Constants, association

One can write acid-base equilibrium constants for the species in the inner compact layer and ion pair association constants for the outer compact layer. In these constants, the concentration or activity of an ion is related to that in the bulk by a term e p(-erp/kT), where yp is the potential appropriate to the layer [25]. The charge density in both layers is given by the algebraic sum of the ions present per unit area, which is related to the number of ions removed from solution by, for example, a pH titration. If the capacity of the layers can be estimated, one has a relationship between the charge density and potential and thence to the experimentally measurable zeta potential [26]. 

The DNA base pairs guanine (G), cytosine (C), adenine (A) and thymine (T). The uracil-2,6-diaminopyridine pair can also form three hydrogen bonds but has a much lower association constant than G-C. 

Auto-association of A-4-thiazoline-2-thione and 4-alkyl derivatives has been deduced from infrared spectra of diluted solutions in carbon tetrachloride (58. 77). Results are interpretated (77) in terms of an equilibrium between monomer and cyclic dimer. The association constants are strongly dependent on the electronic and steric effects of the alkyl substituents in the 4- and 5-positions, respectively. This behavior is well shown if one compares the results for the unsubstituted compound (K - 1200 M" ,). 4-methyl-A-4-thiazoline-2-thione K = 2200 M ). and 5-methyl-4-r-butyl-A-4-thiazoline-2-thione K=120 M ) (58). 

Thus, if theantibody has a high affinity for the antigen, it has a high association constant. Typical association constants range from lO to 10 ° L/mol, and as high as 10 L/mol for some monoclonal antibodies. 

The definition of an association constant for an antibody—antigen reaction can become more complex if the antibody—antigen reaction iavolves a multivalent antigen, as is the case when a polyclonal antisemm is used for detection of an antigen. This type of multivalent binding is termed avidity and is defined by the equation ... 

Specific Conductance. The specific conductance depends on the total concentration of the dissolved ioni2ed substances, ie, the ionic strength of a water sample. It is an expression of the abiUty of the water to conduct an electric current. Freshly distilled water has a conductance of 0.5—2 ]lS/cm, whereas that of potable water generally is 50—1500 ]lS/cm. The conductivity of a water sample is measured by means of an a-c Wheatstone-bridge circuit with a null indicator and a conductance cell. Each cell has an associated constant which, when multiphed by the conductance, yields the specific conductance. 

MW) is the molar concentration of methanol/water associate, and (k) is the "association" constant... 

Chaput, Jeminet and Juillard measured the association constants of several simple polyethylene glycols with Na", K", Cs", and Tl". Phase transfer catalytic processes and most biological processes are more likely to involve the first two cations rather than the latter two, so we will confine the discussion to these. Stability constants for the dimethyl ethers of tetra-, penta-, hexa-, and heptaethylene glycols were determined poten-tiometrically in anhydrous methanol solution and are shown in Table 7.1. In the third column of the table, the ratio of binding constants (Ks/K s) is calculated. Note that Simon and his coworkers have referred to this ratio as the selectivity constant. ... 

The parameter is an analog of the equilibrium association constant. The value of A p itself, rather than the potential is used to characterize the strength of the associative forces. 

Table 6-4. Association constants for complexes between carboxylic acids and nitrogen bases in aprotic solvents and corresponding association constants and site densities for binding of the base to a molecu-larly imprinted polymer.

Furthermore, about 1920 the idea had become prevalent that many common crystals, such as rock salt, consisted of positive and negative ions in contact. It then became natural to suppose that, when this crystal dissolves in a liquid, the positive and negative ions go into solution separately. Previously it had been thought that, in each case when the crystal of an electrolyte dissolves in a solvent, neutral molecules first go into solution, and then a certain large fraction of the molecules are dissociated into ions. This equilibrium was expressed by means of a dissociation constant. Nowadays it is taken for granted that nearly all the common salts in aqueous solution are completely dissociated into ions. In those rare cases where a solute is not completely dissociated into ions, an equilibrium is sometimes expressed by means of an association constant that is to say, one may take as the starting point a completely dissociated electrolyte, and use this association constant to express the fact that a certain fraction of the ions are not free. This point of view leads directly to an emphasis on the existence of molecular ions in solution. When, for example, a solution contains Pb++ ions and Cl- ions, association would lead directly to the formation of molecular ions, with the equilibrium... 

The conductivity of a solution containing such molecular ions may be small compared with the value that would result from complete dissociation into atomic ions. In this way, in the absence of neutral molecules, we can have a weak electrolyte. The association constant for (29) has a value that is, of course, the reciprocal of the dissociation constant for the molecular ion (PbCl)+ the logarithms of the two equilibrium constants have the same numerical value, but opposite sign. 

Table 5. 1 1 Association constants log pL for phosphate and nucleotides with polyamines or metal ions at 25 C... 

The conditional association constant for [18]aneN4 ( cyclic spermine ) with ATP - at pH 7.5 is calculated from the (3L value (Table 5) and protonation constants (Table 1) to be 2.4x 105 M-1, which is larger than the association constants for the linear spermidine (9 xi 02 M ) and spermine (9.5 x 103 M-1)23). It is also of interest that cyclic spermine is selective for ATP over AMP (ratio association constants is 700), while linear spermine prefers ATP to AMP only by a ratio of 26 to 1 43). The selective complexation of biologically important anions is of particular interest, especially if the ligands are converted into selective anion carriers by attachment of lipophilic hydrocarbon chains. 

Table 2. Association constants (K) and second-order rate constants (kL and kc) for p-nitrophenol release from p-nitrophenyl picolinate 1 in the presence of ligand (L) and metal ion (M)a-b...

Thermodynamically it would be expected that a ligand may not have identical affinity for both receptor conformations. This was an assumption in early formulations of conformational selection. For example, differential affinity for protein conformations was proposed for oxygen binding to hemoglobin [17] and for choline derivatives and nicotinic receptors [18]. Furthermore, assume that these conformations exist in an equilibrium defined by an allosteric constant L (defined as [Ra]/[R-i]) and that a ligand [A] has affinity for both conformations defined by equilibrium association constants Ka and aKa, respectively, for the inactive and active states ... 

Assume that ligand A binds to Ri with an equilibrium association constant Ka and Ra by an equilibrium association constant ocKa. The factor a denotes the differential affinity of the agonist for Ra (i.e., a=10 denotes a tenfold greater affinity of the ligand for the Ra state). The effect of a on the ability of the ligand to alter the equilibrium between Ri and Ra can be calculated by examining the... 

From the equilibrium equations, expressions for the various receptor species can be derived and substituted into Equation 3.32. With conversion of all equilibrium association constants to equilibrium dissociation constants, a general binding expression results for radioactive CD4... 

A channel exists in two states open (Ropen) and closed (Rciosed)- A ligand [A] binds to both with an equilibrium association constant K for the closed channel and aK for the closed channel ... 

Both ligands have equilibrium association constants for receptor complexes of Ka and Kb, respectively. The binding of either ligand to the receptor modifies the affinity of the receptor for the other ligand by a factor a. There can be three ligand-bound receptor species namely [A R], [BR], and [BA R] ... 

---