Orly Alter

We describe the use of singular value decomposition in transforming genome-wide expression data from genes x arrays space to reduced diagonalized "eigengenes" x "eigenarrays" space, where the eigengenes (or eigenarrays) are unique orthonormal superpositions of the genes (or arrays). Normalizing the data by filtering out the eigengenes (and eigenarrays) that are inferred to represent noise or experimental artifacts enables meaningful comparison of the expression of different genes across different arrays in different experiments. Sorting the data according to the eigengenes and eigenarrays gives a global picture of the dynamics of gene expression, in which individual genes and arrays appear to be classified into groups of similar regulation and function, or similar cellular state and biological phenotype, respectively. 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.

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.

We describe the use of a higher-order singular value decomposition (HOSVD) in transforming a data tensor of genes × “ x -settings,” that is, different settings of the experimental variable x × “ y -settings,” which tabulates DNA microarray data from different studies, to a “core tensor” of “eigenarrays” × “ x -eigengenes” × “ y -eigengenes.” Reformulating this multilinear HOSVD such that it decomposes the data tensor into a linear superposition of all outer products of an eigenarray, an x - and a y -eigengene, that is, rank-1 “subtensors,” we define the significance of each subtensor in terms of the fraction of the overall information in the data tensor that it captures. We illustrate this HOSVD with an integration of genome-scale mRNA expression data from three yeast cell cycle time courses, two of which are under exposure to either hydrogen peroxide or menadione. We find that significant subtensors represent independent biological programs or experimental phenomena. The picture that emerges suggests that the conserved genes YKU70 , MRE11 , AIF1 , and ZWF1 , and the processes of retrotransposition, apoptosis, and the oxidative pentose phosphate pathway that these genes are involved in, may play significant, yet previously unrecognized, roles in the differential effects of hydrogen peroxide and menadione on cell cycle progression. A genome-scale correlation between DNA replication initiation and RNA transcription, which is equivalent to a recently discovered correlation and might be due to a previously unknown mechanism of regulation, is independently uncovered.

Analysis of the patterns of gene expression in follicular lymphomas from 24 patients suggested that two groups of tumors might be distinguished. All patients, whose biopsies were obtained before any treatment, were treated with rituximab, a monoclonal antibody directed against the B cell antigen, CD20. Gene expression patterns in the tumors that subsequently failed to respond to rituximab appeared more similar to those of normal lymphoid tissues than to gene expression patterns of tumors from rituximab responders. These findings suggest the possibility that the response of follicular lymphoma to rituximab treatment may be predicted from the gene expression pattern of tumors.