Question A1 (25 marks). Your laboratory is studying a bioreaction which requires Mn²+ as a cofactor. In the presence of an excess of the cofactor, normal Michaelis-Menten kinetics is followed; however,

Mn²+ in excess causes issues with scale formation and side redox processes. Decrease of the level of the cofactor, however, slows down the process. You are testing the following rate law: max [S] r = [S] + KM 1+ Kc [Mn²+] 1 1 Kc 1 [Mn²+] [S] r max The process was studied experimentally in a chemostat and the rate data in Table 1 were collected: max [S], mM r, mM-min-¹, great excess of Mn²+ r, mM-min-¹, [Mn²+] = 3 mM + , or in linear form, Км 1 + Table 1 20 0.35 0.21 40 0.54 0.36 60 0.63 0.50 (1) Here, [S] is the concentration of the substrate and r is the rate of the reaction. 80 0.70 0.55 a) Plot the data in coordinates 1/r vs. 1/[S]. Does the effect of the cofactor on the slope and the intercept agree with eq. (1)? [7 marks] b) Use the data in excess of Mn²+ to determine the values of the Michaelis constant KM and the maximal rate max of the uninhibited reaction. c) Determine the dissociation constant Kc of the enzyme-cofactor complex. [6 marks] [6 marks] d) The enzymatic fermenter is currently operating at [S] = 65 mM and [Mn²+] = 12 mM. Your team aims at decreasing Mn²+ to 5 mM, to avoid scaling. How much will the reaction rate drop? Suggest ways to compensate for this drop. [6 marks] Do not forget the units of each quantity you calculate; mark the units on the axes of your plot.