I've been learning about the ClipXP, ClipAP, and Lon proteases. They are proteases from the AAA+ family, which seek out proteins tagged with certain peptide sequences, unfold them, and chop them up.
But what happens when you tag a protease with its own degradation tag? For example, what if you took DNA encoding mf-Lon and added its ssrA tag to the end, and then expressed this sequence in bacteria?
Would this result in any interesting dynamics? Will the protease start trying to degrade itself like an Ouroboros? Will it get stuck trying to do so? Will we observe any interesting dynamics when we incorporate this into a gene circuit?