Difference between revisions of "Triosephosphate isomerase"

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<center><math> v = \frac{ V_{mf}\frac{[DHAP]}{K_{DHAP}} - V_{mr}\frac{[Gly3P]}{K_{Gly3P}}  }{1 + \frac{[DHAP]}{K_{DHAP}} + \frac{[Gly3P]}{K_{Gly3P}} } </math></center>
 
<center><math> v = \frac{ V_{mf}\frac{[DHAP]}{K_{DHAP}} - V_{mr}\frac{[Gly3P]}{K_{Gly3P}}  }{1 + \frac{[DHAP]}{K_{DHAP}} + \frac{[Gly3P]}{K_{Gly3P}} } </math></center>
 +
 +
Modified rate law considering thermodynamic constant is
 +
<center><math> v = \frac{ V_{mf}\frac{[DHAP]}{K_{DHAP}}\left(1 - \frac{[Gly3P]}{K_{eq}[DHAP]} \right)}{1 + \frac{[DHAP]}{K_{DHAP}} + \frac{[Gly3P]}{K_{Gly3P}} } </math></center>
  
 
== Paramters ==
 
== Paramters ==
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==Parameters with uncertainty==
 
==Parameters with uncertainty==
−
* The activity is measured in Activity in the reverse reaction in Hernandez (2006) ''et. al.'' <math>V_{mf}</math> is sampled based on Haldane equation <math>K_{eq} = \frac{V_{forward}*K_{product}}{V_{reverse}*K_{substrate}}</math> using the value <math>K_{eq} = 20.9 \pm 3.1</math>, <math>Km_{Gly3P}</math> and <math>Km_{DHAP}</math>. '''Alternatively''' the reported fixed point value can be considered with the standard deviation calculated based on the same ratio of <math>V_{mf}</math> which is <math>\approx 31%</math>. This gives the value <math>V_{mf}=0.063 \pm 0.028 </math>
+
* The activity is measured in Activity in the reverse reaction in Hernandez (2006) ''et. al.'' <math>V_{mf}</math> is sampled based on Haldane equation <math>K_{eq} = \frac{V_{forward}*K_{product}}{V_{reverse}*K_{substrate}}</math> using the value <math>K_{eq} = 0.047</math>, <math>Km_{Gly3P}</math> and <math>Km_{DHAP}</math>. <br>
 +
'''Alternative-1''' the reported fixed point value can be considered with the standard deviation calculated based on the same ratio of <math>V_{mf}</math> which is <math>\approx 31%</math>. This gives the value <math>V_{mf}=6.19 \pm 1.91 </math><math>U\cdot(\text{mg protein})^{-1}</math><br>
 +
'''Alternative-2''' Calculating <math>V_{mf}</math> from <math>V_{mr}</math> based on Haldane equation which gives the value of 2.911 and with the same percent of erro Std. Dev. is 0.90.
  
 
{|class="wikitable"
 
{|class="wikitable"
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|-
 
|-
 
|<math>V_{mf}</math>
 
|<math>V_{mf}</math>
−
| Sampled based on the Haldane equation.
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| Sampled based on the Haldane equation.<br> '''Alternative:''' <math>6.19 \pm 1.91</math> or <math>2.911 \pm 0.90</math> conversion gives <math>402 \pm 124.62</math>
−
|<math> mM \times min^{-1} </math>  
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|<math>U\cdot(\text{mg protein})^{-1}</math> <br> <math> mM \times min^{-1} </math>  
 
|
 
|
 
|rowspan="5"|
 
|rowspan="5"|
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|-
 
|-
 
|<math>K_{eq}</math>
 
|<math>K_{eq}</math>
−
|<math>20.9 \pm 3.1 (4)</math><ref name="synder_1975"></ref>
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|<math>0.047 \pm 0.00697 (4)</math><ref name="synder_1975"></ref>
 
|mM
 
|mM
−
|
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|<math>K_{eq}(reverse) = 20.9, and so K_{eq}(forward) = \frac{1}{20.9} = 0.047 </math>
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|}
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===Equilibrium constant===
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{| class="wikitable"
 +
! Equilibrium constant
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! Conditions
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! Source
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|-
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| 0.045
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| pH=8, T=25°C
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| Bergmeyer ''Methods of enzymatic analysis'' page 515<ref name="bermeyer74">Bergmeyer H.U. (1974) ''Methods of enzymatic analysis'', Publisher: Verlag Chemie (vol 1)</ref>
 +
|-
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| 0.041
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| pH=7, T=25°C
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| Voet et al.<ref name="voet">Voet, D., Voet., J.G. and Pratt, C. W. (1999) Fundamentals of biochemistry, Wiley</ref> from Newshole et al. (1973) <ref name="newshole73">Newshole, E.A. and Stuart, C. (1973) Regulation in Metabolism, Wiley</ref>p 97:<br/>
 +
<math>\Delta G' = 7.9\ kJ.mol^{-1}</math>, <math>Keq = exp(-\frac{\Delta G'}{RT}) = exp(\frac{-7900}{8.31*298.15}) \approx 0.041</math>
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|-
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| 0.048
 +
| pH=7, T=25°C
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| Lehninger, (1975)<ref name="lehninger75">Lehninger, A.L. (1975) Biochemistry (2nd edn), Worth</ref> p 408:<br/>
 +
<math>\Delta G' = 7.5\ kJ.mol^{-1}</math>, <math>Keq = exp(-\frac{\Delta G'}{RT}) = exp(\frac{-7500}{8.31*298.15}) \approx 0.048</math>
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|-
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| 0.0475
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| pH=7, T=25°C
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| Lehninger, (1975)<ref name="lehninger75">Lehninger, A.L. (1975) Biochemistry (2nd edn), Worth</ref> p 396.
 
|}
 
|}
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 +
*Taking average of all those values give <math>0.0457 \pm 0.002863</math>
  
 
==References==
 
==References==
 
<references/>
 
<references/>

Latest revision as of 14:23, 28 October 2014

This enzyme rapidly inter-converts the molecules Dihydroxyacetone phosphate (DHAP) and Glyceraldehyde 3-phosphate (Gly3P). Gly3P is removed as soon as it is formed to be used in the next step of glycolysis.

Chemical equation

DHAP \rightleftharpoons Gly3P

Rate equation

Reversible Michaelis-Menten is used [1]

v = \frac{ V_{mf}\frac{[DHAP]}{K_{DHAP}} - V_{mr}\frac{[Gly3P]}{K_{Gly3P}} }{1 + \frac{[DHAP]}{K_{DHAP}} + \frac{[Gly3P]}{K_{Gly3P}} }

Modified rate law considering thermodynamic constant is

v = \frac{ V_{mf}\frac{[DHAP]}{K_{DHAP}}\left(1 - \frac{[Gly3P]}{K_{eq}[DHAP]} \right)}{1 + \frac{[DHAP]}{K_{DHAP}} + \frac{[Gly3P]}{K_{Gly3P}} }

Paramters

Parameter Value Units Organism Remarks
V_{mf} 5 [1] mM \times min^{-1} Hela cell line
V_{mr} 42[2] mM \times min^{-1}
Km_{Gly3P} 0.51[1] mM
Km_{DHAP} 1.6[1] mM

Parameters with uncertainty

  • The activity is measured in Activity in the reverse reaction in Hernandez (2006) et. al. V_{mf} is sampled based on Haldane equation K_{eq} = \frac{V_{forward}*K_{product}}{V_{reverse}*K_{substrate}} using the value K_{eq} = 0.047, Km_{Gly3P} and Km_{DHAP}.

Alternative-1 the reported fixed point value can be considered with the standard deviation calculated based on the same ratio of V_{mf} which is \approx 31%. This gives the value V_{mf}=6.19 \pm 1.91 U\cdot(\text{mg protein})^{-1}
Alternative-2 Calculating V_{mf} from V_{mr} based on Haldane equation which gives the value of 2.911 and with the same percent of erro Std. Dev. is 0.90.

Parameter Value Units Organism Remarks
V_{mf} Sampled based on the Haldane equation.
Alternative: 6.19 \pm 1.91 or 2.911 \pm 0.90 conversion gives 402 \pm 124.62 		U\cdot(\text{mg protein})^{-1}
mM \times min^{-1}
V_{mr} 42 \pm 13 (3)[2] mM \times min^{-1}
Km_{Gly3P} 0.40 \pm 0.03 (4)[3] mM Human liver
Km_{DHAP} 0.59 \pm 0.01 (4)[3] mM Human liver
K_{eq} 0.047 \pm 0.00697 (4)[3] mM K_{eq}(reverse) = 20.9, and so K_{eq}(forward) = \frac{1}{20.9} = 0.047

Equilibrium constant

Equilibrium constant Conditions Source
0.045 pH=8, T=25°C Bergmeyer Methods of enzymatic analysis page 515[4]
0.041 pH=7, T=25°C Voet et al.[5] from Newshole et al. (1973) [6]p 97:

\Delta G' = 7.9\ kJ.mol^{-1}, Keq = exp(-\frac{\Delta G'}{RT}) = exp(\frac{-7900}{8.31*298.15}) \approx 0.041

0.048 pH=7, T=25°C Lehninger, (1975)[7] p 408:

\Delta G' = 7.5\ kJ.mol^{-1}, Keq = exp(-\frac{\Delta G'}{RT}) = exp(\frac{-7500}{8.31*298.15}) \approx 0.048

0.0475 pH=7, T=25°C Lehninger, (1975)[7] p 396.
  • Taking average of all those values give 0.0457 \pm 0.002863

References

  1. ↑ 1.0 1.1 1.2 1.3 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
  2. ↑ 2.0 2.1 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. ↑ 3.0 3.1 3.2 Snyder, R.; Lee, E.W. (1975), Triosephosphate isomerase from human and horse liver,Methods Enzymol. 41B, 430-434
  4. ↑ Bergmeyer H.U. (1974) Methods of enzymatic analysis, Publisher: Verlag Chemie (vol 1)
  5. ↑ Voet, D., Voet., J.G. and Pratt, C. W. (1999) Fundamentals of biochemistry, Wiley
  6. ↑ Newshole, E.A. and Stuart, C. (1973) Regulation in Metabolism, Wiley
  7. ↑ 7.0 7.1 Lehninger, A.L. (1975) Biochemistry (2nd edn), Worth
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