If you look at Uworld question ID 12299 it has a wonderful explanation for this. If they share the same epitopes, it will have a downward slope. If they share none of the same epitopes, the line will be horizontal across the graph (indicating no change as the amount of Y added increases)
so how would the graph look for protein x expresses all of the epitopes expressed by protein y, but protein y does not express all of the epitopes expressed by protein x?
I found this, I think it gives kinda of an explanation: If the regression of log ((A'/A) -1) on -log B is linear with a slope of -1, then this indicates that the antagonism is competitive and by definition the agonist and antagonist act at the SAME recognition sites. So basically the more you add Y, the less X is bound, which means they have a same structural component (epitope) and must act on the same site? Don't know if this makes sense...
this question was utter BS, but the way I justified "same epitopes" was that it said "in the context of anti-serum X," i.e., which epitopes would have been developed in the context of the antibodies present. It's unlikely that anti-X antibodies would bind to epitopes on Y that aren't on X. But you could argue there are theoretical epitopes on Y that could be bound by another antibody that doesn't exist in this scenario.
Very drawn out and took me 5 minutes to actually figure out on the test, honestly a waste of time in my opinion, but there you go.
Ran across a question similar to this in another question bank. In that question, there was no change as the concentration of the new protein was added, which meant that the two proteins did not share similar epitopes. In this question, the antibody is just trying to bind its epitope, so adding more or y means less binding of protein x because the antibody favors the proteins the same.
High X is bound when low Y is added, and low X is bound when Y is added. So MAYBE they are competing for the same binding spot/epitope due to this relationship (epitope= antibody binding site) ??????????