Predicting protein folding pathways at the mesoscopic level based on native interactions between secondary structure elements
© Yang and Sze; licensee BioMed Central Ltd. 2008
Received: 05 April 2008
Accepted: 23 July 2008
Published: 23 July 2008
Since experimental determination of protein folding pathways remains difficult, computational techniques are often used to simulate protein folding. Most current techniques to predict protein folding pathways are computationally intensive and are suitable only for small proteins.
By assuming that the native structure of a protein is known and representing each intermediate conformation as a collection of fully folded structures in which each of them contains a set of interacting secondary structure elements, we show that it is possible to significantly reduce the conformation space while still being able to predict the most energetically favorable folding pathway of large proteins with hundreds of residues at the mesoscopic level, including the pig muscle phosphoglycerate kinase with 416 residues. The model is detailed enough to distinguish between different folding pathways of structurally very similar proteins, including the streptococcal protein G and the peptostreptococcal protein L. The model is also able to recognize the differences between the folding pathways of protein G and its two structurally similar variants NuG1 and NuG2, which are even harder to distinguish. We show that this strategy can produce accurate predictions on many other proteins with experimentally determined intermediate folding states.
Our technique is efficient enough to predict folding pathways for both large and small proteins at the mesoscopic level. Such a strategy is often the only feasible choice for large proteins. A software program implementing this strategy (SSFold) is available at http://faculty.cs.tamu.edu/shsze/ssfold.
As early studies revealed that an unfolded protein can fold spontaneously to a three-dimensional structure under suitable environmental conditions [1, 2], traditional approaches to understanding protein folding have focused on the prediction of the native structure. As more studies showed the existence of intermediates and interaction among residues during the protein folding process [3, 4], there is substantial interest to understand the time order of events during the formation of the tertiary structure. From the free energy point of view, each conformation of a protein is associated with a free energy and the protein folds from the high-energy denatured conformation to its folded structure along a funnel-like energy landscape [5, 6].
Although advances in experimental techniques allow the investigation of protein folding pathways at the microsecond timescale [7, 8], experimental determination of protein folding pathways remains difficult. Most studies are only able to identify general characteristics of the folding pathway without much details and are limited to analyzing small proteins. Computational techniques are often used to simulate protein folding and the problem is transformed to energetic optimization problems, that is, computational search for global energy minimum over all possible conformations. The most accurate computational techniques utilize molecular dynamics to determine the order of events that lead to the tertiary structure through atomic-level simulations [9–12]. Due to the extremely large conformation space, these approaches suffer from well-known problems accompanying high dimensionality, including computational expensiveness and ease of trapping in local minima, and are applicable only to small proteins in a short time course.
The problem with representing a protein at the amino acid level is that even with the assumption that each residue has only two states (ordered or disordered), a protein with n residues still has 2 n possible conformations . To overcome this problem, several recent approaches represent a protein at the level of secondary structure elements (SSEs), in which each element corresponds to one helix or one β-strand. By adopting the framework model in which secondary structures are thought to fold relatively independently of the tertiary structure , each SSE is treated as an indivisible unit that interacts with other SSEs as a whole. Since the number of SSEs in a protein is small (Figure 1), this model is much more tractable to simulate. Eyrich et al  assumed that the SSEs are fixed and used a branch-and-bound algorithm to search for near-optimal tertiary structures. Apaydin et al  assumed that each SSE of a protein is already in native conformation and moves as a unit, and used the probabilistic roadmap approach to predict folding pathways. Zaki et al  proposed an algorithm to predict unfolding pathways based on applying a minimum cut procedure to a weighted graph that represents a protein's contact map or interaction strength between SSEs. Although the underlying assumption that intermediate secondary structures are fully folded before the formation of tertiary structures is not satisfied for most proteins, these studies show that such a strategy is sufficient to study protein folding pathways at the mesoscopic level.
In this paper, our goal is to further reduce the conformation space without sacrificing prediction accuracy. This is achieved by assuming that SSEs that do not yet interact with each other are independent and can be treated separately. A conformation is represented by a collection of fully folded structures in which each of them contains a set of interacting SSEs. By using a steepest descent strategy, we show that it is possible to predict the most energetically favorable folding pathway of large proteins with hundreds of residues at the mesoscopic level and this model is detailed enough to distinguish between different folding pathways of structurally very similar proteins. In difference from the technique in , we do not consider the spatially moving process before the SSEs form native contacts, and thus we are able to achieve much better computational efficiency.
Assume that the native structure of a protein is known. The protein folding pathway prediction problem is to find an ordered sequence of intermediate conformations to fill the gap between the unfolded state and the native tertiary structure. At the secondary structure level, a protein can be viewed as an ordered sequence of secondary structure elements (SSEs) interspersed with irregular turns or loops, where each SSE is either a helix or a β-strand, and each β-sheet consists of a variable number of β-strands that are not necessarily consecutive on the primary sequence. We represent each protein by t0s1t1⋯s k t k , where k is the number of SSEs, s i denotes the i th SSE, t j denotes the j th turn, and these elements are in the same order as they appear on the primary sequence. Given the three-dimensional structure of a protein, the assignment of SSEs can be obtained directly from the Protein Data Bank (PDB)  or using programs such as DSSP .
Following  and , we consider each SSE as an indivisible unit that folds independently of the others according to the contacts present in the native structure. This is based on the framework model that assumes that extensive intermediate secondary structures exist before they are assembled into the tertiary structure , and our goal is to predict the interaction order of SSEs during folding. Based on the observation in  and  that a model using only native interactions can explain most experimental results, we assume that the interactions between SSEs or turns are the same as the ones present in the native structure. Although these assumptions are often not satisfied as there are many proteins in which there are no clear secondary structures before the formation of tertiary structures or there are no clear preservations of secondary structures throughout folding, such a strategy is sufficient for studying folding pathways at the mesoscopic level and is often the only feasible choice for large proteins.
where each S i is viewed as an isolated entity and each E(S i ) is obtained separately by extracting the three-dimensional coordinates of its residues from the Protein Data Bank (PDB)  and using the Rosetta software  to compute its free energy. The original Rosetta energy function is used, which is obtained by representing each side chain by a centroid that is located at the center of mass, and computing a weighted sum of the binned probability descriptions of multiple effects, including the solvation and electrostatic effects based on observed distributions in known protein structures, the secondary structure packing effects that include strand pairing, strand arrangement into sheets and helix-strand packing, and the effects of steric repulsion and Van der Waals interactions (more details are available in  and in Table I of ). To take the backbone into consideration, a turn t j is included in the computation of E(S i ) if both of its adjacent SSEs s j (if it exists) and sj+1(if it exists) are included in S i .
We test our strategy on proteins from the Protein Data Bank (PDB)  that have known intermediate folding states from experimental data. We illustrate that our model is detailed enough to distinguish between subtle differences in the folding pathways of the streptococcal protein G, the peptostreptococcal protein L, and variants NuG1 and NuG2 of protein G, which are all structurally very similar proteins. We demonstrate that our approach is applicable to large proteins with hundreds of residues by testing it on the 416 residue pig muscle phosphoglycerate kinase (PGK). We further test it on proteins studied in  and  to validate that our model has very good accuracy.
Proteins GB1, LB1, NuG1 and NuG2
The 56 residue B1 immunoglobulin binding domain of streptococcal protein G (GB1, PDB: 1GB1) and the 62 residue B1 immunoglobulin binding domain of peptostreptococcal protein L (LB1, PDB: 2PTL) have been used extensively as model systems for studying protein folding mechanisms [30–37]. Both GB1 (see Figure 2) and LB1 consist of one β-sheet with four strands and one α-helix. Strands 1 and 2 form an N-terminal β-hairpin, while strands 3 and 4 form a C-terminal β-hairpin. Although GB1 and LB1 have very similar tertiary structures, they have different folding pathways. As suggested by , a detailed model is needed to distinguish between them.
Experimental results showed that the C-terminal β-hairpin in GB1 is formed in the transition state of the folding pathway and serves as the starting point on which the rest of the protein can fold . Similar results were obtained using the diffusion-collision model . Our prediction is consistent with these results. In contrast, experimental results showed that only the N-terminal β-hairpin in LB1 is mainly formed in the transition state and non-random structures can be detected in the region [34, 39]. Our algorithm also predicts that the N-terminal β-hairpin forms earlier than the C-terminal β-hairpin in LB1.
Two protein G variants, NuG1 (PDB: 1MHX) and NuG2 (PDB: 1MI0), were designed to have a different folding mechanism from protein G by replacing some residues of protein G . In NuG1 and NuG2, the stability of the N-terminal β-hairpin is enhanced while the stability of the C-terminal β-hairpin is reduced, with the N-terminal β-hairpin forming contacts earlier than the C-terminal β-hairpin in both cases .
Thomas et al  showed that it is more difficult to distinguish between the folding pathways of protein G and its variants NuG1 and NuG2 than to distinguish between the folding pathways of protein G and protein L. In our predictions in Figure 4, NuG1 and NuG2 have the same folding pathway, with the N-terminal β-hairpin folded first. This is consistent with the experimental results in  and the predictions in .
Pig muscle PGK: a large protein
Phosphoglycerate kinase (PGK) from various organisms has been used as a model system for studying domain-domain interactions of multiple-domain proteins [42–44]. The pig muscle PGK (PDB: 1KF0)  is a large two-domain protein with 416 residues, with the N-terminal domain consisting of residues 1 to 155 and the C-terminal domain consisting of residues 156 to 416. There are 21 α-helices and 17 β-strands, which belong to four different β-sheets A, B, C and D, arranged as follows on the primary sequence: α1 βA4 α2 α3 βA3 α4 βA1 α5 βA2 α6 βB1 βB2 α7 βA5 α8 α9 βA6 α10 βC3 α11 α12 βC2 α13 α14 α15 βC1 βD2 βD1 βD3 α16 βC4 α17 α18 βC5 α19 βC6 α20 α21.
Szilágyi and Vas  suggested a sequential domain refolding mechanism for the pig muscle PGK, in which folding of the C-terminal domain is independent of the N-terminal domain and takes place first, and folding of the N-terminal domain starts after most of the C-terminal domain folds. The authors also suggested that an intermediate consists of a folded C-terminal domain and a still unfolded N-terminal domain. Our prediction is consistent with these experimental results.
The B domain of Staphylococcus aureus protein A (PDB: 1BDD) consists of three α-helices. In our prediction, α2 and α3 interact first, then α1 is added. This is consistent with the result of the out-exchange experiment in  and experimental results under high temperature .
Although two members of the globin protein family, leghemoglobin A (PDB: 1BIN) and myoglobin (PDB: 1MBC), have very low sequence similarity, they both consist of eight α-helices and have very similar tertiary structures. Nishimura et al  compared their folding pathways experimentally. For leghemoglobin A, αG, αH, and part of αE form stable structures first, while αA and αB form in the later stages of the folding pathway. For myoglobin, αA, αG and αH form stable contacts first. The main difference between the two folding pathways is that αA and αB form earlier in the folding pathway of myoglobin than in the folding pathway of leghemoglobin A . Our predictions are able to distinguish between these subtle differences. For leghemoglobin A, αG and αH are predicted to interact first, then αE is added, with αB and αA added later. For myoglobin, αG and αH are also predicted to interact first, then αA is added, followed by αE and αB.
There are two crystal structures for chymotrypsin inhibitor 2 (PDB: 1COA and 2CI2). While 2CI2 consists of 83 residues, 1COA is a fragment of 2CI2 from residues 20 to 83. They both consist of one α-helix and four β-strands, which are arranged as β1α1β2β3β4 in 1COA and β1α1β4β3β2 in 2CI2. In our predictions, 1COA and 2CI2 have the same folding pathway, with the middle two β-strands interacting first, then the α-helix is added, followed by the C-terminal β-strand, and the N-terminal β-strand is added last. For 1COA, simulation by  demonstrated that β2 and β3 form contacts first, then α1 is added to form a folding nucleus. The coalescence of β1 is the rate-limiting step and is completed at the end of the folding process. This is consistent with the result of the out-exchange experiment in  that showed that β2, β3 and α1 form contacts first. Our prediction is consistent with these results.
The all β-sheet protein cardiotoxin III (PDB: 2CRT) consists of five strands. While β1 and β2 form a double-stranded domain, β3, β4 and β5 form a triple-stranded domain. By the amide proton pulse exchange experiment, Sivaraman et al  showed that the triple-stranded domain forms earlier than the double-stranded domain during the refolding process. The carbonyl groups in β3 and the amide groups in β5 form hydrogen bonding partners, which are important for the formation of a hydrophobic cluster . Our prediction is consistent with these results, with β3 and β5 interacting first, then β4 is added to form the triple-stranded domain, followed by β2 and β1 in the double-stranded domain.
Bovine pancreatic trypsin inhibitor BPTI (PDB: 6PTI) is a globular protein with two α-helices and three β-strands, which are arranged as α1β2β1β3α2. Three disulfide bonds between residues 5 and 55, 14 and 38, and 30 and 51 play an important role in stabilizing the native structure , and their formation order was studied in . In our prediction, β1 and β2 interact first, then α2 is added. This brings residues 30 and 51 close together and helps to form the disulfide bond between them. Then α1 is added and this helps to form the disulfide bond between residues 5 and 55, and 14 and 38. Our prediction that β1 and β2 interact earlier than the two α-helices is consistent with the result in .
While our strategy corresponds most closely to the diffusion-collision model that allows folding to proceed independently in different parts of a protein , it is possible to use a modified strategy for other models. For example, to simulate the nucleation-propagation model  or the nucleation-condensation model , in which the existence of a nucleus facilitates further folding, one can iteratively add a SSE that results in the lowest free energy to the nucleus. Since energy computations can still be slow and can take hours, which account for significant amount of computation time in our algorithm, it is also possible to use lower resolution methods to compute energy.
While our strategy finds the most energetically favorable protein folding pathway, there are evidences that multiple folding pathways exist [5, 57]. The ability to analyze multiple folding pathways will also allow the study of protein misfolding . Our approach can be generalized to study the entire free energy landscape  as follows: construct a graph in which each vertex represents a biologically plausible conformation and each edge represents a feasible conformation change, which is similar to the roadmap graph in  and  and the protein folding network in  except that we consider each SSE as an indivisible unit. Various graph-theoretic algorithms can then be used to generate predictions of alternative folding pathways.
We have shown that our procedure has sufficient accuracy to distinguish between subtle differences and our strategy can be applied to large proteins due to its speed. An important future direction is to consider cooperative folding of secondary structures without too much sacrifice in speed, that is, when folding in one secondary structure affects folding in others.
This work was supported by NSF grant DBI-0624077. We thank Yutu Liu for many helpful discussions and for drawing our attention to the problem.
- Levinthal C: Are there pathways for protein folding? J Chim Phys 1968, 65: 44–45.
- Anfinsen C B, Scheraga H A: Experimental and theoretical aspects of protein folding. Adv Protein Chem 1975, 29: 205–300.View ArticlePubMed
- Kim P S, Baldwin R L: Intermediates in the folding reactions of small proteins. Ann Rev Biochem 1990, 59: 631–660.View ArticlePubMed
- Matthews C R: Pathways of protein folding. Ann Rev Biochem 1993, 62: 653–683.View ArticlePubMed
- Dill K A, Chan H S: From Levinthal to pathways to funnels. Nat Struct Biol 1997, 4: 10–19.View ArticlePubMed
- Gruebele M: Protein folding: the free energy surface. Curr Opin Struct Biol 2002, 12: 161–168.View ArticlePubMed
- Eaton WA, Muñoz V, Thompson PA, Chan CK, Hofrichter J: Submillisecond kinetics of protein folding. Curr Opin Struct Biol 1997, 7: 10–14.View ArticlePubMed
- Nölting B, Golbik R, Neira J L, Soler Gonzalez A S, Schreiber G, Fersht A R: The folding pathway of a protein at high resolution from microseconds to seconds. Proc Natl Acad Sci USA 1997, 94: 826–830.PubMed CentralView ArticlePubMed
- Levitt M: Protein folding by restrained energy minimization and molecular dynamics. J Mol Biol 1983, 170: 723–764.View ArticlePubMed
- Daggett V, Levitt M: Realistic simulations of native-protein dynamics in solution and beyond. Ann Rev Biophys Biomol Struct 1993, 22: 353–380.View Article
- Duan Y, Kollman P A: Pathways to a protein folding intermediate observed in a 1-microsecond simulation in aqueous solution. Science 1998, 282: 740–744.View ArticlePubMed
- Daggett V: Molecular dynamics simulations of the protein unfolding/folding reaction. Acc Chem Res 2002, 35: 422–429.View ArticlePubMed
- Kolinski A, Skolnick J: Monte Carlo simulations of protein folding. I. Lattice model and interaction scheme. Proteins 1994, 18: 338–352.View ArticlePubMed
- Yue K, Dill K A: Folding proteins with a simple energy function and extensive conformational searching. Protein Sci 1996, 5: 254–261.PubMed CentralView ArticlePubMed
- Alm E, Baker D: Prediction of protein-folding mechanisms from free-energy landscapes derived from native structures. Proc Natl Acad Sci USA 1999, 96: 11305–11310.PubMed CentralView ArticlePubMed
- Muñoz V, Eaton W A: A simple model for calculating the kinetics of protein folding from three-dimensional structures. Proc Natl Acad Sci USA 1999, 96: 11311–11316.PubMed CentralView ArticlePubMed
- Amato N M, Song G: Using motion planning to study protein folding pathways. J Comput Biol 2002, 9: 149–168.View ArticlePubMed
- Liwo A, Khalili M, Scheraga HA: Ab initio simulations of protein-folding pathways by molecular dynamics with the united-residue model of polypeptide chains. Proc Natl Acad Sci USA 2005, 102: 2362–2367.PubMed CentralView ArticlePubMed
- Kmiecik S, Kolinski A: Characterization of protein-folding pathways by reduced-space modeling. Proc Natl Acad Sci USA 2007, 104: 12330–12335.PubMed CentralView ArticlePubMed
- Kmiecik S, Kolinski A: Folding pathway of the B1 domain of protein G explored by multiscale modeling. Biophys J 2008, 94: 726–736.PubMed CentralView ArticlePubMed
- Berman H M, Westbrook J, Feng Z, Gilliland G, Bhat T N, Weissig H, Shindyalov I N, Bourne P E: The Protein Data Bank. Nucleic Acids Res 2000, 28: 235–242.PubMed CentralView ArticlePubMed
- Nölting B, Andert K: Mechanism of protein folding. Proteins 2000, 41: 288–298.View ArticlePubMed
- Eyrich V A, Standley D M, Felts A K, Friesner R A: Protein tertiary structure prediction using a branch and bound algorithm. Proteins 1999, 35: 41–57.View ArticlePubMed
- Apaydin M S, Singh A P, Brutlag D L, Latombe J C: Capturing molecular energy landscapes with probabilistic conformational roadmaps. Proceedings of the IEEE International Conference on Robotics andAutomation 2001, 932–939.
- Zaki M J, Nadimpally V, Bardhan D, Bystroff C: Predicting protein folding pathways. Bioinformatics 2004, 20 Suppl 1: 386–393.View Article
- Kabsch W, Sander C: Dictionary of protein secondary structure: pattern recognition of hydrogen-bonded and geometrical features. Biopolymers 1983, 22: 2577–2637.View ArticlePubMed
- Rohl C A, Strauss C E M, Misura K M S, Baker D: Protein structure prediction using Rosetta. Methods Enzymol 2004, 383: 66–93.View ArticlePubMed
- Simons K T, Ruczinski I, Kooperberg C, Fox B A, Bystroff C, Baker D: Improved recognition of native-like protein structures using a combination of sequence-dependent and sequence-independent features of proteins. Proteins 1999, 34: 82–95.View ArticlePubMed
- Song G, Thomas S, Dill K A, Scholtz J M, Amato N M: A path planning-based study of protein folding with a case study of hairpin formation in protein G and L. Pacific Symposium on Biocomputing 2003, 240–251.
- Alexander P, Orban J, Bryan P: Kinetic analysis of folding and unfolding the 56 amino acid IgG-binding domain of streptococcal protein G. Biochemistry 1992, 31: 7243–7248.View ArticlePubMed
- Blanco FJ, Rivas G, Serrano L: A short linear peptide that folds into a native stable β-hairpin in aqueous solution. Nat Struct Biol 1994, 1: 584–590.View ArticlePubMed
- Gallagher T, Alexander P, Bryan P, Gilliland G L: Two crystal structures of the B1 immunoglobulin-binding domain of streptococcal protein G and comparison with NMR. Biochemistry 1994, 33: 4721–4729.View ArticlePubMed
- Blanco FJ, Serrano L: Folding of protein G B1 domain studied by the conformational characterization of fragments comprising its secondary structure elements. Eur J Biochem 1995, 230: 634–649.View ArticlePubMed
- Kim D E, Fisher C, Baker D: A breakdown of symmetry in the folding transition state of protein L. J Mol Biol 2000, 298: 971–984.View ArticlePubMed
- McCallister EL, Alm E, Baker D: Critical role of β-hairpin formation in protein G folding. Nat Struct Biol 2000, 7: 669–673.View ArticlePubMed
- Nauli S, Kuhlman B, Baker D: Computer-based redesign of a protein folding pathway. Nat Struct Biol 2001, 8: 602–605.View ArticlePubMed
- Tunnicliffe R B, Waby J L, Williams R J, Williamson M P: An experimental investigation of conformational fluctuations in proteins G and L. Structure 2005, 13: 1677–1684.View ArticlePubMed
- Islam S A, Karplus M, Weaver D L: The role of sequence and structure in protein folding kinetics: the diffusion-collision model applied to proteins L and G. Structure 2004, 12: 1833–1845.View ArticlePubMed
- Yi Q, Scalley Kim M L, Alm E J, Baker D: NMR characterization of residual structure in the denatured state of protein L. J Mol Biol 2000, 299: 1341–1351.View ArticlePubMed
- Thomas S, Tang X, Tapia L, Amato N M: Simulating protein motions with rigidity analysis. J Comput Biol 2007, 14: 839–855.View ArticlePubMed
- Nauli S, Kuhlman B, Le Trong I, Stenkamp R E, Teller D, Baker D: Crystal structures and increased stabilization of the protein G variants with switched folding pathways NuG1 and NuG2. Protein Sci 2002, 11: 2924–2931.PubMed CentralView ArticlePubMed
- Parker M J, Spencer J, Jackson G S, Burston S G, Hosszu L L, Craven C J, Waltho J P, Clarke A R: Domain behavior during the folding of a thermostable phosphoglycerate kinase. Biochemistry 1996, 35: 15740–15752.View ArticlePubMed
- Kovári Z, Flachner B, Náray Szabó G, Vas M: Crystallographic and thiol-reactivity studies on the complex of pig muscle phosphoglycerate kinase with ATP analogues: correlation between nucleotide binding mode and helix flexibility. Biochemistry 2002, 41: 8796–8806.View ArticlePubMed
- Osváth S, Köhler G, Závodszky P, Fidy J: Asymmetric effect of domain interactions on the kinetics of folding in yeast phosphoglycerate kinase. Protein Sci 2005, 14: 1609–1616.PubMed CentralView ArticlePubMed
- Szilágyi A N, Vas M: Sequential domain refolding of pig muscle 3-phosphoglycerate kinase: kinetic analysis of reactivation. Fold Des 1998, 3: 565–575.View ArticlePubMed
- Li R, Woodward C: The hydrogen exchange core and protein folding. Protein Sci 1999, 8: 1571–1590.PubMed CentralView ArticlePubMed
- Itoh K, Sasai M: Flexibly varying folding mechanism of a nearly symmetrical protein: B domain of protein A. Proc Natl Acad Sci USA 2006, 103: 7298–7303.PubMed CentralView ArticlePubMed
- Nishimura C, Prytulla S, Dyson H J, Wright P E: Conservation of folding pathways in evolutionarily distant globin sequences. Nat Struct Biol 2000, 7: 679–686.View ArticlePubMed
- Lazaridis T, Karplus M: "New view'' of protein folding reconciled with the old through multiple unfolding simulations. Science 1997, 278: 1928–1931.View ArticlePubMed
- Sivaraman T, Kumar T K, Chang D K, Lin W Y, Yu C: Events in the kinetic folding pathway of a small, all β-sheet protein. J Biol Chem 1998, 273: 10181–10189.View ArticlePubMed
- Weissman J S, Kim P S: A kinetic explanation for the rearrangement pathway of BPTI folding. Nat Struct Biol 1995, 2: 1123–1130.View ArticlePubMed
- Zhang J X, Goldenberg D P: Mutational analysis of the BPTI folding pathway: I. Effects of aromatic ➞ leucine substitutions on the distribution of folding intermediates. Protein Sci 1997, 6: 1549–1562.PubMed CentralView ArticlePubMed
- Kazmirski SL, Daggett V: Simulations of the structural and dynamical properties of denatured proteins: the "molten coil'' state of bovine pancreatic trypsin inhibitor. J Mol Biol 1998, 277: 487–506.View ArticlePubMed
- Karplus M, Weaver D L: Protein folding dynamics: the diffusion-collision model and experimental data. Protein Sci 1994, 3: 650–668.PubMed CentralView ArticlePubMed
- Abkevich V I, Gutin A M, Shakhnovich E I: Specific nucleus as the transition state for protein folding: evidence from the lattice model. Biochemistry 1994, 33: 10026–10036.View ArticlePubMed
- Fersht A R: Optimization of rates of protein folding: the nucleation-condensation mechanism and its implications. Proc Natl Acad Sci USA 1995, 92: 10869–10873.PubMed CentralView ArticlePubMed
- Viguera A R, Serrano L, Wilmanns M: Different folding transition states may result in the same native structure. Nat Struct Biol 1996, 3: 874–880.View ArticlePubMed
- Dobson C M: Protein folding and misfolding. Nature 2003, 426: 884–890.View ArticlePubMed
- Rao F, Caflisch A: The protein folding network. J Mol Biol 2004, 342: 299–306.View ArticlePubMed
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.