Difference between revisions of "Mitocondrial pyruvate metabolism"
(→In this model) |
|||
(31 intermediate revisions by the same user not shown) | |||
Line 1: | Line 1: | ||
− | [[Category: | + | [[Category:Uncertainty]] |
− | + | '''Mitocondrial pyruvate metabolism(MPM)''' is a pseudo reaction that represents the total ATP production from one unit of pyruvate in the mitochondrian. | |
− | '''Mitocondrial pyruvate metabolism(MPM)''' is | ||
==Chemical reaction== | ==Chemical reaction== | ||
− | <center><math> Pyruvate + 13ADP + 13Pi \ | + | <center><math> Pyruvate + 13ADP + 13Pi \leftrightarrow 13ATP</math></center> |
==Rate equation== | ==Rate equation== | ||
Line 28: | Line 27: | ||
===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 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 <math> | + | *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 656010875.924588</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 32800543.79</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>. | ||
− | *The | + | *The initial 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>. |
− | * | + | * Considering the stoichiometry of the model the value of <math>K_1</math> is <math>5.1344e-017</math>. If we ingnore the stiochiometric constants while calculating <math>K_1</math>, the value calculated from the above mentioned values are <math>0.01045</math> |
+ | *To calculate the uncertainty of <math>K_1</math> we first looked at the uncertainty on the substrate and product concentration. The maximum uncertainty reported for these values are <math>\approx 50%</math>. In our model we considered this <math>50%</math> uncertainty in its mean value giving value of <math>0.01045 \pm 0.0052</math> | ||
+ | |||
+ | *'''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 values== | ||
Line 42: | Line 45: | ||
|- | |- | ||
|<math>K_1</math> | |<math>K_1</math> | ||
− | |<math><math> | + | |<math>7.78E^{-015}</math> '''In our model''' we used <math>0.01045 \pm 0.0052</math> |
+ | | | ||
+ | | | ||
+ | |- | ||
+ | |<math>K_{eq}</math> | ||
+ | |<math>654904512.15</math> | ||
+ | | | ||
+ | | | ||
+ | |} | ||
+ | |||
+ | '''Alternative''' | ||
+ | {|class="wikitable" | ||
+ | ! Parameter | ||
+ | ! Value | ||
+ | ! Organism | ||
+ | ! Remarks | ||
+ | |- | ||
+ | |<math>V</math> | ||
+ | |<math>1.0^{-04}</math> | ||
+ | | | ||
+ | |Constant Flux | ||
+ | |} | ||
+ | |||
+ | ==Parameters with uncertainty== | ||
+ | {|class="wikitable" | ||
+ | ! Parameter | ||
+ | ! Value | ||
+ | ! Organism | ||
+ | ! Remarks | ||
+ | |- | ||
+ | |<math>K_1</math> | ||
+ | |<math>7.78E^{-015} \pm 3.89E^{-015}</math> | ||
+ | | | ||
+ | | | ||
+ | |- | ||
+ | |<math>K_{eq}</math> | ||
+ | |<math>654904512.15 \pm 32745226</math> | ||
| | | | ||
| | | | ||
+ | |} | ||
+ | |||
+ | '''Alternative''' | ||
+ | {|class="wikitable" | ||
+ | ! Parameter | ||
+ | ! Value | ||
+ | ! Organism | ||
+ | ! Remarks | ||
+ | |- | ||
+ | |<math>V</math> | ||
+ | |<math>1.0^{-04}\pm 3.1^{-05}</math> | ||
+ | | | ||
+ | |Constant Flux | ||
|} | |} | ||
==References== | ==References== | ||
<references/> | <references/> |
Latest revision as of 13:20, 12 August 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
![Pyruvate + 13ADP + 13Pi \leftrightarrow 13ATP](/wiki/images/math/3/3/a/33ab7e4982c4158d0489a165f344bccb.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 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
,
. 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
.
- Calculating
- The Flux of pyruvate consumed by mitochondria measured for AS_30D is
[5].
- The initial concentrations for substrates and products are
,
,
and
.
- Considering the stoichiometry of the model the value of
is
. If we ingnore the stiochiometric constants while calculating
, 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 |
---|---|---|---|
![]() |
![]() ![]() |
||
![]() |
![]() |
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)