ERK-Activation

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Reaction

Step 1:

$\text{Erk} + \text{MekPP} \rightleftharpoons \text{ErkP} + \text{MekPP}$

Step 2:

$\text{ErkP} + \text{MekPP} \rightleftharpoons \text{ErkPP} + \text{MekPP}$

Kinetic Equation

Step 1:

$v_{\text{Erk-Activation}} = \frac{k_{cat} \cdot [\text{MekPP}] \cdot [\text{Erk}] \cdot (1-\frac{[\text{ErkP}]}{[\text{Erk}] \cdot K_{eq}})}{Km_{\text{Erk}} \cdot (1 + \frac{[\text{Erk}]}{Km_{\text{Erk}}} + \frac{[\text{ErkP}]}{Km_{\text{ErkP}}})}$

Step 2:

$v_{\text{Erk-Activation}} = \frac{k_{cat} \cdot [\text{MekPP}] \cdot [\text{ErkP}] \cdot (1-\frac{[\text{ErkPP}]}{[\text{ErkP}] \cdot K_{eq}})}{Km_{\text{ErkP}} \cdot (1 + \frac{[\text{ErkP}]}{Km_{\text{ErkP}}} + \frac{[\text{ErkPP}]}{Km_{\text{ErkPP}}})}$

General Information

To be completely activated Erk has to be phoshporylated twice by Mek. First on a tyrosine residue and the on threonine Haystead T.A. et al. (1992). Therefore the Erk-Activation process is included in our model as a two step process and Erk is assumed to be present in thee different conformations: unphosphorylated, monophosphorylated and bisphosphorylated.

final Parameter

Failed to parse (lexing error): K_{\text{Mp42mapk_{unphopshorylated}}} = 476 \cdot 10^{-3} \pm 67.416 \cdot 10^{-3} \mu M

Failed to parse (lexing error): K_{\text{Mp42mapk{pY}}} = 46.6 \cdot 10^{-3} \pm 6.6 \cdot 10^{-3} \mu M (n=5)

Data model Xu et al.:

Failed to parse (lexing error): kcat_{\text{Mp42mapk_{unphopshorylated}}} = 6.48 \cdot 10^{-1} \pm 0.175541 \cdot 6.48 \cdot 10^{-1}\; \frac{1}{s} = 6.48 \cdot 10^{-1} \pm 1.1383\cdot 10^{-1}\; \frac{1}{s}

Failed to parse (lexing error): kcat_{\text{Mp42mapk{pY}}}=6.48 \cdot 10^{-1} \pm 0.175541 \cdot 6.48 \cdot 10^{-1}\; \frac{1}{s} = 6.48 \cdot 10^{-1} \pm 1.1383\cdot 10^{-1}\; \frac{1}{s}

Data BRENDA: Failed to parse (lexing error): kcat_{\text{Mp42mapk_{unphopshorylated}}} = 4.919 \pm 0.51\; \frac{1}{s}

Failed to parse (lexing error): kcat_{\text{Mp42mapk{pY}}} = 4.919 \pm 0.51\; \frac{1}{s}

Parameter

K_{Mp42mapkunphopshorylated} = 476 nM

K_Mp42mapkpY = 46.6 ± 6.6 nM (n=5)

Calculation of the uncertainty of K_{Mp42mapkunphopshorylated}

Because both K_m values were measured be the same group and under the same conditions we assume that both values have the same relative error. The absolute error of K_Mp42mapkpY is given and the relative error is calculated to be $\frac{6.6}{46.6} = 0.1416$, which leads to an absolute error of K_{Mp42mapkunphopshorylated}.

$\rightarrow \sigma_{Mp42mapk_{unphopshorylated}} = 0.1416 \cdot 476\; nM = 67.416\; nM$

Firstly the k_cat-values by Xu et al. Xu et al (2010) were used. And for the uncertainty the averaged relative standard deviation is calculated is used. (see here)

However it was shown that this assumption leads to a too low kcat value. Both ERK and MEK are MAP kinases which might have a similar turnover number. There are no turnover numbers for MEK, so to finally estimate the catalytic constant data of the MAP kinase is used averaged and the standard deviation is claculated (excluded are the values with ATF2DELTA109 and EGFR as substrate).

(EC 2.7.11.24- mitogen-activated protein kinase)

Km_P value and equilibrium constant

The K_m value for the product is assumed to be similar to but slightly smaller than the the K_m value of the substrate because of the similarity of the both species. Therefore the K_m value of the substrate is multiplied by 0.95 to gain the one of the product and the uncertainty is increased by increasing the error on Km_substrate by 50%.

For information about the equilibrium constant please see here.