Stochastic equations for a self-regulating gene

Abstract

Expression of cellular genes is regulated by binding of transcription factors to their promoter, either activating or inhibiting transcription of a gene. Particularly interesting is the case when the expressed protein regulates its own transcription. In this paper, the features of this self-regulating process are investigated. In the presented model here, the gene can be in two states. Either a protein is bound to its promoter or not. The steady state distributions of protein during and just before switching from one state to the next state are analyzed. Moreover, a powerful numerical method based on the corresponding master equation to compute the protein distribution in the steady state is presented and compared to an already-existing method. Additionally the special case of self-regulation, in which protein can only be produced, if one of these proteins is bound to the promoter region, is analyzed. Furthermore, a self-regulating gene is compared to a similar gene, which also has two states and produces the same amount of proteins but is not regulated by its protein-product.