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Michaelis-Menton Equation (modified)

dttom
in Biochemistry and Molecular Biology

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I am considering modified form of Michaelis-Menton equation specially concerning non-competitive inhibition. The picture attached described what I have done...

22457347c4c51b44.jpg

But why must K3 equal K4, I know it is the experimental result, but is there any actual reason can account for this?

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