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Comparative Study
. 2003 Mar 18;100(6):3351-6.
doi: 10.1073/pnas.0530258100. Epub 2003 Mar 11.

Generalized Singular Value Decomposition for Comparative Analysis of Genome-Scale Expression Data Sets of Two Different Organisms

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Free PMC article
Comparative Study

Generalized Singular Value Decomposition for Comparative Analysis of Genome-Scale Expression Data Sets of Two Different Organisms

Orly Alter et al. Proc Natl Acad Sci U S A. .
Free PMC article

Abstract

We describe a comparative mathematical framework for two genome-scale expression data sets. This framework formulates expression as superposition of the effects of regulatory programs, biological processes, and experimental artifacts common to both data sets, as well as those that are exclusive to one data set or the other, by using generalized singular value decomposition. This framework enables comparative reconstruction and classification of the genes and arrays of both data sets. We illustrate this framework with a comparison of yeast and human cell-cycle expression data sets.

Figures

Fig 1.
Fig 1.
Yeast and human genelets. (a) Raster display of −1, the expression of 18 genelets in 18 yeast and human arrays simultaneously, centered at their array-invariant levels. (b) Bar chart of the angular distances showing 〈γ1| and 〈γ2| highly significant in the yeast data relative to the human data, 〈γ3|, 〈γ4|, 〈γ5|, 〈γ6|, 〈γ14|, 〈γ15|, and 〈γ16| almost equally significant in both data sets and 〈γ17| and 〈γ18| highly significant in the human data relative to the yeast data. All other genelets are significant in neither the yeast data nor the human data (see Appendix).
Fig 2.
Fig 2.
Line-joined graphs of the expression levels of the genelets. (a) 〈γ3| (red), 〈γ4| (blue), and 〈γ5| (green), which are associated with the common yeast and human cell-cycle gene-expression oscillations, fit dashed graphs of normalized cosines of two periods and initial phases of π/3 (red), 0 (blue), and −π/3 (green), respectively. (b) 〈γ14| (red), 〈γ15| (blue), and 〈γ16| (green), which also are associated with cell-cycle gene-expression oscillations, fit dashed graphs of normalized cosines of two and a half periods and initial phases of −π/3 (red), π/3 (blue), and 0 (green), respectively. (c) 〈γ1| (red) and 〈γ2| (blue) are associated with the exclusive yeast pheromone response, 〈γ17| (orange) and 〈γ18| (green) are associated with the exclusive human stress response, and 〈γ6| (violet) is associated with both the yeast and human transitions from synchronization response into the cell cycle.
Fig 3.
Fig 3.
Yeast (a–c) and human (d–f) expression reconstructed in the six-dimensional cell-cycle subspaces approximated by two-dimensional subspaces. (a) Yeast array expression, projected onto π/2-phase along the y axis vs. that onto 0-phase along the x axis and color-coded according to the classification of the arrays into the five cell-cycle stages: M/G1 (yellow), G1 (green), S (blue), S/G2 (red), and G2/M (orange). The dashed unit and half-unit circles outline 100% and 50% of added-up (rather than canceled-out) contributions of the six arraylets to the overall projected expression. The arrows describe the projections of the −π/3-, 0-, and π/3-phase arraylets. (b) Yeast expression of 603 cell cycle-regulated genes projected onto π/2-phase along the y axis vs. that onto 0-phase along the x axis and color-coded according to the classification by Spellman et al. (11) (c) Yeast expression of 76 cell cycle-regulated genes color-coded according to the traditional classification. (d) Human array expression color-coded according to the classification of the arrays into the five cell-cycle stages: S (blue), G2 (red), G2/M (orange), M/G1 (yellow), and G1/S (green). (e) Human expression of 750 cell cycle-regulated genes color-coded according to the classification by Whitfield et al. (12) (f) Human expression of 73 cell cycle-regulated genes color-coded according to the traditional classification; the arrows point to 16 human histones that were not classified by Whitfield et al. as cell cycle-regulated based on their overall expression.
Fig 4.
Fig 4.
Yeast (a–d) and human (e–h) expression reconstructed in the six-dimensional cell-cycle subspaces with genes sorted according to their phases in the two-dimensional subspaces that approximate them. (a) Yeast expression of the sorted 4,523 genes in the 18 arrays, centered at their gene- and array-invariant levels, showing a traveling wave of expression. (b) Yeast expression of the sorted 4,523 genes in the 18 arraylets, centered at their array-invariant levels. The expression of the arraylets |α1,3〉, |α1,4〉, |α1,5〉, |α1,14〉, |α1,15〉, and |α1,16〉 displays the sorting. (c) Yeast cell-cycle arraylet expression levels |α1,3〉 (red), |α1,4〉 (blue), and |α1,5〉 (green) fit one-period cosines of π/3 (red), 0 (blue), and −π/3 (green) initial phases. (d) Yeast cell-cycle arraylet expression levels |α1,14〉 (red), |α1,15〉 (blue), and |α1,16〉 (green) fit one-period cosines of −π/3 (red), π/3 (blue), and 0 (green) initial phases. (e) Human expression of the sorted 12,056 genes in the 18 arrays centered at their gene- and array-invariant levels showing a traveling wave of expression. (f) Human expression of the sorted 12,056 genes in the 18 arraylets centered at their array-invariant levels. The expression of the arraylets |α2,3〉, |α2,4〉, |α2,5〉, |α2,14〉, |α2,15〉 and |α2,16〉 displays the sorting. (g) Human cell-cycle arraylet expression levels |α2,3〉 (red), |α2,4〉 (blue), and |α2,5〉 (green) fit one-period cosines of π/3 (red), 0 (blue), and −π/3 (green) initial phases. (h) Human cell-cycle arraylet expression levels |α2,14〉 (red), |α2,15〉 (blue), and |α2,16〉 (green) fit one-period cosines of −π/3 (red), π/3 (blue), and 0 (green) initial phases.

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