We describe the use of singular value decomposition in transforming gene expression data from genes/arrays space to ‘‘eigengenes’’/‘‘eigenarrays’’ space, where the eigengenes and eigenarrays are unique orthonormal superpositions of the genes and arrays, respectively.
2000, O. Alter et al., ‘‘Singular value decomposition for genome-wide expression data processing and modeling,’’ Proc. Natl. Acad. Sci. USA 97 (18), pp. 10101–10106. doi:10.1073/pnas.97.18.10101.
After normalization and sorting, the significant eigengenes and eigenarrays can be associated with observed genome-wide effects of regulators, or with measured samples, in which these regulators are overactive or underactive, respectively.
2002, T. O. Nielsen et al., ‘‘Molecular Characterisation of Soft Tissue Tumours: a Gene Expression Study,’’ Lancet 359 (9314), pp. 1301–1307. doi: 10.1016/S0140-6736(02)08270-3.
The separation of the calponin-positive leiomyosarcoma subgroup from the calponin-negative tumours was dominant, and resulted in an important eigengene and corresponding eigenarray.
2006, C. M. Li and R. R. Klevecz, ‘‘A rapid genome-scale response of the transcriptional oscillator to perturbation reveals a period-doubling path to phenotypic change,’’ Proc. Natl. Acad. Sci. USA 103 (44), pp. 16254–16259. doi: 10.1073/pnas.0604860103.
A reconstruction of the attractor can be seen in the plot of the principal eigengenes 2, 3, and 4.
2008, A. Y. Gracey et al., ‘‘Rhythms of Gene Expression in a Fluctuating Intertidal Environment,’’ Curr. Biol. 18 (19), pp. 1501-1507. doi: 10.1016/j.cub.2008.08.049.
Significantly correlated with the first eigengene were GO terms that we classified as being broadly associated with ‘‘metabolism’’ because this cluster was enriched for genes involved in the tricarboxylic acid cycle (TCA), the electron transport chain, metabolism, ATP synthesis, and protein degradation.
2012, M. J. Hawrylycz et al., ‘‘An anatomically comprehensive atlas of the adult human brain transcriptome,’’ Nature 489 (7416), pp. 391–399. doi: 10.1038/nature11405.
Each module is represented by an ‘eigengene’ corresponding to its expression pattern across structures (first left singular vector of the gene × structure matrix), and genes highly correlated with the module eigengene are called ‘hub’ genes.
2013, J. L. Padilla-Gamiño et al., ‘‘Temperature and CO2 additively regulate physiology, morphology and genomic responses of larval sea urchins, Strongylocentrotus purpuratus’’ Proc. R. Soc. B Biol. Sci. 280 (1759), article 20130155. doi: 10.1098/rspb.2013.0155.
Our gene expression data also indicate that the cystoskeleton is sensitive to shifts in temperature and pCO2: genes encoding fundamental components of the cellular cytoskeleton such as actin and alpha and beta tubulins were upregulated under elevated temperature, but downregulated under elevated pCO2 (eigengene 1).
2014, J. M. Tennessen et al., ‘‘Coordinated metabolic transitions during Drosophila embryogenesis and the onset of aerobic glycolysis’’ G3:Genes|Genomes|Genetics 4 (5), pp. 839–850. doi: 10.1534/g3.114.010652.
The second most significant pattern identified by SVD corresponds to broad upregulation of gene expression midway through embryogenesis and is strikingly similar to the coordinate induction of glycolytic genes that defines the embryonic metabolic transition (EmbMT) (eigengene pattern 2).