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=k[C] Cells C are produced from food S according to the overall growth process cS - C. Monod's equation for the cell growth is analogous to Michaelis-Menten's for enzyme kinetics. Let us formulate a "cellular" variant of the Briggs-Haldane equation (4-18): [S]-[C] K Ky +[S]+K[C The cell plays the role of the enzyme and of the inhibiting product simultaneously. a) Find the limit of the composition of the broth at infinite times. What is the maximum yield of the process? b) Write the solution for (a) in a batch bioreactor as an explicit integral. If you do the problem on paper, there is no need to solve the integral, but solve it if you use Maple. Sketch schematically (on paper) or plot (with Maple) the change of the broth composition with time t. c) Consider a chemostat fed with substrate S; find the composition of the broth as function of the reactor space-timer. d) Derive an equation for the wash-out flow rate vand the respective Twash out of a chemostat from the rate law above, and compare it to eq. (5-19) that follows from Monod's equation. e) Let the chemostat be operated at requal to 4x twash-out. Compute the specific production rate of cells, Fey=v[C]/V, and the composition of the broth. 90 Parameter values: (C) = 0.1 g/L for the batch bioreactor, 0 g/L for the chemostat, =k[C] Cells C are produced from food S according to the overall growth process cS - C. Monod's equation for the cell growth is analogous to Michaelis-Menten's for enzyme kinetics. Let us formulate a "cellular" variant of the Briggs-Haldane equation (4-18): [S]-[C] K Ky +[S]+K[C The cell plays the role of the enzyme and of the inhibiting product simultaneously. a) Find the limit of the composition of the broth at infinite times. What is the maximum yield of the process? b) Write the solution for (a) in a batch bioreactor as an explicit integral. If you do the problem on paper, there is no need to solve the integral, but solve it if you use Maple. Sketch schematically (on paper) or plot (with Maple) the change of the broth composition with time t. c) Consider a chemostat fed with substrate S; find the composition of the broth as function of the reactor space-timer. d) Derive an equation for the wash-out flow rate vand the respective Twash out of a chemostat from the rate law above, and compare it to eq. (5-19) that follows from Monod's equation. e) Let the chemostat be operated at requal to 4x twash-out. Compute the specific production rate of cells, Fey=v[C]/V, and the composition of the broth. 90 Parameter values: (C) = 0.1 g/L for the batch bioreactor, 0 g/L for the chemostat