Measurement of dissociation constants

The following descriptions will be couched primarily in terms of chemical shift changes, which are the most widely used for the measurement of dissociation constants the general principles apply equally to measurements based on other NMR parameters, and these will be touched on later. 

The fast exchange regime is by far the most useful for the measurement of dissociation constants from changes in chemical shift, relaxation or other NMR parameters - a wide range of K values, from 10 pM (or perhaps a little less) to >10 mM, can be accessible. 

Bligh, S.W.A. Haley, T. Lowe, P.N. Measurement of dissociation constants of inhibitors binding to Src SH2 domain protein by non-covalent electrospray ionization mass... 

The ultra-violet spectra of guanidines have often been determined in connection with the measurements of dissociation constants [17, 38,41], and other studies have been repotted [42-44]. There have been many reports on the infra-red spectra [31, 35, 42, 45-48], the nuclear magnetic resonance spectra [38, 49-51] (see also p. 134), the Raman spectra [52-54], force constants [35, 36], and mass spectra [55] of substituted guanidines. 

The measurement of dissociation constants greatly helps the understanding of the mechanisms involved in biomolecular recognition. The dissocia-... 

Gao, H., Yu, Y, Leary, J.A. (2005) Mechanism and Kinetics of Metalloenzyme Phos-phomannose Isomerase Measurement of Dissociation Constants and Effect of Zinc Binding Using ESI-FTICR Mass Spectrometry. Anal. Chem. 77 5596-5603. 

The application of gel electrophoresis to the measurement of dissociation constants of protein-ligand complexes has been studied previously (Yen HC et al. 1993). The dissociation constant in the gel (Kf ) is defined by following equations ... 

Gao, H. Yu, Y. Leary, J. A. Meehanism and kinetics of metalloenzyme phosphomarmose isomerase Measurement of dissociation constants and effect of zinc binding using Esi-Fticr mass spectrometry. Anal. Chem. 2005, 77(17), 5596 5603. 

As we described in Chapter 3, the binding of reversible inhibitors to enzymes is an equilibrium process that can be defined in terms of the common thermodynamic parameters of dissociation constant and free energy of binding. As with any binding reaction, the dissociation constant can only be measured accurately after equilibrium has been established fully measurements made prior to the full establishment of equilibrium will not reflect the true affinity of the complex. In Appendix 1 we review the basic principles and equations of biochemical kinetics. For reversible binding equilibrium the amount of complex formed over time is given by the equation... 

Measurement of dissociation equilibrium constants, which is of particular value in receptor classification and in the study of structure/activity relationships, where the effects of changes in chemical structure on affinity (and efficacy) are explored. 

When attempting to use NMR to measure a dissociation constant, the basic experiment will be to vary the ligand concentration in the presence of a fixed concentration of protein. (The converse experiment, varying the protein concentration, may sometimes be carried out, but is generally less satisfactory because of problems with protein solubility and aggregation.) What one sees in this experiment will depend critically on the rate of... 

The p/<, of a base is actually that of its conjugate acid. As the numeric value of the dissociation constant increases (i.e., pKa decreases), the acid strength increases. Conversely, as the acid dissociation constant of a base (that of its conjugate acid) increases, the strength of the base decreases. For a more accurate definition of dissociation constants, each concentration term must be replaced by thermodynamic activity. In dilute solutions, concentration of each species is taken to be equal to activity. Activity-based dissociation constants are true equilibrium constants and depend only on temperature. Dissociation constants measured by spectroscopy are concentration dissociation constants." Most piCa values in the pharmaceutical literature are measured by ignoring activity effects and therefore are actually concentration dissociation constants or apparent dissociation constants. It is customary to report dissociation constant values at 25°C. 

Conductance measurements also have been used for the estimation of dissociation constants of weak electrolytes. If we use acetic acid as an example, we find that the equivalent conductance A shows a strong dependence on concentration, as illustrated in Figure 20.2. The rapid decline in A with increasing concentration is largely from a decrease in the fraction of dissociated molecules. 

L.L. Sasmor, H. Griffey, R.H. Measurement of macromolecular binding using electrospray mass spectrometry. Determination of dissociation constants for oligonucleotide serum albumin complexes. J. Am. Chem. Soc. 1995, 117, 10765-10766. 

In connection with the subject of the relation between association state and kinetic order, it is germane to mention observations of Roovers and Bywater (45). They measured the dissociation constant for the tetramer , dimer case for polyiso-prenyllithium in benzene. The technique involved a study of the electronic spectra at 272 and 320 nm. If the process they measured can be directly related to the association-dissociation equilibrium, their results can be used to calculate the dissociation constant for the correct dimer monomer system. This value is ca. 2xl0-5 at 30.5°C. If this value is accepted, then the situation is encountered where the degree of dissociation of the polyisoprenyllithium chain ends varies from about 0.10 to... 

ES Difference plot. A solution containing 0.139 mmol of the triprotic acid tris(2-aminoethyl)amine-3HCl plus 0.115 mmol HC1 in 40 mL of 0.10 M KC1 was titrated with 0.490 5 M NaOH to measure acid dissociation constants. 

Logarithms of formation constants, which are proportional to the Gibbs energies of association, are often tabulated. The logarithms of formation constants and pK t values of dissociation constants are identical (Eq. 6-72) and are a measure of the standard... 

A different and independent approach to determine the parameters of KC8 is made by conductivity measurements. The dissociation constant of carbanionic compounds displays no simple temperature dependence according to the van t Hoff equation as Worsfold and Bywater (32) and Szwarc (33) have already shown. When we assume two types of ion pairs, the experimentally measured dissociation constant is given by... 

It can be shown that Km equals the concentration of the substrate at which the reaction velocity is one half of its maximum. The Michaelis-Menten constant is an important figure of merit for the enzyme. It is the measure of its activity. Although it describes a kinetic process, it has the physical meaning of dissociation constant, that is, a reciprocal binding constant. It means that the smaller the Km is, the more strongly the substrate binds to the enzyme. 

The examples cited above illustrate the difficulties of deciding the state of hydration of the species involved in an equilibrium on the basis of solvent isotope effects. This discussion has certain parallels in problems of reaction mechanism where the degree of involvement of water in the transition state (distinction between A-l and A-2 reactions) is at issue. By analogy with the conclusions reached for the dissociation of polybasic acids we may anticipate that it will similarly not be easy to settle such questions by the measurement of rate constants in H20-DzO mixtures. 

Electrochemical measurement of pHa via Eq. (8.3) senses hydronium ion activity rather than its concentration. Hence, electrochemical evaluations of dissociation constants (Af ) yield thermodynamic quantities... 

The acidity constant can also be a measure of dissociation and of how much acidic a particular acid is. The stronger be acid, is more ionised and therefore the greater the concentration of products in the above equation. Hence, a strong acid has a high Ka value. The Ka values for the following ethanoic acid are in brackets and these show that the strongest acid in the series in trichloroacetic acid. 

Several methods have been applied to determinations of dissociation constants of radicals. Most of them are based on measuring a parameter which at any pH is a weighted average of the parameters of the acid and basic forms present at that pH. A plot of the observed parameter versus pH gives the typical sigmoidal curve with an inflection point where pH = pK. Several parameters can be different for the acid and basic forms to allow p/ -measurements. The most commonly used method utilizes differences in the optical absorption spectra of these two forms of radicals. Monitoring by... 

---