If I have an antibody A and a target B, and experimentally titrate the antibody against a single concentration of B, and then measure the % of B that is bound after the solutions reach equilibrium, I should be able to determine the KD of the interaction.
Source below (and others) shows that determining KD is as simple as determining the EC50 of such a curve. Source.
How does that square with the following equation for KD?
$KD = \frac{([A]*[B])}{[AB]}$ where A is unbound antibody, $B$ is unbound antigen, and $AB$ is the bound complex.
Let's say I have 10 pM of target antigen, 50% of which is bound when incubated to equilibrium with 10 pM of antibody. That would mean the antibody and antigen are each 50% bound and 50% unbound.
$KD = 5pM * 5pM / 5pM$ $KD = 5 pM$
So I have calculated a 5 pM KD, not the 10 pM that I would think would be similar to the graph below (assuming they had pM units on the X axis) I'm assuming these types of example graphs refer to the input concentration, right?
Even more confusing, what if the antibody is a really tight binder, such that 10pM of antibody is able to essentially bind 100%, such that 10 pM antibody is able to bind 50% of 20pM of antigen. (1:1 binding assumed)
$KD = ~0.001pM * ~10pM / ~10pM$
Now you have a KD of 0.001pM, but the graph would suggest that 10 pM of antibody is necessary to bind to 50% of the target antigen.