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Competitive Inhibitor

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I understand to identify a competitive inhibitor, the Km increases and the Vmax doesn't change.

I was going through a SB C/P problem (#77) and thought how could Km change based on a constant Vmax?
If Km=1/2Vmax, how does Km decrease/increase while Vmax stays the same?

According to the equation, wouldn't we always expect that with an increase in Vmax, there would be an increase in Km

Probably overthinking again.:yawn:

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