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 --> nitrogen | ||
#α-ketogluterate | #α-ketogluterate | ||
#glutamate | #glutamate | ||
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#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>([glutamine]/k<sub>2</sub>[glutamine])+ V<sub>max</sub>([glutamine]/k<sub>1</sub>[glutamine])- L<sub>2</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>([glutamine]/k<sub>2</sub>[glutamine])+ 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>([gluterate]/k<sub>4</sub>[gluterate]) + V<sub>max</sub>([gluterate]/k<sub>3</sub>[gluterate]) - L<sub>3</sub> | #d<sub>[α-ketogluterate]</sub>/dt = D*u-V<sub>max</sub>([gluterate]/k<sub>4</sub>[gluterate]) + V<sub>max</sub>([gluterate]/k<sub>3</sub>[gluterate]) - L<sub>3</sub> | ||
#d<sub>[nitrogen]</sub>/dt = D*u + [ | #d<sub>[nitrogen]</sub>/dt = D*u + [ammonium] - L<sub>4</sub> | ||
===Parameters for Model=== | ===Parameters for Model=== | ||
Revision as of 17:33, 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([glutamate]/k1[glutamate])+ Vmax([glutamate]/k2[glutamate])- L1
- d[glutamate]/dt = D*u -Vmax([α-ketogluterate]/k3[α-ketogluterate]) + Vmax([α-ketogluterate]/k4[α-ketogluterate])- Vmax([glutamine]/k2[glutamine])+ Vmax([glutamine]/k1[glutamine])- L2
- d[α-ketogluterate]/dt = D*u-Vmax([gluterate]/k4[gluterate]) + 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/ammonia aka carbon/nitrogen)
- ammonia 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.
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