What is the Relationship Between Km and V0 in the Michaelis-Menten Curve?

[TytoAlba95]

Homework Statement

N.A

Relevant Equations

N.A

The relevant formua: V0= (Vmax x )/ (Km + )
From the question:
2(Vmax x 0.5)/ (Km + 0.5) = (Vmax x 1)/ (Km + 1)
=> 2(Vmax x 0.5)/ (Km + 0.5) = (Vmax x 1)/ (Km + 1)
=> 1 x (Km +1) = (Km + 0.5)

Where am I making the mistake?

 

[Ygggdrasil]

This is a conceptual question that does not require any calculations to solve. Consider the shape of a general Michaelis-Menten curve (it may be helpful to draw one). In the region where [ S] < K_m, if you double [ S] will the reaction velocity approximately double? In the region where [S] > K_m, if you double [ S] will the reaction velocity approximately double?

 

[TytoAlba95]

Considering the general Michaelis-Menten curve, in the region where S < Km, the V₀- relationship is linear, so yes the reaction velocity doubles as S approximately doubles.
It is not the same when S > Km, because the slope decreases, the rise of V₀ with S will be less than double.

 

[Ygggdrasil]

Considering the general Michaelis-Menten curve, in the region where S < Km, the V₀- relationship is linear, so yes the reaction velocity doubles as S approximately doubles.
It is not the same when S > Km, because the slope decreases, the rise of V₀ with S will be less than double.

Yes, that is correct. With these principles in mind, this should lead you to the correct response.