General nonlinear framework for the analysis of gene interaction via multivariate expression arrays

A cDNA microarray is a complex biochemical-optical system whose purpose is the simultaneous measurement of gene expression for thousands of genes. In this paper we propose a general statistical approach to finding association s between the expression patterns of genes via the coefficient of determina tion. This coefficient measures the degree to which the transcriptional lev els of an observed gene set can be used to improve the prediction of the tr anscriptional state of a target gene relative to the best possible predicti on in the absence of observations. The method allows incorporation of knowl edge of other conditions relevant to the prediction, such as the applicatio n of particular stimuli or the presence of inactivating gene mutations, as predictive elements affecting the expression level of a given gene. Various aspects of the method are discussed: prediction quantification, unconstrai ned prediction, constrained prediction using ternary perceptrons, and desig n of predictors given small numbers of replicated microarrays, The method i s applied to a set of genes undergoing genotoxic stress for validation acco rding to the manner in which it points toward previously known and unknown relationships, The entire procedure is supported by software that can be ap plied to large gene sets, has a number of facilities to simplify data analy sis, and provides graphics for visualizing experimental data, multiple gene interaction, and prediction logic. (C) 2000 Society of Photo-Optical Instr umentation Engineers. [S1083-3668(00)00204-5].