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Application of information theory to feature selection in protein docking

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Abstract

In the era of structural genomics, the prediction of protein interactions using docking algorithms is an important goal. The success of this method critically relies on the identification of good docking solutions among a vast excess of false solutions. We have adapted the concept of mutual information (MI) from information theory to achieve a fast and quantitative screening of different structural features with respect to their ability to discriminate between physiological and nonphysiological protein interfaces. The strategy includes the discretization of each structural feature into distinct value ranges to optimize its mutual information. We have selected 11 structural features and two datasets to demonstrate that the MI is dimensionless and can be directly compared for diverse structural features and between datasets of different sizes. Conversion of the MI values into a simple scoring function revealed that those features with a higher MI are actually more powerful for the identification of good docking solutions. Thus, an MI-based approach allows the rapid screening of structural features with respect to their information content and should therefore be helpful for the design of improved scoring functions in future. In addition, the concept presented here may also be adapted to related areas that require feature selection for biomolecules or organic ligands.

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Acknowledgments

The authors thank Kristin Kassler and Dr. Christophe Jardin for critically reading the manuscript. The project was funded within the DFG (Deutsche Forschungsgemeinschaft) priority program (SPP 1395) by grants to JH and HS.

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Authors and Affiliations

  1. Bioinformatik, Institut für Biochemie, Friedrich-Alexander-Universität Erlangen-Nürnberg, Fahrstr. 17, 91054, Erlangen, Germany

    Olaf G. Othersen & Heinrich Sticht

  2. Lehrstuhl für Informationsübertragung, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstr. 7, 91058, Erlangen, Germany

    Arno G. Stefani & Johannes B. Huber

Authors
  1. Olaf G. Othersen
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  2. Arno G. Stefani
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  3. Johannes B. Huber
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  4. Heinrich Sticht
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Correspondence to Heinrich Sticht.

Appendix

Appendix

Proof that I ( X ; y j ) is always positive

We will show that

$$ I(X;{y_j}) = \sum\limits_{{{\text{i}} = 1}}^{{{{\text{M}}_{\text{x}}}}} {\Pr \left( {{x_i},{y_j}} \right){{\log }_2}} \frac{{\Pr \left( {{x_i},{y_j}} \right)}}{{\Pr \left( {{x_i}} \right)\Pr \left( {{y_j}} \right)}} $$

is always greater than or equal to 0. For this purpose, the log sum inequality is quoted first [16]:

$$ \sum\limits_{{i = 1}}^{n} {{a_{i}}{{\log }_{2}}\frac{{{a_{i}}}}{{{b_{i}}}} \geqslant } \left( {\sum\limits_{{i = 1}}^{n} {{a_{i}}} } \right){\log _{2}}\frac{{\sum\nolimits_{{i = 1}}^{n} {{a_{i}}} }}{{\sum\nolimits_{{i = 1}}^{n} {{b_{i}}} }}{\text{for}}\;{\text{any}}\;{a_{i}},{b_{i}} \geqslant 0,i = 1 \ldots n. $$

With a i = Pr(x i ,y j ), b i = Pr(x i )Pr(y j ) and n = M x , it follows that

$$ \begin{array}{*{20}{c}} {I\left( {X;{y_j}} \right) = \sum\limits_{{{\text{i}} = 1}}^{{{{\text{M}}_{\text{x}}}}} {\Pr \left( {{x_i},{y_j}} \right)} {{\log }_2}\frac{{\Pr \left( {{x_i},{y_j}} \right)}}{{\Pr \left( {{x_i}} \right)\Pr \left( {{y_j}} \right)}} \geqslant \left( {\sum\limits_{{i = 1}}^{{{M_x}}} {\Pr \left( {{x_i},{y_j}} \right)} } \right)\underbrace{{{{\log }_2}\frac{{\overbrace{{\sum\nolimits_{{i = 1}}^{{{M_x}}} {\Pr \left( {{x_i},{y_j}} \right)} }}^{{\Pr \left( {{y_j}} \right)}}}}{{\underbrace{{\sum\nolimits_{{i = 1}}^{{{M_x}}} {\Pr \left( {{x_i}} \right)\Pr \left( {{y_j}} \right)} }}_{{\Pr \left( {{y_j}} \right)}}}}}}_{{{{\log }_2}1 = 0}} = 0} \hfill \\ { \Rightarrow I\left( {X;{y_j}} \right) \geqslant 0} \hfill \\ \end{array}. $$

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Othersen, O.G., Stefani, A.G., Huber, J.B. et al. Application of information theory to feature selection in protein docking. J Mol Model 18, 1285–1297 (2012). https://doi.org/10.1007/s00894-011-1157-6

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