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Network link prediction by global silencing of indirect correlations

Nature Biotechnology volume 31, pages 720–725 (2013)Cite this article

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Abstract

Predictions of physical and functional links between cellular components are often based on correlations between experimental measurements, such as gene expression. However, correlations are affected by both direct and indirect paths, confounding our ability to identify true pairwise interactions. Here we exploit the fundamental properties of dynamical correlations in networks to develop a method to silence indirect effects. The method receives as input the observed correlations between node pairs and uses a matrix transformation to turn the correlation matrix into a highly discriminative silenced matrix, which enhances only the terms associated with direct causal links. Against empirical data for Escherichia coli regulatory interactions, the method enhanced the discriminative power of the correlations by twofold, yielding >50% predictive improvement over traditional correlation measures and 6% over mutual information. Overall this silencing method will help translate the abundant correlation data into insights about a system's interactions, with applications ranging from link prediction to inferring the dynamical mechanisms governing biological networks.

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Figure 1: Silencing indirect links.
Figure 2: Network inference in model systems.
Figure 3: Inferring regulatory interactions in E. coli.
Figure 4: Silencing in a noisy environment.
Figure 5: Performance with hidden nodes.

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References

  1. Buchanan, M., Caldarelli, G., De Los Rios, P., Rao, F. & Vendruscolo, M. (eds). Networks in Cell Biology (Cambridge University Press, 2010).

  2. Ideker, T. & Sharan, R. Protein networks in disease. Genome Res. 18, 644–652 (2008).

    Article  CAS  Google Scholar 

  3. Kann, M.G. Protein interactions and disease: computational approaches to uncover the etiology of diseases. Brief. Bioinform. 8, 333–346 (2007).

    Article  CAS  Google Scholar 

  4. Albert, R. Scale-free networks in cell biology. J. Cell Sci. 118, 4947–4957 (2005).

    Article  CAS  Google Scholar 

  5. Barabási, A.-L. & Oltvai, Z.N. Network biology: understanding the cell's functional organization. Nat. Rev. Genet. 5, 101–113 (2004).

    Article  Google Scholar 

  6. Vidal, M., Cusick, M.E. & Barabási, A.-L. Interactome networks and human disease. Cell 144, 986–998 (2011).

    Article  CAS  Google Scholar 

  7. Rual, J.F. et al. Towards a proteome-scale map of the human protein-protein interaction network. Nature 437, 1173–1178 (2005).

    Article  CAS  Google Scholar 

  8. Yu, H. et al. High-quality binary protein interaction map of the yeast interactome network. Science 322, 104–110 (2008).

    Article  CAS  Google Scholar 

  9. Braun, P. et al. An experimentally derived confidence score for binary protein-protein interactions. Nat. Methods 6, 91–97 (2009).

    Article  CAS  Google Scholar 

  10. Krogan, N.J. et al. Global landscape of protein complexes in the yeast Saccharomyces cerevisiae. Nature 440, 637–643 (2006).

    Article  CAS  Google Scholar 

  11. Costanzo, M. et al. The genetic landscape of a cell. Science 327, 425–431 (2010).

    Article  CAS  Google Scholar 

  12. Ramani, A.K. et al. A map of human protein interactions derived from co-expression of human mRNAs and their orthologs. Mol. Syst. Biol. 4, 180–195 (2008).

    Article  Google Scholar 

  13. Barzel, B. & Biham, O. Quantifying the connectivity of a network: the network correlation function method. Phys. Rev. E 80, 046104 (2009).

    Article  Google Scholar 

  14. Eisen, M.B. et al. Cluster analysis and display of genome-wide expression patterns. Proc. Natl. Acad. Sci. USA 95, 14863–14868 (1998).

    Article  CAS  Google Scholar 

  15. Butte, A.J. & Kohane, I.S. Mutual information relevance networks: functional genomic clustering using pairwise entropy measurements. Pac. Symp. Biocomput. 5, 415–426 (2000).

    Google Scholar 

  16. Margolin, A.A. et al. ARACNE: an algorithm for the reconstruction of gene regulatory networks in a mammalian cellular context. BMC Bioinformatics 7, S7 (2006).

    Article  Google Scholar 

  17. Guo, S. et al. Uncovering interactions in the frequency domain. PLoS Comput. Biol. 4, e1000087 (2008).

    Article  Google Scholar 

  18. Faith, J.J. et al. Large-scale mapping and validation of Escherichia coli transcriptional regulation from a compendium of expression profiles. PLoS Biol. 5, e8 (2007).

    Article  Google Scholar 

  19. Marbach, D. et al. Wisdom of crowds for robust gene network inference. Nat. Methods 9, 796–804 (2012).

    Article  CAS  Google Scholar 

  20. Lezon, T.R. et al. Using the principle of entropy maximization to infer genetic interaction networks from gene expression patterns. Proc. Natl. Acad. Sci. USA 103, 19033–19038 (2006).

    Article  CAS  Google Scholar 

  21. Ma, S. et al. An Arabidopsis gene network based on the graphical Gaussian model. Genome Res. 17, 1614–1625 (2007).

    Article  CAS  Google Scholar 

  22. Han, L. & Zhu, J. Using matrix of thresholding partial correlation coefficients to infer regulatory network. Biosystems 91, 158–165 (2008).

    Article  CAS  Google Scholar 

  23. Chen, L. & Zheng, S. Studying alternative splicing regulatory networks through partial correlation analysis. Genome Biol. 10, R3 (2009).

    Article  Google Scholar 

  24. Peng, J. et al. Partial correlation estimation by joint sparse regression models. J. Am. Stat. Assoc. 104, 735–746 (2009).

    Article  CAS  Google Scholar 

  25. Yuan, Y. et al. Directed Partial Correlation: inferring large-scale gene regulatory network through induced topology disruptions. PLoS ONE 6, e16835 (2011).

    Article  CAS  Google Scholar 

  26. Adamic, L.A. & Adar, E. Friends and neighbors on the web. Soc. Networks 25, 211–230 (2003).

    Article  Google Scholar 

  27. Alon, U. An Introduction to Systems Biology: Design Principles of Biological Circuits (Chapman & Hall, London, 2006).

  28. Karlebach, G. & Shamir, R. Modeling and analysis of gene regulatory networks. Nat. Rev. Mol. Cell Biol. 9, 770–780 (2008).

    Article  CAS  Google Scholar 

  29. Caldarelli, G., Capocci, A., De Los Rios, P. & Muñoz, M.A. Scale-free networks from varying vertex intrinsic fitness. Phys. Rev. Lett. 89, 258702 (2002).

    Article  CAS  Google Scholar 

  30. Liu, Y.-Y., Slotine, J.-J. & Barabási, A.-L. Observability of complex systems. Proc. Natl. Acad. Sci. USA 110, 2460–2465 (2013).

    Article  CAS  Google Scholar 

  31. Erdős, P. & Rényi, A. On the evolution of random graphs. Publications Math. Inst. Hungarian Acad. Sci. 5, 17–61 (1960).

    Google Scholar 

  32. Albert, R., Jeong, H. & Barabási, A.-L. Error and attack tolerance of complex networks. Nature 406, 378–382 (2000).

    Article  CAS  Google Scholar 

  33. Cohen, R., Erez, K., Ben-Avraham, D. & Havlin, S. Resilience of the Internet to random breakdowns. Phys. Rev. Lett. 85, 4626–4628 (2000).

    Article  CAS  Google Scholar 

  34. Bollobás, B. The Evolution of Random Graphs—the Giant Component. in Random Graphs 2nd ed. (Cambridge University Press, 2001).

  35. Stauffer, D. & Aharony, A. Introduction to Percolation Theory (CRC Press, 1994).

  36. Cohen, R. & Havlin, S. Complex Networks: Structure, Robustness and Function (Cambridge University Press, 2010).

  37. Venkatesan, K. et al. An empirical framework for binary interactome mapping. Nat. Methods 6, 83–90 (2009).

    Article  CAS  Google Scholar 

  38. Kauffman, S. The ensemble approach to understand genetic regulatory networks. Physica A 340, 733–740 (2004).

    Article  CAS  Google Scholar 

  39. Marks, D.S., Hopf, T.A. & Sander, C. Protein structure prediction from sequence variation. Nat. Biotechnol. 30, 1072–1080 (2012).

    Article  CAS  Google Scholar 

  40. Barabási, A.-L. & Albert, R. Emergence of scaling in random networks. Science 286, 509–512 (1999).

    Article  Google Scholar 

  41. Albert, R. & Barabási, A.-L. Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002).

    Article  Google Scholar 

  42. Caldarelli, G. Scale-free Networks (Oxford University Press, 2007).

Download references

Acknowledgements

We thank B. Alipanahi and B. Frey for their valuable insights, A. Sharma, F. Simini, J. Menche, S. Rabello, G. Ghoshal, Y.-Y. Liu, T. Jia, M. Pósfai, C. Song, Y.-Y. Ahn, N. Blumm, D. Wang, Z. Qu, M. Schich, D. Ghiassian, S. Gil, P. Hövel, J. Gao, M. Kitsak, M. Martino, R. Sinatra, G. Tsekenis, L. Chi, B. Gabriel, Q. Jin and Y. Li for discussions, and S.S. Aleva, S. Morrison, J. De Nicolo and A. Pawling for their support. This work was supported by the US National Institutes of Health (NIH), Center of Excellence of Genomic Science (CEGS), Grant number NIH CEGS 1P50HG4233; and the NIH, award number 1U01HL108630-01; DARPA Grant Number 11645021; DARPA Social Media in Strategic Communications project under agreement number W911NF-12-C-0028; the Network Science Collaborative Technology Alliance sponsored by the US Army Research Laboratory under agreement number NS-CTA W911NF-09-02-0053; the Office of Naval Research under agreement number N000141010968; and the Defense Threat Reduction Agency awards WMD BRBAA07-J-2-0035 and BRBAA08-Per4-C-2-0033.

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Authors and Affiliations

  1. Center for Complex Network Research and Departments of Physics, Computer Science and Biology, Northeastern University, Boston, Massachusetts, USA

    Baruch Barzel & Albert-László Barabási

  2. Center for Cancer Systems Biology, Dana-Farber Cancer Institute, Harvard Medical School, Boston, Massachusetts, USA

    Baruch Barzel & Albert-László Barabási

  3. Department of Medicine, Brigham and Women's Hospital, Harvard Medical School, Boston, Massachusetts, USA

    Albert-László Barabási

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  1. Baruch Barzel
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  2. Albert-László Barabási
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Contributions

Both authors designed the research and wrote the paper. B.B. analyzed the empirical data, and did the analytical and numerical calculations.

Corresponding author

Correspondence to Albert-László Barabási.

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The authors declare no competing financial interests.

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Barzel, B., Barabási, AL. Network link prediction by global silencing of indirect correlations. Nat Biotechnol 31, 720–725 (2013). https://doi.org/10.1038/nbt.2601

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