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Proc Natl Acad Sci U S A. Nov 10, 2009; 106(45): 18978–18983.
Published online Oct 28, 2009. doi:  10.1073/pnas.0904407106
PMCID: PMC2770007
Biophysics and Computational Biology

Simultaneous prediction of protein folding and docking at high resolution


Interleaved dimers and higher order symmetric oligomers are ubiquitous in biology but present a challenge to de novo structure prediction methodology: The structure adopted by a monomer can be stabilized largely by interactions with other monomers and hence not the lowest energy state of a single chain. Building on the Rosetta framework, we present a general method to simultaneously model the folding and docking of multiple-chain interleaved homo-oligomers. For more than a third of the cases in a benchmark set of interleaved homo-oligomers, the method generates near-native models of large α-helical bundles, interlocking β sandwiches, and interleaved α/β motifs with an accuracy high enough for molecular replacement based phasing. With the incorporation of NMR chemical shift information, accurate models can be obtained consistently for symmetric complexes with as many as 192 total amino acids; a blind prediction was within 1 Å rmsd of the traditionally determined NMR structure, and fit independently collected RDC data equally well. Together, these results show that the Rosetta “fold-and-dock” protocol can produce models of homo-oligomeric complexes with near-atomic-level accuracy and should be useful for crystallographic phasing and the rapid determination of the structures of multimers with limited NMR information.

Keywords: homo-oligomers, molecular replacement, NMR structure inference, protein structure prediction, symmetry

The majority of expressed proteins function within symmetrical homomeric complexes (13). Although a boon for evolving functional diversity (4), this ubiquity of oligomeric structures poses numerous challenges for modern structural biology. The phasing of crystallographic data by molecular replacement and NMR structural inference are complicated by the increasing number of degrees of freedom and spectral degeneracy, respectively, in multimeric systems. The ability to predict de novo the structures of multiple interacting molecular chains would potentially alleviate these problems, allowing unphased diffraction measurements or ambiguously assigned NMR spectra to be resurrected as constraints or as independent validation for in silico structural inference.

Accurate modeling of previously unseen homomeric structures has not been demonstrated at high resolution. Significant progress has occurred in modeling the folds of individual monomeric soluble proteins (57) and the docking arrangements of predefined monomers (8, 9). However, as proteins interact with other proteins, nucleic acids, or smaller molecules, their lowest free-energy backbone conformations typically shift in response to their partners. These often dramatic structural changes have been a persistent and unsolved issue in blind prediction trials of recent years (8).

In this report, we show how two different methods developed for de novo conformational sampling (for folding and for docking) can be melded into a more general procedure that permits the blind prediction of intertwined complexes of proteins at near-atomic resolution. Some of the test systems involve up to several hundred residues, much larger than previous targets of high-resolution de novo modeling; symmetry plays a crucial role in reducing the number of degrees of freedom that need to be sampled. The new approach is based on the Rosetta framework for molecular modeling (10).

Results and Discussion

Overview of Rosetta “Fold-and-Dock” Protocol.

For each molecular complex, we start from fully extended monomer chains in randomly generated symmetric rigid body arrangements (Fig. 1). The first of two stages of automated de novo modeling alternates sets of fragment insertion moves that perturb the backbone conformation of protein monomers (11) with moves that perturb the symmetric docking arrangement of the monomers (12). The conformational energy is determined by the low-resolution energy function previously developed for monomer protein structure prediction (6, 11) with coarse-grained terms for backbone hydrogen bonds and hydrophobic interactions. Cyclic or dihedral symmetry is maintained by cloning the moves to separate monomers, and each move is accepted or rejected based on the standard Metropolis criterion (12). In the second, high-resolution refinement stage, side chains are built into the backbone conformations in all-atom detail, and small, symmetric perturbations are tested in the context of a reasonably accurate, high-resolution energy function that includes van der Waals interactions, the costs of desolvating atoms, and hydrogen bonds (Fig. 1) (10, 13). The lowest energy models are then clustered, and the five most populous clusters are compared with the experimentally determined structures.

Fig. 1.
Overview of the Rosetta fold-and-dock protocol. Starting with extended protein chains, the protein complex is assembled through alternating cycles of fragment insertions, which change the internal coordinates of the monomer, and rigid body perturbations ...

We first tested the fold-and-dock protocol on a benchmark set of 27 protein complexes with structures previously determined by high-resolution crystallography. Most of these molecules form intertwined structures in which the number of intermolecular contacts approaches one third of the number of intramolecular contacts (Table 1). We have assumed that the stoichiometry of the crystallized complex is known (as can be rapidly ascertained experimentally by, for example, analytical ultracentrifugation), but tested all possible symmetries available to a fixed number of monomers. For example, tetramer complexes were modeled with both D2 and C4 symmetries.

Table 1.
Result of the fold-and-dock protocol on a benchmark of protein complexes solved by crystallography and NMR

Benchmark of Homo-Oligomeric Proteins Solved by X-Ray Crystallography.

Initial tests were carried out on coiled coil structures with simple cyclic geometries as well as more complex dihedral symmetries. These molecules include biologically important complexes such the trimeric coiled coil region of coronin-1 (C3; Fig. 2B) and engineered helical proteins with dihedral symmetry (D2; Fig. 2K).

Fig. 2.
High-resolution structure prediction using the fold-and-dock protocol. (A–I) Comparison between native crystal structure (Left) and most accurate of the five models selected by clustering of the low energy models (Right); PDB ID, 2zta (A); 2akf ...

In each of these cases, at least one of the five most populous clusters produced by the symmetric folding and docking of multiple chains achieves a backbone accuracy approaching 2 Å or better (Cα rmsd; Table 1). Also, in each of these cases, the fine details of hydrophobic side-chain packing are reproduced with near-atomic accuracy (Fig. 2 A–D). As a further, blind test of the method, we predicted the structure of a Golgi-associated coiled coil region (14) whose atomic coordinates were released after our modeling trials. The crystal structure and the single Rosetta dimer prediction agree with a Cα rmsd of 0.94 Å (Fig. 3A). These results demonstrate that the basic principles underlying Crick's “knobs-into-holes”-based manual modeling (15, 16), more constrained conformational searches (17), and other phenomenological rules (18) for the simplest coiled coils can be automatically and quite generally applied to the de novo modeling of complex symmetric helix interaction motifs.

Fig. 3.
High-resolution structure prediction using the fold-and-dock protocol. (A) Blind prediction of the structure of a Golgi-associated coiled coil region (PDB ID 3bbp). Red and green crystal structure, white blind prediction. (B–E) High-resolution ...

Although helical coiled coils have partly stereotyped conformations, the generality of our method allows it to be applied to symmetric complexes with nonstereotyped folds. Thus, we included in the benchmark set targets with intermolecular beta-strand pairings or helix–loop–helix segments. The cases for which fold-and-dock modeling achieved high-resolution models included not only noncanonical helical bundles (Fig. 2G), but also an all-beta protein (Fig. 2H) and mixed alpha-beta proteins including the p53 tetramerization motif (Fig. 2E). Overall, 11 of the 27 tested molecular complexes gave high-resolution Rosetta models with better than 3-Å backbone accuracy over the full oligomer (Table 1). Further tests demonstrated the importance of simultaneously modeling the folds of chains along with their docking arrangement. In 9 of the 11 cases, the protein fold could not be predicted if the monomer sequence was modeled alone (Table 1).

With more than one third of the tested complexes leading to near-atomic resolution models, the rate of success in the benchmark is similar to what is achievable for small monomeric proteins (5, 10). In the cases for which the fold-and-dock method produced high-accuracy models, the extent of convergence of the lowest energy models is a good predictor of model accuracy. For example, there are 10 cases in the benchmark (Table 1), in which at least 40 of the lowest 400 energy models are within 2 Å of each other; nearly all (9 of 10) cases result in high-accuracy models. Perhaps the strongest parallel with previous efforts in modeling biomolecule structures can be drawn from the examples in which the present protocol fails (Table 1). In the majority of these cases (11 out of 16), the energy of the native conformation is lower than the energies achieved with the present level of computational sampling; also, the accuracy of the sampled models is beyond the 2- to 3-Å radius of convergence required to robustly discriminate native-like conformations (8 out of 16 do not sample a single structure better than 3 Å) (Table 1; Fig. S1) (5, 10). Systems with the largest number of degrees of freedom were the most difficult; our protocol failed in all eight cases in which the number of monomer residues exceeded 60. As with the separate problems of monomer structure modeling and docking of prestructured monomers, conformational sampling appears to be the major bottleneck in the simultaneous modeling of the folding and docking of symmetric complexes.

Estimating Phases for Molecular Replacement from High-Resolution Models.

The benchmark tests described above suggest that predicting the structure of multimeric proteins from sequence is an attainable goal. We further tested whether this de novo method might have a practical impact on modeling problems commonly encountered in experimental structural biology. One stringent test of the modeling procedure is its ability to provide estimated phases for X-ray crystal diffraction data of the protein of interest via molecular replacement (19, 20). Idealized and simplified multimeric helix assemblies (21, 22) have indeed allowed recent phasing of diffraction datasets, although these efforts have relied on high-throughput screens of hundreds of stereotyped backbone-only conformations. The high-resolution Rosetta models presented in this study offer the possibility of phasing diffraction datasets for nonstereotyped multimeric complexes.

For 24 of the 28 test cases, crystallographic structure factors were publicly available and permitted molecular replacement trials with the Phaser software. Trials with the lowest energy structures derived from de novo modeling of individual chains led to only one case of unambiguous molecular replacement (Table S1). In contrast, the lowest energy models obtained by simultaneous modeling of the fold and docking arrangement gave phasing successes for 10 of these 24 datasets (Table S1), and enabled automated coordinate building for the majority of crystallized residues, using the ARP/wARP software package (23). Thus, as above, it was critical to simultaneously model the folds of chains along with their docking arrangement.

Inference of Oligomeric Protein Structure from Chemical Shift Data.

As a final test, we applied the Rosetta fold-and-dock method to a difficult problem in NMR structural inference, the modeling of homo-oligomers using limited data. Experimental collection and assignment of distance constraints necessary for structure calculation remains a time-consuming and laborious task. The process is further complicated for homo-oligomers; spectral symmetry renders intra and intermolecular distance constraints indistinguishable. Specialized experiments have been developed to distinguish the two types of data, but these techniques require the preparation of mixed isotopically labeled samples, and typically yield only a few intermolecular constraints. To address this problem, we built on recent findings that NMR structure determination of monomers can be greatly accelerated by coupling de novo modeling with backbone chemical shift data without further NOE, scalar coupling, residual dipolar coupling (RDC), or isotope-edited measurements (24, 25). The structure of a dimeric complex was recently predicted from models of monomeric components generated using chemical shift fragments (26). We brought together the chemical-shift-derived fragment method with our symmetric folding-and-docking method to model eight complexes under investigation by the Northeast Structural Genomics consortium (NESG; Table 1). The set contains proteins with all-α, α/β, as well as all-β secondary structure in the range of 44 to 96 residues per monomer. Models were ranked based on a sum of the all-atom energy and a chemical shift score, which measures how well chemical shifts estimated from the models agree with the experimental values (25). The single model with lowest value of this combined score is taken as the prediction (Table 1 and Fig. 3; Fig. S2).

In six of the eight cases, the lowest energy Rosetta model had near-atomic accuracy (<3-Å Cα rmsd) (Fig. 3 B–D; Fig. S2). The overall rate of success (75%) is higher than the crystal structure benchmark described above (41%), due to enhanced conformational sampling with higher quality chemical-shift-derived fragments. The most remarkable result is seen for the protein HR2106, a mixed α/β protein with a total of 192 residues, resulting in a 1.7-Å model (Fig. 3D). This topologically complex protein is significantly larger than previous reported successes of chemical-shift-aided protein modeling (24, 25).

Blind Prediction of NMR Structures.

For two of the NMR targets, blind predictions were made before NMR structures were released. First, significant convergence was not observed in the modeling of 2k7i, a complex of two 62-residue chains, suggesting that blind prediction would be inaccurate (Fig. S2). Five models were instead selected based on a combination of the all-atom energy and the chemical shift score. The third of these models is quite accurate, giving an rmsd of 3.0 Å (2.7–3.3 Å over the 20 conformers) over secondary structure elements compared with the model obtained with the complete NMR data (Fig. 3E). We investigated whether this quite good model could be distinguished using experimentally measured residual dipolar coupling (RDC) data, which provide orientational information useful for validating NMR structures (27). The correlation between measured and back-calculated residual dipolar couplings (the quality(Q)-factor (28)) was determined for each of the five models, and the third model indeed fit the data the best (Q-factor of 1.06, 1.41, 0.55, 0.73, and 1.03, respectively, for these five models). Thus, additional data can make possible accurate structure determinations when convergence is too poor for the correct structure to be unambigously identified (Fig. S3A).

The second blind NMR test case, for a slightly smaller complex, produced even more striking results. Modeling runs for the protein 2k5j, a complex of two 44-residue (number of structured residues) chains, gave outstanding convergence, with 52 of the 200 lowest energy models within 1.0-Å Cα rmsd of each other, suggesting that the modeling had reached near-atomic accuracy. Indeed, when compared with 20 NMR conformers determined subsequently and independently using a full suite of 2136 NOE constraints (Fig. 3F), the lowest energy Rosetta model achieved an accuracy of 0.79–1.20 Å over all modeled residues, and 0.79–1.09 Å over the secondary structure elements. Despite making use of far less data, the Rosetta model achieves equally good agreement with RDC data compared with the model obtained with the traditional NMR method (Q-factors of 0.36 for the lowest 10 energy models versus 0.38 for 10 first conformers, respectively) (Fig. 3G; Fig. S3B). The RDC comparison suggests that even higher accuracy might be achievable if RDC data are used for fold-and-dock refinement rather than just validation (29); Rosetta models with quality factors as low as 0.24 are present in the generated pool of models (Fig. S3B). Based on these and previous results, chemical-shift-based Rosetta has become an integral part of the NESG high-throughput structure determination pipeline for multimers (30). A third blind prediction of a dimeric structure was validated as this paper went to press. The predicted (lowest energy) structure, a non-intertwined monomer, had a backbone rmsd of 0.8 Å to the subsequently determined crystal structure. This illustrates that the method can produce excellent models for non-intertwined as well as intertwined oligomers–whether the lowest energy structure is intertwined or not is a function of the amino acid sequence, and need not be specified in advance.


We have demonstrated that simultaneous prediction of the fold and docking arrangement for protein complexes with many different symmetries and modest monomer sizes is feasible at high resolution. Further applications of the presented method can be envisioned in conjunction with experimental techniques beyond crystallography and NMR spectroscopy. First, large symmetric complexes are common targets of cryoelectron microscopy. Attaining high-resolution models from these low-resolution data may be possible by incorporating density maps into the conformational search. Second, oligomeric membrane complexes, which have been difficult to characterize experimentally, are attractive targets for the method. Many physiologically important channels and transporters are in a suitable size range for the protocol described here, and chemical cross-linking and accessibility data may provide rapid validation of high-resolution models. Last, the techniques described here, when coupled to existing design algorithms, provide a computational foundation for rationally engineering proteins that self-assemble into symmetric containers, fibrils, and channels of new and useful function.

Materials and Methods

The computational protocol developed in this work builds on previously described methods for de novo (5) and symmetrical protein assembly (12) structure prediction in Rosetta.

Description of Symmetry.

The computational setup used previously in Rosetta to dock already folded monomeric structures into symmetric homo-oligomers has been described previously (12); in this previous work the internal backbone coordinates of each monomer were held fixed. This approach works for non-interleaved homo-oligomers but in general will fail for interleaved structures as the structure of the monomer depends strongly on interactions with other subunits. Here, we have retained the basic framework for modeling symmetric structures while adding in full backbone flexibility to allow monomers to fold up in the context of symmetrically related copies of themselves. During the simulations, backbone, side chain, and rigid body degrees of freedom are all varied. Backbone symmetry is enforced by maintaining identical bond angles, bond lengths, and torsion angles in symmetry-related partners in the system. Side chains are placed using two different methods; combinatorial and one-at-a-time noncombinatorial optimization (31, 32) using a backbone-dependent rotamer library (33). Rotamers are simultaneously inserted into all symmetry related partners of the system, and the energy of the full symmetrical oligomer is evaluated (12, 32). The most straightforward manner to describe rigid body symmetry is to maintain a global reference coordinate system and use symmetry transforms to find the coordinates of symmetry-related partners in the system. This system leads to difficulties in describing complex symmetries and to perform gradient based minimization. Instead, in Rosetta, each symmetry-related partner maintains its own reference coordinate systems that are in themselves related by symmetry. In this setup, the symmetry-related partners have identical coordinates, but in their own reference frames. During the simulation protocol, only rigid body degrees of freedom that maintain symmetry are allowed to vary. The nature of these perturbations depends on the type of symmetry that is simulated. In this work, two types of symmetries are used, cyclic and dihedral symmetry; complete descriptions of the samples degrees of freedom are given in Fig. S4.


For larger oligomers, it is unnecessary to explicitly simulate the whole systems, because a smaller subsystem can describe all of the interactions in the system if interactions at very long distances are ignored. The minimal number of monomers that explicitly needs to be simulated is equal to the number of different interaction surfaces between subunits in the system. To avoid edge effects, the smallest subsystem is a single monomer with all directly neighboring subunits present, and the total energy is calculated as a multiple of the energy of the central monomer.

Energy Function.

The energy function in the low-resolution search is a linear combination of mostly knowledge-based terms modeling residue-environment and residue-residue interactions, secondary structure packing, chain density, and excluded volume (34). The high-resolution energy function is composed of a Lennard–Jones potential to model side-chain packing, an orientation-dependent hydrogen bond term parameterized from quantum mechanics (35) and analysis of high-resolution structures (36), the Lazaridis–Karplus implicit solvation model (37), pair-interaction terms modeling long range electrostatics, a side-chain torsional potential derived from the Dunbrack backbone-dependent rotamer library (33), and backbone torsional potential dependent on secondary structure and amino acid type. Detailed description of the energy terms can be found in Rohl et al. (13) and in supporting information in Kuhlman et al. (38).

Conformational Search Protocol.

The initial state of the simulated system is generated with random rigid body degrees of freedom and the subunit backbones in extended conformations. The protocol starts with a low-resolution symmetrical fragment insertion where torsion angles of randomly selected 3 or 9 residue fragments in the protein chains are replaced with torsion angles from nonhomologous proteins with known structure (6); 40,000 fragment insertions attempts are made. At every 1 in 10 fragment insertions, the rigid body of the protein chains are adjusted using two type of moves: random perturbations (translation/rotation) and sliding of subunits into atomic contact (translation). In the random perturbation step, the subunits are randomly and symmetrically rotated or translated up to 5° or 0.5 Å, respectively. In the sliding step, the subunits are translated into atomic contact along the symmetry axis of the system. In the case of dihedral symmetry, the subunits are consecutively translated into atomic contact along the different symmetry axis in a randomly selected order. Fragment and rigid body moves are accepted based on the Metropolis criteria.

The models produced by the low-resolution protocol are energy minimized using an all-atom Monte Carlo Minimization protocol as previously described (5). A number of different symmetrical moves are used in the refinement: small random perturbation of backbone torsion angles, one-at-a-time (noncombinatorial) rotamer optimization using a backbone-dependent rotamer library (33), gradient-based minimization of the backbone, and side chain degrees of freedom and insertion of nonperturbing three or nine residue fragments. In addition to these moves, random rigid body perturbations were also incorporated into the protocol.

The 2 × 104 to 5 × 106 models were generated using Rosetta@home, and the 400 lowest energy models were clustered based on rms similarity to select the best models. As in previous work (6), modeling runs that did not pass 50th percentile energy cuts half-way and three-quarters of the way through the simulation were terminated. A clustering threshold of 2 Å was used, and five models representing the center of the five largest clusters were selected as predictions. NMR models, which can make use of additional limited experimental information, were selected as described below.

To compare the energies of models generated by the de novo protocol with native structures, the native structures were subjected to all-atom refinement. The native structures were first idealized by replacing the bond angles and bond lengths with the “ideal” values used in the de novo protocol (using a quasi-Newton optimization to adjust the backbone torsion angles to minimize the overall pertubation to the 3D structure) to facilitate comparison.

NMR Structure Inference.

For NMR targets, the standard protein fragment selection procedure in Rosetta was replaced with the chemical shift filtered fragment selection used in CS-Rosetta (25). In the CS-Rosetta method, the software SPARTA (39) is used to predict the backbone and Cβ chemical shifts of a database protein structures for which high-resolution crystal structures are available. Three and nine residue fragments are selected from this structural database based on similarity between predicted chemical shifts and experimentally determined chemical shifts of the target protein (for further details, see ref. 25). The standard fold-and-dock protocol is then used to generate high-resolution models of homo-oligomers.

A single model is predicted for each target protein by selecting the model with lowest Rosetta energy adjusted with a term measuring the similarity between the predicted chemical shift of the model and the experimentally determined shifts (25).


The code is freely available to academic users at www.rosettacommons.org in release Rosetta 2.3.0. For command line, see SI Materials and Methods.

Supplementary Material

Supporting Information:


We thank Keith Laidig and Darwin Alonso for flawless administration of computational resources; the users of Rosetta@home for donating their computer time; developers in the Rosetta community for contributions to our shared codebase; and Suzanne Pfeffer for informing us about the GCC185 coiled-coil sequence before the release of its crystal structure. This work was supported by the Howard Hughes Medical Institute (to D.B.), the Knut and Alice Wallenberg Foundation (to I.A.), the Jane Coffin Childs Foundation and a Burroughs-Wellcome Career Award at the Scientific Interface (to R.D.), the Intramural Research Program of the National Institutes of Health National Institute of Diabetes and Digestive and Kidney Diseases (to Y.S.), and the National Institutes of Health Protein Structure Initiative Grant U54-GM074958 (to T.S. and C.H.A.). C.H.A. holds a Canada Research Chair in Structural Proteomics.


The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

This article contains supporting information online at www.pnas.org/cgi/content/full/0904407106/DCSupplemental.


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