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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">A Collaborative Filtering Approach for Protein-Protein Docking
Scoring Functions</title><author><name sortKey="Bourquard, Thomas" sort="Bourquard, Thomas" uniqKey="Bourquard T" first="Thomas" last="Bourquard">Thomas Bourquard</name><affiliation><nlm:aff id="aff1"><addr-line>Bioinformatics Group, INRIA AMIB, Laboratoire de Recherche en Informatique, Université Paris-Sud, Orsay, France</addr-line></nlm:aff></affiliation><affiliation><nlm:aff id="aff2"><addr-line>Bioinformatics Group, INRIA AMIB, Laboratoire d'Informatique (LIX), École Polytechnique, Palaiseau, France</addr-line></nlm:aff></affiliation><affiliation><nlm:aff id="aff3"><addr-line>INRIA Nancy Grand Est, LORIA, Vandoeuvre-lès-Nancy, France</addr-line></nlm:aff></affiliation></author><author><name sortKey="Bernauer, Julie" sort="Bernauer, Julie" uniqKey="Bernauer J" first="Julie" last="Bernauer">Julie Bernauer</name><affiliation><nlm:aff id="aff2"><addr-line>Bioinformatics Group, INRIA AMIB, Laboratoire d'Informatique (LIX), École Polytechnique, Palaiseau, France</addr-line></nlm:aff></affiliation></author><author><name sortKey="Aze, Jerome" sort="Aze, Jerome" uniqKey="Aze J" first="Jérôme" last="Azé">Jérôme Azé</name><affiliation><nlm:aff id="aff1"><addr-line>Bioinformatics Group, INRIA AMIB, Laboratoire de Recherche en Informatique, Université Paris-Sud, Orsay, France</addr-line></nlm:aff></affiliation></author><author><name sortKey="Poupon, Anne" sort="Poupon, Anne" uniqKey="Poupon A" first="Anne" last="Poupon">Anne Poupon</name><affiliation><nlm:aff id="aff4"><addr-line>BIOS Group, INRA, UMR85, Unité Physiologie de la Reproduction et des Comportements, Nouzilly, France</addr-line></nlm:aff></affiliation><affiliation><nlm:aff id="aff5"><addr-line>CNRS, UMR6175, Nouzilly, France</addr-line></nlm:aff></affiliation><affiliation><nlm:aff id="aff6"><addr-line>Université François Rabelais, Tours, France</addr-line></nlm:aff></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmid">21526112</idno><idno type="pmc">3081294</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3081294</idno><idno type="RBID">PMC:3081294</idno><idno type="doi">10.1371/journal.pone.0018541</idno><date when="2011">2011</date><idno type="wicri:Area/Pmc/Corpus">000087</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">000087</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">A Collaborative Filtering Approach for Protein-Protein Docking
Scoring Functions</title><author><name sortKey="Bourquard, Thomas" sort="Bourquard, Thomas" uniqKey="Bourquard T" first="Thomas" last="Bourquard">Thomas Bourquard</name><affiliation><nlm:aff id="aff1"><addr-line>Bioinformatics Group, INRIA AMIB, Laboratoire de Recherche en Informatique, Université Paris-Sud, Orsay, France</addr-line></nlm:aff></affiliation><affiliation><nlm:aff id="aff2"><addr-line>Bioinformatics Group, INRIA AMIB, Laboratoire d'Informatique (LIX), École Polytechnique, Palaiseau, France</addr-line></nlm:aff></affiliation><affiliation><nlm:aff id="aff3"><addr-line>INRIA Nancy Grand Est, LORIA, Vandoeuvre-lès-Nancy, France</addr-line></nlm:aff></affiliation></author><author><name sortKey="Bernauer, Julie" sort="Bernauer, Julie" uniqKey="Bernauer J" first="Julie" last="Bernauer">Julie Bernauer</name><affiliation><nlm:aff id="aff2"><addr-line>Bioinformatics Group, INRIA AMIB, Laboratoire d'Informatique (LIX), École Polytechnique, Palaiseau, France</addr-line></nlm:aff></affiliation></author><author><name sortKey="Aze, Jerome" sort="Aze, Jerome" uniqKey="Aze J" first="Jérôme" last="Azé">Jérôme Azé</name><affiliation><nlm:aff id="aff1"><addr-line>Bioinformatics Group, INRIA AMIB, Laboratoire de Recherche en Informatique, Université Paris-Sud, Orsay, France</addr-line></nlm:aff></affiliation></author><author><name sortKey="Poupon, Anne" sort="Poupon, Anne" uniqKey="Poupon A" first="Anne" last="Poupon">Anne Poupon</name><affiliation><nlm:aff id="aff4"><addr-line>BIOS Group, INRA, UMR85, Unité Physiologie de la Reproduction et des Comportements, Nouzilly, France</addr-line></nlm:aff></affiliation><affiliation><nlm:aff id="aff5"><addr-line>CNRS, UMR6175, Nouzilly, France</addr-line></nlm:aff></affiliation><affiliation><nlm:aff id="aff6"><addr-line>Université François Rabelais, Tours, France</addr-line></nlm:aff></affiliation></author></analytic><series><title level="j">PLoS ONE</title><idno type="eISSN">1932-6203</idno><imprint><date when="2011">2011</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><p>A protein-protein docking procedure traditionally consists in two successive
tasks: a search algorithm generates a large number of candidate conformations
mimicking the complex existing <italic>in vivo</italic> between two proteins,
and a scoring function is used to rank them in order to extract a native-like
one. We have already shown that using Voronoi constructions and a well chosen
set of parameters, an accurate scoring function could be designed and optimized.
However to be able to perform large-scale <italic>in silico</italic> exploration
of the interactome, a near-native solution has to be found in the ten
best-ranked solutions. This cannot yet be guaranteed by any of the existing
scoring functions.</p><p>In this work, we introduce a new procedure for conformation ranking. We
previously developed a set of scoring functions where learning was performed
using a genetic algorithm. These functions were used to assign a rank to each
possible conformation. We now have a refined rank using different classifiers
(decision trees, rules and support vector machines) in a collaborative filtering
scheme. The scoring function newly obtained is evaluated using 10 fold
cross-validation, and compared to the functions obtained using either genetic
algorithms or collaborative filtering taken separately.</p><p>This new approach was successfully applied to the CAPRI scoring ensembles. We
show that for 10 targets out of 12, we are able to find a near-native
conformation in the 10 best ranked solutions. Moreover, for 6 of them, the
near-native conformation selected is of high accuracy. Finally, we show that
this function dramatically enriches the 100 best-ranking conformations in
near-native structures.</p></div></front><back><div1 type="bibliography"><listBibl><biblStruct><analytic><author><name sortKey="Wodak, Sj" uniqKey="Wodak S">SJ Wodak</name></author><author><name sortKey="Janin, J" uniqKey="Janin J">J Janin</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Sanderson, Cm" uniqKey="Sanderson C">CM Sanderson</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Berman, H" uniqKey="Berman H">H Berman</name></author><author><name sortKey="Westbrook, J" uniqKey="Westbrook J">J Westbrook</name></author><author><name sortKey="Feng, Z" uniqKey="Feng Z">Z Feng</name></author><author><name sortKey="Gilliland, G" uniqKey="Gilliland G">G Gilliland</name></author><author><name sortKey="Bhat, T" uniqKey="Bhat T">T Bhat</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Ritchie, Dw" uniqKey="Ritchie D">DW 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uniqKey="Boissonnat J">JD Boissonnat</name></author><author><name sortKey="Devillers, O" uniqKey="Devillers O">O Devillers</name></author><author><name sortKey="Pion, S" uniqKey="Pion S">S Pion</name></author><author><name sortKey="Teillaud, M" uniqKey="Teillaud M">M Teillaud</name></author><author><name sortKey="Yvinec, M" uniqKey="Yvinec M">M Yvinec</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Pontius, J" uniqKey="Pontius J">J Pontius</name></author><author><name sortKey="Richelle, J" uniqKey="Richelle J">J Richelle</name></author><author><name sortKey="Wodak, S" uniqKey="Wodak S">S Wodak</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Chen, R" uniqKey="Chen R">R Chen</name></author><author><name sortKey="Mintseris, J" uniqKey="Mintseris J">J Mintseris</name></author><author><name sortKey="Janin, J" uniqKey="Janin J">J Janin</name></author><author><name sortKey="Weng, Z" uniqKey="Weng Z">Z 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<front><journal-meta><journal-id journal-id-type="nlm-ta">PLoS One</journal-id><journal-id journal-id-type="publisher-id">plos</journal-id><journal-id journal-id-type="pmc">plosone</journal-id><journal-title-group><journal-title>PLoS ONE</journal-title></journal-title-group><issn pub-type="epub">1932-6203</issn><publisher><publisher-name>Public Library of Science</publisher-name><publisher-loc>San Francisco, USA</publisher-loc></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">21526112</article-id><article-id pub-id-type="pmc">3081294</article-id><article-id pub-id-type="publisher-id">PONE-D-10-06185</article-id><article-id pub-id-type="doi">10.1371/journal.pone.0018541</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="Discipline-v2"><subject>Biology</subject><subj-group><subject>Computational Biology</subject><subj-group><subject>Macromolecular Structure Analysis</subject><subj-group><subject>Macromolecular Complex Analysis</subject><subject>Protein Structure</subject></subj-group></subj-group></subj-group></subj-group><subj-group subj-group-type="Discipline-v2"><subject>Computer Science</subject><subj-group><subject>Computer Modeling</subject></subj-group></subj-group></article-categories><title-group><article-title>A Collaborative Filtering Approach for Protein-Protein Docking
Scoring Functions</article-title><alt-title alt-title-type="running-head">Collaborative Filtering for Protein
Docking</alt-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Bourquard</surname><given-names>Thomas</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref><xref ref-type="aff" rid="aff2"><sup>2</sup></xref><xref ref-type="aff" rid="aff3"><sup>3</sup></xref></contrib><contrib contrib-type="author"><name><surname>Bernauer</surname><given-names>Julie</given-names></name><xref ref-type="aff" rid="aff2"><sup>2</sup></xref></contrib><contrib contrib-type="author"><name><surname>Azé</surname><given-names>Jérôme</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref></contrib><contrib contrib-type="author"><name><surname>Poupon</surname><given-names>Anne</given-names></name><xref ref-type="aff" rid="aff4"><sup>4</sup></xref><xref ref-type="aff" rid="aff5"><sup>5</sup></xref><xref ref-type="aff" rid="aff6"><sup>6</sup></xref><xref ref-type="corresp" rid="cor1"><sup>*</sup></xref></contrib></contrib-group><aff id="aff1"><label>1</label><addr-line>Bioinformatics Group, INRIA AMIB, Laboratoire de Recherche en Informatique, Université Paris-Sud, Orsay, France</addr-line></aff><aff id="aff2"><label>2</label><addr-line>Bioinformatics Group, INRIA AMIB, Laboratoire d'Informatique (LIX), École Polytechnique, Palaiseau, France</addr-line></aff><aff id="aff3"><label>3</label><addr-line>INRIA Nancy Grand Est, LORIA, Vandoeuvre-lès-Nancy, France</addr-line></aff><aff id="aff4"><label>4</label><addr-line>BIOS Group, INRA, UMR85, Unité Physiologie de la Reproduction et des Comportements, Nouzilly, France</addr-line></aff><aff id="aff5"><label>5</label><addr-line>CNRS, UMR6175, Nouzilly, France</addr-line></aff><aff id="aff6"><label>6</label><addr-line>Université François Rabelais, Tours, France</addr-line></aff><contrib-group><contrib contrib-type="editor"><name><surname>Friedberg</surname><given-names>Iddo</given-names></name><role>Editor</role><xref ref-type="aff" rid="edit1"></xref></contrib></contrib-group><aff id="edit1">Miami University, United States of America</aff><author-notes><corresp id="cor1">* E-mail: <email>Anne.Poupon@tours.inra.fr</email></corresp><fn fn-type="con"><p>Conceived and designed the experiments: TB JB JA AP. Performed the
experiments: TB JB JA AP. Analyzed the data: TB JB JA AP. Contributed
reagents/materials/analysis tools: TB JB JA AP. Wrote the paper: TB JB JA
AP.</p></fn></author-notes><pub-date pub-type="collection"><year>2011</year></pub-date><pub-date pub-type="epub"><day>22</day><month>4</month><year>2011</year></pub-date><volume>6</volume><issue>4</issue><elocation-id>e18541</elocation-id><history><date date-type="received"><day>6</day><month>12</month><year>2010</year></date><date date-type="accepted"><day>3</day><month>3</month><year>2011</year></date></history><permissions><copyright-statement>Bourquard et al. This is an open-access article distributed under
the terms of the Creative Commons Attribution License, which permits unrestricted
use, distribution, and reproduction in any medium, provided the original author and
source are credited.</copyright-statement></permissions><abstract><p>A protein-protein docking procedure traditionally consists in two successive
tasks: a search algorithm generates a large number of candidate conformations
mimicking the complex existing <italic>in vivo</italic> between two proteins,
and a scoring function is used to rank them in order to extract a native-like
one. We have already shown that using Voronoi constructions and a well chosen
set of parameters, an accurate scoring function could be designed and optimized.
However to be able to perform large-scale <italic>in silico</italic> exploration
of the interactome, a near-native solution has to be found in the ten
best-ranked solutions. This cannot yet be guaranteed by any of the existing
scoring functions.</p><p>In this work, we introduce a new procedure for conformation ranking. We
previously developed a set of scoring functions where learning was performed
using a genetic algorithm. These functions were used to assign a rank to each
possible conformation. We now have a refined rank using different classifiers
(decision trees, rules and support vector machines) in a collaborative filtering
scheme. The scoring function newly obtained is evaluated using 10 fold
cross-validation, and compared to the functions obtained using either genetic
algorithms or collaborative filtering taken separately.</p><p>This new approach was successfully applied to the CAPRI scoring ensembles. We
show that for 10 targets out of 12, we are able to find a near-native
conformation in the 10 best ranked solutions. Moreover, for 6 of them, the
near-native conformation selected is of high accuracy. Finally, we show that
this function dramatically enriches the 100 best-ranking conformations in
near-native structures.</p></abstract><counts><page-count count="11"></page-count></counts></article-meta></front><body><sec id="s1"><title>Introduction</title><p>Most proteins fulfill their functions through the interaction with other proteins
<xref ref-type="bibr" rid="pone.0018541-Wodak1">[1]</xref>. The
interactome appears increasingly complex as the experimental means used for its
exploration gain in precision <xref ref-type="bibr" rid="pone.0018541-Sanderson1">[2]</xref>. Although structural genomics specially addressing the
question of 3D structure determination of protein-protein complexes have led to
great progress, the low stability of most complexes precludes high-resolution
structure determination by either crystallography or NMR. 3D structure of complexes
are thus poorly represented in the Protein Data Bank (PDB) <xref ref-type="bibr" rid="pone.0018541-Berman1">[3]</xref>. The fast and accurate
prediction of the assembly from the structures of the individual partners, called
protein-protein docking, is therefore of great value <xref ref-type="bibr" rid="pone.0018541-Ritchie1">[4]</xref>. However, available docking
procedures technically suitable for large-scale exploration of the proteome have
shown their limits <xref ref-type="bibr" rid="pone.0018541-Mosca1">[5]</xref>, <xref ref-type="bibr" rid="pone.0018541-Kastritis1">[6]</xref>. Indeed, amongst the easily available methods for such
exploration, a near-native solution is found in the 10 best-ranked solutions (top
10) only for 34% of the studied complexes. For biologists, exploring 10
different conformations for experimental validation is already a huge effort. Making
this exploration knowing that the prediction will be confirmed only in one case out
of three is completely unacceptable. Consequently, large-scale protein-protein
docking will be useful for biologists only if a near-native solution can be found in
the top 10 in almost all cases (ideally in the top 5 or even the top 3).</p><p>A docking procedure consists in two tasks, generally consecutive and largely
independent. The first one, called exploration, consists in building a large number
of candidates by sampling the different possible orientations of one partner
relatively to the other. The second task consists in ranking the candidates using a
scoring function in order to extract near-native conformations. To be accurate,
scoring functions have to take into account both the geometric complementarity and
the physico-chemistry of amino acids in interaction, since they both contribute to
the stability of the assembly <xref ref-type="bibr" rid="pone.0018541-Halperin1">[7]</xref>, <xref ref-type="bibr" rid="pone.0018541-Andrusier1">[8]</xref>.</p><p>Modeling multi-component assemblies often involves computationally expensive
techniques, and exploring all the solutions is often not feasible. Consequently, we
previously introduced a coarse-grained model for protein structure based on the
Voronoi tessellation. This model allowed the set up of a method for discriminating
between biological and crystallographic dimers <xref ref-type="bibr" rid="pone.0018541-Bernauer1">[9]</xref>, and the design of an
optimized scoring function for protein-protein docking <xref ref-type="bibr" rid="pone.0018541-Bernauer2">[10]</xref>, <xref ref-type="bibr" rid="pone.0018541-Bernauer3">[11]</xref>. These results show that this
representation retains the main properties of proteins and proteins assemblies 3D
structures, making it a precious tool for building fast and accurate scoring
methods. We have also explored the possibility to use a power diagram or Laguerre
tessellation model, which gives a more realistic representation of the structure.
However we have shown that this model does not give better results and increases
algorithmic complexity <xref ref-type="bibr" rid="pone.0018541-Bourquard1">[12]</xref>.</p><p>In this study, using the Voronoi representation of protein structure, and an in-lab
conformation generation algorithm, we show different ways of optimizing the scoring
method based on probabilistic multi-classifiers adaptation and genetic
algorithm.</p></sec><sec sec-type="methods" id="s2"><title>Methods</title><sec id="s2a"><title>Structure Representation and Conformation Generation</title><p>Like in our previous work <xref ref-type="bibr" rid="pone.0018541-Bernauer1">[9]</xref>–<xref ref-type="bibr" rid="pone.0018541-Bourquard1">[12]</xref>, a coarse-grain model is
used to represent the protein structure. We define a single node for each
residue (the geometric center of side chain, including
C<italic><sub>a</sub></italic>), the Delaunay triangulation (dual of the
Voronoi diagram) of each partner is then computed using CGAL <xref ref-type="bibr" rid="pone.0018541-Boissonnat1">[13]</xref> and the
Voronoi tessellation is built. The generation of candidate conformations is
performed as follows. For each node, a pseudo-normal vector is built by summing
the vectors linking this node to its neighbors. In non-convex regions, this
vector might point towards the interior of the protein. In this case the
opposite vector is taken. Depending on the amino acid type, the length of this
vector is made equal to the radius of a sphere whose volume is equal to the
average volume occupied by this type of amino acid. This mean volume is taken
from Pontius <italic>et al.</italic><xref ref-type="bibr" rid="pone.0018541-Pontius1">[14]</xref>. For
each possible pair of vectors (one in each partner), one of the vectors is
translated so as to bring its extremity on the extremity of the first vector
(step 1 on <xref ref-type="fig" rid="pone-0018541-g001">Figure 1</xref>). The
second partner is then rotated so as to oppose the two vectors (step 2 on <xref ref-type="fig" rid="pone-0018541-g001">Figure 1</xref>). The second partner
is then rotated around this new axis (step 3 on <xref ref-type="fig" rid="pone-0018541-g001">Figure 1</xref>), and a conformation of the complex
is build every 5° rotation.</p><fig id="pone-0018541-g001" position="float"><object-id pub-id-type="doi">10.1371/journal.pone.0018541.g001</object-id><label>Figure 1</label><caption><title>Conformation generation method.</title></caption><graphic xlink:href="pone.0018541.g001"></graphic></fig><p>Although not all degrees of freedom are considered (the two normal vectors are
always aligned in our method, but we could have considered varying the angle
between them), we obtain a near-native conformation for all the complexes in the
learning set.</p></sec><sec id="s2b"><title>Learning set</title><p>Our positive examples set is composed of native structures. We complemented our
previous set <xref ref-type="bibr" rid="pone.0018541-Bourquard1">[12]</xref> with the reference set from <xref ref-type="bibr" rid="pone.0018541-Chen1">[15]</xref>. This set contains 211
bound-unbound and unbound-unbound complexes (complexes for which the 3D
structure of at least one partner is known). SCOP <xref ref-type="bibr" rid="pone.0018541-Murzin1">[16]</xref> was used to remove
redundancy (for two complexes AB and CD, if A and C belong to the same SCOP
family, and B and D also belong to the same family, the complex is
eliminated).</p><p>Negative examples (decoys, or non-native conformations) were generated by
applying the previously described generation method to each complex of our
native structures set. Only conformations having a minimal interface area of 400
Å<sup>2</sup> and a root mean square deviation (RMSD) relative to the
native conformation higher than 10 Å were retained. Within this ensemble,
15 non-native conformations were chosen for each native conformations, resulting
in 2980 negative examples in the learning set. As observed in our previous
studies, missing values are a serious issue for scoring function optimization.
All the non-native conformations presenting a too high number of missing values
were removed. This number was taken to be twice the number of missing values in
the corresponding native structure. 20 such non-native conformations for each
native structure were randomly chosen from the initial decoys set.</p></sec><sec id="s2c"><title>Training Parameters</title><p>The coarse-grained Voronoi tessellation allows simple description of the
protein-protein interface. 96 training attributes <xref ref-type="bibr" rid="pone.0018541-Bourquard1">[12]</xref> based on properties of
residues and pairs present at the interface have been used. For pair parameters,
residues were binned in six categories: hydrophobic (ILVM), aromatics (FYW),
small (AGSTCP), polar (NQ), positive (HKR) and negative (DE). These categories
are also used to compute the 12 last parameters. Retained parameters are:</p><list list-type="bullet"><list-item><p><italic>c</italic><sub>1</sub>: The Voronoi interface area.</p></list-item><list-item><p><italic>c</italic><sub>2</sub>: The total number of interface
residues.</p></list-item><list-item><p><italic>c</italic><sub>3</sub> to <italic>c</italic><sub>22</sub>: The
fraction of each type of interface residues.</p></list-item><list-item><p><italic>c</italic><sub>23</sub> to <italic>c</italic><sub>42</sub>: The
mean volume of Voronoi cells for the interface residues.</p></list-item><list-item><p><italic>c</italic><sub>43</sub> to <italic>c</italic><sub>63</sub>: The
fraction of pairs of interface residues.</p></list-item><list-item><p><italic>c</italic><sub>64</sub> to <italic>c</italic><sub>84</sub>: The
mean node-node distance in pairs of interface residues.</p></list-item><list-item><p><italic>c</italic><sub>85</sub> to <italic>c</italic><sub>90</sub>: The
fraction of interface residues for each category.</p></list-item><list-item><p><italic>c</italic><sub>91</sub> to <italic>c</italic><sub>96</sub>: The
mean volume of Voronoi cells for the interface residues for each
category.</p></list-item></list><p>All parameters were computed on the complete interface, defined as all the
residues having at least one neighbor belonging to the second partner, including
residues in contact with solvent molecules.</p></sec><sec id="s2d"><title>Genetic algorithm</title><p>Using previously defined training attributes, genetic algorithms are used to find
family of functions that optimize the ROC (Receiver Operating Characteristics)
criterion. We used a <inline-formula><inline-graphic xlink:href="pone.0018541.e001.jpg" mimetype="image"></inline-graphic></inline-formula> scheme, with
<inline-formula><inline-graphic xlink:href="pone.0018541.e002.jpg" mimetype="image"></inline-graphic></inline-formula> parents and <inline-formula><inline-graphic xlink:href="pone.0018541.e003.jpg" mimetype="image"></inline-graphic></inline-formula> children, and a
maximum of 500 generations. We used a classical cross-over and auto-adaptative
mutations. The ROC criterion is commonly used to evaluate the performance of
learning procedures by measuring the area under the ROC curve (AUC). The ROC
curve is obtained by plotting the proportion of true positives against false
positives.</p><p>The scoring functions used in this work have the form:<disp-formula><graphic xlink:href="pone.0018541.e004"></graphic><label>(1)</label></disp-formula>where <inline-formula><inline-graphic xlink:href="pone.0018541.e005.jpg" mimetype="image"></inline-graphic></inline-formula> is the value of
parameter <inline-formula><inline-graphic xlink:href="pone.0018541.e006.jpg" mimetype="image"></inline-graphic></inline-formula> and <inline-formula><inline-graphic xlink:href="pone.0018541.e007.jpg" mimetype="image"></inline-graphic></inline-formula> and
<inline-formula><inline-graphic xlink:href="pone.0018541.e008.jpg" mimetype="image"></inline-graphic></inline-formula> are the weights and centering values respectively for
parameter <inline-formula><inline-graphic xlink:href="pone.0018541.e009.jpg" mimetype="image"></inline-graphic></inline-formula>. <inline-formula><inline-graphic xlink:href="pone.0018541.e010.jpg" mimetype="image"></inline-graphic></inline-formula> and
<inline-formula><inline-graphic xlink:href="pone.0018541.e011.jpg" mimetype="image"></inline-graphic></inline-formula> are optimized by the learning procedure. Learning was
performed in a 10-fold cross-validation setting. Ten groups of models were
randomly chosen, each excluding 10% of the training set. Learning was
repeated <inline-formula><inline-graphic xlink:href="pone.0018541.e012.jpg" mimetype="image"></inline-graphic></inline-formula> times for each training subset. Consequently, each
conformation is evaluated using <inline-formula><inline-graphic xlink:href="pone.0018541.e013.jpg" mimetype="image"></inline-graphic></inline-formula> different scoring
functions, and for final ranking, the sum of the ranks obtained by each function
is used.</p><p>As described in the Results section, the number of functions
<inline-formula><inline-graphic xlink:href="pone.0018541.e014.jpg" mimetype="image"></inline-graphic></inline-formula> used in the computation of the final rank might have an
impact on the quality of the global ranking.</p></sec><sec id="s2e"><title>Collaborative filtering methods</title><p>Several previous studies have shown the strength of Collaborative Filtering (CF)
techniques in Information Retrieval problems <xref ref-type="bibr" rid="pone.0018541-Su1">[17]</xref> to increase the accuracy of the
prediction rate. In a common CF recommender system, there is a list of
<inline-formula><inline-graphic xlink:href="pone.0018541.e015.jpg" mimetype="image"></inline-graphic></inline-formula> users, <inline-formula><inline-graphic xlink:href="pone.0018541.e016.jpg" mimetype="image"></inline-graphic></inline-formula> and a list of
<inline-formula><inline-graphic xlink:href="pone.0018541.e017.jpg" mimetype="image"></inline-graphic></inline-formula> items, <inline-formula><inline-graphic xlink:href="pone.0018541.e018.jpg" mimetype="image"></inline-graphic></inline-formula> and each user
gives a mark to each object. This mark can also be inferred from the user's
behaviour. The final mark of each object is then defined by the ensemble of
marks received from each user.</p><p>In the present work, a classifier is a user, and conformations are the items.
Each classifier (user) assigns to each item (conformation) a binary label (or
mark): <italic>native'</italic> (+) or <italic>non native</italic>(−).</p><p>12 classifiers have been trained on the learning set (see “<xref ref-type="sec" rid="s3">Results and Discussion</xref>”), deriving from
four different methods: decision trees, rules, logistic regression and SVM
(Support Vector Machine). Most optimizations were done using Weka <xref ref-type="bibr" rid="pone.0018541-Hall1">[18]</xref>. The
<italic>SVMlight</italic><xref ref-type="bibr" rid="pone.0018541-Joachims1">[19]</xref>software was used for SVM computations.</p><p>In a first approach, we have used a default voting system: the conformations are
ranked according to the number of + marks they have received. Since we have
12 classifiers, this determines 13 different categories: 12+, 11+,
…, 0+.</p><p>Because 13 categories is far from enough to efficiently ranks a very large number
of conformations, we have also used a second approach using an amplification
average voting system. In this system, the votes of each classifier are weighted
by the precision. Consequently, the + vote of each classifier is different
from the + vote of a different classifier. This results in 2<sup>12</sup>categories. The categories are ordered according to:<disp-formula><graphic xlink:href="pone.0018541.e019"></graphic><label>(2)</label></disp-formula></p><p>Where <inline-formula><inline-graphic xlink:href="pone.0018541.e020.jpg" mimetype="image"></inline-graphic></inline-formula> (respectively <inline-formula><inline-graphic xlink:href="pone.0018541.e021.jpg" mimetype="image"></inline-graphic></inline-formula>) is the sum of the
precisions of the classifiers that have voted + (respectively −) for
conformations of this category. This score is assigned to each conformation of
the considered category.<disp-formula><graphic xlink:href="pone.0018541.e022"></graphic><label>(3)</label></disp-formula></p><p>Where <inline-formula><inline-graphic xlink:href="pone.0018541.e023.jpg" mimetype="image"></inline-graphic></inline-formula> represents the vote of the
<inline-formula><inline-graphic xlink:href="pone.0018541.e024.jpg" mimetype="image"></inline-graphic></inline-formula> classifier and <inline-formula><inline-graphic xlink:href="pone.0018541.e025.jpg" mimetype="image"></inline-graphic></inline-formula> represents its
precision. In a unweighted approach, <inline-formula><inline-graphic xlink:href="pone.0018541.e026.jpg" mimetype="image"></inline-graphic></inline-formula> is set to 1 for
all the classifiers.</p><p>Finally, the CF and GA methods have been coupled. For each conformation evaluated
with at least one positive vote (<inline-formula><inline-graphic xlink:href="pone.0018541.e027.jpg" mimetype="image"></inline-graphic></inline-formula>), the score
<inline-formula><inline-graphic xlink:href="pone.0018541.e028.jpg" mimetype="image"></inline-graphic></inline-formula> of a given conformation <inline-formula><inline-graphic xlink:href="pone.0018541.e029.jpg" mimetype="image"></inline-graphic></inline-formula> is the product of
the rank obtained by <inline-formula><inline-graphic xlink:href="pone.0018541.e030.jpg" mimetype="image"></inline-graphic></inline-formula> in the GA, and
<inline-formula><inline-graphic xlink:href="pone.0018541.e031.jpg" mimetype="image"></inline-graphic></inline-formula>. For conformations receiving only negative votes, the
score <inline-formula><inline-graphic xlink:href="pone.0018541.e032.jpg" mimetype="image"></inline-graphic></inline-formula> is set to be maximal. The evaluated conformations are
then re-ranked according to this score (in decreasing order). It should be noted
that scores (and consequently ranks) obtained through this method are not
necessarily unique. To measure the number of possible ranks for each method,
taking into account the number of examples to classify, we will use the
granularity as defined in equation 4.<disp-formula><graphic xlink:href="pone.0018541.e033"></graphic><label>(4)</label></disp-formula></p><p>Where <inline-formula><inline-graphic xlink:href="pone.0018541.e034.jpg" mimetype="image"></inline-graphic></inline-formula> is a set of evaluated conformations.</p></sec><sec id="s2f"><title>Evaluation of learning accuracy</title><p>The most commonly used criterion for evaluating the efficiency of a learning
procedure is the Area Under the ROC curve (ROC AUC). The ROC curve is obtained
by plotting the proportion of true positives against the proportion of false
positives. A perfect learning should give an AUC of 1 (all the true positives
are found before any of the negatives), whereas a random function has an AUC of
0.5 (each prediction has probabilities of 0.5 to be correct or incorrect).</p><p>To measure the performances of the different scoring functions we use precision,
recall and accuracy using <inline-formula><inline-graphic xlink:href="pone.0018541.e035.jpg" mimetype="image"></inline-graphic></inline-formula> and
<inline-formula><inline-graphic xlink:href="pone.0018541.e036.jpg" mimetype="image"></inline-graphic></inline-formula> as in the confusion matrix (see <xref ref-type="table" rid="pone-0018541-t001">Table 1</xref>). We will also use false negative
rate (FNR) and true negative rate (TNR).</p><table-wrap id="pone-0018541-t001" position="float"><object-id pub-id-type="doi">10.1371/journal.pone.0018541.t001</object-id><label>Table 1</label><caption><title>Confusion matrix.</title></caption><alternatives><graphic id="pone-0018541-t001-1" xlink:href="pone.0018541.t001"></graphic><table frame="hsides" rules="groups"><colgroup span="1"><col align="left" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col></colgroup><thead><tr><td colspan="2" align="left" rowspan="1"></td><td colspan="2" align="left" rowspan="1">solution</td></tr><tr><td colspan="2" align="left" rowspan="1"></td><td align="left" rowspan="1" colspan="1">+</td><td align="left" rowspan="1" colspan="1">-</td></tr></thead><tbody><tr><td align="left" rowspan="1" colspan="1">prediction</td><td align="left" rowspan="1" colspan="1">+</td><td align="left" rowspan="1" colspan="1">TP</td><td align="left" rowspan="1" colspan="1">FP</td></tr><tr><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">FN</td><td align="left" rowspan="1" colspan="1">TN</td></tr></tbody></table></alternatives><table-wrap-foot><fn id="nt101"><label></label><p>TP: true positives, FP: false positives, FN: false negatives, TN:
true negatives.</p></fn></table-wrap-foot></table-wrap><p>These values can be computed as:<disp-formula><graphic xlink:href="pone.0018541.e037"></graphic></disp-formula><disp-formula><graphic xlink:href="pone.0018541.e038"></graphic></disp-formula></p></sec><sec id="s2g"><title>CAPRI Experiments</title><p>To evaluate the accuracy of our CF-GA scoring procedure, we developed two
protocols based on targets 22 to 40 of the CAPRI (Critical Assessment of
PRedicted Interaction) experiment. CAPRI is a blind prediction experiment
designed to test docking and scoring procedures <xref ref-type="bibr" rid="pone.0018541-Janin1">[20]</xref>, <xref ref-type="bibr" rid="pone.0018541-Lensink1">[21]</xref>. In the scoring
experiment, a large set of models submitted by the docking predictors is made
available to the community to test scoring functions independently of
conformation generation algorithms.</p><p>Four targets where eliminated for different reasons:</p><list list-type="bullet"><list-item><p> The structure of target 31 has not yet been released, making it impossible
to evaluate the obtained results.</p></list-item><list-item><p> The native 3D structure of target 30 is still a vexed question <xref ref-type="bibr" rid="pone.0018541-Tong1">[22]</xref>.</p></list-item><list-item><p> Targets 33 and 34 are protein-RNA complexes and our scoring method is not
adapted to this problem yet.</p></list-item></list><p>For each target, the scoring ensemble was evaluated using GA, CF and CF-GA
methods.</p><p>For reasons exposed in “<xref ref-type="sec" rid="s3">Results and
Discussion</xref>”, candidate conformations where evaluated according
to two different sets of criteria.</p><p>In the <inline-formula><inline-graphic xlink:href="pone.0018541.e039.jpg" mimetype="image"></inline-graphic></inline-formula> evaluation, we use only the
<inline-formula><inline-graphic xlink:href="pone.0018541.e040.jpg" mimetype="image"></inline-graphic></inline-formula> criterion, which is the fraction of native contacts (the
fraction of contacts between the two partners in the evaluated conformation that
do exist in the native structure). Four quality classes can be defined:</p><list list-type="bullet"><list-item><p> High (<italic>fnat</italic> ≥0.5),</p></list-item><list-item><p> Medium (0.3≤ <italic>fnat</italic> <0.5),</p></list-item><list-item><p> Acceptable (0.1≤ <italic>fnat</italic> <0.3),</p></list-item><list-item><p> Incorrect (<italic>fnat</italic><0.1)</p></list-item></list><p>CAPRI evaluation <xref ref-type="bibr" rid="pone.0018541-Lensink1">[21]</xref>, <xref ref-type="bibr" rid="pone.0018541-Mendez1">[23]</xref> also uses two other criteria: the
<inline-formula><inline-graphic xlink:href="pone.0018541.e041.jpg" mimetype="image"></inline-graphic></inline-formula> (<italic>RMSD</italic> between prediction and native
structure computed only on interface atoms) and <inline-formula><inline-graphic xlink:href="pone.0018541.e042.jpg" mimetype="image"></inline-graphic></inline-formula>(<italic>RMSD</italic> computed on all the atoms of the smallest protein,
the largest protein of prediction and native structure being superimposed).
Again four quality classes are defined:</p><list list-type="bullet"><list-item><p> High: (<italic>fnat</italic> ≥0.5) and
(<italic>I<sub>RMSD</sub></italic> ≤1 or
<italic>L<sub>RMSD</sub></italic> ≤1)</p></list-item><list-item><p> Medium: [(0.3≤ <italic>fnat</italic> <0.5) and
(<italic>I<sub>RMSD</sub></italic> ≤2.0 or
<italic>L<sub>RMSD</sub></italic> ≤5.0)]<bold>or</bold>[(<italic>fnat</italic> >0.5 and
<italic>I<sub>RMSD</sub></italic>>1.0 or
<italic>I<sub>RMSD</sub></italic>>1.0)]</p></list-item><list-item><p> Acceptable: [(0.1≤ <italic>fnat</italic> <0.3) and
(<italic>I<sub>RMSD</sub></italic> ≤4.0 or
<italic>L<sub>RMSD</sub></italic> ≤10.0)]
<bold>or</bold> [<italic>fnat</italic> >0.3 and
(<italic>L<sub>RMSD</sub></italic> >5.0 or
<italic>I<sub>RMSD</sub></italic> >2.0)]</p></list-item><list-item><p> Incorrect.</p></list-item></list></sec></sec><sec id="s3"><title>Results and Discussion</title><p>In our previous work, we have used different flavors of genetic algorithm (GA)
optimization to obtain scoring functions for protein-protein docking. Since we have
reached the limits of the precision that can be obtained with GA alone, we combined
the GA-based scoring function with scoring functions built using four other learning
algorithms:</p><list list-type="bullet"><list-item><p> Logistic regression (LR) <xref ref-type="bibr" rid="pone.0018541-leCessie1">[24]</xref>;</p></list-item><list-item><p> Support Vector Machines <xref ref-type="bibr" rid="pone.0018541-Schlkopf1">[25]</xref>, using either radial-based function (RBF), linear
kernel (LK), polynomial kernel (PK) or 2 and 4 quadratic kernels (QK2 and
QK4);</p></list-item><list-item><p> Decision trees, using the C4.5 learner <xref ref-type="bibr" rid="pone.0018541-Quinlan1">[26]</xref> and, J48, its
implementation in Weka <xref ref-type="bibr" rid="pone.0018541-Hall1">[18]</xref>, using 2, 5 and 10 as minimum numbers of examples
required to build a leaf (classifiers J48-M2, J48-M5 and J48-M10
respectively);</p></list-item><list-item><p> Two-rules learners, using two different implementations (JRIP <xref ref-type="bibr" rid="pone.0018541-Cohen1">[27]</xref> and PART
<xref ref-type="bibr" rid="pone.0018541-EibeFrank1">[28]</xref>), using again 2, 5 and 10 as minimum numbers of
examples required to build a rule (classifiers JRIP-M2, JRIP-M5, JRIP-M10,
PART-M2, PART-M5 and PART-M10).</p></list-item></list><p>Here we show how these 15 classifiers can be combined, in a collaborative scheme and
with the genetic algorithm procedure.</p><sec id="s3a"><title>Predictions obtained with the genetic algorithm procedure</title><p>The sensitivity (ability to discriminate true positives from false positives,
also called recall) of the genetic algorithm (GA) has been evaluated using the
ROC criterion. Since GA is a heuristic, optimization must be repeated. The
number of repetitions necessary for obtaining a reliable result largely depends
on the specificity of the problem. To determine the number of repetitions needed
in our case, we have plotted the area under the ROC curve (AUC) as a function of
the number of runs. For each value of the number of runs <italic>n</italic>, the
experiment has been repeated 50 times in 10-fold cross-validation. This allows
to compute, for each <italic>n</italic>, the mean value and the variance of the
AUC. As can be seen on <xref ref-type="fig" rid="pone-0018541-g002">Figure
2</xref>, the AUC reaches a plateau (0.866, the difference with AUC with 1
repetition is significant) when the number of runs is higher than 30, and the
variance is then less than 10<sup>−9</sup>.</p><fig id="pone-0018541-g002" position="float"><object-id pub-id-type="doi">10.1371/journal.pone.0018541.g002</object-id><label>Figure 2</label><caption><title>Genetic Algorithm performance as a function of the number of
runs.</title><p>For each number of runs <inline-formula><inline-graphic xlink:href="pone.0018541.e043.jpg" mimetype="image"></inline-graphic></inline-formula>, the
measure of the AUC has been repeated 50 times using a 10-fold
cross-validation protocol. Average, minimum and maximum values are
plotted.</p></caption><graphic xlink:href="pone.0018541.g002"></graphic></fig><p>Based on this result, GA runs will be repeated 30 times in the following.</p></sec><sec id="s3b"><title>Classifiers</title><p>The precision, recall and accuracy have been computed for each of the chosen
classifiers. Three of them (LK, PK and QK4) have precision lower than 0.5,
meaning that their predictions are even worse than random. Consequently these
three classifiers were discarded. The values obtained for the remaining 12
classifiers are given in <xref ref-type="table" rid="pone-0018541-t002">Table
2</xref>. The results obtained show that the different classifiers have very
good accuracies. This result is largely due to the fact that the number of
positive examples is about ten times lower than the number of negative examples.
Consequently, a classifier which predicts all candidates as negative would have
an accuracy of 0.9, but a precision of 0 and a recall of 0 for the positive
examples. SVM-RBF has a precision of 1, showing that this classifier does not
give any false positives, however, the recall is only 0.606, which means that it
misses 40% of the positives. Apart from SVM-RBF, all classifiers have
relatively low precision and recall.</p><table-wrap id="pone-0018541-t002" position="float"><object-id pub-id-type="doi">10.1371/journal.pone.0018541.t002</object-id><label>Table 2</label><caption><title>Precision, recall and accuracy of the retained classifiers.</title></caption><alternatives><graphic id="pone-0018541-t002-2" xlink:href="pone.0018541.t002"></graphic><table frame="hsides" rules="groups"><colgroup span="1"><col align="left" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col></colgroup><thead><tr><td align="left" rowspan="1" colspan="1">Classifier</td><td align="left" rowspan="1" colspan="1">Precision</td><td align="left" rowspan="1" colspan="1">Recall</td><td align="left" rowspan="1" colspan="1">Accuracy</td></tr></thead><tbody><tr><td align="left" rowspan="1" colspan="1">SVM-RBF</td><td align="left" rowspan="1" colspan="1">1.000</td><td align="left" rowspan="1" colspan="1">0.606</td><td align="left" rowspan="1" colspan="1">0.975</td></tr><tr><td align="left" rowspan="1" colspan="1">PART-M2</td><td align="left" rowspan="1" colspan="1">0.777</td><td align="left" rowspan="1" colspan="1">0.737</td><td align="left" rowspan="1" colspan="1">0.970</td></tr><tr><td align="left" rowspan="1" colspan="1">J48-M2</td><td align="left" rowspan="1" colspan="1">0.704</td><td align="left" rowspan="1" colspan="1">0.697</td><td align="left" rowspan="1" colspan="1">0.963</td></tr><tr><td align="left" rowspan="1" colspan="1">JRIP-N10</td><td align="left" rowspan="1" colspan="1">0.665</td><td align="left" rowspan="1" colspan="1">0.520</td><td align="left" rowspan="1" colspan="1">0.954</td></tr><tr><td align="left" rowspan="1" colspan="1">JRIP-N2</td><td align="left" rowspan="1" colspan="1">0.65</td><td align="left" rowspan="1" colspan="1">0.591</td><td align="left" rowspan="1" colspan="1">0.955</td></tr><tr><td align="left" rowspan="1" colspan="1">PART-M10</td><td align="left" rowspan="1" colspan="1">0.645</td><td align="left" rowspan="1" colspan="1">0.561</td><td align="left" rowspan="1" colspan="1">0.953</td></tr><tr><td align="left" rowspan="1" colspan="1">PART-M5</td><td align="left" rowspan="1" colspan="1">0.642</td><td align="left" rowspan="1" colspan="1">0.626</td><td align="left" rowspan="1" colspan="1">0.955</td></tr><tr><td align="left" rowspan="1" colspan="1">SVM-Q2</td><td align="left" rowspan="1" colspan="1">0.64</td><td align="left" rowspan="1" colspan="1">0.727</td><td align="left" rowspan="1" colspan="1">0.958</td></tr><tr><td align="left" rowspan="1" colspan="1">J48-M5</td><td align="left" rowspan="1" colspan="1">0.630</td><td align="left" rowspan="1" colspan="1">0.586</td><td align="left" rowspan="1" colspan="1">0.953</td></tr><tr><td align="left" rowspan="1" colspan="1">JRIP-N5</td><td align="left" rowspan="1" colspan="1">0.615</td><td align="left" rowspan="1" colspan="1">0.566</td><td align="left" rowspan="1" colspan="1">0.951</td></tr><tr><td align="left" rowspan="1" colspan="1">Logistic</td><td align="left" rowspan="1" colspan="1">0.607</td><td align="left" rowspan="1" colspan="1">0.414</td><td align="left" rowspan="1" colspan="1">0.947</td></tr><tr><td align="left" rowspan="1" colspan="1">J48-M10</td><td align="left" rowspan="1" colspan="1">0.564</td><td align="left" rowspan="1" colspan="1">0.465</td><td align="left" rowspan="1" colspan="1">0.944</td></tr></tbody></table></alternatives><table-wrap-foot><fn id="nt102"><label></label><p>Classifiers have been trained on the same learning set as the genetic
algorithm, in 10-fold cross-validation.</p></fn></table-wrap-foot></table-wrap><p>The different classifiers have first been combined using an uniform collaborative
filtering scheme. In this configuration, each classifier votes for each
conformation. Its vote can be <italic>positive</italic> or
<italic>negative</italic>. Consequently, a given conformation can receive
from 12 to 0 positive votes. Thus, 13 different groups are created, which can be
ordered by decreasing numbers of positive votes. When applied to the learning
set in 10-fold cross-validation, the three best categories (13, 12, and 11
positive votes) contain only native conformations (<xref ref-type="fig" rid="pone-0018541-g003">Figure 3</xref>). This means that the 73 best ranked
conformations are true positives.</p><fig id="pone-0018541-g003" position="float"><object-id pub-id-type="doi">10.1371/journal.pone.0018541.g003</object-id><label>Figure 3</label><caption><title>True positive rate for uniform and weighted collaborative
filtering.</title><p>The true positive rate (green) and the total number of positives are
plotted for uniform (left) and weighted (right) collaborative filtering,
as a function of the category. The vertical and horizontal dotted lines
give the category, and the corresponding number of conformations
predicted as positives, above which the true positive rate decreases
under 1.</p></caption><graphic xlink:href="pone.0018541.g003"></graphic></fig><p>However, when considering thousands of conformations, 13 categories are not
sufficient for efficiently ranking, since many non-equivalent conformations have
the same rank (granularity 0.05). To address this problem, we have used an
averaged voting protocol (weighted collaborative filtering). Each classifier
still votes “positive” or “negative” for each
conformation, but the vote is weighted by the precision of the classifier. Since
the 12 precisions are all different, the votes of the different classifiers are
not equivalent anymore, which results in
2<sup>12</sup> = 4096 different categories. Consequently,
conformations can be classified in 4096 categories, which can be ranked as a
function of their positive score (<inline-formula><inline-graphic xlink:href="pone.0018541.e044.jpg" mimetype="image"></inline-graphic></inline-formula>, see <xref ref-type="sec" rid="s2">Methods</xref>). Again, the best categories contain
only true positives (see <xref ref-type="fig" rid="pone-0018541-g003">Figure
3</xref>). The results are even better than those obtained with uniform CF,
since the first non-native conformation belongs to category 31, which means that
the 91 best ranked conformations are natives.</p><p>However, when considering millions of conformations, 4096 categories are still
not sufficient (granularity 0.15). For example, when using the weighted-CF
method on the learning set, the best category (only positive votes) contains 24
conformations. Consequently, this method cannot be used for ranking large data
sets.</p></sec><sec id="s3c"><title>Combination of collaborative filtering and genetic algorithm</title><p>Since CF efficiently eliminates non-native conformations, we have used CF to
weight the GA score (see <xref ref-type="sec" rid="s2">Methods</xref>). This is
what we call the collaborative filtering - genetic algorithm (CF-GA) method. The
averaged voting configuration was used, and the CF-GA score is obtained by
multiplying the GA score by the ratio of the exponential of positive and
negative CF scores. Consequently, the score of conformations classified as
negatives by a majority of classifiers have very low CF-GA scores. <xref ref-type="fig" rid="pone-0018541-g004">Figure 4</xref> shows the evolutions
of AUC, true negative rate (TNR) and false negative rate (FNR) as we add more
classifiers in the CF (in increasing precision order).</p><fig id="pone-0018541-g004" position="float"><object-id pub-id-type="doi">10.1371/journal.pone.0018541.g004</object-id><label>Figure 4</label><caption><title>Evolution of AUC, true negative rate (TNR) and false negative rate
(FNR) in CF-GA using increasing number of classifiers.</title><p>Classifiers were added to the collaborative filter, using averaged
voting, in increasing precision order. For example, abscissa
“JRIP-N5” corresponds to the CF-GA method using J48-M10,
Logistic and JRIP-N5 classifiers. Green and red curves correspond to AUC
of GA method (which is constant since it doesn't use the
classifiers, shown for comparison) and CF-GA method respectively. TNR:
true negative rate; FNR: false negative rate.</p></caption><graphic xlink:href="pone.0018541.g004"></graphic></fig><p>Another way of combining the two methods is to: first classify the candidate
conformations using the CF, retain only the candidates of the best classes, then
use the GA to rank them. To evaluate this approach, we retained all the
candidate conformations which rank was lower than
<inline-formula><inline-graphic xlink:href="pone.0018541.e045.jpg" mimetype="image"></inline-graphic></inline-formula> (<inline-formula><inline-graphic xlink:href="pone.0018541.e046.jpg" mimetype="image"></inline-graphic></inline-formula> have been tested).
These were then ranked using GA. The best results have been obtained with
<inline-formula><inline-graphic xlink:href="pone.0018541.e047.jpg" mimetype="image"></inline-graphic></inline-formula>, but this method proved less efficient than the CF-GA
(see <italic>CF then GA</italic> in <xref ref-type="table" rid="pone-0018541-t003">Table 3</xref>).</p><table-wrap id="pone-0018541-t003" position="float"><object-id pub-id-type="doi">10.1371/journal.pone.0018541.t003</object-id><label>Table 3</label><caption><title>Evaluation of the CF-GA method.</title></caption><alternatives><graphic id="pone-0018541-t003-3" xlink:href="pone.0018541.t003"></graphic><table frame="hsides" rules="groups"><colgroup span="1"><col align="left" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col></colgroup><thead><tr><td colspan="2" align="left" rowspan="1">Target</td><td colspan="12" align="left" rowspan="1">With RMSD filtering</td><td colspan="8" align="left" rowspan="1">No RMSD filtering</td></tr><tr><td colspan="2" align="left" rowspan="1"></td><td colspan="4" align="left" rowspan="1">GA</td><td colspan="3" align="left" rowspan="1">CF</td><td colspan="5" align="left" rowspan="1">CF-GA</td><td colspan="5" align="left" rowspan="1">CF – GA</td><td colspan="3" align="left" rowspan="1">CF then GA</td></tr><tr><td colspan="2" align="left" rowspan="1"></td><td colspan="2" align="left" rowspan="1">best</td><td align="left" rowspan="1" colspan="1">N</td><td align="left" rowspan="1" colspan="1">R</td><td align="left" rowspan="1" colspan="1">best</td><td align="left" rowspan="1" colspan="1">N</td><td align="left" rowspan="1" colspan="1">R</td><td colspan="2" align="left" rowspan="1">best</td><td colspan="2" align="left" rowspan="1">N</td><td align="left" rowspan="1" colspan="1">R</td><td colspan="2" align="left" rowspan="1">best</td><td colspan="2" align="left" rowspan="1">N</td><td align="left" rowspan="1" colspan="1">R</td><td align="left" rowspan="1" colspan="1">best</td><td align="left" rowspan="1" colspan="1">N</td><td align="left" rowspan="1" colspan="1">R</td></tr></thead><tbody><tr><td colspan="22" align="left" rowspan="1"><italic>fnat</italic> criterion
only</td></tr><tr><td colspan="2" align="left" rowspan="1">T22</td><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e048.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">3</td><td align="left" rowspan="1" colspan="1">4</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e049.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">2</td><td align="left" rowspan="1" colspan="1">3</td><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e050.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1">2</td><td align="left" rowspan="1" colspan="1">4</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e051.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1">2</td><td colspan="2" align="left" rowspan="1">4</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e052.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">2</td><td align="left" rowspan="1" colspan="1">4</td></tr><tr><td colspan="2" align="left" rowspan="1">T23</td><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e053.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">10</td><td align="left" rowspan="1" colspan="1">1</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e054.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">9</td><td align="left" rowspan="1" colspan="1">1</td><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e055.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1">9</td><td align="left" rowspan="1" colspan="1">1</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e056.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1">10</td><td colspan="2" align="left" rowspan="1">1</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e057.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">10</td><td align="left" rowspan="1" colspan="1">1</td></tr><tr><td colspan="2" align="left" rowspan="1">T25</td><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e058.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">1</td><td align="left" rowspan="1" colspan="1">5</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e059.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">2</td><td align="left" rowspan="1" colspan="1">2</td><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e060.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1">2</td><td align="left" rowspan="1" colspan="1">2</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e061.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1">4</td><td colspan="2" align="left" rowspan="1">2</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e062.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">4</td><td align="left" rowspan="1" colspan="1">2</td></tr><tr><td colspan="2" align="left" rowspan="1">T26</td><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e063.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">2</td><td align="left" rowspan="1" colspan="1">6</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e064.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">5</td><td align="left" rowspan="1" colspan="1">1</td><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e065.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1">5</td><td align="left" rowspan="1" colspan="1">1</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e066.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1">6</td><td colspan="2" align="left" rowspan="1">1</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e067.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">7</td><td align="left" rowspan="1" colspan="1">1</td></tr><tr><td colspan="2" align="left" rowspan="1">T27</td><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e068.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">3</td><td align="left" rowspan="1" colspan="1">6</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e069.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">5</td><td align="left" rowspan="1" colspan="1">1</td><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e070.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1">4</td><td align="left" rowspan="1" colspan="1">1</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e071.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1">5</td><td colspan="2" align="left" rowspan="1">1</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e072.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">6</td><td align="left" rowspan="1" colspan="1">1</td></tr><tr><td colspan="2" align="left" rowspan="1">T29</td><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e073.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">2</td><td align="left" rowspan="1" colspan="1">5</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e074.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">4</td><td align="left" rowspan="1" colspan="1">1</td><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e075.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1">2</td><td align="left" rowspan="1" colspan="1">2</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e076.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1">6</td><td colspan="2" align="left" rowspan="1">2</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e077.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">6</td><td align="left" rowspan="1" colspan="1">2</td></tr><tr><td colspan="2" align="left" rowspan="1">T32</td><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e078.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">2</td><td align="left" rowspan="1" colspan="1">3</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e079.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">2</td><td align="left" rowspan="1" colspan="1">3</td><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e080.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1">3</td><td align="left" rowspan="1" colspan="1">10</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e081.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1">2</td><td colspan="2" align="left" rowspan="1">6</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">16</td></tr><tr><td colspan="2" align="left" rowspan="1">T35</td><td colspan="2" align="left" rowspan="1">-</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e082.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">1</td><td align="left" rowspan="1" colspan="1">2</td><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e083.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1">1</td><td align="left" rowspan="1" colspan="1">1</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e084.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1">1</td><td colspan="2" align="left" rowspan="1">1</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">-</td></tr><tr><td colspan="2" align="left" rowspan="1">T37</td><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e085.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">1</td><td align="left" rowspan="1" colspan="1">1</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e086.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">1</td><td align="left" rowspan="1" colspan="1">5</td><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e087.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1">1</td><td align="left" rowspan="1" colspan="1">3</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e088.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1">1</td><td colspan="2" align="left" rowspan="1">3</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">16</td></tr><tr><td colspan="2" align="left" rowspan="1">T39</td><td colspan="2" align="left" rowspan="1">-</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">107</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">48</td><td colspan="2" align="left" rowspan="1">-</td><td colspan="2" align="left" rowspan="1">0</td><td align="left" rowspan="1" colspan="1">99</td><td align="left" rowspan="1" colspan="1">-</td><td colspan="2" align="left" rowspan="1">0</td><td colspan="2" align="left" rowspan="1">205</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">-</td></tr><tr><td colspan="2" align="left" rowspan="1">T40A</td><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e089.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">2</td><td align="left" rowspan="1" colspan="1">2</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e090.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">2</td><td align="left" rowspan="1" colspan="1">1</td><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e091.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1">3</td><td align="left" rowspan="1" colspan="1">1</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e092.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1">4</td><td colspan="2" align="left" rowspan="1">1</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e093.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">5</td><td align="left" rowspan="1" colspan="1">1</td></tr><tr><td colspan="2" align="left" rowspan="1">T40B</td><td colspan="2" align="left" rowspan="1">-</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">13</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">13</td><td colspan="2" align="left" rowspan="1">-</td><td colspan="2" align="left" rowspan="1">0</td><td align="left" rowspan="1" colspan="1">16</td><td align="left" rowspan="1" colspan="1">-</td><td colspan="2" align="left" rowspan="1">0</td><td colspan="2" align="left" rowspan="1">48</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">40</td></tr><tr><td colspan="22" align="left" rowspan="1">All <italic>CAPRI</italic>criteria</td></tr><tr><td align="left" rowspan="1" colspan="1">T25</td><td colspan="2" align="left" rowspan="1">-</td><td colspan="2" align="left" rowspan="1">0</td><td align="left" rowspan="1" colspan="1">13</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e094.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">1</td><td colspan="2" align="left" rowspan="1">5</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e095.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">1</td><td colspan="2" align="left" rowspan="1">5</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e096.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1">2</td><td colspan="2" align="left" rowspan="1">6</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e097.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">2</td><td align="left" rowspan="1" colspan="1">6</td></tr><tr><td align="left" rowspan="1" colspan="1">T29</td><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e098.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1">1</td><td align="left" rowspan="1" colspan="1">8</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e099.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">2</td><td colspan="2" align="left" rowspan="1">1</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e100.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">2</td><td colspan="2" align="left" rowspan="1">2</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e101.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1">6</td><td colspan="2" align="left" rowspan="1">2</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e102.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">6</td><td align="left" rowspan="1" colspan="1">1</td></tr><tr><td align="left" rowspan="1" colspan="1">T32</td><td colspan="2" align="left" rowspan="1">-</td><td colspan="2" align="left" rowspan="1">0</td><td align="left" rowspan="1" colspan="1">36</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e103.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">1</td><td colspan="2" align="left" rowspan="1">3</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e104.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">1</td><td colspan="2" align="left" rowspan="1">10</td><td align="left" rowspan="1" colspan="1">-</td><td colspan="2" align="left" rowspan="1">0</td><td colspan="2" align="left" rowspan="1">18</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">16</td></tr><tr><td align="left" rowspan="1" colspan="1">T35</td><td colspan="2" align="left" rowspan="1">-</td><td colspan="2" align="left" rowspan="1">0</td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">0</td><td colspan="2" align="left" rowspan="1">NA</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">0</td><td colspan="2" align="left" rowspan="1">NA</td><td align="left" rowspan="1" colspan="1">-</td><td colspan="2" align="left" rowspan="1">0</td><td colspan="2" align="left" rowspan="1">167</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">-</td></tr><tr><td align="left" rowspan="1" colspan="1">T37</td><td colspan="2" align="left" rowspan="1">-</td><td colspan="2" align="left" rowspan="1">0</td><td align="left" rowspan="1" colspan="1">14</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">0</td><td colspan="2" align="left" rowspan="1">13</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">0</td><td colspan="2" align="left" rowspan="1">17</td><td align="left" rowspan="1" colspan="1">-</td><td colspan="2" align="left" rowspan="1">0</td><td colspan="2" align="left" rowspan="1">18</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">18</td></tr><tr><td align="left" rowspan="1" colspan="1">T39</td><td colspan="2" align="left" rowspan="1">-</td><td colspan="2" align="left" rowspan="1">0</td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">0</td><td colspan="2" align="left" rowspan="1">NA</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">0</td><td colspan="2" align="left" rowspan="1">NA</td><td align="left" rowspan="1" colspan="1">-</td><td colspan="2" align="left" rowspan="1">0</td><td colspan="2" align="left" rowspan="1">652</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">-</td></tr><tr><td align="left" rowspan="1" colspan="1">T40A</td><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e105.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1">1</td><td align="left" rowspan="1" colspan="1">3</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e106.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">1</td><td colspan="2" align="left" rowspan="1">1</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e107.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">1</td><td colspan="2" align="left" rowspan="1">1</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e108.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1">5</td><td colspan="2" align="left" rowspan="1">1</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e109.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">4</td><td align="left" rowspan="1" colspan="1">1</td></tr><tr><td align="left" rowspan="1" colspan="1">T40B</td><td colspan="2" align="left" rowspan="1">-</td><td colspan="2" align="left" rowspan="1">0</td><td align="left" rowspan="1" colspan="1">28</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">0</td><td colspan="2" align="left" rowspan="1">13</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">0</td><td colspan="2" align="left" rowspan="1">16</td><td align="left" rowspan="1" colspan="1">-</td><td colspan="2" align="left" rowspan="1">0</td><td colspan="2" align="left" rowspan="1">48</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">33</td></tr></tbody></table></alternatives><table-wrap-foot><fn id="nt103"><label></label><p>Best quality conformation found in the top 10 ranked solutions from
target 22 to target 40 for genetic algorithm (GA), collaborative
filtering (CF) and combination of the previous two (CF-GA) methods,
with RMSD filtering. Same results are given for the CF-GA method
without RMSD filtering, and for the <italic>CF then GA</italic>method. N: Numbers of acceptable or better solutions in the top 10;
R: rank of the first acceptable or better solution for each target.
Numbers of high quality (<inline-formula><inline-graphic xlink:href="pone.0018541.e110.jpg" mimetype="image"></inline-graphic></inline-formula>),
medium quality (<inline-formula><inline-graphic xlink:href="pone.0018541.e111.jpg" mimetype="image"></inline-graphic></inline-formula>),
acceptable (<inline-formula><inline-graphic xlink:href="pone.0018541.e112.jpg" mimetype="image"></inline-graphic></inline-formula>) and
incorrect conformations in each ensemble and for each method when
using RMSD filtering are given in <xref ref-type="table" rid="pone-0018541-t004">Table 4</xref>.</p></fn></table-wrap-foot></table-wrap><table-wrap id="pone-0018541-t004" position="float"><object-id pub-id-type="doi">10.1371/journal.pone.0018541.t004</object-id><label>Table 4</label><caption><title>Total number of conformations is each category before and after RMSD
filtering, using <inline-formula><inline-graphic xlink:href="pone.0018541.e113.jpg" mimetype="image"></inline-graphic></inline-formula>criterion.</title></caption><alternatives><graphic id="pone-0018541-t004-4" xlink:href="pone.0018541.t004"></graphic><table frame="hsides" rules="groups"><colgroup span="1"><col align="left" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col></colgroup><thead><tr><td align="left" rowspan="1" colspan="1"></td><td colspan="6" align="left" rowspan="1">GA</td><td colspan="4" align="left" rowspan="1">CF</td><td colspan="5" align="left" rowspan="1">CF-GA</td><td colspan="5" align="left" rowspan="1">Without RMSD filtering</td></tr><tr><td align="left" rowspan="1" colspan="1">Target</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e114.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e115.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e116.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">I</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e117.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e118.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e119.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">I</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e120.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e121.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e122.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1">I</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e123.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e124.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e125.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">I</td></tr></thead><tbody><tr><td colspan="21" align="left" rowspan="1"><italic>fnat</italic> criterion
only</td></tr><tr><td align="left" rowspan="1" colspan="1">T22</td><td align="left" rowspan="1" colspan="1">12</td><td colspan="2" align="left" rowspan="1">14</td><td colspan="2" align="left" rowspan="1">6</td><td align="left" rowspan="1" colspan="1">40</td><td align="left" rowspan="1" colspan="1">12</td><td align="left" rowspan="1" colspan="1">13</td><td align="left" rowspan="1" colspan="1">7</td><td align="left" rowspan="1" colspan="1">40</td><td align="left" rowspan="1" colspan="1">12</td><td align="left" rowspan="1" colspan="1">13</td><td colspan="2" align="left" rowspan="1">8</td><td align="left" rowspan="1" colspan="1">36</td><td align="left" rowspan="1" colspan="1">32</td><td colspan="2" align="left" rowspan="1">29</td><td align="left" rowspan="1" colspan="1">98</td><td align="left" rowspan="1" colspan="1">113</td></tr><tr><td align="left" rowspan="1" colspan="1">T23</td><td align="left" rowspan="1" colspan="1">4</td><td colspan="2" align="left" rowspan="1">10</td><td colspan="2" align="left" rowspan="1">23</td><td align="left" rowspan="1" colspan="1">12</td><td align="left" rowspan="1" colspan="1">4</td><td align="left" rowspan="1" colspan="1">10</td><td align="left" rowspan="1" colspan="1">23</td><td align="left" rowspan="1" colspan="1">12</td><td align="left" rowspan="1" colspan="1">2</td><td align="left" rowspan="1" colspan="1">10</td><td colspan="2" align="left" rowspan="1">24</td><td align="left" rowspan="1" colspan="1">13</td><td align="left" rowspan="1" colspan="1">24</td><td colspan="2" align="left" rowspan="1">36</td><td align="left" rowspan="1" colspan="1">189</td><td align="left" rowspan="1" colspan="1">37</td></tr><tr><td align="left" rowspan="1" colspan="1">T25</td><td align="left" rowspan="1" colspan="1">1</td><td colspan="2" align="left" rowspan="1">0</td><td colspan="2" align="left" rowspan="1">2</td><td align="left" rowspan="1" colspan="1">42</td><td align="left" rowspan="1" colspan="1">1</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">2</td><td align="left" rowspan="1" colspan="1">38</td><td align="left" rowspan="1" colspan="1">1</td><td align="left" rowspan="1" colspan="1">0</td><td colspan="2" align="left" rowspan="1">2</td><td align="left" rowspan="1" colspan="1">2</td><td align="left" rowspan="1" colspan="1">13</td><td colspan="2" align="left" rowspan="1">2</td><td align="left" rowspan="1" colspan="1">13</td><td align="left" rowspan="1" colspan="1">88</td></tr><tr><td align="left" rowspan="1" colspan="1">T26</td><td align="left" rowspan="1" colspan="1">12</td><td colspan="2" align="left" rowspan="1">4</td><td colspan="2" align="left" rowspan="1">21</td><td align="left" rowspan="1" colspan="1">165</td><td align="left" rowspan="1" colspan="1">10</td><td align="left" rowspan="1" colspan="1">8</td><td align="left" rowspan="1" colspan="1">21</td><td align="left" rowspan="1" colspan="1">166</td><td align="left" rowspan="1" colspan="1">9</td><td align="left" rowspan="1" colspan="1">7</td><td colspan="2" align="left" rowspan="1">20</td><td align="left" rowspan="1" colspan="1">167</td><td align="left" rowspan="1" colspan="1">537</td><td colspan="2" align="left" rowspan="1">33</td><td align="left" rowspan="1" colspan="1">106</td><td align="left" rowspan="1" colspan="1">641</td></tr><tr><td align="left" rowspan="1" colspan="1">T27</td><td align="left" rowspan="1" colspan="1">29</td><td colspan="2" align="left" rowspan="1">39</td><td colspan="2" align="left" rowspan="1">39</td><td align="left" rowspan="1" colspan="1">186</td><td align="left" rowspan="1" colspan="1">34</td><td align="left" rowspan="1" colspan="1">36</td><td align="left" rowspan="1" colspan="1">40</td><td align="left" rowspan="1" colspan="1">183</td><td align="left" rowspan="1" colspan="1">32</td><td align="left" rowspan="1" colspan="1">37</td><td colspan="2" align="left" rowspan="1">40</td><td align="left" rowspan="1" colspan="1">192</td><td align="left" rowspan="1" colspan="1">399</td><td colspan="2" align="left" rowspan="1">131</td><td align="left" rowspan="1" colspan="1">106</td><td align="left" rowspan="1" colspan="1">654</td></tr><tr><td align="left" rowspan="1" colspan="1">T29</td><td align="left" rowspan="1" colspan="1">0</td><td colspan="2" align="left" rowspan="1">3</td><td colspan="2" align="left" rowspan="1">0</td><td align="left" rowspan="1" colspan="1">67</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">2</td><td align="left" rowspan="1" colspan="1">12</td><td align="left" rowspan="1" colspan="1">60</td><td align="left" rowspan="1" colspan="1">1</td><td align="left" rowspan="1" colspan="1">1</td><td colspan="2" align="left" rowspan="1">16</td><td align="left" rowspan="1" colspan="1">58</td><td align="left" rowspan="1" colspan="1">62</td><td colspan="2" align="left" rowspan="1">78</td><td align="left" rowspan="1" colspan="1">59</td><td align="left" rowspan="1" colspan="1">163</td></tr><tr><td align="left" rowspan="1" colspan="1">T32</td><td align="left" rowspan="1" colspan="1">1</td><td colspan="2" align="left" rowspan="1">0</td><td colspan="2" align="left" rowspan="1">8</td><td align="left" rowspan="1" colspan="1">171</td><td align="left" rowspan="1" colspan="1">1</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">7</td><td align="left" rowspan="1" colspan="1">172</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">1</td><td colspan="2" align="left" rowspan="1">9</td><td align="left" rowspan="1" colspan="1">172</td><td align="left" rowspan="1" colspan="1">1</td><td colspan="2" align="left" rowspan="1">11</td><td align="left" rowspan="1" colspan="1">184</td><td align="left" rowspan="1" colspan="1">376</td></tr><tr><td align="left" rowspan="1" colspan="1">T35</td><td align="left" rowspan="1" colspan="1">0</td><td colspan="2" align="left" rowspan="1">0</td><td colspan="2" align="left" rowspan="1">3</td><td align="left" rowspan="1" colspan="1">168</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">2</td><td align="left" rowspan="1" colspan="1">157</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td colspan="2" align="left" rowspan="1">1</td><td align="left" rowspan="1" colspan="1">159</td><td align="left" rowspan="1" colspan="1">0</td><td colspan="2" align="left" rowspan="1">0</td><td align="left" rowspan="1" colspan="1">8</td><td align="left" rowspan="1" colspan="1">491</td></tr><tr><td align="left" rowspan="1" colspan="1">T37</td><td align="left" rowspan="1" colspan="1">2</td><td colspan="2" align="left" rowspan="1">2</td><td colspan="2" align="left" rowspan="1">23</td><td align="left" rowspan="1" colspan="1">339</td><td align="left" rowspan="1" colspan="1">1</td><td align="left" rowspan="1" colspan="1">3</td><td align="left" rowspan="1" colspan="1">24</td><td align="left" rowspan="1" colspan="1">337</td><td align="left" rowspan="1" colspan="1">4</td><td align="left" rowspan="1" colspan="1">0</td><td colspan="2" align="left" rowspan="1">21</td><td align="left" rowspan="1" colspan="1">347</td><td align="left" rowspan="1" colspan="1">45</td><td colspan="2" align="left" rowspan="1">34</td><td align="left" rowspan="1" colspan="1">119</td><td align="left" rowspan="1" colspan="1">1497</td></tr><tr><td align="left" rowspan="1" colspan="1">T39</td><td align="left" rowspan="1" colspan="1">1</td><td colspan="2" align="left" rowspan="1">1</td><td colspan="2" align="left" rowspan="1">5</td><td align="left" rowspan="1" colspan="1">325</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">1</td><td align="left" rowspan="1" colspan="1">6</td><td align="left" rowspan="1" colspan="1">324</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">1</td><td colspan="2" align="left" rowspan="1">5</td><td align="left" rowspan="1" colspan="1">321</td><td align="left" rowspan="1" colspan="1">4</td><td colspan="2" align="left" rowspan="1">1</td><td align="left" rowspan="1" colspan="1">20</td><td align="left" rowspan="1" colspan="1">1275</td></tr><tr><td align="left" rowspan="1" colspan="1">T40A</td><td align="left" rowspan="1" colspan="1">1</td><td colspan="2" align="left" rowspan="1">0</td><td colspan="2" align="left" rowspan="1">7</td><td align="left" rowspan="1" colspan="1">247</td><td align="left" rowspan="1" colspan="1">1</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">7</td><td align="left" rowspan="1" colspan="1">244</td><td align="left" rowspan="1" colspan="1">1</td><td align="left" rowspan="1" colspan="1">0</td><td colspan="2" align="left" rowspan="1">5</td><td align="left" rowspan="1" colspan="1">248</td><td align="left" rowspan="1" colspan="1">366</td><td colspan="2" align="left" rowspan="1">36</td><td align="left" rowspan="1" colspan="1">119</td><td align="left" rowspan="1" colspan="1">1439</td></tr><tr><td align="left" rowspan="1" colspan="1">T40B</td><td align="left" rowspan="1" colspan="1">2</td><td colspan="2" align="left" rowspan="1">1</td><td colspan="2" align="left" rowspan="1">2</td><td align="left" rowspan="1" colspan="1">249</td><td align="left" rowspan="1" colspan="1">2</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">1</td><td align="left" rowspan="1" colspan="1">249</td><td align="left" rowspan="1" colspan="1">2</td><td align="left" rowspan="1" colspan="1">1</td><td colspan="2" align="left" rowspan="1">0</td><td align="left" rowspan="1" colspan="1">186</td><td align="left" rowspan="1" colspan="1">165</td><td colspan="2" align="left" rowspan="1">22</td><td align="left" rowspan="1" colspan="1">72</td><td align="left" rowspan="1" colspan="1">1701</td></tr><tr><td colspan="21" align="left" rowspan="1">All <italic>CAPRI</italic>criteria</td></tr><tr><td align="left" rowspan="1" colspan="1">T25</td><td colspan="2" align="left" rowspan="1">0</td><td colspan="2" align="left" rowspan="1">0</td><td align="left" rowspan="1" colspan="1">1</td><td align="left" rowspan="1" colspan="1">44</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">1</td><td align="left" rowspan="1" colspan="1">40</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">1</td><td colspan="2" align="left" rowspan="1">0</td><td align="left" rowspan="1" colspan="1">44</td><td align="left" rowspan="1" colspan="1">0</td><td colspan="2" align="left" rowspan="1">6</td><td align="left" rowspan="1" colspan="1">14</td><td align="left" rowspan="1" colspan="1">96</td></tr><tr><td align="left" rowspan="1" colspan="1">T29</td><td colspan="2" align="left" rowspan="1">0</td><td colspan="2" align="left" rowspan="1">0</td><td align="left" rowspan="1" colspan="1">3</td><td align="left" rowspan="1" colspan="1">67</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">2</td><td align="left" rowspan="1" colspan="1">72</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">1</td><td colspan="2" align="left" rowspan="1">2</td><td align="left" rowspan="1" colspan="1">73</td><td align="left" rowspan="1" colspan="1">1</td><td colspan="2" align="left" rowspan="1">76</td><td align="left" rowspan="1" colspan="1">66</td><td align="left" rowspan="1" colspan="1">219</td></tr><tr><td align="left" rowspan="1" colspan="1">T32</td><td colspan="2" align="left" rowspan="1">0</td><td colspan="2" align="left" rowspan="1">1</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">179</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">1</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">180</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td colspan="2" align="left" rowspan="1">1</td><td align="left" rowspan="1" colspan="1">181</td><td align="left" rowspan="1" colspan="1">0</td><td colspan="2" align="left" rowspan="1">3</td><td align="left" rowspan="1" colspan="1">12</td><td align="left" rowspan="1" colspan="1">557</td></tr><tr><td align="left" rowspan="1" colspan="1">T35</td><td colspan="2" align="left" rowspan="1">0</td><td colspan="2" align="left" rowspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">161</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">159</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td colspan="2" align="left" rowspan="1">0</td><td align="left" rowspan="1" colspan="1">160</td><td align="left" rowspan="1" colspan="1">0</td><td colspan="2" align="left" rowspan="1">0</td><td align="left" rowspan="1" colspan="1">3</td><td align="left" rowspan="1" colspan="1">496</td></tr><tr><td align="left" rowspan="1" colspan="1">T37</td><td colspan="2" align="left" rowspan="1">0</td><td colspan="2" align="left" rowspan="1">3</td><td align="left" rowspan="1" colspan="1">3</td><td align="left" rowspan="1" colspan="1">360</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">2</td><td align="left" rowspan="1" colspan="1">3</td><td align="left" rowspan="1" colspan="1">360</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">3</td><td colspan="2" align="left" rowspan="1">2</td><td align="left" rowspan="1" colspan="1">367</td><td align="left" rowspan="1" colspan="1">11</td><td colspan="2" align="left" rowspan="1">46</td><td align="left" rowspan="1" colspan="1">42</td><td align="left" rowspan="1" colspan="1">1596</td></tr><tr><td align="left" rowspan="1" colspan="1">T39</td><td colspan="2" align="left" rowspan="1">0</td><td colspan="2" align="left" rowspan="1">1</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">371</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">331</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td colspan="2" align="left" rowspan="1">0</td><td align="left" rowspan="1" colspan="1">327</td><td align="left" rowspan="1" colspan="1">0</td><td colspan="2" align="left" rowspan="1">3</td><td align="left" rowspan="1" colspan="1">1</td><td align="left" rowspan="1" colspan="1">1296</td></tr><tr><td align="left" rowspan="1" colspan="1">T40A</td><td colspan="2" align="left" rowspan="1">0</td><td colspan="2" align="left" rowspan="1">0</td><td align="left" rowspan="1" colspan="1">2</td><td align="left" rowspan="1" colspan="1">252</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">2</td><td align="left" rowspan="1" colspan="1">250</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">1</td><td colspan="2" align="left" rowspan="1">0</td><td align="left" rowspan="1" colspan="1">253</td><td align="left" rowspan="1" colspan="1">90</td><td colspan="2" align="left" rowspan="1">151</td><td align="left" rowspan="1" colspan="1">150</td><td align="left" rowspan="1" colspan="1">1569</td></tr><tr><td align="left" rowspan="1" colspan="1">T40B</td><td colspan="2" align="left" rowspan="1">2</td><td colspan="2" align="left" rowspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">252</td><td align="left" rowspan="1" colspan="1">2</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">250</td><td align="left" rowspan="1" colspan="1">1</td><td align="left" rowspan="1" colspan="1">1</td><td colspan="2" align="left" rowspan="1">0</td><td align="left" rowspan="1" colspan="1">187</td><td align="left" rowspan="1" colspan="1">102</td><td colspan="2" align="left" rowspan="1">54</td><td align="left" rowspan="1" colspan="1">30</td><td align="left" rowspan="1" colspan="1">1774</td></tr></tbody></table></alternatives><table-wrap-foot><fn id="nt104"><label></label><p>Numbers of high quality (<inline-formula><inline-graphic xlink:href="pone.0018541.e126.jpg" mimetype="image"></inline-graphic></inline-formula>),
medium quality (<inline-formula><inline-graphic xlink:href="pone.0018541.e127.jpg" mimetype="image"></inline-graphic></inline-formula>),
acceptable (<inline-formula><inline-graphic xlink:href="pone.0018541.e128.jpg" mimetype="image"></inline-graphic></inline-formula>) and
incorrect (I) conformations in the CAPRI scoring ensembles for each
target using <inline-formula><inline-graphic xlink:href="pone.0018541.e129.jpg" mimetype="image"></inline-graphic></inline-formula>criterion only or all CAPRI criteria, with and without RMSD
filtering.</p></fn></table-wrap-foot></table-wrap><p>Using the 12 classifiers, the AUC is 0.98, but more importantly, the FNR is only
0.09, meaning that more than 90% of the conformations classified as
natives are indeed natives. Unlike collaborative filtering (CF), the GA method
gives unique ranks for all conformations (granularity 1). Using the CF-GA
method, the global granularity is lower, mostly because conformations classified
as non-natives by a majority of classifiers have very few different, but very
high, ranks. However, the scores obtained by the 100 best ranked conformations
are almost always unique (granularity 0.995), which allows an efficient sorting
of the best conformations.</p><p>Finally, our tests have shown that similar conformations have a tendency to have
very close ranks. To obtain as much diversity as possible in the best ranked
solutions, we removed this redundancy using the RMSD between the conformations.
A conformation is kept only if its RMSD with better ranked conformations is
higher than 5 Å.</p><p>Analysis of the most informative parameters in CF and GA allows to better
understand the complementarity of the two methods. Indeed, whereas in GA the
most informative parameters measure properties of individual residues, CF relies
mostly on parameters relative to contacts at the interface. Interestingly, the
distance between small amino acids (AGSTCP) appears as the most discriminating
parameters in 9 of the 10 analysed filters (the two SVM filters have been
excluded). 5 other distances appear in the 10 most discriminating parameters for
CF: Hydrophobic-Small, Polar-Positive, Hydrophobic-Negative, Negative-Negative
and Polar-Small. The remaining 4 parameters are frequencies of pairs:
Hydrophobic-Negative, Polar-Positive, Hydrophobic-Hydrophobic and
Polar-Negative. Among the 10 most informative parameters in GA, 7 are relative
to individual residues: volumes of R, E, K, P and I; and frequencies of K and 2.
The surface of the interface appears in 4th position, and only 2 parameters are
relative to contacts at the interface: frequency of Hydrophobic-Polar pairs and
distances between Hydrophobic amino acids in contact.</p></sec><sec id="s3d"><title>Ranking of CAPRI ensembles</title><p>The CF-GA ranking was applied to CAPRI targets, which were excluded from the
learning set. Since no acceptable or better solutions was present in the scoring
ensembles for targets 24, 36 and 38, these targets were removed of the
analysis.</p><p>In a first evaluation, we have used only the <inline-formula><inline-graphic xlink:href="pone.0018541.e130.jpg" mimetype="image"></inline-graphic></inline-formula> (fraction of
native contacts, see <xref ref-type="sec" rid="s2">Methods</xref>) as a quality
measure for all structures in the different scoring ensembles. As explained in
the <xref ref-type="sec" rid="s2">Methods</xref> section, CAPRI evaluators do
consider the <inline-formula><inline-graphic xlink:href="pone.0018541.e131.jpg" mimetype="image"></inline-graphic></inline-formula> criterion, but also <inline-formula><inline-graphic xlink:href="pone.0018541.e132.jpg" mimetype="image"></inline-graphic></inline-formula> and
<inline-formula><inline-graphic xlink:href="pone.0018541.e133.jpg" mimetype="image"></inline-graphic></inline-formula> which are different and complementary measures of the
distance between the proposed conformation and the native structure. We were
unable to reproduce faithfully these measures since they require manual
modifications of both the proposed conformation and the native structure (see
<xref ref-type="sec" rid="s2">Methods</xref>). Only for targets T25, T29,
T32, T35, T37, T39 and T40 were these measures available from the CAPRI website.
Consequently, although the <inline-formula><inline-graphic xlink:href="pone.0018541.e134.jpg" mimetype="image"></inline-graphic></inline-formula> indicator is less
stringent than the criteria used by CAPRI evaluators, all targets have been
analysed using solely the <inline-formula><inline-graphic xlink:href="pone.0018541.e135.jpg" mimetype="image"></inline-graphic></inline-formula> criterion. In
parallel, for those targets for which they are available, an evaluation using
all CAPRI criteria has been conducted.</p><p>We first evaluated the ability of our scoring method to find the native structure
within the scoring ensemble. For each target, the native structure was
introduced in the scoring ensemble. We were able to rank the native solution in
the top 10 for 5 out of 12 targets, and in the top 100 for 9 out of 12
targets.</p><p>Our next test was to rank the conformations in the CAPRI ensembles, and count the
number of acceptable or better solutions in the top 10. <xref ref-type="table" rid="pone-0018541-t003">Table 3</xref> shows the results obtained using GA,
CF and CF-GA. Numbers of high quality <inline-formula><inline-graphic xlink:href="pone.0018541.e136.jpg" mimetype="image"></inline-graphic></inline-formula>), medium quality
(<inline-formula><inline-graphic xlink:href="pone.0018541.e137.jpg" mimetype="image"></inline-graphic></inline-formula>), acceptable (<inline-formula><inline-graphic xlink:href="pone.0018541.e138.jpg" mimetype="image"></inline-graphic></inline-formula>) and incorrect
conformations in each ensemble and for each method when using RMSD Filtering are
given in <xref ref-type="table" rid="pone-0018541-t004">Table 4</xref>.</p><p>As can be seen in <xref ref-type="table" rid="pone-0018541-t003">Table 3</xref>,
CF-GA is able to rank at least one acceptable or better solution in the top 10
for 10 out of 12 targets. The rank of the first acceptable or better solution is
even lower than 4 for 9 targets, and medium quality or better for 8 targets (it
should be noted however that for target 35 only acceptable or incorrect
conformations were present in the ensemble). When considering all of the CAPRI
criteria, CF-GA ranks acceptable or better solutions in the top 10 for 4 out of
8 targets. Interestingly, there seems to be no correlation between our ability
to rank the native solution in the top 10 and our ability to ranked an
acceptable or better solution in the top 10. Indeed, for targets T22, T26, T27,
T29 and T40_A, the native structure is not ranked in the top 10 (even not in the
top 100 for T27 and T29), but acceptable or better conformations are found.</p><p>CF and CF-GA give very similar results. The best quality conformations and
numbers of acceptable or better solutions found in the top 10 are equivalent.
However, the average rank of the first acceptable conformation is lower for CF
than for CF-GA (3 <italic>vs.</italic> 3.81; target 39 was excluded from this
computation since we considered that the ranks obtained were too high to be
significant).</p><p>When not using RMSD filtering, the use of the <inline-formula><inline-graphic xlink:href="pone.0018541.e139.jpg" mimetype="image"></inline-graphic></inline-formula> criterion
doesn't affect CF-GA global performance. However, using all CAPRI criteria,
CF-GA ranks an acceptable or better conformation in the top 10 for only 3
targets out of 8. For target 32, the high quality solution that is found at rank
10 with RMSD filtering, appears at rank 18 without RMSD filtering. More
generally, results in <xref ref-type="table" rid="pone-0018541-t003">Table
3</xref> also show that using RMSD filtering decreases the mean rank of the
first acceptable or better solution (3.81 <italic>vs.</italic> 6.36, excluding
target 39), but also decreases the mean number of acceptable or better solutions
in the top 10 (2.67 <italic>vs.</italic> 3.42, including target 39).</p><p>To further evaluate these methods, the enrichment in acceptable or better
solutions in the 20% best ranked and 20% worst ranked
conformations were computed. Results (<xref ref-type="table" rid="pone-0018541-t005">Table 5</xref>) clearly show that the top 20%
is largely enriched in acceptable or better solutions, and even more in medium
or better solutions when considering the <inline-formula><inline-graphic xlink:href="pone.0018541.e140.jpg" mimetype="image"></inline-graphic></inline-formula> criterion. The
comparison between these two categories is more difficult when using all of the
CAPRI criteria, since in most cases the computation cannot be made. It can also
be seen that CF-GA is better at enriching the top 20% in acceptable or
better solutions. It should also be noted that for the three methods, using
CAPRI criteria, no acceptable or better solution is ranked in the worst
20%.</p><table-wrap id="pone-0018541-t005" position="float"><object-id pub-id-type="doi">10.1371/journal.pone.0018541.t005</object-id><label>Table 5</label><caption><title>Enrichment in acceptable or better solutions.</title></caption><alternatives><graphic id="pone-0018541-t005-5" xlink:href="pone.0018541.t005"></graphic><table frame="hsides" rules="groups"><colgroup span="1"><col align="left" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col></colgroup><thead><tr><td align="left" rowspan="1" colspan="1"></td><td colspan="4" align="left" rowspan="1">CF-GA</td><td colspan="4" align="left" rowspan="1">CF</td><td colspan="4" align="left" rowspan="1">GA</td></tr><tr><td align="left" rowspan="1" colspan="1">Target</td><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e141.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e142.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e143.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e144.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e145.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e146.jpg" mimetype="image"></inline-graphic></inline-formula></td></tr><tr><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1">E<inline-formula><inline-graphic xlink:href="pone.0018541.e147.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">E<inline-formula><inline-graphic xlink:href="pone.0018541.e148.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">E<inline-formula><inline-graphic xlink:href="pone.0018541.e149.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">E<inline-formula><inline-graphic xlink:href="pone.0018541.e150.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">E<inline-formula><inline-graphic xlink:href="pone.0018541.e151.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">E<inline-formula><inline-graphic xlink:href="pone.0018541.e152.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">E<inline-formula><inline-graphic xlink:href="pone.0018541.e153.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">E<inline-formula><inline-graphic xlink:href="pone.0018541.e154.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">E<inline-formula><inline-graphic xlink:href="pone.0018541.e155.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">E<inline-formula><inline-graphic xlink:href="pone.0018541.e156.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">E<inline-formula><inline-graphic xlink:href="pone.0018541.e157.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">E<inline-formula><inline-graphic xlink:href="pone.0018541.e158.jpg" mimetype="image"></inline-graphic></inline-formula></td></tr></thead><tbody><tr><td colspan="13" align="left" rowspan="1">20% best ranked
conformations</td></tr><tr><td align="left" rowspan="1" colspan="1">T22</td><td align="left" rowspan="1" colspan="1"><italic>0.6</italic></td><td align="left" rowspan="1" colspan="1">0.74</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1"><italic>0.45</italic></td><td align="left" rowspan="1" colspan="1"><italic>0.58</italic></td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1"><italic>0.56</italic></td><td align="left" rowspan="1" colspan="1">0.74</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td></tr><tr><td align="left" rowspan="1" colspan="1">T23</td><td align="left" rowspan="1" colspan="1">1.19</td><td align="left" rowspan="1" colspan="1">1.75</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">1.19</td><td align="left" rowspan="1" colspan="1">1.75</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">1.23</td><td align="left" rowspan="1" colspan="1">1.63</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td></tr><tr><td align="left" rowspan="1" colspan="1">T25</td><td align="left" rowspan="1" colspan="1">3.33</td><td align="left" rowspan="1" colspan="1">5</td><td align="left" rowspan="1" colspan="1">3</td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1">3.04</td><td align="left" rowspan="1" colspan="1">4.56</td><td align="left" rowspan="1" colspan="1">4.56</td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1">1.67</td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td></tr><tr><td align="left" rowspan="1" colspan="1">T26</td><td align="left" rowspan="1" colspan="1">1.5</td><td align="left" rowspan="1" colspan="1">1.26</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">1.58</td><td align="left" rowspan="1" colspan="1">1.71</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">1.41</td><td align="left" rowspan="1" colspan="1">0.95</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td></tr><tr><td align="left" rowspan="1" colspan="1">T27</td><td align="left" rowspan="1" colspan="1">1.1</td><td align="left" rowspan="1" colspan="1">1.22</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">1.07</td><td align="left" rowspan="1" colspan="1">1.12</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">1.1</td><td align="left" rowspan="1" colspan="1">1.1</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td></tr><tr><td align="left" rowspan="1" colspan="1">T29</td><td align="left" rowspan="1" colspan="1">6.67</td><td align="left" rowspan="1" colspan="1">5</td><td align="left" rowspan="1" colspan="1">5</td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1">1.89</td><td align="left" rowspan="1" colspan="1">2.64</td><td align="left" rowspan="1" colspan="1">5.29</td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1">1.21</td><td align="left" rowspan="1" colspan="1">2.71</td><td align="left" rowspan="1" colspan="1">1.81</td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td></tr><tr><td align="left" rowspan="1" colspan="1">T32</td><td align="left" rowspan="1" colspan="1">2.78</td><td align="left" rowspan="1" colspan="1">5</td><td align="left" rowspan="1" colspan="1">5</td><td align="left" rowspan="1" colspan="1">5</td><td align="left" rowspan="1" colspan="1">2.5</td><td align="left" rowspan="1" colspan="1">5</td><td align="left" rowspan="1" colspan="1">5.03</td><td align="left" rowspan="1" colspan="1">5.03</td><td align="left" rowspan="1" colspan="1">2.53</td><td align="left" rowspan="1" colspan="1">5.06</td><td align="left" rowspan="1" colspan="1">5.06</td><td align="left" rowspan="1" colspan="1">NA</td></tr><tr><td align="left" rowspan="1" colspan="1">T35</td><td align="left" rowspan="1" colspan="1">1.78</td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1">2.48</td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1">NA</td></tr><tr><td align="left" rowspan="1" colspan="1">T37</td><td align="left" rowspan="1" colspan="1">1.86</td><td align="left" rowspan="1" colspan="1">2.51</td><td align="left" rowspan="1" colspan="1">3.34</td><td align="left" rowspan="1" colspan="1">3.34</td><td align="left" rowspan="1" colspan="1">1.25</td><td align="left" rowspan="1" colspan="1">2.5</td><td align="left" rowspan="1" colspan="1">3</td><td align="left" rowspan="1" colspan="1">2.5</td><td align="left" rowspan="1" colspan="1">2.04</td><td align="left" rowspan="1" colspan="1">3.82</td><td align="left" rowspan="1" colspan="1">4.08</td><td align="left" rowspan="1" colspan="1">3.4</td></tr><tr><td align="left" rowspan="1" colspan="1">T39</td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1">0.72</td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1">NA</td></tr><tr><td align="left" rowspan="1" colspan="1">T40A</td><td align="left" rowspan="1" colspan="1">3.75</td><td align="left" rowspan="1" colspan="1">5</td><td align="left" rowspan="1" colspan="1">4.98</td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1">3.71</td><td align="left" rowspan="1" colspan="1">4.94</td><td align="left" rowspan="1" colspan="1">4.94</td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1">3.32</td><td align="left" rowspan="1" colspan="1">4.98</td><td align="left" rowspan="1" colspan="1">4.98</td><td align="left" rowspan="1" colspan="1">4.98</td></tr><tr><td align="left" rowspan="1" colspan="1">T40B</td><td align="left" rowspan="1" colspan="1">1.99</td><td align="left" rowspan="1" colspan="1">3.32</td><td align="left" rowspan="1" colspan="1">4.98</td><td align="left" rowspan="1" colspan="1">4.98</td><td align="left" rowspan="1" colspan="1">3.29</td><td align="left" rowspan="1" colspan="1">4.94</td><td align="left" rowspan="1" colspan="1">4.94</td><td align="left" rowspan="1" colspan="1">4.94</td><td align="left" rowspan="1" colspan="1">3.71</td><td align="left" rowspan="1" colspan="1">3.71</td><td align="left" rowspan="1" colspan="1">3.71</td><td align="left" rowspan="1" colspan="1">1.85</td></tr><tr><td align="left" rowspan="1" colspan="1"><bold>Average</bold></td><td align="left" rowspan="1" colspan="1"><bold>2.21</bold></td><td align="left" rowspan="1" colspan="1"><bold>2.8</bold></td><td align="left" rowspan="1" colspan="1"><bold>4.04</bold></td><td align="left" rowspan="1" colspan="1"><bold>3.33</bold></td><td align="left" rowspan="1" colspan="1"><bold>1.93</bold></td><td align="left" rowspan="1" colspan="1"><bold>2.7</bold></td><td align="left" rowspan="1" colspan="1"><bold>4.62</bold></td><td align="left" rowspan="1" colspan="1"><bold>4.16</bold></td><td align="left" rowspan="1" colspan="1"><bold>1.56</bold></td><td align="left" rowspan="1" colspan="1"><bold>2.24</bold></td><td align="left" rowspan="1" colspan="1"><bold>3.27</bold></td><td align="left" rowspan="1" colspan="1"><bold>2.05</bold></td></tr><tr><td colspan="13" align="left" rowspan="1">20% worst ranked
conformations</td></tr><tr><td align="left" rowspan="1" colspan="1">T22</td><td align="left" rowspan="1" colspan="1">1.65</td><td align="left" rowspan="1" colspan="1">1.85</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">1.2</td><td align="left" rowspan="1" colspan="1">1.34</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">1.53</td><td align="left" rowspan="1" colspan="1">1.66</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td></tr><tr><td align="left" rowspan="1" colspan="1">T23</td><td align="left" rowspan="1" colspan="1"><italic>0.66</italic></td><td align="left" rowspan="1" colspan="1">0.7</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1"><italic>0.66</italic></td><td align="left" rowspan="1" colspan="1">0.7</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">1.09</td><td align="left" rowspan="1" colspan="1">1.23</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td></tr><tr><td align="left" rowspan="1" colspan="1">T25</td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1">1.52</td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td></tr><tr><td align="left" rowspan="1" colspan="1">T26</td><td align="left" rowspan="1" colspan="1">0.82</td><td align="left" rowspan="1" colspan="1">0.63</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">0.92</td><td align="left" rowspan="1" colspan="1">0.57</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">1.13</td><td align="left" rowspan="1" colspan="1">1.9</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td></tr><tr><td align="left" rowspan="1" colspan="1">T27</td><td align="left" rowspan="1" colspan="1">0.91</td><td align="left" rowspan="1" colspan="1">0.79</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">0.93</td><td align="left" rowspan="1" colspan="1">0.91</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">0.92</td><td align="left" rowspan="1" colspan="1">0.73</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td></tr><tr><td align="left" rowspan="1" colspan="1">T29</td><td align="left" rowspan="1" colspan="1">3.33</td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1"><italic>0.38</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1">1.51</td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td></tr><tr><td align="left" rowspan="1" colspan="1">T32</td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1">NA</td></tr><tr><td align="left" rowspan="1" colspan="1">T35</td><td align="left" rowspan="1" colspan="1">1.78</td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1">NA</td></tr><tr><td align="left" rowspan="1" colspan="1">T37</td><td align="left" rowspan="1" colspan="1">0.56</td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1">0.54</td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td></tr><tr><td align="left" rowspan="1" colspan="1">T39</td><td align="left" rowspan="1" colspan="1">1.44</td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1">2.15</td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1">NA</td></tr><tr><td align="left" rowspan="1" colspan="1">T40A</td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1">NA</td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td></tr><tr><td align="left" rowspan="1" colspan="1">T40B</td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td><td align="left" rowspan="1" colspan="1"><italic>0</italic></td></tr><tr><td align="left" rowspan="1" colspan="1"><bold>Average</bold></td><td align="left" rowspan="1" colspan="1"><bold>0.93</bold></td><td align="left" rowspan="1" colspan="1"><bold>0.36</bold></td><td align="left" rowspan="1" colspan="1"><bold>0</bold></td><td align="left" rowspan="1" colspan="1"><bold>0</bold></td><td align="left" rowspan="1" colspan="1"><bold>0.69</bold></td><td align="left" rowspan="1" colspan="1"><bold>0.32</bold></td><td align="left" rowspan="1" colspan="1"><bold>0</bold></td><td align="left" rowspan="1" colspan="1"><bold>0</bold></td><td align="left" rowspan="1" colspan="1"><bold>0.51</bold></td><td align="left" rowspan="1" colspan="1"><bold>0.5</bold></td><td align="left" rowspan="1" colspan="1"><bold>0</bold></td><td align="left" rowspan="1" colspan="1"><bold>0</bold></td></tr></tbody></table></alternatives><table-wrap-foot><fn id="nt105"><label></label><p>The enrichment in acceptable or better conformations
(E<inline-formula><inline-graphic xlink:href="pone.0018541.e159.jpg" mimetype="image"></inline-graphic></inline-formula>) is
computed as the proportion of such conformations in the 20%
best ranked conformations (respectively worst ranked conformations)
divided by the proportion of such conformations is the complete set.
Same computation for medium quality or better conformations
(E<inline-formula><inline-graphic xlink:href="pone.0018541.e160.jpg" mimetype="image"></inline-graphic></inline-formula>).
These enrichments are computed using either
<inline-formula><inline-graphic xlink:href="pone.0018541.e161.jpg" mimetype="image"></inline-graphic></inline-formula> or
CAPRI criteria (<inline-formula><inline-graphic xlink:href="pone.0018541.e162.jpg" mimetype="image"></inline-graphic></inline-formula>), and
for the three methods (GA: genetic algorithm, CF: collaborative
filtering, CF-GA: hybrid method). Values in italic are not
statistically significant.</p></fn></table-wrap-foot></table-wrap><p>We have compared these results with the ones obtained by other scoring groups on
the 12 targets. As can be seen from <xref ref-type="table" rid="pone-0018541-t006">Table 6</xref>, two of the targets for which we do
not find an acceptable or better solution in the top 10 (T35 with all CAPRI
criteria, and T39 with either quality measures) were difficult targets, and only
one group obtained an acceptable solution for T35, none for T39. It should also
be noted that target 35 is not a biological complex, but the assembly of two
different modules belonging to the same protein chain.</p><table-wrap id="pone-0018541-t006" position="float"><object-id pub-id-type="doi">10.1371/journal.pone.0018541.t006</object-id><label>Table 6</label><caption><title>Best conformation present in the top 10 for different scoring
groups.</title></caption><alternatives><graphic id="pone-0018541-t006-6" xlink:href="pone.0018541.t006"></graphic><table frame="hsides" rules="groups"><colgroup span="1"><col align="left" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col></colgroup><thead><tr><td align="left" rowspan="1" colspan="1">Groups</td><td align="left" rowspan="1" colspan="1">T22</td><td align="left" rowspan="1" colspan="1">T23</td><td align="left" rowspan="1" colspan="1">T25</td><td align="left" rowspan="1" colspan="1">T26</td><td align="left" rowspan="1" colspan="1">T27</td><td align="left" rowspan="1" colspan="1">T29</td><td align="left" rowspan="1" colspan="1">T32</td><td align="left" rowspan="1" colspan="1">T35</td><td align="left" rowspan="1" colspan="1">T37</td><td align="left" rowspan="1" colspan="1">T39</td><td align="left" rowspan="1" colspan="1">T40A</td><td align="left" rowspan="1" colspan="1">T40B</td></tr></thead><tbody><tr><td align="left" rowspan="1" colspan="1">C Wang</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e163"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e164"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e165"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e166"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e167"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e168"></graphic></disp-formula></td></tr><tr><td align="left" rowspan="1" colspan="1">A.M.J.J Bonvin</td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e169"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e170"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e171"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e172"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e173"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e174"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e175"></graphic></disp-formula></td></tr><tr><td align="left" rowspan="1" colspan="1">H. Wolfson</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e176"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e177"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e178"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e179"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e180"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1">0</td></tr><tr><td align="left" rowspan="1" colspan="1">P. A. Bates</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e181"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e182"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e183"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e184"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1">0</td></tr><tr><td align="left" rowspan="1" colspan="1">Z. Weng</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e185"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e186"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e187"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e188"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e189"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1">0</td></tr><tr><td align="left" rowspan="1" colspan="1">J. F.-Recio</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e190"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e191"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e192"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td></tr><tr><td align="left" rowspan="1" colspan="1">X. Zou</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e193"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e194"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e195"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e196"></graphic></disp-formula></td></tr><tr><td align="left" rowspan="1" colspan="1">T. Haliloglu</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e197"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e198"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e199"></graphic></disp-formula></td></tr><tr><td align="left" rowspan="1" colspan="1">C. J. Camacho</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e200"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e201"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e202"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e203"></graphic></disp-formula></td></tr><tr><td align="left" rowspan="1" colspan="1">M. Takeda-Shitaka</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e204"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e205"></graphic></disp-formula></td></tr><tr><td align="left" rowspan="1" colspan="1">I. Vakser</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e206"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">-</td><td align="left" rowspan="1" colspan="1">-</td></tr><tr><td align="left" rowspan="1" colspan="1">CF-GA Method</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e207.jpg" mimetype="image"></inline-graphic></inline-formula><xref ref-type="table-fn" rid="nt107">a</xref></td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e208.jpg" mimetype="image"></inline-graphic></inline-formula><xref ref-type="table-fn" rid="nt107">a</xref></td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e209"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e210.jpg" mimetype="image"></inline-graphic></inline-formula><xref ref-type="table-fn" rid="nt107">a</xref></td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e211.jpg" mimetype="image"></inline-graphic></inline-formula><xref ref-type="table-fn" rid="nt107">a</xref></td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e212"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e213"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1">0</td><td align="left" rowspan="1" colspan="1"><disp-formula><graphic xlink:href="pone.0018541.e214"></graphic></disp-formula></td><td align="left" rowspan="1" colspan="1">0</td></tr></tbody></table></alternatives><table-wrap-foot><fn id="nt106"><label></label><p><inline-formula><inline-graphic xlink:href="pone.0018541.e215.jpg" mimetype="image"></inline-graphic></inline-formula>: no acceptable or better solution found, -:
group has not participated,</p></fn><fn id="nt107"><label>a</label><p>: <inline-formula><inline-graphic xlink:href="pone.0018541.e216.jpg" mimetype="image"></inline-graphic></inline-formula> evaluation.</p></fn></table-wrap-foot></table-wrap><p>Target 37 was found by most scorers. Our failure for this target is probably
related to the fact that this complex is made of three protein chains (A, C and
D), and the docking was conducted using only two of these chains. The resulting
candidate interfaces, since they represent only a portion of the native
interface, are two small to be favourably ranked by our method. Target 40 is
also a trimer (chains A, B and C), but this time with two distinct interfaces
(CA: target 40A, and CB: target 40B). The GA-CF method successfully finds the CA
interface, but fails to favourably rank a good conformation for interface CB.
The CA interface is significantly larger than CB (1009.5
<italic>Å<sup>2</sup> vs.</italic> 731.3
<italic>Å<sup>2</sup></italic>). Here again, the size of this
second interface is two small for our method, especially since much larger
interfaces (corresponding to the CA interface) are found in the proposed
conformations.</p><p>For targets 22, 23, 26 and 27, the CAPRI criteria for all proposed conformations
are not available. We have compared the categories given to the different
conformations by the two criteria sets. Results shown <xref ref-type="table" rid="pone-0018541-t007">Table 7</xref> show that 99.4% of the
conformations evaluated as high quality using the
<inline-formula><inline-graphic xlink:href="pone.0018541.e217.jpg" mimetype="image"></inline-graphic></inline-formula> criterion are evaluated as at least acceptable using all
criteria (76.8% are even evaluated as medium or better), and 84.7%
of the conformations evaluated as medium using the
<inline-formula><inline-graphic xlink:href="pone.0018541.e218.jpg" mimetype="image"></inline-graphic></inline-formula> criterion are evaluated as acceptable or better using
CAPRI criteria. Consequently, the solutions found in the top 10 for targets 22,
23, 26 and 27 would very likely be considered as acceptable or better using
CAPRI criteria. The conformations retained for targets 22, 23, 26 and 27 have
<inline-formula><inline-graphic xlink:href="pone.0018541.e219.jpg" mimetype="image"></inline-graphic></inline-formula> values of 0.95, 0.61, 0.45 and 1 respectively. Upon
visual inspection (see <xref ref-type="fig" rid="pone-0018541-g005">Figure
5</xref>), and global RMSD computation, we estimated that their CAPRI status
would be high, medium, acceptable and high respectively.</p><fig id="pone-0018541-g005" position="float"><object-id pub-id-type="doi">10.1371/journal.pone.0018541.g005</object-id><label>Figure 5</label><caption><title>Conformations retained for targets 22, 23, 26 and 27.</title><p>Native structure in orange, prediction in blue.</p></caption><graphic xlink:href="pone.0018541.g005"></graphic></fig><table-wrap id="pone-0018541-t007" position="float"><object-id pub-id-type="doi">10.1371/journal.pone.0018541.t007</object-id><label>Table 7</label><caption><title>Comparison between <inline-formula><inline-graphic xlink:href="pone.0018541.e220.jpg" mimetype="image"></inline-graphic></inline-formula> and
<inline-formula><inline-graphic xlink:href="pone.0018541.e221.jpg" mimetype="image"></inline-graphic></inline-formula>evaluations.</title></caption><alternatives><graphic id="pone-0018541-t007-7" xlink:href="pone.0018541.t007"></graphic><table frame="hsides" rules="groups"><colgroup span="1"><col align="left" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col></colgroup><thead><tr><td align="left" rowspan="1" colspan="1"></td><td colspan="4" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e222.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">Total</td></tr><tr><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e223.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e224.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e225.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e226.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">Incorrect</td><td align="left" rowspan="1" colspan="1"></td></tr></thead><tbody><tr><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e227.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1">204</td><td align="left" rowspan="1" colspan="1">298</td><td align="left" rowspan="1" colspan="1">148</td><td align="left" rowspan="1" colspan="1">4</td><td align="left" rowspan="1" colspan="1">654</td></tr><tr><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e228.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1">21</td><td align="left" rowspan="1" colspan="1">106</td><td align="left" rowspan="1" colspan="1">23</td><td align="left" rowspan="1" colspan="1">150</td></tr><tr><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0018541.e229.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1">44</td><td align="left" rowspan="1" colspan="1">547</td><td align="left" rowspan="1" colspan="1">591</td></tr><tr><td align="left" rowspan="1" colspan="1">Incorrect</td><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1">7069</td><td align="left" rowspan="1" colspan="1">7069</td></tr><tr><td align="left" rowspan="1" colspan="1"><bold>Total</bold></td><td align="left" rowspan="1" colspan="1">204</td><td align="left" rowspan="1" colspan="1">319</td><td align="left" rowspan="1" colspan="1">298</td><td align="left" rowspan="1" colspan="1">7643</td><td align="left" rowspan="1" colspan="1">8464</td></tr></tbody></table></alternatives><table-wrap-foot><fn id="nt108"><label></label><p>For all the conformations in the CAPRI scoring ensembles, the
classifications as high-quality, medium-quality, acceptable or
incorrect conformation using only <inline-formula><inline-graphic xlink:href="pone.0018541.e230.jpg" mimetype="image"></inline-graphic></inline-formula>, or
complete CAPRI are compared. For example, there are 298
conformations classified as medium-quality using CAPRI criteria and
high-quality by <inline-formula><inline-graphic xlink:href="pone.0018541.e231.jpg" mimetype="image"></inline-graphic></inline-formula>criterion.</p></fn></table-wrap-foot></table-wrap><p>Apart from the results obtained by our scoring function, this study shows that
the <inline-formula><inline-graphic xlink:href="pone.0018541.e232.jpg" mimetype="image"></inline-graphic></inline-formula> criterion, although and because it is less stringent
than the CAPRI criteria, allows a better estimation of the performances of
prediction methods. Indeed, predictions that correctly identify the interface
area on both protein would be considered <italic>incorrect</italic> using the
CAPRI criteria, but <italic>acceptable</italic> using the
<inline-formula><inline-graphic xlink:href="pone.0018541.e233.jpg" mimetype="image"></inline-graphic></inline-formula> criterion. For predictions having correct contacts,
classified as <italic>high</italic> with the <inline-formula><inline-graphic xlink:href="pone.0018541.e234.jpg" mimetype="image"></inline-graphic></inline-formula>, the CAPRI
criteria often classifies them as <italic>medium</italic> or even
<italic>low</italic>, mostly because of errors in global relative
orientations of the two partners. Consequently, the <italic>incorrect</italic>class with the CAPRI criteria doesn't distinguish between these
predictions, which have a very high biological utility, and predictions having
few native contacts, which are <italic>biologically</italic> wrong. Thus it
appears that, from the biologist's point of view, the
<inline-formula><inline-graphic xlink:href="pone.0018541.e235.jpg" mimetype="image"></inline-graphic></inline-formula> criterion is certainly more useful.</p><p>Globally the CF-GA method performs very well, ranking acceptable or better
solutions in the top 10 for 8 out of 12 targets. The comparison with other
methods is very difficult, since the other methods are evolving and the
different groups have not participated to the same rounds. However, it can be
seen that the performances of CF-GA compare favorably with current
well-performing techniques.</p></sec><sec id="s3e"><title>Conclusion</title><p>We have shown that the use of a collaborative filtering strategy combined to a
learning procedure leads to an efficient method. Using this technique, we are
able to rank at least one acceptable or better solution in top 10 for 10 out of
12 CAPRI targets using solely the <inline-formula><inline-graphic xlink:href="pone.0018541.e236.jpg" mimetype="image"></inline-graphic></inline-formula> criterion, and 4
out of 8 when using all CAPRI criteria, in cases where scoring ensembles contain
acceptable or better solutions. We have also shown that the set of 20%
best ranked conformations is largely enriched in medium or better conformations,
whereas the set of 20% worst ranked solutions contains very few good
models.</p><p>The use of RMSD-filtering allows to increase the diversity of the conformations
present in the top 10, which decreases the mean rank of the first acceptable or
better conformation, but also decreases the number of acceptable or better
conformations in the top 10. This is an advantage in an exploration perspective,
since the proposed conformations are very different from each other. But this is
also a disadvantage in an optimization or refinement perspective, since, for
example, a very favourably ranked medium quality conformation can eliminate a
high quality conformation having a slightly higher rank.</p><p>Finally, we have seen that our method fails on trimers. In the case of target 40
this is largely due to the fact that our method searches the best interface, and
is not trained to look for multiple interfaces. Finding these interfaces would
probably require training the method specifically on complexes with more than
two chains.</p></sec></sec></body><back><fn-group><fn fn-type="conflict"><p><bold>Competing Interests: </bold>The authors have declared that no competing interests exist.</p></fn><fn fn-type="financial-disclosure"><p><bold>Funding: </bold>The authors have no support or funding to report.</p></fn></fn-group><ref-list><title>References</title><ref id="pone.0018541-Wodak1"><label>1</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Wodak</surname><given-names>SJ</given-names></name><name><surname>Janin</surname><given-names>J</given-names></name></person-group><year>2002</year><article-title>Structural basis of macromolecular recognition.</article-title><source>Adv Protein Chem</source><volume>61</volume><fpage>9</fpage><lpage>73</lpage><pub-id pub-id-type="pmid">12461820</pub-id></element-citation></ref><ref id="pone.0018541-Sanderson1"><label>2</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Sanderson</surname><given-names>CM</given-names></name></person-group><year>2009</year><article-title>The cartographers toolbox: building bigger and better human
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optimization.</article-title><source>In: Fifteenth International Conference on Machine Learning</source><fpage>144</fpage><lpage>151</lpage></element-citation></ref></ref-list></back></pmc></record>Pour manipuler ce document sous Unix (Dilib)
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