Determination of Association Constants

The association constant (the synonymous expressions binding constant, stability constant, or complex constant can be found in the literature) K for complex formation of guest molecules with host CyD can be determined from NMR titration experiments. Assuming a given stoichiometry of the complex  

Since the rates of complex formation and decomposition are usually faster than the NMR time scale, the chemical shift averaged signals dobs are observed  

Owing to their accuracy and simplicity of determination, chemical shift titrations make up the vast majority of NMR titration experiments. A number of other -spin nuclei, or are also used for this purpose [3, 4]. One should 

Host-Guest Orientation and Geometry of CyD Inclusion Complexes 

In the complex of carbazol-viologen-linked compound 2 with a-CyD, NOEs have been observed between H-5 and one H-6 host protons and the spacer methylene protons [15]. Orientation of the guest molecule could be revealed from the NOE correlations between another host methylene proton H-6 and carbazole a and d ones, strongly suggesting that the carbazole moiety protrudes from the narrow rim of the host cavity. In the NOESY spectmm of the doxorubicin (3)-y-CyD complex, insertion of the D ring into the host cavity is confirmed by the H-1(G)/H- 

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Purification of solvents and salts is essential for reliable electrochemical studies and measurements. A water content of 20ppm already corresponds to a 10 3molL solution. This is in the concentration range of dilute solutions used in conductivity studies for the determination of association constants (see Sec.7.3.2). Traces of water may affect chemical equilibria and therefore act on specific conductivities and limiting ion conductivities. For example, addition of 30 ppm water to a 2xl0-4 mol LT1 solution of LiBF4 in THF at 15 °C increases its conductivity by 4.4 percent (precision of measurements about 0.02 percent) 380 ppm water causes an increase by 51.7 percent see Fig. 3 [20J. 

The commonly used method for the determination of association constants is by conductivity measurements on symmetrical electrolytes at low salt concentrations. The evaluation may advantageously be based on the low-concentration chemical model (lcCM), which is a Hamiltonian model at the McMillan-Mayer level including short-range nonelectrostatic interactions of cations and anions [89]. It is a feature of the lcCM that the association constants do not depend on the physical... 

Valko, I. E., Siren, H., and Riekkola, M. L. (1997). Determination of association constants of dansyl-amino acids and beta-cyclodextrin in N-methylformamide by capillary electrophoresis. Electrophoresis 18, 919-923. 

Zampronio, C.G. Giannakopulos, A.E. Zeller, M. Bitziou, E. Macpherson, J.V. Derrick, P.J. Production and properties of nanoelectrospray emitters used in fourier transform ion cyclotron resonance mass spectrometry implications for determination of association constants for noncovalent complexes. Anal. Chem. 2004, 76, 5172-5179. 

As with other methods, ACE and its relatives provide experimental data corresponding to a mean value of concentrations governed by interrelated equilibria. Determination of association constants requires a suitable mathematical model with only few parameters to be estimated. 

S Fanali, P Bocek. A practical procedure for the determination of association constants of the analyte—chiral selector equilibria by capillary zone electrophoresis. Electrophoresis 17 1912-1924, 1996. 

A Amini, N Merclin, S Bastami, D Westerlund. Determination of association constants between enantiomers of orciprenaline and me thy 1-/3-cyclodextrin as chiral selector by capillary zone electrophoresis using a partial filling technique. Electrophoresis 20 180-188, 1999. 

Eielding L. Determination of association constants (Ka) fi om solution NMR data. Tetrahedron 2000 56 6151-6170. 

The best-developed way to measure the association of ions is through the measurement of electrical conductance of dilute solutions. As mentioned, this realization occurred in the nineteenth century to Arrhenius and Ostwald. An elaborate development of conductance equations suitable to a range of ion concentrations of millimolar and lower by many authors (see Refs. 5, 33 and 34 for critical reviews) has made the determination of association constants common. Unfortunately, in dealing with solutions this dilute, the presence of impurities becomes very difficult to control and experimenters should exercise due caution, since this has been the source of many incorrect results. For example, 20 ppm water corresponds to 1 mM water in PC solution, so the effect of even small contaminants can be profound, especially if they upset the acid-base chemistry of association. The interpretation of these conductance measurements leads, by least squares analysis of the measurements, to a determination of the equivalent conductance at infinite dilution, Ao, the association constant for a positively and negatively charged ion pair, KA, and a distance of close approach, d, using a conductance equation of choice. One alternative is to choose the Bjerrum parameter for the distance, which is defined by... 

Soon afterward, Kronman, who has made a long study of a-lactalbumin reactions, considered that there was an experimental artifact in the use of chelating metal ion buffers (e.g., EGTA and EDTA) in the determination of association constants for metal ions with proteins by fluorescence titration. Kronman and Bratcher (1983) concluded that their observations explained the discrepancy between As,i for Ca(ll) and bovine a-lactalbumin reported by Kronman et al. (1981) (2.7 X 10 M ), Permyakov et al. (1981) (6.3 X 10 M" ), and Murakami et al. (1982) (4 x 10 Af- ). 

Sadlej-Sosnowska, N. Eluorometric determination of association constants of three estrogens with cyelodextrins. J. Eluoresc. 1997, 7(3), 195-200. 

Determination of Association Constants by High-Performance Affinity Chromatography10... 

The determination of association constants, using diffusion NMR, is based on the fact that there is a fast exchange between the free and bound states of the guest. However, there are important applications of diffusion measurements in the case of slow exchange. Such an example is the study of molecular capsules and the encapsulation phenomenon, as will be outlined in the next section. 

Interaction of electron acceptors with bases. Part 15. Determination of association constants of organic charge-transfer complexes by n.m.r. spectroscopy, R. Foster and C. A. Fyfe, Trans. Faraday Soc., 1965, 61, 1626. 

It is noteworthy that extraction may be both a research tool and an ultimate goal in host-guest chemistry, the latter case being still rather rare. As a tool, extraction is common since the works of Cram and co-workers [28-33], who introduced and widely used it for the determination of association constants for amine-macrocycle complexation (see also the review by Cram and Trueblood in Ref. 8). This technique may be summarized as follows. 

Diffusion measurements make possible the determination of association constants for complexes with small chemical shift changes induced by the association. A representative example of such application is the evaluation of association constants for the complexes of y-CyD with 12-crown-4 and its tetraaza and tetrathia analogues [27]. A titration experiment with self-diffusion coefficient detection was also used for determination of the association constants of the 1-adamantanecarboxylic acid- -CyD complex at two temperatures [28]. 

The association constants for CyD complexes with chiral guests are generally different and mostly quantitatively determined by the chemical shift titration experiments. However, as mentioned above, other NMR parameters, such as relaxation rates [10, 70] or self-diffusion coefficients, may also be used. Both those parameters were successfully applied for the enantiodifferentiation and determination of association constants in complexes of the trifluoroacetate salts of the enantiomers of amphetamine, ephedrine, and propranolol with 2,6-di-O-dodecyl-a-CyD and its p analogue [71]. The DOSY technique was employed for the determination of diffusion coefficients of enantiomers of cyclohexanone derivatives complexed with a-, j8-and y-CyDs as well as with their per-O-methylated analogues [72]. 

A general problem in the determination of association constants with the help of NMR titration appeared for the complexes II-16/B-2 and II-16/D-3 (Table 12.2). Different association constants were obtained by using signals from different protons (e.g., protons of the tropylium moiety and the dimethylamino group of guest D-3). This finding can be interpreted as the formation of isomeric complexes in which different parts of the guest molecule are oriented into the interior of the host molecule (see Scheme 12.13). In such cases, the determination of the microscopic association constants of both complexes is not possible. Obviously the formation of isomeric... 

Shinkai, S. Araki, K. Matsuda, T. Manabe, O. NMR determination of association constants for aqueous calixar-ene complexes and guest template effects on the conformational freedom. Bull. Chcm. Soc. Jpn. 1989. 62, 3856. 

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