Modeling of loops in proteins: a multi-method approach

Comparative modeling remains the most dependable and routinely used method for protein structure prediction [1, 2]. The alternative term of homology modeling is frequently used. That is because the identification of a structural template (or templates) is typically based (although not always) on the homology relation between the target protein and the templates, which is usually reflected by a certain level of sequence similarity. When a template is being identified by some advanced Fold Recognition (FR) techniques, it is sometimes possible to identify templates that are structurally similar to the target without any obvious homology relations. This could be a genuine case of convergent evolution or (more frequently) the case when remote homology just can not be detected. Template free, de novo structure prediction is much more difficult and less dependable, although a steady progress is observed in this area of computational biology [3, 4]. Most contemporary methods for de novo structure predictions heavily depend on certain aspects of evolutionary relationships between protein sequences and structures. The evolutionary methods are essential for the derivation of statistical potentials for de novo modeling and/or are employed in various strategies for extracting structure building blocks from known protein structures [5, 6].

Classical homology modeling consists of three steps. First, a template for modeling needs to be identified and sequence alignment between the template and target sequences has to be generated. Usually, template identification is performed by certain standard tools, such as PSI-BLAST, and the resulting alignment is subsequently rectified by other tools and eventually by manual expert corrections. Remote templates can also be identified by FR procedures [7]. With the decreasing level of sequence similarity, which implies increasing evolutionary distance and thereby increasing structural differences between the template and the target, alignments become more and more ambiguous. Accuracy of classical comparative modeling heavily relies on the fidelity of the template-target alignment.

In the second stage the aligned fragments of templates are used to generate the corresponding fragments of the target structure. In the simplest case of a single template only, this step reduces to mere copying the template coordinates according to the alignment. In the case of multiple templates a consensus scaffold could be built, for instance via the distribution of the spatial restrains read from the templates, as it is implemented in the MODELLER method [8]. The key component of this stage of modeling is construction of loop regions that are frequently missing in the template scaffold. In certain newer approaches to comparative modeling the entire structure of the target is built using templates as sources of restraints of various types [3, 9]. The main aim and challenge of such approaches is to be able to build a model of the target structure which is more similar to the true structure of the target than to any of the templates used, especially for distant homology based modeling.

The third, and final, stage of modeling is structure refinement which involves repacking the side chains and energy minimization of the entire structure [10].

The above scheme, or its variants, of comparative modeling remains the best choice when significant fragments of the alignment are error-free, which is usually the case in the range of high level sequence similarity (e.g. 40%, or more, of identical residues in the alignment). In the "twilight zone" of low sequence similarity the alignments contain significant errors. These could be sometimes corrected by building a multi-template consensus modeling scaffold [11]. Alternatively, it is possible to design a completely different modeling schemes, in which the alignment is built simultaneously to the actual modeling process [12].

In this paper we address the issue of loop modeling, separating it from the alignment problem. The test set of proteins with missing loops consists of two sub-sets. The first subset, containing missing loops of 4-12 residues, has been taken from a recent work by Rossi, et al., excluding the cases of incomplete chains in the corresponding PDB entries [13]. The work provides a comprehensive comparison of loop modeling performance of the most popular comparative modeling software. The loop database employed in the work of Rossi was adapted from a compiled loop database assembled by Jacobson et al [13, 14]. Additionally, the database used in this work was expanded with cases of much longer loops, up to 25 residues (the second sub-set). The database covers all the structural classes of proteins, with 186 internal loops of various length. The expanded range of the modeled loop lenghts addresses the possibility of the extension of the range of applicability and accuracy of challenging instances of comparative modeling. Four methods of loop modeling are compared in this work: MODELLER, ROSETTA, CABS and a combination of MODELLER with CABS. Since MODELLER is a commonly accepted reference standard in comparative modeling, the results are qualitatively (although indirectly) comparable with other approaches [13, 15–20]. It should be noted that MODELLER is representative software for distance geometry and energy minimizations, while ROSETTA and CABS employ knowledge-based free search of a discretized conformational space. Thus, the comparison given in this paper should provide additional insights into the range of applicability of these qualitatively different approaches to protein molecular modeling. Previous computational experiments with the reconstruction of missing fragments of protein structures indicated that the coarse grained models (an early version of CABS and two other modeling tools based on similar principles) performed relatively well in the range of large fragments [21]. At this point we would like to present a comprehensive evaluation in a wide range of loop modeling instances.

Using MODELLER, we generated 500 examples of individual loop regions, which were subsequently ranked by the DOPE statistical potential [22]. Top ranked means the highest rank, while the "best" result means a structure that is closest to the actual experimental, structure of the loop. Similarly, ROSETTA models were ranked with ROSETTA potentials. CABS modeling provides a trajectory containing several hundred instances. These were subject to the clustering procedure. Interestingly, in most cases the medoid from the entire simulation was closer to the true structure than the largest clusters' medoids. This suggest very good convergence of CABS simulations. Consequently, the medoid structures were reported as the top-ranked models.

The statistics of the results is shown in Figure 1, in which the loops of a given length are described by average values of cRMSD of the loop fragments (coordinate Root-Mean-Square Deviation) from the corresponding crystallographic structures. To extract the loop cRMSD values protein structures without the modeled loop fragments were superimposed and the deviation was computed only for the loops. In the entire text the values of cRMSD are reported for Cα traces only. Corresponding data for all atom structures are essentially the same. The plots in Figure 1 clearly show two major trends. The first is obvious: with the increasing size of loops the average accuracy of modeling decreases. The second trend indicates, as expected, that the distribution of the quality of models, as measured by the difference between the best model and the top ranked models is much larger for MODELLER and ROSETTA as compared with CABS. For very long loops (20 and more residues) CABS results are on average better than for MODELLER and ROSETTA. The hybrid-CABS modeling takes advantages of different methods. Using top10 models generated by MODELLER the new method leads to results as good as MODELLER for short loops and noticeably better models in the range of long loops. When comparing with original CABS simulations the hybrid-CABS is much more accurate for short loops. This is illustrated in Figure 2. The results with hybrid-CABS show that there is always an added value in combining different modeling methods.

Figure 3 and Figure 4 show the distributions of cRMSD for 186 cases studied. The distribution is quite broad, especially for longer loops. Use of distinct modeling techniques increases chances for obtaining good quality models. Unfortunately, all methods produce results of scattered quality. The problem how to identify the cases for which the models are of good accuracy remains unsolved.

In this work we have shown that de novo protein loops modeling using ROSETTA and CABS-based software is complementary to the classical modeling with MODELLER, the golden standard of comparative modeling. The proposed hybrid modeling pipeline, where ten top ranked (according to DOPE statistical potential) MODELLER models are used as templates for CABS, allows for meaningful loop modeling for a broad range of loop length. The hybrid MODELLER-CABS method takes advantage of the local accuracy of MODELLER structures and the efficient sampling of local free-energy minima by CABS. The hybrid-CABS method described in this work extends the applicability range of protein comparative modeling. Further increase of accuracy for large loops will require better ranking of resulting models. Model-ranking in the range of moderate- and low-resolution computational structures remains a challenging problem for the entire structure-prediction field. In this case, a small step in this direction was performed by a combination of different modeling techniques.

The dataset employed in this work is summarized in Table 1. The cases of shorter loops, up to 12 residues, are taken from the work of Rossi et al. who used a loop database developed by Jacobson et al. [13, 14]. The longer loops were selected from the same protein structures as continuous fragments of coil structures, according to the DSSP definition of secondary structure. Dangling ends are excluded from our test, similarly as it was done by others. Dangling ends are frequently structurally poorly defined, and therefore the results of their simulations are difficult to interpret. The dataset is available for download (Additional file 2).