  Systems biology studies the structure and behavior of complex gene regulatory
networks. One of its aims is to develop a quantitative understanding of the
modular components that constitute such networks. The self-regulating gene is a
type of auto regulatory genetic modules which appears in over 40% of known
transcription factors in E. coli. In this work, using the technique of Poisson
Representation, we are able to provide exact steady state solutions for this
feedback model. By using the methods of synthetic biology (P.E.M. Purnick and
Weiss, R., Nature Reviews, Molecular Cell Biology, 2009, 10: 410-422) one can
build the system itself from modules like this.
