Sos-Removal

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The binding affinity of phosphorylated Sos to Grb2 is less than of unphosphorylated Sos(Hu and Bowtell, 1996). So the inactivation is assumed to occure due to a phosphorylation. Experiments showed that this phosphorylation is catalyzed by Erk. However there are two different kinds of active Erk: the mono-(pT) and the biphosphorylated Erk (pTpY), which show different activities.(Kholodenko et al. 1999)

Binding Reaction

active Sos-Removal:

$\text{activeSos} + \text{ErkPP} \rightleftharpoons \text{removedSos} + \text{ErkPP}$ $\text{activeSos} + \text{ErkP} \rightleftharpoons \text{removedSos} + \text{ErkP}$

inactive Sos-Removal:

$\text{inactiveSos} + \text{ErkPP} \rightleftharpoons \text{removedSos} + \text{ErkPP}$ $\text{inactiveSos} + \text{ErkP} \rightleftharpoons \text{removedSos} + \text{ErkP}$

Kinetic Equation

active Sos-Removal:

$v_{\text{Sos-Removal}} = \frac{k_{cat} \cdot [\text{ErkPP}] \cdot [\text{activeSos}] \cdot (1-\frac{[\text{removedSos}]}{[\text{activeSos}] \cdot K_{eq}})}{Km_{\text{activeSos}} \cdot (1 + \frac{[\text{activeSos}]}{Km_{\text{activeSos}}} + \frac{[\text{removedSos}]}{Km_{\text{removedSos}}})}$

$v_{\text{Sos-Removal}} = \frac{k_{cat} \cdot [\text{ErkP}] \cdot [\text{activeSos}] \cdot (1-\frac{[\text{removedSos}]}{[\text{activeSos}] \cdot K_{eq}})}{Km_{\text{activeSos}} \cdot (1 + \frac{[\text{activeSos}]}{Km_{\text{activeSos}}} + \frac{[\text{removedSos}]}{Km_{\text{removedSos}}})}$

inactive Sos-Removal:

$v_{\text{Sos-Removal}} = \frac{k_{cat} \cdot [\text{ErkPP}] \cdot [\text{inactiveSos}] \cdot (1-\frac{[\text{removedSos}]}{[\text{inactiveSos}] \cdot K_{eq}})}{Km_{\text{inactiveSos}} \cdot (1 + \frac{[\text{inactiveSos}]}{Km_{\text{inactiveSos}}} + \frac{[\text{removedSos}]}{Km_{\text{removedSos}}})}$

$v_{\text{Sos-Removal}} = \frac{k_{cat} \cdot [\text{ErkP}] \cdot [\text{inactiveSos}] \cdot (1-\frac{[\text{removedSos}]}{[\text{inactiveSos}] \cdot K_{eq}})}{Km_{\text{inactiveSos}} \cdot (1 + \frac{[\text{inactiveSos}]}{Km_{\text{inactiveSos}}} + \frac{[\text{removedSos}]}{Km_{\text{removedSos}}})}$

final Parameter

$\text{K}_{\text{ERKPP}}(\text{EGFR peptide}) = 6.56 \cdot 10^2 \pm 62.0\ \mu M$

$\text{kcat}_{\text{ERKPP}}(\text{EGFR peptide}) = 31.6 \pm 0.11\ \frac{1}{s}$

$\text{K}_{\text{ERKP}}(\text{EGFR peptide}) = 2.8 \cdot 10^3 \pm 6.91 \cdot 10^2\ \mu M$

$\text{kcat}_{\text{ERKP}} (\text{EGFR peptide})= 6.99 \pm 0.109\ \frac{1}{s}$

alternative values (Xu et al (2010)):

$\text{kcat}_{\text{both}} = 3.89106 \cdot 10^{-3} \pm 4.04495 \cdot 10^{-4} \ \frac{1}{s}$

Parameter

Data found in BRENDA for EGF receptor peptide as substrate (EC 2.7.11.24- mitogen-activated protein kinase), which is published by Zhang et al. (2008) is used.

(EC 2.7.11.24- mitogen-activated protein kinase)

K_{EGFR peptide(residues 661-681)}(ERKPP) = 656 ± 62 μM  ; pH7, 25 °C, biphosphorylated p38α, mouse

kcat_{EGFR peptide(residues 661-681)}(ERKPP) = 31.6 ± 1.1 s^-1 pH7, 25 °C, biphosphorylated p38α, mouse

K_{EGFR peptide(residues 661-681)}(ERKP) = 2800 ± 691 μM pH7, 25 °C, p38α pT, mouse

Kcat_{EGFR peptide(residues 661-681)}(ERKP) = 6.99 ± 1.09 s^-1 ; pH7, 25 °C, p38α pT, mouse

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.