Abstract is: In mathematics, and in particular in group theory, a cyclic permutation (or cycle) is a permutation of the elements of some set X which maps the elements of some subset S of X to each other in a cyclic fashion, while fixing (that is, mapping to themselves) all other elements of X. If S has k elements, the cycle is called a k-cycle. Cycles are often denoted by the list of their elements enclosed with parentheses, in the order to which they are permuted. For example, given X = {1, 2, 3, 4}, the permutation (1, 3, 2, 4) that sends 1 to 3, 3 to 2, 2 to 4 and 4 to 1 (so S = X) is a 4-cycle, and the permutation (1, 3, 2) that sends 1 to 3, 3 to 2, 2 to 1 and 4 to 4 (so S = {1, 2, 3} and 4 is a fixed element) is a 3-cycle. On the other hand, the permutation that sends 1 to 3, 3 to 1, 2 to 4 and 4 to 2 is not a cyclic permutation because it separately permutes the pairs {1, 3} and {2, 4}. The set S is called the orbit of the cycle. Every permutation on finitely many elements can be decomposed into cycles on disjoint orbits. The individual cyclic parts of a permutation are also called cycles, thus the second example is composed of a 3-cycle and a 1-cycle (or fixed point) and the third is composed of two 2-cycles, and denoted (1, 3) (2, 4).
| permutation | Q161519 |
| P646 | Freebase ID | /m/029smz |
| P2671 | Google Knowledge Graph ID | /g/1yqccmg_b |
| P2812 | MathWorld ID | CyclicPermutation |
| CircularPermutation | ||
| P6366 | Microsoft Academic ID | 77670614 |
| P4215 | nLab ID | cyclic permutation |
| P10283 | OpenAlex ID | C77670614 |
| P1482 | Stack Exchange tag | https://stackoverflow.com/tags/circular-permutations |
| P1889 | different from | permutation cycle | Q114290211 |
| P6104 | maintained by WikiProject | WikiProject Mathematics | Q8487137 |
| Q41929555 | A Phase1b Dose Escalation Study of Recombinant Circularly Permuted TRAIL in Patients With Relapsed or Refractory Multiple Myeloma |
| Q30192704 | A circularly permuted alpha-amylase-type alpha/beta-barrel structure in glucan-synthesizing glucosyltransferases. |
| Q35602272 | A circularly permuted recombinant interleukin 4 toxin with increased activity |
| Q54275528 | A fully active variant of dihydrofolate reductase with a circularly permuted sequence. |
| Q40197990 | A multicenter, open-label phase II study of recombinant CPT (Circularly Permuted TRAIL) plus thalidomide in patients with relapsed and refractory multiple myeloma |
| Q43275168 | A single circularly permuted GFP sensor for inositol-1,3,4,5-tetrakisphosphate based on a split PH domain |
| Q36526336 | Absence of circularly permuted and largely redundant sequences in the genome of visna virus |
| Q50231866 | Alignment of partial denaturation maps of circularly permuted DNA by computer |
| Q42063986 | Alteration of the disulfide-coupled folding pathway of BPTI by circular permutation |
| Q57486612 | An algorithm to generate a random cyclic permutation |
| Q40411964 | Analysis of DNA curvature using circular permutation of 5' end labelled fragments |
| Q41776140 | Analysis of p300/CBP histone acetyltransferase regulation using circular permutation and semisynthesis |
| Q36737313 | Aspartate transcarbamoylase containing circularly permuted catalytic polypeptide chains |
| Q33928863 | BAliBASE (Benchmark Alignment dataBASE): enhancements for repeats, transmembrane sequences and circular permutations |
| Q112205824 | CPDB |
| Q50783960 | Circular Permutation Probes for Illuminating Phosphorylation of Estrogen Receptor |
| Q27663603 | Circular Permutation Provides an Evolutionary Link between Two Families of Calcium-dependent Carbohydrate Binding Modules |
| Q27680939 | Circular Permutation of a WW Domain: Folding Still Occurs after Excising the Turn of the Folding-Nucleating Hairpin |
| Q39919408 | Circular Permutation of the Genome of a Temperate Bacteriophage from Streptococcus cremoris BK5. |
| Q21045391 | Circular Permutations in the Molecular Evolution of DNA Methyltransferases |
| Q21045382 | Circular and circularly permuted forms of bovine pancreatic trypsin inhibitor |
| Q51526220 | Circular permutation and deletion studies of myoglobin indicate that the correct position of its N-terminus is required for native stability and solubility but not for native-like heme binding and folding. |
| Q36526239 | Circular permutation as a tool to reduce surface entropy triggers crystallization of the signal recognition particle receptor beta subunit |
| Q37272110 | Circular permutation directs orthogonal assembly in complex collagen peptide mixtures |
| Q34247553 | Circular permutation in the Ω-loop of TEM-1 β-lactamase results in improved activity and altered substrate specificity |
| Q34121626 | Circular permutation of 5-aminolevulinate synthase as a tool to evaluate folding, structure and function. |
| Q21045400 | Circular permutation of 5-aminolevulinate synthase. Mapping the polypeptide chain to its function |
| Q44433320 | Circular permutation of 5-aminolevulinate synthase: effect on folding, conformational stability, and structure |
| Q27659891 | Circular permutation of Bacillus circulans xylanase: a kinetic and structural study |
| Q33600868 | Circular permutation of DNA cytosine-N4 methyltransferases: in vivo coexistence in the BcnI system and in vitro probing by hybrid formation |
| Q34661562 | Circular permutation of a synthetic eukaryotic chromosome with the telomerator |
| Q41836162 | Circular permutation of betaB2-crystallin changes the hierarchy of domain assembly |
| Q40962435 | Circular permutation of granulocyte colony-stimulating factor |
| Q41931923 | Circular permutation of ligand-binding module improves dynamic range of genetically encoded FRET-based nanosensor |
| Q27681135 | Circular permutation of the Trp-cage: fold rescue upon addition of a hydrophobic staple |
| Q40962132 | Circular permutation of the granulocyte colony-stimulating factor receptor agonist domain of myelopoietin |
| Q50503354 | Circular permutation of the starch-binding domain: inversion of ligand selectivity with increased affinity |
| Q36279175 | Circular permutation within the coenzyme binding domain of the tetrameric glyceraldehyde-3-phosphate dehydrogenase from Bacillus stearothermophilus. |
| Q21045398 | Circular permutation: a different way to engineer enzyme structure and function |
| Q36606023 | Circular, but not circularly permuted, deoxyribonucleic acid reacts slower than linear deoxyribonucleic acid with complementary linear deoxyribonucleic acid |
| Q54653083 | Circularly Permuted tRNAs as Specific Photoaffinity Probes of Ribonuclease P RNA Structure |
| Q37341502 | Circularly permuted GTPase YqeH binds 30S ribosomal subunit: Implications for its role in ribosome assembly. |
| Q48149408 | Circularly permuted TRAIL plus thalidomide and dexamethasone versus thalidomide and dexamethasone for relapsed/refractory multiple myeloma: a phase 2 study. |
| Q27740449 | Circularly permuted beta-lactamase from Staphylococcus aureus PC1 |
| Q54625285 | Circularly permuted dihydrofolate reductase of E. coli has functional activity and a destabilized tertiary structure. |
| Q30425613 | Circularly permuted dihydrofolate reductase possesses all the properties of the molten globule state, but can resume functional tertiary structure by interaction with its ligands. |
| Q54612605 | Circularly permuted interleukin 4 retains proliferative and binding activity. |
| Q21131234 | Circularly permuted tRNA genes: their expression and implications for their physiological relevance and development |
| Q55023866 | Circularly permuted variants of two CG-specific prokaryotic DNA methyltransferases. |
| Q44487911 | Circularly permuted viral pRNA active and specific in the packaging of bacteriophage phi 29 DNA. |
| Q39721447 | Cloning of the BssHII restriction-modification system in Escherichia coli : BssHII methyltransferase contains circularly permuted cytosine-5 methyltransferase motifs |
| Q41757212 | Clostridium thermocellum thermostable lichenase with circular permutations and modifications in the N-terminal region retains its activity and thermostability |
| Q37301645 | Coexpression of human alpha- and circularly permuted beta-globins yields a hemoglobin with normal R state but modified T state properties |
| Q36329006 | Communication between RNA folding domains revealed by folding of circularly permuted ribozymes |
| Q36896248 | Construction and behavior of circularly permuted and telocentric chromosomes in Saccharomyces cerevisiae |
| Q44886641 | Construction of a dual chain pseudotetrameric chicken avidin by combining two circularly permuted avidins. |
| Q35541106 | Construction of a random circular permutation library using an engineered transposon |
| Q21045383 | Correct folding of circularly permuted variants of a beta alpha barrel enzyme in vivo |
| Q51484944 | Creation of a Ligand-Dependent Enzyme by Fusing Circularly Permuted Antibody Variable Region Domains. |
| Q37513233 | Crystal structure of YjeQ from Thermotoga maritima contains a circularly permuted GTPase domain |
| Q27650764 | Crystal structure of YlqF, a circularly permuted GTPase: implications for its GTPase activation in 50 S ribosomal subunit assembly |
| Q34365838 | Crystal structure of the highly divergent pseudouridine synthase TruD reveals a circular permutation of a conserved fold |
| Q27733384 | Crystal structure of transaldolase B from Escherichia coli suggests a circular permutation of the alpha/beta barrel within the class I aldolase family |
| Q27748895 | Crystal structures and properties of de novo circularly permuted 1,3-1,4-beta-glucanases |
| Q40139013 | DNA analysis of insect iridescent virus 6: evidence for circular permutation and terminal redundancy. |
| Q49847727 | Designing fluorescent biosensors using circular permutations of riboswitches |
| Q58609377 | Developing a circularly permuted variant of Renilla luciferase as a bioluminescent sensor for measuring Caspase-9 activity in the cell-free and cell-based systems |
| Q48248286 | Effect of circular permutation on the structure and function of type 1 blue copper center in azurin. |
| Q51723976 | Effect of genetic circular permutation near the active site on the activity and stability of an enzyme inhibitor. |
| Q30978533 | Effect of linker sequence on the stability of circularly permuted variants of ribonuclease T1. |
| Q55396225 | Effects of Recombinant Circularly Permuted Tumor Necrosis Factor (TNF)-Related Apoptosis-Inducing Ligand (TRAIL) (Recombinant Mutant Human TRAIL) in Combination with 5-Fluorouracil in Human Colorectal Cancer Cell Lines HCT116 and SW480. |
| Q43714268 | Effects of circular permutation on the cis-cleavage reaction of a hepatitis delta virus ribozyme: application to trans-acting ribozyme design |
| Q52531980 | Effects of the length of a glycine linker connecting the N-and C-termini of a circularly permuted dihydrofolate reductase. |
| Q24802652 | Efficiently folding and circularly permuted variants of the Sapphire mutant of GFP |
| Q33301701 | Engineering a circularly permuted GFP scaffold for peptide presentation |
| Q56896871 | Engineering allosteric regulation into the hinge region of a circularly permuted TEM-1 beta-lactamase |
| Q48845824 | Engineering carboxypeptidase G2 circular permutations for the design of an autoinhibited enzyme. |
| Q53599196 | Engineering of Yarrowia lipolytica lipase Lip8p by circular permutation to alter substrate and temperature characteristics. |
| Q35201549 | Engineering strictosidine synthase: rational design of a small, focused circular permutation library of the β-propeller fold enzyme |
| Q56342158 | Erratum: Engineering a circularly permuted GFP scaffold for peptide presentation |
| Q40126037 | Evidence for circular permutation of the prophage genome of Bacillus subtilis bacteriophage phi 105. |
| Q47793083 | Eye lens betaB2-crystallin: circular permutation does not influence the oligomerization state but enhances the conformational stability |
| Q47214217 | Facilitating circular permutation using Restriction Free (RF) cloning. |
| Q21045378 | Favin versus concanavalin A: Circularly permuted amino acid sequences |
| Q50646885 | Folding and misfolding in a naturally occurring circularly permuted PDZ domain |
| Q48199582 | Folding of Circularly Permuted Transfer RNAs |
| Q35211896 | Generating random circular permutation libraries |
| Q27673349 | High-resolution structure prediction of a circular permutation loop |
| Q41057955 | Immunogenicity of a Yersinia pestis vaccine antigen monomerized by circular permutation |
| Q34976159 | Improved biocatalysts from a synthetic circular permutation library of the flavin-dependent oxidoreductase old yellow enzyme |
| Q56900836 | Improving a circularly permuted TEM-1 beta-lactamase by directed evolution |
| Q21045401 | Improving the Catalytic Activity of Candida antarctica Lipase B by Circular Permutation |
| Q36640559 | In vivo assembly of aspartate transcarbamoylase from fragmented and circularly permuted catalytic polypeptide chains |
| Q54607525 | Increased antitumor activity of a circularly permuted interleukin 4-toxin in mice with interleukin 4 receptor-bearing human carcinoma. |
| Q47726701 | Interruption of the phage T4 chromosome transfer into the cell. Cyclic permutations of genes, and infective activity of the fragmented genome. |
| Q44031713 | Intersubunit circular permutation of human hemoglobin |
| Q41744157 | Intratumoral administration of recombinant circularly permuted interleukin-4-Pseudomonas exotoxin in patients with high-grade glioma. |
| Q50909723 | Investigating the structural and functional consequences of circular permutation on lipase B from Candida antarctica |
| Q33287881 | Ligand binding and circular permutation modify residue interaction network in DHFR. |
| Q36281540 | Molecular cloning and physical mapping of the genome of insect iridescent virus type 6: further evidence for circular permutation of the viral genome |
| Q40468549 | Mutations in circularly permuted GTPase family genes AtNOA1/RIF1/SVR10 and BPG2 suppress var2-mediated leaf variegation in Arabidopsis thaliana. |
| Q47839109 | Non-random circular permutation of phage P22 DNA. |
| Q53656683 | Perturbed folding kinetics of circularly permuted RNAs with altered topology. |
| Q33435243 | Phase II open-label study of recombinant circularly permuted TRAIL as a single-agent treatment for relapsed or refractory multiple myeloma |
| Q36480863 | Physical Connectivity Mapping by Circular Permutation of Human Telomerase RNA Reveals New Regions Critical for Activity and Processivity |
| Q48829827 | Preclinical development of a recombinant toxin containing circularly permuted interleukin 4 and truncated Pseudomonas exotoxin for therapy of malignant astrocytoma |
| Q33928741 | Probing RNA structure and function, by circular permutation |
| Q34058603 | Probing the functional mechanism of Escherichia coli GroEL using circular permutation |
| Q21045407 | 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 |
| Q37260556 | Random circular permutation of genes and expressed polypeptide chains: application of the method to the catalytic chains of aspartate transcarbamoylase |
| Q58459587 | Rational Modification of Ligand-Binding Preference of Avidin by Circular Permutation and Mutagenesis |
| Q27650202 | Rational modification of ligand-binding preference of avidin by circular permutation and mutagenesis |
| Q38325156 | Redesigning the single-chain variant of the restriction endonuclease PvuII by circular permutation. |
| Q43421759 | Restriction endonuclease and genetic mapping studies indicate that the vegetative genome of the temperate, salmonella-specific bacteriophage, Epsilon 15, is circularly-permuted |
| Q35082961 | STRUCTURAL AND FUNCTIONAL CONSEQUENCES OF CIRCULAR PERMUTATION ON THE ACTIVE SITE OF OLD YELLOW ENZYME |
| Q45788071 | Small differences in electrophoretic mobility among circularly permuted sequence isomers of duck hepatitis B virus linear, single-stranded DNA |
| Q51657940 | Sorting Circular Permutations by Bounded Transpositions |
| Q46611446 | Sorting Circular Permutations by Super Short Reversals. |
| Q27671196 | Structural Analysis of Papain-Like NlpC/P60 Superfamily Enzymes with a Circularly Permuted Topology Reveals Potential Lipid Binding Sites |
| Q27657026 | Structural Redesign of Lipase B from Candida antarctica by Circular Permutation and Incremental Truncation |
| Q44910111 | Structural and functional effects of circular permutation on firefly luciferase: in vitro assay of caspase 3/7. |
| Q27678220 | Structural consequences of cutting a binding loop: two circularly permuted variants of streptavidin |
| Q34575303 | Structural stabilization of GTP-binding domains in circularly permuted GTPases: implications for RNA binding |
| Q36595441 | Structure and restriction enzyme maps of the circularly permuted DNA of staphylococcal bacteriophage phi 11. |
| Q27640036 | Structure of a circularly permuted phosphoglycerate kinase |
| Q27643046 | Structure of circularly permuted DsbA(Q100T99): preserved global fold and local structural adjustments |
| Q39930507 | Structure of herpes simplex virus DNA: topography of the molecule. I. Absence of circularly permuted sequences |
| Q45393703 | Structure of herpes simplex virus DNA: topography of the molecule. I. Absence of circularly permuted sequences. |
| Q21045384 | Swaposins: circular permutations within genes encoding saposin homologues |
| Q53353883 | TOS1 is circularly permuted 1,3-beta-glucanase. |
| Q33322212 | Tandem duplication, circular permutation, molecular adaptation: how Solanaceae resist pests via inhibitors |
| Q39959514 | Temperate Bacillus bacteriophage SP16 genome is circularly permuted and terminally redundant |
| Q45850177 | Terminal redundancy and circular permutation of mycoplasma virus L3 DNA. |
| Q28361323 | Testing the role of chain connectivity on the stability and structure of dihydrofolate reductase from E. coli: fragment complementation and circular permutation reveal stable, alternatively folded forms |
| Q43120115 | The Rho GTPase inactivation domain in Vibrio cholerae MARTX toxin has a circularly permuted papain-like thiol protease fold |
| Q35956927 | The Structure of a Thermophilic Kinase Shapes Fitness upon Random Circular Permutation |
| Q30163979 | The crystal structure of YloQ, a circularly permuted GTPase essential for Bacillus subtilis viability |
| Q47991365 | The folding pathway of an engineered circularly permuted PDZ domain |
| Q36275847 | The genome of frog virus 3, an animal DNA virus, is circularly permuted and terminally redundant |
| Q50129307 | The glucose transporter of Escherichia coli with circularly permuted domains is active in vivo and in vitro |
| Q27683667 | The structure of the deacetylase domain of Escherichia coli PgaB, an enzyme required for biofilm formation: a circularly permuted member of the carbohydrate esterase 4 family |
| Q48065170 | Theoretical permutation gel electrophoretic analysis of a curved DNA fragment located in circular permutation |
| Q36280940 | Thermodynamic and structural consequences of flexible loop deletion by circular permutation in the streptavidin-biotin system |
| Q27728950 | Three-dimensional structure of favin: saccharide binding-cyclic permutation in leguminous lectins |
| Q34563323 | Towards tricking a pathogen's protease into fighting infection: the 3D structure of a stable circularly permuted onconase variant cleavedby HIV-1 protease |
| Q47848340 | Transient population dynamics in periodic matrix models: methodology and effects of cyclic permutations |
| Q27671536 | Uncoupling Intramolecular Processing and Substrate Hydrolysis in the N-Terminal Nucleophile Hydrolase hASRGL1 by Circular Permutation |
| Q30671409 | Use of circular permutation and end modification to position photoaffinity probes for analysis of RNA structure |
| Q43206038 | Use of circular permutation to assess six bulges and four loops of DNA-packaging pRNA of bacteriophage phi29. |
| Q36726279 | cpRAS: a novel circularly permuted RAS-like GTPase domain with a highly scattered phylogenetic distribution |
| Q846303 | biogeochemical cycle | instance of | P31 |
| Q114290211 | permutation cycle | different from | P1889 |
| Arabic (ar / Q13955) | تبديل دائري | wikipedia |
| Catalan (ca / Q7026) | Cicle (permutació) | wikipedia |
| Zyklische Permutation | wikipedia | |
| Cyclic permutation | wikipedia | |
| Esperanto (eo / Q143) | Cikla permuto | wikipedia |
| Permutación cíclica | wikipedia | |
| Persian (fa / Q9168) | جایگشت دوری | wikipedia |
| Permutation circulaire | wikipedia | |
| Cykel (wiskunde) | wikipedia | |
| Permutação circular | wikipedia | |
| Permutare ciclică | wikipedia | |
| Циклическая перестановка | wikipedia | |
| Циклична пермутација | wikipedia | |
| Cyklisk permutation | wikipedia | |
| ta | வட்ட வரிசைமாற்றம் | wikipedia |
| Циклічна перестановка | wikipedia | |
| yue | 循環表示 | wikipedia |
| 圆排列 | wikipedia |
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