Sarah Carratt: Week 6: Difference between revisions

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[[Image:cycle.jpg|thumb|upright=2.5|Variables in Context]]
[[Image:cycle.jpg|thumb|upright=2.5|Variables in Context]]


#nitrogen
#ammonium → nitrogen
#α-ketogluterate
#α-ketogluterate
#glutamate
#glutamate
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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.
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.


===System of Differential Equations===
===Differential Equations and Discussion of Terms===


[] = concentration of enclosed


===Discussion of Terms===
D = dilution rate


u = feed concentration
k<sub>1</sub>, k<sub>2</sub>, k<sub>3</sub>, k<sub>4</sub> = rate constants
V<sub>max</sub> = enzyme concentrations (constant)
L<sub>1</sub>, L<sub>2</sub>, L<sub>3</sub>,  L<sub>4</sub> = loss of state variable to outside factors/processes in cell and also because of the backwards conversions/cycle
#d<sub>[glutamine]</sub>/dt = D*u - V<sub>max</sub>([glutamine]/k<sub>1</sub>[glutamine])+ V<sub>max</sub>([glutamate]/k<sub>2</sub>[glutamate])- L<sub>1</sub>
#d<sub>[glutamate]</sub>/dt = D*u -V<sub>max</sub>([α-ketogluterate]/k<sub>3</sub>[α-ketogluterate]) + V<sub>max</sub>([α-ketogluterate]/k<sub>4</sub>[α-ketogluterate])- V<sub>max</sub>([glutamate]/k<sub>2</sub>[glutamate])+ V<sub>max</sub>([glutamine]/k<sub>1</sub>[glutamine])- L<sub>2</sub>
#d<sub>[α-ketogluterate]</sub>/dt = D*u-V<sub>max</sub>([α-ketogluterate]/k<sub>4</sub>[α-ketogluterate]) + V<sub>max</sub>([gluterate]/k<sub>3</sub>[gluterate]) - L<sub>3</sub>
#d<sub>[nitrogen]</sub>/dt = D*u + [ammonium] - L<sub>4</sub>


===Parameters for Model===
===Parameters for Model===


#V<sub>max</sub> (k*[enzymes]<sub>0</sub>: GDA, GS, NAD-GDH, NADPH-GDH)
#D (dilution rate) CONSTANT
#u (includes glucose/ammonium aka carbon/nitrogen)
##ammonium changes
##glucose is constant


===Relationship between ter Schure ''et al'' and Parameters===
===Relationship between ter Schure ''et al'' and Parameters===


All variables are connected to ter Schure. Originally, I was confused with how to include carbon/glucose, but I believe that it is accounted for in the feed concentration and dilution. I shouldn't need a fifth equation for glucose. The major difference between my parameters and ter Schure is that I have not focused on individual enzymes. I tried to factor them into my equation but I'm not sure they can be accounted for in the same ways.
==Correct Answers==
STATE VARIABLES:
#α-ketogluterate
#Glutamate
#Glutamine
#Ammonium → Nitrogen
WHAT IS THE SYSTEM?
#'''Cell'''
#Chemostat Reactor
UNITS:
#moles/volume
#moles/(volume*time)
EQUATIONS:
#d[α-ketogluterate]/dt = -V<sub>4</sub>([α-ketogluterate]/k<sub>4</sub>+[α-ketogluterate]) + V<sub>3</sub>([glutamate]/k<sub>3</sub>+[glutamate])
#d[glutamine]/dt = -V<sub>1</sub>([glutamine]/k<sub>1</sub>+[glutamine]) + V<sub>2</sub>([glutamate]/k<sub>2</sub>+[glutamate])
#d[glutamate]/dt = V<sub>1</sub>([glutamine]/k<sub>1</sub>+[glutamine])- V<sub>2</sub>([glutamate][ammonium]/k<sub>2</sub>+[glutamate][ammonium]) + V<sub>3</sub>([α-ketogluterate][ammonium]/k<sub>3</sub>+[α-ketogluterate][ammonium]) - V<sub>4</sub>([glutamate]/k<sub>4</sub>+[glutamate]) + V<sub>5</sub>([α-ketogluterate][glutamine]/k<sub>5</sub>+[α-ketogluterate][glutamine])
#d[ammonium]/dt = D*u + V<sup>a</sup><sub>1</sub>([glutamine]/k<sup>a</sup><sub>1</sub>+[glutamine])+ V<sup>a</sup><sub>4</sub>([glutamate]/k<sup>a</sup><sub>4</sub>+[glutamate])
EQUATIONS WITH SIMPLE VARIABLES:
#d[A]/dt = -V<sub>4</sub>([A]/k<sub>4</sub>+[A]) + V<sub>3</sub>([B]/k<sub>3</sub>+[B])
#d[B]/dt = V<sub>1</sub>([C]/k<sub>1</sub>+[C])- V<sub>2</sub>([B][D]/k<sub>2</sub>+[B][D]) + V<sub>3</sub>([A][D]/k<sub>3</sub>+[A][D]) - V<sub>4</sub>([B]/k<sub>4</sub>+[B]) + V<sub>5</sub>([A][C]/k<sub>5</sub>+[A][C])
#d[C]/dt = -V<sub>1</sub>([C]/k<sub>1</sub>+[C]) + V<sub>2</sub>([B]/k<sub>2</sub>+[B])
#d[D]/dt = D*u + V<sup>a</sup><sub>1</sub>([C]/k<sup>a</sup><sub>1</sub>+[C])+ V<sup>a</sup><sub>4</sub>([B]/k<sup>a</sup><sub>4</sub>+[B])
A=first substrate (α-ketogluterate), B=second substrate (glutamate), C=third substrate (glutamine), D=fourth substrate (ammonium)
NOTES:
#D*u = source, inflow (dilution rate*feed concentration)
#V<sub><nowiki>#</nowiki></sub> = enzyme level, accounts for loss, "hides amount of enzyme" (k*e<sub>0</sub>: GDA, GS, NAD-GDH, NADPH-GDH)
#the "L" constant is troubling in terms of units
#strategy: fit to orignial equations, E+S↔ES→E+P and E+P↔EP→E+S
#α-ketogluterate has no nitrogen, glutamate has one, glutamine has two
#food for thought: conserved? 2 substrate model="right"? what if you set d/dt=0 to look at equilibrium? use steady state to find constants?


{{Template:SarahCarratt}}
{{Template:SarahCarratt}}

Latest revision as of 20:16, 23 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).

Online Sources

Student Response

Variables Needed for a Model

Variables in Context
  1. ammonium → 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

Vmax = 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 - Vmax([glutamine]/k1[glutamine])+ Vmax([glutamate]/k2[glutamate])- L1
  2. d[glutamate]/dt = D*u -Vmax([α-ketogluterate]/k3[α-ketogluterate]) + Vmax([α-ketogluterate]/k4[α-ketogluterate])- Vmax([glutamate]/k2[glutamate])+ Vmax([glutamine]/k1[glutamine])- L2
  3. d[α-ketogluterate]/dt = D*u-Vmax([α-ketogluterate]/k4[α-ketogluterate]) + Vmax([gluterate]/k3[gluterate]) - L3
  4. d[nitrogen]/dt = D*u + [ammonium] - L4

Parameters for Model

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

Relationship between ter Schure et al and Parameters

All variables are connected to ter Schure. Originally, I was confused with how to include carbon/glucose, but I believe that it is accounted for in the feed concentration and dilution. I shouldn't need a fifth equation for glucose. The major difference between my parameters and ter Schure is that I have not focused on individual enzymes. I tried to factor them into my equation but I'm not sure they can be accounted for in the same ways.

Correct Answers

STATE VARIABLES:

  1. α-ketogluterate
  2. Glutamate
  3. Glutamine
  4. Ammonium → Nitrogen

WHAT IS THE SYSTEM?

  1. Cell
  2. Chemostat Reactor

UNITS:

  1. moles/volume
  2. moles/(volume*time)

EQUATIONS:

  1. d[α-ketogluterate]/dt = -V4([α-ketogluterate]/k4+[α-ketogluterate]) + V3([glutamate]/k3+[glutamate])
  2. d[glutamine]/dt = -V1([glutamine]/k1+[glutamine]) + V2([glutamate]/k2+[glutamate])
  3. d[glutamate]/dt = V1([glutamine]/k1+[glutamine])- V2([glutamate][ammonium]/k2+[glutamate][ammonium]) + V3([α-ketogluterate][ammonium]/k3+[α-ketogluterate][ammonium]) - V4([glutamate]/k4+[glutamate]) + V5([α-ketogluterate][glutamine]/k5+[α-ketogluterate][glutamine])
  4. d[ammonium]/dt = D*u + Va1([glutamine]/ka1+[glutamine])+ Va4([glutamate]/ka4+[glutamate])

EQUATIONS WITH SIMPLE VARIABLES:

  1. d[A]/dt = -V4([A]/k4+[A]) + V3([B]/k3+[B])
  2. d[B]/dt = V1([C]/k1+[C])- V2([B][D]/k2+[B][D]) + V3([A][D]/k3+[A][D]) - V4([B]/k4+[B]) + V5([A][C]/k5+[A][C])
  3. d[C]/dt = -V1([C]/k1+[C]) + V2([B]/k2+[B])
  4. d[D]/dt = D*u + Va1([C]/ka1+[C])+ Va4([B]/ka4+[B])

A=first substrate (α-ketogluterate), B=second substrate (glutamate), C=third substrate (glutamine), D=fourth substrate (ammonium)

NOTES:

  1. D*u = source, inflow (dilution rate*feed concentration)
  2. V# = enzyme level, accounts for loss, "hides amount of enzyme" (k*e0: GDA, GS, NAD-GDH, NADPH-GDH)
  3. the "L" constant is troubling in terms of units
  4. strategy: fit to orignial equations, E+S↔ES→E+P and E+P↔EP→E+S
  5. α-ketogluterate has no nitrogen, glutamate has one, glutamine has two
  6. food for thought: conserved? 2 substrate model="right"? what if you set d/dt=0 to look at equilibrium? use steady state to find constants?


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
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