Integrative analysis of many weighted co-expression networks using tensor computation.

Area of Science:

• Computational Biology
• Network Science
• Systems Biology

Background:

• Biological networks are rapidly accumulating, necessitating advanced integrative analysis tools.
• Existing methods often struggle with large, weighted networks, leading to information loss when dichotomizing edges.
• Analyzing weighted networks is crucial for capturing biological complexity.

Purpose of the Study:

• To develop a novel computational framework for mining recurrent heavy subgraphs in massive weighted biological networks.
• To address limitations of existing methods that primarily focus on unweighted networks.
• To enable a more comprehensive understanding of biological network organization and function.

Main Methods:

• Developed a tensor-based computational framework for heavy 3D subtensor discovery with sparse constraints.
• Employed a multi-stage, convex relaxation protocol and non-uniform edge sampling.
• Applied the method to 130 co-expression networks.

Main Results:

• Identified 11,394 recurrent heavy subgraphs, grouped into 2,810 families, representing meaningful biological modules.
• Demonstrated that recurrence in multiple networks increases the likelihood of a subgraph being biologically significant.
• Detected patterns overlooked by unweighted graph analyses and mapped gene network modules onto the phenome.
• Discovered high-order dynamic cooperativeness in protein complex and transcriptional regulatory networks.

Conclusions:

• The tensor-based framework effectively mines recurrent heavy subgraphs in weighted biological networks.
• Integrative analysis of weighted networks provides deeper biological insights than unweighted approaches.
• The identified modules and dynamic cooperativeness offer a genome-wide mapping of gene networks onto phenotypes, advancing systems biology.