problem: 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) find out the enzyme concentration in the reaction mix, when the turnover number of the enzyme, k_{cat} is 250 s^{-1}.
problem: 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) find out the average cell mass yield factor, Y_{X/S} in this fermentation.
b) find out the maximum specific growth rate, μ_{MAX}, in the logarithmic growth phase.
c) find out the volumetric growth rate, dX/dt = r_{X} at time=125 min.
d) find out 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) find out the concentration of left over substrate at time = 130, again assuming that the average yield factor can be used.
problem: Continuous (chemostat) fermentation
A genetically modified yeast is cultivated at pH = 3.3 and temperature = 37^{o}C). Values of substrate flow, F, cell mass concentration, X_{1}, concentration of glucose, S_{1} (the limiting substrate component), and product concentration, P_{1}, 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, S_{0}, contains 50.0 g glu/l and no product (P_{0} = 0), and the working volume, V, is 500 ml. k_{e} = k_{d} = 0.
a) describe 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 find out these constants.
d) At D = 0.46 h^{-1} and same conditions as given above find out Y_{X/S}, r_{X}, r_{S}, r_{P}, and Y_{P/S}.