Problem 5. Autoregulated cascade: Gene X encodes a repressor that represses gene Y, which also encodes a repressor. Both X and Y negatively regulate their own promoters. (a) Draw the circuit diagram. (b). At time t=0, X begins to be produced at rate B, starting from an initial concentration of X=0. What are the dynamics of X and Y? What are the response times of X and Y? Graph X and Y. Assume logic input functions, with repression thresholds K, Kw for the action of X on its own promoter and on the Y promoter and Kw for the action of Y on its own promoter. Assume Y starts at Kyy, and X starts at 0. (c) At time t=0, production of X stops after a long period of production, and X concentration decays from an initial steady-state level. What are the dynamics of X and Y? What are the response times of X and Y? Graph X and Y