Multi-step regulation of transcription kinetics explains the non-linear relation between RNA polymerase II density and mRNA expression in Dosage Compensation

In heterogametic organisms, expression of unequal number of X chromosomes in males and females is balanced by a process called dosage compensation. In Drosophila and mammals, dosage compensation involves nearly two-fold up-regulation of the X chromosome mediated by dosage compensation complex (DCC). Experimental studies on the role of DCC on RNA polymerase II (Pol II) transcription in mammals disclosed a non-linear relationship between Pol II densities at different transcription steps and mRNA expression. An ~20-30% increase in Pol II densities corresponds to a rough 200% increase in mRNA expression and two-fold up-regulation. Here, using a simple kinetic model of Pol II transcription calibrated by in vivo measured rate constants of different transcription steps in mammalian cells, we demonstrate how this non-linearity can be explained by multi-step transcriptional regulation. Moreover, we show how multi-step enhancement of Pol II transcription can increase mRNA production while leaving Pol II densities unaffected. Our theoretical analysis not only recapitulates experimentally observed Pol II densities upon two-fold up-regulation but also points to a limitation of inferences based on Pol II profiles from chromatin immunoprecipitation sequencing (ChIP-seq) or global run-on assays.