Sarah Carratt: Week 6: Difference between revisions
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[[Image:cycle.jpg|thumb|upright=2.5|Variables in Context]] | [[Image:cycle.jpg|thumb|upright=2.5|Variables in Context]] | ||
#ammonium | #ammonium → nitrogen | ||
#α-ketogluterate | #α-ketogluterate | ||
#glutamate | #glutamate | ||
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L<sub>1</sub>, L<sub>2</sub>, L<sub>3</sub>, L<sub>4</sub> = loss of state variable to outside factors/processes in cell and also because of the backwards conversions/cycle | L<sub>1</sub>, L<sub>2</sub>, L<sub>3</sub>, L<sub>4</sub> = loss of state variable to outside factors/processes in cell and also because of the backwards conversions/cycle | ||
#d<sub>[glutamine]</sub>/dt = D*u - V<sub>max</sub>([ | #d<sub>[glutamine]</sub>/dt = D*u - V<sub>max</sub>([glutamine]/k<sub>1</sub>[glutamine])+ V<sub>max</sub>([glutamate]/k<sub>2</sub>[glutamate])- L<sub>1</sub> | ||
#d<sub>[glutamate]</sub>/dt = D*u -V<sub>max</sub>([α-ketogluterate]/k<sub>3</sub>[α-ketogluterate]) + V<sub>max</sub>([α-ketogluterate]/k<sub>4</sub>[α-ketogluterate])- V<sub>max</sub>([ | #d<sub>[glutamate]</sub>/dt = D*u -V<sub>max</sub>([α-ketogluterate]/k<sub>3</sub>[α-ketogluterate]) + V<sub>max</sub>([α-ketogluterate]/k<sub>4</sub>[α-ketogluterate])- V<sub>max</sub>([glutamate]/k<sub>2</sub>[glutamate])+ V<sub>max</sub>([glutamine]/k<sub>1</sub>[glutamine])- L<sub>2</sub> | ||
#d<sub>[α-ketogluterate]</sub>/dt = D*u-V<sub>max</sub>([ | #d<sub>[α-ketogluterate]</sub>/dt = D*u-V<sub>max</sub>([α-ketogluterate]/k<sub>4</sub>[α-ketogluterate]) + V<sub>max</sub>([gluterate]/k<sub>3</sub>[gluterate]) - L<sub>3</sub> | ||
#d<sub>[nitrogen]</sub>/dt = D*u + [ammonium] - L<sub>4</sub> | #d<sub>[nitrogen]</sub>/dt = D*u + [ammonium] - L<sub>4</sub> | ||
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All variables are connected to ter Schure. Originally, I was confused with how to include carbon/glucose, but I believe that it is accounted for in the feed concentration and dilution. I shouldn't need a fifth equation for glucose. The major difference between my parameters and ter Schure is that I have not focused on individual enzymes. I tried to factor them into my equation but I'm not sure they can be accounted for in the same ways. | All variables are connected to ter Schure. Originally, I was confused with how to include carbon/glucose, but I believe that it is accounted for in the feed concentration and dilution. I shouldn't need a fifth equation for glucose. The major difference between my parameters and ter Schure is that I have not focused on individual enzymes. I tried to factor them into my equation but I'm not sure they can be accounted for in the same ways. | ||
==Correct Answers== | |||
STATE VARIABLES: | |||
#α-ketogluterate | |||
#Glutamate | |||
#Glutamine | |||
WHAT IS THE SYSTEM? | |||
#'''Cell''' | |||
#Chemostat Reactor | |||
UNITS: | |||
#moles/volume | |||
#moles/(volume*time) | |||
#d[glutamine]/dt = -V<sub>1</sub>([glutamine]/k<sub>1</sub>+[glutamine]) + V<sub>2</sub>([glutamate]/k<sub>2</sub>+[glutamate]) | |||
#d[glutamate]/dt = -V<sub>2</sub>([glutamate]/k<sub>2</sub>+[glutamate]) + V<sub>3</sub>([α-ketogluterate]/k<sub>3</sub>+[α-ketogluterate]) - V<sub>1</sub>([glutamine]/k<sub>1</sub>+[glutamine]) - L<sub>2</sub> | |||
#d[α-ketogluterate]/dt = D*u-V<sub>max</sub>([α-ketogluterate]/k<sub>4</sub>+[α-ketogluterate]) + V<sub>max</sub>([gluterate]/k<sub>3</sub>+[gluterate]) - L<sub>3</sub> | |||
NOTES: | |||
#D*u = source, inflow (dilution rate*feed concentration) | |||
#V<sub><nowiki>#</nowiki></sub> = enzyme level, accounts for loss, "hides amount of enzyme" (k*e<sub>0</sub>: GDA, GS, NAD-GDH, NADPH-GDH) | |||
#the "L" constant is troubling in terms of units | |||
#strategy: fit to orignial equations, E+S↔ES→E+P and E+P↔EP→E+S | |||
#α-ketogluterate has no nitrogen, glutamate has one, glutamine has two | |||
{{Template:SarahCarratt}} | {{Template:SarahCarratt}} |
Revision as of 11:18, 22 February 2011
Instructions
- List the state variables needed to model the process of interest.
- Propose at least one system of differential equations you think will model the dynamics.
- Discuss the terms in your equation(s) in order to justify your choices.
- List all parameters your model requires for numerical simulation.
- Discuss the relationship between the data in the papers by ter Schure et al and the state variables (and parameters).
Online Sources
Student Response
Variables Needed for a Model
- ammonium → nitrogen
- α-ketogluterate
- glutamate
- glutamine
These four variables are the things that we will need to watch/model as they change over time. In the image, these variables can be seen in context of nitrogen metabolism.
Differential Equations and Discussion of Terms
[] = concentration of enclosed
D = dilution rate
u = feed concentration
k1, k2, k3, k4 = rate constants
Vmax = enzyme concentrations (constant)
L1, L2, L3, L4 = loss of state variable to outside factors/processes in cell and also because of the backwards conversions/cycle
- d[glutamine]/dt = D*u - Vmax([glutamine]/k1[glutamine])+ Vmax([glutamate]/k2[glutamate])- L1
- d[glutamate]/dt = D*u -Vmax([α-ketogluterate]/k3[α-ketogluterate]) + Vmax([α-ketogluterate]/k4[α-ketogluterate])- Vmax([glutamate]/k2[glutamate])+ Vmax([glutamine]/k1[glutamine])- L2
- d[α-ketogluterate]/dt = D*u-Vmax([α-ketogluterate]/k4[α-ketogluterate]) + Vmax([gluterate]/k3[gluterate]) - L3
- d[nitrogen]/dt = D*u + [ammonium] - L4
Parameters for Model
- Vmax (k*[enzymes]0: GDA, GS, NAD-GDH, NADPH-GDH)
- D (dilution rate) CONSTANT
- u (includes glucose/ammonium aka carbon/nitrogen)
- ammonium changes
- glucose is constant
Relationship between ter Schure et al and Parameters
All variables are connected to ter Schure. Originally, I was confused with how to include carbon/glucose, but I believe that it is accounted for in the feed concentration and dilution. I shouldn't need a fifth equation for glucose. The major difference between my parameters and ter Schure is that I have not focused on individual enzymes. I tried to factor them into my equation but I'm not sure they can be accounted for in the same ways.
Correct Answers
STATE VARIABLES:
- α-ketogluterate
- Glutamate
- Glutamine
WHAT IS THE SYSTEM?
- Cell
- Chemostat Reactor
UNITS:
- moles/volume
- moles/(volume*time)
- d[glutamine]/dt = -V1([glutamine]/k1+[glutamine]) + V2([glutamate]/k2+[glutamate])
- d[glutamate]/dt = -V2([glutamate]/k2+[glutamate]) + V3([α-ketogluterate]/k3+[α-ketogluterate]) - V1([glutamine]/k1+[glutamine]) - L2
- d[α-ketogluterate]/dt = D*u-Vmax([α-ketogluterate]/k4+[α-ketogluterate]) + Vmax([gluterate]/k3+[gluterate]) - L3
NOTES:
- D*u = source, inflow (dilution rate*feed concentration)
- V# = enzyme level, accounts for loss, "hides amount of enzyme" (k*e0: GDA, GS, NAD-GDH, NADPH-GDH)
- the "L" constant is troubling in terms of units
- strategy: fit to orignial equations, E+S↔ES→E+P and E+P↔EP→E+S
- α-ketogluterate has no nitrogen, glutamate has one, glutamine has two
Individual Assignments
Class Assignments
Class Notes
Internal Links
BIOL398-01/S11:Assignments | BIOL398-01/S11:People | BIOL398-01/S11:Sarah Carratt |