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 [tex]K_M = [/tex] then
[tex]v_0 = v_{max}\frac{}{K_M+}=v_{max}\frac{}{2}=\frac{v_{max}}{2}[/tex]

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.

 

[quicknote]

Thank you for your question. The relationship between Km and enzyme concentration is a complex one and may not be intuitive at first. Let me explain in more detail below.

Km is the Michaelis constant, which is a measure of the affinity of an enzyme for its substrate. It represents the substrate concentration at which the enzyme is working at half of its maximum velocity (Vmax). In other words, it is the concentration of substrate required to achieve half of the maximum reaction rate.

Now, let's consider the equation you mentioned, Vmax = k2[E]. This equation shows that the maximum reaction rate (Vmax) is directly proportional to the enzyme concentration ([E]). This means that increasing the enzyme concentration will lead to an increase in Vmax. However, this does not necessarily mean that Km will also increase.

The reason for this is that Km is not solely dependent on enzyme concentration. It is also influenced by the affinity of the enzyme for its substrate, which is determined by the enzyme's structure and active site. Even if the enzyme concentration is increased, the affinity of the enzyme for its substrate will remain the same, and therefore, Km will not change.

In other words, Km is a measure of the enzyme-substrate interaction and is not affected by changes in enzyme concentration. It is possible for two enzymes with different concentrations to have the same Km value, as long as they have the same affinity for their substrate.

I hope this clarifies the relationship between Km and enzyme concentration. If you have any further questions, please feel free to ask.