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<?xml version='1.0' encoding='utf-8'?>
<t:test xmlns:t="http://www.ncbi.nlm.nih.gov/ns/test" xmlns="http://www.w3.org/1999/xhtml">
<t:title>Correlation analysis of the side-chains conformational distribution in bound and unbound
proteins</t:title>
<t:citation>BMC Bioinformatics. 2012; 13: 236. </t:citation>
<t:links>
<a href="http://www.ncbi.nlm.nih.gov/pmc/journals/" class="navlink">Journal List</a>
<a class="navlink" href="http://www.ncbi.nlm.nih.gov/pmc/journals/13/">BMC Bioinformatics</a>
<a class="navlink" href="http://www.ncbi.nlm.nih.gov/pmc/issues/204821/">v.13; 2012</a>
</t:links>
<t:alt-formats>
<a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3479416/" class="">Article</a>
<a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3479416/epub/" class="">ePub (beta)</a>
<a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3479416/pdf/1471-2105-13-236.pdf" class=""
>PDF (707K)</a>
</t:alt-formats>
<t:content>
<article data-type="main">
<div class="jrb">
<div class="t"> BMC Bioinformatics </div>
<div class="p"> BioMed Central </div>
</div>
<header class="fm-sec">
<h1 class="content-title">Correlation analysis of the side-chains conformational
distribution in bound and unbound proteins</h1>
<p class="contribs"> Tatsiana Kirys, Anatoly M Ruvinsky, [...], and Ilya A Vakser </p>
<p>
<a href="#__ffn_sectitle">Additional article information</a>
</p>
</header>
<div id="__abstractid453541" class="sec">
<h2 class="head no_bottom_margin" id="__abstractid453541title">Abstract</h2><!--article-meta-->
<div>
<div id="__sec1" class="sec sec-first">
<h3>Background</h3>
<p id="__p1">Protein interactions play a key role in life processes. Characterization of
conformational properties of protein-protein interactions is important for
understanding the mechanisms of protein association. The rapidly increasing amount of
experimentally determined structures of proteins and protein-protein complexes
provides foundation for research on protein interactions and complex formation. The
knowledge of the conformations of the surface side chains is essential for modeling of
protein complexes. The purpose of this study was to analyze and compare dihedral angle
distribution functions of the side chains at the interface and non-interface areas in
bound and unbound proteins. </p>
</div>
<div id="__sec2" class="sec">
<h3>Results</h3>
<p id="__p2">To calculate the dihedral angle distribution functions, the configuration
space was divided into grid cells. Statistical analysis showed that the similarity
between bound and unbound interface and non-interface surface depends on the amino
acid type and the grid resolution. The correlation coefficients between the
distribution functions increased with the grid spacing increase for all amino acid
types. The Manhattan distance showing the degree of dissimilarity between the
distribution functions decreased accordingly. Short residues with one or two dihedral
angles had higher correlations and smaller Manhattan distances than the longer
residues. Met and Arg had the slowest growth of the correlation coefficient with the
grid spacing increase. The correlations between the interface and non-interface
distribution functions had a similar dependence on the grid resolution in both bound
and unbound states. The interface and non-interface differences between bound and
unbound distribution functions, caused by biological protein-protein interactions or
crystal contacts, disappeared at the 70° grid spacing for interfaces and
30° for non-interface surface, which agrees with an average span of the
side-chain rotamers. </p>
</div>
<div id="__sec3" class="sec sec-last">
<h3>Conclusions</h3>
<p id="__p3">The two-fold difference in the critical grid spacing indicates larger
conformational changes upon binding at the interface than at the rest of the surface.
At the same time, transitions between rotamers induced by interactions across the
interface or the crystal packing are rare, with most side chains having local
readjustments that do not change the rotameric state. The analysis is important for
better understanding of protein interactions and development of flexible docking
approaches. </p>
</div>
</div>
<div class="sec">
<strong class="kwd-title">Keywords: </strong><span class="kwd-text">Protein interactions,
Protein docking, Molecular recognition, Conformational analysis</span>
</div>
</div>
<div id="__sec4" class="sec">
<h2 class="head no_bottom_margin" id="__sec4title">Background</h2>
<p id="__p4">Protein-protein interactions play a key role in life processes. Characterization of
conformational changes in proteins upon binding is important for understanding the
mechanisms of protein association and for our ability to model it. Dependence of
side-chain dihedral angle distribution on the conformation of the backbone has been
investigated in earlier studies [1-5]. The side-chain dihedral angles are not evenly
distributed, but for the most part are tightly clustered. A number of unbound rotamer
libraries have been described previously [1-14] (see [15] for a review). Dunbrack and
Cohen [1] used Bayesian statistics to estimate populations and dihedral angles for all
amino acids rotamers at all <img src="assets/x03C6.gif" border="0"
alt="[var phi]" title=""/> and ψ values. A backbone-dependent rotamer library
[15] was obtained by dividing <img src="assets/x03C6.gif" border="0"
alt="[var phi]" title=""/> and ψ dihedral space into 10°×<img
src="assets/x2009.gif" border="0" alt=" " title=""/>10° bins,
χ angles into 120° bins, and calculating frequencies and average values of
rotamers for each amino acid. A backbone-independent rotamer library was generated in a
similar way. In a recent study [16], a new version of the backbone-dependent rotamer
library was developed. It consists of rotamer frequencies, mean dihedral angles, and
variances as a function of the backbone dihedral angles. In one of the latest
backbone-independent rotamer libraries, the “Penultimate rotamer library”
[5] by Lovell, Richardson and colleagues, the dihedral angle space was clustered and
rotamer positions were defined as the distribution mode. </p>
<p id="__p5">Comparison of the side-chain distribution in the core and on the surface [3],
conducted on 19 protein structures available in 1978, revealed a small variation of the
χ<sub>1</sub> rotamers distribution. A later study [17] on a set of 50
non-homologous proteins showed that for all side chains, except Asp, Asn and Glu, the
distributions of χ<sub>1</sub> rotamers on the surface and in the core are not
significantly different. </p>
<p id="__p6">Comparison of the χ<sub>1</sub> and χ<sub>2</sub> distributions
at the interface and non-interface surface was performed by Guharoy et al. [18].
Distributions were divided into bins as in the Dunbrack’s backbone-independent
rotamer library [1]. Empirical free energies of inter-rotamer transitions were calculated
and compared for the interface and non-interface areas. The rotamers free energies were
different at the interface and non-interface, whereas bound and unbound free energies were
essentially the same. </p>
<p id="__p7">Conformations of surface residues in protein structures determined by
crystallography are affected by the crystal packing. The area of the protein surface
involved in the crystal contacts is generally smaller than in biological interfaces [19],
and the interface packing is looser [20]. Studies of the crystal packing effect on the
surface side chains [21-23] showed that<img src="assets/x2009.gif"
border="0" alt=" " title=""/>~<img src="assets/x2009.gif" border="0"
alt=" " title=""/>20% of the exposed side chains change conformation, and the change
increases with the increase of the side-chain solvent accessibility. Large polar or
charged residues Arg, Lys, Glu, Gln, as well as Ser were found to be most flexible [21]. </p>
<p id="__p8">The purpose of this study was to analyze and compare dihedral angle
distribution functions of the side chains at the interface and non-interface areas in
bound and unbound proteins. Such analysis is important for better understanding of protein
interactions and development of flexible docking approaches. The dihedral-angle
distribution functions (DADF) were calculated on a cubic grid dividing the dihedral space
into cells for each residue type, at interface and non-interface surface, in bound and
unbound structures. The correlation coefficients between bound and unbound, interface and
non-interface DADFs were calculated, along with the Manhattan distance, as a measure of
dissimilarity between the DADFs. All the correlation coefficients depended on the amino
acid type and the grid resolution. The correlation coefficients always increased with the
increase of the grid spacing, whereas the Manhattan distances decreased accordingly. Short
residues with one or two dihedral angles had higher correlations and smaller Manhattan
distances at small grid spacing than the longer residues. The correlation between the
interface and non-interface DADFs showed a similar dependence on the grid resolution in
both bound and unbound states. The differences between bound and unbound DADFs induced by
biological protein-protein interactions or crystal contacts disappeared at the 70°
grid spacing for interfaces and 30° for non-interface surface. The two-fold
difference in the critical grid spacing indicates larger changes at the interface than on
the rest of the surface. While the earlier studies [18,24,25] observed this trend for the
side-chain rotamers, this study validates it by a more general approach based on the
DADFs. </p>
</div>
<div id="__sec5" class="sec">
<h2 class="head no_bottom_margin" id="__sec5title">Methods</h2>
<p
id="__p9">The analysis was performed on the non-redundant D<span class="small-caps"
>ockground</span> Benchmark 3 set of bound and corresponding unbound protein structures
[26]. The set consists of 233 complexes, with the unbound structures of both interacting
proteins for 99 complexes, and the unbound structure of one interacting protein for 134
complexes. The following criteria were used for generating the set: sequence identity
between bound and unbound structures<img src="assets/x2009.gif" border="0"
alt=" " title=""/>><img src="assets/x2009.gif" border="0" alt=" "
title=""/>97%; sequence identity between complexes<img
src="assets/x2009.gif" border="0" alt=" " title=""/><<img
src="assets/x2009.gif" border="0" alt=" " title=""/>30%; and
homomultimers, crystal packing, and obligate complexes excluded. </p>
<p id="__p10">The core residues change conformation upon binding less than the surface ones
[24]. Thus, our study focused on the surface residues only. Surface residues were defined
as those with the relative solvent-accessible surface area<img
src="assets/x2009.gif" border="0" alt=" " title=""/>≥<img
src="assets/x2009.gif" border="0" alt=" " title=""/>25% in bound and
unbound state. The change of the residue solvent-accessible surface area (SASA) upon
binding was used to differentiate the interface residues from the non-interface ones. SASA
was calculated using Naccess [27]. The interface residues were defined as those losing<img
src="assets/x2009.gif" border="0" alt=" " title=""/>><img
src="assets/x2009.gif" border="0" alt=" " title=""/>1<img
src="assets/x2009.gif" border="0" alt=" " title=""/>Å<sup>2</sup>
SASA upon binding. The statistics of the interface and non-interface residues in the bound
and unbound structures are summarized in Table . The difference between the numbers of
bound and unbound interface/non-interface residues reflects the difference between the
number of bound and unbound protein structures in the D<span class="small-caps"
>ockground</span> set. </p>
<!--table ft1--><!--table-wrap mode=article t1-->
<div class="table-wrap iconblock ten_col whole_rhythm clearfix" id="T1">
<a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3479416/table/T1/"
onclick="return startTarget(this, 'table',1024,800)" target="table" rid-ob="ob-T1"
rid-figpopup="T1" class="table img_link icnblk_img figpopup"><img border="0"
alt="Table 1" title="Table 1" class="small-thumb" src="assets/T1.thumb.png"
src-large="assets/T1.previmg.png"/></a><div class="icnblk_cntnt">
<div>
<a class="figpopup" href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3479416/table/T1/" target="table"
rid-figpopup="T1" rid-ob="ob-T1"
onclick="return startTarget(this, 'table',1024,800)">Table 1</a>
</div>
<!--caption a4-->
<div>
<span>Number of surface residues in bound and unbound proteins</span>
</div>
</div>
</div>
<p id="__p14">Side chain conformations were represented by dihedral angles, calculated by
Dangle [28]. All dihedral angles varied from −180° to 180°, with
exception of the last dihedral angle in Phe, Tyr, Asp and Glu [2], which varied from
0° to 180° due to the symmetry of the terminal aromatic and charged
groups. To calculate the distribution functions, the configuration space was divided into
cells by a cubic grid. </p>
<p id="__p15">DADFs were calculated as the occupancy of the grid cells separately for each
residue type for interface and non-interface, bound and unbound residues. Thus, there were
four DADFs for each residue type: interface bound, interface unbound, non-interface bound,
and non-interface unbound. Figure 1 shows a two-dimensional distribution function of Asp
dihedral angles for the non-interface unbound residues. </p>
<!--fig ft0--><!--fig mode=article f1-->
<div class="fig iconblock ten_col whole_rhythm clearfix" id="F1" co-legend-rid="lgnd_F1">
<a class="icnblk_img figpopup" href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3479416/figure/F1/"
target="figure" rid-figpopup="F1" rid-ob="ob-F1"
onclick="return startTarget(this, 'figure',1024,800)"><img src="assets/1471-2105-13-236-1.gif" class="small-thumb" alt="Figure 1 "
title="Figure 1 " src-large="assets/1471-2105-13-236-1.jpg"/></a>
<div class="icnblk_cntnt" id="lgnd_F1">
<div>
<a class="figpopup" href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3479416/figure/F1/" target="figure"
rid-figpopup="F1" rid-ob="ob-F1"
onclick="return startTarget(this, 'figure',1024,800)">Figure 1 </a>
</div>
<!--caption a4-->
<div>
<span>Dihedral angle distribution of non-interface Asp in unbound structures.</span>
</div>
</div>
</div>
<p id="__p17">To compare distributions X and Y, the corresponding n-dimensional space (n is
the number of the dihedral angles in the side chain) was split into m cubes with a fixed
side length. The occupancy in each cell was calculated (Figure 1). The correlation
coefficient r [29] between unbound (X) and bound (Y) DADFs was calculated as: </p>
<div id="__p18">
<div class="disp-formula" id="bmcM1">
<div class="f">
<math id="M1" name="1471-2105-13-236-i1" overflow="scroll"
><mrow><mi>r</mi><mo>=</mo><mfrac><mstyle displaystyle="true"
><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>m</mi></munderover><mrow><mfenced
open="(" close=")"
><mrow><msub><mi>X</mi><mi>i</mi></msub><mo>−</mo><mover
accent="true"><mi>X</mi><mo stretchy="true"
>¯</mo></mover></mrow></mfenced><mfenced open="(" close=")"
><mrow><msub><mi>Y</mi><mi>i</mi></msub><mo>−</mo><mover
accent="true"><mi>Y</mi><mo stretchy="true"
>¯</mo></mover></mrow></mfenced></mrow></mstyle><mrow><msqrt><mstyle
displaystyle="true"
><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>m</mi></munderover><mrow><msup><mfenced
open="(" close=")"
><mrow><msub><mi>X</mi><mi>i</mi></msub><mo>−</mo><mover
accent="true"><mi>X</mi><mo stretchy="true"
>¯</mo></mover></mrow></mfenced><mn>2</mn></msup></mrow></mstyle></msqrt><msqrt><mstyle
displaystyle="true"
><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>m</mi></munderover><mrow><msup><mfenced
open="(" close=")"
><mrow><msub><mi>Y</mi><mi>i</mi></msub><mo>−</mo><mover
accent="true"><mi>Y</mi><mo stretchy="true"
>¯</mo></mover></mrow></mfenced><mn>2</mn></msup></mrow></mstyle></msqrt></mrow></mfrac><mtext>,</mtext></mrow></math>
</div>
<div class="l">(1) </div>
</div>
</div>
<p id="__p19">where X<sub>i</sub> and Y<sub>i</sub> are the probabilities of bound and
unbound side-chain conformations in a grid cell i, <math id="M2"
name="1471-2105-13-236-i2" overflow="scroll"><mrow><mover accent="true"><mi>X</mi><mo
stretchy="true"
>¯</mo></mover><mo>=</mo><mfrac><mn>1</mn><mi>m</mi></mfrac><mstyle
displaystyle="true"
><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>m</mi></munderover><mrow><msub><mi>X</mi><mi>i</mi></msub></mrow></mstyle></mrow></math>
and <math id="M3" name="1471-2105-13-236-i3" overflow="scroll"><mrow><mover accent="true"
><mi>Y</mi><mo stretchy="true"
>¯</mo></mover><mo>=</mo><mfrac><mn>1</mn><mi>m</mi></mfrac><mstyle
displaystyle="true"
><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>m</mi></munderover><mrow><msub><mi>Y</mi><mi>i</mi></msub></mrow></mstyle></mrow></math>
are the average probabilities of bound and unbound side-chain conformations. To determine
the degree of similarity between two probability distributions the Manhattan distance [30]
was calculated as: </p>
<div id="__p20">
<div class="disp-formula" id="bmcM2">
<div class="f">
<math id="M4" name="1471-2105-13-236-i4" overflow="scroll"><mrow><mi>d</mi><mfenced
open="(" close=")"
><mrow><mi>X</mi><mo>,</mo><mi>Y</mi></mrow></mfenced><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mstyle
displaystyle="true"
><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>m</mi></munderover><mrow><mfenced
open="|" close="|"
><mrow><msub><mi>X</mi><mi>i</mi></msub><mo>−</mo><msub><mi>Y</mi><mi>i</mi></msub></mrow></mfenced></mrow></mstyle></mrow></math>
</div>
<div class="l">(2) </div>
</div>
</div>
<p id="__p21">The Manhattan distance equals 0 for two identical DADFs, and increases up to 1
with the decrease of the DADFs similarity (higher similarity between the DADFs corresponds
to lower values of the Manhattan distance). </p>
</div>
<div id="__sec6" class="sec">
<h2 class="head no_bottom_margin" id="__sec6title">Results and discussion</h2><p id="__p22"
>The discrete probability distribution of the amino acid side-chain χ angles
depended on the starting point of splitting and the size of the grid spacing. An example
of a probability function with 20° grid spacing and different starting points of
splitting for non-interface unbound Ser is shown in Figure 2. The distribution was divided
into cells with a predefined step size, starting with a randomly chosen point, and the
probability in each cell was calculated. To remove the effect of splitting, correlation
coefficients were calculated 100 and 1000 times with the same splitting step but random
starting point of splitting. Then, the average correlation coefficients were calculated.
We found no significant difference between the correlation coefficients averaged 100 or
1000 times. Tests of statistical significance of the correlation [31] between bound and
unbound distributions, and non-interface and interface distributions showed that all
correlation values were significant, with p-values far below 0.001. </p>
<!--fig ft0--><!--fig mode=article f1--><div
class="fig iconblock ten_col whole_rhythm clearfix" id="F2" co-legend-rid="lgnd_F2"><a
class="icnblk_img figpopup" href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3479416/figure/F2/" target="figure"
rid-figpopup="F2" rid-ob="ob-F2" onclick="return startTarget(this, 'figure',1024,800)"
><img src="assets/1471-2105-13-236-2.gif" class="small-thumb" alt="Figure 2 "
title="Figure 2 " src-large="assets/1471-2105-13-236-2.jpg"/></a><div
class="icnblk_cntnt" id="lgnd_F2">
<div>
<a class="figpopup" href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3479416/figure/F2/" target="figure"
rid-figpopup="F2" rid-ob="ob-F2"
onclick="return startTarget(this, 'figure',1024,800)">Figure 2 </a>
</div>
<!--caption a4-->
<div>
<span>Dihedral angle distribution of non-interface unbound Ser with 20° grid
spacing and different splitting points.</span>
</div>
</div>
</div>
<p id="__p24">Analysis showed that the correlation coefficients depend on the grid spacing
(Figure 3). Generally, larger steps corresponded to higher correlation values (larger
cells yielded more smooth/similar distributions). Table shows the grid spacing at which
the correlation reaches a high level of 0.7. Most amino acids had high correlation between
bound and unbound interface/non-interface distributions for grid spacing<img
src="assets/x2009.gif" border="0" alt=" " title=""/>≤<img
src="assets/x2009.gif" border="0" alt=" " title=""/>20°, except
Met and Arg at the interface and non-interface, and Glu and Gln at the interface. The
correlation coefficient for Met and Arg increased with the grid spacing increase and
reached the high level of 0.7 at the 70° grid spacing for interface, and
30° for non-interface. The two-fold difference in the critical grid spacing
indicates higher flexibility of these amino acids at the interface [24]. Since the
120° distance between two adjacent side-chain rotamers is significantly larger
than the critical grid spacing, the use of large clustering radii for bound and unbound
rotamer libraries [24] would produce similar results. </p>
<!--fig ft0--><!--fig mode=article f1--><div
class="fig iconblock ten_col whole_rhythm clearfix" id="F3" co-legend-rid="lgnd_F3"><a
class="icnblk_img figpopup" href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3479416/figure/F3/" target="figure"
rid-figpopup="F3" rid-ob="ob-F3" onclick="return startTarget(this, 'figure',1024,800)"
><img src="assets/1471-2105-13-236-3.gif" class="small-thumb" alt="Figure 3 "
title="Figure 3 " src-large="assets/1471-2105-13-236-3.jpg"/></a><div
class="icnblk_cntnt" id="lgnd_F3">
<div>
<a class="figpopup" href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3479416/figure/F3/" target="figure"
rid-figpopup="F3" rid-ob="ob-F3"
onclick="return startTarget(this, 'figure',1024,800)">Figure 3 </a>
</div>
<!--caption a4-->
<div>
<span><strong>Correlation between dihedral angle
distributions</strong><strong>.</strong> (<strong>A</strong>) Interface bound vs.
unbound, (<strong>B</strong>) non-interface bound vs. unbound, (<strong>C</strong>)
non-interface vs. interface unbound, and (<strong>D</strong>) non-interface vs.
interface bound. For each grid spacing, 100 tests were performed</span>
<b>...</b>
</div>
</div>
</div>
<!--table ft1--><!--table-wrap mode=article t1--><div
class="table-wrap iconblock ten_col whole_rhythm clearfix" id="T2"><a
href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3479416/table/T2/"
onclick="return startTarget(this, 'table',1024,800)" target="table" rid-ob="ob-T2"
rid-figpopup="T2" class="table img_link icnblk_img figpopup"><img border="0"
alt="Table 2" title="Table 2" class="small-thumb" src="assets/T2.thumb.png"
src-large="assets/T2.previmg.png"/></a><div class="icnblk_cntnt">
<div>
<a class="figpopup" href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3479416/table/T2/" target="table"
rid-figpopup="T2" rid-ob="ob-T2"
onclick="return startTarget(this, 'table',1024,800)">Table 2</a>
</div>
<!--caption a4-->
<div>
<span>The minimal grid spacing corresponding to correlation coefficient 0.7 between
bound and unbound interface/non-interface dihedral angle distribution</span>
</div>
</div>
</div>
<p id="__p29">Although the results showed high degree of similarity between the
distributions, correlation values for Met and Arg were noticeably lower than for other
amino acids. Analysis of the results for Met revealed that although the covariance of
distributions for all amino acids with three dihedral angles were the same, the standard
deviation for Met was higher (Table ), leading to the lower correlation value for Met. In
the case of Arg, although the standard deviations of Lys were twice larger than that of
Arg, the covariance of Arg was ten times smaller than that of Lys, yielding the overall
lower correlation for Arg. </p>
<!--table ft1--><!--table-wrap mode=article t1--><div
class="table-wrap iconblock ten_col whole_rhythm clearfix" id="T3"><a
href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3479416/table/T3/"
onclick="return startTarget(this, 'table',1024,800)" target="table" rid-ob="ob-T3"
rid-figpopup="T3" class="table img_link icnblk_img figpopup"><img border="0"
alt="Table 3" title="Table 3" class="small-thumb" src="assets/T3.thumb.png"
src-large="assets/T3.previmg.png"/></a><div class="icnblk_cntnt">
<div>
<a class="figpopup" href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3479416/table/T3/" target="table"
rid-figpopup="T3" rid-ob="ob-T3"
onclick="return startTarget(this, 'table',1024,800)">Table 3</a>
</div>
<!--caption a4-->
<div>
<span>Correlation between interface bound and unbound distributions for 30°
grid spacing</span>
</div>
</div>
</div>
<p id="__p31">Equation<img src="assets/x2009.gif" border="0" alt=" " title=""
/>2 was used to calculate the Manhattan distance between bound and unbound
interface/non-interface distributions. As in the case of correlation, the metric value
depended on the grid spacing, with larger steps corresponding to more coarse-grained
distributions. Thus, tests were conducted with different steps: 10°, 30°,
50°, 70°, and 90°. The distance between the distributions
decreased with the step increase (Figure 4). In most cases, the Manhattan distances for
the interface were greater than for the non-interface. The distances between interface
unbound and bound distributions for all long amino acids with three and four dihedral
angles were the largest (Figure 4A). It agrees with our previous findings that long amino
acids have higher flexibility in binding [24]. The Manhattan distance between the
probability functions was<img src="assets/x2009.gif" border="0" alt=" "
title=""/><<img src="assets/x2009.gif" border="0" alt=" "
title=""/>30% for most amino acids, starting with 50° grid spacing, except for
Met and Arg interface bound vs. unbound and non-interface vs. interface distributions. For
these distributions, the distance was<img src="assets/x2009.gif" border="0"
alt=" " title=""/><<img src="assets/x2009.gif" border="0" alt=" "
title=""/>30% at grid spacing 70°, and<img src="assets/x2009.gif"
border="0" alt=" " title=""/><<img src="assets/x2009.gif"
border="0" alt=" " title=""/>35% for Met interface bound vs. unbound and Arg bound
non-interface vs. interface. The high similarity between the DADFs at the 50° grid
spacing is a result of the small number of rotamer-to-rotamer transitions induced by
interactions across the interface or the crystal packing. Most side chains have local
readjustments (Figure 5) that do not change the rotameric state. </p>
<!--fig ft0--><!--fig mode=article f1--><div
class="fig iconblock ten_col whole_rhythm clearfix" id="F4" co-legend-rid="lgnd_F4"><a
class="icnblk_img figpopup" href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3479416/figure/F4/" target="figure"
rid-figpopup="F4" rid-ob="ob-F4" onclick="return startTarget(this, 'figure',1024,800)"
><img src="assets/1471-2105-13-236-4.gif" class="small-thumb" alt="Figure 4"
title="Figure 4" src-large="assets/1471-2105-13-236-4.jpg"/></a><div
class="icnblk_cntnt" id="lgnd_F4">
<div>
<a class="figpopup" href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3479416/figure/F4/" target="figure"
rid-figpopup="F4" rid-ob="ob-F4"
onclick="return startTarget(this, 'figure',1024,800)">Figure 4</a>
</div>
<!--caption a4-->
<div>
<span><strong>Manhattan distance between dihedral angle distributions.</strong>
(<strong>A</strong>) Interface bound vs. unbound, (<strong>B</strong>)
non-interface bound vs. unbound, (<strong>C</strong>) non-interface vs. interface
unbound, (<strong>D</strong>) non-interface vs. interface bound.</span>
</div>
</div>
</div>
<!--fig ft0--><!--fig mode=article f1--><div
class="fig iconblock ten_col whole_rhythm clearfix" id="F5" co-legend-rid="lgnd_F5"><a
class="icnblk_img figpopup" href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3479416/figure/F5/" target="figure"
rid-figpopup="F5" rid-ob="ob-F5" onclick="return startTarget(this, 'figure',1024,800)"
><img src="assets/1471-2105-13-236-5.gif" class="small-thumb" alt="Figure 5 "
title="Figure 5 " src-large="assets/1471-2105-13-236-5.jpg"/></a><div
class="icnblk_cntnt" id="lgnd_F5">
<div>
<a class="figpopup" href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3479416/figure/F5/" target="figure"
rid-figpopup="F5" rid-ob="ob-F5"
onclick="return startTarget(this, 'figure',1024,800)">Figure 5 </a>
</div>
<!--caption a4-->
<div>
<span><strong>Examples of side-chain conformational changes upon
binding</strong><strong>.</strong> (<strong>A</strong>) Immunoglobulin and
(<strong>B</strong>) alpha-chymotrypsin in the unbound (blue) and bound (magenta)
states. The core residues are shown as surface. The interface residues are shown in
bold colors. The bound</span>
<b>...</b>
</div>
</div>
</div>
</div>
<div id="__sec7" class="sec">
<h2 class="head no_bottom_margin" id="__sec7title">Conclusions</h2><p id="__p34">The
dihedral-angle distribution functions were calculated for each amino acid type for
interface and non-interface surface residues, in bound and unbound protein structures. To
generate the distribution functions, the configuration space was divided into cells by a
cubic grid. Correlation coefficients between bound and unbound interface and non-interface
distribution functions were calculated. The similarity between the distributions was also
quantified by the Manhattan distance. The results showed that all the correlation
coefficients depend on amino acid type and the grid resolution. For all amino acid types,
the correlation coefficients increased with the increase of the grid spacing. The
Manhattan distances between the distribution functions decreased accordingly. Short
residues with one or two dihedral angles had higher correlations and smaller Manhattan
distances than the longer residues. Met and Arg had the lowest correlation coefficients at
any grid spacing. The correlations between the interface and non-interface distribution
functions had a similar dependence on the grid resolution in both bound and unbound
states. The interface and non-interface difference between bound and unbound distribution
functions, induced by biological protein-protein interactions or crystal contacts,
disappeared at the 70° grid spacing for interfaces and 30° for
non-interface surface, in agreement with an average span of a side-chain rotamer. The
two-fold difference in the critical grid spacing indicates larger conformational changes
upon binding at the interface than at the rest of the surface. At the same time,
transitions between rotamers induced by interactions across the interface or the crystal
packing are rare, with most side chains having local readjustments that do not change the
rotameric state. </p>
<p id="__p35">Conformational sampling based on the side chain dihedral angle distributions
may optimize flexible docking protocols by reflecting conformational preferences of the
bound proteins. The results suggest that the site- (interface vs. non-interface) and
residue-specific grid spacing smaller than the critical values should be used in the
sampling. The minimal grid spacing (Table ) reflects intra-rotamer amino acid local
readjustments upon binding. Thus, using such steps in conformational sampling may
accelerate the flexible docking search by reflecting the size of these readjustments. </p>
</div>
<div id="__sec8" class="sec">
<h2 class="head no_bottom_margin" id="__sec8title">Competing interests</h2><p id="__p36">The
authors declare that they have no competing interests. </p>
</div>
<div id="__sec9" class="sec"><h2 class="head no_bottom_margin" id="__sec9title">Authors'
contributions</h2><p id="__p37">All authors conceived and designed the research. TK and
AMR carried out the calculations, and all authors analyzed the results. The manuscript was
drafted by TK and written/revised by all authors, who read and approved the final
manuscript. </p>
</div>
<div id="__sec10" class="sec">
<h2 class="head no_bottom_margin" id="__sec10title">Authors' information</h2><p id="__p38"
>TK is a PhD student at the United Institute of Informatics Problems, National Academy of
Sciences of Belarus and a Research Assistant at the Center for Bioinformatics, The
University of Kansas; AMR is an Assistant Research Professor at the Center for
Bioinformatics, The University of Kansas; AVT is the General Director of the United
Institute of Informatics Problems, National Academy of Sciences of Belarus; and IAV is the
Director of the Center for Bioinformatics and Professor of Bioinformatics and Molecular
Biosciences at The University of Kansas. </p>
</div>
<div id="__sec11" class="bk-sec"><h2 class="head no_bottom_margin" id="__sec11title"
>Acknowledgements</h2><!--back--><p id="__p39">This study was supported by grant
R01GM074255 from the NIH. </p>
</div>
<div id="__ffn_sec" class="sec">
<h2 class="head no_bottom_margin" id="__ffn_sectitle">Article information</h2><div
class="fm-sec">
<div class="fm-citation half_rhythm no_top_margin clearfix">
<div class="small">
<div class="inline_block nine_col va_top">
<div>
<div>
<span class="citation-version"/><span class="citation-abbreviation">BMC
Bioinformatics. </span><span class="citation-publication-date">2012;
</span><span class="citation-volume">13</span><span class="citation-issue"
/><span class="citation-flpages">: 236. </span>
</div>
<div>
<span class="fm-vol-iss-date">Published online 2012 September 17. </span>
<span class="doi">doi:  <a
href="http://dx.doi.org/10.1186%2F1471-2105-13-236" target="pmc_ext"
onclick="focuswin('pmc_ext')">10.1186/1471-2105-13-236</a></span>
</div>
</div>
</div>
<div class="inline_block three_col va_top show-overflow align_right"><div
class="fm-citation-ids">
<div class="fm-citation-pmcid">
<span class="fm-citation-ids-label">PMCID: </span><span>PMC3479416</span>
</div>
</div>
</div>
</div>
</div>
<div class="half_rhythm">
<div class="contrib-group fm-author">
<a href="http://www.ncbi.nlm.nih.gov/sites/entrez?cmd=search&db=PubMed&term=%20Kirys%20T%5Bauth%5D"
>Tatsiana Kirys</a>,<sup>1,</sup><sup>2</sup>
<a href="http://www.ncbi.nlm.nih.gov/sites/entrez?cmd=search&db=PubMed&term=%20Ruvinsky%20AM%5Bauth%5D"
>Anatoly M Ruvinsky</a>,<sup>1</sup>
<a href="http://www.ncbi.nlm.nih.gov/sites/entrez?cmd=search&db=PubMed&term=%20Tuzikov%20AV%5Bauth%5D"
>Alexander V Tuzikov</a>,<sup>2</sup> and <a
href="http://www.ncbi.nlm.nih.gov/sites/entrez?cmd=search&db=PubMed&term=%20Vakser%20IA%5Bauth%5D">Ilya
A Vakser</a><sup><img
src="assets/corrauth.gif"
alt="corresponding author"/></sup><sup>1,</sup><sup>3</sup>
</div>
</div>
<div class="fm-panel small half_rhythm"><div class="fm-authors-info fm-panel half_rhythm">
<div class="fm-affl">
<sup>1</sup>Center for Bioinformatics, The University of Kansas, 66047, Lawrence,
KS, USA </div>
<div class="fm-affl">
<sup>2</sup>United Institute of Informatics Problems, National Academy of Sciences,
220012, Minsk, Belarus </div>
<div class="fm-affl">
<sup>3</sup>Department of Molecular Biosciences, The University of Kansas, Lawrence,
66045, KS, USA </div>
<div>
<sup><img
src="assets/corrauth.gif"
alt="corresponding author"/></sup>Corresponding author. </div>
<div>
<span class="contrib-email" id="A1">Tatsiana Kirys: <span class="e_id496200"
>tatsiana/at/ku.edu</span><script type="text/javascript" language="JavaScript"
><!--
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}
catch (e) {
}//--></script>; </span>
<span class="contrib-email" id="A2">Anatoly M Ruvinsky: <span class="e_id438667"
>ruvinsky/at/ku.edu</span><script type="text/javascript" language="JavaScript"
><!--
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initUnObscureEmail("e_id438667", '<a href="' + reverseAndReplaceString('ude.uk/ta/yksnivur:otliam', '/at/', '@') + '">' + reverseAndReplaceString('ude.uk/ta/yksnivur', '/at/', '@') + '</a>')
}
catch (e) {
}//--></script>; </span>
<span class="contrib-email" id="A3">Alexander V Tuzikov: <span class="e_id450733"
>tuzikov/at/newman.bas-net.by</span><script type="text/javascript"
language="JavaScript"
><!--
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}
catch (e) {
}//--></script>; </span>
<span class="contrib-email" id="A4">Ilya A Vakser: <span class="e_id457872"
>vakser/at/ku.edu</span><script type="text/javascript" language="JavaScript"
><!--
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}
catch (e) {
}//--></script></span>
</div>
</div>
<div class="fm-article-notes fm-panel half_rhythm">
<div class="fm-pubdate half_rhythm">Received January 23, 2012; Accepted September 11,
2012. </div>
</div>
<div class="fm-cpl-info fm-panel half_rhythm">
<div class="fm-copyright half_rhythm"><a href="http://www.ncbi.nlm.nih.gov/pmc/about/copyright.html"
>Copyright</a> ©2012 Kirys et al.; licensee BioMed Central Ltd. </div>
<div class="fm-copyright half_rhythm"> This is an Open Access article distributed
under the terms of the Creative Commons Attribution License (<a
href="http://creativecommons.org/licenses/by/2.0" target="pmc_ext"
onclick="focuswin('pmc_ext')">http://creativecommons.org/licenses/by/2.0</a>),
which permits unrestricted use, distribution, and reproduction in any medium,
provided the original work is properly cited. </div>
</div>
</div>
<h6 class="courtesy-note no_margin small">Articles from <span
class="acknowledgment-journal-title">BMC Bioinformatics</span> are provided here
courtesy of <strong>BioMed Central</strong></h6>
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</article>
<article data-type="table-wrap" id="ob-T1"><!--table-wrap mode="anchored" t5-->
<div class="table-wrap table anchored whole_rhythm" id="T1">
<h3>Table 1</h3>
<!--caption a7-->
<div class="caption">
<p id="__p11">Number of surface residues in bound and unbound proteins </p>
</div>
<div class="large_tbl"><table frame="hsides" rules="groups" border="1"
class="rendered small default_table">
<thead valign="top">
<tr>
<th align="left"><strong>Amino acid</strong></th>
<th align="center"
><strong>Interface</strong><strong>U</strong><sup><strong>a</strong></sup><strong>/B</strong><sup><strong>b</strong></sup></th>
<th align="right"><strong>Non-interface U/B</strong></th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left" valign="bottom">Ser<hr/></td>
<td align="center" valign="bottom">333/429<hr/></td>
<td align="right" valign="bottom">2409/2934<hr/></td>
</tr>
<tr>
<td align="left" valign="bottom">Val<hr/></td>
<td align="center" valign="bottom">175/259<hr/></td>
<td align="right" valign="bottom">1003/1116<hr/></td>
</tr>
<tr>
<td align="left" valign="bottom">Thr<hr/></td>
<td align="center" valign="bottom">321/406<hr/></td>
<td align="right" valign="bottom">2021/2375<hr/></td>
</tr>
<tr>
<td align="left" valign="bottom">Cys<hr/></td>
<td align="center" valign="bottom">40/58<hr/></td>
<td align="right" valign="bottom">183/190<hr/></td>
</tr>
<tr>
<td align="left" valign="bottom">Pro<hr/></td>
<td align="center" valign="bottom">250/295<hr/></td>
<td align="right" valign="bottom">1727/2029<hr/></td>
</tr>
<tr>
<td align="left" valign="bottom">Ile<hr/></td>
<td align="center" valign="bottom">136/202<hr/></td>
<td align="right" valign="bottom">560/638<hr/></td>
</tr>
<tr>
<td align="left" valign="bottom">Leu<hr/></td>
<td align="center" valign="bottom">245/348<hr/></td>
<td align="right" valign="bottom">1095/1258<hr/></td>
</tr>
<tr>
<td align="left" valign="bottom">Asn<hr/></td>
<td align="center" valign="bottom">291/350<hr/></td>
<td align="right" valign="bottom">1902/2074<hr/></td>
</tr>
<tr>
<td align="left" valign="bottom">Asp<hr/></td>
<td align="center" valign="bottom">329/433<hr/></td>
<td align="right" valign="bottom">2448/2856<hr/></td>
</tr>
<tr>
<td align="left" valign="bottom">His<hr/></td>
<td align="center" valign="bottom">126/174<hr/></td>
<td align="right" valign="bottom">682/741<hr/></td>
</tr>
<tr>
<td align="left" valign="bottom">Phe<hr/></td>
<td align="center" valign="bottom">108/176<hr/></td>
<td align="right" valign="bottom">457/487<hr/></td>
</tr>
<tr>
<td align="left" valign="bottom">Tyr<hr/></td>
<td align="center" valign="bottom">202/296<hr/></td>
<td align="right" valign="bottom">636/718<hr/></td>
</tr>
<tr>
<td align="left" valign="bottom">Trp<hr/></td>
<td align="center" valign="bottom">63/100<hr/></td>
<td align="right" valign="bottom">187/220<hr/></td>
</tr>
<tr>
<td align="left" valign="bottom">Gln<hr/></td>
<td align="center" valign="bottom">268/357<hr/></td>
<td align="right" valign="bottom">1687/1888<hr/></td>
</tr>
<tr>
<td align="left" valign="bottom">Glu<hr/></td>