (8) Cacioppo, E.; Pusey, M. L. J. Crystal Growth. 1991, 114, 286-292. (9) Ries-Kautt, M.; Ducruix, A. Phase diagrams. In Crystallization of Nucleic Acids and Proteins: A Practical Approach; Ducruix, A., Giege. R., Eds.; Oxford University Press: New York, 1992; pp 195-228.
Quantifying Main Trends in Lysozyme Nucleation (10) Galkin, O.; Vekilov, P. G. J. Am. Chem. Soc. 2000, 122, 156163. (11) Forsythe, E.; Pusey, M. L. J. Cryst. Growth. 1994, 139, 8994. (12) Kuramitsu, S.; Ikeda, K.; Hamaguchi, K. J. Biochem. 1977, 82, 585-597. (13) Iyer, G. H.; Dasgupta, S.; Bell, J. A. J. Cryst. Growth. 2000, 217, 429-440. (14) Blake, C. C. F.; Mair, G. A.; North, A. C. T.; Phillips, D. C.; Sarma, V. R. Proc. R. Soc. B 1967, 167, 365-377.
Crystal Growth & Design, Vol. 1, No. 4, 2001 337 (15) Lim, K.; Nadarajah, A.; Forsythe, E. L.; Pusey, M. L. Acta Crystallogr. 1998, D54, 899-904. (16) Back, J. F. Biochim. Biophys. Acta 1984, 799, 319-321. (17) Thomas, B. R.; Vekilov, P. G.; Rosenberger, F. Acta Crystallogr. 1998, D54, 226-236. (18) Mullin, J. W. Crystallization, 3rd ed.; Butterworth-Heinemann: Oxford, UK, 1993; p 182.
CG0155088
