Biomacromolecules 2004, 5, 2289-2296
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Comparison between Denaturant- and Temperature-Induced Unfolding Pathways of Protein: A Lattice Monte Carlo Simulation Ho Sup Choi, June Huh, and Won Ho Jo* Hyperstructured Organic Materials Research Center, School of Material Science and Engineering, Seoul National University, Seoul 151-744, Korea Received June 8, 2004; Revised Manuscript Received August 26, 2004
Denaturant-induced unfolding of protein is simulated by using a Monte Carlo simulation with a lattice model for protein and denaturant. Following the binding theory for denaturant-induced unfolding, the denaturant molecules are modeled to interact with protein by nearest-neighbor interactions. By analyzing the conformational states on the unfolding pathway of protein, the denaturant-induced unfolding pathway is compared with the temperature-induced unfolding pathway under the same condition; that is, the free energies of unfolding under two different pathways are equal. The two unfoldings show markedly different conformational distributions in unfolded states. From the calculation of the free energy of protein as a function of the number fraction (Q0) of native contacts relative to the total number of contacts, it is found that the free energy of the largely unfolded state corresponding to low Q0 (0.1 < Q0 < 0.5) under temperatureinduced unfolding is lower than that under denaturant-induced unfolding, whereas the free energy of the unfolded state close to the native state (Q0 > 0.5) is lower in denaturant-induced unfolding than in temperatureinduced unfolding. A comparison of two unfolding pathways reveals that the denaturant-induced unfolding shows a wider conformational distribution than the temperature-induced unfolding, while the temperatureinduced unfolding shows a more compact unfolded state than the denaturant-induced unfolding especially in the low Q0 region (0.1 < Q0 < 0.5). Introduction Denaturant refers to a reagent that decreases the stability of protein and leads to a structural change from its specific, compact, and three-dimensional structure to an unfolded state. Examples of denaturant are urea and guanidinium chloride, both of which have very similar chemical structures but differ in their efficiency to denature proteins. In contrast, sugars, glycerol, and poly(ethylene glycol) stabilize proteins.1-3 It is known that the protein stabilizers are excluded from the protein surface, and, therefore, the protein is preferentially hydrated in the presence of stabilizing solutes, whereas denaturant increases the solubility of protein and interacts preferentially with the protein surface.4 Earlier studies have suggested that urea and guanidinium chloride interact with both nonpolar and polar surfaces of protein more favorably than does water.4 A recent molecular dynamics simulation on the unfolding of barnase in aqueous urea has shown that most of the urea molecules in the first solvation shell of the protein form at least one hydrogen bond with the protein.5 It has also been reported experimentally that urea denatures proteins by reducing hydrophobic interactions and by directly binding to the amide units via hydrogen bonds.6 The conformational transition in the presence of denaturant is highly cooperative and reversible. Interestingly, it has been * To whom correspondence should be addressed. E-mail: whjpoly@ plaza.snu.ac.kr. Fax: +82-2-885-1748. Tel: +82-2-880-7192.
observed experimentally for a large number of different proteins that the free energy of unfolding ∆FD-N is a linear function of denaturant concentration in a relatively narrow range of the denaturant concentration. Accordingly, the dependence of the free energy of unfolding on the denaturant concentration C can be generally described as H 2O ∆FD-N(C) ) ∆FD-N - mC
(1)
H2O where ∆FD-N is the free energy of unfolding at zero denaturant concentration and m is the constant slope of a plot of ∆FD-N(C) versus C. Using the linear relationship of H 2O can be obtained by extrapolating FD-N(C) to eq 1, ∆FD-N zero denaturant concentration. Some theoretical methods have been developed to explain the interaction of denaturant with protein.7-11 Among them, the binding model of denaturant has widely been used because of its simplicity. The binding model assumes that the denaturant interacts with solvent-exposed groups on a protein molecule via direct binding and, hence, denatures the protein by reducing hydrophobic interactions in the protein. In the binding model, if all the binding sites of protein are identical, the free energy of unfolding in the presence of denaturant is defined as H2O - ∆nRT ln(1 + KbC) ∆FD-N(C) ) ∆FD-N
(2)
where ∆n is the difference in the number of binding sites between denatured (D) and native (N) states and Kb is an
10.1021/bm049663p CCC: $27.50 © 2004 American Chemical Society Published on Web 10/05/2004
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equilibrium binding constant. If KbC , 1, eq 2 can be approximated as H2O ∆FD-N(C) ≈ ∆FD-N - ∆nRTKbC
(3)
where ∆nRTKb corresponds to the m value of eq 1. Although the theoretical models provide fairly reasonable explanations particularly for the dependence of the free energy of unfolding on the concentration of denaturant, the pathway of denaturant-induced unfolding is not clearly understood. Monitoring the unfolding pathway of proteins is very difficult, if not impossible, because the conformational spectrum of a protein is formidably wide. Therefore, it is very important to develop a simplified model that nevertheless implies the essence of folding/unfolding phenomena, rendering an investigation of the unfolding pathway computationally tractable. Another important question on the unfolding of proteins is whether different unfolding methods yield different pathways of unfolding. For instance, it may be very informative to examine the similarity or difference between the pathway of denaturant-induced unfolding and the pathway of temperature-induced unfolding. The present work is concerned with the comparison between two different protein-unfolding methods: denaturant-induced unfolding and temperature-induced unfolding. For this purpose, a lattice Monte Carlo method is employed to simplify the conformational states of a protein, which enables us to systematically analyze the conformational state on the unfolding pathway. This paper is organized as follows. We begin in the next section with describing the lattice model for a 27-bead protein molecule and denaturant molecules and the calculation method of thermodynamic quantities used in this study. In Results and Discussion, the free energy profiles for both denaturant-induced unfolding and temperatureinduced unfolding are presented and compared to each other. Finally, the conclusions are summarized in the last section.
Model and Simulation Methods Three-Dimensional Lattice Model for Protein and Denaturant. The lattice-based model has been widely used to study the thermodynamic and kinetic properties of protein folding because of its simplicity. Although the model largely simplifies the molecular complexity of real proteins, it contains basic features of protein folding in both thermodynamic and kinetic aspects: the unique native structure (i.e., only one conformation with the global energy minimum); a large number of conformations (the Levinthal paradox); a cooperative folding transition occurring at the level of domains; and fast folding to the native state at conditions under which the native state is thermodynamically stable. Of course, the geometric simplification of the lattice model loses some detailed features of a real protein molecule such as lack of the notion of secondary structure, nonphysical balance between the number of buried and the number of exposed residues, and lack of proteinlike interplay between short and long-range interactions. Nevertheless, the lattice model often becomes more advantageous for prediction of
thermodynamic features of protein folding, because the sacrifice of geometric accuracy in the lattice model allows us to characterize the collection of all possible sequences and the collection of all possible chain conformations, which is not possible in the full atomistic model. Here, a brief description of the lattice protein model used in this study is provided as follows. A protein molecule is modeled as a cubic lattice heteropolymer consisting of 27 beads, each of which represents an amino acid residue.12-14 In this model, a contact is made only when two nonbonded residues are located at a unit distance from each other. Therefore, a fully compact selfavoiding chain in a 3 × 3 × 3 cube has 28 contacts, and the total number of compact conformations unrelated by symmetry in the 3 × 3 × 3 cube is 103 346.15 The total energy of the protein E is given as E)
∑
Bij∆(ri - rj)
(4)
1ei 0.5) where the protein retains more native contacts. Because the probabilities of the native state PN are the same, the free energy difference demonstrates that denaturantinduced unfolding shows a different conformational distribu-
Figure 7. Contribution of contact energy (a) and entropy (b) to the free energy of the protein. The free energy of the protein is represented in Figure 5.
tion of the unfolded state along Q0 as compared with temperature-induced unfolding. When the free energy of protein F is decomposed into the contact energy (E) between amino acid residues and the conformational entropy of the protein (S), as shown in Figure 7, it is realized that the averaged contact energy of protein under denaturant-induced unfolding is higher than that under temperature-induced unfolding in the low Q0 region (0.1 < Q0 < 0.5), while there is no significant difference of contact energy between the two unfoldings in the high Q0 region (Q0 > 0.5). This implies that the unfolded state of denaturantinduced unfolding loses more contacts than that of temperature-induced unfolding in low Q0 region (0.1 < Q0 < 0.5).
Monte Carlo Simulation of Protein Unfolding
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Figure 8. Plots of the averaged number of contacts between residues versus Q0. Temperature-induced unfolding simulation (broken line) was performed at T ) 1.77 and C ) 0.00, and denaturant-induced unfolding simulation (solid line) was performed at T ) 1.00 and C ) 0.05.
Because the magnitude of the binding energy between protein and denaturant is equal to that of the average contact energy between residues, the binding of denaturant to protein can compete with the contact between residues. Therefore, a contact between residues can be replaced by a contact between a residue and a denaturant, leading to an unfolded structure that has fewer contacts between residues as compared to that of temperature-induced unfolding. Consequently, the number of possible unfolded conformations under denaturant-induced unfolding becomes larger as a result of the binding of denaturant to protein, resulting in the denaturant-induced unfolding having a higher conformational entropy, as shown in Figure 7b. The averaged number of contacts calculated from unfolded states corresponding to each Q0 is shown in Figure 8, which shows that the unfolded structure from denaturant-induced unfolding has fewer contacts than that from temperatureinduced unfolding. It is also realized from Figure 8 that the difference of the number of contacts is greater in the low Q0 region (0.1 < Q0 < 0.5). Figure 9 shows the contour map of the number of sampled conformations during simulation on the surface of the contact energy and Q0. In the high region (Q0 > 0.5), the number of sampled conformations under denaturant-induced unfolding is larger than that under temperature-induced unfolding. This is observed in all concentration ranges examined in this study. Recently, the dependence of the urea-induced stability on the size of the protein has been reported by Shimizu and Chan.23 Using the free energy calculation for pairwise hydrophobic association in aqueous solutions of urea, they reported that the denatured protein retains the nativelike compactness. In addition, it has been reported that a denatured protein retains nativelike topology even under a relatively concentrated condition of 8 M urea.24 From these results, it is suggested that an increase in the concentration of urea would not lead to further significant expansion of the urea-denatured chains. This result is also observed in our simulation. Our simulation results show that the unfolded structure even at relatively high concentration of denaturant (C ) 0.05-0.07) still retains 25-30% of native contacts (Figure 6) and roughly 70% of the number of contacts of fully compact structure (Figure 8), indicating that denatured protein persists a nativelike semicompact structure rather than
Figure 9. Contour map of log v(Q0, ), where v(Q0, ) is the number of conformations corresponding to the bin (Q0, ). The size of each bin is 1/28 in Q0 and 1 in (see the model and simulation method in the text for details): (a) temperature-induced unfolding at T ) 1.77 and C ) 0.00, (b) denaturant-induced unfolding T ) 1.00 and C ) 0.05.
a loosely expanded structure. Although there are some simplifications in our denaturant model such as that the size dependences of denaturant and side chain of amino acid are ignored, the simple denaturant model based on the binding theory can reproduce the experimentally observed characteristics of denaturant-induced unfolding. Concluding Remarks The denaturant-induced unfolding has been investigated by using a Monte Carlo simulation. When the denaturantinduced unfolding pathway is compared with the temperature-induced unfolding pathway, the two unfolding pathways show different conformational distributions at unfolded and transition states. The free energy of unfolded states corresponding to low Q0 (0.1 < Q0 < 0.5) under temperatureinduced unfolding is lower than the case under denaturantinduced unfolding, whereas the free energy of the unfolded state close to the native state (Q0 > 0.5) is higher under temperature-induced unfolding than under denaturant-induced unfolding. It is realized that the denaturant-induced unfolding
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shows a wider conformational distribution than the temperature-induced unfolding, because denaturant molecules bound to a protein molecule break contacts between amino acid residues, resulting in higher conformational entropy. On the other hand, the temperature-induced unfolding passes through more compact unfolded states than the denaturant-induced unfolding especially in the low Q0 region (0.1 < Q0 < 0.5). It should be noted that our model has two important simplifications: one is an assumption that the size of a denaturant is equal to that of an amino acid residue, and the other one is that the effect of the water molecule on denaturation is implicitly taken into account by introducing the pairwise hydrophobic interaction Bij, which is temperature-independent. As a result, our model may not describe the cold denaturation25-27 but only shows the temperatureinduced unfolding. Moreover, it has been reported that the protein folding pathway can be affected by temperature.28 Hence, further refinement for our model is needed to accommodate the effect of temperature on the state of water for studying temperature-dependent properties as well as the cold denaturation. Acknowledgment. The authors thank the Korea Science and Engineering Foundation (KOSEF) for financial support through the Hyperstructured Organic Materials Research Center (HOMRC). References and Notes (1) Gekko, K.; Timasheff, S. N. Biochemistry 1981, 20, 4667. (2) Lee, J. C.; Timasheff, S. N. J. Biol. Chem. 1981, 256, 7193.
Choi et al. (3) Lee, J. C.; Timasheff, S. N. J. Biol. Chem. 1981, 256, 625-631. (4) Creighton, T. E. Proteins: Structures and Molecular Properties; WH Freeman: New York, 1993; Chapter 7. (5) Tirado-Rivas, J.; Orozco, M.; Jorgensen, W. L. Biochemistry 1997, 36, 7313. (6) Zou, Q.; Habermann-Rottinghaus, S. M.; Murphy, K. P. Proteins 1998, 31, 107. (7) Schellman, J. A. Biophys. Chem. 2002, 96, 91. (8) Alonso, D. O. V.; Dill, K. A. Biochemistry 1991, 30, 5974. (9) Courtenay, E. S.; Capp, M. W.; Saecker, R. M.; Record, M. T., Jr. Proteins 2000, 4, 72. (10) Myers, J. K.; Pace, C. N.; Scholtz, J. M. Protein Sci. 1995, 4, 2138. (11) Makhatadze, G. I. J. Phys. Chem. B 1999, 103, 4781. (12) Sali, A.; Shakhnovich, E.; Karplus, M. Nature 1994, 369, 248. (13) Sali, A.; Shakhnovich, E.; Karplus, M. J. Mol. Biol. 1994, 235, 1614. (14) Shakhnovich, E.; Gutin, A. M. Proc. Natl. Acad. Sci. U.S.A. 1993, 90, 7195. (15) Chan, H. S.; Dill, K. A. J. Chem. Phys. 1990, 92, 3118. (16) Plaxco, K. W.; Simons, K. T.; Baker, D. J. Mol. Biol. 1998, 277, 985. (17) Gutin, A. M.; Abkevich, V. I.; Shakhnovich, E. I. Proc. Natl. Acad. Sci. U.S.A. 1995, 92, 1282. (18) Onuchic, J. N.; Socci, N. D.; Luthey-Schulten, Z.; Wolynes, P. G. Folding Des. 1996, 1, 441. (19) Verdier, P. H.; Stockmayer, W. H. J. Chem. Phys. 1962, 36, 227. (20) Madras, N.; Sokal, A. D. J. Stat. Phys. 1987, 47, 573. (21) Schulz, G. E.; Schirmer, R. H. Principles of Protein Structure; Springer-Verlag: New York, 1979. (22) Ferrenberg, A. M.; Swendsen, R. H. Phys. ReV. Lett. 1988, 61, 2635. (23) Shimizu, S.; Chan, H. S. Proteins 2002, 49, 560. (24) Shortle, D.; Ackerman, M. S. Science 2001, 293, 487. (25) Collet, O. Europhys. Lett. 2001, 53, 93. (26) Kunugi, S.; Tanaka, N. Biochim. Biophys. Acta 2002, 1595, 329. (27) Marques, M.; Borreguero, J. M.; Stanley, H. E.; Dokholyan, N. V. Phys. ReV. Lett. 2003, 91, 138103. (28) Borreguero, J. M.; Ding, F.; Buldyrev, S. V.; Stanley, H. E.; Dokholyan, N. V. Biophys. J. 2004, 87, 521.
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