Quick question about enzyme allosteric inhibition

Are you asking how would inhibition affect K_m and V_max?
Do you know the definitions for K_m and V_max and what they mean?

 

Is inhibition the same as inactivation?

 

Can be an effect on either or both.
Monod originally invented the terms 'K system' and 'v system' for effects on K and v respectively.
(I think K effects are more common, but also effects that are purely 100% one or the other are not all that common, though sometimes the v effect is fairly small.)
And with a given enzyme you may find a K effect with one substrate and a v effect with another. There is nothing in theory that says that any effect has to be one or another.

You will realise of course that many allosteric enzymes do not have a K_m, because, especially in presence of an inhibitor, the substrate dependency of the reaction rate is not Michaelian but co-operative. The affinity can be expressed by the S_0.5, the substrate concentration at half-saturation which is equal to K_m in the case of non-cooperative kinetics. An allosteric inhibition in a K system will increase S_0.5 (shift v,S curves to right). An allosteric inhibitor in a v-system will reduce V_max. Both practically by definition! S_0.5 is more an empirical than a thermodynamic affinity parameter, the thermodynamic one is the 'median ligand concentration' equal to S_0.5 only for symmetrical* curves but that I imagine is for later if at all.

*against log that is