CRYSTAL GROWTH & DESIGN
The Nucleation of Lysozyme from a Fluctuation Point of View
2005 VOL. 5, NO. 3 1125-1127
Jan Drenth* Laboratory for Biophysical Chemistry, University of Groningen, Nyenborgh 4, 9747 AG Groningen, Netherlands Received November 9, 2004;
Revised Manuscript Received February 23, 2005
ABSTRACT: The enzyme lysozyme is a useful model for the study of protein nucleation. The nucleation of lysozyme can be very well discussed in the framework of classical nucleation theory. However, the crystallization process develops differently below and above the critical temperature, Tc, of liquid-liquid phase separation. Above Tc, nucleation follows the line of the classical theory, but below Tc, nucleation is preceded by the growth of protein concentration fluctuations. This results in a relationship between the induction time vs. temperature curve and the left branch of the liquid-liquid phase separation curve. In fact, these two curves are equal. The transition in the nature of the nucleation process near Tc is in accordance with a principle proposed several years ago by Prigogine and colleagues. Introduction
Materials and Methods
Lysozyme is the prototype compound for studying protein nucleation and crystallization. It has been extensively discussed in the literature.1-6 The nucleation step of the crystallization process can be perfectly well explained with classical nucleation theory.5 This does not mean that the assumption in this theory of stable and unstable solid aggregates is always valid. It is also possible that the unstable aggregates are fluctuations in the protein concentration. The presence of density fluctuations in colloid and protein solutions has been experimentally verified, for instance, by smallangle light scattering showing the presence of density fluctuations during the crystallization of colloids7 or by studying density fluctuations in supersaturated lysozyme solutions by dynamic and static light scattering.8 In a recent review, dense liquid precursors and fluctuations in protein nucleation and crystallization were discussed.9 The fluctuations are especially strong near the liquid-liquid phase separation curve. In this article, we consider the growth of the density fluctuations after supersaturation has been established. The growth starts from the very moderate Brownian motion in the undersaturated solution and continues until a large enough protein concentration is reached for easy nucleus formation to happen. With this process of fluctuation growth, we can nicely explain the shape of the induction time τ vs. temperature curve10 (Figure 1). Moreover, it finds the relation between this curve and the left branch of the phase separation curve as determined by Muschol and Rosenberger11 (Figure 2). They are, in fact, equal (Figure 1). Furthermore, as a function of temperature, a transition exists from nucleation with density fluctuations as an intermediate state to nucleation with the unstable solid aggregates of the classical nucleation theory. This is a perfect example of a concept developed several years ago by Prigogine and colleagues.12-15
We have measured the induction time for lysozyme crystallization by means of NMR (Figure 1). The experimental procedures and the data obtained have been described earlier.5 In short, a three times crystallized, dialyzed, and lyophilized hen egg white lysozyme preparation of Sigma (lot 20K0956) was used without further purification. The protein was dissolved in 0.1 M sodium acetate buffer, pH 4.5, to an effective concentration of 33.8 mg/mL. To achieve supersaturation, an equal volume of 10% NaCl in the same buffer was added. The final solution contained 16.9 mg/mL lysozyme at pH 4.5. The induction time results are correlated with the liquid-liquid phase separation data published by Muschol and Rosenberger,11 also for 5% NaCl and pH 4.5.
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[email protected]. Tel: 31 50 3634382. Fax: 31 50 3634800.
Results It has been experimentally shown that in a supersaturated solution of a colloid and of proteins the solute concentration is not constant but fluctuates.7,8 Locally, regions of high and low concentration appear and disappear. Ten Wolde and Frenkel16 in their computer simulation of protein crystallization find that highdensity fluctuations near the critical point of liquidliquid phase separation affect the route to crystallization. The fluctuations are very moderate in the undersaturated solution but start to grow after supersaturation has been established. It is interesting to follow these fluctuations in the temperature vs protein concentration phase diagram. The fluctuations express themselves as oscillations along a horizontal line in that diagram (Figure 2). While growing below the critical temperature Tc, they will meet the left branch of the phase separation curve. At this point, they become in equilibrium with the high concentration solution of the right branch. A tiny amount of the high concentration solution will be formed as a microdroplet. This microdroplet appears and disappears with the fluctuation. Once it assumes a crystalline order, the process stabilizes and a crystal starts to grow. The transformation to the crystalline
10.1021/cg049616g CCC: $30.25 © 2005 American Chemical Society Published on Web 03/23/2005
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Crystal Growth & Design, Vol. 5, No. 3, 2005
Drenth
ment with the experimentally determined τ vs temperature curve (Figure 1). Moreover, it suggests a relationship between this curve and the left branch of the liquid-liquid phase separation curve. Indeed it appears that the induction times, τ, are proportional to the protein concentration difference between A and B in Figure 2. Therefore, the induction time curve is equal to the left branch of the phase separation curve (Figure 1). Above Tc the induction time is extremely long. This can be explained by assuming classical nucleation with the formation of solid aggregates and without intermediate concentration fluctuations. Therefore, a transition from fluctuations to unstable solid aggregates happens near Tc. Discussion
Figure 1. The induction time τ for the crystallization of lysozyme is plotted as a function of temperature. The squares are the experimental points. To limit the size of the figure, the data point at τ ) 74 h, temperature 25 °C, has been left out. The black dots indicate the experimental points measured by Muschol and Rosenberger for the determination of the left branch of their phase separation curve.11 The concentration of the black dots in mg/mL is taken as the A f B distance in Figure 2. They are plotted as a function of temperature. Their scale is on the right Y-axis. The induction time is scaled for optimal superposition of the two data sets. The strange fact that we compare induction time with a concentration difference is explained by the proportionality between the induction times and the distances such as A to B in Figure 2. The protein concentration is constant at 16.9 mg/mL, pH 4.5, and 5% NaCl as the precipitating agent.
Figure 2. The phase diagram of lysozyme for 5% NaCl as the precipitating agent and pH 4.5. Tc is the critical temperature. The thin vertical line indicates the average protein concentration. It is the starting point for the protein concentration peaks that move to the right, like from A to B. This figure was adapted from ref 11.
state is apparently very fast in this “blinking” microdroplet. The protein molecules are nearly as close together as in the crystal and reshuffle easily to the lower-energy crystalline state. Crystals start to grow within minutes.11 Below Tc, nucleation is a two-step process, the first step being the growth of fluctuations. When their amplitude has reached a sufficiently high level, in a second step rapid reordering of the protein molecules leads to a nucleus. As a consequence, below Tc, the induction times, τ, are relatively short. Above Tc, the situation is completely different. The advantage of the phase separation is missing, and nucleation is a much slower process. This picture is in complete agree-
In our work, we have slightly modified classical nucleation theory: below the critical temperature, Tc, concentration fluctuations replace unstable solid aggregates. After supersaturation has been established, the fluctuations grow, powered by the energy of attraction between the protein molecules. In fact, the fluctuations are oscillations between a high-entropy/lowenthalpy state (low protein concentration) and a lowentropy/high-enthalpy state (high protein concentration). The latter includes the surface energy of the concentration peaks. The energy of attraction between the protein molecules depends on the temperature. When the temperature is increased, the energy of attraction decreases favoring the high-entropy/low-enthalpy state. Concurrently, the induction time, τ, increases. Our explanation for this observation is that below Tc the induction time is proportional to the concentration difference between the starting concentration and the concentration at the phase-separation curve (A to B in Figure 2). This is confirmed by the superposition of the induction time curve onto the left branch of the phase separation curve (Figure 1). At temperatures above Tc, the situation is different and fluctuations do not play a significant role. Concentration fluctuations can be regarded as transient phase separations on a microscale. When the temperature rises to a value above Tc, there is no macro phase separation anymore, and we must assume that the transient micro phase separations are also not of much significance. The conclusion is that above Tc nucleation proceeds as in the classical nucleation theory by the formation of solid aggregates without concentration fluctuations as intermediates. The appearance of nuclei in this region as a function of supersaturation has been measured by Galkin and Vekilov17 for lysozyme at pH 4.5, 12.6 °C, and 2.5%, 3%, and 4% NaCl. It seems that protein nucleation is an excellent example of a concept developed by Prigogine and colleagues.12-15 They pointed out that nonequilibrium states close to equilibrium or further away from it behave differently. If close to equilibrium, the nonequilibrium state moves smoothly to equilibrium. This is not true if the nonequilibrium state is far from equilibrium. Then an intermediate state is formed, which may have some sort of ordering, usually as fluctuations. Under certain conditions, these fluctuations enhance as a function of time. In protein crystallization, supersaturation is rather high compared with small compounds.
Nucleation of Lysozyme
Therefore, the protein to be crystallized from a supersaturated solution is fairly far from equilibrium, and once supersaturation has been established, a state of fluctuations in the protein concentration forms. This occurs at temperatures below the critical temperature, Tc. With an increase in temperature to values above Tc while keeping the protein concentration constant, the supersaturation decreases and concentration fluctuations do not play a significant role anymore. Instead, a gradual increase in size of solid aggregates occurs as found by Galkin and Vekilov17. We have limited ourselves to lysozyme with NaCl as the precipitating agent. This should be extended to more proteins and PEG as the precipitant. But it can be expected that the results apply qualitatively also to other proteins for which the solubility increases with temperature. Acknowledgment. I thank my colleague Cor Haas who provided the foundation for this work. I am indebted to Dr. Stojanoff, Prof. Garcia Ruiz, and Prof. Nicolis for discussions and suggestions. I thank Prof. Bauke Dijkstra for generous hospitality in his laboratory. References (1) Ataka, M.; Asai, M. Biophys. J. 1990, 58, 807.
Crystal Growth & Design, Vol. 5, No. 3, 2005 1127 (2) Niimura, N.; Minezaki, Y.; Ataka, M.; Katsura, T. J. Cryst. Growth 1995, 154, 136. (3) Peters, R.; Georgalis, Y.; Saenger, W. Acta Crystallogr. 1998, D54, 873. (4) Judge, R. A.; Jacobs, R. S.; Frazier, T.; Snell, E. H.; Pusey, M. L. Biophys. J. 1999, 77, 1585-1593. (5) Drenth, J.; Dijkstra, K.; Haas, C.; Leppert, J.; Ohlenschla¨ger, O. J. Phys. Chem. B 2003, 107, 4203. (6) Garcia-Ruiz, J. M. J. Struct. Biol. 2003, 142, 22. (7) Scha¨tzel, K.; Ackerson, B. J. Phys. Rev. Lett. 1992, 68, 337. (8) Manno, M.; Xiao, C.; Bulone, D.; Martorana, V.; San Biagio, P. L. Phys. Rev. E 2003, 68, 011904,1. (9) Vekilov, P. G. Cryst. Growth Des. 2004, 4, 671. (10) The induction time is the period between the moment supersaturation has been established and the appearance of the first crystals. (11) Muschol, M.; Rosenberger, F. J. Chem. Phys. 1997, 107, 1953. (12) Nicolis, G.; Prigogine, I. Self-Organization in Nonequilibrium systems; John Wiley & Sons: New York 1977. (13) Glansdorff, G.; Prigogine, I. Thermodynamic Theory of Structure, Stability and Fluctuations; Wiley - Interscience: London 1971. (14) Nicolis, G.; Nicolis, C. Physica A 2003, 323, 139. (15) Nicolis, G.,; Basios, V.; Nicolis, C. J. Chem. Phys. 2004, 120, 7708. (16) Ten Wolde, P. R.; Frenkel, D. Science 1997, 277, 1975. (17) Galkin, O.; Vekilov, P. G. J. Am. Chem. Soc. 2000, 122, 156.
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