[1] A mechanism for enzyme-catalyzed reactions was proposed by the pair of scientists, German biochemist Leonor Michaelis and Canadian physician Maud Menten in 1913. It is based on the following behavior that many of these reactions exhibit: (a) A rate proportional to the concentration of enzyme introduced into the mixture [Eo] or CEO (b) At low reactant concentration the rate is proportional to the reactant concentration, [A] or CA (c) At high reactant concentration the rate levels off and becomes independent of reactant concentration. enzyme The duo guessed that the reaction, A B proceeded as follows: k1 A+EX k2 k3 x 2B+E where X is an intermediate made up of a complex between substrate A and the enzyme E. This is coupled with two assumptions, (i) [E.] = [E] + [X], where [E] (or Ceo) is the concentration of the enzyme initially fed into the reacting system, whereas [E] (or Ce) and [X] (or Cx) are the free enzyme and intermediate concentrations at any time, and (ii) the first reaction step in the proposed mechanism was assumed to be [x] at equilibrium such that K = [A][E] [1.1] Based on these information, trace the derivation of the rate of disappearance of A, expressed algebraically as - A = kcat CEOCA where Km = Michaelis constant. What are kcat and Kmin terms of the rate KM+CA constants, k1, k2 and k3? [1.2] Suppose that instead of the second assumption (ii) above, the assumption dx/dt = 0 was made. What would be the final rate equation, -ra? What are kcat and Km in terms of the rate constants, ki, kz and k3