I was told that for an allosteric enzyme regulation to work, the enzyme in account should contain at least 2 subunits, but I can't understand why this is necessary.

I think enzyme regulation is different from competitive inhibition as the former just stabilize the T state shifting the equilibrium but not directly competing for active site as in the latter case.

And I think enzyme regulation is also different from non-competitive inhibition as non-competitive inhibition directly bind and inhibit the R state while the former just stabilize the T state, so it is in an equilibrium, an increase in substrate concentration could shift back the equilibrium. But this is not the case in non-competitive inhibition as the inhibitor also binds with the enzyme-substrate complex, a certain amount of active ingredient are definitely inactivated.

I don't know these two understandings are correct or not. When I try to explain it by that, 'the enzyme must have at least 2 subunits as the binding of regulator would not directly affect the polypeptide chain containing the active site', this explanation should fail as I can't see any reason that a regulator binding to an allosteric site of an enzyme with single chain only when the enzyme is in T state could make any difference from an enzyme with 2 chains (subunits).

I hope there are somebody to answer my question... even discuss is helpful... Thanks.

Actually it is easy. You have to think more in terms of mechanism. On which part does a competitive inhibitor bind on the enzyme, and where doe allosteric inhibitors bind?

A competitive inhibitor binds directly to the active site and an allosteric one binds to an allosteric site away from the active site, both of them bind the enzyme in R state.

So is the binding to R state by these inhibitor but the binding to T state of those regulators what make a difference?

And why single chain protein, assuming it does have an allosteric binding site and flipping between T and R states, not be effective in regulation by these regulators?

Wait a tick, I may have misunderstood your question. Are asking whether several subunits (i.e. protomers) are needed? The latter is dependent a bit on what model for allosteric inhibition is used.

Yes the question is about whether polysubunit is needed. But it focuses on regulation rather than inhibition. I think regulation is different from inhibition that regulator binds to T state but allosteric inhibitor binds to R state. (otherwise regulator would have a lower max. reaction velocity, but the max. velocity remains in fact)