So far, I know about competitive, non-competitive inhibitors and allosteric inhibitor. Which ones are reversible and which ones are irreversible?
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These modes of inhibition are reversible. They describe a particular modification of the working of the enzyme (change of affinity, of maximum velocity, of both) due to the reversible binding of an inhibitor to a particular site.
On the other hand irreversible inhibition stops the enzyme from working through an inhibitor that binds irreversibly : no more transformation of substrate occurs after that. One cannot define a velocity, affinity, or IC50, for a non-working enzyme, thus "competitive", "non-competitive", "uncompetitive" are not useful concepts in that case.