Application of the fractional stable distributions for approximation of gene expression profiles

Abstract

At the present time reliably established that probability density functions of gene expression of microarray experiments possess a number of universal properties. First of all these distributions have power asymptotic and secondly the shape of these distributions are inherent for all organisms and tissues. This fact led to appearance of a number works where authors are investigating various probability distributions for approximation of empirical distributions of gene expression. Nevertheless all these distributions aren't limit distribution and aren't solution of any equations. These facts by our opinion are essential shortcoming of these probability laws. Besides, expression of individual gene aren't accidental event and it depends from expression other genes. This allows to talk about existence of genic regulatory net in the cell. In the work the class of fractional stable distributions (FSD) are described. This class of distributions is limit distribution of sum independent identical distributed random variables. These distributions have power-law asymptotic and this fact allow us to apply their for approximation of experimental densities gene expression of microarray experiments. The parameters of FSDs are statistically estimated by experimental dates and empirical density is compared whit theoretical density. In the work the algorithms of parameters estimation and simulating of FSD variables are presented. The results of such comparison allow to make conclusion that empirical densities of gene expression can be approximate by FSD.