Decoy binding dynamics were modeled using a simple model given below.
The dissociation constant of Cas9 and dCas9 binding was shown to be 0.5 nM 1. From average duration of DNA binding events, the rate of dissociation was found to be 0.01 per minute for a complete match and up to 10 for an unspecific match 1. This gives a forward reaction rate for binding of 0.02 per minute per nM. From this the effect of different starting concentrations of dCas9 is shown on the amount of repression for different copy numbers of target plasmids. Thus, with too much dCas9 the repression of the reporter gene in the presence of the target becomes too high. It could be seen that it is more useful to produce low concentrations of dCas9.
Making reporter mismatches, represented by increasing the dissociation constant, creates a more sensitive response at the cost of repressive strength. With a slightly less matched reporter sequence, the response was more sensitive but with even less matching, the amount of repression in the absence of target goes up.