Recall the Central Dogma for biology, which is depicted in simplified form in the block diagram Fig. E24.7. In this case, it is assumed that nuclear transport can be ignored. Let X denote an environmental perturbation to the system.

(a) Explain briefly the biological process denoted by G_a, G_b, G_c, and the variable Y.

(b) Find a general expression for Y(s)/X(s), that is, the overall closed-loop transfer function. It should be simplified to contain only a numerator expression and a denominator expression without additional fractions.

(c) Consider now the specific values for the biological processes: G_a = 5, G_b = 0.5/s, and G_c = 3/s. Evaluate your expression from part (b) for this case and simplify accordingly. Is the closed-loop stable?

Gp G. Ga Figure E24.7