ERK-Inactivation

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Reaction

Step 1:

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

Step 2:

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

Rate Equation

Step 1:

$v_{\text{Dephosphorylation Step 1}} = \frac{\text{k1}_{\text{cat}} \cdot [\text{PP2A}] \cdot [\text{ErkPP}] \cdot (1-\frac{[\text{ErkP}]}{[\text{ErkPP}] \cdot \text{K}_{\text{eq}}})}{\text{Km}_{\text{ErkPP}} \cdot (1 + \frac{[\text{ErkPP}]}{\text{Km}_{\text{ErkPP}}} + \frac{[\text{ErkP}]}{\text{Km}_{\text{ErkP}}})}$

Step 2:

$v_{\text{Dephosphorylation Step 2}} = \frac{\text{k2}_{\text{cat}} \cdot [\text{PP2A}] \cdot [\text{ErkP}] \cdot (1-\frac{[\text{Erk}]}{[\text{ErkP}] \cdot \text{K2}_{\text{eq}}})}{\text{Km}_{\text{ErkP}} \cdot (1 + \frac{[\text{ErkP}]}{\text{Km}_{\text{ErkP}}} + \frac{[\text{Erk}]}{\text{Km}_{\text{Erk}}})}$

final Parameter

$k1_{cat} = 0.7035 \pm 0.02151\ \frac{1}{s}$

$K_{m} = 1.502 \pm 0.13348\ \mu M$

$k2_{cat} = 0.7035 \pm 0.02151\ \frac{1}{s}$

$K_{m} = 1.502 \pm 0.13348\ \mu M$

Parameter

Notes

References

Calculation of kcat Dephosphorylation by HePTP $k_{cat}=0.86 \pm 0.034 \frac{1}{s}$ Dephosphorylation by MKP $k_{cat}=0.547 \pm 0.012 \frac{1}{s}$ Averaging $k_{cat} = \frac{0.86 + 0.547}{2}\ \frac{1}{s} = 0.7035\ \frac{1}{s}$ $\sigma_{kcat} = \frac{\frac{0.034}{0.86} + \frac{0.012}{0.547}}{2} \cdot 0.7035\ \frac{1}{s} = 0.02151\ \frac{1}{s}$ Calculation of Km Averaging $K_{m} = \frac{0.144 + 2.86}{2}\ \mu M = 1.502\ \mu M$ $\sigma_{Km} = \frac{\frac{0.012}{0.144} + \frac{0.27}{2.86}}{2} \cdot 1.502\ \mu M = 0.13348\ \mu M$

Zhang Y. et al (2008) Zhang Y. et al (2008)

Background Information

There are several phosphatases which dephosphorylate ERK, among them phosphatase 2A (PP2A), MAPK phosphatase 3, HePTP and protein phosphatase-1 (PP1). PP2A is more effective than PP1 and it is used by Brown KS and Sethan JP in their model. Xu et al. 2010 based theit model on this model and also elicit their initial conditions from this model. We introduced PP2A in our model to use the measured kcat values and our initial concentration we elicit form Brown and Sethan in a similar way to Xu et al. so that the relation of the concentrations is concerved.

Km_P value and equilibrium constant

The K_m value for the product is assumed to be similar but slightly higher 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 1.05 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.