Gene Regulatory Networks: The Impact of Distance between Genes

Gilles Bernot, Jean-Paul Comet, Enrico Formenti, Siamak Taati
We analyze the basic building block of gene regulation networks using a simple stochastic model. We consider a network consisting only of two interacting genes: an activator (or repressor) gene that produces proteins of type S and a target gene that is activated (or repressed, respectively) by proteins of type S. We identify the role of distance between the two interacting genes by calculating the relative density of those activator proteins that until time t have succeeded in reaching the
more » ... n reaching the vicinity of the target gene via an unbiased three-dimensional Brownian motion. The latter quantity seen as a function of time has a sigmoidal shape (like a simple delay line) that is sharper and taller when the two genes are closer to each other. This suggests an evolutionary pressure towards making the interacting genes closer to each other to make their interactions more efficient and more reliable.