Intrinsic dissociation constants

The overall dissociation constant obtained comprises the intrinsic dissociation constants for the ligands and the equilibrium constant for the conformational transition [68],... 

Strictly, the intrinsic dissociation constants should be defined in... 

The behavior of hydrogen ions in the gel is very similar to that in polyelectrolyte solutions and the same theoretical treatment may be applied. The pH of a polyelectrolyte solution is dependent on the intrinsic dissociation constant (p °) of the functional group—which is normally that of a monomer—on the degree of ionization (a), and on the potential... 

A graphical procedure used to determine, in cooperative systems, values for L (the ratio of the T to R state in the absence of any binding ligand in the Monod-Wyman-Changeux model) and n (the stoichiometry of binding) in exclusive binding systems (c = 0 where c = i.e., the ratio of the intrinsic dissociation constants for... 

It had been previously shown by Rapoport et al. (8) that native PPase binds two divalent metal ions (Mg2+, Co +, Mn +) per subunit. We have now used equilibrium dialysis to extend these studies, by measuring the effect of added Pi on Mn2+ and Co + binding (9). The results (Figure 1) demonstrate that in the presence of Pi a third divalent metal ion is bound per subunit. For Mn2+, one intrinsic dissociation constant characterizes the bind-... 

The titration curve of native chymotrypsinogen is reversible between pH 2.5 and pH 11. Analysis by the methods of Section VI shows that the neutral pH region can be described by a single intrinsic dissociation constant for all three groups which titrate in the region, together with a w... 

Values for pK and pKj of the half-reactions [3.6.38a and b] can be obtained after making some model assumption. In site binding analyses and K. or variants thereof, are usually called intrinsic dissociation constants (or binding constants for the reverse reaction), in distinction to the corresponding apparent dissociation constants K (app.) and K. (app.) having, c,, etc. In the equa-tlon instead of x , c , etc. The apparent ones are measured. Differences... 

In the case where A and B are identical, K equals Kb and Kc equals Kd- It follows that Ki equals 2Ka and K2 equals 0.5/ff. Therefore, the thermodynamic dissociation constants differ from the intrinsic dissociation constants, with the ratio K /K2 equal to 4(Ka/Kc). Whether or not there are electrostatic interactions that affect Ki and K2 (discussed in the following sections), the statistical factor of 4 will always be present. A comparison of K1/K2 for a series of symmetrical dicarboxylic acids HOOC—(CH2) — COOH is given in Figure 1. As n increases, electrostatic effects should approach zero and KalKc should approach unity, leaving only a statistical factor of 4, as is evident in this figure. 

The theory requires two assumptions that the dissociable groups may be divided into a small number of classes, each of which may be characterized by a single intrinsic dissociation constant (Kini)i and that the ampholyte may be represented as a sphere over Avhich the net charge is uniformly distributed. If n,- denotes the total number of groups of class i, and r< of these are dissociated at a given pH where the average net charge on the molecule is Z, then... 

Intrinsic Dissociation Constants from Analysis of Titration Curves... 

In some cases the quantities p(/ Ci t), and m yielded by analysis of titration curves may furnish special clues to the structure of particular proteins. For example, if ordinarily dissociable groups participate in formation of intramolecular bonds abnormal values for their intrinsic dissociation constants may result, or their number may even appear to be smaller than that found by amino acid assay. Examples will be furnished in the later sections on stoichiometry and on unreactive prototropic groups. 

As stated earlier, we hope to determine complex stoichiometry through the use of the Hummel-Dreyer technique. A calculation of stoichiometry at the point of polymer saturation will provide the average number of binding sites per polymer molecule, from which an intrinsic dissociation constant may be estimated. Currently, calculations of complexation stoichiometries have been hampered by a chromatographic overlap of the protein peak with that of the complex, and also by the extremely high polydispersity of the PDMDAAC samples. 

An advantage to assessing ligand binding data with the Adair equation is that this derivation does make assumptions about the type or presence of cooperativity. Instead, cooperativity is evaluated using T n the macroscopic or apparent dissociation constants, and the statistically related microscopic or intrinsic dissociation constants which describe... 

The first right-hand expression is written in activities, and this quotient gives the intrinsic dissociation constant. The second right-hand expression is made up of two factors, a quotient of (molar or molal) concentrations that may be called the stoichiometric dissociation constant, and a quotient of activity coefficients. All dissociation constants, association constants K = 1 /ATD), and solubility products in reference books are intrinsic constants. They apply to concentrations only if the solution is extremely dilute for all ionic species. In other cases, one has to know the activity coefficients. y0, i.e., y for a nonionic species, will mostly be close to unity, but y+ and y will generally be < 1, the more so for a higher ion concentration. One may define the free... 

It is generally difficult to determine the ion activity coefficients, and one commonly makes shift with values calculated with semiempirical equations see Section 2.3.2. Anyway, y decreases with an increase in total ionic strength. This means that adding any other electrolyte will decrease the activity coefficients, causing the solubility and the dissociation to increase. For instance, if KNO3 is added to a solution of CaCl2, this affects the latter s dissociation equilibrium. y+ and y decrease and y0 remains at 1, and—since the intrinsic dissociation constant remains unaltered—it thus follows from (2.25) that the concentrations of Ca2+ and CP increase and that of the undissociated salt decreases. 

Depending on the values of the resistance terms / , one may get very different values for the measured half-saturation concentrations for the various transport procedures. Nevertheless, all these are derivable (if the carrier model holds) from the intrinsic dissociation constant K and the appropriate pair of resistance terms. 

In Eqn, 39 we have had to introduce new symbols over those in Eqn, 30 to account for the presence of two substrates S and P. There is now an intrinsic dissociation constant R for each substrate. Resistances terms R,2 and Rji, describing the zero trans situation, are defined for each substrate and also for the equilibrium exchange experiment R involving just a single substrate S or P. There are also defined cross-resistances R and for the situation where S is present only at one side of the membrane and P only at the other. These cross-resistances can be derived from the resistances obtainable by single substrate experiments (see Table 6 where these... 

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