Difference between revisions of "Mitocondrial pyruvate metabolism"
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*The rate law is defined as <center><math>v = K_1[Pyruvate][ADP]^{13}[Pi]^{13}\left(1-\frac{\frac{[ATP]^{13}}{[Pyruvate][ADP]^{13}[Pi]^{13}}}{K_{eq}}\right)</math></center><br> | *The rate law is defined as <center><math>v = K_1[Pyruvate][ADP]^{13}[Pi]^{13}\left(1-\frac{\frac{[ATP]^{13}}{[Pyruvate][ADP]^{13}[Pi]^{13}}}{K_{eq}}\right)</math></center><br> | ||
− | *The overall standard free-energy change for Pyruvate metabolism is <math>\Delta G^o{'}= -50.3 Kj/Mol</math><ref>Nelson D. and Cox M. (2008), ''Lehninger Principles of Biochemistry'', Fight Edition, W.H. Freeman and Company, ISBN-10: 071677108X</ref><ref name="Takusagawas_Note">http://crystal.res.ku.edu/taksnotes/Biol_638/notes/chp_16.pdf</ref>. | + | *The overall standard free-energy change for Pyruvate metabolism is <math>\Delta G^o{'}= -50.3 Kj/Mol</math><ref>Nelson D. and Cox M. (2008), ''Lehninger Principles of Biochemistry'', Fight Edition, W.H. Freeman and Company, ISBN-10: 071677108X</ref><ref name="Takusagawas_Note">http://crystal.res.ku.edu/taksnotes/Biol_638/notes/chp_16.pdf</ref>. '''Note''' The overall standard free energy is calculated by adding the standard free energy for all the reactions in TCA cycle. |
::Calculating <math>K_{eq}</math> value from these free energy gives <math>\Delta G' = - 50.3\ kJ.mol^{-1}</math>, <math>Keq = exp(-\frac{\Delta G'}{RT}) = exp(\frac{50300}{8.31*298.15}) \approx 654904512.15</math>. In order to ensure that the uncertainty does not affect the model equilibrium a small uncertainty of 5% can be considered for transporter. In our model we have applied this approach. So <math>K_{eq} = 654904512.15 \pm 32745226</math>. | ::Calculating <math>K_{eq}</math> value from these free energy gives <math>\Delta G' = - 50.3\ kJ.mol^{-1}</math>, <math>Keq = exp(-\frac{\Delta G'}{RT}) = exp(\frac{50300}{8.31*298.15}) \approx 654904512.15</math>. In order to ensure that the uncertainty does not affect the model equilibrium a small uncertainty of 5% can be considered for transporter. In our model we have applied this approach. So <math>K_{eq} = 654904512.15 \pm 32745226</math>. | ||
*The Flux of pyruvate consumed by mitochondria measured for AS_30D is <math> v = 1.8</math> <ref name="Hernandez2011"> Marín-Hernández A, Gallardo-Pérez JC, Rodríguez-Enríquez S et al (2011) Modeling cancer glycolysis. Biochim Biophys Acta 1807:755–767 ([http://dx.doi.org/10.1016/j.bbabio.2010.11.006 doi])</ref>. | *The Flux of pyruvate consumed by mitochondria measured for AS_30D is <math> v = 1.8</math> <ref name="Hernandez2011"> Marín-Hernández A, Gallardo-Pérez JC, Rodríguez-Enríquez S et al (2011) Modeling cancer glycolysis. Biochim Biophys Acta 1807:755–767 ([http://dx.doi.org/10.1016/j.bbabio.2010.11.006 doi])</ref>. |
Revision as of 11:31, 3 July 2014
Mitocondrial pyruvate metabolism(MPM) is a pseudo reaction that represents the total ATP production from one unit of pyruvate in the mitochondrian.
Contents
Chemical reaction
Rate equation
- Chemical reactions proceed to equilibrium within closed systems. For a simple reaction it is defined as where forward and reverse rates are equal.
- Equilibrium is not reached in open system due to influx and outflux. Mass action ratio[1] for reaction is defined as where subscript ob represents observable at a given point.
- Deviation from equilibrium is measured with Disequilibrium constant as
- Given the simple uni molecular reaction the mass action equation can be modified as
Considering and we have,
- The generalized arbitrary mass action ratio gives us
For eg. for the reaction , the rate law would be
- This equation demonstrates how a rate expression can be divided into parts that include both kinetics and thermodynamic properties [2].
- Given the net rate of reaction , we have
In this model
- The rate law is defined as
- The overall standard free-energy change for Pyruvate metabolism is [3][4]. Note The overall standard free energy is calculated by adding the standard free energy for all the reactions in TCA cycle.
- Calculating value from these free energy gives , Failed to parse (Cannot store math image on filesystem.): Keq = exp(-\frac{\Delta G'}{RT}) = exp(\frac{50300}{8.31*298.15}) \approx 654904512.15 . In order to ensure that the uncertainty does not affect the model equilibrium a small uncertainty of 5% can be considered for transporter. In our model we have applied this approach. So Failed to parse (Cannot store math image on filesystem.): K_{eq} = 654904512.15 \pm 32745226 .
- The Flux of pyruvate consumed by mitochondria measured for AS_30D is [5].
- The steady state concentrations for substrates and products are , , and .
- The value calculated from the above mentioned values are Failed to parse (Cannot store math image on filesystem.): 7.78E-015
- To calculate the uncertainty of we first looked at the uncertainty on the substrate and product concentration. The maximum uncertainty reported for these values are . In our model we considered this uncertainty in its mean value giving value of
Parameter values
Parameter | Value | Organism | Remarks |
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Parameters with uncertainty
Parameter | Value | Organism | Remarks |
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References
- ↑ Hess B. and Brand K. (1965), Enzymes and metabolite profiles. In Control of energy metabolism. III. Ed. B. Chance, R. K. Estabrook and J. R. Williamson. New York: Academic Press
- ↑ Sauro H M, Enzyme Kinetics for Systems Biology, Second Edition, Ambrosius Publishing (2013), ISBN-10: 0-9824773-3-3
- ↑ Nelson D. and Cox M. (2008), Lehninger Principles of Biochemistry, Fight Edition, W.H. Freeman and Company, ISBN-10: 071677108X
- ↑ http://crystal.res.ku.edu/taksnotes/Biol_638/notes/chp_16.pdf
- ↑ Marín-Hernández A, Gallardo-Pérez JC, Rodríguez-Enríquez S et al (2011) Modeling cancer glycolysis. Biochim Biophys Acta 1807:755–767 (doi)