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Random matrix analysis of localization properties of gene coexpression network
Sarika Jalan1, Norbert Solymosi, Gábor Vattay
1Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, 117456, Republic of Singapore.
Summary
This study applies random matrix theory to gene coexpression networks, revealing that network properties align with random matrix predictions for bulk eigenvalues but deviate for localized ones, indicating important network nodes.
Area of Science:
- Systems Biology
- Network Analysis
- Computational Biology
Background:
- Gene coexpression networks are crucial for understanding gene function and regulation.
- Random matrix theory (RMT) provides a framework for analyzing complex systems with many interacting components.
Purpose of the Study:
- To investigate the applicability of random matrix theory to the statistical properties of gene coexpression networks.
- To identify network nodes with potential biological significance by analyzing deviations from RMT predictions.
Main Methods:
- Analysis of gene coexpression network adjacency matrix using random matrix theory.
- Calculation of nearest-neighbor spacing distribution and spectral rigidity.
- Eigenvector analysis employing the inverse participation ratio (IPR).
Main Results:
- The nearest-neighbor spacing distribution follows Gaussian orthogonal ensemble statistics.
- Spectral rigidity aligns with RMT predictions within a certain range but deviates thereafter.
- IPR analysis reveals that while bulk eigenvalues are consistent with RMT, some eigenvalues are localized, suggesting important network nodes.
Conclusions:
- Gene coexpression networks exhibit characteristics consistent with random matrix theory, particularly in their bulk spectral properties.
- Deviations from RMT predictions, especially localized eigenvalues identified via IPR, highlight potentially critical nodes within the network.
- This approach offers a novel method for identifying key regulatory elements in biological networks.
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