Bioche Problems

Cell Metabolism and Growth 1. Consider a culture of bacteria with empirical biomass formula CH1.7O0.46N0.18 (MWB = 23.6 g/mole) growing aerobically on glucose (C6H12O6). You decide to measure the yield coefficients for glucose and oxygen and find that YX/S = 85 g biomass/mole glucose; YX/O2 = 39 g biomass/mole O2. This organism secretes no appreciable amounts of product under these conditions. a. Show that the measured values of YX/S and YX/O2 are stoichiometrically consistent with each other, stating all assumptions. b. A batch culture of this organism initially contains 0.01 g of biomass inoculum and 20 mmol glucose. The culture is incubated overnight, and subsequent optical density measurements suggest that the cells are no longer growing. The total biomass in the culture is calculated to be 1.0 g. Estimate the final amount of glucose in the medium (mmol), and speculate on what caused the plateau in biomass amount.

3. Consider a batch culture of bacteria with empirical biomass formula CH1.6O0.55N0.20

(MWB = 25.2 g/mole).

The bioreactor is a closed, rigid vessel into which liquid medium containing 10 mmol glucose (C6H12O6) and an excess of ammonium sulfate is added. The headspace contained humidified air initially. After some time, during which a net growth of 0.3 g dry cell weight was achieved, the headspace gas was analyzed. After accounting for the appropriate liquid concentration of O2 in equilibrium with the headspace, it was found that a total of 15 mmol O2 was consumed. This organism secretes no appreciable amounts of product under these conditions. a. Estimate the yield coefficient of substrate, YX/S (g DCW/mole glucose) and the final amount of glucose in the medium (mmol). b. Estimate how much CO2 was produced (mmol).

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4. A bacterial culture is carried out using pyruvate (C3H4O3) as the growth substrate. The nitrogen source is composed of ammonium salts. The empirical biomass formula is CH1.8O0.5N0.17 (MWB = 24.2 g DCW/mol). a. Based on this information alone, estimate the maximum theoretical yield of biomass per mole of pyruvate (g DCW/mol). The culture described above is carried out aerobically, and no secreted products are detected. Based on measurements of CO2 concentrations in the headspace and dissolved in the medium, you determine that 45 mmol CO2 is liberated for every g DCW biomass produced. b. Estimate the actual biomass yield per mole of pyruvate (g DCW/mol). c. Explain the difference between your answers in parts a & b.

Bioreactors 1. A microorganism is cultured in a 10 L batch bioreactor, which initially contained 100 g/L growth substrate (considered to be a "high" concentration) and 0.2 g/L biomass. You are told by a colleague that the doubling time for this culture (in exponential phase) is very reproducible, with td = 1.25 hours. After 6 total hours in culture, you measure the cell density and substrate concentration: t = 6 h: x = 1.24 g/L; S = 73 g/L. Estimate: a. The maximum specific growth rate, μmax (h-1). b. The yield coefficient, YX/S (g biomass/g substrate). c. The cell density at stationary phase (g/L). d. The total culture time required to reach stationary phase (h). e. The apparent lag time, tlag (h).

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2. Consider the growth of a microorganism in batch culture, inoculated at a density of 0.1 g/L, growing on glucose as the limiting substrate with initial concentration S0 = 10 g/L. After a lag time of approximately 3 h, the culture grows exponentially, with a doubling time of 2 h. Stationary phase is reached after a total time of 14 h. Estimate: a. μmax (h-1) b. YX/S (g/g) c. The total time in culture to reach stationary phase if S0 were 2 g/L, assuming that this concentration is also sufficient to support maximal growth. 3. Consider a continuous, aerobic bacterial culture in a chemostat with sterile feed. Three different dilution rates D are tested for a glucose feed concentration Sf = 10 mM, and the biomass concentration x and glucose concentration S in the exit stream are measured. The results are as follows: D (h-1) 0.05 0.5 5

x (g/L) 0.248 0.208 0

S (mM) 0.067 1.667 10

a. Estimate the glucose yield coefficient YX/S (g biomass/mole glucose). b. Assuming Monod growth kinetics, estimate the maximum specific growth rate μmax (h-1) and the Monod constant KS (mM).

4. Under substrate-limited conditions, a microorganism exhibits the following net specific growth rate, μnet, and yield coefficient, YX/S: μnet (h-1) = 0.70 S/(0.1 + S), with S in g/L; YX/S (g DCW/g) = 0.40 The available growth medium contains 10 g/L substrate. a. When a batch bioreactor containing 100 L of the growth medium is inoculated with 1.0 g DCW of biomass, estimate the maximum cell density achieved, and the approximate time required to achieve it, after exponential growth is initiated.

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b. You decide instead to culture the microorganism in a chemostat, using the same growth medium as the (sterile) feed. Estimate the dilution rate (h-1) at which the chemostat will achieve maximum steady-state productivity of biomass. c. Calculate and compare the overall biomass productivities (g DCW/L/h) of the two scenarios in parts a & b. What other consideration will make the batch process even less productive compared to the chemostat? 5. Consider a culture of bacteria making a valuable product in a chemostat operated at steady state. The liquid feed is sterile and contains 50 mM glucose (the limiting growth substrate S). In a series of steady state runs, the dilution rate D is increased incrementally, and the cell density exiting the chemostat is measured for each: D (h-1) 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.52 0.53

x (g/L) 1.58 2.17 2.47 2.65 2.76 2.83 2.86 2.84 2.74 2.25 1.32 0

a. Explain why the cell density can increase as the flow rate is increased, as shown here with D < 0.35 h-1. b. At what dilution rate should you operate the chemostat to optimize productivity of a strictly growth-associated product? Explain the basis for your answer. c. At what dilution rate should you operate the chemostat to optimize productivity of a strictly non-growth-associated product? Explain the basis for your answer.

6. Consider cell growth in a chemostat at steady state, with sterile feed. In bench-scale experiments, it is found that the specific growth rate is inhibited at high glucose concentrations S , modeled according to the phenomenological expression μ (h-1) = 0.6S/(0.2 + S + 0.1S2), with S in g/L. 4

a. If the glucose concentration in the feed is 10 g/L, estimate the minimum dilution rate at which cell washout would occur. b. Is the dilution rate estimated in part a the highest that will support cell growth in the bioreactor? Justify and briefly explain your answer.

7. Ethanol (C2H5OH) is produced by a microorganism cultured anaerobically in a chemostat. The empirical biomass formula is CH2O0.45N0.19 under these conditions. The sterile feed contains a "high" concentration (20 mM) of glucose, an excess of ammonium salts, and no ethanol. When the dilution rate is set at 0.1 h-1, the exit stream contains 2 mM glucose and 0.45 g/L biomass. It is safe to assume that ethanol is the only secreted product. a. Determine the expected concentration of ethanol (mM) in the exit stream. b. The dilution rate chosen probably does not optimize biomass productivity. Briefly explain how you know this to be the case and speculate on why this dilution rate may have been chosen.

9. Consider the growth of a microorganism in batch culture. When the substrate concentration is high, the cell density doubles every 0.75 h, the observed substrate yield coefficient is 0.3 g DCW/g, and substrate consumption is allocated towards biosynthesis (60%), maintenance (10%), as well as product formation (30%). The product formation is strictly growth-associated. The batch reactor is inoculated with 0.01 g DCW/L and 10 g/L substrate. a. Estimate the maximum cell density and the time (after lag phase) required to achieve it. b. Determine the value of the maintenance coefficient (g substrate/g DCW-h). c. When the cell density reaches its peak value, the substrate concentration is measured and found to be 0.05 g/L. Estimate the value of the saturation constant, KS (g/L). https://www.che.ncsu.edu/haughlab/bioche_probs.html

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