Sarah Carratt: Week 6

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).

Online Sources

• Microbiology Paper
• Bacteriology Paper

Student Response

Variables Needed for a Model

Variables in Context

1. ammonia --> nitrogen
2. α-ketogluterate
3. glutamate
4. glutamine

These four variables are the things that we will need to watch/model as they change over time. In the image, these variables can be seen in context of nitrogen metabolism.

Differential Equations and Discussion of Terms

[] = concentration of enclosed

D = dilution rate

u = feed concentration

k₁, k₂, k₃, k₄ = rate constants

V_max = enzyme concentrations (constant)

L₁, L₂, L₃, L₄ = loss of state variable to outside factors/processes in cell and also because of the backwards conversions/cycle

1. d_[glutamine]/dt = D*u - V_max([glutamate]/k₁+[glutamate])+ V_max([glutamate]/k₂+[glutamate])- L₁
2. d_[glutamate]/dt = D*u -V_max([α-ketogluterate]/k₃+[α-ketogluterate]) + V_max([α-ketogluterate]/k₄+[α-ketogluterate])- V_max([glutamine]/k₂+[glutamine])+ V_max([glutamine]/k₁+[glutamine])- L₂
3. d_{[α-ketogluterate]}/dt = D*u-V_max([gluterate]/k₄+[gluterate]) + V_max([gluterate]/k₃+[gluterate]) - L₃
4. d_[nitrogen]/dt = D*u + [ammonia] - L₄

Parameters for Model

1. V_max (k*[enzymes]₀: GDA, GS, NAD-GDH, NADPH-GDH)
2. D (dilution rate) CONSTANT
3. u (includes glucose/ammonia aka carbon/nitrogen)
   1. ammonia changes
   2. glucose is constant

Navigation Guide

Individual Assignments

Sarah Carratt: Week 2	Sarah Carratt: Week 6	Sarah Carratt: Week 11
Sarah Carratt: Week 3	Sarah Carratt: Week 7	Sarah Carratt: Week 12
Sarah Carratt: Week 4	Sarah Carratt: Week 8	Sarah Carratt: Week 13
Sarah Carratt: Week 5	Sarah Carratt: Week 9	Sarah Carratt: Week 14

Class Assignments

Shared Journal: Week 1	Shared Journal: Week 6	Shared Journal: Week 11
Shared Journal: Week 2	Shared Journal: Week 7	Shared Journal: Week 12
Shared Journal: Week 3	Shared Journal: Week 8	Shared Journal: Week 13
Shared Journal: Week 4	Shared Journal: Week 9	Shared Journal: Week 14
Shared Journal: Week 5	Shared Journal: Week 10

Class Notes

Sarah Carratt_1.18.11	Sarah Carratt_2.3.11	Sarah Carratt_2.22.11
Sarah Carratt_1.20.11	Sarah Carratt_2.8.11	Sarah Carratt_2.24.11
Sarah Carratt_1.25.11	Sarah Carratt_2.10.11	Sarah Carratt_3.1.11
Sarah Carratt_1.27.11	Sarah Carratt_2.15.11	Sarah Carratt_3.3.11
Sarah Carratt_2.1.11	Sarah Carratt_2.17.11	Sarah Carratt_3.8.11

Internal Links

BIOL398-01/S11:Assignments

BIOL398-01/S11:People

BIOL398-01/S11:Sarah Carratt