Polarizable atomic multipole X-ray refinement: application to peptide crystals
Identifieur interne : 000101 ( Ncbi/Merge ); précédent : 000100; suivant : 000102Polarizable atomic multipole X-ray refinement: application to peptide crystals
Auteurs : Michael J. Schnieders [États-Unis] ; Timothy D. Fenn [États-Unis] ; Vijay S. Pande [États-Unis] ; Axel T. Brunger [États-Unis]Source :
- Acta Crystallographica Section D: Biological Crystallography [ 0907-4449 ] ; 2009.
Abstract
A method to accelerate the computation of structure factors from an electron density described by anisotropic and aspherical atomic form factors
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DOI: 10.1107/S0907444909022707
PubMed: 19690373
PubMed Central: 2733883
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Fenn</name><affiliation wicri:level="1"><nlm:aff id="b">Department of Molecular and Cellular Physiology, Stanford, CA 94305,<country>USA</country></nlm:aff><country xml:lang="fr">États-Unis</country><wicri:regionArea># see nlm:aff country strict</wicri:regionArea></affiliation><affiliation wicri:level="1"><nlm:aff id="c">Howard Hughes Medical Institute,<country>USA</country></nlm:aff><country xml:lang="fr">États-Unis</country><wicri:regionArea># see nlm:aff country strict</wicri:regionArea></affiliation></author><author><name sortKey="Pande, Vijay S" sort="Pande, Vijay S" uniqKey="Pande V" first="Vijay S." last="Pande">Vijay S. Pande</name><affiliation wicri:level="1"><nlm:aff id="a">Department of Chemistry, Stanford, CA 94305,<country>USA</country></nlm:aff><country xml:lang="fr">États-Unis</country><wicri:regionArea># see nlm:aff country strict</wicri:regionArea></affiliation></author><author><name sortKey="Brunger, Axel T" sort="Brunger, Axel T" uniqKey="Brunger A" first="Axel T." last="Brunger">Axel T. Brunger</name><affiliation wicri:level="1"><nlm:aff id="b">Department of Molecular and Cellular Physiology, Stanford, CA 94305,<country>USA</country></nlm:aff><country xml:lang="fr">États-Unis</country><wicri:regionArea># see nlm:aff country strict</wicri:regionArea></affiliation><affiliation wicri:level="1"><nlm:aff id="c">Howard Hughes Medical Institute,<country>USA</country></nlm:aff><country xml:lang="fr">États-Unis</country><wicri:regionArea># see nlm:aff country strict</wicri:regionArea></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmid">19690373</idno><idno type="pmc">2733883</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2733883</idno><idno type="RBID">PMC:2733883</idno><idno type="doi">10.1107/S0907444909022707</idno><date when="2009">2009</date><idno type="wicri:Area/Pmc/Corpus">000473</idno><idno type="wicri:Area/Pmc/Curation">000473</idno><idno type="wicri:Area/Pmc/Checkpoint">000622</idno><idno type="wicri:Area/Ncbi/Merge">000101</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">Polarizable atomic multipole X-ray refinement: application to peptide crystals</title><author><name sortKey="Schnieders, Michael J" sort="Schnieders, Michael J" uniqKey="Schnieders M" first="Michael J." last="Schnieders">Michael J. Schnieders</name><affiliation wicri:level="1"><nlm:aff id="a">Department of Chemistry, Stanford, CA 94305,<country>USA</country></nlm:aff><country xml:lang="fr">États-Unis</country><wicri:regionArea># see nlm:aff country strict</wicri:regionArea></affiliation></author><author><name sortKey="Fenn, Timothy D" sort="Fenn, Timothy D" uniqKey="Fenn T" first="Timothy D." last="Fenn">Timothy D. Fenn</name><affiliation wicri:level="1"><nlm:aff id="b">Department of Molecular and Cellular Physiology, Stanford, CA 94305,<country>USA</country></nlm:aff><country xml:lang="fr">États-Unis</country><wicri:regionArea># see nlm:aff country strict</wicri:regionArea></affiliation><affiliation wicri:level="1"><nlm:aff id="c">Howard Hughes Medical Institute,<country>USA</country></nlm:aff><country xml:lang="fr">États-Unis</country><wicri:regionArea># see nlm:aff country strict</wicri:regionArea></affiliation></author><author><name sortKey="Pande, Vijay S" sort="Pande, Vijay S" uniqKey="Pande V" first="Vijay S." last="Pande">Vijay S. Pande</name><affiliation wicri:level="1"><nlm:aff id="a">Department of Chemistry, Stanford, CA 94305,<country>USA</country></nlm:aff><country xml:lang="fr">États-Unis</country><wicri:regionArea># see nlm:aff country strict</wicri:regionArea></affiliation></author><author><name sortKey="Brunger, Axel T" sort="Brunger, Axel T" uniqKey="Brunger A" first="Axel T." last="Brunger">Axel T. Brunger</name><affiliation wicri:level="1"><nlm:aff id="b">Department of Molecular and Cellular Physiology, Stanford, CA 94305,<country>USA</country></nlm:aff><country xml:lang="fr">États-Unis</country><wicri:regionArea># see nlm:aff country strict</wicri:regionArea></affiliation><affiliation wicri:level="1"><nlm:aff id="c">Howard Hughes Medical Institute,<country>USA</country></nlm:aff><country xml:lang="fr">États-Unis</country><wicri:regionArea># see nlm:aff country strict</wicri:regionArea></affiliation></author></analytic><series><title level="j">Acta Crystallographica Section D: Biological Crystallography</title><idno type="ISSN">0907-4449</idno><idno type="eISSN">1399-0047</idno><imprint><date when="2009">2009</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><p>A method to accelerate the computation of structure factors from an electron density described by anisotropic and aspherical atomic form factors <italic>via</italic> fast Fourier transformation is described for the first time.</p></div></front><back><div1 type="bibliography"><listBibl><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct></listBibl></div1></back></TEI><pmc article-type="research-article"><pmc-dir>properties open_access</pmc-dir>
<front><journal-meta><journal-id journal-id-type="nlm-ta">Acta Crystallogr D Biol Crystallogr</journal-id><journal-id journal-id-type="publisher-id">Acta Cryst. D</journal-id><journal-title-group><journal-title>Acta Crystallographica Section D: Biological Crystallography</journal-title></journal-title-group><issn pub-type="ppub">0907-4449</issn><issn pub-type="epub">1399-0047</issn><publisher><publisher-name>International Union of Crystallography</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">19690373</article-id><article-id pub-id-type="pmc">2733883</article-id><article-id pub-id-type="publisher-id">dz5164</article-id><article-id pub-id-type="doi">10.1107/S0907444909022707</article-id><article-id pub-id-type="coden">ABCRE6</article-id><article-id pub-id-type="pii">S0907444909022707</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Papers</subject></subj-group></article-categories><title-group><article-title>Polarizable atomic multipole X-ray refinement: application to peptide crystals</article-title><alt-title>Polarizable atomic multipole X-ray refinement</alt-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Schnieders</surname><given-names>Michael J.</given-names></name><xref ref-type="aff" rid="a">a</xref></contrib><contrib contrib-type="author"><name><surname>Fenn</surname><given-names>Timothy D.</given-names></name><xref ref-type="aff" rid="b">b</xref><xref ref-type="aff" rid="c">c</xref></contrib><contrib contrib-type="author"><name><surname>Pande</surname><given-names>Vijay S.</given-names></name><xref ref-type="aff" rid="a">a</xref><xref ref-type="corresp" rid="cor">*</xref></contrib><contrib contrib-type="author"><name><surname>Brunger</surname><given-names>Axel T.</given-names></name><xref ref-type="aff" rid="b">b</xref><xref ref-type="aff" rid="c">c</xref><xref ref-type="corresp" rid="cor">*</xref></contrib><aff id="a"><label>a</label>Department of Chemistry, Stanford, CA 94305,<country>USA</country></aff><aff id="b"><label>b</label>Department of Molecular and Cellular Physiology, Stanford, CA 94305,<country>USA</country></aff><aff id="c"><label>c</label>Howard Hughes Medical Institute,<country>USA</country></aff></contrib-group><author-notes><corresp id="cor">Correspondence e-mail: <email>pande@stanford.edu</email>, <email>brunger@stanford.edu</email></corresp></author-notes><pub-date pub-type="ppub"><day>01</day><month>9</month><year>2009</year></pub-date><pub-date pub-type="epub"><day>14</day><month>8</month><year>2009</year></pub-date><pub-date pub-type="pmc-release"><day>14</day><month>8</month><year>2009</year></pub-date><pmc-comment> PMC Release delay is 0 months and 0 days and was based on the
<volume>65</volume><issue>Pt 9</issue><issue-id pub-id-type="publisher-id">d090900</issue-id><fpage>952</fpage><lpage>965</lpage><supplementary-material content-type="local-data"><media xlink:href="d-65-00952-sup1.pdf" mimetype="application" mime-subtype="pdf"><caption><p>Click here for additional data file.</p></caption></media><p>Supplementary material file. DOI: <ext-link ext-link-type="uri" xlink:href="http://dx.doi.org/10.1107/S0907444909022707/dz5164sup1.pdf">10.1107/S0907444909022707/dz5164sup1.pdf</ext-link></p><media xlink:href="d-65-00952-sup1.pdf" xlink:type="simple" id="d32e135" position="anchor" mimetype="application" mime-subtype="pdf"></media></supplementary-material><supplementary-material content-type="local-data"><media xlink:href="d-65-00952-sup2.pdf" mimetype="application" mime-subtype="pdf"><caption><p>Click here for additional data file.</p></caption></media><p>Supplementary material file. DOI: <ext-link ext-link-type="uri" xlink:href="http://dx.doi.org/10.1107/S0907444909022707/dz5164sup2.pdf">10.1107/S0907444909022707/dz5164sup2.pdf</ext-link></p><media xlink:href="d-65-00952-sup2.pdf" xlink:type="simple" id="d32e142" position="anchor" mimetype="application" mime-subtype="pdf"></media></supplementary-material><history><date date-type="received"><day>24</day><month>4</month><year>2009</year></date><date date-type="accepted"><day>13</day><month>6</month><year>2009</year></date></history><permissions><copyright-statement>© Schnieders et al. 2009</copyright-statement><copyright-year>2009</copyright-year><license license-type="open-access" xlink:href="http://creativecommons.org/licenses/by/2.0/uk/"><license-p>This is an open-access article distributed under the terms of the Creative Commons Attribution Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are cited.</license-p></license></permissions><self-uri xlink:type="simple" xlink:href="http://dx.doi.org/10.1107/S0907444909022707">A full version of this article is available from Crystallography Journals Online.</self-uri><abstract abstract-type="toc"><p>A method to accelerate the computation of structure factors from an electron density described by anisotropic and aspherical atomic form factors <italic>via</italic> fast Fourier transformation is described for the first time.</p></abstract><abstract><p>Recent advances in computational chemistry have produced force fields based on a polarizable atomic multipole description of biomolecular electrostatics. In this work, the Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field is applied to restrained refinement of molecular models against X-ray diffraction data from peptide crystals. A new formalism is also developed to compute anisotropic and aspherical structure factors using fast Fourier transformation (FFT) of Cartesian Gaussian multipoles. Relative to direct summation, the FFT approach can give a speedup of more than an order of magnitude for aspherical refinement of ultrahigh-resolution data sets. Use of a sublattice formalism makes the method highly parallelizable. Application of the Cartesian Gaussian multipole scattering model to a series of four peptide crystals using multipole coefficients from the AMOEBA force field demonstrates that AMOEBA systematically underestimates electron density at bond centers. For the trigonal and tetrahedral bonding geometries common in organic chemistry, an atomic multipole expansion through hexadecapole order is required to explain bond electron density. Alternatively, the addition of interatomic scattering (IAS) sites to the AMOEBA-based density captured bonding effects with fewer parameters. For a series of four peptide crystals, the AMOEBA–IAS model lowered <italic>R</italic><sub>free</sub> by 20–40% relative to the original spherically symmetric scattering model.</p></abstract><kwd-group><kwd>scattering factors</kwd><kwd>aspherical</kwd><kwd>anisotropic</kwd><kwd>force fields</kwd><kwd>multipole</kwd><kwd>polarization</kwd><kwd>AMOEBA</kwd><kwd>bond density</kwd><kwd>direct summation</kwd><kwd>FFT</kwd><kwd>SGFFT</kwd><kwd>Ewald</kwd><kwd>PME</kwd></kwd-group></article-meta></front><floats-group><fig id="fig1" position="float"><label>Figure 1</label><caption><p>The local multipole frame of the carbonyl O atom of the peptide backbone is shown. The positive <italic>z</italic> axis is along the C=O bond and the <italic>x</italic> axis is chosen in the O=C—C<sup>α</sup> plane in the direction of the C<sup>α</sup> atom. The <italic>y</italic> axis is directed into the page in order to achieve a right-handed coordinate system. Also shown are the nonzero multipole moments of the O atom and a qualitative representation of their shape. The <italic>d</italic><sub><italic>z</italic></sub> Cartesian Gaussian dipole (in Debye units) places electron density along the C=O bond, while the trace of the Cartesian Gaussian quadrupole (in Buckingham units) positions electron density approximately at lone-pair positions.</p></caption><graphic xlink:href="d-65-00952-fig1"></graphic></fig><fig id="fig2" position="float"><label>Figure 2</label><caption><p>The scaling of the Cartesian Gaussian multipole model, truncated at quadrupole order, is plotted on a log–log scale for computation of the intensity-based maximum-likelihood target function (MLI) for direct summation, FFT and SGFFT. Direct summation scales linearly with the product of the number of atoms, the number of reflections and the number of symmetry operators. Computation of the crystallographic target function by FFT of the Cartesian Gaussian multipole electron density shows a speedup of a factor of between 1.8 and 14.5 compared with direct summation. A further speedup factor of nearly four is achieved using the SGFFT method on a four-processor machine.</p></caption><graphic xlink:href="d-65-00952-fig2"></graphic></fig><fig id="fig3" position="float"><label>Figure 3</label><caption><p>(<italic>a</italic>) IAM, (<italic>b</italic>) IAM–IAS, (<italic>c</italic>) AMOEBA and (<italic>d</italic>) AMOEBA–IAM refinements, respectively, for GY<sub>2</sub>. The <italic>F</italic><sub>o</sub> − <italic>F</italic><sub>c</sub> and 2<italic>F</italic><sub>o</sub> − <italic>F</italic><sub>c</sub> σ<sub>A</sub>-weighted electron-density maps are contoured at 3.5σ and shown in green and gray, respectively. Both the IAM and AMOEBA models fail to explain the electron density at bond centers seen in the data. In addition, the IAM model does not account for lone-pair density on the O atom.</p></caption><graphic xlink:href="d-65-00952-fig3"></graphic></fig><fig id="fig4" position="float"><label>Figure 4</label><caption><p>The precision of numerical computation of the <italic>R</italic><sub>work</sub> and <italic>R</italic><sub>free</sub> values <italic>via</italic> FFT is compared with analytic direct summation as a function of the isotropic increase <italic>B</italic><sub>add</sub> in ADP parameters for P<sub>2</sub>A<sub>4</sub> under the AMOEBA scattering model. Note that <italic>B</italic><sub>add</sub> = 8π<sup>2</sup><italic>U</italic><sub>add</sub>. </p></caption><graphic xlink:href="d-65-00952-fig4"></graphic></fig><fig id="fig5" position="float"><label>Figure 5</label><caption><p>The improvement arising from the AMOEBA–IAS scattering model, relative to the IAM model, is plotted as a function of relative percentage improvement in <italic>R</italic><sub>free</sub> value and the relative AMOEBA potential energy per residue. For all data sets, the best <italic>R</italic><sub>free</sub> value and lowest potential energy per residue were achieved using the AMOEBA–IAS scattering model. 1 kcal mol<sup>−1</sup> = 4.186 kJ mol<sup>−1</sup>.</p></caption><graphic xlink:href="d-65-00952-fig5"></graphic></fig><fig id="fig6" position="float"><label>Figure 6</label><caption><p>For the inter-atomic scattering sites of the IAM–IAS (<italic>a</italic>) and AMOEBA–IAS (<italic>b</italic>) scattering models, the refined Gaussian full-width at half-maximum (FWHM) is plotted <italic>versus</italic> partial charge magnitude. The majority of charges for the IAM–IAS model and all charges for the AMOEBA–IAS are negative. The sub-angstrom FWHM values are consistent with very localized bond densities.</p></caption><graphic xlink:href="d-65-00952-fig6"></graphic></fig><table-wrap id="table1" position="float"><label>Table 1</label><caption><title>Comparison of computational efficiency of direct-summation, FFT and SGFFT methods for the computation of the Cartesian Gaussian multipole scattering factors</title><p>The permanent multipole expansion was truncated at atomic quadrupoles and polarization was included <italic>via</italic> induced dipoles. The FFT method shows a speedup factor of 1.8–14.5 relative to direct summation. Parallelization by SGFFT provided an additional factor of 3.7–3.9 using four processors. All calculations were performed on a MacPro workstation with 2 × 2.66 GHz Dual Core Intel Xeon processors.</p></caption><table frame="hsides" rules="groups"><thead valign="bottom"><tr><th style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="bottom">PDB code</th><th style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" char="." charoff="50" valign="bottom">Atoms</th><th style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" char="." charoff="50" valign="bottom">Reflections</th><th style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" char="." charoff="50" valign="bottom"><italic>N</italic><sub>symm</sub></th><th style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" char="." charoff="50" valign="bottom">Atoms × reflections × <italic>N</italic><sub>symm</sub> × 10<sup>−6</sup></th><th style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" char="." charoff="50" valign="bottom">Direct (s)</th><th style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" char="." charoff="50" valign="bottom">FFT (s)</th><th style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" char="." charoff="50" valign="bottom">Direct/FFT</th><th style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" char="." charoff="50" valign="bottom">SGFFT (s)</th><th style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" char="." charoff="50" valign="bottom">Direct/SGFFT</th></tr></thead><tbody valign="top"><tr><td style="" rowspan="1" colspan="1" align="left" valign="top"><ext-link ext-link-type="uri" xlink:href="http://scripts.iucr.org/cgi-bin/cr.cgi?rm=pdb&pdbId=1ejg">1ejg</ext-link></td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">642</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">112209</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">2</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">144.1</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">49.9</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">28.1</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">1.8</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">7.3</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">6.8</td></tr><tr><td style="" rowspan="1" colspan="1" align="left" valign="top"><ext-link ext-link-type="uri" xlink:href="http://scripts.iucr.org/cgi-bin/cr.cgi?rm=pdb&pdbId=2vb1">2vb1</ext-link></td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">2544</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">187165</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">1</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">476.1</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">301.8</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">91.5</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">3.3</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">23.6</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">12.8</td></tr><tr><td style="" rowspan="1" colspan="1" align="left" valign="top"><ext-link ext-link-type="uri" xlink:href="http://scripts.iucr.org/cgi-bin/cr.cgi?rm=pdb&pdbId=1fn8">1fn8</ext-link></td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">4294</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">158550</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">1</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">680.8</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">245.1</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">45.8</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">5.4</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">12.4</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">19.8</td></tr><tr><td style="" rowspan="1" colspan="1" align="left" valign="top"><ext-link ext-link-type="uri" xlink:href="http://scripts.iucr.org/cgi-bin/cr.cgi?rm=pdb&pdbId=1dy5">1dy5</ext-link></td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">4835</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">159422</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">2</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">1541.6</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">505.6</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">37.0</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">13.7</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">9.7</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">52.1</td></tr><tr><td style="" rowspan="1" colspan="1" align="left" valign="top"><ext-link ext-link-type="uri" xlink:href="http://scripts.iucr.org/cgi-bin/cr.cgi?rm=pdb&pdbId=1us0">1us0</ext-link></td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">6865</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">511265</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">2</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">7019.7</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">2346.2</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">162.3</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">14.5</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">42.3</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">55.5</td></tr></tbody></table></table-wrap><table-wrap id="table2" position="float"><label>Table 2</label><caption><title>Refinement systems</title></caption><table frame="hsides" rules="groups"><thead valign="bottom"><tr><th style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="bottom">Molecule</th><th style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="bottom">Space group and unit-cell parameters (Å, °)</th><th style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="bottom">Non-H atoms</th><th style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="bottom">H atoms</th><th style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="bottom">Bonds</th><th style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="bottom"><italic>d</italic><sub>min</sub> (Å)</th><th style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="bottom">Reflections</th></tr></thead><tbody valign="top"><tr><td style="" rowspan="1" colspan="1" align="left" valign="top">YG<sub>2</sub></td><td style="" rowspan="1" colspan="1" align="left" valign="top"><italic>P</italic>2<sub>1</sub>2<sub>1</sub>2<sub>1</sub>, <italic>a</italic> = 7.98, <italic>b</italic> = 9.54, <italic>c</italic> = 18.32</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">22</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">19</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">40</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">0.43</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">4766</td></tr><tr><td style="" rowspan="1" colspan="1" align="left" valign="top">P<sub>2</sub>A<sub>4</sub></td><td style="" rowspan="1" colspan="1" align="left" valign="top"><italic>P</italic>2<sub>1</sub>2<sub>1</sub>2<sub>1</sub>, <italic>a</italic> = 10.13, <italic>b</italic> = 12.50, <italic>c</italic> = 19.50</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">35</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">36</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">72</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">0.37</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">24878</td></tr><tr><td style="" rowspan="1" colspan="1" align="left" valign="top">AYA + 3 waters</td><td style="" rowspan="1" colspan="1" align="left" valign="top"><italic>P</italic>2<sub>1</sub>, <italic>a</italic> = 8.12, <italic>b</italic> = 9.30, <italic>c</italic> = 12.53, β = 91.21</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">26</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">27</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">50</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">0.59</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">5019</td></tr><tr><td style="" rowspan="1" colspan="1" align="left" valign="top">AYA + ethanol</td><td style="" rowspan="1" colspan="1" align="left" valign="top"><italic>P</italic>2<sub>1</sub>, <italic>a</italic> = 8.85, <italic>b</italic> = 9.06, <italic>c</italic> = 12.36, β = 94.56</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">26</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">27</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">52</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">0.59</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">5258</td></tr></tbody></table></table-wrap><table-wrap id="table3" position="float"><label>Table 3</label><caption><title>Refinement statistics and the relative AMOEBA potential energy per asymmetric unit are given for four small peptide crystals using the IAM, IAM–IAS, AMOEBA and AMOEBA–IAS scattering models</title><p>In all cases, the lowest <italic>R</italic><sub>free</sub> was found using the AMOEBA–IAS scattering model. Furthermore, the structure with the lowest AMOEBA potential energy per asymmetric unit also corresponded to AMOEBA–IAS refinement.</p></caption><table frame="hsides" rules="groups"><thead valign="bottom"><tr><th style="" rowspan="1" colspan="1" align="left" valign="bottom"> </th><th style="" rowspan="1" colspan="1" align="left" valign="bottom"> </th><th style="" rowspan="1" colspan="1" align="left" valign="bottom"> </th><th style="" rowspan="1" colspan="1" align="left" valign="bottom"> </th><th style="border-bottom:1px solid black;" rowspan="1" colspan="2" align="left" valign="bottom"><italic>R</italic><sub>work</sub>/<italic>R</italic><sub>free</sub> (%)</th><th style="" rowspan="1" colspan="1"> </th></tr><tr><th style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="bottom">Molecule</th><th style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="bottom">Scattering model</th><th style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="bottom"><italic>N</italic><sub>param</sub></th><th style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="bottom"><italic>N</italic><sub>data</sub>/<italic>N</italic><sub>param</sub></th><th style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="bottom"><italic>I</italic><sub>obs</sub>/σ(<italic>I</italic><sub>obs</sub>) > 0</th><th style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="bottom"><italic>I</italic><sub>obs</sub>/σ(<italic>I</italic><sub>obs</sub>) > 3</th><th style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="bottom">Energy<xref ref-type="table-fn" rid="tfn1">†</xref> (kcal mol<sup>−1</sup>)</th></tr></thead><tbody valign="top"><tr><td style="" rowspan="1" colspan="1" align="left" valign="top">YGG</td><td style="" rowspan="1" colspan="1" align="left" valign="top">IAM</td><td style="" rowspan="1" colspan="1" align="left" valign="top">274</td><td style="" rowspan="1" colspan="1" align="left" valign="top">17.4</td><td style="" rowspan="1" colspan="1" align="left" valign="top">4.73/4.74</td><td style="" rowspan="1" colspan="1" align="left" valign="top">4.41/4.60</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">36.5</td></tr><tr><td style="" rowspan="1" colspan="1" align="left" valign="top"> </td><td style="" rowspan="1" colspan="1" align="left" valign="top">IAM–IAS</td><td style="" rowspan="1" colspan="1" align="left" valign="top">349</td><td style="" rowspan="1" colspan="1" align="left" valign="top">13.7</td><td style="" rowspan="1" colspan="1" align="left" valign="top">3.93/4.01</td><td style="" rowspan="1" colspan="1" align="left" valign="top">3.59/3.86</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">7.2</td></tr><tr><td style="" rowspan="1" colspan="1" align="left" valign="top"> </td><td style="" rowspan="1" colspan="1" align="left" valign="top">AMOEBA</td><td style="" rowspan="1" colspan="1" align="left" valign="top">355</td><td style="" rowspan="1" colspan="1" align="left" valign="top">13.4</td><td style="" rowspan="1" colspan="1" align="left" valign="top">4.50/4.56</td><td style="" rowspan="1" colspan="1" align="left" valign="top">4.16/4.37</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">6.8</td></tr><tr><td style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="top"> </td><td style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="top">AMOEBA–IAS</td><td style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="top">430</td><td style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="top">11.1</td><td style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="top">3.54/3.72</td><td style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="top">3.17/3.50</td><td style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">0.0</td></tr><tr><td style="" rowspan="1" colspan="1" align="left" valign="top">PPAAAA</td><td style="" rowspan="1" colspan="1" align="left" valign="top">IAM</td><td style="" rowspan="1" colspan="1" align="left" valign="top">339</td><td style="" rowspan="1" colspan="1" align="left" valign="top">73.4</td><td style="" rowspan="1" colspan="1" align="left" valign="top">4.25/4.22</td><td style="" rowspan="1" colspan="1" align="left" valign="top">3.65/3.73</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">32.2</td></tr><tr><td style="" rowspan="1" colspan="1" align="left" valign="top"> </td><td style="" rowspan="1" colspan="1" align="left" valign="top">IAM–IAS</td><td style="" rowspan="1" colspan="1" align="left" valign="top">417</td><td style="" rowspan="1" colspan="1" align="left" valign="top">59.7</td><td style="" rowspan="1" colspan="1" align="left" valign="top">3.56/3.48</td><td style="" rowspan="1" colspan="1" align="left" valign="top">3.00/3.01</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">18.3</td></tr><tr><td style="" rowspan="1" colspan="1" align="left" valign="top"> </td><td style="" rowspan="1" colspan="1" align="left" valign="top">AMOEBA</td><td style="" rowspan="1" colspan="1" align="left" valign="top">417</td><td style="" rowspan="1" colspan="1" align="left" valign="top">59.7</td><td style="" rowspan="1" colspan="1" align="left" valign="top">4.24/4.23</td><td style="" rowspan="1" colspan="1" align="left" valign="top">3.69/3.77</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">12.9</td></tr><tr><td style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="top"> </td><td style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="top">AMOEBA–IAS</td><td style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="top">495</td><td style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="top">50.3</td><td style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="top">3.42/3.42</td><td style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="top">2.86/2.94</td><td style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">0.0</td></tr><tr><td style="" rowspan="1" colspan="1" align="left" valign="top">AYA + 3 waters</td><td style="" rowspan="1" colspan="1" align="left" valign="top">IAM</td><td style="" rowspan="1" colspan="1" align="left" valign="top">342</td><td style="" rowspan="1" colspan="1" align="left" valign="top">14.7</td><td style="" rowspan="1" colspan="1" align="left" valign="top">2.75/2.79</td><td style="" rowspan="1" colspan="1" align="left" valign="top">2.67/2.71</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">17.5</td></tr><tr><td style="" rowspan="1" colspan="1" align="left" valign="top"> </td><td style="" rowspan="1" colspan="1" align="left" valign="top">IAM–IAS</td><td style="" rowspan="1" colspan="1" align="left" valign="top">411</td><td style="" rowspan="1" colspan="1" align="left" valign="top">12.2</td><td style="" rowspan="1" colspan="1" align="left" valign="top">2.24/2.47</td><td style="" rowspan="1" colspan="1" align="left" valign="top">2.16/2.39</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">4.1</td></tr><tr><td style="" rowspan="1" colspan="1" align="left" valign="top"> </td><td style="" rowspan="1" colspan="1" align="left" valign="top">AMOEBA</td><td style="" rowspan="1" colspan="1" align="left" valign="top">423</td><td style="" rowspan="1" colspan="1" align="left" valign="top">11.9</td><td style="" rowspan="1" colspan="1" align="left" valign="top">2.40/2.55</td><td style="" rowspan="1" colspan="1" align="left" valign="top">2.31/2.47</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">4.7</td></tr><tr><td style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="top"> </td><td style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="top">AMOEBA–IAS</td><td style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="top">492</td><td style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="top">10.2</td><td style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="top">1.72/2.03</td><td style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="left" valign="top">1.64/1.95</td><td style="border-bottom:1px solid black;" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">0.0</td></tr><tr><td style="" rowspan="1" colspan="1" align="left" valign="top">AYA + ethanol</td><td style="" rowspan="1" colspan="1" align="left" valign="top">IAM</td><td style="" rowspan="1" colspan="1" align="left" valign="top">342</td><td style="" rowspan="1" colspan="1" align="left" valign="top">15.4</td><td style="" rowspan="1" colspan="1" align="left" valign="top">3.30/3.50</td><td style="" rowspan="1" colspan="1" align="left" valign="top">3.20/3.33</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">23.1</td></tr><tr><td style="" rowspan="1" colspan="1" align="left" valign="top"> </td><td style="" rowspan="1" colspan="1" align="left" valign="top">IAM–IAS</td><td style="" rowspan="1" colspan="1" align="left" valign="top">423</td><td style="" rowspan="1" colspan="1" align="left" valign="top">12.4</td><td style="" rowspan="1" colspan="1" align="left" valign="top">2.32/2.66</td><td style="" rowspan="1" colspan="1" align="left" valign="top">2.21/2.49</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">14.8</td></tr><tr><td style="" rowspan="1" colspan="1" align="left" valign="top"> </td><td style="" rowspan="1" colspan="1" align="left" valign="top">AMOEBA</td><td style="" rowspan="1" colspan="1" align="left" valign="top">435</td><td style="" rowspan="1" colspan="1" align="left" valign="top">12.1</td><td style="" rowspan="1" colspan="1" align="left" valign="top">3.42/3.75</td><td style="" rowspan="1" colspan="1" align="left" valign="top">3.32/3.58</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">3.7</td></tr><tr><td style="" rowspan="1" colspan="1" align="left" valign="top"> </td><td style="" rowspan="1" colspan="1" align="left" valign="top">AMOEBA–IAS</td><td style="" rowspan="1" colspan="1" align="left" valign="top">516</td><td style="" rowspan="1" colspan="1" align="left" valign="top">10.2</td><td style="" rowspan="1" colspan="1" align="left" valign="top">1.90/2.25</td><td style="" rowspan="1" colspan="1" align="left" valign="top">1.79/2.08</td><td style="" rowspan="1" colspan="1" align="char" char="." charoff="50" valign="top">0.0</td></tr></tbody></table><table-wrap-foot><fn id="tfn1"><label>†</label><p>1 kcal mol<sup>−1</sup> = 4.186 kJ mol<sup>−1</sup>.</p></fn></table-wrap-foot></table-wrap></floats-group></pmc><affiliations><list><country><li>États-Unis</li></country></list><tree><country name="États-Unis"><noRegion><name sortKey="Schnieders, Michael J" sort="Schnieders, Michael J" uniqKey="Schnieders M" first="Michael J." last="Schnieders">Michael J. Schnieders</name></noRegion><name sortKey="Brunger, Axel T" sort="Brunger, Axel T" uniqKey="Brunger A" first="Axel T." last="Brunger">Axel T. Brunger</name><name sortKey="Brunger, Axel T" sort="Brunger, Axel T" uniqKey="Brunger A" first="Axel T." last="Brunger">Axel T. Brunger</name><name sortKey="Fenn, Timothy D" sort="Fenn, Timothy D" uniqKey="Fenn T" first="Timothy D." last="Fenn">Timothy D. Fenn</name><name sortKey="Fenn, Timothy D" sort="Fenn, Timothy D" uniqKey="Fenn T" first="Timothy D." last="Fenn">Timothy D. Fenn</name><name sortKey="Pande, Vijay S" sort="Pande, Vijay S" uniqKey="Pande V" first="Vijay S." last="Pande">Vijay S. Pande</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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