RasRap1-Inactivation

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Reaction

$\text{activeRas} + \text{GAP} \rightleftharpoons \text{inactiveRas} + \text{GAP}$

$\text{activeRap1} + \text{GAP} \rightleftharpoons \text{inactiveRap1} + \text{GAP}$

Kinetic Equation

$v_{\text{Ras-Inactivation}} = \frac{\text{k}_{\text{cat}} \cdot [\text{GAP}] \cdot [\text{activeRas}] \cdot (1-\frac{[\text{inactiveRas}]}{[\text{activeRas}] \cdot \text{K}_{\text{eq}}})}{\text{Km}_{\text{activeRas}} \cdot (1 + \frac{[\text{activeRas}]}{\text{Km}_{\text{activeRas}}} + \frac{[\text{inactiveRas}]}{\text{Km}_{\text{inactiveRas}}})}$

$v_{\text{Rap1-Inactivation}} = \frac{\text{k}_{\text{cat}} \cdot [\text{GAP}] \cdot [\text{activeRap1}] \cdot (1-\frac{[\text{inactiveRap1}]}{[\text{activeRap1}] \cdot \text{K}_{\text{eq}}})}{\text{Km}_{\text{activeRap1}} \cdot (1 + \frac{[\text{activeRap1}]}{\text{Km}_{\text{activeRap1}}} + \frac{[\text{inactiveRap1}]}{\text{Km}_{\text{inactiveRap1}}})}$

General Information

The inactivation of Ras is du to its intrinsic hydrolase function. This process is accelerated by a further GTPase-activating protein (GAP). Because Ras and Rap1 are similiar enzymes , the same parameter for both inactivation reactions are used. And the standard deviation of Ras is assumed to be 1.5 times larger than the measured one, and the for Rap1 1.75 times larger, because it the measurement were done with Ras. As equilibrium constant the same constant as for the activation is used.

final Parameter

Inactivation of Ras:

$\text{Km}_{\text{activeRas}} = 8.58 \pm 6.27 \cdot 1.5 = 8.58 \pm 9.40\ \mu M$
$\text{k}_{\text{cat}} = 7.733 \pm 1.7 \cdot 1.5 \frac{1}{s} = 7.733 \pm 2.55 \; \frac{1}{s}$

Inactivation of Rap1:

$\text{Km}_{\text{activeRap1}} = 8.58 \pm 6.27 \cdot 1.75\ \mu M = 8.58 \pm 10.97\ \mu M$
$\text{k}_{\text{cat}} = 7.733 \pm 1.7 \cdot 1.75\ \frac{1}{s} = 7.733 \pm 2.975\; \frac{1}{s}$

Parameter

Notes	References
The five measured Km values are used to calculate the Km value and a first estimation for the standard deviation. This standard deviation is then for Ras increased by 1.5 and for Rap by 1.75. Calculation of Km $\frac{5.0 + 3.4 + 5.8 + 9.7 + 19}{5}\; \pm\; stdev(5,3.4,5.8,9.7,19)\; \mu M = 8.58\; \pm\; 6.27\; \mu M$ Calculation of kcat $\frac{1.1\cdot10^6 + 1.8\cdot10^6}{3}\; \frac{1}{Ms} = 7.733\; \frac{1}{s}$ To estimate the error the difference between the largest and the smallest value is calculated and set to σ. $\sigma_{k_{cat}} = \frac{9.3 - 5.9}{2}\; \frac{1}{s} = 1.7\; \frac{1}{s}$	Ahmadian et al. (1996)
	KmactiveRas = 9.7 μM (GAP) KmactiveRas = 19 μM (GAP334) Gideon P. et al. (1992)

Km_P value and equilibrium constant

The K_m value for the product is assumed to be similar to 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.