In this problem, you will model the transient phase of the enzyme-substrate reaction. S + E C P + E When the reaction first begins, we can assume that S = S_0 is constant. This is a good assumption when S > > E_0 and when conversion of S to P is slow, i.e. K2 < < k_ - 1. a) Write the rate equation for the complex C. b) Derive an expression for the time dependent concentration of the complex C(t) in terms of k_1, k_ - 1, k2, S_0, and E_0. Assume that the concentration of C is zero at t = 0. c) Sketch the solution C(t) vs. t d) Find C(t) at steady state, i.e. when t approaches infinity. Compare with the steady state solution that we derived in class. e) How long does it take the system to reach steady state? Assume that k_ - 1 + k_2+ k_1 S_0 = 1000 sec^-1, and that the system is essentially at steady state when the concentration is 99% of C at steady state.