- Supplemental material for O. Alter and G. H. Golub, "Reconstructing the Pathways of a Cellular System from Genome-Scale Signals by Using Matrix and Tensor Computations,"

- Abstract:

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 × genes network as a linear superposition of genes × 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.

- A PDF format file, readable by Adobe Acrobat Reader.

- Alter_Golub_PNAS_2005.pdf

- A PDF format file, readable by Adobe Acrobat Reader.

- Alter_Golub_PNAS_2005_Appendix.pdf

- Mathematica 5.2 code files, executable by Mathematica.

- Mathematica Notebook 1: EVD.nb
- Mathematica Notebook 2: Pseudoinverse.nb
- Mathematica Notebook 3: HOEVD.nb

- PDF format files, readable by Adobe Acrobat Reader.

- Mathematica Notebook 1: EVD.nb.pdf
- Mathematica Notebook 2: Pseudoinverse.nb.pdf
- Mathematica Notebook 3: HOEVD.nb.pdf

- Tab-delimited text format files, readable by both Mathematica and Microsoft Excel.

- Dataset 1: Cell_Cycle_Expression.txt

- Reproduced from Spellman et al.

- Dataset 2: Cycle_Genes.txt

- Reproduced from Roberts et al.

- Dataset 3: Cell_Cycle_Binding.txt
- Dataset 4: Develop_Binding.txt
- Dataset 5: Biosynthesis_Binding.txt

- Reproduced from Lee et al.