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Fitting a geometric graph to a protein-protein interaction network
Desmond J Higham1, Marija Rasajski, Natasa Przulj
1Department of Mathematics, University of Strathclyde, Glasgow G1 1XH, UK.
Bioinformatics (Oxford, England)
|March 18, 2008
Summary
This study introduces a novel algorithm to embed protein-protein interaction (PPI) networks into Euclidean space, revealing a significant geometric structure. The findings support the hypothesis that PPI networks possess inherent geometric properties, aiding in understanding biological function and evolution.
Area of Science:
- Systems Biology and Bioinformatics
- Network Science
- Computational Biology
Background:
- Protein-protein interaction (PPI) networks are crucial for understanding biological function and evolution.
- Geometric random graphs have been proposed as a model for PPI networks, where connectivity relates to proximity in a metric space.
- A key challenge is to computationally test and validate the geometric properties of PPI networks.
Purpose of the Study:
- To develop and validate an algorithm for embedding protein-protein interaction networks into low-dimensional Euclidean space.
- To test the hypothesis that PPI networks exhibit geometric structure, where connectivity reflects Euclidean proximity.
- To assess the effectiveness of the embedding using Receiver Operator Characteristic (ROC) curve analysis.
Main Methods:
- Developed a network embedding algorithm based on multi-dimensional scaling.
- Utilized the square root of path length in the network as the Euclidean distance.
- The algorithm exploits sparsity for computational efficiency, with O(N^2) complexity.
Main Results:
- The algorithm successfully identified geometric structure in artificial networks, even with added noise.
- Analysis of 19 PPI networks revealed the presence of geometric effects, with 2D Euclidean space often sufficient.
- A high-confidence yeast PPI network showed strong geometric structure (ROC area of 0.89), similar to noisy geometric networks.
Conclusions:
- The results provide strong support for the hypothesis that protein-protein interaction networks possess an underlying geometric structure.
- The developed embedding algorithm is effective in detecting and quantifying this geometric property.
- This geometric perspective offers new insights into the organization and evolution of biological networks.
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