545:
addition, in the example above two non-synonymous and one synonymous substitution occurred at the third site; however, because substitutions restored the original sequence, there is no evidence of any substitution. As the divergence time between two sequences increases, so too does the amount of multiple substitutions. Thus "long branches" in a dN/dS analysis can lead to underestimates of both dN and dS, and the longer the branch, the harder it is to correct for the introduced noise. Of course, the ancestral sequence is usually unknown, and two lineages being compared will have been evolving in parallel since their last common ancestor. This effect can be mitigated by constructing the ancestral sequence; the accuracy of this sequence is enhanced by having a large number of sequences descended from that common ancestor to constrain its sequence by
529:, which is coded by the codons AAT or AAC, a high C->T exchange rate will increase the proportion of synonymous substitutions at this codon, whereas a high C→A exchange rate will increase the rate of non-synonymous substitutions. Because it is rather common for transitions (T↔C & A↔G) to be favoured over transversions (other changes), models must account for the possibility of non-homogeneous rates of exchange. Some simpler approximate methods, such as those of Miyata & Yasunaga and Nei & Gojobori, neglect to take these into account, which generates a faster computational time at the expense of accuracy; these methods will systematically overestimate N and underestimate S.
676:
ratio at specific codons within a gene sequence. For instance, the frequency-tuning region of an opsin may be under enhanced selective pressure when a species colonises and adapts to new environment, whereas the region responsible for initializing a nerve signal may be under purifying selection. In
647:
are chemically similar to one another, whereas other substitutions may place an amino acid with wildly different properties to its precursor. In most situations, a smaller chemical change is more likely to allow the protein to continue to function, and a large chemical change is likely to disrupt the
544:
In addition, as time progresses, it is possible for a site to undergo multiple modifications. For instance, a codon may switch from AAA→AAC→AAT→AAA. There is no way of detecting multiple substitutions at a single site, thus the estimate of the number of substitutions is always an underestimate. In
651:
An additional concern is that the effects of time must be incorporated into an analysis, if the lineages being compared are closely related; this is because it can take a number of generations for natural selection to "weed out" deleterious mutations from a population, especially if their effect on
476:
Of course, it is necessary to perform a statistical analysis to determine whether a result is significantly different from 1, or whether any apparent difference may occur as a result of a limited data set. The appropriate statistical test for an approximate method involves approximating dN −
417:
Approximate methods involve three basic steps: (1) counting the number of synonymous and nonsynonymous sites in the two sequences, or estimating this number by multiplying the sequence length by the proportion of each class of substitution; (2) counting the number of synonymous and nonsynonymous
472:
acting on protein coding genes. A ratio greater than 1 implies positive or
Darwinian selection (driving change); less than 1 implies purifying or stabilizing selection (acting against change); and a ratio of exactly 1 indicates neutral (i.e. no) selection. However, a combination of positive and
532:
Further, there may be a bias in which certain codons are preferred in a gene, as a certain combination of codons may improve translational efficiency. A 2022 study reported that synonymous mutations in representative yeast genes are mostly strongly non-neutral, which calls into question the
409:, and counting methods. However, unless the sequences to be compared are distantly related (in which case maximum-likelihood methods prevail), the class of method used makes a minimal impact on the results obtained; more important are the assumptions implicit in the chosen method.
720:> 1 are candidates to be experiencing positive selection. This form of test can either identify sites that further laboratory research can examine to determine possible selective pressure; or, sites believed to have functional significance can be assigned into different K
443:
In order to quantify the number of substitutions, one may reconstruct the ancestral sequence and record the inferred changes at sites (straight counting – likely to provide an underestimate); fitting the substitution rates at sites into predetermined categories
648:
chemical structure and cause the protein to malfunction. However, incorporating this into a model is not straightforward as the relationship between a nucleotide substitution and the effects of the modified chemical properties is very difficult to determine.
473:
purifying selection at different points within the gene or at different times along its evolution may cancel each other out. The resulting averaged value can mask the presence of one of the selections and lower the seeming magnitude of another selection.
477:
dS with a normal approximation, and determining whether 0 falls within the central region of the approximation. More sophisticated likelihood techniques can be used to analyse the results of a
Maximum Likelihood analysis, by performing a
421:
These steps, particularly the latter, require simplistic assumptions to be made if they are to be achieved computationally; for reasons discussed later, it is impossible to exactly determine the number of multiple substitutions.
434:
to complete all three steps simultaneously. It estimates critical parameters, including the divergence between sequences and the transition/transversion ratio, by deducing the most likely values to produce the input data.
568:
ratio is a good indicator of selective pressure at the sequence level, evolutionary change can often take place in the regulatory region of a gene which affects the level, timing or location of gene expression.
144:
in a protein chain. However, there are more codons (64) than amino acids found in proteins (20), so many codons are effectively synonyms. For example, the DNA codons TTT and TTC both code for the amino acid
577:
analysis will not detect such change. It will only calculate selective pressure within protein coding regions. In addition, selection that does not cause differences at an amino acid level—for instance,
612:
method requires a rather strong signal in order to detect selection. In order to detect selection between lineages, then the selection, averaged over all sites in the sequence, must produce a K
157:, so a change from the middle A to T does change the resulting protein, for better or (more likely) worse, so the change is not a synonym. These changes are illustrated in the tables below.
525:
are swapped, as certain mutations are more probable than others. For instance, some lineages may swap C to T more frequently than they swap C to A. In the case of the amino acid
405:(rather than being genetic switches, controlling development or the rate of activity of other genes). Methods can be classified into three groups: approximate methods,
1094:
Rocha EP, Smith JM, Hurst LD, Holden MT, Cooper JE, Smith NH, Feil EJ (March 2006). "Comparisons of dN/dS are time dependent for closely related bacterial genomes".
831:"Better" means that the change is advantageous and will be selected for by natural selection. "Worse" means that the change is harmful, and will be selected against.
84:), in the same period. The latter are assumed to be neutral, so that the ratio indicates the net balance between deleterious and beneficial mutations. Values of K
1488:"A new method for estimating synonymous and nonsynonymous rates of nucleotide substitution considering the relative likelihood of nucleotide and codon changes"
593:= 1, it could be due to relaxed selection, or to a chimera of positive and purifying selection at the locus. A solution to this limitation would be to apply K
1830:
640:
rate to take multiple values across sites and across lineages; the inclusion of more lineages also increases the power of a sites-based approach.
632:
at that site—implying that the site must be under selective pressure in all sampled lineages. This limitation can be moderated by allowing the K
1870:
956:
Kosakovsky Pond SL, Frost SD (May 2005). "Not so different after all: a comparison of methods for detecting amino acid sites under selection".
61:
1523:"A likelihood approach for comparing synonymous and nonsynonymous nucleotide substitution rates, with application to the chloroplast genome"
552:
Methods that account for biases in codon usage and transition/transversion rates are substantially more reliable than those that do not.
620:
greater than one—quite a feat if regions of the gene are strongly conserved. In order to detect selection at specific sites, then the K
1901:
1661:
Yang Z, Nielsen R (January 2000). "Estimating synonymous and nonsynonymous substitution rates under realistic evolutionary models".
1823:
149:, so a change from the third T to C makes no difference to the resulting protein. On the other hand, the codon GAG codes for
1290:
Comeron JM (December 1995). "A method for estimating the numbers of synonymous and nonsynonymous substitutions per site".
643:
Further, the method lacks the capability to distinguish between positive and negative nonsynonymous substitutions. Some
1978:
712:
to exceed 1 in some sites improves the fit of the model. If this is the case, then sites fitting into the class where K
1335:
Goldman N, Yang Z (September 1994). "A codon-based model of nucleotide substitution for protein-coding DNA sequences".
1988:
1816:
1957:
320:
279:
69:
406:
1393:
Ina Y (February 1995). "New methods for estimating the numbers of synonymous and nonsynonymous substitutions".
1804:
SeqinR: A free and open biological sequence analysis package for the R language that includes KaKs calculation
452:(computationally expensive). Given enough data, all three of these approaches will tend to the same result.
1952:
1896:
215:
177:
77:
910:
704:
ratio is constrained to be < 1 in all sites to one where it may take any value, and see if permitting K
105:
1875:
1860:
585:
Another issue is that heterogeneity within a gene can make a result hard to interpret. For example, if K
1438:
Li WH (January 1993). "Unbiased estimation of the rates of synonymous and nonsynonymous substitution".
696:
The first step in identifying whether positive selection acts on sites is to compare a test where the K
822:
are count estimates, which represent the total numbers of non-synonymous and synonymous substitutions.
168:
ratio measures the relative rates of synonymous and nonsynonymous substitutions at a particular site.
1865:
1703:
1447:
1402:
1299:
1103:
1042:
1558:"Simple methods for estimating the numbers of synonymous and nonsynonymous nucleotide substitutions"
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915:
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1983:
1921:
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1614:
1579:
1544:
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1418:
1381:
1352:
1315:
1268:
1219:
1170:
1119:
1068:
1011:
973:
938:
505:
ratio is a more powerful test of the neutral model of evolution than many others available in
469:
315:
685:
ratio at each site. However this is computationally expensive and in practise, a number of K
448:
approach; poor for small data sets); and generating an individual substitution rate for each
1942:
1906:
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1410:
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1307:
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1250:
1209:
1201:
1160:
1150:
1111:
1058:
1050:
1003:
965:
928:
920:
478:
57:
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being advantageous. If beneficial mutations are assumed to make little contribution, then K
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1937:
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1592:
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1539:
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1504:
1487:
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841:
518:
1364:
Hurst LD (September 2002). "The Ka/Ks ratio: diagnosing the form of sequence evolution".
994:
Hurst LD (September 2002). "The Ka/Ks ratio: diagnosing the form of sequence evolution".
1707:
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65:
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1627:
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1007:
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116:
Selection acts on variation in phenotypes, which are often the result of mutations in
1972:
1916:
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1080:
357:
262:
253:
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146:
129:
1745:"KaKs_Calculator: calculating Ka and Ks through model selection and model averaging"
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1430:
1327:
1031:"Synonymous mutations in representative yeast genes are mostly strongly non-neutral"
546:
307:
205:
125:
1593:"Evolution of the Zfx and Zfy genes: rates and interdependence between the genes"
1155:
1692:"Computing Ka and Ks with a consideration of unequal transitional substitutions"
1115:
1054:
16:
Ratio estimating the balance between nonsynonymous and synonymous substitutions
693:
classes are established, and each site is assigned to the best-fitting class.
644:
526:
522:
348:
244:
141:
137:
1799:
Free online server tool that calculates KaKs ratios among multiple sequences
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1548:
1513:
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1356:
1319:
1190:"Quantitative prediction of molecular clock and ka/ks at short timescales"
1628:"PAML: a program package for phylogenetic analysis by maximum likelihood"
93:
92:
significantly above 1 are unlikely to occur without at least some of the
20:
1798:
1459:
1414:
1311:
402:
352:
248:
117:
1808:
1239:"Why time matters: codon evolution and the temporal dynamics of dN/dS"
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303:
201:
133:
121:
1812:
1743:
Zhang Z, Li J, Zhao XQ, Wang J, Wong GK, Yu J (November 2006).
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order to detect such effects, one would ideally calculate the K
628:
ratio must be greater than one when averaged over all included
418:
substitutions; and (3) correcting for multiple substitutions.
668:
Additional information can be gleaned by determining the K
899:"Statistical methods for detecting molecular adaptation"
468:
ratio is used to infer the direction and magnitude of
652:
fitness is weak. This limits the usefulness of the K
1930:
1889:
1846:
601:analysis across many species at individual codons.
660:ratio for comparing closely related populations.
68:. It is calculated as the ratio of the number of
76:), in a given period of time, to the number of
1824:
8:
1137:Kryazhimskiy S, Plotkin JB (December 2008).
766:are used interchangeably. Note however that
64:and beneficial mutations acting on a set of
1029:Shen X, Song S, Li C, Zhang J (June 2022).
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372:Altered protein may or may not cause harm
56:, is used to estimate the balance between
1768:
1749:Genomics, Proteomics & Bioinformatics
1725:
1715:
1643:
1608:
1573:
1538:
1503:
1262:
1237:Mugal CF, Wolf JB, Kaj I (January 2014).
1213:
1164:
1154:
1062:
932:
914:
582:—cannot be detected by these techniques.
1632:Computer Applications in the Biosciences
272:
170:
856:
737:
397:of two or more nucleotide sequences of
1188:Peterson GI, Masel J (November 2009).
897:Yang Z, Bielawski JP (December 2000).
481:to distinguish between a null model (K
1675:10.1093/oxfordjournals.molbev.a026236
1610:10.1093/oxfordjournals.molbev.a040003
1575:10.1093/oxfordjournals.molbev.a040410
1540:10.1093/oxfordjournals.molbev.a040152
1505:10.1093/oxfordjournals.molbev.a040343
1349:10.1093/oxfordjournals.molbev.a040153
430:The maximum-likelihood approach uses
374:(e.g. disease) or give new advantage
7:
1556:Nei M, Gojobori T (September 1986).
1591:Pamilo P, Bianchi NO (March 1993).
1521:Muse SV, Gaut BS (September 1994).
533:assumptions underlying use of the K
1139:"The population genetics of dN/dS"
521:in the frequency at which various
509:as it requires fewer assumptions.
14:
1902:Models of nucleotide substitution
1690:Zhang Z, Li J, Yu J (June 2006).
903:Trends in Ecology & Evolution
728:classes before the model is run.
140:. Each codon represents a single
267:Normal protein, normal function
1663:Molecular Biology and Evolution
1645:10.1093/bioinformatics/13.5.555
1597:Molecular Biology and Evolution
1562:Molecular Biology and Evolution
1527:Molecular Biology and Evolution
1492:Molecular Biology and Evolution
1337:Molecular Biology and Evolution
1243:Molecular Biology and Evolution
1194:Molecular Biology and Evolution
958:Molecular Biology and Evolution
489:= 1) and the observed results.
66:homologous protein-coding genes
1486:, Wu CI, Luo CC (March 1985).
1440:Journal of Molecular Evolution
1395:Journal of Molecular Evolution
1292:Journal of Molecular Evolution
1096:Journal of Theoretical Biology
780:are different parameters from
153:while the codon GTG codes for
1:
1761:10.1016/S1672-0229(07)60007-2
1378:10.1016/S0168-9525(02)02722-1
1008:10.1016/S0168-9525(02)02722-1
925:10.1016/S0169-5347(00)01994-7
1156:10.1371/journal.pgen.1000304
70:nonsynonymous substitutions
2005:
1958:Nonsynonymous substitution
1116:10.1016/j.jtbi.2005.08.037
1055:10.1038/s41586-022-04823-w
426:Maximum-likelihood methods
407:maximum-likelihood methods
321:Nonsynonymous substitution
280:nonsynonymous substitution
72:per non-synonymous site (K
664:Individual codon approach
1696:BMC Evolutionary Biology
840:Often but not always a "
385:Methods for estimating K
104:estimates the degree of
78:synonymous substitutions
1953:Synonymous substitution
1897:Models of DNA evolution
1626:Yang Z (October 1997).
216:Synonymous substitution
178:synonymous substitution
106:evolutionary constraint
1717:10.1186/1471-2148-6-44
80:per synonymous site (K
1876:Stabilizing selection
1861:Directional selection
1255:10.1093/molbev/mst192
1206:10.1093/molbev/msp175
970:10.1093/molbev/msi105
1866:Disruptive selection
456:Interpreting results
401:genes that code for
1979:Molecular evolution
1931:Molecular processes
1856:Balancing selection
1840:Molecular evolution
1708:2006BMCEE...6...44Z
1452:1993JMolE..36...96L
1407:1995JMolE..40..190I
1304:1995JMolE..41.1152C
1108:2006JThBi.239..226R
1047:2022Natur.606..725S
580:balancing selection
507:population genetics
413:Approximate methods
282:
180:
62:purifying selection
1989:Statistical ratios
1871:Negative selection
1460:10.1007/bf02407308
1415:10.1007/bf00167113
1366:Trends in Genetics
1312:10.1007/bf00173196
996:Trends in Genetics
432:probability theory
395:sequence alignment
273:
218:
213:harmless mutation;
171:
136:, groups of three
1966:
1965:
1848:Natural selection
1200:(11): 2595–2603.
1041:(7915): 725–731.
517:There is often a
470:natural selection
378:
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363:structural change
316:Missense mutation
286:Type of structure
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184:Type of structure
58:neutral mutations
1996:
1943:Gene duplication
1907:Allele frequency
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35:, also known as
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1948:Silent mutation
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1794:KaKs_Calculator
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1143:PLOS Genetics
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741:
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694:
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631:
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513:Complications
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266:
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263:Phenylalanine
261:
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254:Phenylalanine
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151:Glutamic acid
148:
147:Phenylalanine
143:
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130:DNA sequences
127:
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107:
95:
79:
71:
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63:
59:
55:
50:
43:
38:
34:
22:
1911:
1752:
1748:
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1669:(1): 32–43.
1666:
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1600:
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1561:
1530:
1526:
1495:
1491:
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1443:
1439:
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1340:
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547:phylogenetic
543:
531:
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384:
360:
308:DNA sequence
256:
206:DNA sequence
159:
126:genetic code
115:
48:
41:
40:
36:
24:
18:
1912:Ka/Ks ratio
744:The terms K
645:amino acids
556:Limitations
523:nucleotides
341:↓ codes for
335:↓ codes for
332:↓ codes for
237:↓ codes for
231:↓ codes for
228:↓ codes for
138:nucleotides
1973:Categories
1917:Tajima's D
852:References
527:Asparagine
399:homologous
349:Amino acid
278:causing a
245:Amino acid
176:causing a
142:amino acid
1702:(1): 44.
1081:249520936
911:CiteSeerX
549:methods.
259:no change
94:mutations
1984:Genetics
1779:17531802
1736:16740169
1683:10666704
1476:21618703
1431:25430897
1386:12175810
1328:19262479
1273:24129904
1224:19661199
1175:19081788
1124:16239014
1073:35676473
1016:12175810
978:15703242
943:11114436
630:lineages
541:ratio.
446:Bayesian
403:proteins
120:-coding
21:genetics
1770:5054075
1727:1552089
1704:Bibcode
1654:9367129
1619:8487630
1584:3444411
1549:7968485
1514:3916709
1468:8433381
1448:Bibcode
1423:7699723
1403:Bibcode
1357:7968486
1320:8587111
1300:Bibcode
1264:3879453
1215:2912466
1166:2596312
1104:Bibcode
1064:9650438
1043:Bibcode
934:7134603
493:Utility
381:Methods
353:Protein
298:Result
249:Protein
196:Result
118:protein
112:Context
1890:Models
1777:
1767:
1734:
1724:
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1079:
1071:
1061:
1035:Nature
1014:
976:
941:
931:
913:
393:use a
367:Valine
338:
292:Change
289:Before
234:
190:Change
187:Before
155:Valine
134:codons
124:. The
23:, the
1484:Li WH
1472:S2CID
1427:S2CID
1324:S2CID
1077:S2CID
732:Notes
604:The K
497:The K
460:The K
450:codon
389:and K
351:in a
306:in a
304:Codon
295:After
247:in a
204:in a
202:Codon
193:After
160:The K
122:genes
54:ratio
33:ratio
1775:PMID
1732:PMID
1679:PMID
1650:PMID
1615:PMID
1580:PMID
1545:PMID
1510:PMID
1464:PMID
1419:PMID
1382:PMID
1353:PMID
1316:PMID
1269:PMID
1220:PMID
1171:PMID
1120:PMID
1069:PMID
1012:PMID
974:PMID
939:PMID
815:and
801:and
794:(or
787:and
773:and
752:and
1765:PMC
1757:doi
1722:PMC
1712:doi
1671:doi
1640:doi
1605:doi
1570:doi
1535:doi
1500:doi
1456:doi
1411:doi
1374:doi
1345:doi
1308:doi
1259:PMC
1251:doi
1210:PMC
1202:doi
1161:PMC
1151:doi
1112:doi
1100:239
1059:PMC
1051:doi
1039:606
1004:doi
966:doi
929:PMC
921:doi
808:).
325:GTG
312:GAG
221:TTC
210:TTT
132:as
39:or
19:In
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724:/K
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656:/K
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624:/K
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597:/K
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537:/K
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485:/K
464:/K
274:A
172:A
164:/K
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100:/K
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799:A
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785:N
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