Multi-dimensional correlations for gene coexpression and application to the large-scale data of Arabidopsis

Background: Recent improvements in DNA microarray techniques have made a large variety of gene expression data available in public databases. This data can be used to evaluate the strength of gene coexpression by calculating the correlation of expression patterns among different genes between many experiments. However, gene expression levels differ significantly across various tissues in higher organisms, as well as in different cellular location in eukaryotes in different cell state. Thus the usual correlation measure can only evaluate the difference of tissues or cellular localizations, and cannot adequately elucidate the functional relationship from the coexpression of genes. Method: We propose a new measure of coexpression by expanding the generally used correlation into a multidimensional one. We used principal component analyses to identify the major factors of gene expression correlation, and then re-calculate the correlation by subtracting the major components in order to remove biases cased by a few experiments. The repeated subtractions of the major components yielded a set of correlation values for each pair of genes. We observed the correlation changes when the first ten principal components were subtracted step-by-step in large-scale Arabidopsis expression data. Results: We found two extreme patterns of correlation changes, corresponding to stable and fragile coexpression. Our new indexes provided a good means to determine the functional relationships of the genes, by examining a few examples, and higher performance of Gene Ontology term prediction by using the support vector machine and the multidimensional correlation.