Biomedical Engineering Reference
In-Depth Information
Chapter 4
Predictor Ranking using Modified
Zhegalkin Functions
Inference of the underlying gene regulatory network structure (i.e. predictors and
functions) from gene expression is an important challenge in genomics. With con-
tinuing 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 mi-
croarrays 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 modi-
fied 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.
4.1
Background and Previous Work
Advances in microarray technology have allowed biologists the opportunity to mea-
sure the expression of thousands, or even tens of thousands of genes simultaneously.
This large amount of gene expression data can be analyzed for modeling and infer-
ring the gene regulatory network. Several methods have been proposed to model the
expression data, particularly Boolean networks which use binary (Boolean) repre-
sentation for gene expression. Boolean networks (B Ns) [
1
] are commonly used for
GRN inference [
2
], [
4
] and intervention [
5
], [
6
]. In the Boolean network, gene ex-
pression are binary valued, either 1 (ON) or 0 (OFF). A binary-valued representation
is used, as many genes have been observed to exhibit switch-like behavior. In the
Boolean network, gene expressions are updated at the next time point according to
