A high-affinity, binary Eu^(3+) receptor site consisting of 1,4,7,10-tetraazacyclododecane-1,7-diacetate (DO2A) was constructed with the goal of improving the detection of dipicolinic acid (DPA), a major component of bacterial spores. Ternary Eu(DO2A)(DPA)− complex solutions (1.0 µM crystallographically characterized TBA·Eu(DO2A)(DPA)) were titrated with EuCl_3 (1.0 nM−1.0 mM); increased Eu^(3+) concentration resulted in a shift in equilibrium population from Eu(DO2A)(DPA)^− to Eu(DO2A)^+ and Eu(DPA)^+, which was monitored via the ligand field sensitive ^5D_0 → ^7F_3 transition (λ_(em) = 670−700 nm) using luminescence spectroscopy. A best fit of luminescence intensity titration data to a two-state thermodynamic model yielded the competition equilibrium constant (K_c), which in conjunction with independent measurement of the Eu(DPA)^+ formation constant (K_a) allowed calculation of the ternary complex formation constant (K_a^′). With this binding affinity by competition (BAC) assay, we determined that K_a^′ = 10^(8.21) M^(−1), which is ∼1 order of magnitude greater than the formation of Eu(DPA)^+. In general, the BAC assay can be employed to determine ligand binding constants of systems where the lanthanide platform (usually a binary complex) is stable and the ligand bound versus unbound states can be spectroscopically distinguished
