Difference between revisions of "Mitocondrial pyruvate metabolism"
Line 28: | Line 28: | ||
===In this model=== | ===In this model=== | ||
− | + | *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> | |
− | + | *The <math>K_{eq}</math> value for the reactions that converts pyruvate has been defined as <math>0.00001</math> in <ref name="Owusu_2004">Owusu-Apenten R. ''Introduction to Food Chemistry'', First Edition, CRC Press (2004), ISBN-10: 084931724X </ref><center>[[File:Pyruvate_Keq.png|550px|link=]]</center> | |
− | + | *The flux value at steady state is <math> v = 1 \times 10^{-4}</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 steady state concentrations for substrates and products are <math>ATP=8.7 \pm 3 (5)</math>, <math>ADP = 2.7 \pm 1.3</math>, <math>Pyruvate = 8.5 \pm 3.6</math> and <math>Pi = 7.5</math>. | |
− | + | *The <math>K_1</math> value calculated from the above mentioned values are | |
==Parameter values== | ==Parameter values== |
Revision as of 11:39, 12 May 2014
Mitocondrial pyruvate metabolism(MPM) is an enzyme that generates ATP form pyruvate.
Chemical reaction
![Pyruvate + 13ADP + 13Pi \rightarrow 13ATP](/wiki/images/math/8/c/1/8c1f1d258edc09e0bf6a00a60726ecc6.png)
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
![v=K_1A-K_2B](/wiki/images/math/4/f/9/4f987b54432b9936018bfd10963d900c.png)
![v=K_1A \left(1-\frac{K_2B}{K_1A} \right)](/wiki/images/math/0/3/7/037f9459550126e5cd2441ef1640a0a0.png)
Considering and
we have,
![v=K_1A \left(1-\frac{\tau}{K_{eq}} \right)](/wiki/images/math/3/f/9/3f943c876067cef366aa637f2c84b76c.png)
- The generalized arbitrary mass action ratio gives us
![v = K_1A^{n_1}B^{n_2} \ldots \left(1-\frac{\tau}{K_{eq}} \right)](/wiki/images/math/c/b/8/cb8c7324e3da3f18cc6db89df26713fe.png)
![v = K_1A^{n_1}B^{n_2} \ldots (1 - \rho)](/wiki/images/math/1/8/5/185e5a66573702fc1d0b17b55b30ecac.png)
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
![v = v_f \left(1 - \rho \right)](/wiki/images/math/f/6/a/f6a215a344f21d60a655289cb93408d4.png)
In this model
- The rate law is defined as
- The
value for the reactions that converts pyruvate has been defined as Failed to parse (Cannot store math image on filesystem.): 0.00001 in [3]
- The flux value at steady state is
[4].
- The steady state concentrations for substrates and products are
,
,
and
.
- The
value calculated from the above mentioned values are
Parameter values
Parameter | Value | Organism | Remarks |
---|---|---|---|
![]() |
![]() |
HeLa cell line | 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
- ↑ Owusu-Apenten R. Introduction to Food Chemistry, First Edition, CRC Press (2004), ISBN-10: 084931724X
- ↑ 4.0 4.1 Marín-Hernández A, Gallardo-Pérez JC, Rodríguez-Enríquez S et al (2011) Modeling cancer glycolysis. Biochim Biophys Acta 1807:755–767 (doi)