Reconstructing the pathways of a cellular system from genome-scale signals by using matrix and tensor computations.
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.
Alter
Orly
O
Department of Biomedical Engineering and Institute for Cellular and Molecular Biology, University of Texas, Austin, TX 78712, USA.
Golub
Gene H
GH
D019295:Computational Biology / Q000379:methods*; D003198:Computer Simulation; D015966:Gene Expression Regulation, Fungal; D016681:Genome, Fungal / Q000235:genetics*; D020411:Oligonucleotide Array Sequence Analysis; D012333:RNA, Messenger / Q000235:genetics / Q000378:metabolism; D012441:Saccharomyces cerevisiae / Q000166:cytology* / Q000235:genetics*; D015398:Signal Transduction
D012333:RNA, Messenger