Genetic network models and statistical properties of gene expression data in knock-out experiments

It is shown here how gene knock-out experiments can be simulated in Random Boolean Networks (RBN), which are well-known simplified models of genetic networks. The results of the simulations are presented and compared with those of actual experiments in S. cerevisiae. RBN with two incoming links per node have been considered, and the Boolean functions have been chosen at random among the set of so-called canalizing functions. Genes are knocked-out (i.e. silenced) one at a time, and the variations in the expression levels of the other genes, with respect to the unperturbed case, are considered. Two important variables are defined: (i) avalanches, which measure the size of the perturbation generated by knocking out a single gene, and (ii) susceptibilities, which measure how often the expression of a given gene is modified in these experiments. A remarkable observation is that the distributions of avalanches and susceptibilities are very robust, i.e. they are very similar in different random networks; this should be contrasted with the distribution of other variables that show a high variance in RBN. Moreover, the distribution of avalanches and susceptibilities of the RBN models are close to those observed in actual experiments performed with S. cerevisiae, where the changes in gene expression levels have been recorded with DNA microarrays. These findings suggest that these distributions might be "generic" properties, common to a wide range of genetic models and real genetic networks. The importance of such generic properties is discussed.