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Avalekander Week 11: Difference between revisions
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→Background: adding more info
Avalekander (talk | contribs) (→Background: adding more background from the paper) |
Avalekander (talk | contribs) (→Background: adding more info) |
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*Q=volumetric inflow rate (vol/time) | *Q=volumetric inflow rate (vol/time) | ||
*V= volume of the mixture in the tank (constant) | *V= volume of the mixture in the tank (constant) | ||
*y(t)= concentration of nutrients | |||
Rate of change of nutrient = inflow rate – outflow rate – rate consumed in the tank. | Rate of change of nutrient = inflow rate – outflow rate – rate consumed in the tank. | ||
*The model of consumption is called | *The model of consumption is called Michaelis-Menten: | ||
*qu= inflow rate | |||
*qy(t)= outflow rate | |||
*=qu-qy(t)-(Er(y/K + y)x(t): consumption rate/rate of metabolism | |||
*x= yeast cell concentration | |||
*E= unit conversion rate between biomass (the units of x) and nutrient concentration | |||
*r= Maximum rate of system (Vmax) | |||
*K= Nutrient concentration at which the reaction rate is half of Vmax (r) | |||
*At equilibrium the equations are set to zero | |||
*x cannot be zero though | |||
*Nutrient concentration at zero: y=qK/(r-q) | |||
*Cell concentration at zero: x=(u-y)/E | |||
*The steady state nutrient concentration is independent of the feed rate u, while the cell population depends linearly on u | |||
==Methods== | ==Methods== | ||
