Sarah Carratt: Week 5: Difference between revisions
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Revision as of 00:58, 14 February 2011
Instructions
- First, make sure you understand which variables are the state variables (dependent variables that determine the concentrations) and which variables are parameters (e.g., rate constants).
- Simulate this system with different values for the constants and the initial concentrations of nutrients and cells. The initial nutrient level can be =0, but the constants and the initial cell population size need to be positive.
- Can you make any observations about how the system behaves? The matlab models of the enzyme kinetics may be helpful: this system has two state variables, so you’ll need x(1) and x(2), dxdt(1) and dxdt(2) as in the Michaelis‐Menten substrate/product model.
- Adapt the system to a logistic growth model. Simulate this system with different values for the constants and the initial concentrations of nutrients and cells. The initial nutrient level can be =0, but the constants and the initial cell population size need to be positive. Can you make any observations about how the system behaves?
- Suggest some additional adjustments. For example, look at the nutrient dependent growth rate in the Malthus model. Or, think about the waste products the yeast might produce. Are any of them toxic to the yeast? Where might that lead?
Student Response
Part One
STATE VARIABLES:
- n(t) = concentration of nutrient = u - (u - n0) e -Dt
- y = concentration of cells in the mixture = y0ert
PARAMETERS:
- D = 1/time= dilution rate
- u = mass or molar = feed concentration
- V = volume of mixture
- r =growth of cells
- M = an = carrying capacity of cells
POPULATION MODEL: File:SarahCarratt Population
OBSERVATIONS: I can't manage to graph the figure correctly in Matlab, and at 11:58....I give up. At this point, my options are to copy another student or admit that I have been confused since Thursday and give up.
Part Two
LOGISTIC MODEL:
OBSERVATIONS:
- (
ADJUSTMENTS:
- (
Individual Assignments
Class Assignments
Class Notes
Internal Links
| BIOL398-01/S11:Assignments | BIOL398-01/S11:People | BIOL398-01/S11:Sarah Carratt |
