Small binding-site clearance delays are not negligible in gene expression modeling

During the templated biopolymerization processes of transcription and translation, a macromolecular machine, either an RNA polymerase or a ribosome, binds to a specific site on the template. Due to the sizes of these enzymes, there is a waiting time before one clears the binding site and another can bind. These clearance delays are relatively short, and one might think that they could be neglected. However, in the case of transcription, these clearance delays are associated with conservation laws, resulting in surprisingly large effects on the bifurcation diagrams in models of gene expression networks. We study an example of this phenomenon in a model of a gene regulated by a non-coding RNA displaying bistability. Neglecting the binding-site clearance delays in this model can only be compensated for by making ad hoc, unphysical adjustments to the model's kinetic constants.