[Signifier]

I have two substrates (phosphate and carbonate). They competitively bind for the same ligand, L.

I have titrated L with phosphate, and I have a dissociation constant for L and just phosphate. The Kd is 20 millimolar.

I have titrated L with carbonate, and I have a dissociation constant for L and just carbonate. The Kd is 0.3 millimolar.

I have titrated L with phosphate in the presence of a FIXED amount of carbonate, and I have a dissociation constant for L and phosphate in the presence of carbonate. The Kd for phosphate in the presence of carbonate is 2.1 millimolar as measured.

Now, obviously, this last dissociation constant is different from the first dissociation constant (L and phosphate only), because phosphate and carbonate compete with each other.

I would like to THEORETICALLY PREDICT what the Kd for L and phosphate in the presence of carbonate is, and compare this to the 2.1 millimolar Kd that I actually measured.

I have: concentrations of phosphate and carbonate for all studies, concentration of ligand L for all studies, full photometric titration spectra, and the above calculated dissociation constants.

I do not have: extinction coefficients, etc.

What equations can I use to calculate this "mixture" dissociation constant?

Thanks for any and ALL suggestions!

BTW, is this the right board for this?