Here we present CPSARST (Circular Permutation Search Aided by Ramachandran Sequential Transformation), an efficient tool for searching for CPs. It describes three-dimensional protein structures as one-dimensional text strings by using a Ramachandran sequential transformation (RST) algorithm 40, which transforms protein structures through a Ramachandran (RM) map organized by nearest-neighbor clustering. This linear encoding methodology converts complicated and time-consuming structural comparison problems into string comparisons that can be done very rapidly. CPSARST has also achieved high efficiency by duplicating the query structure and working through a 'double filter-and-refine' strategy. These approaches are illustrated in Figure 1. A web service and a stand-alone Java program of CPSARST are available at 41. CPSARST not only inherits the speed advantages of sequence-based methods but retains sensitivity to detect distantly related CPs mostly detectable only by structure-based methods. To the best of our knowledge, it is the first structural similarity search method that makes large scale all-against-all database searches for CP achievable and practicable. We suppose that this procedure can be applied to reveal the evolutionary importance of CP and detect novel protein structural relationships. Several novel CP relationships have been detected by CPSARST and are reported in this article; also, some rational estimations of the prevalence of CP in protein structural databases have been made by doing all-against-all database searches of non-redundant Protein Data Bank (PDB) and SCOP.

Although CPSARST basically uses structurally meaningful RM strings to search protein databases, its algorithm is actually applicable to amino acid sequences. To evaluate their amino acid sequence-based algorithm, Uliel et al. performed in silico random CP followed by various levels of regular mutations (substitutions, insertions and deletions) on a number of proteins 38. We adapted this approach in a more thorough manner and developed a random CP dataset containing 20,000 chains (RCP dataset; see Materials and methods) to assess the performance of CPSARST with amino acid sequences. Two parameters were monitored: the proportion of cases in which the exact permutation site was retrieved; and the percentage distance of the retrieved permutation site to the exact one, which is defined as:

D ( % ) = Number of residues off the exact permutation site Sequence length × 100 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8GiVeY=Pipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=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@721D@

As shown in Figure 2a, the percentage of exact matched cases retrieved by CPSARST remains over 80% until the sequence identities fall between 40% and 30%. When we made a 50% exact matches cut, the results indicated CPSARST ensures that at least 50% of the retrieved cases are exact as long as the sequence identities are higher than 22%.

The curve of the percentage distance of CPSARST has a half hyperbolic shape (Figure 2b). Provided that the sequence identity is > 20%, the percentage distance will be < 1%. Combining these data, we suggest that when our approach is applied to amino acid sequences, it will be reliable in detecting CPs with sequence identities as low as about 20%.

Since there are many artificial CPs, each with a definite parent protein, a known permutation site, and sometimes some regular mutations, they provide a good resource to assess the performance of a CP search method. We used keyword searches to find the engineered CPs recorded in the PDB 42, and subjected them to CPSARST searches. As summarized in Table 1, among the 15 non-redundant cases, all the parent proteins were successfully retrieved. Their average percentage distance is only 0.08%, which means that the CP sites identified are very close to the exact ones, demonstrating the high accuracy of CPSARST for engineered CPs.

To our knowledge, current CP-detecting methods based on structural comparisons work in only a pair-wise fashion. Although CPSARST is a database search procedure, it can be simplified to perform pair-wise comparisons (see Materials and methods). Here, we used naturally occurring CP candidates to test the performance of CPSARST. These candidate pairs were detected by doing all-against-all searches against a non-redundant PDB dataset (see below for details) and then filtering out engineered permutants. The 'structural diversity' defined by Lu 43 that integrates the concepts of normalized alignment size and root mean square distance (RMSD) was used to evaluate the quality of pair-wise comparisons:

structure diversity = RMSD ( alignment size avg(N q ,N s ) ) 1 .5 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8GiVeY=Pipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=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@5FDB@

where avg(N_q, N_s) is the average size of the query and subject protein. Lower structural diversities stand for higher structural alignment qualities of the assessed methods. The results are listed in Tables 2 and 3. In terms of structural diversity, the performance of CPSARST is better than that of SHEBA 11 and is comparable to SAMO 34. In addition, CPSARST is 9.3 times faster than SAMO in these pair-wise comparisons (Table 2). Protein size has no effect on the alignment qualities of these structure-based methods while the running time increases as the size becomes larger. This increase in running time is lowest for CPSARST, apparently much lower than that of SAMO. Sequence identities greatly influence the performance, especially for SHEBA (Table 3). The differences in structural diversities calculated by CPSARST and SAMO are not obvious until the sequence identity of the CP pair becomes lower than 20%.

CPSARST runs very rapidly in pair-wise comparisons. When searching databases, its speed will be even higher since it does not work in a pair-wise manner but with a 'double filter-and-refine' strategy. Chen had estimated that using SAMO to compare two proteins mostly took around ten seconds 34. Searching the current PDB (approximately 90,000 polypeptides) by one-against-all comparisons will, therefore, require over 15,000 minutes. However, CPSARST can do this one-against-all comparison in 1.7 minutes (see below). As shown by these naturally occurring cases, CPSARST achieves a high speed with a reasonable compromise in alignment accuracy.

To examine the database searching performance of CPSARST, two non-redundant protein databases were used, the 90% sequence identity subsets of PDB (January 2007) and the ASTRAL SCOP dataset (v.1.71) 44, which were abbreviated as nrPDB-90 (14,422 polypeptides) and nrSCOP-90 (11,688 domains), respectively (see Additional data files 1 and 2 for lists of entry IDs). As summarized in Table 4, the all-against-all survey of large protein databases like nrPDB-90 took 65.7 hours. Since there were approximately 200 million protein pairs for this database (14,422 × 14,422), these data demonstrated that CPSARST could scan around 52,800 pairs per minute. At this speed, a full search of the current PDB could be finished in 1.7 minutes per query protein. In comparison with 6.4 minutes required by the sequence-based UFAU method (developed by S Uliel, A Fliess, A Amir and R Unger) 38 and 15,000 minutes by the structure-based SAMO 34, CPSARST runs fairly fast. Besides, CPSARST gives the user two parameters, expectation value (E-value) and CP score, to evaluate the significance of the retrieved information.

As a database search method, CPSARST provides a list of hits ranked by the statistically meaningful E-value. Given that a hit has a similarity score S, the E-value is the number of different alignments with scores equivalent to or better than S that are expected to occur in this particular database search by chance 454647. A lower E-value indicates a higher significance for the score. This statistical significance is a useful indicator of the reliability of the search results.

To determine the extent to which two proteins are related by a CP, we used the CP scoring scheme described by Vesterstrom and Taylor 39. The minimum value of this CP score is -1 for a pair of completely linearly aligned proteins, and its maximum value is 1 for a perfect CP alignment. In general, a small positive CP score indicates that only a small fraction of the protein is permutated while a larger one reveals that the CP site is closer to the middle of the polypeptide chain.

In the survey of nrPDB-90 and nrSCOP-90, we had set the RMSD cutoff as 5 Å, the E-value cutoff as 0.1 and the CP score threshold as 0.2. Under these criteria, 2,911 and 4,228 candidate pairs were identified in nrPDB-90 and nrSCOP-90, respectively. For nrPDB-90, the 2,911 candidate pairs consisted of 1,822 different polypeptides, that is 12.6% (1,822 of 14,422) of the polypeptides have CP relationships with at least one other polypeptide. For nrSCOP-90, the proportion is 17.6% (2,060 of 11,688).

After visual inspections of superimposed CP pairs detected by CPSARST, we found that it is possible for proteins with very different functions and divergent amino acid sequences to share CP relationships structurally, forming novel CP families, which are difficult to identify using conventional comparison methods. For instance, although glycine betaine-binding proteins (GBBPs), molybdate-binding proteins and Klebsiella aerogenes cysteine regulon transcriptional activator CysB share similar overall structures when judged by the naked eye, their sequence identity is low (< 24%; calculated by FASTA 48) and structural relatedness is hard to detect by conventional methods (Figure 3). CPSARST detected CP relationships among GBBPs themselves and among these three groups of proteins. To our knowledge, these CP relationships have not been reported previously. Figure 3 illustrates that the functional and evolutionary relationships among these proteins cannot be correctly determined by their raw sequences; their ligand-interacting residues are not well-aligned and proteins with more similar functions are separated while those with less similar functions cluster together in the phylogram tree. However, the circularly permuted sequences retrieved by CPSARST can be well-aligned and the phylogram tree agrees with the functional relatedness among these proteins. A superimposition of six of these proteins is also shown in Figure 3 to demonstrate their structural similarity and the conserved position of their ligand binding pockets.

We examined the candidate pairs detected by CPSARST with RMSD ≤ 3.5 Å by visual inspection of superimposed structures and found that approximately 55%, 25% and 20% are mainly alpha, mainly beta, and alpha-beta structures, respectively. These CP pairs are listed, each with a superimposed image, in Additional data file 3; many well-known CP cases are listed, such as some lectins, glucanases, transaldolases, methyltransferases, ferredoxins, protease inhibitors and GTPases. Furthermore, a large number of these CP relationships have not been reported yet, for example, chorismate mutases ([PDB:1CSM] versus [PDB:2AO2]); some (approximately 20%) even involve hypothetical proteins, implying that CPSARST can be applied to suggest possible functions for hypothetical proteins.

Rat Rab3A is a small G protein with GTPase activity 49. CPSARST detected that it has a CP relationship with a conserved hypothetical protein YlqF from Bacillus subtilis, the structure of which was determined by the New York Structural Genomics Research Consortium. When we searched with YlqF against the PDB using the DALI server 50, a number of isomerases, elongation factors, G proteins, transferases and other hypothetical proteins with inconvincible quality of structural alignments, i.e. small alignment sizes and large RMSD, were returned (Additional data file 4). However, CPSARST detected that many G proteins superimpose well with YlqF, suggesting that it may possess GTP binding/GTPase activity (Table 5). Figure 4 shows that DALI can only partially align Rab3A and YlqF (alignment size, 96; RMSD, 2.9 Å), while CPSARST successfully detects the CP relationship between them (alignment size, 130; RMSD, 3.2 Å).

Jung and Lee 29 suggested that when a pair of proteins can be well-aligned, with or without CP of the sequences, they are symmetric CPs. Considering this definition, proteins containing repeats or duplications will be included. However, Uliel et al. 30 supposed that these should be differentiated from true CPs. In our point of view, the certification of a CP relationship between symmetric proteins is conditional upon the observation of a reasonable increase in sequence homology after the CP. For instance, B. subtilis thiaminase I 51 and Variovorax sp. Pal2 phosphonopyruvate hydrolase 52 are a pair of symmetric TIM-barrel proteins detected by CPSARST that superimpose well, with (alignment size, 151; RMSD, 2.4 Å) or without (alignment size, 158; RMSD, 2.7 Å) CP. Their sequence identity rises from 10.1% to 24.3% upon CP. As shown in Figure 5, their ligand-interacting residues are not well-aligned without CP while, for each protein, these functionally important residues can be aligned with physiochemically related amino acids on the other protein with CP. Therefore, we suggest that this is a true CP case.

Generally speaking, although protein similarity search methods based on amino acid sequence alignments are much faster than those based on structural comparisons, they are less sensitive in detecting remote homology 53. In the case of detecting CP, sequence-based methods have met great challenges because of the evolutionary complexity and diversity of circular permutants. Except the post-translational modification model, all the other proposed mechanisms for CP involve at least two stages of genetic modifications in evolution (see Background), implying that the formation of CP may require a long period during which other common mutations (substitutions, insertions and deletions) can accumulate to such an extent that the circular permutants have much diverged from the parent protein in sequence. Therefore, sequence-based methods may be limited in identifying distantly related CPs. For instance, Uliel et al. used an amino acid sequence-based heuristic algorithm to screen the entire Swiss-Prot database (version 34.0; approximately 80,000 proteins) and the Pfam database 54 for CP pairs, and identified only 32 cases 30. However, in the same year, Jung and Lee 29 used a structure-based algorithm to survey a protein dataset (3,035 domains) collected from SCOP and reported that approximately 47% (1,433 of 3,035) of the domains each had at least one circular permutant. Furthermore, they discovered that less than 0.3% of the abundant symmetric CPs have > 30% sequence identities. Although this large difference is partially caused by the fact that Uliel et al. used more stringent criteria to identify CP, it basically indicates that amino acid sequence-based methods can miss many distantly related CPs 34.

Among the CP candidate pairs detected by CPSARST in nrSCOP-90, 27.5% can be considered as symmetric CPs (Table 4). Similar to the observation of Jung and Lee, few of these symmetric CPs (2.6%) have sequence identities > 30%. Furthermore, although 91% of the naturally occurring CP pairs listed in Table 2 have sequence identities ≤ 20%, CPSARST shows good performance when compared with other structure-based methods. These data demonstrate that CPSARST is able to detect CPs with low sequence identities.

In most cases, it is not easy to achieve high accuracy and speed simultaneously for a database search method; instead, some compromising balance is usually reached. Judging from the fact that using previous structure-based CP-detecting methods such as SAMO to search the current PDB requires more than 15,000 minutes 34 per query, it is reasonable that speed should be weighted more than accuracy in the field of CP searching, especially in this post-genomic era when the amount of protein structural data is increasing rapidly. CPSARST has been shown to achieve accuracy substantially higher than sequence-based UFAU (Figure 2) and comparable to structure-based SAMO (Tables 2 and 3); as to the speed, it can scan 52,800 database proteins per minute (Table 4), approximately 4 and 8,824 times faster than UFAU and SAMO, respectively. This improvement in speed is achieved by two features: it transforms three-dimensional information of protein structures into one-dimensional text strings and, thus, converts structural comparison problems into text sequence alignment problems, which can be solved much more rapidly; and, in both the screening and refinement stages, CPSARST does not stick to the absolute qualities of the alignments. By focusing on the relative qualities between two rounds of alignments, it can rapidly sieve out useful information. We call this strategy 'double filter-and-refine'. Here we propose that it is efficient, flexible and applicable to other biological research fields, especially where the data analyses require large-scale computational power.

Previous studies have made conflicting conclusions; some presumed that CP is rare in nature 61430 - approximately 5% as indicated by Vogel and Morea 14 - while others supposed that CP is frequent 12934 - approximately 47% as estimated by Jung and Lee 29. In our observation, studies based on structural analyses usually discovered more CPs than sequence-based ones; besides, studies that consider the whole protein as the unit that undergoes CP would conclude that CP is rare whereas those viewing the domain as the unit that undergoes CP would suggest CP to be frequent.

As we have discussed, it is reasonable that more cases of CP are detected by structural comparison than by amino acid sequence alignment. However, although proteins with similar structures are usually functionally related 55, when a pair of structurally and functionally similar proteins share extremely low sequence identity, we still cannot exclude the possibility that they are just the products of convergent evolution 565758 and do not share the same origin. In the case of identifying CP, it is noteworthy that even if a pair of proteins shows a high extent of CP topologically, it does not directly mean that an evolutionary CP event has indeed taken place. Therefore, we argue that detecting CP only by structure would result in too many false positives when judged from the point of view of molecular evolution. This is why we have set up a user-adjustable sequence identity filter in the web service of CPSARST 41 (see Materials and methods). When this filter was not enabled, the prevalence of CP estimated by CPSARST was 12.6-17.6% (see Results). When we considered that a real CP should have a higher sequence identity in the CP alignment than in the linear alignment, around one-fourth of the candidate pairs counted in Table 4 was filtered out, lowering the estimated prevalence of CP to 9.0-13.0%.

The fact that the frequency of CP estimated by CPSARST is only one-third of that estimated by Jung and Lee 29 is probably because of the more stringent criteria used by CPSARST. We set the RMSD cutoff as 5 Å, the CP score threshold as 0.2 and the least permutation size as 20% for a pair of proteins to be considered as CP candidates; similar criteria were not seen in the report of Jung and Lee. Also, considering their methodology, there is a large likelihood that proteins containing repeats and duplications are regarded as CPs, many of which have been treated as false cases by Uliel et al. 30 and us (see Materials and methods). When we loosened the criteria to 6 Å (RMSD cutoff), 0.1 (CP score threshold) and 10% (least permutation size), and did not filter out proteins containing repeats, the CP prevalence estimated by CPSARST was 34.7-36.7% (see Additional data file 5 for statistics), similar to Jung and Lee's estimation. However, since they did not provide any supplementary list of their CP candidates, we are unable to check our speculation.

To our knowledge, all the currently available CP-detecting methods are more sensitive to global CP (the unit undergoing CP is the whole protein) than partial CP (the CP is within a region of the protein), as is CPSARST. To detect partial CP, domain databases such as SCOP and Pfam are usually used as the target databases instead of the PDB and Swiss-Prot. Although considering the domain as the unit undergoing CP, that is, partial CP, can identify more candidates (as shown in Table 4), some scientists have argued that these cases should be considered as 'swaps' rather than CPs 30. This controversy is another cause of the conflicting conclusions about the prevalence of CP.

To sum up, despite the conflicting conclusions made by previous studies, there seem to be rational explanations for this situation. We suppose that the identification of CPs requires a precise definition of CP depending on the purpose of the study. In our opinion, if evolutionary importance and mechanisms are concerned, global CP with reasonable sequence identity limitation will be suitable, while partial CP without limitation of sequence identity in the definition may help scientists to discover novel functional relationships among proteins and to reveal the principles of protein folding.

The performance of CPSARST suggests that it is an efficient approach to the detection of CPs in large protein structural datasets; routine bank-against-bank searches are thus achievable. The multiple indexes produced by CPSARST, for example, the structural similarity score, statistically meaningful E-value, sequence identity, alignment size, RMSD and CP score, are beneficial to develop automated procedures such as a functional assignment system for novel hypothetical proteins. Also, information retrieved by bank-against-bank searches can be organized into a CP database.

Since the first observation of CP in plant lectins 5, many natural and artificial cases have been studied and several CP detecting methods have been developed; however, there is still no CP database and no standard procedure for evaluating CP detection methods. We suppose that a well-organized CP database will help move this field forward. It could provide a standard for the evaluations of CP-related programs, such as CP search tools and predictors of viable CP sites 59, and provide information to reveal the evolutionary mechanisms of CP.

CP has been applied to X-ray crystallography 22, modification of enzymes 15, creation of novel fusion proteins 2528, and construction of protein switches and sensors 2627. All these applications depend on a proper choice of position to create CP. A CP database offering plenty of materials for the discovery of the rules by which Nature selects CP sites should be advantageous to the technical applications of CP.

Although interesting, there is still much uncertainty about the evolutionary mechanisms and importance of CP 6182930. Weiner et al. 60 have proposed that the frequency of incomplete or intermediate CP may help determine the major mechanism of CP. The 'double filter-and-refine' strategy of CPSARST is very flexible. With extended boundary criteria, CPSARST can specifically detect incomplete or intermediate CP. The ability of CPSARST to perform rapid bank-against-bank searches by structural comparisons gives it the potential to reveal how, why and to what extent Nature achieves protein evolutionary and functional diversity by using CP.

CPSARST describes three-dimensional protein structures as one-dimensional strings by using a RST algorithm 40. The torsion angles (φ,δ) of a number of proteins were plotted onto a 10° × 10° dissected RM map. The 1,296 cells on this map were then clustered into 22 groups by nearest-neighbor clustering 61 based on their spot numbers and angular distances. These groups were assigned a set of English letters called 'Ramachandran codes'. Coordinates of a protein structure could be accordingly transformed into a text string. The scoring matrix for these codes was produced by using a 'regenerative approach' 40. This linear encoding system converts complicated and time-consuming structural comparison problems into sequence comparisons, which can be done very rapidly. It has been applied to protein structural similarity searching and achieved speeds hundreds of thousands of times higher than CE with an acceptable compromise of accuracy 40. The structural string generated by RST is different from the amino acid sequence in nature; therefore, we termed it 'Ramachandran sequence' or 'Ramachandran string'.

A hundred polypeptide sequences each longer than 100 residues and sharing < 40% sequence identities were randomly selected from the PDB to perform in silico circular permutations. Regular mutations, i.e. substitutions, insertions and deletions, were introduced in the ratio 150:1:1 to generate random CPs, resulting in 100 levels of decreasing sequence identities/similarities for every polypeptide sequence. The collection of these computer-generated random CPs is called the RCP dataset.

The substitution rates of various amino acids used to generate the RCP dataset were calculated by analyzing a large number of multiple alignment blocks, the sequences of which shared < 45% identity, as described previously 62. Since every sequence in the RCP dataset was evolved independently to avoid any possible bias, we supposed that it is suitable for the evaluation of CP detection methods. RCP has two subsets, the identity subset and similarity subset, each containing 10,000 CP pairs (100 parent sequences × 100 circular permutants). They are listed in Additional data file 6.

Comparisons between each parent sequence and its CPs in the identity subset of the RCP dataset were performed by the traditional heuristic method blast 45. Two parameters were monitored to assess the performance: the percentage of cases in which the exact permutation site was retrieved; and the average percentage distance of the found permutation site to the exact one (see Results). Another two parameters were monitored to optimize the filter for RM sequence searches: the ratio of similarity scores and the negative logarithm in base 10 (-log₁₀) of the E-value ratios, before and after the duplication of query sequences (see Additional data file 7 for the results). We found that all the score ratios are equal to or higher than 1, indicating that when the sequence of a CP is duplicated (DL), it always aligns to its parent sequence better than the normal length (NL). As to the E-value ratios, that is, -log₁₀(E-value_DL/E-value_NL), approximately 80% of them are larger than 2, which stands for a 10²-fold improvement of the significance of the similarity score after duplicating the query sequence (see Results for detailed information about E-values).

It has been supposed that using heuristic methods like blast to search for CPs is difficult because an unambiguous reconstruction of the alignment results is problematic 38. CPSARST, however, overcomes this problem by duplicating the query structure, doing two rounds (with and without the duplication) of database searches, and analyzing the results mutually. The hits with improved alignment qualities are picked as CP candidates, the permutation sites of which can be easily determined from the alignment results of duplicated sequences. In the screening stage, the search results of RM strings were filtered with simple criteria referring to previous studies and our experimental results on RCP amino acid sequences mentioned above. The permutation site should be at between 20% and 80% along the length of the query protein, ensuring a significant permutation size (20%). It has been supposed that a tiny permutation size is unlikely a real CP 39. The size of the candidate could be different from that of the query protein by at most 50% because proteins of very different sizes are improbable candidates for CPs 38. The similarity score of the duplicated query string (Score_DL) should be higher than that of the normal query string (Score_NL), and the -log₁₀ value of the E-value ratio should be larger than -0.5 (see Additional data file 7 for detailed information about these settings):

S c o r e D L S c o r e N L > 1 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8GiVeY=Pipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=yqpe0xbbG8A8frFve9Fve9Fj0dmeaabaqaciaacaGaaeqabaqabeGadaaakeaajuaGdaWcaaqaaiaadofacaWGJbGaam4BaiaadkhacaWGLbWaaSbaaeaacaWGebGaamitaaqabaaabaGaam4uaiaadogacaWGVbGaamOCaiaadwgadaWgaaqaaiaad6eacaWGmbaabeaaaaGccqGH+aGpcaaIXaaaaa@3F58@

− log ⁡ 10 ( E v a l u e D L E v a l u e N L ) > − 0.5 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2Caerbhv2BYDwAHbqedmvETj2BSbqee0evGueE0jxyaibaiKI8=vI8GiVeY=Pipec8Eeeu0xXdbba9frFj0xb9Lqpepeea0xd9q8qiYRWxGi6xij=hbbc9s8aq0=yqpe0xbbG8A8frFve9Fve9Fj0dmeaabaqaciaacaGaaeqabaqabeGadaaakeaacqGHsislciGGSbGaai4BaiaacEgadaWgaaWcbaGaaGymaiaaicdaaeqaaOGaaiikaKqbaoaalaaabaGaamyraiaadAhacaWGHbGaamiBaiaadwhacaWGLbWaaSbaaeaacaWGebGaamitaaqabaaabaGaamyraiaadAhacaWGHbGaamiBaiaadwhacaWGLbWaaSbaaeaacaWGobGaamitaaqabaaaaOGaaiykaiabg6da+iabgkHiTiaaicdacaGGUaGaaGynaaaa@4A4C@

The refinement of search results of RM sequences were performed by FAST, an accurate structural alignment algorithm 4063 and a CP scoring scheme developed by Vesterstrom and Taylor 39, following these steps. Step 1: for each candidate, the putative permutation site is parsed from the alignment result of the duplicated query string. Step 2: performing two rounds of FAST structural alignments. The first round is a normal linear alignment. In the second round, the circularly permuted alignment, the PDB file of the query structure was manipulated by exchanging the amino- and carboxy-terminal halves according to the putative permutation site so that FAST will do the structural alignment 'backside first'. Step 3: if the FAST alignment size after CP is no larger than 50% of the smaller size of the query and subject proteins, it is screened out. Step 4: the RMSD cutoff of the CP alignment is set as 5 Å. Step 5: in order to differentiate true CP from protein with internal repeats or duplications, two criteria have been set: the alignment size of the CP alignment should be larger than that of the linear alignment; and the FAST similarity score 63 or TOP score 43 (see formula (2)) calculated from the CP alignment should gain at least 25% improvement over the linear alignment. Step 6: the CP score 39 was calculated from the aligned positions by FAST. It has a theoretical minimum value of -1 (a completely linear alignment) and a maximum value of 1 (a perfect CP). Although Vesterstrom and Taylor suggested that an alignment with this CP score higher than 0.25 can be considered as a significant CP, we find that 0.2 is still suitable in our multi-filter system. Step 7: the putative CP site is refined by parsing the output of FAST structural alignment.

The procedure of the database search tool CPSARST can be simplified to perform pair-wise structure alignments as follows. First, transform the query and subject protein structures into RM sequences Q and S, respectively. Second, duplicate Q string to QQ, and align it to S. Third, find the best local alignment and trace it back to the 'start point', which is the putative permutation site. For example, if in the best local alignment, the fragment between residues q₁ and q₂ of Q is aligned to the fragment between s₁ and s₂ of S, then the permutation site of Q will be traced back to q₁ - s₁ + 1. Fourth, introduce a CP into the query structure according to the putative CP site. Compare this new structure with the subject protein by using an accurate structural alignment algorithm mentioned above.

CPSARST basically works on the structurally meaningful RM strings transformed by RST; however, since there have been many errors and inconsistencies reported in PDB entries 64, a few polypeptides (approximately 2%) cannot be successfully transformed into RM strings. Therefore, in the implementation of CPSARST, we have added two extra rounds of amino acid sequence alignment searches, one by the normal length and the other by the duplicated sequence, prior to the RM string searches. Besides, the sequence homology filter can be enabled to guarantee a higher evolutionary significance of the search results (see Discussion), and several parameters are adjustable by the users according their needs or the property of materials.