Conor Keith Week 6: Difference between revisions

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===Problem 4===  
===Problem 4===  
*State variables:  
*State variables:  
**c=external ammonia concentration mM
**c = external ammonia concentration mM
**<math>\alpha</math>=cytosolic alpha-ketoglutarate <math>\mu</math>mol<math>\cdot</math>g<math>X^{-1}</math>
**<math>\alpha</math> = cytosolic alpha-ketoglutarate <math>\mu</math>mol<math>\cdot</math>g<math>X^{-1}</math>
**X=biomass g<math>\cdot</math>l^-1
**X = biomass g<math>\cdot</math>l^-1
===Problem 5===
===Problem 5===
*<math>\frac{d\alpha}{dt} = yr_1 - r_2 - \mu\frac{c}{c+K}</math>
*<math>\frac{d\alpha}{dt} = cr_1 - r_2 - \mu\frac{c}{c+K}</math>
*<math>\frac{dc}{dt} = D(c_0 - c) - X\mu\frac{c}{c+K}</math>
*<math>\frac{dc}{dt} = D(c_0 - c) - X\mu\frac{c}{c+K}</math>
*<math>\frac{dX}{dt} = X\mu\frac{c}{c+K} - DX</math>
*<math>\frac{dX}{dt} = X\mu\frac{c}{c+K} - DX</math>
===Problem 6===
*The alpha-ketoglutarate equation is very similar to the one used in (ter Schure et al, 1998). It models the metabolic cycle that converts ammonia to AKG to glutamate, and back to ammonia.
*<math>r_1</math> = rate of internal flux of AKG
**This rate is calculated in (ter Schure et al, 1998). This is the  rate at which ammonia is converted  into AKG
*<math>r_2</math> = rate of flux through NAD-GDH
**This determines the reaction rate of glutamate to ammonia.
*<math>\mu</math> = critical specific growth rate
**Similar to Vmax from previous models
*K = binding constant for transporters for limiting substrate (ammonia)
*<math>\mu\frac{c}{c+K}</math> = conversion factor used in previous models in previous assignments.
*D = dilution rate (hr<math>^{-1}</math>)
*<math>c_0</math> = initial amount of ammonia in reservoir


=Conclusion=  
=Conclusion=  
*I created a system of three differential equations that I believe models the behavior of cytosolic alpha-ketoglutarate after a pulse of ammonia is introduced to a chemostat environment. In the nitrogen metabolism cycle, ammonia reacts with alpha-ketoglutarate to produce glutamate. During amino acid synthesis, an ammonium ion is fixed to cytosolic AKG to produce glutamate. This leads me to believe that a pulse of ammonia will lead to higher rates of amino acid synthesis, and thus an increase of AKG to meet the demand created  by the pulse.


=Acknowledgements=  
=Acknowledgements=  
*I received assistance from Dr. Fitzpatrick and Dr. Dahlquist in class on Tuesday. Other than what was previously mentioned, this assignment was completed by me without help from an outside source.


=References=  
=References=  
*N.A.W. van Riel, M.L.F. Giuseppin, E.G. TerSchure, C.T. Verrips, A Structured, Minimal parameter Model of the Central Nitrogen Metabolism in Saccharomyces cerevisiae: the Prediction of the Behaviour of Mutants, Journal of Theoretical Biology, Volume 191, Issue 4, 1998, Pages 397-414, ISSN 0022-5193, http://dx.doi.org/10.1006/jtbi.1997.0600.
(http://www.sciencedirect.com/science/article/pii/S0022519397906007)
*N.A.W. van Riel, M.L.F. Giuseppin, C.T. Verrips, Dynamic Optimal Control of Homeostasis: An Integrative System Approach for Modeling of the Central Nitrogen Metabolism in Saccharomyces cerevisiae, Metabolic Engineering, Volume 2, Issue 1, 2000, Pages 49-68, ISSN 1096-7176, http://dx.doi.org/10.1006/mben.1999.0137.
(http://www.sciencedirect.com/science/article/pii/S1096717699901374)
*ter Schure, E. G., Silljé, H. H., Raeven, L. J., Boonstra, J., Verkleij, A. J., & Verrips, C. T. (1995). Nitrogen-regulated transcription and enzyme activities in continuous cultures of Saccharomyces cerevisiae. Microbiology, 141(5), 1101-1108, DOI: 10.1099/13500872-141-5-1101.
*[[BIOL398-05/S17:Week 6|Week 6 Assignment]]
[[User:Conor Keith|Conor Keith]] 01:17, 23 February 2017 (EST)


{{Template:Conor Keith}}
{{Template:Conor Keith}}

Latest revision as of 23:17, 22 February 2017

Purpose

  • The purpose of this assignment is to construct a hypothesis regarding the effect of ammonia feed rate on a quantity of interest. The quantity of interest in my case is cytosolic alpha-ketoglutarate.

Workflow

  • For this assignment, I read the two articles by van Riel et al, and the article by ter Schure et al. I took notes as I read the papers, trying to find a connection between the 40 mM ammonia pulse used in the experiment and cytosolic alpha-ketoglutarate. I noticed that levels of cytosolic alpha-ketoglutarate increased with the ammonia pulse. I then constructed a system of differential equations that I believe model the connection between the ammonia pulse and cytosolic alpha-ketoglutarate. The system contains three equations; one describing the change in ammonia concentration, one describing the change in biomass, and one describing the change in cytosolic alpha-ketoglutarate.

Results

Problem 1

  • I chose the central nitrogen metabolism process project for my model.

Problem 2

  • I read all 3 of the papers under the central nitrogen metabolism process section. Most of my focus was centered on the Structured, Minimal Parameter paper.

Problem 3

  • Hypothesis: An increase in ammonia feed concentration via ammonia pulse will result in higher levels of cytosolic alpha-ketoglutarate.

Problem 4

  • State variables:
    • c = external ammonia concentration mM
    • [math]\displaystyle{ \alpha }[/math] = cytosolic alpha-ketoglutarate [math]\displaystyle{ \mu }[/math]mol[math]\displaystyle{ \cdot }[/math]g[math]\displaystyle{ X^{-1} }[/math]
    • X = biomass g[math]\displaystyle{ \cdot }[/math]l^-1

Problem 5

  • [math]\displaystyle{ \frac{d\alpha}{dt} = cr_1 - r_2 - \mu\frac{c}{c+K} }[/math]
  • [math]\displaystyle{ \frac{dc}{dt} = D(c_0 - c) - X\mu\frac{c}{c+K} }[/math]
  • [math]\displaystyle{ \frac{dX}{dt} = X\mu\frac{c}{c+K} - DX }[/math]

Problem 6

  • The alpha-ketoglutarate equation is very similar to the one used in (ter Schure et al, 1998). It models the metabolic cycle that converts ammonia to AKG to glutamate, and back to ammonia.
  • [math]\displaystyle{ r_1 }[/math] = rate of internal flux of AKG
    • This rate is calculated in (ter Schure et al, 1998). This is the rate at which ammonia is converted into AKG
  • [math]\displaystyle{ r_2 }[/math] = rate of flux through NAD-GDH
    • This determines the reaction rate of glutamate to ammonia.
  • [math]\displaystyle{ \mu }[/math] = critical specific growth rate
    • Similar to Vmax from previous models
  • K = binding constant for transporters for limiting substrate (ammonia)
  • [math]\displaystyle{ \mu\frac{c}{c+K} }[/math] = conversion factor used in previous models in previous assignments.
  • D = dilution rate (hr[math]\displaystyle{ ^{-1} }[/math])
  • [math]\displaystyle{ c_0 }[/math] = initial amount of ammonia in reservoir

Conclusion

  • I created a system of three differential equations that I believe models the behavior of cytosolic alpha-ketoglutarate after a pulse of ammonia is introduced to a chemostat environment. In the nitrogen metabolism cycle, ammonia reacts with alpha-ketoglutarate to produce glutamate. During amino acid synthesis, an ammonium ion is fixed to cytosolic AKG to produce glutamate. This leads me to believe that a pulse of ammonia will lead to higher rates of amino acid synthesis, and thus an increase of AKG to meet the demand created by the pulse.

Acknowledgements

  • I received assistance from Dr. Fitzpatrick and Dr. Dahlquist in class on Tuesday. Other than what was previously mentioned, this assignment was completed by me without help from an outside source.

References

  • N.A.W. van Riel, M.L.F. Giuseppin, E.G. TerSchure, C.T. Verrips, A Structured, Minimal parameter Model of the Central Nitrogen Metabolism in Saccharomyces cerevisiae: the Prediction of the Behaviour of Mutants, Journal of Theoretical Biology, Volume 191, Issue 4, 1998, Pages 397-414, ISSN 0022-5193, http://dx.doi.org/10.1006/jtbi.1997.0600.

(http://www.sciencedirect.com/science/article/pii/S0022519397906007)

  • N.A.W. van Riel, M.L.F. Giuseppin, C.T. Verrips, Dynamic Optimal Control of Homeostasis: An Integrative System Approach for Modeling of the Central Nitrogen Metabolism in Saccharomyces cerevisiae, Metabolic Engineering, Volume 2, Issue 1, 2000, Pages 49-68, ISSN 1096-7176, http://dx.doi.org/10.1006/mben.1999.0137.

(http://www.sciencedirect.com/science/article/pii/S1096717699901374)

  • ter Schure, E. G., Silljé, H. H., Raeven, L. J., Boonstra, J., Verkleij, A. J., & Verrips, C. T. (1995). Nitrogen-regulated transcription and enzyme activities in continuous cultures of Saccharomyces cerevisiae. Microbiology, 141(5), 1101-1108, DOI: 10.1099/13500872-141-5-1101.
  • Week 6 Assignment

Conor Keith 01:17, 23 February 2017 (EST)

Assignment Pages:

Individual Journal Entries :

Shared Journal Pages:

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