Determination of second-order association constants by global analysis of 1H and 13C NMR chemical shifts. Application to the complexation of sodium fusidate and potassium helvolate by beta- and gamma-cyclodextrin.

The host-guest interaction between the steroid antibiotics sodium fusidate and potassium helvolate as guests and the hosts beta- and gamma-cyclodextrin was studied by 13C and 1H NMR techniques. The analysis of chemical shifts of individual nuclei leads to inconsistent values of the association constants and fails generally in the case of mixtures of 1:1 and 1:2 stoichiometries. The problem of parameter correlation is identified and the global analysis of two or more nuclei is proposed as a very effective method for the detection of complexes of higher stoichiometries and for the precise determination of the involved association constants. A matrix formulation of global analysis and the determination of confidence intervals is described. An analytical solution of the cubic equation, necessary for the description of higher order complexes, is presented in detail and its use together with commercial fitting software is compared with dedicated implementations. gamma-Cyclodextrin forms with both studied steroids, sodium fusidate and potassium helvolate, 1:1 complexes with high values of the association constants, K(1)=(60+/-24)x10(3)lmol(-1), and K(2)=(22+/-9)x10(3)lmol(-1), respectively. To the contrary, beta-cyclodextrin forms 1:1 and 1:2 (guest:host) complexes with both steroids, with moderate K(1) and low K(2) values (K(1)=(0.74+/-0.13)x10(3)lmol(-1), K(2)=(0.210+/-0.075)x10(3)lmol(-1)), and (K(1)=(2.42+/-0.87)x10(3)lmol(-1), K(2)=(0.06+/-0.09)x10(3)lmol(-1)), respectively.