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A much easier approach is the application of the complex-forming agent in the mobile phase. Then the retention determination should be carried out with and without the complexing agent in the mobile phase. The complex stability constant is in relation to the change of the retention. Many HPLC methods have been developed for determination of the stability of various inclusion complexes of cyclodextrin using different theoretical and practical considerations. From the different distribution of the uncomplexed X and complexed CX molecules between the mobile and the stationary phases the complex stability constant can be determined according to Eq. (27).
Ê — [ªÕÄò
* “ [XL, [CL (27)
Figure 8 Elution of drugs on 10-cm columns filled with polymer-coated silica (broken line: support without /Ç-cyclodextrin; solid lines support with /Ç-cyclodextrin). (1) warfarin; (2) indo-methacin; (3) propranolol; (4) furosemide; (5) diazepam; (6) phenylbutazone. (From Ref. 61.)
where m and s refer to the mobile and the stationary phase, respectively. [Ñ], [X], and [XC] refer to the cyclodextrin, guest molecule, and the cyclodextrin-guest molecule complex concentration, respectively. Ê is the stability constant of 1:1 cyclodextrin-guest molecule complex. The apparent concentration distribution can be expressed by Eq. (28).
[X]s + [CX]S [X]m + [CXI
By combining Eqs. (27) and (28), Eq. (29) can be obtained:
Dx + (Dc Ê [C]J
1 + (Ê [C] J
where Dx and Dc are the distribution of the guest and the cyclodextrin molecule in the mobile and stationary phases, respectively.
When the addition of cyclodextrin to the mobile phase does not significantly change the void volume of the column, the distribution ratios can be calculated from the retention times according to Eqs. (30)-(32).
where ts, tc, and tcx are the retention times of the guest molecule, the cyclodextrin molecule, and the complexed molecules at a given cyclodextrin concentration in the mobile phase, respectively. The /obs means the retention time of the X molecule at a given cyclodextrin concentration in the mobile phase. The t0 refers to the dead time, and the Vs/Vm is the phase ratio. By substituting Equations (30)-(32) into Eq. (29) Eq. (33) can be obtained:
(tx + Q (Ê [Ñ])
r°bs 1 + (Ê [C]J ^
By rearranging Eq. (33), Eq. (34) can be obtained:
------[Ck- = -ISs- + 1 ---------------------------------------------------(34)
-----Ê ~ ‘ob,----Ê - t,.---ê (/, - t J---------------------------------------------------------
Equation (34) provides the possibility for determination of the Ê stability constant and tcx values from the slope and the intercept of the plot [C]m/(tm - tobs) versus [C]m plot. When the retention times are long or tK is unknown, the retention time of the X molecule can be determined at various cyclodextrin concentrations in the mobile phase. Several cyclodextrin complex stability constants have already been determined by these chromatographic methods [62-70].
In general, the HPLC method for the determination of cyclodextrin complex stability constants or, more exactly, relative strength of the interactions, can be applied when only one species of the solute (i.e., the neutral molecule) is exclusively present, only 1:1 is the stoi-chiometry of the complex formation, and the cyclodextrins do not influence the properties of the stationary phase. Under the circumstances, the HPLC method offers a precise determi-nation of complex stability constants in solution. Unlike other methods, HPLC can be applied with relatively impure samples without further purification, as separation takes place during the measurements. Because of the low concentrations in the eluant, the low solubility of the molecules cannot disturb the measurements, whereas poor sample solubility often limits the use of traditional techniques. However, the HPLC method can be applied for the association constant measurements only when the rate of equilibration in the mobile phase is rapid, compared with the time of the chromatographic run. Otherwise poor peak shape and peak splitting can cause difficulties in the retention determination.
B. Determination of Drug-Protein-Binding Constants by HPLC
The most important binding constants characterize drug-protein interactions. It has been well recognized for more than 40 years that the pharmacological activity of a drug molecule de-pends on the concentration of the free molecule in biological compartments. The binding of drugs to a protein influences its pharmacokinetics. Basically, the drug-receptor interaction also can be considered as drug-protein binding. Acidic drugs mostly bind to albumin in plasma, whereas basic drugs preferentially bind to ^,-acid glycoprotein. Stereoselective binding of racemic mixtures of drugs has been frequently established [71,72], and its importance in storage and transport processes has been reviewed . Numerous methods, such as equilibrium dialysis, fluorescence spectroscopy , circular dicroism , and gel column centrifugation [76-80], have been used to study drug-protein binding. In general, the methods can be divided into spectroscopic and nonspectroscopic ones. The nonspectroscopic methods usually involve separation of the free ligands from the bound species. They included soft-gel chromatography, HPLC, ultrafiltration, ultracentrifugation, and equilibrium dialysis. These methods can be applied as complementary, rather than competitive, and it is always advisable to use more than one method for the binding measurements. Sebille et al.  have published a concise review about the separation procedures to reveal and follow drug-protein binding. The applications of HPLC for the determination of drug-protein binding has been discussed in detail .