Enzyme and fermentation kinetics

Question

Question: Enzyme kinetics

For an enzyme that follows Michealis-Menten kinetics, the initial velocity at different substrate concentration has been determined.

a) Determine K_M and V_MAX.

b) The experiments are replicated with addition of a reversible inhibitor (the new results are shown in below table). Determine the effect of the inhibitor on K_M and V_MAX and the type of inhibition.

c) Calculate the enzyme concentration in the reaction mix, when the turnover number of the enzyme, k_cat is 250 s^-1.

Question: Batch fermentation

For aerobic cultivation of yeast the cell mass concentration, X_t, and the concentration of the limiting substrate component (glucose), S_t, has been determined.

a) Calculate the average cell mass yield factor, Y_X/S in this fermentation.

b) Calculate the maximum specific growth rate, μ_MAX, in the logarithmic growth phase.

c) Calculate the volumetric growth rate, dX/dt = r_X at time=125 min.

d) Calculate the volumetric substrate utilization rate, r_S, and the specific substrate utilization rate, q_S, of the yeast at time = 170 min, assuming that the average yield factor can be used to determine r_S.

e) Calculate the concentration of left over substrate at time = 130, again assuming that the average yield factor can be used.
 
Question: Continuous (chemostat) fermentation

A genetically modified yeast is cultivated at pH = 3.3 and temperature = 37^oC). Values of substrate flow, F, cell mass concentration, X₁, concentration of glucose, S₁ (the limiting substrate component), and product concentration, P₁, was measures throughout fermentation. The product is a protein – not a primary metabolite – and the substrate utilization for product formation, r_S = Y_X/P,stoich . q_p . X, is so low that it can be neglected. All samples were taken after steady state had been established. The feed stream, S₀, contains 50.0 g glu/l and no product (P₀ = 0), and the working volume, V, is 500 ml. k_e = k_d = 0.

a) Explain k_e and k_d.

b) Examine if the growth if following Monod kinetics and if this is the case determine K_S and μ_MAX.

c) Examine if the substrate utilization kinetics can be expressed by growth constants Y_X/S, true and m_S and if this is the case calculate these constants.

d) At D = 0.46 h^-1 and same conditions as given above calculate Y_X/S, r_X, r_S, r_P, and Y_P/S.