Difference between revisions of "Hexose-6-phosphate isomerase"

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(→‎Parameters with uncertainty)
(→‎Parameters with uncertainty)
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==Parameters with uncertainty==
 
==Parameters with uncertainty==
 
[[Category:Uncertainty]]
 
[[Category:Uncertainty]]
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* The V is measured in the reverse order for the enzyme (<math>V_{mr}</math>) in <ref name="Hernandez_2006"> Marín-Hernández A , Rodríguez-Enríquez S, Vital-González P A, ''et al.'' (2006). ''Determining and understanding the control of glycolysis in fast-growth tumor cells. Flux control by an over-expressed but strongly product-inhibited hexokinase''. FEBS J., 273 , pp. 1975–1988([http://dx.doi.org/doi:10.1111/j.1742-4658.2006.05214.x doi]) </ref> as <math>3 \pm 1.7</math><math>U\cdot(\text{mg protein})^{-1}</math>. The <math>V_{mf}</math> is calculated based on Haldane equation. The same relative percent error for <math>V_{mr}</math> is used to define the uncertainty of this parameter. The value is <math>0.17 \pm 0.09</math> <math>U\cdot(\text{mg protein})^{-1}</math>. Converting this value into <math>mM\cdot(min)^{-1}</math> gives the value of 0.01105 <math>mM\cdot(min)^{-1}</math>. But in the model the authors considered the value of 0.4. Averaging these two values give the mean and Std. Dev. as <math>0.205525 \pm 0.2750</math>
+
* The V is measured in the reverse order for the enzyme (<math>V_{mr}</math>) in <ref name="Hernandez_2006"> Marín-Hernández A , Rodríguez-Enríquez S, Vital-González P A, ''et al.'' (2006). ''Determining and understanding the control of glycolysis in fast-growth tumor cells. Flux control by an over-expressed but strongly product-inhibited hexokinase''. FEBS J., 273 , pp. 1975–1988([http://dx.doi.org/doi:10.1111/j.1742-4658.2006.05214.x doi]) </ref> as <math>3 \pm 1.7</math><math>U\cdot(\text{mg protein})^{-1}</math>. The <math>V_{mf}</math> is calculated based on Haldane equation. The same relative percent error for <math>V_{mr}</math> is used to define the uncertainty of this parameter. The value is <math>0.17 \pm 0.09</math> <math>U\cdot(\text{mg protein})^{-1}</math>. In the supplement of <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 value is reported as 1.2 <math>U\cdot(\text{mg protein})^{-1}</math>. Same error ratio for <math>V_{mr}</math> reported in <ref name="Hernandez_2006"> is used in the model. After necessary calculation for unit conversion, the value is then <math> 78 \pm 44.2 </math><math>mM\cdot(min)^{-1}</math>  
  
 
*The uncertainty of <math>Km_{Fru6P}</math> for HeLa cell line are calculated based on the same proportion of uncertainty for AS-30D cell reported in the paper Marín-Hernández ''et. al.'', ''Modeling cancer glycolysis'' <ref name="Hernandez2011"></ref>.  
 
*The uncertainty of <math>Km_{Fru6P}</math> for HeLa cell line are calculated based on the same proportion of uncertainty for AS-30D cell reported in the paper Marín-Hernández ''et. al.'', ''Modeling cancer glycolysis'' <ref name="Hernandez2011"></ref>.  
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|<math>V_{mf}</math>
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|<math>0.205525 \pm 0.2750</math>
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|<math>78 \pm 44.2</math>
 
|<math> mM\cdot(min)^{-1} </math>
 
|<math> mM\cdot(min)^{-1} </math>
 
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|<math>V_{mr}</math>
 
|<math>V_{mr}</math>
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|<math>3 \pm 1.7 </math>
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|<math>195 \pm 110.5 </math>
 
|<math>U\cdot(\text{mg protein})^{-1}</math>
 
|<math>U\cdot(\text{mg protein})^{-1}</math>
 
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Revision as of 10:10, 16 October 2014

The enzyme Hexose-6-phosphate isomerase converts Glucose 6-phosphate (Glc6P) into its isomer Fructose 6-phosphate (Fru6P). Isomers have the same molecular formula, but the atoms of each molecule are arranged differently.

Chemical reaction

Glc6P \rightleftharpoons Fru6P

Rate equation

Reversible competitive inhibition with Ery4P, 6PG and FBP. [1]

v=\frac{V_{mf}\frac{[Glc6P]}{Km_{Glc6P}} - V_{mr} \frac{[Fru6P]}{Km_{Fru6P}} }{ 1 + \frac{[Glc6P]}{Km_{Glc6P}} + \frac{[Fru6P]}{Km_{Fru6P}} + \frac{[ERY4P]}{Ki_{ERY4P}} + \frac{[6PG]}{Ki_{6PG}} + \frac{[Fru1,6BP]}{Ki_{Fru1,6BP}} }

Substituting with Haldane equation to ensure thermodynamic consistency we have

v= \frac{V_{mf}\frac{[Glc6P]}{Km_{Glc6P}}\left(1 - \frac{[Fru6P]}{K_{eq}[Glc6P]} \right)}{ 1 + \frac{[Glc6P]}{Km_{Glc6P}} + \frac{[Fru6P]}{Km_{Fru6P}} + \frac{[ERY4P]}{Ki_{ERY4P}} + \frac{[6PG]}{Ki_{6PG}} + \frac{[Fru1,6BP]}{Ki_{Fru1,6BP}} }

Parameter values

Parameter Value Units Organism Remarks
V_{mf} 0.4 [1] mM \times min^{-1} HeLa cell line 3 cell assays
V_{mr} 0.9[1] mM \times min^{-1} 1 cell assay
Km_{Glc6P} 0.4 \pm 0.03 mM[1] mM 3 cell assays
Km_{Fru6P} 0.05[1] mM 2 cell assays
Ki_{ERY4P} 0.001[1] mM Adjusted in the interval based on activity
Ki_{Fru1,6BP} 0.06[1] mM Adjusted in the interval based on activity
Ki_{6PG} 0.015[1] mM Adjusted in the interval based on activity

Parameters with uncertainty

  • The V is measured in the reverse order for the enzyme (V_{mr}) in [2] as 3 \pm 1.7U\cdot(\text{mg protein})^{-1}. The V_{mf} is calculated based on Haldane equation. The same relative percent error for V_{mr} is used to define the uncertainty of this parameter. The value is 0.17 \pm 0.09 U\cdot(\text{mg protein})^{-1}. In the supplement of [1] the value is reported as 1.2 U\cdot(\text{mg protein})^{-1}. Same error ratio for V_{mr} reported in Cite error: Closing </ref> missing for <ref> tag.
  • The value of Ki_{Ery4P}, Ki_{Fru1,6BP} and Ki_{6PG} are the averaged from the forward and reverse reaction value listed in Table S6 [1].
  • The uncertainty for Ki_{Ery4P} in HeLa cell line is mentioned in the forward reaction as 1 \pm 0.07 \mu M and in the reverse direction as 0.86 \mu M. The mean value is calcualated as \frac{1 + 0.86}{2} \mu M and the standard deviation is calculated based on the same ratio mentioned in forward reaction which comes as 0.00093 \pm 0.000063 in mM.
  • Same principle is used for Ki_{6PG}. The mean value is \frac{0.0176+0.0155}{2} = 0.017 and the standard deviation is calculted based on the same ratio of reverse reaction for HeLa cell line; 0.0043
  • There are two reported value for Ki_{Fru1,6BP}; 0.1[3], 0.06[1]. The mean and standard deviation are calcualted from these two values.
Parameter Value Units
V_{mf} 78 \pm 44.2 mM\cdot(min)^{-1}
V_{mr} Failed to parse (Cannot store math image on filesystem.): 195 \pm 110.5 U\cdot(\text{mg protein})^{-1}
Km_{Glc6P} 0.4 \pm 0.03 mM mM
Km_{Fru6P} 0.05 \pm 0.0214 mM
Ki_{ERY4P} 0.0009 \pm 0.000063 mM
Ki_{Fru1,6BP} 0.08 \pm 0.02 mM
Ki_{6PG} 0.017 \pm 0.0043 mM

Equilibrium constant

Equilibrium constant Conditions Source
0.50 pH=7, T=25°C Lehninger, (2008)[4] p 553:

\Delta G' = 1.7\ kJ.mol^{-1}, Keq = exp(-\frac{\Delta G'}{RT}) = exp(\frac{-1700}{8.31*298.15}) \approx 0.50

0.51 pH=7, T=25°C Lehninger, (1975)[5] p 396: Keq(reverse)=1.97 => Keq(forward)=1/1.97=0.51.
0.41 pH=7, T=25°C Voet et al.[6] from Newshole et al. (1973) [7]p 97:

\Delta G' = 2.2\ kJ.mol^{-1}, Keq = exp(-\frac{\Delta G'}{RT}) = exp(\frac{-2200}{8.31*298.15}) \approx 0.41

  • Averaging these values gives 0.47 \pm 0.05

Refences

  1. ↑ 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 Marín-Hernández A, Gallardo-Pérez JC, Rodríguez-Enríquez S et. al. (2011). Modeling cancer glycolysis. Biochim Biophys Acta 1807:755–767 (doi) Cite error: Invalid <ref> tag; name "Hernandez2011" defined multiple times with different content Cite error: Invalid <ref> tag; name "Hernandez2011" defined multiple times with different content Cite error: Invalid <ref> tag; name "Hernandez2011" defined multiple times with different content
  2. ↑ Marín-Hernández A , Rodríguez-Enríquez S, Vital-González P A, et al. (2006). Determining and understanding the control of glycolysis in fast-growth tumor cells. Flux control by an over-expressed but strongly product-inhibited hexokinase. FEBS J., 273 , pp. 1975–1988(doi)
  3. ↑ Marin-Hernandez, A., Gallardo-Perez, J. C., Ralph, S. J., Rodriguez-Enriquez, S. & Moreno-Sanchez, R. (2009), HIF-1α modulates energy metabolism in cancer cells by inducing over-expression of specific glycolytic isoforms. Mini-Rev. Med. Chem. 9, 1084–1101
  4. ↑ David L. Nelson, Michael M. Cox (2008), Lehninger Principles of Biochemistry (5th edn), W. H. Freeman and Company
  5. ↑ Lehninger, A.L. (1975) Biochemistry (2nd edn), Worth
  6. ↑ Voet, D., Voet., J.G. and Pratt, C. W. (1999) Fundamentals of biochemistry, Wiley
  7. ↑ Newshole, E.A. and Stuart, C. (1973) Regulation in Metabolism, Wiley
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