As it is evident from the list above, there are many biologically meaningful definitions of protein similarity. Several methods have been proposed and there is a variety of structure classification servers and databases available, each of them with its own interface, philosophy and, most importantly, biological conception of what "similarity" means. Paradoxically, the availability of all these methods with their unique interfaces and underlying biological hypotheses makes it more, and not less difficult for a structural biologist to decide which method to apply in which cases. Moreover, it is common to find papers related to protein structure comparison where the authors claim that their new method is better than another on a small set of test cases. These types of comparison can be misleading in at least two ways. First, changing the algorithm used to compare structures often inadvertently introduces a different comparison criterion, hence changing the problem itself. Secondly, the comparisons are usually done on a reduced number of data sets with characteristics that make them suitable to the new (implicit) criterion. In this paper we take the view that there is not one problem of protein structural comparison but rather many different, yet related, structural similarity problems where each of them might be best tackled with a different method. Hence, attempting to find the best method for protein structure comparison is a chimera. Instead, in line with other recent suggestions 4344 that the integration of a variety of feature detection techniques could enhance protein comparison, we advocate here an integrative approach that harnesses the best in each available method. This change in philosophy allows us to treat the assessment of protein structure comparisons as a decision support problem in which the task of the bioinformatician is to build up computer facilities that empower the user to make an informed decision with the minimum possible overhead. The advantage of this viewpoint is that it does not call for the abolition of one method in favour of another one but rather for the intelligent integration of every possible protein structure comparison method into one unified tool.

In this paper, we take the first steps towards the creation of an intelligent decision support system for protein structure comparison. We introduce a new meta-server for Protein (Structure) Comparison, Knowledge, Similarity, and Information (ProCKSI) implementing the protocol, published by Krasnogor and Pelta 24, and substantially extending it. This server facilitates protein structural comparison by allowing the user to compare multiple protein structures seamlessly using multiple similarity methods through a unique and integrated interface. As ProCKSI adheres to the philosophy mentioned above where different conceptions of similarities can be used under different circumstances, it deals well with comparisons of both very divergent structures and quite similar ones. Until now, methods were proposed that work well in either of these cases but not in both simultaneously. The first case is dealt with using the top level of the protocol, namely, the Universal Similarity Metric (USM, 45) and the latter case by means of the Maximum Contact Map Overlap (MaxCMO) method 202123. As it has been shown in other contexts (e.g. protein structure prediction) that meta-servers sometimes outperform human experts 4647, the similarity results returned by these two methods can also be complemented with other comparison methods, and even integrated into a consensus similarity assessment. Hence, motivated by the observations above and in recognition that a) in many situations a very detailed comparison is needed and b) biologists may also want to compare a protein set from several viewpoints or conceptions of similarity simultaneously, ProCKSI harvests results from well-established external protein comparison servers and methods. It makes them available and readily comparable with one another, and combines the various similarity measures to give a consensus similarity profile for a given dataset.

The first level of similarity assessment utilises the USM as a similarity measure between two protein structures s₁ and s₂. Their contact map representations are then used to approximate heuristically the Kolmogorov complexity of the proteins, comparing their information content. The approximation of the Kolmogorov complexity is done using a compression algorithm (e.g. compress, gzip, bzip2, ppmz2). The pairwise similarities are then expressed as the Normalised Compression Distance (see Eq. 1), NCD, where K(s_i) represents the Kolmogorov complexity of object s_i and where K(s_i|s_j) is the conditional complexity. NCD is a very effective universal, i.e. problem-domain independent, similarity metric particularly with distantly related structures 24 and sequences 48.

N C D ( s 1 , s 2 ) = m a x { K ( s 1 | s 2 ) , K ( s 2 | s 1 ) } m a x { K ( s 1 ) , K ( s 2 ) } MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@669B@

As the USM is a very general metric, for more fine grained comparisons ProCKSI implements a metaheuristic to compute the Maximum Contact Map Overlap (MaxCMO) of pairs of proteins counting the number of equivalent residues (alignments) and additionally the number of equivalent contacts (overlaps). Under the MaxCMO model, an amino acid residue a₁ from one protein is aligned to an amino acid residue a₂ from a second protein if a contact of a₁ in the first protein (C(a₁)) can also be aligned to a contact of a₂ in the second protein (C(a₂)) closing a cycle of size 4 in the graph representation of the contact map. A further restriction for the overlaps is that they should not produce crossing edges. That is, if a₁ is aligned to a₂, C(a₁) is aligned to C(a₂) and, without loss of generality, a₁ <C(a₁) (i.e. the atom or residue a₁ appears before than C(a₁) in the sequence) then a₂ <C(a₂). Thus, an overlap in this model is a strong indication of topological similarity between the pair of proteins as it takes into consideration the local environment of each of the aligned residues. In addition to the two methods previously described, ProCKSI utilises the DaliLite workbench 849 and the Combinatorial Extension (CE) method 11, both providing the statistical significance of an alignment (Z-score), the TM-align method 50 using TM-scores, and the FAST method 28 providing SN-scores as their key similarity measure.

The results are analysed with standard clustering methods. The clusters thus obtained can be visualised using either a linear, a circular or a hyperbolic representation of the hierarchical similarity tree 51 that captures the dataset's structural organisation. Additional analysis tools permit the comparison and integration of multiple similarity measures, so as to give a consensus similarity cluster. The analysis tools cannot only be used with ProCKSI's results but also in combination with additional similarity matrices that the user provides. Through this mechanism, the set of similarity matrices can be extended by any similarity measure that the user deems to be important allowing one to refine the similarity consensus for a given dataset. It allows the user to add different information which is not produced by the methods currently integrated with ProCKSI.

In addition to its core protocol for protein comparison as described above, ProCKSI aims to give an overall picture of the protein universe by providing, for each protein in the dataset, as much information and knowledge as possible. To this end, ProCKSI directly links to the PDB repository 52, the Structural Classification of Proteins (SCOP) database 5354, and the Protein Structure Classification (CATH) database 5556. Sometimes, it might be useful not only to know more about the structure itself but also to get information about the literature where a certain protein occurs. ProCKSI therefore links to the information hyperlinked over proteins (iHOP) service 5758 providing an interactive network of proteins within the related literature.

In the next section we show the general architecture and workflow of ProCKSI and explain in detail the features introduced above.

The server can handle protein structure files in the Protein Data Bank (PDB) format, which can be downloaded directly from the PDB repository 52 by entering the PDB codes of the proteins. Alternatively, they can be uploaded from the user's local hard disc sequentially, i.e. one protein file at a time, or as archives (TAR, ZIP) containing multiple protein structure files. In either case, compressed files and archives in Z-, GZ-, or BZ2-format are also supported. The user can add further files, delete redundant ones, and decompose structure files into all their models and chains. The user may select a subset of chains to be compared against each other, or perform an all-against-all chain comparison. If a PDB file was considered invalid, e.g. due to incomplete or ambiguous data within the file, the user has the opportunity to correct the errors before submitting the request for calculation. That is, the Dataset Management provides a flexible and user friendly interface for preparing the dataset for the further comparison in just a few steps.

Once the protein files have been validated, the user must specify the calculation parameters, including the similarity methods to be used. Each comparison method requires specific parameters, which the Calculation Management allows to be set up. In the case of a similarity calculation with the USM method a USM equation 2459 and a compression type must be chosen; for the MaxCMO method the number of restarts for the randomised solver has to be specified. The more restarts, the better the overlap values obtained, but this, of course, comes at the cost of compute time. All other methods take their standard parameters. When using the USM or MaxCMO method, each protein structure is then automatically converted into a contact map (Figure 2 – centre), based on a user-defined distance threshold and an exclusion window. The latter parameter specifies the number of nearest neighbour atoms in the sequence to be ignored while calculating the contact map.

As there is no general agreement on how to best represent a protein structure for comparison purposes, either C_α atoms 606162 or C_β atoms 63646566 can be chosen. The former representation focuses on the structure's backbone, whereas the latter one takes the residues' side chains into account. Alternatively and in contrast to other web servers (e.g. 67), ProCKSI offers to calculate the residues' centres of mass in order to include both the backbone and side chain contributions at once.

After a similarity comparison request has been submitted, it is added to a queue and the server returns a confirmation page that directly links to the Overview Manager. This gives a summary of all calculation parameters and the status, the submission, start and end times of all methods (tasks) that have been requested. As soon as all tasks have finished, the user receives a notification email and the expiration time (currently 7 days) for the entire request. Thereafter, the data are deleted.

ProCKSI returns a large variety of data and intermediate results that are handled through the Structures, Task and Analysis Management subsystems. These are described next.

The evaluation of the CASP6 results is a challenging task, as it involves many protein structure files of a widely varying degree of similarity. Although protein scientists will often be interested in good alignments between pairs of closely related proteins, the capability of properly aligning distantly related structures is useful in ab-initio (new fold) structure prediction and the assessment of the predicted structures 74. In CASP, the evaluators need to deal with literally tens of thousands of protein structure candidates that are often not too similar to the targets. The case of very different protein structures sometimes baffles structural alignment methods including LGA 12 that are regularly used to evaluate CASP results. ProCKSI, on the other hand, is likely to be less prone to producing a misleading ranking, because it harvests the results from various methods averaging them in order to produce a consensus.

For our experiments, we have chosen targets from both the CASP6 CM/easy and CM/hard category. The differentiation of targets into easy and hard is related to the degree of difficulty of predicting a model for the target using a given template, but does not reflect the evaluation process. For CM/easy targets, homologous structures can be found in databases, which might lead to many fairly good models. These can be very similar to each other and difficult to rank properly. On the other hand, the evaluation of the CM/hard category is not straightforward either, as the structural similarity between model and target can be very low, due to the more difficult structural prediction task.

In the following, we discuss three examples (targets T0231, T0211 and T0196) that illustrate how ProCKSI deals with the difficulties described above. The targets were compared to all models proposed by the prediction servers that produced a native-like protein model including side chains. We used C_β atoms to represent the protein structure in this experiment in order to be consistent with the assessment of the CASP6 experiment 66 thus taking the positions of the side chains into account. ProCKSI's results from methods using contact maps, namely USM similarity, MaxCMO/Overlap and MaxCMO/Align values, and its new ProCKSI/Consensus method (using a total-evidence approach 47 combining all three taking the arithmetic average) are compared against GDT-TS, the main measure for structural similarity in CASP 75. We provide the GDT-TS ranking results obtained from a sequence dependent analysis (SDA) as used in the official CASP evaluation procedure, and additionally from a sequence independent analysis (SIA), as MaxCMO's algorithm works in this mode.

Table 1 shows the ranking results of target T0231, a protein from the CM/easy category. This structure is the most conserved structure in CASP6 76, i.e. homologous ones can be found in various databases, making its prediction simpler than it would otherwise be. The availability of several good, only slightly different models, makes the ranking process difficult as small differences between the candidate structures must be detected and evaluated. ProCKSI's results are in very good agreement with GDT-TS (SDA), the community's gold standard. At least three targets ranked in the top five places by GDT-TS (SDA) can be found in similar places when using any of ProCKSI's similarity measures. More specifically, not only does ProCKSI find some major agreement in the most similar models for this target but also the three least similar models as ranked by MaxCMO/Overlap, MaxCMO/Align and ProCKSI/Consensus match perfectly the ranking of GDT-TS (SDA).

Focusing on target T0211 of the CM/hard category 76 we find that GDT-TS (SDA) and ProCKSI/Consensus consider the same models for the first and second best models and that also the last six places, i.e. worst models, show considerable agreement (Table 2).

Interestingly, the results obtained by ProCKSI and GDT-TS running in sequence independent mode differ more, when given targets T0231 and T0211, than when GDT-TS operates in sequence dependent mode. For example, considering T0231, we obtain no agreement between ProCKSI's top 5 models and GDT-TS (SIA) and only two (ProCKSI/Consensus) or three (MaxCMO) matches in the bottom 5 ranked models. These are quite surprising results as one would have expected the results of ProCKSI to match the sequence independent operation mode of GDT-TS better than the sequence dependent one, as ProCKSI does not use sequence information. Noting that CASP results are evaluated on the sequence dependent mode and that ProCKSI produced good agreement with it, we will investigate in the near future whether adding GDT-TS (SIA) to ProCKSI's pool of methods would be advantageous.

Using target T0196 as a third example taken from the CM/hard category, we show that the combination of similarity criteria into a consensus can sometimes detect a better model than GDT-TS (SDA)(see Table 3 for details). Figure 3 illustrates the 3D structures of those models that are considered by the different methods to be the most similar to the target structure, called the "winner" of a certain method in the following. The ProCKSI/Consensus similarity measure detects a model that better resembles the overall structural features of T0196. More specifically, the candidate model selected by GDT-TS (SDA) has a fairly long segment of the chain that was not predicted correctly (blue), a helix structure was incorrectly suggested (orange) and the β sheets are in the wrong places (green). This model is ranked last by ProCKSI/Consensus.

Next, we analysed the sequence similarities between the target structure and the winner of each method. Using the MaxCMO method to produce all sequence alignments, we obtained up to 76.7% (target vs. winner of GDT-TS), up to 98.6% (target vs. winner of MaxCMO/Overlap) and up to 95.8% (target vs. winner of USM and ProCKSI/Consensus) correctly aligned residues, having taken the best results of multiple MaxCMO runs. This illustrates that the MaxCMO method does not only detect the most similar model according to its overlap values, but also gives the better alignment with the highest sequence similarity. When using GDT-TS in sequence independent mode instead, both methods suggest the same model for the best structural match and even agree with almost all models within the top five in the ranking.

Summing up, we found a very good agreement between ProCKSI/Consensus and CASP's GDT-TS method, although the two run in different modes: the former obtains its results from sequence-independent calculations while the latter additionally uses sequence information. When both methods suggest a different winner in their rankings, the ProCKSI/Consensus method can detect a better model with a higher similarity (value) and even a higher sequence similarity.

In the following, we perform an additional (and more detailed) analysis of ProCKSI's functionality by concentrating on a set of protein kinases (PK). These are then compared and clustered according to their structural similarity. These structure-only based results are then compared with the original classification scheme by Hanks and Hunter (HH) 73 that was based on sequence similarity. As was the case for the CASP targets, ProCKSI's integration of several structural similarity criteria allows it to reproduce the original classification without using sequence information.

Kinases are proteins that catalyse the transfer of a phosphate to a protein substrate and form a reversible equilibrium with phosphatases as their counterpart 77. They comprise a huge group of enzymes that play an essential role in most of the major cellular processes such as cellular differentiation and repair, cell proliferation, etc 78. In an attempt to organise the set of protein kinases, Hanks and Hunter 73 classified them accordingly to their sequence into 5 broad groups (super-families), 44 families, and 51 domains (sub-families). Several additions and refinements to this classification (e.g. 79808182) were later introduced.