Artigo Acesso aberto Revisado por pares

Sticky DNA: Effect of the Polypurine·Polypyrimidine Sequence

2002; Elsevier BV; Volume: 277; Issue: 42 Linguagem: Inglês

10.1074/jbc.m205210200

ISSN

1083-351X

Autores

Alexandre A. Vetcher, Марек Напиерала, Robert D. Wells,

Tópico(s)

Microtubule and mitosis dynamics

Resumo

The polypurine·polypyrimidine sequence requirements for the formation of sticky DNA were evaluated inEscherichia coli plasmid systems to determine the potential occurrence of this conformation throughout biological systems. A mirror repeat, dinucleotide tract of (GA·TC)37, which is ubiquitous in eukaryotes, formed sticky DNA, but shorter sequences of 10 or 20 repeats were inert. (GGA·TCC)ninserts (where n = 126, 159, and 222 bp) also formed sticky DNA. As shown previously, the control sequence (GAA·TTC)150 (450 bp) readily adopted the X-shaped sticky structure; however, this structure has never been found for the nonpathogenic (GAAGGA·TCCTTC)65 of the same approximate length (390 bp). A sequence that is replete with polypurine·polypyrimidine tracts that can form triplexes and slipped structures but lacks long repeating motifs (the 2.5-kbp intron 21 sequence from the polycystic kidney disease gene 1) was also inert. Interestingly, tracts of (GAA·TTC)n (wheren = 176 or 80) readily formed sticky DNA with (GAAGGA·TCCTTC)65 cloned into the same plasmid when the pair of inserts was in the direct, but not in the indirect (inverted), orientation. The stabilities of the triple base (Watson-Crick and Hoogsteen) interactions in the DNA/DNA associated triplex region of the sticky conformations account for these observations. Our results have significant chemical and biological implications for the structure and function of this unusual DNA conformation in Friedreich's ataxia. The polypurine·polypyrimidine sequence requirements for the formation of sticky DNA were evaluated inEscherichia coli plasmid systems to determine the potential occurrence of this conformation throughout biological systems. A mirror repeat, dinucleotide tract of (GA·TC)37, which is ubiquitous in eukaryotes, formed sticky DNA, but shorter sequences of 10 or 20 repeats were inert. (GGA·TCC)ninserts (where n = 126, 159, and 222 bp) also formed sticky DNA. As shown previously, the control sequence (GAA·TTC)150 (450 bp) readily adopted the X-shaped sticky structure; however, this structure has never been found for the nonpathogenic (GAAGGA·TCCTTC)65 of the same approximate length (390 bp). A sequence that is replete with polypurine·polypyrimidine tracts that can form triplexes and slipped structures but lacks long repeating motifs (the 2.5-kbp intron 21 sequence from the polycystic kidney disease gene 1) was also inert. Interestingly, tracts of (GAA·TTC)n (wheren = 176 or 80) readily formed sticky DNA with (GAAGGA·TCCTTC)65 cloned into the same plasmid when the pair of inserts was in the direct, but not in the indirect (inverted), orientation. The stabilities of the triple base (Watson-Crick and Hoogsteen) interactions in the DNA/DNA associated triplex region of the sticky conformations account for these observations. Our results have significant chemical and biological implications for the structure and function of this unusual DNA conformation in Friedreich's ataxia. Friedreich's ataxia polypurine retarded band polypyrimidine The salient clinical and molecular biological features of Friedreich's ataxia (FRDA)1as well as the properties of DNA three-stranded structures (triplexes) and sticky DNA were reviewed in the companion paper (1Vetcher A.A. Napierala M. Iyer R. Chastain P.D. Griffith J.D. Wells R.D. J. Biol. Chem. 2002; 277: 39217-39227Abstract Full Text Full Text PDF PubMed Scopus (61) Google Scholar). Because this novel DNA structure was discovered (2Sakamoto N. Chastain P.D. Parniewski P. Ohshima K. Pandolfo M. Griffith J.D. Wells R.D. Mol. Cell. 1999; 3: 465-475Abstract Full Text Full Text PDF PubMed Scopus (278) Google Scholar) in the long GAA·TTC mutation in intron 1 of the frataxin gene, which is responsible for most cases of FRDA (3Campuzano V. Montermini L. Molto M.D. Pianese L. Cossee M. Cavalcanti F. Monros E. Rodius F. Duclos F. Monticelli A. Zara F. Canizares J. Koutnikova H. Bidichandani S.I. Gellera C. Brice A. Trouillas P., De Michele G. Filla A., De Frutos R. Palau F. Patel P.I., De Donato S. Mandel J.L. Cocozza S. Koenig M. Pandolfo M. Science. 1996; 271: 1423-1427Crossref PubMed Scopus (2323) Google Scholar, 4Durr A. Cossee M. Agid Y. Campuzano V. Mignard C. Penet C. Mandel J.L. Brice A. Koenig M. N. Engl. J. Med. 1996; 335: 1169-1175Crossref PubMed Scopus (894) Google Scholar, 5Montermini L. Andermann E. Labuda M. Richter A. Pandolfo M. Cavalcanti F. Pianese L. Iodice L. Farina G. Monticelli A. Turano M. Filla A., De Michele G. Cocozza S. Hum. Mol. Genet. 1997; 6: 1261-1266Crossref PubMed Scopus (187) Google Scholar, 6Montermini L. Kish S.J. Jiralerspong S. Lamarche J.B. Pandolfo M. Neurology. 1997; 49: 606-610Crossref PubMed Scopus (71) Google Scholar, 7Montermini L. Richter A. Morgan K. Justice C.M. Julien D. Castellotti B. Mercier J. Poirier J. Capozzoli F. Bouchard J.P. Lemieux B. Mathieu J. Vanasse M. Seni M.H. Graham G. Andermann F. Andermann E. Melancon S.B. Keats B.J., Di Donato S. Pandolfo M. Ann. Neurol. 1997; 41: 675-682Crossref PubMed Scopus (250) Google Scholar), we wished to determine the sequence requirements for its stabilization. Sticky DNA is a polypurine·polypurine· polypyrimidine (R·R·Y) triplex; hence, the features must include a mirror repeat sequence. However, the role of the distribution of purines and pyrimidines on the complementary strands has not been explored. Also, because a (GAAGGA·TCCTTC)65 tract is present in the same intron, the significance of the DNA sequence on triplex and sticky DNA formation may have further relevance. At present, the function of this unusual repeating hexanucleotide tract is unclear, especially because it does not track through family pedigrees with the disease or inhibit transcription (2Sakamoto N. Chastain P.D. Parniewski P. Ohshima K. Pandolfo M. Griffith J.D. Wells R.D. Mol. Cell. 1999; 3: 465-475Abstract Full Text Full Text PDF PubMed Scopus (278) Google Scholar, 8Ohshima K. Sakamoto N. Labuda M. Poirier J. Moseley M.L. Montermini L. Ranum L.P. Wells R.D. Pandolfo M. Neurology. 1999; 53: 1854-1857Crossref PubMed Google Scholar, 9Sakamoto N. Ohshima K. Montermini L. Pandolfo M. Wells R.D. J. Biol. Chem. 2001; 276: 27171-27177Abstract Full Text Full Text PDF PubMed Scopus (157) Google Scholar, 10Sakamoto N. Larson J.E. Iyer R.R. Montermini L. Pandolfo M. Wells R.D. J. Biol. Chem. 2001; 276: 27178-27187Abstract Full Text Full Text PDF PubMed Scopus (67) Google Scholar). The effect of GGA·TCC-interrupted triplets in long GAA·TTC repeat tracts was investigated (10Sakamoto N. Larson J.E. Iyer R.R. Montermini L. Pandolfo M. Wells R.D. J. Biol. Chem. 2001; 276: 27178-27187Abstract Full Text Full Text PDF PubMed Scopus (67) Google Scholar) to determine some of the sequence requirements for sticky DNA and to evaluate further the veracity of its long GAA·GAA·TTC triplex structure. Studies were conducted on a family of seven periodically substituted inserts (all ∼130 repeats in length) which contain 0, 4, 7, 8, 11, 20, or 50% substitution of GAA·TTC with GGA·TCC triplets. A relatively small amount of substitution (less than 11%) caused no inhibitory effects. However, higher levels of GGA·TCC interruptions reduced the formation of sticky DNA, alleviated transcription inhibition, and reduced genetic instabilities. We wished to further our studies with long DNA tracts with uniformly repeating polypurine·pyrimidine sequence motifs such as GA·TC, GGA·TCC, and GAAGGA·TCCTTC. Herein, we have evaluated the capacity of related types of long repeating R·Y sequences to form the sticky DNA structure, including GA·TC, GGA·TCC, and GAAGGA·TCCTTC. Also, the ability of the FRDA GAA·TTC repeat to interact with each of these three repeat sequences was determined. These results provide important confirmatory evidence on the R·R·Y conformation of sticky DNA and give insights into possible DNA loop interactions in FRDA chromosomes. A companion article (1Vetcher A.A. Napierala M. Iyer R. Chastain P.D. Griffith J.D. Wells R.D. J. Biol. Chem. 2002; 277: 39217-39227Abstract Full Text Full Text PDF PubMed Scopus (61) Google Scholar) demonstrates that sticky DNA is only formed intramolecularly between a pair of GAA·TTC tracts in one DNA molecule. Plasmid preparations after isolation from Escherichia coli contain monomeric as well as dimeric (and higher oligomeric) isoforms of DNA. The typical biological dimer studied herein is shown in Fig.1. Plasmids containing a single GA·TC tract (which are pUC9 derivatives) and plasmids containing one GGA·TCC tract (which are pUC19 derivatives) used in these studies are shown in Table I and have been described previously (11Collier D.A. Wells R.D. J. Biol. Chem. 1990; 265: 10652-10658Abstract Full Text PDF PubMed Google Scholar, 12Ohshima K. Kang S. Larson J.E. Wells R.D. J. Biol. Chem. 1996; 271: 16773-16783Abstract Full Text Full Text PDF PubMed Scopus (94) Google Scholar). pBS4.0, which is a pBluescript KS derivative harboring the 2.5-kb R·Y tract from intron 21 of the PKD1gene, has also been described previously (13Van Raay T.J. Burn T.C. Connors T.D. Petri L.R. Germino G.G. Klinger K.W. Landes G.M. Microb. Comp. Genomics. 1996; 1: 317-327PubMed Google Scholar, 14Bacolla A. Jaworski A. Connors T.D. Wells R.D. J. Biol. Chem. 2001; 276: 18597-18604Abstract Full Text Full Text PDF PubMed Scopus (55) Google Scholar). Plasmids with two R·Y tracts, which are pBR322 derivatives, are shown in Fig.2. The constructions of these DNAs are described below.Table IAmount of RB formed from plasmid dimers as a function of the sequence and length of the repeating tractPlasmidVectorInsert repeating sequenceRB formation%pGA10pUC9(GA·TC)180pGA20pUC9(GA·TC)200pGA37pUC9(GA·TC)3723pRW3191pUC19(GGA·TCC)160pRW3193pUC19(GGA·TCC)300pRW3194pUC19(GGA·TCC)4225pRW3195pUC19(GGA·TCC)5344pRW3892pUC19NotI(GGA·TCC)7449pRW3822pSPL3(GAA·TTC)150100pMP193pSPL3(GAAGGA·TCCTTC)630pBS4.0pBluescript KS−2.5-kbp R·Y0To compare the yield of RB formed from plasmid dimers containing different lengths of (GA·TC)n, (GGA·TCC)n, and (GAAGGA· TCCTTC)65, we studied purified dimers of each plasmid (see "Experimental Procedures"). Yields of RB (in percent) were compared with the amount observed from purified dimers of pRW3822 (1Vetcher A.A. Napierala M. Iyer R. Chastain P.D. Griffith J.D. Wells R.D. J. Biol. Chem. 2002; 277: 39217-39227Abstract Full Text Full Text PDF PubMed Scopus (61) Google Scholar, 2Sakamoto N. Chastain P.D. Parniewski P. Ohshima K. Pandolfo M. Griffith J.D. Wells R.D. Mol. Cell. 1999; 3: 465-475Abstract Full Text Full Text PDF PubMed Scopus (278) Google Scholar, 9Sakamoto N. Ohshima K. Montermini L. Pandolfo M. Wells R.D. J. Biol. Chem. 2001; 276: 27171-27177Abstract Full Text Full Text PDF PubMed Scopus (157) Google Scholar, 10Sakamoto N. Larson J.E. Iyer R.R. Montermini L. Pandolfo M. Wells R.D. J. Biol. Chem. 2001; 276: 27178-27187Abstract Full Text Full Text PDF PubMed Scopus (67) Google Scholar) under the same conditions (HindIII cleavage for pUC9 derivatives, EcoRI cleavage for pUC19 and pSPL3 derivatives, and SacI cleavage for the pBluescript KS− derivative). All plasmids had the superhelical density as isolated from E. coli (−ς = 0.05) (25Lilley D. Nature. 1986; 320: 14-15Crossref PubMed Scopus (38) Google Scholar, 26Bliska J.B. Cozzarelli N.R. J. Mol. Biol. 1987; 194: 205-218Crossref PubMed Scopus (220) Google Scholar, 27Zacharias W. Jaworski A. Larson J.E. Wells R.D. Proc. Natl. Acad. Sci. U. S. A. 1988; 85: 7069-7073Crossref PubMed Scopus (76) Google Scholar). In parallel studies, the isolated monomeric forms of all 11 plasmids were studied; no RB was found in any case. The actual sequence of the insert in pRW3892 is ((AGG)58CCTGG(AGG)16·(CCT)16CCAGG(CCT)58), as described earlier (12Ohshima K. Kang S. Larson J.E. Wells R.D. J. Biol. Chem. 1996; 271: 16773-16783Abstract Full Text Full Text PDF PubMed Scopus (94) Google Scholar), but it is designated as (GGA·TCC)74 for simplicity. Open table in a new tab Figure 2Schematic diagram of plasmids containing two R·Y tracts used to determine the influence of the insert orientation and sequence on RB formation. The vector is pBR322. The plasmids have unique recognition sites for EcoRI and forEcoNI, which are separated by the inserts.View Large Image Figure ViewerDownload (PPT) To compare the yield of RB formed from plasmid dimers containing different lengths of (GA·TC)n, (GGA·TCC)n, and (GAAGGA· TCCTTC)65, we studied purified dimers of each plasmid (see "Experimental Procedures"). Yields of RB (in percent) were compared with the amount observed from purified dimers of pRW3822 (1Vetcher A.A. Napierala M. Iyer R. Chastain P.D. Griffith J.D. Wells R.D. J. Biol. Chem. 2002; 277: 39217-39227Abstract Full Text Full Text PDF PubMed Scopus (61) Google Scholar, 2Sakamoto N. Chastain P.D. Parniewski P. Ohshima K. Pandolfo M. Griffith J.D. Wells R.D. Mol. Cell. 1999; 3: 465-475Abstract Full Text Full Text PDF PubMed Scopus (278) Google Scholar, 9Sakamoto N. Ohshima K. Montermini L. Pandolfo M. Wells R.D. J. Biol. Chem. 2001; 276: 27171-27177Abstract Full Text Full Text PDF PubMed Scopus (157) Google Scholar, 10Sakamoto N. Larson J.E. Iyer R.R. Montermini L. Pandolfo M. Wells R.D. J. Biol. Chem. 2001; 276: 27178-27187Abstract Full Text Full Text PDF PubMed Scopus (67) Google Scholar) under the same conditions (HindIII cleavage for pUC9 derivatives, EcoRI cleavage for pUC19 and pSPL3 derivatives, and SacI cleavage for the pBluescript KS− derivative). All plasmids had the superhelical density as isolated from E. coli (−ς = 0.05) (25Lilley D. Nature. 1986; 320: 14-15Crossref PubMed Scopus (38) Google Scholar, 26Bliska J.B. Cozzarelli N.R. J. Mol. Biol. 1987; 194: 205-218Crossref PubMed Scopus (220) Google Scholar, 27Zacharias W. Jaworski A. Larson J.E. Wells R.D. Proc. Natl. Acad. Sci. U. S. A. 1988; 85: 7069-7073Crossref PubMed Scopus (76) Google Scholar). In parallel studies, the isolated monomeric forms of all 11 plasmids were studied; no RB was found in any case. The actual sequence of the insert in pRW3892 is ((AGG)58CCTGG(AGG)16·(CCT)16CCAGG(CCT)58), as described earlier (12Ohshima K. Kang S. Larson J.E. Wells R.D. J. Biol. Chem. 1996; 271: 16773-16783Abstract Full Text Full Text PDF PubMed Scopus (94) Google Scholar), but it is designated as (GGA·TCC)74 for simplicity. Mixtures of supercoiled dimeric and higher oligomeric forms of the pUC9 and pUC19 derivatives were isolated after overnight growth in E. coli SURE strain, as described (1Vetcher A.A. Napierala M. Iyer R. Chastain P.D. Griffith J.D. Wells R.D. J. Biol. Chem. 2002; 277: 39217-39227Abstract Full Text Full Text PDF PubMed Scopus (61) Google Scholar). Fragments containing the (GAA·TTC)176 tract and the (GAAGGA·TCCTTC)65 tract were prepared from pRW3808 (15Sambrook J. Russell D. Molecular Cloning: A Laboratory Manual. 3rd Ed. Cold Spring Harbor Laboratory Press, Cold Spring Harbor, NY2001Google Scholar,16Ohshima K. Montermini L. Wells R.D. Pandolfo M. J. Biol. Chem. 1998; 273: 14588-14595Abstract Full Text Full Text PDF PubMed Scopus (272) Google Scholar) and pMP193 (2Sakamoto N. Chastain P.D. Parniewski P. Ohshima K. Pandolfo M. Griffith J.D. Wells R.D. Mol. Cell. 1999; 3: 465-475Abstract Full Text Full Text PDF PubMed Scopus (278) Google Scholar), respectively, by BssHII andHaeIII digestion (New England Biolabs, Inc.) followed by filling in the recessed BssHII 3′ termini with 0.1 unit of the Klenow fragment of E. coli DNA polymerase I (U. S. Biochemical Corp.) and dCTP plus dGTP (0.1 mm each) (17Napierala M. Parniewski P. Pluciennik A. Wells R.D. J. Biol. Chem. 2002; 277: 34087-34100Abstract Full Text Full Text PDF PubMed Scopus (52) Google Scholar). The repeating tracts are flanked by 34 and 54 bp of the human FRDA gene (3Campuzano V. Montermini L. Molto M.D. Pianese L. Cossee M. Cavalcanti F. Monros E. Rodius F. Duclos F. Monticelli A. Zara F. Canizares J. Koutnikova H. Bidichandani S.I. Gellera C. Brice A. Trouillas P., De Michele G. Filla A., De Frutos R. Palau F. Patel P.I., De Donato S. Mandel J.L. Cocozza S. Koenig M. Pandolfo M. Science. 1996; 271: 1423-1427Crossref PubMed Scopus (2323) Google Scholar). The digested DNA was electrophoresed in a 7% polyacrylamide gel, stained with EtBr, and the band containing the triplet repeat fragment was excised. The DNA was eluted from the excised band, purified by phenol-chloroform extraction, and precipitated with ethanol (15Sambrook J. Russell D. Molecular Cloning: A Laboratory Manual. 3rd Ed. Cold Spring Harbor Laboratory Press, Cold Spring Harbor, NY2001Google Scholar). Linearized pBR322 was ligated with the (GAA·TTC)176-containing insert. The ligation and all subsequent cloning steps were performed as described earlier (17Napierala M. Parniewski P. Pluciennik A. Wells R.D. J. Biol. Chem. 2002; 277: 34087-34100Abstract Full Text Full Text PDF PubMed Scopus (52) Google Scholar). Clones that included trinucleotide repeat sequence tracts, cloned intoPvuII site, were subsequently digested byEcoRI/HindIII, followed by filling in the recessed 3′ termini. Subsequent blunt end ligation of these DNAs with the insert harboring the (GAAGGA·TCCTTC)65 tract enabled the construction of a set of plasmids (pRW5000–pRW5005) harboring the (GAAGGA· TCCTTC)65 tract in the EcoRI site of pBR322 in both orientations and the (GAA·TTC)176 tract in the PvuII site; the two inserts were oriented as direct repeats or inverted repeats (Fig. 2). pRW5001 and pRW5003, harboring (GAA·TTC)80, were isolated as deletion mutants of pRW5000 and pRW5002, respectively. From the other side, subsequent blunt end ligation of the above mentioned DNA, harboring the (GAA·TTC)176 tract in orientation I, with the insert, harboring the (GAA·TTC)176 tract, enabled the construction of a pair of plasmids (pRW4886–pRW4887), harboring a pair of the (GAA·TTC)176 tracts both in direct and inverted orientations (Fig. 2). For the preparation of the plasmid harboring two contiguous inserts, where two directly oriented (GAA·TTC)60 are separated by 88 bp of human flanking sequence, a number of clones from (GAA·TTC)60 blunt end ligation into the PvuII site of pBR322 (1Vetcher A.A. Napierala M. Iyer R. Chastain P.D. Griffith J.D. Wells R.D. J. Biol. Chem. 2002; 277: 39217-39227Abstract Full Text Full Text PDF PubMed Scopus (61) Google Scholar) were studied. All plasmids were fully characterized by restriction mapping (to determine the orientation and length of the cloned trinucleotide repeat sequence) and dideoxy sequencing of both strands with Thermo Sequenase Radiolabeled Terminator Cycle Sequencing kit (U. S. Biochemical Corp.). The presence of sticky DNA in a DNA preparation is determined routinely by the detection of a substantially RB on agarose gel electrophoresis after plasmid linearization as described (1Vetcher A.A. Napierala M. Iyer R. Chastain P.D. Griffith J.D. Wells R.D. J. Biol. Chem. 2002; 277: 39217-39227Abstract Full Text Full Text PDF PubMed Scopus (61) Google Scholar). Prior investigations (2Sakamoto N. Chastain P.D. Parniewski P. Ohshima K. Pandolfo M. Griffith J.D. Wells R.D. Mol. Cell. 1999; 3: 465-475Abstract Full Text Full Text PDF PubMed Scopus (278) Google Scholar, 9Sakamoto N. Ohshima K. Montermini L. Pandolfo M. Wells R.D. J. Biol. Chem. 2001; 276: 27171-27177Abstract Full Text Full Text PDF PubMed Scopus (157) Google Scholar, 10Sakamoto N. Larson J.E. Iyer R.R. Montermini L. Pandolfo M. Wells R.D. J. Biol. Chem. 2001; 276: 27178-27187Abstract Full Text Full Text PDF PubMed Scopus (67) Google Scholar) demonstrated that long tracts of GAA·TTC repeats readily form a new type of complex triplex called sticky DNA. However, a closely related repeating hexanucleotide sequence, GAAGGA·TCCTTC, does not form sticky DNA under identical conditions (2Sakamoto N. Chastain P.D. Parniewski P. Ohshima K. Pandolfo M. Griffith J.D. Wells R.D. Mol. Cell. 1999; 3: 465-475Abstract Full Text Full Text PDF PubMed Scopus (278) Google Scholar, 8Ohshima K. Sakamoto N. Labuda M. Poirier J. Moseley M.L. Montermini L. Ranum L.P. Wells R.D. Pandolfo M. Neurology. 1999; 53: 1854-1857Crossref PubMed Google Scholar, 9Sakamoto N. Ohshima K. Montermini L. Pandolfo M. Wells R.D. J. Biol. Chem. 2001; 276: 27171-27177Abstract Full Text Full Text PDF PubMed Scopus (157) Google Scholar, 10Sakamoto N. Larson J.E. Iyer R.R. Montermini L. Pandolfo M. Wells R.D. J. Biol. Chem. 2001; 276: 27178-27187Abstract Full Text Full Text PDF PubMed Scopus (67) Google Scholar). Furthermore, studies on a family of mutated GAA·TTC repeat tracts in plasmids containing various amount of GGA·TCC interruptions (ranging from 4 to 50%) revealed that GAA·TTC repeats with less than 20% interruptions form triplexes and/or sticky DNA similar to the uninterrupted repeat sequence (10Sakamoto N. Larson J.E. Iyer R.R. Montermini L. Pandolfo M. Wells R.D. J. Biol. Chem. 2001; 276: 27178-27187Abstract Full Text Full Text PDF PubMed Scopus (67) Google Scholar). To investigate further the sequence requirements for the formation of sticky DNA, we constructed and characterized families of recombinant plasmids containing all purines on one strand and all pyrimidines on the complementary strands of the inserts. (GA·TC)n (where n = 10, 20, and 37) as well as (GGA·TCC)n (wheren = 16, 30, 42, 53, and 74) were prepared. Investigations were also conducted on a plasmid containing a 2.5-kbp R·Y tract that is present in intron 21 of the polycystic kidney disease 1 (PKD1) gene (14Bacolla A. Jaworski A. Connors T.D. Wells R.D. J. Biol. Chem. 2001; 276: 18597-18604Abstract Full Text Full Text PDF PubMed Scopus (55) Google Scholar). This sequence contains 23 perfect mirror repeats that can form DNA triplexes with stems of at least 10 bp and are clustered into three distinct regions of the 2.5-kbp tract. More than a thousand perfect tandem repeats, which will form slipped structures (18), are present. The dinucleotides TC and CT are the most common; however, they are excluded from the 5′-end where the mirror repeats predominate. The trinucleotide repeats are mostly CCT and are localized within one end of the tract. Pentanucleotide repeats include CTCCC, CTCCT, and CCCAT. These pentanucleotide repeats are also clustered within the R·Y tract. In summary, thisPKD1 sequence shows the presence of many mirror and direct repeats that are localized within the sequence. This tract contains the highest density of unorthodox simple sequence repeat features (mirror, direct repeats, and R·Y strand bias) of any known sequence of this length (14Bacolla A. Jaworski A. Connors T.D. Wells R.D. J. Biol. Chem. 2001; 276: 18597-18604Abstract Full Text Full Text PDF PubMed Scopus (55) Google Scholar). To analyze the sequence requirements of the R·Y region for sticky DNA formation in the dimeric form, we isolated dimers from plasmid preparations grown in E. coli SURE cells. The accompanying paper (1Vetcher A.A. Napierala M. Iyer R. Chastain P.D. Griffith J.D. Wells R.D. J. Biol. Chem. 2002; 277: 39217-39227Abstract Full Text Full Text PDF PubMed Scopus (61) Google Scholar) demonstrates that only dimeric and higher oligomeric, but not monomeric, forms of the plasmids will form sticky DNA. Thus, it was concluded (1Vetcher A.A. Napierala M. Iyer R. Chastain P.D. Griffith J.D. Wells R.D. J. Biol. Chem. 2002; 277: 39217-39227Abstract Full Text Full Text PDF PubMed Scopus (61) Google Scholar) that two long tracts of R·Y must be present in one plasmid to generate sticky DNA. The plasmid monomeric forms of uninterrupted as well as periodically interrupted long GAA·TTC repeats will not form sticky DNA (1Vetcher A.A. Napierala M. Iyer R. Chastain P.D. Griffith J.D. Wells R.D. J. Biol. Chem. 2002; 277: 39217-39227Abstract Full Text Full Text PDF PubMed Scopus (61) Google Scholar). Also, we would have liked to investigate the behaviors of long homopolymeric tracts of A·T as well as G·C. However, these investigations are precluded by the extreme genetic instability of these simple sequences (19Klein R.D. Wells R.D. J. Biol. Chem. 1982; 257: 12954-12961Abstract Full Text PDF PubMed Google Scholar, 20Klein R.D. Wells R.D. J. Biol. Chem. 1982; 257: 12962-12969Abstract Full Text PDF PubMed Google Scholar). Studies were conducted to evaluate the capacity of the sequences described above and listed in Table I to form sticky DNA. Fig.1 A shows the generic structure of a biological dimer, obviously containing two identical tracts of the repeating sequences. The repeats were dinucleotide or trinucleotide or hexanucleotide or 2.5-kb R·Y tracts. Fig. 1 B shows the gel electrophoretic analyses for the GA·TC tract; Fig. 1 C shows the electrophoretic analysis for the GGA·TCC tracts, and Dpresents the control data for (GAA·TTC)150 and a similar length of the repeating hexanucleotide sequence (pMP193). The dimers of pUC9-derived plasmids harboring GA·TC tracts revealed the formation of sticky DNA for pGA37 which contains 37 dimeric repeats; however, little or no sticky DNA was observed for the plasmids containing the two shorter dinucleotide repeat tracts (10 and 20 units in length) (Fig. 1 and Table I). Unfortunately, longer repeat tracts of GA·TC were not available for investigation. Thus, repeating dinucleotide sequences containing all purines on one strand and all pyrimidines on the complementary strand can also form sticky DNA. Studies were also conducted on the repeating trinucleotide sequence, GGA·TCC, containing 16–74 triplet repeats. This sequence contains 66% GC, whereas the FRDA mutation contains only 33% GC. Interestingly, the three plasmids (pUC19 derivatives) which contain 42–74 repeats readily formed sticky DNA, whereas the two shorter inserts did not have this capability (Fig. 1 and Table I). Hence, the threshold length for sticky DNA formation is between 40 and 74 bp for GA·TC, 90 and 126 bp for GGA·TCC, and 99 and 177 bp for GAA·TTC. No hereditary neurological diseases have been identified yet where GGA·TCC is involved in its etiology (18). A R·Y sequence containing an irregular distribution of A and G nucleotides in the polypurine strain was investigated to evaluate the necessity of a repetitive sequence. The 2.5-kbp tract from intron 21 of the PKD1 gene was employed because of its known sequence features (for review, see Ref. 14Bacolla A. Jaworski A. Connors T.D. Wells R.D. J. Biol. Chem. 2001; 276: 18597-18604Abstract Full Text Full Text PDF PubMed Scopus (55) Google Scholar) as well as its interesting biological characteristics. This 2.5-kbp sequence contains four P1 nuclease-sensitive regions (18), which apparently form triplexes (14Bacolla A. Jaworski A. Connors T.D. Wells R.D. J. Biol. Chem. 2001; 276: 18597-18604Abstract Full Text Full Text PDF PubMed Scopus (55) Google Scholar,18). One of these regions contains a 404-bp noninterrupted R·Y tract (13Van Raay T.J. Burn T.C. Connors T.D. Petri L.R. Germino G.G. Klinger K.W. Landes G.M. Microb. Comp. Genomics. 1996; 1: 317-327PubMed Google Scholar). Because this length is approximately twice the known threshold (described above) for the formation of sticky DNA for GAA·TTC as well as GGA·TCC, we felt that it might be possible for thisPKD1 insert to adopt a sticky DNA structure. However, as revealed in Table I, no RB was found. Because this 404-bp R·Y tract contains no mirror repeats with at least 80% matching triple base interactions (13Van Raay T.J. Burn T.C. Connors T.D. Petri L.R. Germino G.G. Klinger K.W. Landes G.M. Microb. Comp. Genomics. 1996; 1: 317-327PubMed Google Scholar, 14Bacolla A. Jaworski A. Connors T.D. Wells R.D. J. Biol. Chem. 2001; 276: 18597-18604Abstract Full Text Full Text PDF PubMed Scopus (55) Google Scholar) that are longer than ∼200 bp, this result is not unexpected. Further gel electrophoretic analyses revealed that the RB found with GA·TC as well as with GGA·TCC inserts were, in fact, sticky DNA, by evaluating the lengths of the arms in the X-shaped structures formed after cleavage at different unique restriction sites. For the pUC19 derivatives, the DNAs were linearized with Eco0109I,EcoRI or NdeI and for pUC9 derivatives, the plasmids were cleaved with EcoRI or HindIII. In all cases, the correlation described earlier (2Sakamoto N. Chastain P.D. Parniewski P. Ohshima K. Pandolfo M. Griffith J.D. Wells R.D. Mol. Cell. 1999; 3: 465-475Abstract Full Text Full Text PDF PubMed Scopus (278) Google Scholar) between the extent of retardation of the RB and the distance between the restriction enzyme cleavage site and the R·Y tract was observed (data not shown). Further investigations on the role of DNA sequence on the capacity of two tracts of different types of R·Y sequences to form sticky DNA were conducted. Plasmids containing one tract of (GAAGGA·TCCTTC)65 and another block of (GAA·TTC)176 were prepared and characterized (Fig. 2). Similar plasmids were also prepared in which the (GAA·TTC)176 was replaced with (GAA·TTC)80. Plasmids were characterized which contained the inserts in the direct repeat orientations as well as in the inverted repeat orientations (Fig. 2). Prior investigations (1Vetcher A.A. Napierala M. Iyer R. Chastain P.D. Griffith J.D. Wells R.D. J. Biol. Chem. 2002; 277: 39217-39227Abstract Full Text Full Text PDF PubMed Scopus (61) Google Scholar) revealed that only plasmids containing inserts in the direct repeat orientation could form sticky DNA, and our current work confirms this conclusion (TableII).Table IIAmount of RB formed from plasmids harboring two inserts as a function of repeating sequence orientations and the length of the (GAA·TTC)n tractPlasmidOrientation of (GAAGGA·TCCTTC)65Orientation of (GAA·TTC)nnRB formation%pRW4886NAaNA, not applicable.NA176100pRW4887NANA1760pRW5000II17689pRW5001II8053pRW5002III1760pRW5003III800pRW5004IIII17688pRW5005III1760a NA, not applicable. Open table in a new tab Table II reveals that pRW4886, which contains two tracts of 176 repeats of GAA·TTC in the direct repeat orientation (Fig. 2), readily forms sticky DNA (as described under "Experimental Procedures"). However, pRW4887, containing the same inserts but in the inverted repeat orientation (Fig. 2), were devoid of this capability, as expected (1Vetcher A.A. Napierala M. Iyer R. Chastain P.D. Griffith J.D. Wells R.D. J. Biol. Chem. 2002; 277: 39217-39227Abstract Full Text Full Text PDF PubMed Scopus (61) Google Scholar). Interestingly, pRW5000 and pRW5004 readily formed sticky DNA; these plasmids contain one tract of (GAAGGA· TCCTTC)65 and one tract of (GAA·TTC)176; both inserts in the two plasmids are in the direct repeat orientation, but the pair of repeats are inverted in pRW5004 compared with pRW5000. Accordingly, it is apparent that the GGAGAA tract from the repeating hexanucleotide sequence is aligning and Hoogsteen pairing in an antiparallel manner with the GAAGAA sequence from the repeating triplet sequence. Thus, five of six (83%) of the base oppositions are "normal" G·G·A and A·A·T structures with only one G·A·T opposition that is less stable (10Sakamoto N. Larson J.E. Iyer R.R. Montermini L. Pandolfo M. Wells R.D. J. Biol. Chem. 2001; 276: 27178-27187Abstract Full Text Full Text PDF PubMed Scopus (67) Google Scholar). Therefore, by our previous analysis (Table II of Ref.1Vetcher A.A. Napierala M. Iyer R. Chastain P.D. Griffith J.D. Wells R.D. J. Biol. Chem. 2002; 277: 39217-39227Abstract Full Text Full Text PDF PubMed Scopus (61) Google Scholar), this extent (17%) of "misoppositions" should be tolerated. However, the investigations described above (Table I) in which two tracts of the (GAAGGA·TCCTTC)65 would be required to pair successfully to form sticky DNA was forbidden; this result is as expected (1Vetcher A.A. Napierala M. Iyer R. Chastain P.D. Griffith J.D. Wells R.D. J. Biol. Chem. 2002; 277: 39217-39227Abstract Full Text Full Text PDF PubMed Scopus (61) Google Scholar) because only four of six (66%) of the correct oppositions would be present, which is insufficient to stabilize sticky DNA (1Vetcher A.A. Napierala M. Iyer R. Chastain P.D. Griffith J.D. Wells R.D. J. Biol. Chem. 2002; 277: 39217-39227Abstract Full Text Full Text PDF PubMed Scopus (61) Google Scholar,10Sakamoto N. Larson J.E. Iyer R.R. Montermini L. Pandolfo M. Wells R.D. J. Biol. Chem. 2001; 276: 27178-27187Abstract Full Text Full Text PDF PubMed Scopus (67) Google Scholar). As expected, pRW5001 also forms sticky DNA, and thus a (GAA·TTC)80 tract can replace the 176-mer and still effectively pair with the repeating hexamer. Also, all plasmids with inserts in the inverted orientation (pRW4887, 5002, 5003, and 5005) were incapable of adopting the sticky structure (1Vetcher A.A. Napierala M. Iyer R. Chastain P.D. Griffith J.D. Wells R.D. J. Biol. Chem. 2002; 277: 39217-39227Abstract Full Text Full Text PDF PubMed Scopus (61) Google Scholar). The effect of the length of the pBR322 DNA sequence between two tracts of (GAA·TTC)60 was investigated to evaluate further the factors involved in the stabilization of sticky DNA. For the plasmids shown in Fig. 1 as well as Fig. 2, the repeat sequences were separated by more than 2,000 bp. To evaluate whether one very long GAA·TTC tract could fold back on itself to form sticky DNA and/or to determine the influence of a very short intervening sequence, we prepared and characterized pRW4881 (Fig.3), which contains 88 bp of human FRDA flanking sequence between a pair of (GAA·TTC)60sequences. The plasmid has two cleavage sites for BssHII, which are separated by a (GAA·TTC)60 tract. After cleavage of pRW4881 with BssHII and electrophoretic analysis for sticky DNA (Fig. 3), RB is found. The extent of retardation is as expected because the location of the cleavage sites is close to the (GAA·TTC)60 tract (2Sakamoto N. Chastain P.D. Parniewski P. Ohshima K. Pandolfo M. Griffith J.D. Wells R.D. Mol. Cell. 1999; 3: 465-475Abstract Full Text Full Text PDF PubMed Scopus (278) Google Scholar). Thus, the stabilizing forces for sticky DNA generated by the fold-back of two GAA·TTC sequences that are proximal are sufficiently great to enable the formation of sticky DNA. Sharp bending of the 88-bp intervening sequence must have been caused by the stabilization and pairing of the GAA·TTC tracts. Because this 88 bp is shorter than the known persistence length of DNA, which is 450 Å or 130 bp (21Gray Jr., H.B. Hearst J.E. J. Mol. Biol. 1968; 35: 111-129Crossref PubMed Scopus (97) Google Scholar, 22Hearst J.E. Stockmayer W.H. J. Chem. Phys. 1962; 37: 1425-1433Crossref Scopus (282) Google Scholar), we conclude that the interactive forces created by the pair of GAA·TTC tracts must be substantial. Sticky DNA was described (2Sakamoto N. Chastain P.D. Parniewski P. Ohshima K. Pandolfo M. Griffith J.D. Wells R.D. Mol. Cell. 1999; 3: 465-475Abstract Full Text Full Text PDF PubMed Scopus (278) Google Scholar, 9Sakamoto N. Ohshima K. Montermini L. Pandolfo M. Wells R.D. J. Biol. Chem. 2001; 276: 27171-27177Abstract Full Text Full Text PDF PubMed Scopus (157) Google Scholar, 10Sakamoto N. Larson J.E. Iyer R.R. Montermini L. Pandolfo M. Wells R.D. J. Biol. Chem. 2001; 276: 27178-27187Abstract Full Text Full Text PDF PubMed Scopus (67) Google Scholar) as an X-shaped DNA molecule found in plasmids containing long tracts of GAA·TTC after linearization of the plasmid molecule. The lengths of GAA·TTC required for its formation correspond to the tracts found in intron 1 of the frataxin gene of FRDA patients (2Sakamoto N. Chastain P.D. Parniewski P. Ohshima K. Pandolfo M. Griffith J.D. Wells R.D. Mol. Cell. 1999; 3: 465-475Abstract Full Text Full Text PDF PubMed Scopus (278) Google Scholar). Sticky DNA was stabilized by negative supercoiling as well as divalent metal ions. The long GAA·TTC repeats form R·R·Y triplexes at neutral pH (23Le Doan T. Perrouault L. Praseuth D. Habhoub N. Decout J.L. Thuong N.T. Lhomme J. Helene C. Nucleic Acids Res. 1987; 15: 7749-7760Crossref PubMed Scopus (522) Google Scholar). The companion article (1Vetcher A.A. Napierala M. Iyer R. Chastain P.D. Griffith J.D. Wells R.D. J. Biol. Chem. 2002; 277: 39217-39227Abstract Full Text Full Text PDF PubMed Scopus (61) Google Scholar) demonstrates the necessity of two tracts of GAA·TTC in one molecule for the intramolecular formation of sticky DNA. Interestingly, a tract of (GAAGGA·TCCTTC)65 is also present in intron 1 of the frataxin gene (8Ohshima K. Sakamoto N. Labuda M. Poirier J. Moseley M.L. Montermini L. Ranum L.P. Wells R.D. Pandolfo M. Neurology. 1999; 53: 1854-1857Crossref PubMed Google Scholar) but does not inhibit transcription (9Sakamoto N. Ohshima K. Montermini L. Pandolfo M. Wells R.D. J. Biol. Chem. 2001; 276: 27171-27177Abstract Full Text Full Text PDF PubMed Scopus (157) Google Scholar, 12Ohshima K. Kang S. Larson J.E. Wells R.D. J. Biol. Chem. 1996; 271: 16773-16783Abstract Full Text Full Text PDF PubMed Scopus (94) Google Scholar) nor track with the disease in family pedigrees; alternatively, sticky DNA effectively inhibits transcription (9Sakamoto N. Ohshima K. Montermini L. Pandolfo M. Wells R.D. J. Biol. Chem. 2001; 276: 27171-27177Abstract Full Text Full Text PDF PubMed Scopus (157) Google Scholar). We have evaluated some of the sequence requirements for the mirror repeat R·Y insert tracts to form sticky DNA. The following R·Y tracts were investigated: GA·TC, GAA·TTC, GGA·TCC, GAAGGA·TCCTTC, and the 2.5-kbp R·Y tract from intron 21 of the polycystic kidney disease gene 1. The GA·TC repeat sequence is distributed widely in a variety of genomes (24Toth G. Gaspari Z. Jurka J. Genome Res. 2000; 10: 967-981Crossref PubMed Scopus (1100) Google Scholar). However, expanded repeats of GGA·TCC have not been discovered to date in conjunction with a hereditary neurological disease (18). In plasmids containing a pair of tracts of the identical repeat sequences, we found that sufficiently long tracts of GA·TC, GGA·TCC, and GAA·TTC adopted the sticky conformation. Alternatively, neither the GAAGGA·TCCTTC repeating hexanucleotide sequence nor the 2.5-kbp R·Y tract from the PKD1 gene adopted this unusual conformation. Because the two purine strands in the R·R·Y complex must be antiparallel (23Le Doan T. Perrouault L. Praseuth D. Habhoub N. Decout J.L. Thuong N.T. Lhomme J. Helene C. Nucleic Acids Res. 1987; 15: 7749-7760Crossref PubMed Scopus (522) Google Scholar), these results are readily explained from the known types of Hoogsteen bp schemes shown in Fig. 4; T·A·A and C·G·G are quite stable and favored structures, whereas T·A·G, C·G·A, and C·G·A+ are less favored. Accordingly, Fig.5 I demonstrates the facile triplex formation for GA·TC as well as GAA·TTC and Fig.5 II shows the stable bp interactions for GGA·TCC repeats.Figure 5Model of the possible triad interactions in all frames for the formation of sticky DNA. I, all possible base pairing frames for formation of triplexes by two tracts of GAA·TTC repeats. a,b, and c show the three frames for formation of triplexes. Filled boxes with white letters show the position of mismatched triplexes: T·A·G (gray boxes) and C·G·A (black boxes). II, all possible base pairing frames for the formation of triplexes between a pair of GGA·TCC repeat sequences. III, all possible base pairing frames for the formation of triplexes by a pair of GAAGGA·TCCTTC repeats. IV, all possible base pairing frames for formation of triplexes between GAA·TTC and the R strand of GAAGGA·TCCTTC repeats. Obviously, the same pairing rules hold for the pairing of the R strand of GAA·TTC with the Watson-Crick duplex of GAAGGA·TCCTTC.View Large Image Figure ViewerDownload (PPT) Alternatively, Fig. 5 III shows that for GAAGGA·TCCTTC interacting with the identical sequence in an intramolecular reaction, only four of six (66%) of the triple base oppositions are stable, even in the optimal frame. This figure shows the potential pairing schemes in all six frames. Thus, this degree of stability is insufficient for the formation of sticky DNA (10Sakamoto N. Larson J.E. Iyer R.R. Montermini L. Pandolfo M. Wells R.D. J. Biol. Chem. 2001; 276: 27178-27187Abstract Full Text Full Text PDF PubMed Scopus (67) Google Scholar) and provides a rational basis for the negative results shown in Table I for this sequence. Studies were also conducted with plasmids containing GAAGGA·TCCTTC and GAA·TTC in the same plasmid in direct repeat orientations. These plasmids showed the formation of sticky DNA. Fig. 5 IV shows that in the proper frames (a and d), five of six of the pairs are in stable Hoogsteen structures (Fig. 4 A). This extent of pairing is sufficient to enable the formation of a stable triplex (10Sakamoto N. Larson J.E. Iyer R.R. Montermini L. Pandolfo M. Wells R.D. J. Biol. Chem. 2001; 276: 27178-27187Abstract Full Text Full Text PDF PubMed Scopus (67) Google Scholar). Also, as expected, when two tracts of GAA·TTC are present in the same plasmid (pRW4886) (Fig. 2), a stable sticky DNA structure was observed. In summary, the composite results demonstrate that the formation of sticky DNA requires the formation of at least 83% of acceptable Hoogsteen and Watson-Crick base oppositions. Accordingly, these data provide strong confirmatory evidence for the purine-purine antiparallel triplex structures proposed in Figs. 4 and5. Furthermore, our current results are in excellent agreement with prior studies (1Vetcher A.A. Napierala M. Iyer R. Chastain P.D. Griffith J.D. Wells R.D. J. Biol. Chem. 2002; 277: 39217-39227Abstract Full Text Full Text PDF PubMed Scopus (61) Google Scholar), which showed that sticky DNA was an R·R·Y triplex with the purine strands in the antiparallel orientation. This investigation (1Vetcher A.A. Napierala M. Iyer R. Chastain P.D. Griffith J.D. Wells R.D. J. Biol. Chem. 2002; 277: 39217-39227Abstract Full Text Full Text PDF PubMed Scopus (61) Google Scholar) with a family of inserts in recombinant plasmid dimers with varying extents of interruptions between the extremes of pure GAA·TTC repeats (0% of GGA·TCC in the GAA·TTC repeats) and the repeating hexanucleotide sequence GAAGGA·TCCTTC (50% of GGA·TCC in the GAA·TTC repeats) revealed that more than 20% interruptions by GGA·TCC in the GAA·TTC repeat sequence abolished the formation of sticky DNA. In summary, all of these results considered together provide important confirmatory evidence for sticky DNA as an R·R·Y triplex with the base pairing schemes shown in Fig. 4 A with the two purine strands in the antiparallel arrangement. The salient features of FRDA as well as its human and molecular genetic properties were reviewed in the Introduction to the companion paper (1Vetcher A.A. Napierala M. Iyer R. Chastain P.D. Griffith J.D. Wells R.D. J. Biol. Chem. 2002; 277: 39217-39227Abstract Full Text Full Text PDF PubMed Scopus (61) Google Scholar). In patients, the expanded GAA·TTC repeats (66–1,700 or more) may form sticky DNA and thereby inhibit transcription; prior investigations (9Sakamoto N. Ohshima K. Montermini L. Pandolfo M. Wells R.D. J. Biol. Chem. 2001; 276: 27171-27177Abstract Full Text Full Text PDF PubMed Scopus (157) Google Scholar, 16Ohshima K. Montermini L. Wells R.D. Pandolfo M. J. Biol. Chem. 1998; 273: 14588-14595Abstract Full Text Full Text PDF PubMed Scopus (272) Google Scholar) showed the efficiency of sticky DNA in transcription inhibition, which could explain the reduction ofX25 mRNA in patients, which would result in a diminution of the amount of the frataxin protein, thus causing the disease pathology. The first intron of the frataxin gene also contains a (GAAGGA·TCCTTC)65 tract, which is nonpathogenic (8Ohshima K. Sakamoto N. Labuda M. Poirier J. Moseley M.L. Montermini L. Ranum L.P. Wells R.D. Pandolfo M. Neurology. 1999; 53: 1854-1857Crossref PubMed Google Scholar). Unlike the GAA·TTC repeat, this hexamer repeat does not form an antiparallel triplex and/or sticky DNA, does not inhibit transcription, and does not associate with the FRDA disease state (8Ohshima K. Sakamoto N. Labuda M. Poirier J. Moseley M.L. Montermini L. Ranum L.P. Wells R.D. Pandolfo M. Neurology. 1999; 53: 1854-1857Crossref PubMed Google Scholar, 9Sakamoto N. Ohshima K. Montermini L. Pandolfo M. Wells R.D. J. Biol. Chem. 2001; 276: 27171-27177Abstract Full Text Full Text PDF PubMed Scopus (157) Google Scholar, 10Sakamoto N. Larson J.E. Iyer R.R. Montermini L. Pandolfo M. Wells R.D. J. Biol. Chem. 2001; 276: 27178-27187Abstract Full Text Full Text PDF PubMed Scopus (67) Google Scholar). Because our investigations demonstrated the facility of formation of sticky DNA between long tracts of GAA·TTC and this neighboring hexanucleotide repeat, it is possible that these two sequences interact to form a potent block for transcription in FRDA patients. We thank Drs. Albino Bacolla, Adam Jaworski, Vladimir Potaman, and Richard R. Sinden for helpful discussions.

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