1. Nitrogen Metabolism Model Nicholas Rohacz, Student Seaver 120, Feb. 24 2011

2. Outline • Discuss purpose of Nitrogen Metabolism Model • Present state variables and explain • State differential equations and discuss • Explanation of terms used in differential equations • Discuss parameters • Graph resulting from simulation of Nitrogen Model • Trends resulting in changing of parameters • Trends (cont’d) • Discussion of modeling process

3. Purpose • The purpose of this model is to determine how the concentrations of glutamate, glutamine, and -ketoglutarate change over time. • Also how these concentrations change along with changes in the concentrations of the state variables. • The significance of this model is to show how nitrogen metabolism is affected

4. State Variables • k , shown in the equations as k1, k2, k3, k4, and k5, represent the five reaction rates for the five separate pathways. • Vmax, shown in the equations as V1, V2, V3, V4, and V5, represents the volume of the mixture, =k(n)*e0 • D represents the dilution rate, which is the flux of ammonium into the cell. • u is the feed rate, or the rate at which ammonium is pumped into the system.

5. Parameters • [mate] is the starting concentration of glutamate in the system. • [mine] is the starting concentration of glutamine in the system. • [-keto] is the starting concentration of -ketoglutarate in the system. • [NH4] is the starting concentration of ammonium in the system.

6. Differential Equations • d[mate]/dt = -V3*[mate]/(k3+[mate]) + V4*(([-keto]*[NH4])/(k4+[-keto]*[NH4])) - V2*(([mate]*[NH4])/(k2+[mate]*[NH4])) + V1*[mine]/(k1+[mine]) + V5*(([-keto]*[mine])/(k5+[-keto]*[mine])) • d[mine]/dt = -V1*[mine]/(k1+[mine]) + V2*(([mate]*[NH4])/(k2+[mate]*[NH4])) • d[-keto]/dt = -V4*(([-keto]*[NH4])/(k4+[-keto]*[NH4]) + V3*[mate]/(k3+[mate])) • d[NH4+]/dt = D*u + V1*[mine]/(k1+[mine]) + V3*[mate]/(k3+[mate]) - V2*(([mate]*[NH4])/(k2+[mate]*[NH4])) - V4*(([-keto]*[NH4])/(k4+[-keto]*[NH4]))

7. Explanation of Terms • D*u is the inflow, only used in ammonium rate. • V1*[mine]/(k1+[mine]) represents the pathway from glutamine to glutamate, produces ammonium ion. • V2*(([mate]*[NH4+])/(k2+[mate]*[NH4+])) represents the pathway from glutamate to glutamine, consumes ammonium. • V3*[mate]/(k3+[mate]) represents pathway from glutamate to -ketoglutarate, produces ammonium ion, this is a two substrate reaction. • V4*(([-keto]*[NH4+])/(k4+[-keto]*[NH4+])) represents pathway from -ketoglutarate to glutamate, consumes ammonium ion, this is a two substrate reaction. • V5*(([-keto]*[mine])/(k5+[-keto]*[mine])) represents the process where -ketoglutarate and glutamine exchange an ammonium ion • +/- represent the the production/consumption of product

8. Graph

9. Trends D=.05 => D=.29 V=1 => V=5 k=2 => k=.5

10. Trends (cont’d) u=5 => u=20 k=2 => k=.5

11. Discussion • The concentrations of glutamine and -ketoglutarate stayed relatively constant over time, even with changes in the state variables. • Glutamate increased linearly due to three pathways producing glutamate, two consuming it, essentially, 3x-2x=x. • Ammonium has a period of loss, due to the formation of the glutamate and glutamine substrate, and then one of growth, due to the backwards pathway. • Some future directions to explore would be if there was enough stress on the system would it differ in how much substrate was produced.

12. References • Not sure how to reference my own class, however, I would like to thank Dr. Dahlquist and Dr. Fitzpatrick for picture, from class on 2/17/11. URL: https://mylmuconnect.lmu.edu/webapps/portal/frameset.jsp?tab_tab_group_id=_2_1&url=%2Fwebapps%2Fblackboard%2Fexecute%2Flauncher%3Ftype%3DCourse%26id%3D_21252_1%26url%3D