An analytical rate expression for the kinetics of gene transcription mediated by dimeric transcription factors

To model gene transcription kinetics, empirical fitting with the Hill function or S-system is often used. In this study, we derived an analytical expression for gene transcription rates in a manner similar to that developed for enzyme kinetics to describe the kinetics of gene transcription mediated by dimeric transcription factors (TFs) such as Gcn4p, a Saccharomyces cerevisiae master gene regulator. We showed that the analytical rate expression and its parameters estimated from several sets of experimental data could accurately reproduce the experimentally measured promoter-binding activity of Gcn4p. Furthermore, the analytical rate expression allowed us to derive analytically, rather than fit empirically, the parameters of the Hill function and S-system for use in modelling transcription kinetics. We found that a plot of gene transcription rate against Gcn4p concentration gave a sigmoidal dose-response curve with a positive co-operativity Hill coefficient (approximately 1.25), in accordance with previous experimental findings on the promoter binding of dimeric TFs. The characteristics of the dose-response curve around the estimated cellular Gcn4p concentration suggest that transcription regulation is efficiently controlled under physiological conditions. This work is a useful initial step towards analytically modelling and simulating complicated gene transcription networks.