A Polynomial Approach to Structural Gene Dynamics Modelling

A new approach for modelling the dynamics of gene expression from time series microarray data is presented. A modelling method based on a continuous representation of Boolean functions in the form of Zhegalkin Polynomials is proposed. Structural information known from theoretical biology like the canalizing property can be included as well as continuous measurements of gene expression levels. As an example, its applicability to yeast data is demonstrated. The complexity of the problem requires efficient methods and tools. The discrete set of all Canalizing Boolean models consistent with the measurements is large and grows exponentially as the connectivity degree of each gene increases. This set can be defined in terms of the Zhegalkin Polynomial coefficients. Moreover, this paper gives two theorems on structural properties of Canalizing Zhegalkin Polynomials. An algorithm based upon them shows how these results can be used for identifying Canalizing Boolean functions.