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MCAT-What is the effect of an uncompetitive inhibitor on Kcat?

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I know that an uncompetitive inhibitor (UCI) decreases both Km and Vmax, as it binds allosterically and to either E or ES
Kcat is defined as the catalytic turnover rate of the enzyme = # products produced per second per active site
Would you agree that with an UCI, Km decreases, hence the E affinity towards S increases, hence E has a higher turn over rate, hence a higher Kcat should be expected?
I couldn't find the answer online. Thank you for taking the time.

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