Mitocondrial pyruvate metabolism
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 initial concentrations for substrates and products are , , and .
- We ingnored the stiochiometric constants while calculating the parameter . The value calculated from the above mentioned values are
- 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
- Alternative As this is a psuedo-reaction, the above mentioned formula fails to reach steady state. So a constant flux mentioned in Hernandez et. al. can be used. The maximum relative precent of error for other constant fluxes are reported to be 31%. We consider the same relative percent error for this reaction because of it being a psuedo-reaction.
Parameter values
Parameter | Value | Organism | Remarks |
---|---|---|---|
In our model we used | |||
Alternative
Parameter | Value | Organism | Remarks |
---|---|---|---|
Constant Flux |
Parameters with uncertainty
Parameter | Value | Organism | Remarks |
---|---|---|---|
Alternative
Parameter | Value | Organism | Remarks |
---|---|---|---|
Constant Flux |
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)