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Ab Initio Protein Structure Prediction Using Chunk-TASSER

Center for the Study of Systems Biology, School of Biology, Georgia Institute of Technology, Atlanta, Georgia

Correspondence: Address reprint requests to Jeffrey Skolnick, E-mail: skolnick{at}gatech.edu.

	ABSTRACT

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION ACKNOWLEDGEMENTS REFERENCES

 
We have developed an ab initio protein structure prediction method called chunk-TASSER that uses ab initio folded supersecondary structure chunks of a given target as well as threading templates for obtaining contact potentials and distance restraints. The predicted chunks, selected on the basis of a new fragment comparison method, are folded by a fragment insertion method. Full-length models are built and refined by the TASSER methodology, which searches conformational space via parallel hyperbolic Monte Carlo. We employ an optimized reduced force field that includes knowledge-based statistical potentials and restraints derived from the chunks as well as threading templates. The method is tested on a dataset of 425 hard target proteins 250 amino acids in length. The average TM-scores of the best of top five models per target are 0.266, 0.336, and 0.362 by the threading algorithm SP³, original TASSER and chunk-TASSER, respectively. For a subset of 80 proteins with predicted -helix content 50%, these averages are 0.284, 0.356, and 0.403, respectively. The percentages of proteins with the best of top five models having TM-score 0.4 (a statistically significant threshold for structural similarity) are 3.76, 20.94, and 28.94% by SP³, TASSER, and chunk-TASSER, respectively, overall, while for the subset of 80 predominantly helical proteins, these percentages are 2.50, 23.75, and 41.25%. Thus, chunk-TASSER shows a significant improvement over TASSER for modeling hard targets where no good template can be identified. We also tested chunk-TASSER on 21 medium/hard targets <200 amino-acids-long from CASP7. Chunk-TASSER is 11% (10%) better than TASSER for the total TM-score of the first (best of top five) models. Chunk-TASSER is fully automated and can be used in proteome scale protein structure prediction.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION ACKNOWLEDGEMENTS REFERENCES

 
Protein structure is important for understanding protein function as well as being useful in drug design (1,2). To keep pace with current genome sequencing projects as well as to narrow the gap between structure determination and sequence data, computational structure prediction methods are indispensable (3). Protein structure prediction methods can be classified into three categories (4): comparative modeling, fold recognition, and ab initio methods. Comparative modeling and fold recognition methods predict protein structures based on already solved structures (5–13). These template-based methods depend strongly on the recognition of homologous/analogous templates in the Protein Data Bank (14). On the other hand, ab initio methods being template-free can, in principle, predict protein structures without the necessity of identifying a structurally related, solved protein structure.

Ab initio protein structure prediction is not only useful for providing low-resolution structures that help the annotation of protein function (13,15,16), but is also fundamentally important for understanding the mechanism of protein folding (17). While there have been many efforts dedicated to ab initio protein structure prediction, no consistently reliable algorithm is currently available (18–30). In practice, ab initio methods fall into two groups: physics-based and knowledge-based. Methods in the first group fold proteins using only physical principles (30–32). The main obstacles that physics-based ab initio protein structure prediction methods face are the lack of accurate energy functions and the requirement of extensive computational power to find the global minimum of the energy function. Despite their conceptual appeal, this method is currently not as successful as knowledge-based approaches that make use of information from solved protein structures—in particular, knowledge-based potentials (18).

Over the past several years, we have developed the Threading ASSEmbly Refinement (TASSER) methodology (13,33) for automated tertiary structure prediction that generates full-length models by rearranging the continuous fragments identified by threading. It is a kind of hybrid method that has the capacity to do template-free as well as template-based modeling. TASSER can significantly refine the initial template alignment structures provided by threading methods (33). Furthermore, TASSER has some success in modeling template-free targets of small sizes when decoupled from threading templates (34). In this work, we develop a variant of the TASSER methodology called chunk-TASSER that utilizes consensus contacts and distance restraints from ab initio folded protein chunks of supersecondary structure in addition to information extracted from threading templates. Modeling of protein chunks is much more efficient than full-length modeling in that the sampling space is much smaller, and thus large proteins can be handled. However, it does tend to favor global topologies of lower contact order. The method is assessed on a large set of 425 effectively hard targets 250 residues in length where the structure of the closest identified template is at best weakly related to that of the target. The results are compared to the SP³ threading method (35,36) and the original TASSER approach (13,33). Significant improvement of chunk-TASSER over both SP³ and TASSER is observed for these hard targets. We also tested chunk-TASSER on 21 CASP7 targets <200 residues in length that our threading algorithm classified as medium/hard targets.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION ACKNOWLEDGEMENTS REFERENCES

 
Fig. 1 shows the flow chart of chunk-TASSER. It consists of threading and fragment library generation by the SP³ method (35,36), ab initio folding of chunks and chunk model selection, TASSER (33) full-model assembly using contact potentials and distance restraints extracted from selected chunks, threading templates that also provide the initial starting structure, and final model selection.

View larger version (53K): [in this window] [in a new window]   FIGURE 1  Flowchart of chunk-TASSER.

Another change made to SP³ that increases its sensitivity is the inclusion of profiles generated by PSIBLAST with a looser e-value cutoff of 1.0. To the target sequence, the sequence profile is replaced by the average of two profiles with e-value cutoffs 0.001 and 1.0, and to the templates, the structurally derived profile is replaced by the average of original and the PSIBLAST profile with an e-value cutoff of 1.0.

We extend the SP³ threading method to compute local sequence similarity by computing and recording the alignment score at each query sequence position aligned to each template during threading. The position-dependent score is then smoothed by averaging over a nine-residue sliding window. For each position, nine-residue-long fragments of the top 25 scored templates are selected to form the fragment library for the ab initio folding of chunks (18).

Ab initio folding of chunks and chunk model selection
Chunks are defined as three consecutive regular secondary structure (helix or strand) segments including their enclosed two loops. The total number of chunks for a given target is N_segment – 2, where N_segment is the number of regular secondary structure segments. Chunk structures are predicted independently by a fragment insertion method as in Simons et al. (18) but with our own implementation and force field. Each residue is described by its main chain atoms (N, C, C, O), C_ß atom, and side-chain center of mass. The force field contains the following terms:

1. The DFIRE-all atom distance-dependent pairwise statistical potential for main chain and C_ß atoms (38).
   
2. The distance-dependent pairwise statistical potential DFIRE-SCM for the side-chain center of mass (39).
   
3. The TASSER hydrogen-bond term based on C coordinates (29).
   
4. An excluded volume term for the main chain and C_ß atoms.
   

The description of DFIRE-based terms 1 and 2 are published elsewhere (38,39). The relative weight of terms 1 and 2 is set to one, since they are based on the same principle and procedure.

For the TASSER hydrogen-bond term, only main-chain hydrogen bonds are considered, and they are dependent on the C coordinates by (29)

(1)

where u_i and v_i are unit vectors defined by the C coordinates: l_i = r_i,i+1/|r_i,i+1|, u_i = (l_i-1 – l_i)/|l_i-1 – l_i|, v_i = u_i x l_i/| u_i x l_i|, where r_i,i+1 is the C -C bond vector from residue i to i+1. The terms u_i · u_j and |v_i · v_j| impose a bias to a specific C -C bond vector orientation of regular H-bonds. The expression _i,j defines the conditions when residue i is hydrogen-bonded to residue j:

(2)

H-bond formation also depends on the predicted secondary structure: H-bonds between residues in strand and helix are prohibited. Here, is a stiffness modulation factor that is used to enhance the H-bond in the better-assigned secondary structure regions. It is set to 1.5 if a regular helix or strand structure is predicted; otherwise, it is set to 1.0. We shall optimize the relative weight w_HB of this hydrogen-bond term relative to the other three terms.

The excluded volume term 4 is defined as

(3)

where r is the distance between two atoms and r₀ is an atom-type-dependent minimal-allowed distance of two atoms taken from Ramachandran and Sasisekharan (40). Its relative weight to DFIRE terms is set to one, since its weight is not as important as whether it is included or not in the force field.

Monte Carlo (MC) simulated annealing is used to sample chunk structure conformations with a fragment insertion method (18) for ab initio chunk model prediction. Initially, a structure with random main-chain torsional angles is built. At each step in the MC procedure, a residue is randomly selected and then a nine- or three-residue-long fragment corresponding to the picked residue is randomly selected from the 25 fragments in the library obtained by the above-described chunk fragment generation procedure and inserted into the position by substituting the backbone torsional angles with those from the fragment. A new conformation is accepted or rejected according to the canonical Metropolis protocol.

The usual way of selecting models that are closer to native from a set of decoys generated by ab initio approaches is to cluster the models and select the most populated clusters. The success of a clustering method depends on the fact that lower free energy conformations are closer to native than higher ones. Since chunk models are not full protein models, this free energy condition may not be satisfied. Therefore, we developed and tested an alternative way of selecting chunk models that uses the information from the fragment library used for conformational sampling. The score E_chunk for ranking chunk models is

(4)

where E_frg is calculated by the following fragment comparison method: For each residue position in the chunk model, a nine residue fragment with the given residue in the middle (less in the N- or C-terminus, for example: the fragment for the first residue will be residues 1–5, the fragment associated with the second residue considers residues 1–6, ..., the fifth residues 1–9, ..., and the last residue, residues (N_r-4) – N_r with N_r being the last residue) is compared with the 25 corresponding fragments in the fragment library by their root mean-square deviation (RMSD). E_frg is the average RMSD over the 25 fragments and over all chunk-residue positions. The value w_d is the relative weight of the two terms and will be optimized. E_dfire is the DFIRE energy (38). N_r is the residue length of the chunk model. Models are ranked by their E_chunk score, and those with lower scores are selected.

Full-length model assembly by TASSER and final model selection
TASSER (13) represents a protein by a C and side-chain center of mass representation in both off- and on-lattice space. The initial full-length model is built by connecting the continuous template-provided fragments (off-lattice building blocks) by a random walk confined to lattice bond vectors. If the specified number of unaligned residues cannot span the gap, a long C-C bond remains, and a springlike force draws sequential fragments together until a physically reasonable bond length is achieved. Parallel hyperbolic Monte Carlo (MC) sampling (41) with replica exchange explores conformational space by rearranging the continuous fragments excised from the template. During assembly, the template fragments are kept rigid and off-lattice to retain their geometric accuracy; unaligned regions are modeled on a cubic lattice by an ab initio procedure and serve as linkage points for rigid body fragment rotations. Conformations are selected using an optimized force field which includes knowledge-based statistical potentials describing short-range backbone correlations, pairwise interactions, hydrogen bonding, secondary structure propensities, consensus C and side-chain center of mass contacts, and short and long distance restraints for C atoms. TASSER obtains these sequence-specific contact potentials and distance restraints from threading templates and/or fragments. The complete details of the TASSER force field are given in the literature (13,29) and references therein. Here, we give the contact potential and distance restraint terms that are relevant to this study. The contact potential between the C atoms or side-chain centers of mass is calculated as

(5)

where (x) and (x) are step functions defined as

(6)

and where p_ij is the probability of the i^th residue C or side-chain center of mass in contact with that of the j^th residue obtained from threading templates/fragments, and r_ij is the distance between residues i and j. The value p⁰ defines the minimal probability that two residues are predicted to be in contact and 6 Å is the distance cutoff for contacting residues. The first term in Eq. 5 favors pairs predicted as being in contact that are within 6 Å, whereas the secondary term penalizes predicted contact pairs that are farther apart than 6 Å when the total violation exceeds a threshold value of N_cp.

Local distance restraints for C atoms with a less-than-six-residue sequence separation are collected from the threading templates/fragments. They are incorporated into the force field by

(7)

where |j–i|<6, d_ij is the predicted average distance between the i^th residue and j^th residues, and _ij is the root mean-square deviation of the predictions. The second term in Eq. 7 is a penalty when the cumulative normalized deviations to the predicted distance map exceeds the number of predictions N_dp.

Long-distance restraints for C atoms are calculated in the force field as

(8)

where |j–i| > 6, N_ij is the number of distance predictions between the i^th and j^th residues extracted from the templates/fragments, and d_ij(k) is the k^th distance prediction of the i^th and j^th residues.

The weights w_r1, w_r2, w_r3, w_r4, and w_r5 as well as those of other terms in TASSER not described above were optimized against a set of nonredundant decoys (29).

Chunk-TASSER uses ab initio folded chunks as well as threading templates/fragments for consensus contact potentials and distance restraint predictions. In this study, the top 10 (ranked by SP³ Z-scores) threading templates and the top five chunk models for each chunk are included in the prediction of contact probability and distance restraints. Contacts and distance pairs from selected threading templates and chunk models are counted with equal weights in the prediction. For example, if there are n₁ distance pairs from templates and n₂ pairs from chunk models between residue i and j, the total distance pairs for residue i and j is (n₁ + n₂); and if there are n₃ pairs within 6 Å (in contact), then the contact probability p_ij in Eq. 5 will be n₃/(n₁+ n₂). When p_ij > p⁰ = 0.3, we consider residues i and j to be involved in a real contact in the native structure, and the contact potential is effective in Eq. 5. The threading templates/fragments also serve as starting structures in the chunk-TASSER simulation as they do in TASSER. Therefore, the only difference between chunk-TASSER and TASSER is that chunk-TASSER has contact and distance information from the selected ab initio folded chunks whereas TASSER does not. The final full-length models are selected by clustering the low energy trajectories (containing 16,000 energies) using SPICKER (42).

Benchmark sets and parameter optimization
Benchmarking structures were randomly picked from the Protein DataBank released between May 28, 2004 and September, 2005. The threading library used structures deposited before May 28, 2004. All structures share <35% sequence identity with each other. No resolution and domain number requirements are imposed on these sets other than they are single-chain structures and that the predicted number of chunks 1. In optimizing the parameter w_HB (the relative weight of the TASSER hydrogen-bond term in folding chunks) and w_d (the relative weight of the DFIRE energy term used in ranking the chunk models), we used 60 structures (optimization set) that share <35% sequence identity with the 425 testing structures 250 amino-acid (AA)-long (testing set). Lists of these two sets can be found at http://cssb.biology.gatech.edu/chunk-TASSER.

To make the optimization set and testing set effectively hard targets, all structures with a TM-score (43) 0.4 to each target are removed from the threading library (44). We optimized the parameters to maximize the total TM-score of the top five selected chunk models on the 60-protein set. The optimization procedure is done iteratively by fixing one and changing the other. For example, we set an initial value for w_HB, then let w_d change within a range of 0–0.1; next, we set w_d to its optimal value and let w_HB change within 0–5, etc. The procedure is iterated until the optimal values of w_HB and w_d do not change. The resulting parameters are (w_HB, w_d) = (0.5, 0.01). For a realistic small-scale test, we used 21 medium/hard targets <200 AA long from CASP7 with threading library structures and sequence database released before the CASP7 season.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION ACKNOWLEDGEMENTS REFERENCES

 
Chunk model selection procedure
For each target, a total of 5000 chunk models were generated regardless of the number of chunks (N_chunk) the target has, i.e., the number of models per chunk is 5000/N_chunk. This makes the time needed to generate chunk models about the same for all targets. For a typical 150-AA-long target, it takes 75 CPU hours on a dual core 2.0 GHz Opteron CPU to generate 5000 chunk models (1 model/min). This can be easily distributed to several independent computers. To test how accurate the models are when chunks are included into TASSER, we select the top five best chunk models according to their RMSD to native in combination with the top 10 threading templates (selected according to threading Z-score) to construct contact potentials and distance restraints for chunk-TASSER to build full length models. The cumulative TM-score of chunk-TASSER on the 425 testing set proteins in this ideal scenario is shown in Table 1. The average TM-score of the best of top five SPICKER (42) cluster full-length models is 0.407. Approximately half of the targets have models with TM-scores 0.4 to native structure.

1. Top five best chunk models.
   
2. Top five chunk clusters selected by SPICKER (42).
   
3. Top five chunk models selected by E_chunk.
   
4. Top 10 chunk models selected by E_chunk.
   

View larger version (14K): [in this window] [in a new window]   FIGURE 2  Examples of chunk ranking score Echunk versus chunk RMSD to native. (a) 1wiia chunk 1, covering residues 34–59. (b) 1sumb chunk 2, covering residues 38–137.

View larger version (10K): [in this window] [in a new window]   FIGURE 3  Comparison of the prediction results by TASSER and chunk-TASSER on the 425-protein set. Shown in the plot is the number of proteins having models with TM-score greater than the given threshold versus the TM-score threshold.

View larger version (10K): [in this window] [in a new window]   FIGURE 4  Comparison of the TM-scores obtained from chunk-TASSER and TASSER on the 80 -proteins.

View this table: [in this window] [in a new window]   TABLE 4  TM-scores of first (best of top five) models by SP3, TASSER, ROSETTA (15,18), and chunk-TASSER for the 21 CASP7 targets

View larger version (26K): [in this window] [in a new window]   FIGURE 5  Representative predictions by chunk-TASSER. Models are superimposed onto the native structure with thick lines representing models and thin lines natives. Numbers in parentheses are TM-scores of the models to native.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION ACKNOWLEDGEMENTS REFERENCES

Although chunk-TASSER shows significant improvement over original TASSER for hard targets, there is still much room for further improvement as indicated by the big gap between the realistic scenario 3 and the ideal scenario 1 (see Table 1). The current chunk model selection procedure is far from satisfactory. Further improvement can be achieved by more accurate selection of chunk models and generation of more near-native chunk models. As in TASSER, improvement can also be gained through more sensitive template identification from the structure library or from other modeling approaches. For example, using an approach like iterative TASSER (49,50), one can use the models from a first round of chunk-TASSER modeling in a second round of chunk-TASSER. This possibility of improvement is currently under investigation. Since chunk-TASSER, like TASSER, models a protein only in terms of its C atoms and side-chain centers of mass, its accuracy is limited by the force-field resolution (1.5 Å). Therefore, development of methods to refine chunk-TASSER models and to rebuild the finer structural details using full atomic potentials is also needed.

Recently, our laboratory has developed the TASSER-Lite algorithm (51) that implements a limited time TASSER simulation. The algorithm was used in MetaTASSER (unpublished) that participated in CASP7 and was among one of the top performing servers. We are currently investigating a similar strategy for chunk-TASSER that will facilitate its public use.

	ACKNOWLEDGEMENTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION ACKNOWLEDGEMENTS REFERENCES

 
We thank Dr. Adrian Arakaki for help in preparation of the figures.

This research was supported in part by grant Nos. GM-37408 and GM-48835 of the Division of General Medical Sciences of the National Institutes of Health.

	FOOTNOTES

 
Editor: Jose Onuchic.

Submitted on March 30, 2007; accepted for publication May 9, 2007.

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