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Lect 9 Chemostat

# Lect 9 Chemostat - The Chemostat Read Chapter 4.2 ~ 4.6 and...

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Unformatted text preview: The Chemostat Read: Chapter 4.2 ~ 4.6 and 4.9 ~ 4.10 Mathema¡cal Models in Biology (2005), Leah E delstein-Keshet The Chemostat • An apparatus for the continuous culture of bacterial populations in a steady state. • Nutrients are supplied continuously to the culture vessel. • The cells in the vessel grow continuously on these nutrients. • Residual nutrients and cells are removed from the vessel at the same rate by an overflow, thus maintaining the culture at a constant volume. The Chemostat Your Task • Derive a mathematical model of bacteria growth in a chemostat • Use the model to design the system so that – The flow rate will not be so great as to wash out the entire culture – The nutrient replenishment is sufficiently rapid so the culture is able to grow normally Building The Model • Variables Nutrient Concentration C(t) mass/vol in growth chamber Bacteria Density N(t) #/vol in growth chamber Building The Model • Parameters Stock Nutrient C mass/vol Concentration Volume of growth V vol. Chamber Inflow/Outflow Rate F vol/time Bacteria growth rate k 1/time Yield constant 1/ α #/mass Assumptions • Growth chamber is well mixed – No spatial variations • There is a single, growth limiting nutrient • Bacteria growth rate depend on nutrient availability, that is k = k(C) • Nutrient depletion occurs continuously as result of reproduction...
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Lect 9 Chemostat - The Chemostat Read Chapter 4.2 ~ 4.6 and...

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