PLOS/Circular permutation in proteins

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10.1371/journal.pcbi.1002445


Authors
Spencer Bliven, Andreas Prlić
About the Authors 

Spencer Bliven
AFFILIATION: Bioinformatics Program, University of California, San Diego , 9500 Gilman Drive, La Jolla, CA 92093

Andreas Prlić
AFFILIATION: San Diego Supercomputer Center, University of California San Diego , 9500 Gilman Drive, Mailcode 0505 La Jolla, CA 92093-0505


Schematic representation of a circular permutation in two proteins. The first protein (outer circle) has the sequence a-b-c. After the permutation the second protein (inner circle) has the sequence c-a-b. The letters N and C indicate the location of the amino- and carboxy-termini of the protein sequences and how their positions change relative to each other.

Circular permutation describes a type of relationship between proteins, whereby the proteins have a changed order of amino acids in their protein sequence, such that the sequence of the first portion of one protein (adjacent to the N-terminus) is related to that of the second portion of the other protein (near its C-terminus), and vice versa (see figure 1). This is directly analogous to the mathematical notion of a cyclic permutation over the set of residues in a protein.

Circular permutation can be the result of evolutionary events, post-translational modifications, or artificially engineered mutations. The result is a protein structure with different connectivity, but overall similar three-dimensional (3D) shape. The homology between portions of the proteins can be established by observing similar sequences between N- and C-terminal portions of the two proteins, structural similarity, or other methods.

History[edit | edit source]

Two proteins that are related by a circular permutation. Concanavalin A (left), from the Protein Data Bank (PDB: 3cna​), and peanut lectin (right), from PDB: 2pel​, which is homologous to favin. The termini of the proteins are highlighted by blue and green spheres, and the sequence of residues is indicated by the gradient from blue (N-terminus) to green (C-terminus). The 3D fold of the two proteins is highly similar; however, the N- and C- termini are located on different positions of the protein.[1]

In 1979, Bruce Cunningham and his colleagues discovered the first instance of a circularly permuted protein in nature.[1] After determining the peptide sequence of the lectin protein favin, they noticed its similarity to a known protein - concanavalin A - except that the ends were circularly permuted (see figure 2). Later work confirmed the circular permutation between the pair[2] and showed that concanavalin A is permuted post-translationally[3] through cleavage and an unusual protein ligation.[4]

After the discovery of a natural circularly permuted protein, researchers looked for a way to emulate this process. In 1983, David Goldenberg and Thomas Creighton were able to create a circularly permuted version of a protein by chemically ligating the termini to create a cyclic protein, then introducing new termini elsewhere using trypsin.[5] In 1989, Karolin Luger and her colleagues introduced a genetic method for making circular permutations by carefully fragmenting and ligating DNA.[6] This method allowed for permutations to be introduced at arbitrary sites, and is still used today to design circularly permuted proteins in the lab.

Despite the early discovery of post-translational circular permutations and the suggestion of a possible genetic mechanism for evolving circular permutants, it was not until 1995 that the first circularly permuted pair of genes were discovered. Saposins are a class of proteins involved in sphingolipid catabolism and lipid antigen presentation in humans. Christopher Ponting and Robert Russell identified a circularly permuted version of a saposin inserted into plant aspartic proteinase, which they nicknamed swaposin.[7] Saposin and swaposin were the first known case of two natural genes related by a circular permutation.

Hundreds of examples of protein pairs related by a circular permutation were subsequently discovered in nature or produced in the laboratory. The Circular Permutation Database[8] contains 2,238 circularly permuted protein pairs with known structures, and many more are known without structures.[9] The CyBase database collects proteins that are cyclic, some of which are permuted variants of cyclic wild-type proteins.[10] SISYPHUS is a database that contains a collection of hand-curated manual alignments of proteins with non-trivial relationships, several of which have circular permutations.[11]

Evolution[edit | edit source]

There are two main models that are currently being used to explain the evolution of circularly permuted proteins: permutation by duplication and fission and fusion. The two models have compelling examples supporting them, but the relative contribution of each model in evolution is still under debate.[12] Other, less common, mechanisms have been proposed, such as "cut and paste"[13] or "exon shuffling".

Permutation by Duplication[edit | edit source]

The permutation by duplication mechanism for producing a circular permutation. First, a gene is duplicated in place. Next, start and stop codons are introduced, resulting in a circularly permuted gene.

The earliest model proposed for the evolution of circular permutations is the permutation by duplication mechanism.[1] In this model, a precursor gene first undergoes a duplication and fusion to form a large tandem repeat. Next, start and stop codons are introduced at corresponding locations in the duplicated gene, removing redundant sections of the protein (see figure 3).

One surprising prediction of the permutation by duplication mechanism is that intermediate permutations can occur. For instance, the duplicated version of the protein should still be functional, since otherwise evolution would quickly select against such proteins. Likewise, partially duplicated intermediates where only one terminus was truncated should be functional. Such intermediates have been extensively documented in protein families such as DNA methyltransferases.[14]


Saposin and Swaposin[edit | edit source]

Suggested relationship between saposin and swaposin. They could have evolved from a similar gene.[15] Both consist of 4 alpha helices with the order of helices being permuted relative to each other.

An example for permutation by duplication is the relationship between saposin and swaposin. Saposins are highly conserved glycoproteins that consist of an approximately 80 amino acid residue long protein forming a four alpha helical structure. They have a nearly identical placement of cysteine residues and glycosylation sites. The cDNA sequence that codes for saposin is called prosaposin. It is a precursor for four cleavage products, the saposins A, B, C, and D. The four saposin domains most likely arose from two tandem duplications of an ancestral gene.[16] This repeat suggests a mechanism for the evolution of the relationship with the plant-specific insert (PSI) (see figure 4). The PSI is a domain exclusively found in plants, consisting of approximately 100 residues and found in plant aspartic proteases.[17] It belongs to the saposin-like protein family (SAPLIP) and has the N- and C- termini "swapped", such that the order of helices is 3-4-1-2 compared with saposin, thus leading to the name "swaposin".[7] For a review on functional and structural features of saposin-like proteins, see Bruhn (2005).[18]

Fission and Fusion[edit | edit source]

The fission and fusion mechanism of circular permutation. Two separate genes arise (potentially from the fission of a single gene). If the genes fuse together in different orders in two orthologues, a circular permutation occurs.

Another model for the evolution of circular permutations is the fission and fusion model. The process starts with two partial proteins. These may represent two independent polypeptides (such as two parts of a heterodimer), or may have originally been halves of a single protein that underwent a fission event to become two polypeptides (see figure 5).

The two proteins can later fuse together to form a single polypeptide. Regardless of which protein comes first, this fusion protein may show similar function. Thus, if a fusion between two proteins occurs twice in evolution (either between paralogues within the same species or between orthologues in different species) but in a different order, the resulting fusion proteins will be related by a circular permutation.

Evidence for a particular protein having evolved by a fission and fusion mechanism can be provided by observing the halves of the permutation as independent polypeptides in related species, or by demonstrating experimentally that the two halves can function as separate polypeptides.[19]

Transhydrogenases[edit | edit source]

Transhydrogenases in various organisms can be found in three different domain arrangements. In cattle, the three domains are arranged sequentially. In the bacteria E. coli, Rb. capsulatus, and R. rubrum, the transhydrogenase consists of two or three subunits. Finally, transhydrogenase from the protist E. tenella consists of a single subunit that is circularly permuted relative to cattle transhydrogenase.[20]

An example for the fission and fusion mechanism can be found in nicotinamide nucleotide transhydrogenases.[20] These are membrane-bound enzymes that catalyze the transfer of a hydride ion between NAD(H) and NADP(H) in a reaction that is coupled to transmembrane proton translocation. They consist of three major functional units (I, II, and III) that can be found in different arrangement in bacteria, protozoa, and higher eukaryotes (see figure 6). Phylogenetic analysis suggests that the three groups of domain arrangements were acquired and fused independently.[12]

Other Processes that can Lead to Circular Permutations[edit | edit source]

Post-translational Modification[edit | edit source]

The two evolutionary models mentioned above describe ways in which genes may be circularly permuted, resulting in a circularly permuted mRNA after transcription. Proteins can also be circularly permuted via post-translational modification, without permuting the underlying gene. Circular permutations can happen spontaneously through auto-catalysis, as in the case of concanavalin A (see figure 2).[4] Alternately, permutation may require restriction enzymes and ligases.[5]

The Role of Circular Permutations in Protein Engineering[edit | edit source]

Many proteins have their termini located close together in 3D space.[21][22] Because of this, it is often possible to design circular permutations of proteins. Today, circular permutations are generated routinely in the lab using standard genetics techniques.[6] Although some permutation sites prevent the protein from folding correctly, many permutants have been created with nearly identical structure and function to the original protein.

The motivation for creating a circular permutant of a protein can vary. Scientists may want to improve some property of the protein, such as

  • Reduce proteolytic susceptibility. The rate at which proteins are broken down can have a large impact on their activity in cells. Since termini are often accessible to proteases, designing a circularly permuted protein with less accessible termini can increase the lifespan of that protein in the cell.[23]
  • Improve catalytic activity. Circularly permuting a protein can sometimes increase the rate at which it catalyzes a chemical reaction, leading to more efficient proteins.[24]
  • Alter substrate or ligand binding. Circularly permuting a protein can result in the loss of substrate binding, but can occasionally lead to novel ligand binding activity or altered substrate specificity.[25]
  • Improve thermostability. Making proteins active over a wider range of temperatures and conditions can improve their utility.[26]

Alternately, scientists may be interested in properties of the original protein, such as

  • Fold order. Determining the order in which different parts of a protein fold is challenging due to the extremely fast time scales involved. Circularly permuted versions of proteins will often fold in a different order, providing information about the folding of the original protein.[27][28][29]
  • Essential structural elements. Artificial circularly permuted proteins can allow parts of a protein to be selectively deleted. This gives insight into which structural elements are essential or not.[30]
  • Modify quaternary structure. Circularly permuted proteins have been shown to take on different quaternary structure than wild-type proteins.[31]
  • Find insertion sites for other proteins. Inserting one protein as a domain into another protein can be useful. For instance, inserting calmodulin into green fluorescent protein (GFP) allowed researchers to measure the activity of calmodulin via the florescence of the split-GFP.[32] Regions of GFP that tolerate the introduction of circular permutation are more likely to accept the addition of another protein while retaining the function of both proteins.
  • Design of novel biocatalysts and biosensors. Introducing circular permutations can be used to design proteins to catalyze specific chemical reactions,[33][24] or to detect the presence of certain molecules using proteins. For instance, the GFP-calmodulin fusion described above can be used to detect the level of calcium ions in a sample.[32]

Algorithmic Detection of Circular Permutations[edit | edit source]

Many sequence alignment and protein structure alignment algorithms have been developed assuming linear data representations and as such are not able to detect circular permutations between proteins. Two examples of frequently used methods that have problems correctly aligning proteins related by circular permutation are dynamic programming and many hidden Markov models. As an alternative to these, a number of algorithms are built on top of non-linear approaches and are able to detect topology-independent similarities, or employ modifications allowing them to circumvent the limitations of dynamic programming. The table below is a collection of such methods.

The algorithms are classified according to the type of input they require. Sequence-based algorithms require only the sequence of two proteins in order to create an alignment. Sequence methods are generally fast and suitable for searching whole genomes for circularly permuted pairs of proteins. Structure-based methods require 3D structures of both proteins being considered. They are often slower than sequence-based methods, but are able to detect circular permutations between distantly related proteins with low sequence similarity. Some structural methods are topology independent, meaning that they are also able to detect more complex rearrangements than circular permutation.

NAME Type Description Author Year Availability Reference
FBPLOT Sequence Draws dot plots of suboptimal sequence alignments Zuker 1991 [34]
Bachar et al Structure, topology independent Uses geometric hashing for the topology independent comparison of proteins Bachar et al. 1993 [35]
Uliel at al Sequence First suggestion of how a sequence comparison algorithm for the detection of circular permutations can work Uliel et al. 1999 [36]
SHEBA Structure Duplicates a sequence in the middle; uses SHEBA algorithm for structure alignment; determines new cut position after structure alignment Jung & Lee 2001 [37]
Multiprot Structure, Topology independent Calculates a sequence order independent multiple protein structure alignment Shatsky 2004 server, download [38]
RASPODOM Sequence Modified Needleman & Wunsch sequence comparison algorithm Weiner et al. 2005 server [39]
CPSARST Structure Describes protein structures as one-dimensional text strings by using a Ramachandran sequential transformation (RST) algorithm. Detects circular permutations through a duplication of the sequence represention and "double filter-and-refine" strategy. Lo, Lyu 2008 server [40]
GANGSTA + Structure Works in two stages: Stage one identifies coarse alignments based on secondary structure elements. Stage two refines the alignment on residue level and extends into loop regions. Schmidt-Goenner et al. 2009 server, download [41]
SANA Structure Detect initial aligned fragment pairs (AFPs). Build network of possible AFPs. Use random-mate algorithm to connect components to a graph. Wang et al. 2010 download [42]
CE-CP Structure Built on top of the combinatorial extension algorithm. Duplicates atoms before alignment, truncates results after alignment Bliven et al. 2010 server, download [43]

Acknowledgments[edit | edit source]

A stub of this article authored primarily by AP was previously published on Wikipedia. The authors built on the version of 00:53, 29 May 2011 and were careful not to include the work of others for licensing reasons and rather provide a complete re-write of the first version. Still, they would like to thank individuals from the Wikipedia community for subsequent contributions to the original stub.

Further Reading[edit | edit source]

  • David Goodsell (2010) Concanavalin A and Circular Permutation Research Collaboratory for Structural Biology (RCSB) Protein Data Bank (PDB) Molecule of the Month April 2010
  • Yu and Lutz (2011), for a review of the use of circular permutation in protein design.[22]
  • Weiner & Bornberg-Bauer (2006), for a review of evolutionary mechanisms for circular permutations.[12]
  • Cyclic permutation

References[edit | edit source]

  1. ↑ 1.0 1.1 1.2 Cunningham, B. A.; Hemperly, J. J.; Hopp, T. P.; Edelman, G. M. (1979). "Favin versus concanavalin A: Circularly permuted amino acid sequences". Proceedings of the National Academy of Sciences of the United States of America 76 (7): 3218–3222. doi:10.1073/pnas.76.7.3218. PMID 16592676. PMC 383795. //www.ncbi.nlm.nih.gov/pmc/articles/PMC383795/. 
  2. ↑ Einspahr, H.; Parks, E. H.; Suguna, K.; Subramanian, E.; Suddath, F. L. (1986). "The crystal structure of pea lectin at 3.0-A resolution". The Journal of Biological Chemistry 261 (35): 16518–16527. doi:10.1016/S0021-9258(18)66597-4. PMID 3782132. 
  3. ↑ Carrington, D. M.; Auffret, A.; Hanke, D. E. (1985). "Polypeptide ligation occurs during post-translational modification of concanavalin A". Nature 313 (5997): 64–67. doi:10.1038/313064a0. PMID 3965973. 
  4. ↑ 4.0 4.1 Bowles, D. J.; Pappin, D. J. (1988). "Traffic and assembly of concanavalin A". Trends in Biochemical Sciences 13 (2): 60–64. doi:10.1016/0968-0004(88)90030-8. PMID 3070848. 
  5. ↑ 5.0 5.1 Goldenberg, D. P.; Creighton, T. E. (1983). "Circular and circularly permuted forms of bovine pancreatic trypsin inhibitor". Journal of Molecular Biology 165 (2): 407–413. doi:10.1016/s0022-2836(83)80265-4. PMID 6188846. 
  6. ↑ 6.0 6.1 Luger, K.; Hommel, U.; Herold, M.; Hofsteenge, J.; Kirschner, K. (1989). "Correct folding of circularly permuted variants of a beta alpha barrel enzyme in vivo". Science 243 (4888): 206–210. doi:10.1126/science.2643160. PMID 2643160. 
  7. ↑ 7.0 7.1 Ponting, C. P.; Russell, R. B. (1995). "Swaposins: Circular permutations within genes encoding saposin homologues". Trends in Biochemical Sciences 20 (5): 179–180. doi:10.1016/s0968-0004(00)89003-9. PMID 7610480. 
  8. ↑ Circular Permutation Database. http://sarst.life.nthu.edu.tw/cpdb/ Accessed 16 February, 2012.
  9. ↑ Lo, W. C.; Lee, C. C.; Lee, C. Y.; Lyu, P. C. (2009). "CPDB: A database of circular permutation in proteins". Nucleic Acids Research 37 (Database issue): D328-32. doi:10.1093/nar/gkn679. PMID 18842637. PMC 2686539. //www.ncbi.nlm.nih.gov/pmc/articles/PMC2686539/. 
  10. ↑ Kaas, Q.; Craik, D. J. (2010). "Analysis and classification of circular proteins in CyBase". Biopolymers 94 (5): 584–591. doi:10.1002/bip.21424. PMID 20564021. 
  11. ↑ Andreeva, A.; Prlić, A.; Hubbard, T. J.; Murzin, A. G. (2007). "SISYPHUS--structural alignments for proteins with non-trivial relationships". Nucleic Acids Research 35 (Database issue): D253-9. doi:10.1093/nar/gkl746. PMID 17068077. PMC 1635320. //www.ncbi.nlm.nih.gov/pmc/articles/PMC1635320/. 
  12. ↑ 12.0 12.1 12.2 Weiner j, 3rd; Bornberg-Bauer, E. (2006). "Evolution of circular permutations in multidomain proteins". Molecular Biology and Evolution 23 (4): 734–743. doi:10.1093/molbev/msj091. PMID 16431849. 
  13. ↑ Bujnicki, J. M. (2002). "Sequence permutations in the molecular evolution of DNA methyltransferases". BMC Evolutionary Biology 2: 3. doi:10.1186/1471-2148-2-3. PMID 11914127. PMC 102321. //www.ncbi.nlm.nih.gov/pmc/articles/PMC102321/. 
  14. ↑ Jeltsch, A. (1999). "Circular permutations in the molecular evolution of DNA methyltransferases". Journal of Molecular Evolution 49 (1): 161–164. doi:10.1007/pl00006529. PMID 10368444. 
  15. ↑ Ponting, C. P.; Russell, R. B. (1995). "Swaposins: Circular permutations within genes encoding saposin homologues". Trends in Biochemical Sciences 20 (5): 179–180. doi:10.1016/s0968-0004(00)89003-9. PMID 7610480. 
  16. ↑ Hazkani-Covo, E.; Altman, N.; Horowitz, M.; Graur, D. (2002). "The evolutionary history of prosaposin: Two successive tandem-duplication events gave rise to the four saposin domains in vertebrates". Journal of Molecular Evolution 54 (1): 30–34. doi:10.1007/s00239-001-0014-0. PMID 11734895. 
  17. ↑ Guruprasad, K.; Törmäkangas, K.; Kervinen, J.; Blundell, T. L. (1994). "Comparative modelling of barley-grain aspartic proteinase: A structural rationale for observed hydrolytic specificity". FEBS Letters 352 (2): 131–136. doi:10.1016/0014-5793(94)00935-x. PMID 7925961. 
  18. ↑ Bruhn, H. (2005). "A short guided tour through functional and structural features of saposin-like proteins". The Biochemical Journal 389 (Pt 2): 249–257. doi:10.1042/BJ20050051. PMID 15992358. PMC 1175101. //www.ncbi.nlm.nih.gov/pmc/articles/PMC1175101/. 
  19. ↑ Lee, J.; Blaber, M. (2011). "Experimental support for the evolution of symmetric protein architecture from a simple peptide motif". Proceedings of the National Academy of Sciences of the United States of America 108 (1): 126–130. doi:10.1073/pnas.1015032108. PMID 21173271. PMC 3017207. //www.ncbi.nlm.nih.gov/pmc/articles/PMC3017207/. 
  20. ↑ 20.0 20.1 Hatefi, Y.; Yamaguchi, M. (1996). "Nicotinamide nucleotide transhydrogenase: A model for utilization of substrate binding energy for proton translocation". FASEB Journal : Official Publication of the Federation of American Societies for Experimental Biology 10 (4): 444–452. doi:10.1096/fasebj.10.4.8647343. PMID 8647343. 
  21. ↑ Thornton, J. M.; Sibanda, B. L. (1983). "Amino and carboxy-terminal regions in globular proteins". Journal of Molecular Biology 167 (2): 443–460. doi:10.1016/s0022-2836(83)80344-1. PMID 6864804. 
  22. ↑ 22.0 22.1 Yu, Y.; Lutz, S. (2011). "Circular permutation: A different way to engineer enzyme structure and function". Trends in Biotechnology 29 (1): 18–25. doi:10.1016/j.tibtech.2010.10.004. PMID 21087800. 
  23. ↑ Whitehead, T. A.; Bergeron, L. M.; Clark, D. S. (2009). "Tying up the loose ends: Circular permutation decreases the proteolytic susceptibility of recombinant proteins". Protein Engineering, Design & Selection : Peds 22 (10): 607–613. doi:10.1093/protein/gzp034. PMID 19622546. 
  24. ↑ 24.0 24.1 Cheltsov, A. V.; Barber, M. J.; Ferreira, G. C. (2001). "Circular permutation of 5-aminolevulinate synthase. Mapping the polypeptide chain to its function". The Journal of Biological Chemistry 276 (22): 19141–19149. doi:10.1074/jbc.M100329200. PMID 11279050. PMC 4547487. //www.ncbi.nlm.nih.gov/pmc/articles/PMC4547487/. 
  25. ↑ Qian, Z.; Lutz, S. (2005). "Improving the catalytic activity of Candida antarctica lipase B by circular permutation". Journal of the American Chemical Society 127 (39): 13466–13467. doi:10.1021/ja053932h. PMID 16190688. 
  26. ↑ Topell, S.; Hennecke, J.; Glockshuber, R. (1999). "Circularly permuted variants of the green fluorescent protein". FEBS Letters 457 (2): 283–289. doi:10.1016/s0014-5793(99)01044-3. PMID 10471794. 
  27. ↑ Viguera, A. R.; Serrano, L.; Wilmanns, M. (1996). "Different folding transition states may result in the same native structure". Nature Structural Biology 3 (10): 874–880. doi:10.1038/nsb1096-874. PMID 8836105. 
  28. ↑ Capraro, D. T.; Roy, M.; Onuchic, J. N.; Jennings, P. A. (2008). "Backtracking on the folding landscape of the beta-trefoil protein interleukin-1beta?". Proceedings of the National Academy of Sciences of the United States of America 105 (39): 14844–14848. doi:10.1073/pnas.0807812105. PMID 18806223. PMC 2567455. //www.ncbi.nlm.nih.gov/pmc/articles/PMC2567455/. 
  29. ↑ Zhang, P.; Schachman, H. K. (1996). "In vivo formation of allosteric aspartate transcarbamoylase containing circularly permuted catalytic polypeptide chains: Implications for protein folding and assembly". Protein Science : A Publication of the Protein Society 5 (7): 1290–1500. doi:10.1002/pro.5560050708. PMID 8819162. PMC 2143468. //www.ncbi.nlm.nih.gov/pmc/articles/PMC2143468/. 
  30. ↑ Huang, Y. M.; Nayak, S.; Bystroff, C. (2011). "Quantitative in vivo solubility and reconstitution of truncated circular permutants of green fluorescent protein". Protein Science : A Publication of the Protein Society 20 (11): 1775–1780. doi:10.1002/pro.735. PMID 21910151. PMC 3267941. //www.ncbi.nlm.nih.gov/pmc/articles/PMC3267941/. 
  31. ↑ Beernink, P. T.; Yang, Y. R.; Graf, R.; King, D. S.; Shah, S. S.; Schachman, H. K. (2001). "Random circular permutation leading to chain disruption within and near alpha helices in the catalytic chains of aspartate transcarbamoylase: Effects on assembly, stability, and function". Protein Science : A Publication of the Protein Society 10 (3): 528–537. doi:10.1110/ps.39001. PMID 11344321. PMC 2374132. //www.ncbi.nlm.nih.gov/pmc/articles/PMC2374132/. 
  32. ↑ 32.0 32.1 Baird, G. S.; Zacharias, D. A.; Tsien, R. Y. (1999). "Circular permutation and receptor insertion within green fluorescent proteins". Proceedings of the National Academy of Sciences of the United States of America 96 (20): 11241–11246. doi:10.1073/pnas.96.20.11241. PMID 10500161. PMC 18018. //www.ncbi.nlm.nih.gov/pmc/articles/PMC18018/. 
  33. ↑ Turner, N. J. (2009). "Directed evolution drives the next generation of biocatalysts". Nature Chemical Biology 5 (8): 567–573. doi:10.1038/nchembio.203. PMID 19620998. 
  34. ↑ Zuker, M. (1991). "Suboptimal sequence alignment in molecular biology. Alignment with error analysis". Journal of Molecular Biology 221 (2): 403–420. doi:10.1016/0022-2836(91)80062-y. PMID 1920426. 
  35. ↑ Bachar, O.; Fischer, D.; Nussinov, R.; Wolfson, H. (1993). "A computer vision based technique for 3-D sequence-independent structural comparison of proteins". Protein Engineering 6 (3): 279–288. doi:10.1093/protein/6.3.279. PMID 8506262. 
  36. ↑ Uliel, S.; Fliess, A.; Amir, A.; Unger, R. (1999). "A simple algorithm for detecting circular permutations in proteins". Bioinformatics (Oxford, England) 15 (11): 930–936. doi:10.1093/bioinformatics/15.11.930. PMID 10743559. 
  37. ↑ Jung, J.; Lee, B. (2001). "Circularly permuted proteins in the protein structure database". Protein Science : A Publication of the Protein Society 10 (9): 1881–1886. doi:10.1110/ps.05801. PMID 11514678. PMC 2253204. //www.ncbi.nlm.nih.gov/pmc/articles/PMC2253204/. 
  38. ↑ Shatsky, M.; Nussinov, R.; Wolfson, H. J. (2004). "A method for simultaneous alignment of multiple protein structures". Proteins 56 (1): 143–156. doi:10.1002/prot.10628. PMID 15162494. 
  39. ↑ Weiner j, 3rd; Thomas, G.; Bornberg-Bauer, E. (2005). "Rapid motif-based prediction of circular permutations in multi-domain proteins". Bioinformatics (Oxford, England) 21 (7): 932–937. doi:10.1093/bioinformatics/bti085. PMID 15788783. 
  40. ↑ Lo, W. C.; Lyu, P. C. (2008). "CPSARST: An efficient circular permutation search tool applied to the detection of novel protein structural relationships". Genome Biology 9 (1): R11. doi:10.1186/gb-2008-9-1-r11. PMID 18201387. PMC 2395249. //www.ncbi.nlm.nih.gov/pmc/articles/PMC2395249/. 
  41. ↑ Schmidt-Goenner, T.; Guerler, A.; Kolbeck, B.; Knapp, E. W. (2010). "Circular permuted proteins in the universe of protein folds". Proteins 78 (7): 1618–1630. doi:10.1002/prot.22678. PMID 20112421. 
  42. ↑ Wang, L.; Wu, L. Y.; Wang, Y.; Zhang, X. S.; Chen, L. (2010). "SANA: An algorithm for sequential and non-sequential protein structure alignment". Amino Acids 39 (2): 417–425. doi:10.1007/s00726-009-0457-y. PMID 20127263. 
  43. ↑ Prlic, A.; Bliven, S.; Rose, P. W.; Bluhm, W. F.; Bizon, C.; Godzik, A.; Bourne, P. E. (2010). "Pre-calculated protein structure alignments at the RCSB PDB website". Bioinformatics (Oxford, England) 26 (23): 2983–2985. doi:10.1093/bioinformatics/btq572. PMID 20937596. PMC 3003546. //www.ncbi.nlm.nih.gov/pmc/articles/PMC3003546/. 
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