Predicting protein folding pathways at the mesoscopic level based on native interactions between secondary structure elements
© Yang and Sze. 2008
Received: 05 April 2008
Accepted: 23 July 2008
Published: 23 July 2008
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© Yang and Sze. 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 t 0 s 1 t 1⋯s k t k , where k is the number of SSEs, s i denotes the ith SSE, t j denotes the jth 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 s j+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.
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 .
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: α 1 β A4 α 2 α 3 β A3 α 4 β A1 α 5 β A2 α 6 β B1 β B2 α 7 β A5 α 8 α 9 β A6 α 10 β C3 α 11 α 12 β C2 α 13 α 14 α 15 β C1 β D2 β D1 β D3 α 16 β C4 α 17 α 18 β C5 α 19 β C6 α 20 α 21.
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, α 2 and α 3 interact first, then α 1 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, α G, α H, and part of α E form stable structures first, while α A and α B form in the later stages of the folding pathway. For myoglobin, α A, α G and α H form stable contacts first. The main difference between the two folding pathways is that α A and α B 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, α G and α H are predicted to interact first, then α E is added, with α B and α A added later. For myoglobin, α G and α H are also predicted to interact first, then α A is added, followed by α E and α B.
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 β 1 α 1 β 2 β 3 β 4 in 1COA and β 1 α 1 β 4 β 3 β 2 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 β 2 and β 3 form contacts first, then α 1 is added to form a folding nucleus. The coalescence of β 1 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 β 2, β 3 and α 1 form contacts first. Our prediction is consistent with these results.
The all β-sheet protein cardiotoxin III (PDB: 2CRT) consists of five strands. While β 1 and β 2 form a double-stranded domain, β 3, β 4 and β 5 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 β 3 and the amide groups in β 5 form hydrogen bonding partners, which are important for the formation of a hydrophobic cluster . Our prediction is consistent with these results, with β 3 and β 5 interacting first, then β 4 is added to form the triple-stranded domain, followed by β 2 and β 1 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 α 1 β 2 β 1 β 3 α 2. 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, β 1 and β 2 interact first, then α 2 is added. This brings residues 30 and 51 close together and helps to form the disulfide bond between them. Then α 1 is added and this helps to form the disulfide bond between residues 5 and 55, and 14 and 38. Our prediction that β 1 and β 2 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.
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.