Dephosphorylation

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Binding Reaction

$\text{phosphorylated-enzyme} \rightleftharpoons \text{unphosphorylated-enzyme}$

Kinetic equation

$v_{dephosphorylation} = \frac{v_{max} \cdot [\text{phosphorylated-enzyme}] \cdot (1-\frac{[\text{unphosphorylated-enzyme}]}{[\text{phosphorylated-enzyme}] \cdot K_{eq}})}{Km_{\text{phosphorylated-enzyme}} \cdot (1 + \frac{[\text{phosphorylated-enzyme}]}{Km_{\text{phosphorylated-enzyme}}} + \frac{[\text{unphosphorylated-enzyme}]}{Km_{\text{unphosphorylated-enzyme}}})}$

General Information

The most enzymes in the MAP-Kinase signaling pathway are activated by phosphorylation. The inactivation is therefore due to a dephosphorylation step. The amino acids that are phosphorylated are tyrosine, serine, threonine, so the three main dephosphatases address phosphate residues at these side chains. In BRENDA there are several values measured, for the Km and vmax value. In contrast to the reactions in which the enyzme that catalyses the reaction appears also as substrate in the model the concentration of the dephosphatases is assumed to be constant and therefore the v_max value instead or the k_cat value is used. Because of the reason that it is not clear which dephoshpatase is mainly responsible for the inactivation an average of all measured dephosphatase values is used in our model as K_m and as k_cat the ones used by Xu et al (2010) are used and the standard deviation is calculated by assuming the same averaged relative error as for the measured values.(Calculation of the averaged relative error).

final Parameter

$v_{max}(BRaf-Inactivation) = 7.59316 \pm 0.78935\ \frac{mol}{s}$

$v_{max}(C3G-Inactivation) = 2109.86 \pm 219.33\ \frac{mol}{s}$

$v_{max}(Mek-Inactivation) = 632.512 \pm 65.753 \ \frac{mol}{s}$

$v_{max}(Raf1-Inactivation) = 13119.7 \pm 1363.9\ \frac{mol}{s}$

$K_{m} = 3.83 \cdot 10^{3} \pm 1.40 \cdot 10^{2}\ \mu M$

Parameter

Notes	Data
There are three main deophosphatases, phosphoserine phosphatase (EC 3.1.3.3), phosphoprotein phosphatase (EC 3.1.3.16), protein-tyrosine phosphatase (3.1.3.48). The data available in BRENDA is used to calculate the average and standard deviation.	EC 3.1.3.3 - phosphoserine phosphatase EC 3.1.3.16 - phosphoprotein phosphatase EC 3.1.3.48 - protein-tyrosine phosphatase average Km [mM] average all 0.75 7.43 3.31 3.83 mM std 1.29 27.74 12.90 1.40 mM

Screenshots of the BRENDA database

3.1.3.3-phosphoserine phosphatase

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  3.1.3.3-phosphoserine phosphatase

3.1.3.16-phosphoprotein phosphatase

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  3.1.3.16-phosphoprotein phosphatase Km

3.1.3.48 protein-tyrosine-phosphatase

K_m

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  3.1.3.48 protein-tyrosine-phosphatase Km1

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  3.1.3.48 protein-tyrosine-phosphatase Km2

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  3.1.3.48 protein-tyrosine-phosphatase Km3

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  3.1.3.48 protein-tyrosine-phosphatase Km4

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  3.1.3.48 protein-tyrosine-phosphatase Km5

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.