Numerical reconstruction of gene expression measurements from mixed cell populations

We propose a procedure for numerically decomposing gene expression measurements obtained from a mixed cell population into estimates of the expression levels for the biologically distinct components of the mixture. The motivating application is the problem of obtaining the tumor cell expression signal from a tissue sample that contains tumor cells as well as various types of normal cells. We propose that a numerical restoration procedure may partially substitute for a physical fractionation when the latter is not feasible. The procedure is based on a hierarchical probability model that reflects the relationship between the underlying chemical mixture and the observable aggregate measurements. Using a Monte Carlo procedure, reconstructions of the latent signal components are obtained, along with estimates of the normal and tumor expression distributions, and estimates of the fraction of normal cells in each tissue sample. Among other uses, these values can be used to diagnose differential expression between the tumor and normal cell populations. We demonstrate the procedure using simulated data and a microarray dataset from a colon cancer study.