Nick Rohacz: Week 6: Difference between revisions
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==Instructions== | ==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). | |||
==State Variables== | ==State Variables== | ||
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==Differential Equations== | ==Differential Equations== | ||
#d[glutamate]/dt = Du-D[glutamate]-Vmax([a-keto]/k3+[a-keto])+Vmax([a-keto]/k4+[a-keto])- Vmax([glutamine]/k2+[glutamine])+Vmax([glutamine]/k1+[glutamine]) - X | #d[glutamate]/dt = Du-D[glutamate]-Vmax([a-keto]/k3+[a-keto])+Vmax([a-keto]/k4+[a-keto])- Vmax([glutamine]/k2+[glutamine])+Vmax([glutamine]/k1+[glutamine]) - X | ||
#d[glutamine]/dt = | #d[glutamine]/dt =-Vmax([glutamine]/k1+[glutamine])+Vmax([glutamate]/k2+[glutamate]) - X | ||
#d[a-ketoglutarate]/dt = Du-D[a-keto]-Vmax([glutarate]/k4+[glutarate])+Vmax([glutarate]/k3+[gluterate]) - X | #d[a-ketoglutarate]/dt = Du-D[a-keto]-Vmax([glutarate]/k4+[glutarate])+Vmax([glutarate]/k3+[gluterate]) - X | ||
#d[NH<sup>+</sup><sub>4</sub>]dt = Du+[NH<sub>4</sub><sup>+</sup>] | #d[NH<sup>+</sup><sub>4</sub>]dt = Du+[NH<sub>4</sub><sup>+</sup>] | ||
Revision as of 10:50, 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).
State Variables
- The state variables needed to model the process are nitrogen, glutamate, glutamine, a-ketoglutarate
Differential Equations
- d[glutamate]/dt = Du-D[glutamate]-Vmax([a-keto]/k3+[a-keto])+Vmax([a-keto]/k4+[a-keto])- Vmax([glutamine]/k2+[glutamine])+Vmax([glutamine]/k1+[glutamine]) - X
- d[glutamine]/dt =-Vmax([glutamine]/k1+[glutamine])+Vmax([glutamate]/k2+[glutamate]) - X
- d[a-ketoglutarate]/dt = Du-D[a-keto]-Vmax([glutarate]/k4+[glutarate])+Vmax([glutarate]/k3+[gluterate]) - X
- d[NH+4]dt = Du+[NH4+]
Discussion
- Differential equations follow the format, inflow - outflow - loss, Du is the loss, D[conc] is the outflow, the loss is Vmax and all following terms.
Parameters
- Parameters are D, which is dilution rate which varied, Vmax which is the volume of the chemostat, u which is the feed of nitrogen and carbon and are constant.
- k1 represents GDH1, k2 is GDH2, k3 is GLN1.
- X represents the other side reactions carried out from due to GLN3, GCN4 and other side reactions.
Relationship
- The data in the second paper focus on different parameters than in the first paper. The dilution rate is one term that was constant in the first paper but changing in the second, while the concentration of nitrogen in the feed was changing in the first and constant in the second. With the nitrogen feed constant in the second paper, the biomass did not increase as much, as in the first paper when more nitrogen resulted in more biomass up to a degree.
- After enough nitrogen was put into the feed, residual concentration was detected, however residual concentration was absent in the second paper.
Nicholas A. Rohacz 02:54, 22 February 2011 (EST)
