Petri nets and ODE as complementary tools in analysis of signaling pathways

Abstract

Regulation of gene expression is one of the most important problems analyzed in systems biology. It involves, among other, interactions of mRNA with miRNA - a small (21-25 nt) single–stranded non–coding RNA molecule. Its main function is post-transcriptional regulation of gene expression leading to gene silencing. It is achieved either by inhibition of translation or by degradation of mRNA. The detailed mechanisms employed include inhibition of attaching the 60s ribosomal subunit, premature ribosome drop-off or inhibition of protein elongation process, cleavage of mRNA or destabilization of mRNA. Another mechanism of regulation of gene expression involves reactive oxygen species (ROS - radical and non-radical oxygen species formed by the partial reduction of oxygen) which, being released from mitochondrium cytochrome C and inducing DNA damage, induce the apoptosis pathway. ROS level can be regulated by antioxidant systems existing in a cell. This paper presents analysis of a model of gene regulation based on these molecules, in which Petri net is used to find the key reactions and, subsequently, an ODE-based model is used to verify these conclusions.