Predictor Ranking using Modified Zhegalkin Functions

Abstract

Inference of the underlying gene regulatory network structure (i.e. predictors and functions) from gene expression is an important challenge in genomics. With continuing improvements in microarray technology, the ability to measure expression levels of many genes has improved significantly, making available large amount of gene expression data for analysis. In previous chapters, all gene expressions have been assumed to be digital in nature. However, actual gene expressions (from microarrays for example) are continuous. On the other hand, many genes have been observed to exhibit switch-like or Boolean behavior. In this chapter, we utilize modified Zhegalkin polynomials to express the Boolean behavior of gene expression in an analog or continuous manner. Given gene expression data in the form of microarray measurements normalized to the unit interval, we present a method for ranking and selecting predictors which fits the data with the least mean square error according to the modified Zhegalkin function. Our methods are validated on synthetic gene expressions from a mutated mammalian cell-cycle network and then demonstrated on measured gene expressions from a melanoma network study. The results of our approach can be used to identify potential genes in future expression experiments or for possible targeted drug development experiments.