# Carmen E. Castaneda: Week 6

### A Quantitative Look at Nitrogen Metabolism

- List the state variables needed to model the process of interest.

The state variables needed to model a process are Nitrogen, alpha-ketoglutarate, glutamate, and glutamine.

- 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.

In the first equation, I have taken into consideration the gain due to the glutamine reaction and from the alpha-ketoglutarate and subtracted the loss due to the glutamate reaction, the alpha-ketoglutarate and loss to cell function, L. The V's in the equation has to do with the V max of each reaction.

In the second equation, we have the gain from the glutamate reaction and I subtracted the loss due to the glutamine reaction and loss to cell function, L. The V's in the equation has to do with the V max of each reaction.

In the third equation, we have the gain due to the alpha-ketoglutarate reaction and subtracted the loss due to alpha-ketoglutarate reaction. The V's in the equation has to do with the V max of each reaction.

In the fourth equation we have the gain from the glutamine reaction, glutamate reaction, and the alpha-ketoglutarate reaction and subtract the loss due to the alpha-ketoglutarate reaction and to the cell function, L. The V's in the equation has to do with the V max of each reaction.

- List all parameters your model requires for numerical simulation.

The parameters my model requires for numerical simulation are the dillution rate, ammonia intake rate, glucose intake rate. I have also used the enzymes, NADPH, NAD, GS, GDA, as parameters because although they do have an effect on the states variables their fluctuation when our system is at steady state their fluctuation is negligible.

- Discuss the relationship between the data in the papers by ter Schure
*et al*and the state variables (and parameters).

The state variables follow from the papers since these are the things that tended to fluctuate over time. Similarly from the papers we learn that the parameters do not really change over time once the system has reached steady state.