2686
J. Phys. Chem. B 2008, 112, 2686-2693
Oscillatory Molecular Driving Force for Protein Folding at High Concentration: A Molecular Simulation Diannan Lu and Zheng Liu* Department of Chemical Engineering, Tsinghua UniVersity, Beijing 100084, China ReceiVed: August 29, 2007; In Final Form: December 12, 2007
This paper presents a Langevin dynamics simulation that suggests a novel way to fold protein at high concentration, a fundamental issue in neurodegenerative diseases in vivo and the production of recombinant proteins in vitro. The simulation indicates that the folding of a coarse-grained β-barrel protein at high concentration follows the “collapse-rearrangement” mechanism but it yields products of various forms, including single proteins in the native, misfolded, and uncollapsed forms and protein aggregates. Misfolded and uncollapased proteins are the “nucleus” of the aggregates that also encapsulate some correctly folded proteins (native proteins). An optimum hydrophobic interaction strength (/p) between the hydrophobic beads of the model protein, which results from a compromise between the kinetics of collapse and rearrangement, is identified for use in increasing the rate of folding over aggregating. Increased protein concentration hinders the structural transitions in both collapse and rearrangement and thus favors aggregation. A new method for protein folding at high concentration is proposed, which uses an oscillatory molecular driving force (/p) to promote the dissociation of aggregates in the low /p regime while promoting folding at a high /p. The advantage of this method in enhancing protein folding while depressing aggregation is illustrated by a comparison with the methods based on direct dilution or applying a denaturant gradient.
Introduction Protein folding at high concentration is of fundamental importance for both the therapeutic treatment of neurodegenerative diseases1-3 caused by protein misfolding and the aggregation and production of recombinant proteins expressed in the form of inclusion body, in which aggregation often limits the yield of active protein. In the area of protein refolding, recent years have witnessed the development of the methods of adding osmolytes,4-6 surfactants,7-9 and polymers10-16 as artificial chaperones and implementing a denaturant gradient17-19 or a protein concentration gradient.20-23 On the other hand, remarkable progress have been made in “protein aggregation in silico”24 such as folding funnels of isolated protein25and multi-protein systems,26 polymer or surfactant-assisted protein folding,27-30 and protein aggregation of lattice and off-lattice model proteins.31-34 Hall and co-workers have used extensive discontinuous molecular dynamics simulation to investigate the formation of fibril-like aggregation and showed that partially folded or unfolded proteins are more likely to aggregate.35-42 Cellmer et al. have shown the existence of “hot” sites for aggregation, which can guide a following “design out” via genetic engineering.24 They also have presented Langevin dynamics for the folding of three β-barrel proteins and discussed the multiple routes of aggregation.34 More recently, Lu et al. proposed from Langevin dynamics simulation results a novel idea to smoothen the rugged energy funnel in order to facilitate folding into the native conformation and demonstrated it by refolding lysozyme in a decreasing temperature environment using a temperature responsive polymer as artificial chaperone.43 The present work was performed in the context of the above * Corresponding author. E-mail:
[email protected] (Z.L.). Phone: 86-10-6277 9876. Fax: 86-10-6277 0304.
efforts and focused on the enhancement of protein folding while depressing aggregation, which is the fundamental problem of protein folding at high concentration. The present study began with the Langevin dynamics for the folding and aggregation of a β-barrel model protein44 at a high concentration up to 6.15 mM, that is, 100 protein molecules in the simulation box. By monitoring the folding and aggregation at a concentration of 3.01 mM, that is, 49 protein molecules in the simulation box, the folding products of different conformations and their folding trajectories were obtained. The structural transition leading to various products including folded, misfolded, and aggregated ones was then obtained as a function of both /p that intrinsically determines the intra- and intermolecular hydrophobic interaction strength and protein concentration that magnifies the protein-protein interactions. A new idea for protein folding at a high concentration is proposed, in which an oscillatory molecular driving force, that is, oscillatory /p, is applied. The effectiveness of this method in dissociating protein aggregate at a low /p regime while promoting folding at a high /p is illustrated by comparison with two routinely used methods: direct dilution and folding in denaturant gradient. Models and Methods Protein Model. The β-barrel model protein with sequence B9N3(LB)4N3B9N3(LB)5L29 proposed by Veishans et al.44 is shown in Figure 1, where B, L, and N denote hydrophobic, hydrophilic, and neutral bead, respectively. The native conformation shown in Figure 1 was determined by the simulating annealing method.29,34 The form of the potential function is the same as in previous studies.29 The RATTLE algorithm for enforcing bond lengths
10.1021/jp076940o CCC: $40.75 © 2008 American Chemical Society Published on Web 02/12/2008
Oscillatory Molecular Driving Force
J. Phys. Chem. B, Vol. 112, No. 9, 2008 2687
(σ ) 0.38 nm) was used in the present work. The angle potential (V(θ)) is harmonic,
V(θ) )
kθ(θ - θ0)2 ∑ angles
(1)
where θ is the angle between three connected beads, θ0 is the equilibrium angle of 105°, and kθ is equal to 10 h/(rad)2, where h ) 5.0 kJ/mol. The dihedral potential has three minima, corresponding to one trans state and two gauche states, and is of the form:
V(φ) )
∑
[A(1 + cos φ) + B(1 + cos(3φ))]
(2)
dihedrals
where φ is the dihedral angle. For dihedrals containing two or more N beads, A ) 0 and B ) 0.2h. For all other dihedral angels, A ) 1.2h and B ) 1.2h. Nonlocal interactions, that is, those between beads separated by at least two bonds, were described by
V(r) )
[( )
∑ 4Ch
pairs
σ r
12
-
( )]
/pD
σ
6
r
(3)
where r is the distance between the two beads. For BB pairs, C ) 1 and D ) 1; for LB and LL pairs, C ) 1/3 and D ) -1, and for BN, LN, NN pairs, C ) 1 and D ) 0. B is hydrophobic because of its attractive potential while L is hydrophilic because of its repulsive potential. N is neutral and also repulsive in NN, NL, and NB pairs. In the case of multi-protein simulations, this definition of the nonlocal potential was used for all two-body interactions, regardless of whether the beads were on the same or different protein chain. The dimensionless parameter /p reflects the hydrophobic interaction strength between hydrophobic beads of model protein, and a high /p implies a strong hydrophobic interaction between protein beads. In practice, /p can be tuned by the denaturant concentration, and a high /p indicates a low denaturant concentration and vice versa.45 Simulation Methods. As in the previous simulation of a single confined protein,29 velocity Langevin dynamics coupled with the velocity-Verlet algorithm was performed using Gromacs as the platform.46 The force function is
mi
d2ri dt
2
) - miξi
dri + Fi(r) + ° dt ri
(4)
where mi ) 2.2 × 10-22 g/mol is the average mass of amino acid, ri is the position of bead i, ξi ) 1/(5.0 ps) is the friction constant, Fi(r) is the configurational force, and ° is the random ri force that is related to the temperature through the fluctuationdissipation theorem. The radius of gyration of the protein is
R2g )
2
r2ij ∑ ∑ N(N - 1) i 1.6 nm, which are the native, misfolded, and uncollapased state, respectively. The snapshots show the existence of the abovementioned six kinds of protein products, that is, IN, IM, IU, AN, AM, and AU. Figure 2b shows one folding trajectory leading to a single protein in the native state, in which the denatured protein first falls into a collapsed state, as characterized by a reduction of Rg to below 1.60 nm at t ) 0.61 ns, which then rearranged to the native state, as characterized by reduction of χ below 0.35 at t ) 2.47 ns. This shows that the folding of the β-barrel protein at high concentration keeps the “collapse-rearrangement” mechanism,47,48 similar to its single counterpart.29 Figure 2c shows one folding trajectory to a native protein that is encapsulated in an aggregate. For clarity, the native protein is magnified and drawn with the ball-stick model, while the other proteins in the aggregate are drawn with the stick model. Here again, the folding of the model protein to the native conformation followed the two-step mechanism but at a much slower collapsing and rearranging rate compared with single native protein is shown in Figure 2b. This is due, in the present case, to the hydrophobic interaction among the proteins, which, being attractive by nature, retards both the collapsing and rearranging. In addition, the snapshots (ball-stick model) show that the hydrophobic beads located at the surface of the native protein interact with other proteins and form aggregate. Figure 2d,e shows the folding trajectories to an isolated misfolded state and a misfolded state in an aggregate, respectively. In both cases, a hydrophobic collapse occurred but yielded structures with accessible hydrophobic beads. This thus makes the misfolded protein the nucleus of the aggregate. Again, the hydrophobic interaction among the protein molecules hinders the structural transitions of the encapsulated protein, as compared to its counterpart in the isolated form. Figure 2f shows the folding trajectory leading to an unfolded protein in an aggregate. A single unfolded conformation is unstable under this condition, which causes the protein to
fold.29,30 However, in the case of a high concentration, the hydrophobic interaction with neighboring counterparts forms an aggregate and, thus, “freezes” this uncollapsed conformation. It can be concluded from Figure 2 that the folding of a β-barrel protein at a high concentration follows the “collapserearrangement” mechanism but yields various types of protein products. The hydrophobic interaction among the proteins hinders, as compared to that of the single protein, both collapsing and rearrangement. The misfolded and uncollapsed states are the core of the protein aggregate, as described elsewhere.34,49 Moreover, the aggregate may also contain the correctly folded state. The dissociation of the aggregate is expected to release the correctly folded state and also enable the misfolded (Figure 2e) and unfolded protein (Figure 2f) to fold to the native state. Folding of a Single β-Barrel Protein. Figure 3 gives the yield of the different folding states of a single β-barrel protein at different /p, which is the hydrophobic interaction among the protein beads, mimicking the variation of the denaturant concentration.33,45 Here, T ) 150 K and Cp ) 0.06 mM; that is, the simulation box contains one β-barrel protein. As shown in Figure 3a,d, the maximum folding yield, yIN, is obtained at /p ) 0.8, where the highest initial folding rate, which is determined from the slope of the folding curve, is also achieved. An apparent initial rate for yIU and yIM can also be obtained from Figure 3b,c where a higher /p leads to a shorter collapsing time but a significantly increased amount of misfolded states. This can be interpreted as that too high a hydrophobic interaction among the protein beads, although accelerating collapsing, promotes the formation of the misfolded state. In practice, /p can be tuned with the denaturant concentration.12,50-52 The yields of different folding products as a function of /p are also noteworthy: a weak /p favors the undesired unclasped states while a strong /p leads to unwanted misfolded proteins, as shown in Figure 3d. Thus, a suitable /p that balances the collapse and rearrangement kinetics is the key to a high folding yield and fast folding rate.33,45 Folding of the β-Barrel Protein at High Concentration: Folding Yield and Kinetics. As shown in Figure 2, the interaction among the proteins makes protein folding at high concentration more complicated and gives extensively diversified products, as compared with the folding of a single protein. For protein folding at high concentration, two major operation parameters are /p and Cp, which determine the strength and frequency of the intra- and intermolecular hydrophobic interaction, respectively. Figure 4 shows the folding yield and kinetics of β-barrel protein at different concentrations at T ) 150 K. Similar to the folding of a single β-barrel protein shown in Figure 3, an optimum /p exists for a maximum yIN (Figure 4a) and also a minimum yA (Figure 4b). When Cp ) 1.85 mM for example, the optimum /p is 0.8 where the overall folding rate is the highest (Figure 4c) while that for forming aggregates is slowest (Figure 4d). A high /p, for example, /p ) 1.2, accelerates protein collapsing (Figure 3b), and the misfolding of the model protein is also accelerated (Figure 3c). This reduces the folding rate of the model protein (Figure 3a and Figure 4c) and also increases protein aggregation (Figure 4b,d), especially during the initial folding stage, due to the exposed hydrophobic patches of uncollapsed and misfolded protein (Figure 2). At a low /p, for example, /p ) 0.6, both collapsing and misfolding rate are reduced simultaneously (Figure 3b,c), and the folding rate is low (Figure 3a and Figure 4c). Moreover, the slower collapsing rate also indicates that a long-lived uncollapsed state acts as the nucleus (Figure 2f) for protein aggregation (Figure
Oscillatory Molecular Driving Force
J. Phys. Chem. B, Vol. 112, No. 9, 2008 2689
Figure 2. Folding product distribution, folding trajectories, and corresponding snapshots. The protein, whose trajectory is shown in figure, is presented as a ball-stick model, and the other proteins in the aggregate are presented as stick models. (a) Overall distribution of folding products: the x axis is the radius of gyration (Rg); the y axis is the structural overlap function (χ), and the z axis is the probability of appearance of a specific conformation. The sum of probability of total conformations shown in this figure is 1. (b) Formation of a single protein in the native state. (c) Formation of the native state encapsulated in the aggregates. (d) Formation of a single protein in the misfolded state. (e) Formation of the misfolded state encapsulated in the aggregates. (f) Formation of the uncollapsed state encapsulated in the aggregates.
2690 J. Phys. Chem. B, Vol. 112, No. 9, 2008
Lu and Liu
Figure 3. Isolated protein folding at different values of the hydrophobic interaction, /p. (a) yIN as a function of folding time. (b) yIU as a function of folding time. (c) yIM as a function of folding time. (d) yIN, yIM and yIU as a function of /p.
4b). At an extremely low /p, for example, /p < 0.4, the hydrophobic interaction is not enough to induce either intramolecularly hydrophobic collapse nor intermolecularly aggregating. This results in an extremely low rate for both folding and aggregating (Figure 4c,d) and, consequently, poor yields for both the correctly folded state and the aggregates (Figure 4a,b). On the other hand, the protein concentration (Cp) determines the frequency of protein collision. Thus, an increase in protein concentration increases intermolecular interactions. In the present study, the hydrophobic interaction among the proteins not only hinders the individual protein structure transitions (Figure 4e), but also enhances the formation of protein aggregates, especially at the initial stage (Figure 4f). The intensified aggregation at a high concentration has also been identified by Bratko et al. in their simulation using lattice model protein.53 In practice, a high concentration denaturant, such as 8 M urea or 6 M GdnHCl,52 which gives a small /p, is used to fully dissolve protein aggregates to the isolated and unfolded state, for example, yIU ) 1.0 at /p ) 0.2 (Figure 3d). The optimum denaturant concentration for protein refolding, as simulated above, has been observed for many proteins such as lysozyme,12,13 carbonic anhydrase,16 recombinant human growth hormone,52 and interferon-2.16,54 Also, the negative influence of the protein concentration on the folding yield shown by Figure 4 had also been reported for lysozyme, carbonic anhydrase, R-fetoprotein, and interferon-2.12,15,52,54,55 Oscillatory /p for Protein Folding at High Concentration: Molecular Simulation. Figure 3 shows that a high /p, that is, /p ) 1.0, accelerates “hydrophobic collapsing” of unfolded proteins (Figure 3b), while a low /p, that is, /p ) 0.6, favors protein structural transitions and simultaneously depresses
misfolding (Figure 3c). This is also true of the protein folding at high concentration shown in Figure 4, where the protein aggregate is formed with the uncollapased and misfolded protein as the “nucleus”. From these simulations, we get the idea of using an oscillatory /p to drive protein folding at a high concentration, whereby aggregates are forced to dissociate at a low /p, to provide free protein molecules that fold to the native conformation once /p oscillates to the high value. To examine the effectiveness of this new method, we set up two conventional methods, quick dilution (QD)52,55 and denaturant gradient (DG),19 as references. QD is performed by directly adding denatured protein of high concentration into the refolding buffer. DG could be realized in a gel column pre-equilibrated with a refolding buffer containing urea of specific concentration, that is, 2 M. During the refolding, the denatured protein dissolved in the solution containing 8 M urea was added to the top of the column, which was followed by continuous elution with the refolding buffer containing, for example, 2 M urea. A longitudinal gradient of the urea concentration was thus established in the void volume of the column, for example, from 8 M to 2 M, for protein refolding.19 To simulate QD, /p was tuned from 0.01 to 1.0 at t ) 0 ns to initiate protein folding and held until the end of the simulation. To simulate DG, /p was linearly increased from 0.6 to 1.0 within 2 ns; that is, the model protein experienced a denaturant gradient, and then /p was maintained at 1.0 until the end of the simulation. For the OS method to fold protein, /p was tuned from 0.01 to 1.0 at t ) 0 ns and held at 1.0 for 2 ns. Then /p was adjusted from 1.0 to 0.6 to dissociate protein aggregates. After 2 ns, /p was tuned to 1.0 again which allowed dissociated protein to fold. The results are shown in Figure 5.
Oscillatory Molecular Driving Force
J. Phys. Chem. B, Vol. 112, No. 9, 2008 2691
Figure 4. Folding and aggregating of the β-barrel model protein at high concentration. (a) Yield of native protein, yIN. (b) Yield of aggregates, yA. (c) yIN as a function of folding time at different /p, Cp ) 1.85mM. (d) yA as a function of folding time at different /p, Cp ) 1.85mM. (e) yIN as a function of folding time at different Cp, /p ) 0.8. (f) yA as a function of folding time at different Cp, /p ) 0.8.
Figure 5a shows that the OS method gives the highest folding yield (yIN) while QD gives the lowest. Moreover, the OS method give less aggregates (yA), as compared with the QD and DG methods (Figure 5b). From the top part of Figure 5c, it can be seen that the QD and OS methods give a faster initial collapsing rate than the DG method, because of the higher /p during the first 2 ns, and also more aggregates, as can be expected from Figure 4d. For the OS method, as shown by Figure 5c, once /p is tuned from 1.0 to 0.6 at t ) 2.0 ns, the yield of uncollapsed and nonnative protein increases (Figure 5c); that is, the dissociation of the aggregates occurs. Once /p is tuned back 1.0, isolated
proteins including those dissociated from the aggregates start to collapse and rearrange to the native conformation. This thus gives more correctly folded proteins and less aggregates, as shown in Figure 5d. The different folding kinetics and yields shown in Figure 5 are noteworthy because they give the possibility for the dynamic control of the protein folding process by promoting the transition from the global-minimum energy state (aggregate) to a localminimum energy state56 (native). The exploration of the use of an oscillatory /p is thus of great interest for protein structure transition both in vitro and in vivo. In nature, protein folding in vivo is performed with a molecular chaperone such as GroEL/
2692 J. Phys. Chem. B, Vol. 112, No. 9, 2008
Lu and Liu
Figure 5. Comparison of different folding strategies. (a) Folding yield, yIN. (b) Yield of aggregates, yA. (c) Time profile of folding. (d) Time profile of aggregation.
GroES, which can recognize, capture the misfolded and/or newly synthesized protein, fold it in the cavity, and deliver the native protein upon the input of ATP.57,58 Todd et al. have shown that chaperones repeatedly bind kinetically trapped proteins, randomly disrupt their structure, release them in less folded states, and thus allow substrate proteins multiple opportunities to fold to the thermodynamically stable state.59 Thirumalai and Lorimer have shown that the repeated interaction with GroEL gives the substrate protein a higher free energy and thus facilitates its subsequent folding to the native conformation.60 The OS method, in contrast, uses the implementation of an oscillatory molecular driving force that triggers the dissociation of aggregates and enables dissociated protein folding to the native conformation. In addition to its potential for in vitro protein refolding, the OS method may find applications in vivo, as a complementary tool to treat protein aggregation diseases.
acterized by the application of an oscillatory /p is proposed for protein folding at high concentration. The advantages of this method in dissociating aggregates at a low /p while triggering folding at the following high /p are shown by comparison with the quick dilution and denaturant gradient methods. This method may find many applications that require increased folding over aggregation, for example, protein folding both in vivo and in vitro.
Conclusion
References and Notes
Langevin dynamics simulation shows that the folding of a β-barrel protein at high concentration follows the two-step mechanism, that is, collapsing and rearrangement, similar to its single counterpart. The hydrophobic interaction among the proteins undergoing structural transition yields products that include the native, misfolded, uncollapsed, and aggregated state. The uncollapased and misfolded states are the “nucleus” of the aggregates that also contain native proteins. An optimal hydrophobic interaction strength between hydrophobic beads of model protein (/p), at which an improved folding over aggregation is achieved. The aggregation is intensified once protein concentration increases. A novel method that is char-
(1) Dobson, C. M. Trends Biochem. Sci. 1999, 24, 329. (2) Gregersen, N.; Bross, P.; Vang, S.; Christensen, J. H. Annu. ReV. Genomics Human Genet. 2006, 7, 103. (3) Chiti, F.; Dobson, C. M. Annu. ReV. Biochem. 2006, 75, 333. (4) Kim, S. H.; Yan, Y. B.; Zhou, H. M. Biochem. Cell Biol.-Biochimie Et Biologie Cellulaire 2006, 84, 30. (5) Mishra, R.; Seckler, R.; Bhat, R. J. Biol. Chem. 2005, 280, 15553. (6) Ou, W. B.; Park, Y. D.; Zhou, H. M. Int. J. Biochem. Cell Biol. 2002, 34, 136. (7) Wang, J.; Lu, D. N.; Lin, Y.; Liu, Z. Biochem. Eng. J. 2005, 24, 269. (8) Cruz, R. D.; Whitby, F. G.; Buczek, O.; Bulaj, G. J. Pept. Res. 2003, 61, 202. (9) Krause, M.; Rudolph, R.; Schwarz, E. FEBS Lett. 2002, 532, 253. (10) Lu, D. N.; Zhang, K.; Liu, Z. Biochem. Eng. J. 2005, 25, 141.
Acknowledgment. This work was supported by the National Natural Science Foundation under Grant No. 20576061 and by the Ministry of Science and Technology through 973 Project under Grant No. 2003CB716004. The authors would like to express their thanks to Professor Dezheng Wang, Department of Chemical Engineering, Tsinghua University, for his generous help in the revision of this manuscript.
Oscillatory Molecular Driving Force (11) Lu, D. N.; Liu, Z. X.; Zhang, M. L.; Wang, X. G.; Liu, Z. Biochem. Eng. J. 2006, 27, 336. (12) Lu, D.; Liu, Z. X.; Zhang, M. L.; Liu, Z.; Zhou, H. M. Biochem. Eng. J. 2005, 24, 55. (13) Lu, D. N.; Liu, Z. Acta Polym. Sinica 2004, 573. (14) Cleland, J. L.; Wang, D. I. C. Bio-Technology 1990, 8, 1274. (15) Cleland, J. L.; Hedgepeth, C.; Wang, D. I. C. J. Biol. Chem. 1992, 267, 13327. (16) Cleland, J. L.; Builder, S. E.; Swartz, J. R.; Winkler, M.; Chang, J. Y.; Wang, D. I. C. Bio-Technology 1992, 10, 1013. (17) Prinsloo, E.; Oosthuizen, V.; Muramoto, K.; Naude, R. J. Prot. Expression Purif. 2006, 47, 179. (18) Li, M.; Zhang, G. F.; Su, Z. G. J. Chromatogr. A 2002, 959, 113. (19) Gu, Z. Y.; Su, Z. G.; Janson, J. C. J. Chromatogr. A 2001, 918, 311. (20) Winter, J.; Lilie, H.; Rudolph, R. Anal. Biochem. 2002, 310, 148. (21) Buswell, A. M.; Ebtinger, M.; Vertes, A. A.; Middelberg, A. P. J. Biotechnol. Bioeng. 2002, 77, 435. (22) Katoh, S.; Katoh, Y. Process Biochem. 2000, 35, 1119. (23) Katoh, S.; Sezai, Y.; Yamaguchi, T.; Katoh, Y.; Yagi, H.; Nohara, D. Process Biochem. 1999, 35, 297. (24) Cellmer, T.; Bratko, D.; Prausnitz, J. M.; Blanch, H. W. Trends Biotechnol. 2007, 25, 254. (25) Wolynes, P. G.; Onuchic, J. N.; Thirumalai, D. Science 1995, 267, 1619. (26) Bratko, D.; Cellmer, T.; Prausnitz, J. M.; Blanch, H. W. Biotechnol. Bioeng. 2007, 96, 1. (27) Lu, D. N.; Liu, Z. J. Chem. Phys. 2005, 123. (28) Lu, D. N.; Liu, Z.; Liu, Z. X.; Zhang, M. L.; Ouyang, P. J. Chem. Phys. 2005, 122. (29) Lu, D. N.; Liu, Z.; Wu, J. Z. Biophys. J. 2006, 90, 3224. (30) Lu, D. N.; Liu, Z.; Wu, J. Z. J. Chem. Phys. 2007, 126, 13. (31) Bratko, D.; Cellmer, T.; Prausnitz, J. M.; Blanch, H. W. J. Am. Chem. Soc. 2006, 128, 1683. (32) Cellmer, T.; Bratko, D.; Prausnitz, J. M.; Blanch, H. Proc. Natl. Acad. Sci. 2005, 102, 11692. (33) Nguyen, H. D.; Hall, C. K. Biotechnol. Bioeng. 2002, 80, 823. (34) Cellmer, T.; Bratko, D.; Prausnitz, J. M.; Blanch, H. Biotechnol. Bioeng. 2005, 89, 78. (35) Hall, C. K.; Waggner, V. A. Computational approaches to fibril structure and formation. In Amyloid, Prions, and Other Protein Aggregates, Pt B; Elsevier Academic Press Inc: San Diego, 2006; Vol. 412; pp 338.
J. Phys. Chem. B, Vol. 112, No. 9, 2008 2693 (36) Marchut, A. J.; Hall, C. K. Biophys. J. 2006, 90, 4574. (37) Marchut, A. J.; Hall, C. K. Comput. Biol. Chem. 2006, 30, 215. (38) Marchut, A. J.; Hall, C. K. Proteins: Struc., Funct., Bioinfo. 2007, 66, 96. (39) Marchut, A. J.; Smith, A. V.; Hall, C. K. Proteins: Struc., Funct., Bioinfo. 2006, 63, 709. (40) Nguyen, H. D.; Hall, C. K. Proc. Natl. Acad. Sci. 2004, 101, 16180. (41) Nguyen, H. D.; Hall, C. K. J. Biol. Chem. 2005, 280, 9074. (42) Nguyen, H. D.; Hall, C. K. J. Am. Chem. Soc. 2006, 128, 1890. (43) Lu, D. N.; Wu, J. Z.; Liu, Z. J. Phys. Chem. B 2007, 111, 12303. (44) Veitshans, T.; Klimov, D.; Thirumalai, D. Folding Design 1997, 2, 1. (45) Gupta, P.; Hall, C. K.; Voegler, A. Fluid Phase Equilib. 1999, 160, 87. (46) van de Spoel, D.; Lindahl, E.; Hess, B.; van Buuren, A. R.; Meulenhoff, P. J.; Tieleman, D. P.; Sijbers, A. L. T. M.; Feenstra, K. A.; van Drunen, R.; Berendsen, H. J. C. Gromacs User Manual Version 3.2, www.gromacs.org, 2004. (47) Dill, K. A. Biochemistry 1985, 24, 1501. (48) Levitt, M.; Warshel, A. Nature 1975, 253, 693. (49) Clark, L. A. Protein Sci. 2005, 14, 653. (50) Nishida, S.; Nada, T.; Terazima, M. Biophys. J. 2005, 89, 2004. (51) Kuhlman, B.; Luisi, D. L.; Evans, P. A.; Raleigh, D. P. J. Mol. Biol. 1998, 284, 1661. (52) Clark, E. D. Curr. Opin. Biotechnol. 2001, 12, 202. (53) Bratko, D.; Blanch, H. W. J. Chem. Phys. 2001, 114, 561. (54) Jin, T.; Guan, Y. X.; Fei, Z. Z.; Yao, S. J.; Cho, M. G. World J. Microbiol. Biotechnol. 2005, 21, 797. (55) Leong, S. S. J.; Middelberg, A. P. J. Food Bioprod. Process. 2006, 84, 9. (56) Jahn, T. R.; Radford, S. E. Febs J. 2005, 272, 5962. (57) Stan, G.; Thirumalai, D.; Lorimer, G. H.; Brooks, B. R. J. Biomol. Struct. Dyn. 2007, 24, 757. (58) Cheung, M. S.; Thirumalai, D. J. Mol. Biol. 2006, 357, 632. (59) Todd, M. J.; Lorimer, G. H.; Thirumalai, D. Proc. Natl. Acad. Sci. U.S.A. 1996, 93, 4030. (60) Thirumalai, D.; Lorimer, G. H. Annu. ReV. Biophys. Biomol. Struct. 2001, 30, 245.
