Reconstructing the pathways of a cellular system from genome-scale signals by using matrix and tensor computations

Area of Science:

• Systems Biology
• Genomics
• Network Analysis

Background:

• Cellular systems involve complex gene interactions.
• Understanding these interactions requires analyzing genome-scale networks.
• Nondirectional correlation networks provide a basis for gene association studies.

Purpose of the Study:

• To reconstruct cellular pathways from genome-scale gene correlation networks.
• To develop and apply matrix eigenvalue decomposition (EVD) and higher-order EVD (HOEVD) for pathway reconstruction.
• To simulate pathway observation using pseudoinverse projection.

Main Methods:

• Matrix eigenvalue decomposition (EVD) to represent networks as superpositions of rank-1 subnetworks.
• Pseudoinverse projection to identify common subnetworks between data and basis signals.
• Comparative higher-order EVD (HOEVD) to analyze series of networks, identifying pathways and transitions.
• Discretization of subnetworks and couplings for pathway-dependent gene relation analysis.

Main Results:

• EVD identifies functionally independent pathways within gene networks.
• Pseudoinverse projection simulates observation of pathways common to different experimental signals.
• HOEVD reveals common and exclusive pathways and transitions across a series of networks.
• Boolean functions highlight differential, pathway-specific gene relationships.

Conclusions:

• EVD, pseudoinverse projection, and HOEVD are effective for reconstructing cellular pathways from genome-scale networks.
• These methods allow for the identification of independent pathways and their dynamics.
• The approach was successfully illustrated using yeast DNA microarray data, demonstrating its applicability in systems biology.