Design of shortest double-stranded DNA sequences covering all k-mers with applications to protein-binding microarrays and synthetic enhancers
Identifieur interne : 000792 ( Pmc/Corpus ); précédent : 000791; suivant : 000793Design of shortest double-stranded DNA sequences covering all k-mers with applications to protein-binding microarrays and synthetic enhancers
Auteurs : Yaron Orenstein ; Ron ShamirSource :
- Bioinformatics [ 1367-4803 ] ; 2015.
Url:
DOI: 10.1093/bioinformatics/btv084
PubMed: 25805721
PubMed Central: 4393528
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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Design of shortest double-stranded DNA sequences covering all <italic>k</italic>-mers with applications to protein-binding microarrays and synthetic enhancers</title><author><name sortKey="Orenstein, Yaron" sort="Orenstein, Yaron" uniqKey="Orenstein Y" first="Yaron" last="Orenstein">Yaron Orenstein</name></author><author><name sortKey="Shamir, Ron" sort="Shamir, Ron" uniqKey="Shamir R" first="Ron" last="Shamir">Ron Shamir</name></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmid">25805721</idno><idno type="pmc">4393528</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4393528</idno><idno type="RBID">PMC:4393528</idno><idno type="doi">10.1093/bioinformatics/btv084</idno><date when="2015">2015</date><idno type="wicri:Area/Pmc/Corpus">000792</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">000792</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">Design of shortest double-stranded DNA sequences covering all <italic>k</italic>-mers with applications to protein-binding microarrays and synthetic enhancers</title><author><name sortKey="Orenstein, Yaron" sort="Orenstein, Yaron" uniqKey="Orenstein Y" first="Yaron" last="Orenstein">Yaron Orenstein</name></author><author><name sortKey="Shamir, Ron" sort="Shamir, Ron" uniqKey="Shamir R" first="Ron" last="Shamir">Ron Shamir</name></author></analytic><series><title level="j">Bioinformatics</title><idno type="ISSN">1367-4803</idno><idno type="eISSN">1367-4811</idno><imprint><date when="2015">2015</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader></TEI><pmc article-type="correction"><pmc-dir>properties open_access</pmc-dir>
<front><journal-meta><journal-id journal-id-type="nlm-ta">Bioinformatics</journal-id><journal-id journal-id-type="iso-abbrev">Bioinformatics</journal-id><journal-id journal-id-type="publisher-id">bioinformatics</journal-id><journal-id journal-id-type="hwp">bioinfo</journal-id><journal-title-group><journal-title>Bioinformatics</journal-title></journal-title-group><issn pub-type="ppub">1367-4803</issn><issn pub-type="epub">1367-4811</issn><publisher><publisher-name>Oxford University Press</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">25805721</article-id><article-id pub-id-type="pmc">4393528</article-id><article-id pub-id-type="doi">10.1093/bioinformatics/btv084</article-id><article-id pub-id-type="publisher-id">btv084</article-id><article-categories><subj-group subj-group-type="heading"><subject>Erratum</subject></subj-group></article-categories><title-group><article-title>Design of shortest double-stranded DNA sequences covering all <italic>k</italic>-mers with applications to protein-binding microarrays and synthetic enhancers</article-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Orenstein</surname><given-names>Yaron</given-names></name></contrib><contrib contrib-type="author"><name><surname>Shamir</surname><given-names>Ron</given-names></name></contrib></contrib-group><pub-date pub-type="ppub"><day>15</day><month>4</month><year>2015</year></pub-date><pub-date pub-type="epub"><day>22</day><month>3</month><year>2015</year></pub-date><pub-date pub-type="pmc-release"><day>22</day><month>3</month><year>2015</year></pub-date><pmc-comment> PMC Release delay is 0 months and 0 days and was based on the
<volume>31</volume><issue>8</issue><fpage>1340</fpage><lpage>1340</lpage><permissions><copyright-statement>© The Author 2015. Published by Oxford University Press.</copyright-statement><copyright-year>2015</copyright-year><license xlink:href="http://creativecommons.org/licenses/by-nc/4.0/" license-type="creative-commons"><license-p>This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (<ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by-nc/4.0/">http://creativecommons.org/licenses/by-nc/4.0/</ext-link>), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com</license-p></license></permissions><counts><page-count count="1"></page-count></counts></article-meta></front><body><p>doi:10.1093/bioinformatics/btt230 <italic>Bioinformatics</italic> (2013) <bold>29</bold>(13), <related-article related-article-type="corrected-article" id="d35e90" vol="29" page="i71" xlink:href="23813011" ext-link-type="pubmed">i71–i79</related-article></p><p>In the above paper, there were several mistakes due to copyediting error. In Theorem 1 ‘if’ should be replaced by ‘iff’ and should read as follows: For odd <italic>k</italic>, an RC complete sequence s achieves the lower bound (Proposition 1) iff there exist two edge-disjoint paths with no repeating edges, corresponding to <italic>s</italic> and RC(<italic>s</italic>), that together cover all edges of the de Bruijn graph of order <italic>k</italic> − 1.</p><p>In Algorithm 1 ‘although’ should be replaced by ‘while’, and should read as follows:</p><p>1. Initially all edges are unmarked, <inline-formula><mml:math id="MM1"><mml:mrow><mml:mi mathvariant="script" class="calligraphy">F</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="script" class="calligraphy">R</mml:mi><mml:mo>=</mml:mo><mml:mo>∅</mml:mo></mml:mrow></mml:math></inline-formula>,</p><p> and <inline-formula><mml:math id="MM2"><mml:mrow><mml:mi>A</mml:mi><mml:mo>=</mml:mo><mml:mo>{</mml:mo><mml:mi>u</mml:mi><mml:mo>}</mml:mo></mml:mrow></mml:math></inline-formula>, an arbitrary vertex.</p><p>2. While <inline-formula><mml:math id="MM3"><mml:mrow><mml:mi>A</mml:mi><mml:mo>≠</mml:mo><mml:mo>∅</mml:mo></mml:mrow></mml:math></inline-formula> do</p><p>3. <inline-formula><mml:math id="MM4"><mml:mrow><mml:mi>F</mml:mi><mml:mo>=</mml:mo><mml:mi>R</mml:mi><mml:mo>=</mml:mo><mml:mo>∅</mml:mo></mml:mrow></mml:math></inline-formula>.</p><p>4. Pick any starting vertex <inline-formula><mml:math id="MM5"><mml:mrow><mml:mi>v</mml:mi><mml:mo>=</mml:mo><mml:mo stretchy="false">[</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mspace width="-0.2em"></mml:mspace><mml:mo>…</mml:mo><mml:mspace width="-0.2em"></mml:mspace><mml:mo>,</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">]</mml:mo></mml:mrow></mml:math></inline-formula> from <italic>A</italic>.</p><p>5. While there exists an unmarked edge <inline-formula><mml:math id="MM6"><mml:mrow><mml:mi>e</mml:mi><mml:mo>=</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mspace width="-0.2em"></mml:mspace><mml:mo>…</mml:mo><mml:mspace width="-0.2em"></mml:mspace><mml:mo>,</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math></inline-formula></p><p> outgoing from <italic>v</italic> do</p><p>6. Append <italic>e</italic> to <italic>F</italic>. Prepend <italic>RC</italic>(<italic>e</italic>) to <italic>R</italic>.</p><p>7. Mark <italic>e</italic> and <italic>RC</italic>(<italic>e</italic>).</p><p>8. Set <inline-formula><mml:math id="MM7"><mml:mrow><mml:mi>v</mml:mi><mml:mo>=</mml:mo><mml:mo stretchy="false">[</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mspace width="-0.2em"></mml:mspace><mml:mo>…</mml:mo><mml:mspace width="-0.2em"></mml:mspace><mml:mo>,</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mo stretchy="false">]</mml:mo></mml:mrow></mml:math></inline-formula>; <inline-formula><mml:math id="MM8"><mml:mrow><mml:mi>A</mml:mi><mml:mo>=</mml:mo><mml:mi>A</mml:mi><mml:mo>∪</mml:mo><mml:mo>{</mml:mo><mml:mi>v</mml:mi><mml:mo>}</mml:mo></mml:mrow></mml:math></inline-formula>.</p><p>9. Remove <italic>v</italic> from <italic>A</italic>.</p><p>10. If <inline-formula><mml:math id="MM9"><mml:mrow><mml:mi>F</mml:mi><mml:mo>≠</mml:mo><mml:mo>∅</mml:mo></mml:mrow></mml:math></inline-formula>, add <italic>F</italic> to <inline-formula><mml:math id="MM10"><mml:mi mathvariant="script" class="calligraphy">F</mml:mi></mml:math></inline-formula>; add <italic>R</italic> to <inline-formula><mml:math id="MM11"><mml:mi mathvariant="script" class="calligraphy">R</mml:mi></mml:math></inline-formula>;</p><p>11. Merge the cycles in <inline-formula><mml:math id="MM12"><mml:mi mathvariant="script" class="calligraphy">F</mml:mi></mml:math></inline-formula> to obtain a single forward path.</p><p> Do the same for <inline-formula><mml:math id="MM13"><mml:mi mathvariant="script" class="calligraphy">R</mml:mi></mml:math></inline-formula>.</p></body></pmc></record>Pour manipuler ce document sous Unix (Dilib)
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