1. Mathematical Model of Nitrogen Metabolism in Yeast
Lauren Magee
Lucia Ramirez
Department of Mathematics and Engineering
Loyola Marymount University
March 3, 2015

2. Outline Modeling with Yeast Model Model in relation with articles
Define all state variables, terms, and parameters involved in the system of differential equations
Analysis of steady-state
Simulation of dynamics
Model in relation with articles

3. Outline Modeling with Yeast Model Model in relation with articles
Define all state variables, terms, and parameters involved in the system of differential equations
Analysis of steady-state
Simulation of dynamics
Model in relation with articles

4. Background
The article “The Concentration of Ammonia Regulates Nitrogen Metabolism in Saccharomyces cerevisiae” from Journal of Bacteriology provides numerous models outlining the effects that changes in ammonia concentration have on the nitrogen metabolism of yeast.
Figure 1C will be compared to our own model as both consider the concentration of ammonia and the subsequent concentration of each reactant.
The article “Nitrogen regulated transcription and enzyme activities in continuous cultures of Saccaromyces cerevisiae” provides additional information on the activities of yeast in continuous cultures of difference dilution rates under nitrogen limitation.
The article focused on the changes in carbon and nitrogen fluxes and what effect the dilution rates had on the transcription of nitrogen regulating genes.

5. Central Nitrogen Metabolism Pathway
van Riel & Sontag (2006) IEEE Proc. –Syst. Biol. 153:

6. Outline Modeling with Yeast Model Model in relation with articles
Define all state variables, terms, and parameters involved in the system of differential equations
Analysis of steady-state
Simulation of dynamics
Model in relation with articles

7. Differential Equations and Variables
A + C 2B r3 B C
System of differential equations

8. Differential Equations and VariablesC r1 r2
r-1
r-2 r3 r3
db/dt =
r1a
- r-1b
- r2b
+ r-2c
+ 2r3ac

9. Steady-state Analysis
da/dt = 0,
c = (r-1 / r3)(b/a) – r1/r3
db/dt = 0,
c = r2b /(r-2 + r3a)
dc/dt = 0,
- r1/r3 c
b/a

10. Graphical Output of the Dynamic’s Simulation
All parameters equal to 1

11. Modifying r-1 parameter
Set r-1= 2

12. Outline Modeling with Yeast Model Model in relation with articles
Define all state variables, terms, and parameters involved in the system of differential equations
Analysis of steady-state
Simulation of dynamics
Model in relation with articles

13. When the Ammonium Concentration Is Increased in the Feed, Glutamate and Glutamine Increase
Ammonium flux and respiratory quotient are constant
TCA cycle

14. Discussion
"If the ammonia concentration is the regulator, this may imply that S. cerevisiae has an ammonia sensor which could be a two-component sensing system for nitrogen…"
The two component system could be referring to the two step reaction that occurs in the yeast. The first component is the reaction transforming α-ketoglutarate into glutamate and then the second component is the reaction transforming glutamate into glutamine.
The two ammonia-incorporating enzymes NAD-GDH and GS may also be relevant to a two component model as they are directly influenced by the ammonia concentration present and essential to the carry out of nitrogen metabolism.
The concept of two components could also be referring to the extracellular and intracellular concentrations of nitrogen, which both provide a unique measure. For the hypothetical ammonia sensor to run, both concentrations must be considered.

15. Summary Modeling with Yeast Model Model in relation with articles
State variables
System of Differential Equations
Terms
Parameters
Analysis of steady-state
Simulation of dynamics with graphical output
Model in relation with articles

16. Work Cited
ter Schure, E.G., Sillje, H.H.W., Verkleij, A.J., Boonstra, J., and Verrips, C.T. (1995) Journal of Bacteriology 177:
Schure, E. G. Ter, H. H. W. Sillje, L. J. R. M. Raeven, J. Boonstra, A. J. Verkleij, and C. T. Verrips. (1995) Microbiology 141.5: