Alondra Vega: Week 6: Difference between revisions
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*** This differential equation tries to model the change over time of the amino acid α-ketogluterate. It shows the gain and the lost from glutamate. It also shows the loss of α-ketogluterate to the TCA cycle, denoted by C3. Again the V<sub>max</sub> shown in the formula are different, since it takes different enzymes to carry out the different processes. D denotes the dilution rate and u shows the feed concentration. | *** This differential equation tries to model the change over time of the amino acid α-ketogluterate. It shows the gain and the lost from glutamate. It also shows the loss of α-ketogluterate to the TCA cycle, denoted by C3. Again the V<sub>max</sub> shown in the formula are different, since it takes different enzymes to carry out the different processes. D denotes the dilution rate and u shows the feed concentration. | ||
**d[nitrogen]/dt = Du + [NH<sub>4</sub><sup>+</sup>] | **d[nitrogen]/dt = Du + [NH<sub>4</sub><sup>+</sup>] | ||
***For the nitrogen model, I feel that the only item that is affecting the nitrogen production is the gain of | ***For the nitrogen model, I feel that the only item that is affecting the nitrogen production is the gain of ammonium into the cell. The dilution rate and the feed concentration should also b taken into account. | ||
*The parameters are described as follows. D is the dilution rate and it is fixed. The glucose and | *The parameters are described as follows. D is the dilution rate and it is fixed. The glucose and ammonium concentrations are both included in u since it is the feed concentration. This value will change according to how much ammonium is added, since that is the treatment variable. The glucose concentration is fixed. The enzymes are the ones that carry the reactions out. for the purposes of this model we have GDA, GS, NAD-GDH, and NADPH-GDH. These enzymes are incorporated in the V<sub>max</sub> and in the k variables. That is what makes those values unique. We learned in class that V<sub>max</sub>= ke<sub>0</sub> (k times the initial amount of enzyme). | ||
*I feel that my state variables do correspond to the ''ter Schure et al.'' paper to an extent. In my differential equations I do not mention the genes that are involved in these processes and I feel that they play a key role. I am just not sure how to include them in there. I also, do not mention carbon, just | *I feel that my state variables do correspond to the ''ter Schure et al.'' paper to an extent. In my differential equations I do not mention the genes that are involved in these processes and I feel that they play a key role. I am just not sure how to include them in there. I also, do not mention carbon, just ammonium. I feel that this is appropriate since that is the item that we are trying to make conclusions and make a final conclusion on. Other than those things, I feel that I have included everything that is on the paper. | ||
{{Template:Alondra Vega}} | {{Template:Alondra Vega}} | ||
[[Category:BIOL398-01/S11]] | [[Category:BIOL398-01/S11]] | ||
Revision as of 10:34, 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).
Model Trial 1
- There are a couple of state variables of interest in our model. State variables are the "things" for a lack of a better term that change over time. For our model we will be interested in modeling what happens with nitrogen, glutamine, glutamate, and α-ketogluterate. This means that we essentially need at least four differential equations that will model these amino acids and nitrogen over time.
- The Set of differential equations.
- d[glutamine]/dt = Du - Vmax([glutamate]/k1+[glutamate])+ Vmax([glutamate]/k2+[glutamate])- C.
- This differential equation tries to describe what is happening with glutamate over time.Vmax shows the enzyme concentrations, thus it is a constant. Glutamine is "transformed" into glutamate, thus we lose some of glutamate. This is why we subtract the concentration of glutamine and we try to take into account the enzyme production that goes into play by dividing it (k1). There is back procedure where glutamate will go back and help make glutamine again. We add that concentration and a different Vmax along with a different k, since it represents different enzymes. The constant C to show that glutamine is also lost to other processes in the cell. D denotes the dilution rate and u shows the feed concentration.
- d[glutamate]/dt = Du -Vmax([α-ketogluterate]/k3+[α-ketogluterate]) + Vmax([α-ketogluterate]/k4+[α-ketogluterate])- Vmax([glutamine]/k2+[glutamine])+ Vmax([glutamine]/k1+[glutamine])- C2.
- This differential equation tries to show how glutamate is changing over time. It shows the gain and loss from the amino acid α-ketogluterate, with different Vmax values since different enzymes are being used in each reaction. It also shows the effect that glutamate has on the system when only looking at glutamine. Glutamate also acts in different processes in the cell thus we must subtract what is being lost to other amino acids in the cell, this is denoted in the equation as C2. D denotes the dilution rate and u shows the feed concentration.
- d[α-ketogluterate]/dt = Du-Vmax([gluterate]/k4+[gluterate]) + Vmax([gluterate]/k3+[gluterate]) - C3.
- This differential equation tries to model the change over time of the amino acid α-ketogluterate. It shows the gain and the lost from glutamate. It also shows the loss of α-ketogluterate to the TCA cycle, denoted by C3. Again the Vmax shown in the formula are different, since it takes different enzymes to carry out the different processes. D denotes the dilution rate and u shows the feed concentration.
- d[nitrogen]/dt = Du + [NH4+]
- For the nitrogen model, I feel that the only item that is affecting the nitrogen production is the gain of ammonium into the cell. The dilution rate and the feed concentration should also b taken into account.
- d[glutamine]/dt = Du - Vmax([glutamate]/k1+[glutamate])+ Vmax([glutamate]/k2+[glutamate])- C.
- The parameters are described as follows. D is the dilution rate and it is fixed. The glucose and ammonium concentrations are both included in u since it is the feed concentration. This value will change according to how much ammonium is added, since that is the treatment variable. The glucose concentration is fixed. The enzymes are the ones that carry the reactions out. for the purposes of this model we have GDA, GS, NAD-GDH, and NADPH-GDH. These enzymes are incorporated in the Vmax and in the k variables. That is what makes those values unique. We learned in class that Vmax= ke0 (k times the initial amount of enzyme).
- I feel that my state variables do correspond to the ter Schure et al. paper to an extent. In my differential equations I do not mention the genes that are involved in these processes and I feel that they play a key role. I am just not sure how to include them in there. I also, do not mention carbon, just ammonium. I feel that this is appropriate since that is the item that we are trying to make conclusions and make a final conclusion on. Other than those things, I feel that I have included everything that is on the paper.
