Gene X encodes a repressor that represses gene Y, which alsoencodes a repressor. Both X and Y negatively regulate their ownpromoters. (a) At time t=0, X begins to be produced at rate β,starting from an initial concentration of X=0. What are thedynamics of X and Y? What are the response times of X and Y? Assumelogic input functions, with repression thresholds Kxx, Kxy for theaction of X on its own promoter and on the Y promoter and Kyy forthe action of Y on its own promoter. (b) At time t=0, production ofX stops after a long period of production, and X concentrationdecays from an initial steady-state level. What are the dynamics ofX and Y? What are the response times of X and Y?
