a genetically modified yeast is cultivated at ph

Question

A genetically modified yeast is cultivated at pH = 3.3 and temperature = 37°C). 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, rS = 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.

F (ml/h)	50	100	150	200	250	300
X1 (g DCM/l)	17.7	21.5	23.2	24.0	24.5	24.0
S1 (g glu/l)	0.036	0.089	0.171	0.320	0.667	2.40
P1 (mg prod/l)	115	75	58	48	42	36

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 m_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.