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

Proc Natl Acad Sci U S A. 2005 Dec 6;102(49):17559-64. doi: 10.1073/pnas.0509033102. Epub 2005 Nov 28.


We describe the use of the matrix eigenvalue decomposition (EVD) and pseudoinverse projection and a tensor higher-order EVD (HOEVD) in reconstructing the pathways that compose a cellular system from genome-scale nondirectional networks of correlations among the genes of the system. The EVD formulates a genes x genes network as a linear superposition of genes x genes decorrelated and decoupled rank-1 subnetworks, which can be associated with functionally independent pathways. The integrative pseudoinverse projection of a network computed from a "data" signal onto a designated "basis" signal approximates the network as a linear superposition of only the subnetworks that are common to both signals and simulates observation of only the pathways that are manifest in both experiments. We define a comparative HOEVD that formulates a series of networks as linear superpositions of decorrelated rank-1 subnetworks and the rank-2 couplings among these subnetworks, which can be associated with independent pathways and the transitions among them common to all networks in the series or exclusive to a subset of the networks. Boolean functions of the discretized subnetworks and couplings highlight differential, i.e., pathway-dependent, relations among genes. We illustrate the EVD, pseudoinverse projection, and HOEVD of genome-scale networks with analyses of yeast DNA microarray data.

Publication types

  • Research Support, N.I.H., Extramural
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Computational Biology / methods*
  • Computer Simulation
  • Gene Expression Regulation, Fungal
  • Genome, Fungal / genetics*
  • Oligonucleotide Array Sequence Analysis
  • RNA, Messenger / genetics
  • RNA, Messenger / metabolism
  • Saccharomyces cerevisiae / cytology*
  • Saccharomyces cerevisiae / genetics*
  • Signal Transduction


  • RNA, Messenger