Low-resolution structural modeling of protein interactome

Abstract

Structural characterization of protein–protein interactions across the broad spectrum of scales is key to our understanding of life at the molecular level. Low-resolution approach to protein interactions is needed for modeling large interaction networks, given the significant level of uncertainties in large biomolecular systems and the high-throughput nature of the task. Since only a fraction of protein structures in interactome are determined experimentally, protein docking approaches are increasingly focusing on modeled proteins. Current rapid advancement of template-based modeling of protein–protein complexes is following a long standing trend in structure prediction of individual proteins. Protein–protein templates are already available for almost all interactions of structurally characterized proteins, and about one third of such templates are likely correct.

There is nothing worse than a sharp image of a fuzzy concept. (Ansel Adam, US nature photographer, 1902–1984)

Introduction

The essence of the low-resolution approach to modeling of proteins and their interactions is in the epigraph to this paper. Indeed, when the high-resolution details of protein structure are highly unreliable, it is better not to include them in the picture. Structural characterization of protein–protein interactions (PPI) across the broad spectrum of scales is key to our understanding of life at the molecular level. Recently, the low-resolution/coarse-grained modeling approaches have been increasingly gaining popularity. Still, many biomolecular scientists will likely tell you that only the high resolution protein structures have an appreciable value, and the low-resolution ones add little to biology. Coincidentally, one could conclude that because computational modeling of large and heterogeneous macromolecular systems has limited accuracy, it is thus rarely useful. Such a notion, of course, is incompatible with the rapid development of the multiscale approaches to systems biology and, simply put, studies of the physical phenomena in general that inherently involve approximation.

Approximation is in the heart of physics, numerical analysis, and other branches of ‘exact sciences.’ Ironically, the most ‘inexact’ of them — molecular life science — is still not quite at home with this most basic concept. In fact, numerous studies involving low-resolution structural information have added a great amount of knowledge on the fundamental mechanisms of soluble and membrane proteins. Simply put, any level of physical characterization of a protein, as opposed to its absence, is valuable. The level of structure resolution is biologically relevant if it captures the functional elements of the structure. If such elements are large, then even ultralow resolution can provide important insights. When it comes to modeling of PPI, the high-resolution protein–protein docking is not necessary for a number of important biological questions where docking can be useful, such as the design of PPI inhibitors and other experimental and computational studies that take over from protein docking once it predicts the protein–protein interface.

Low resolution does not negate high-resolution. To the contrary, it is a prerequisite for our ability to obtain the high-resolution accuracy in modeling, through refinement of the low-resolution predictions. The whole paradigm of ‘refinement’ comes from the notion of an approximate model, which reflect the reality at a lower precision, and which is subject to the improvement of the precision. The low-resolution modeling of PPI is especially important in the efforts to model large PPI networks, up to the level of interactome, in the context of modeling the entire cell. The low-resolution approach is the only currently available tool for such modeling, given the high-throughput requirements of low computational cost per interaction, and the significant level of uncertainties inevitable in very large heterogeneous systems. The first credible model of a cell will be low resolution.

Low-resolution protein recognition factors

The geometric complementarity between interacting protein structures, the cornerstone of protein–protein docking methodology since its inception, is an essential predictor of interacting modes at low resolution [1]. A fundamental question concerning protein association is whether it is determined by local structural elements or whether there are also large-scale structural motifs that facilitate the formation of the complex. The local physicochemical and steric factors are responsible for the final ‘lock’ of the molecules when their binding sites are already in close proximity. At the same time, there are structural factors that contribute to bringing the binding sites to such proximity. An important insight into the basic rules of protein recognition is provided by the studies of large-scale structural recognition factors, such as recognition of proteins deprived of atom-size structural features [1,2], backbone complementarity in protein recognition [3], macromolecular assemblies [4], and binding- related anisotropy of protein shape [5,6]. The practical importance of the large-scale recognition factors for docking is that they often allow one to ignore local structural inaccuracies (e.g. those caused by conformational changes).

Intermolecular energy funnel is the ultimate low-resolution concept. The large-scale structural recognition factors in protein association have to do with the funnel-like intermolecular energy landscape [7]. It has been shown that simple energy functions, including coarse-grained (low-resolution) models, reveal major landscape characteristics, such as the number and distribution of the funnel-like energy basins, transition between low and high resolution, and funnel size [8]. The intermolecular energy landscapes are further characterized by conformational properties of interacting proteins [9–11].

Coarse-grained flexibility in protein interactions

The unbound/bound difference in protein backbone is often insignificant [12] and the formation of a complex can be described by the side-chain conformational changes [13–16]. However, the analysis of large-scale structural flexibility is important for understanding protein–protein association and our ability to model them [17, 18]. The coarse-graining of protein structures allows exploration of structural dynamics of large macromolecular systems at long time scales [19•,20]. It also allows comparison with low-resolution experimental data, which often are the only available structural information on the system [21]. Coarse-grained elastic networks modeling of structure fluctuations showed that, on average, the interface is more rigid than the rest of the protein surface [22,23], and the interface mobility is correlated with the interface type, size and obligate nature of the complex [23]. In structural modeling of protein–protein complexes, the coarse-graining approaches are used to model structural flexibility in protein assembly [10,19•, 24, 25]. Low-resolution allows implicit accounting for local conformational flexibility without sampling the internal degrees of freedom, and thus is useful in docking [1,26]. The residue frequencies in co-crystallized protein–protein complexes provide an opportunity to develop residue-residue statistical potentials for docking and scoring of PPI [27,28]. Such potentials provide a coarse-grained alternative to atomic-resolution statistical potentials, allowing greater tolerance to conformational changes.

Docking of models

Direct experimental approaches to structure determination (primarily, X-ray crystallography and NMR) are capable of determining only a fraction of all protein structures. Thus the structures of most proteins in genomes have to be modeled by high throughput computational techniques. The major difference between the experimental structure and a model, in general, is a lower accuracy of the latter. The accuracy of the protein models may vary significantly, based on the availability of modeling templates and their similarity to the target, from ~1 Å RMSD (high-sequence similarity to templates) to >6Å RMSD (low-sequence similarity to templates, or no templates). Thus, in addition to computational efficiency (e.g. high-throughput, in case of large-scale modeling) the docking procedure has to be capable of tolerating significant structural inaccuracies. Docking cannot yield greater precision than the precision of the interacting proteins. However, even in the extreme case of low precision (~10 Å relative shift of the proteins) the results provide meaningful structural information on the interface location on one or both proteins and the general shape of the complex.

Computationally inexpensive methodology is required for structural modeling of the interactome. For systematic evaluation of expected accuracy in high-throughput modeling of binding sites, the analysis of target/template sequence alignments was performed on a representative protein–protein set [29•]. For most of the complexes, the alignments containing all interface residues were found, even in cases of poor overall alignments, inadequate for modeling of the whole proteins. The alignment of the interfaces significant enough to produce the binding site structure suitable for docking was found in about half of the complexes. An early study [30], systematically simulated structural inaccuracies of modeled proteins, starting from a representative set of co-crystallized proteins, and generating an array of distorted structures for each protein, with inaccuracies from 1 to 10Å. The models were docked at low-resolution and the results correlated with the accuracy of the models. The data showed that docking of even highly inaccurate protein models (~6 Å RMSD from the X-ray structure) still yields structurally meaningful results, accurate enough to predict binding interfaces and to serve as starting points for further structural analysis. The utility of the modeled proteins in protein–protein docking was further demonstrated by other systematic studies, involving docking approaches based on computational geometry [31,32] validated on benchmark protein–protein sets [31] and the nuclear pore complex [32], and Rosetta-based docking of antibody–antigen homology models [33]. The template-based docking approaches increasingly focus on the modeled structures as part of the docking protocol [34,35•] or the subject of structural alignment [36••,37••]. •]. Modeled proteins attract increasing attention as drug targets. Studies of binding pockets on modeled protein receptors, and docking of ligands to modeled receptors showed significant tolerance to the structural inaccuracies and the general utility of the modeled receptors [38–43]. In our most recent study, a new large benchmark suite of models with controlled distortions for 320 protein complexes was built using combination of homology modeling, low energy trajectories, and simulated annealing. For each X-ray monomer in the dataset, six models were generated with the pre-defined values of C^α RMSD between the native and the model structures (examples in Figure 1).

Figure 1.

Examples of simulated models. The X-ray structure is shown for comparison, with the binding site in gray.

The rise of the template-based docking

The physical principles of protein binding and folding are the same, thus their modeling shares many aspects. Prediction of individual protein structures has evolved from the ‘first principles’ approaches to the currently dominating template-based modeling, largely because of the difficulty the template-free methods face in delivering reliable solutions, and the explosive growth of the number of experimentally determined protein structures. Protein docking is significantly younger than the individual protein structure prediction, and much less advanced in its transition to the template-based approaches. The two factors that contributed to the evolution of the individual protein prediction determine the current lesser role of the template-based methodologies in protein docking. First, the template-free techniques have been relatively more successful in the prediction of protein complexes than in the prediction of individual proteins. The reason is that the docking first approximation (rigid-body docking), applicable in many cases, has to cope with only six degrees of freedom, which is incomparable with the number of degrees of freedom in the prediction of individual proteins at any meaningful level of approximation. Second, the number of experimentally determined structures of protein–protein complexes is far less than the number of such structures for individual proteins. However, with the advances in the experimental determination of protein complexes the situation is rapidly changing.

The template of the complex may be detected based on the sequence of the target proteins [34,35•]. However, since the docking problem assumes the knowledge of the components structure, a growing number of approaches take advantage of structural alignment techniques, for full and/or interface structure alignment [36••,44–53]. The template-based structure-comparison approaches (Figure 2) align backbones, secondary structure, and/or other coarse-grained elements of the structure. This reflects the low-resolution nature of the macrostructural recognition factors, fundamentally based on the backbone recognition, dating back to the early studies [3].

Figure 2.

Template-based docking by structural alignment.

To assess the predictive value of the template-based approach, it was benchmarked on protein–protein structures in PDB released in 2009–2011, utilizing template structures released before 2009. The templates were found for almost all new complexes, and more than a third of the new complexes were predicted correctly, with interface RMSD < 5 Å [37••]. The template-based docking, in general, performed in the community-wide assessment of docking techniques (Critical Assessment of PRediction of Interactions — CAPRI) with limited success [54], in sharp contrast with the significantly higher than the free docking success rates on the docking benchmark sets [53]. The reason is that CAPRI targets have high representation of novel structures, reflecting the effort of the crystallographers providing the targets to avoid ‘trivial’ complexes that are similar to the ones already in PDB. However, in typical ‘real case’ modeling of protein–protein complexes of biological interest, the novelty of the structure usually is not a consideration and the existence of homologous co-crystallized complexes is welcome. Thus, the docking benchmarks, which follow the increasing availability of co-crystallized homologous complexes, are representative of the biological community needs.

Since the experimentally determined structure of protein–protein complexes is generally more difficult to obtain than the structure of individual proteins, the availability of templates for protein–protein docking is a key issue. Comparative studies of protein–protein interfaces determined that the library of protein interfaces is close to complete [55••], and that it is generally possible to find representatives of the possible binding modes of a given protein [36••,56•]. Still, there are many structurally common binding regions among proteins that are not related to fold classification [57]. The direct way to assess the availability of templates for protein–protein complexes in PDB is to have the structural similarity metric that is correlated with the experimentally determined binding mode. Such a metric can be used in PPI datasets to see what percentage of PPI corresponds to the metric’s values for good templates. Recent results obtained in an all-to-all pairwise comparison of 989 co-crystallized complexes [37••] show a strikingly distinct phase transition to the same binding mode at minimal TM-score (the lowest of the two component proteins TM-scores [58]) of 0.4. Thus the values of the minimal TM-score > 0.4 can be used in detecting good templates of the complex. Remarkably, such structural templates were found for nearly all complexes in a database of known PPI, where the structure of the individual components of the interaction is determined by X-ray or can be built by homology [37••].

Proteome-scale modeling

To adequately model large systems of PPI, it is important to understand and simulate the environment in which the proteins interact in vivo. This environment is densely populated, which strongly affects protein diffusion, binding and conformational transitions. The investigations of the ‘crowding’ effects in such environment range from studies of protein stability and other conformational properties [59–61], and detection of binding regions [62], to the role of hydrodynamic interactions in cells [63•] and physical limits of cells and proteomes [64].

Structural characterization is essential for the proteome-scale modeling of PPI networks (Figure 3) [65,66•, 67•,68]. Modeling templates are available for a significant part of soluble proteins in genomes [69], including those in known PPI [37••]. The approaches to genome-wide structural modeling of PPI are either ‘traditional’ template-free docking [70,71] or the template-based docking [36••, 37••, 55••, 56•, 72–74]. The latter, while potentially providing much greater success rate [53], critically depends on the availability of the templates [36••, 37•• ,55••, 56•]. In a recent study [37••], the X-ray structures of the proteins were complemented by homology models and the templates for their complexes were detected in PDB. Figure 4 shows the results for five genomes with the largest number of known PPI. Structural alignments yielded a dramatic increase in the structural coverage of complexes, from the coverage provided by the sequence alignment. The structural templates were found for nearly all (33 537 out of 33 840, or 99%) complexes in which both components could be built. ‘No template’ in Figure 4 indicates no template for individual proteins, not for the complex. Thus, contrary to the common perception of rarity of the templates for complexes, as opposed to the structure prediction of individual proteins where the template-based modeling has long been the default approach, the limiting factor in interactome modeling is actually the availability of the templates for the individual proteins (more protein–protein templates are still needed for greater accuracy of modeling). The structural coverage of interactome should increase with more structures of individual proteins experimentally determined, and with more sophisticated modeling of individual proteins at lower levels of target/template similarity. The ability to detect templates for almost all complexes is a consequence of the proteins modeling by sequence similarity, followed by protein–protein modeling by structure similarity (which is significantly broader in scope than the sequence similarity, since structure is more conserved than sequence).

Figure 3.

Structural modeling of interactome. The flowchart shows modeling of two proteins (blue and green) interaction (orange) from the PPI network, through determination of their individual structures (X-ray structure from PDB or modeling), and the structure of their complex (X-ray structure from PDB or modeling by template-based or free docking).

Figure 4.

Structural coverage of PPI in five genomes with the largest number of known protein interactions. Complexes with the X-ray structure are in red, and complexes with a sequence template are in green. Complexes for which the structure of the monomers is known or can be built by homology are in blue — structural templates are available for 99% of such complexes

Future of PPI modeling

The quasi-complete low-resolution description of interactome is likely not that far down the road. Templates are already available for almost all interactions of structurally characterized proteins, and about one third of such templates are likely correct. The limiting factor is the availability of templates for individual proteins. With more experimentally determined protein structures becoming available, more accurate genome-wide maps of PPIs, and the growing computational resources allowing application of more sophisticated template detection approaches, our ability to structurally model PPI at the level of interactome should rapidly develop.

With the advance of the template-based docking, the free docking will not fade away — there are many protein encounters in the crowded cell environment, which are not likely to correspond to energetically stable co-crystallized templates. And the high-resolution modeling of PPI will be there too, as the next step in our ability to reveal the full picture, in all its clarity.