Sarah Carratt: Week 6
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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
- ammonia --> 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 + [ammonia] - L4
Parameters for Model
Relationship between ter Schure et al and Parameters
Individual Assignments
Class Assignments
Class Notes
Internal Links
BIOL398-01/S11:Assignments | BIOL398-01/S11:People | BIOL398-01/S11:Sarah Carratt |