Km and Vmax dependence on enzyme concentration

[p3t3r1]

We know that Vmax depends on enzyme concentration since Vmax = k2[E]

However, what I have trouble grasp is that why Km does not depend on enzyme concentration if Km is the substrate concentration where V = 1/2 Vmax. If you increase Vmax, shouldn't Km increase as well since it is dependent on it?

I asked my biochem prof today and he gave some explanation about substrate concentration which I didn't catch. I am hoping someone can clarify it here. thanks!

 

[alxm]

If $$K_M =$$ then
$$v_0 = v_{max}\frac{<s>}{K_M+<s>}=v_{max}\frac{<s>}{2<s>}=\frac{v_{max}}{2}</s></s></s></s>$$

Note though, that this doesn't mean $$K_M$$ is dependent on . $$K_M$$ is defined as a measure of the equilibrium constant for E + S <-> ES. Which is not dependent on any concentration, as long as the reaction is first order, which Michaelis-Menten kinetics assumes. (it also assumes a steady-state where [ES] is near-constant)

I see http://en.wikipedia.org/wiki/Michaelis–Menten_kinetics" has a thorough derivation of Michaelis-Menten kinetics, btw.