Intrinsic pKa values

Figure 3-2 Acid-base titration curve for hen lysozyme at 0.1 ionic strength and 25°C. O, initial titration from the pH attained after dialysis , hack titration after exposure to pH 1.8 A, hack titration after exposure to pH 11.1. The solid curve was constructed on the basis of "intrinsic" pKa values based on NMR data. From Kuramitsu and Hamaguchi5...

Knowles JR (1976) The intrinsic pKa-values of functional groups in enzymes improper deductions from the pH-dependence of steady-state parameters. CRC Crit Rev Biochem 4 165-173... 

Table 2. Predicted intrinsic and apparent pKa values for the Cys403 residue in Yersinia phosphatase for different models of the structure the data refer to a temperature of 293 K and an ionic strength corresponding to 150 mM of monovalent salt. See the text for the detailed description of the conditions under which each pK estimation was made. The experimentally determined value is 4.67 [39]...

From these equations it is possible to predict the effective lipophilicity (log D) of an acidic or basic compound at any pH value. The data required in order to use the relationship in this way are the intrinsic lipophilicity (log P), the dissociation constant (pKa) and the pH of the aqueous phase. The overaU effect of these relahonships is the effechve hpophilicity of a compound, at physiological pH, is approximately the log P value minus one unit of hpophilicity, for every unit of pH the pKa value is below (for acids) and above (for bases) pH 7.4. Obviously for compounds with mul-hfunchonal ionizable groups the relahonship between log P and log D, as weU as log D as a function of pH become more complex [65, 68, 70]. For diprotic molecules there are already 12 different possible shapes of log D-pH plots. 

Figure 6.8 shows the Bjerrum plots for an weak acid (benzoic acid, pKa 3.98, log So — 1.55, log mol/L [474]), a weak base (benzydamine, pKa 9.26, log So —3.83, log mol/L [472]), and an ampholyte (acyclovir, pKa 2.34 and 9.23, log So — 2.16, log mol/L I/40N ). These plots reveal the pKa and pA pp values as the pcH values at half-integral % positions. By simple inspection of the dashed curves in Fig. 6.8, the pKa values of the benzoic acid, benzydamine, and acyclovir are 4.0, 9.3, and (2.3, 9.2), respectively. The pA pp values depend on the concentrations used, as is evident in Fig. 6.8. It would not have been possible to deduce the constants by simple inspection of the titration curves (pH vs. volume of titrant, as in Fig. 6.7). The difference between pKa and pA pp can be used to determine log So, the intrinsic solubility, or log Ksp, the solubility product of the salt, as will be shown below.

Since the pKa values of the compounds studied are reliably known (Table 6.1), it was possible to calculate the A shifts (Table 6.2). These shifts were used to calculate the corrected aqueous intrinsic solubilities So, also listed in Table 6.2. 

We have already seen (p. 56) that the Ka, and hence pKa, value for an acid is not an intrinsic attribute of the species itself, because it varies from one solvent to another the value depending on the overall system of which the acid is a constituent. Values are normally quoted for aqueous solution, unless otherwise specified, because most data are available for that solvent. Most values are also quoted as at 25°, again because most data were obtained at this temperature. A constant temperature has to be specified as Ka, an equilibrium constant, varies with temperature. We have been concerned above with the relative... 

Fig. 5A The dependence on pH of the deuterium isotope effect in the hammerhead ri-bozyme-catalyzed reaction. Black circles show rate constants in H2O gray circles show rate constants in D2O. Solid curves are experimentally determined curves. The apparent plateau of cleavage rates above pH 8 is due to disruptive effects on the deprotonation of uridine and guanosine residues. Dotted lines are theoretical lines calculated from pKa values of hydrated Mg ions of 11.4 in H2O and 12.0 in D2O and on the assmnption that there is no intrinsic isotope effect (a=kH2o/kD2o=l is the coefficient of the intrinsic isotope effect). The following equation was used to plot the graph of pL vs log(rate) log kobs=log(kmax)-log(l+10

The release kinetics of polyelectrolyte-containing controlled release compositions were modeled by Ozturk et al. [331]. According to this analysis the drug release rate depends on intrinsic solubilities as well as pKa values of the drug and polymer. Explicit relationships between release rates and these factors were derived, resulting in successful predictions of experimental data. 

Similar isotope effects for human isoenzyme I (157c) on kc t and Km for C02 hydration are 1.7. Silverman and Tu (161) report an isotope effect of 2.5 for H2180 release and suggest that the intrinsic isotope effect of intramolecular H+ transfer might be significantly smaller in isoenzyme I than in isoenzyme II. Hence, the H20-splitting step might also limit the rate of C02 hydration in isoenzyme I. Human isoenzyme I has three titratable active-site histidines with pKa values... 

An alternative approach to the experimental estimation of REs utilizes equilibrium (protonation) data rather than thermochemical data, the idea being that comparisons of the basicities of pyrrole and its benzo fused analogues with those of non-aromatic systems which form cations of 7r-electron structure similar to the aromatic compounds should furnish a measure of the loss of RE accompanying protonation of the aromatic system (76T1767, 72CI(L)335). Thus, for the a-protonation of N-methylpyrrole, the model non-aromatic system was chosen as (20). Combination of pKa values for the protonation of the aromatic and non-aromatic molecules, taking into account the intrinsic resonance stabilization of the... 

The difference in pKa values between the proton donor and the proton acceptor in Eq. 9-97 can be expressed as the Gibbs energy change which at 25°C is equal to 5.71 x ApKa. This is often referred to as the thermodynamic barrier AG 0 to a reaction and AG can be expressed as the sum of the thermodynamic barrier AG0 plus an intrinsic barrier AG in. . For the proton transfer of Eq. 9-97 the intrinsic barrier (for step b) is thought to be near zero so that AG 5.71 ApfCa. 

From this we can conclude that two pKa values can be as much as eight units apart and AG will still be less than 50 kj / mol, low enough to permit rapid enzymatic reactions. However, for transfer of a proton from a C-H bond to a catalytic group, for example, to form an enolate ion for an aldol condensation (Chapter 13), the intrinsic barrier is known to be about 50 kj / mol.141 In this case, to allow rapid enzymatic reaction either the thermodynamic barrier must be very low, as a result of closely matching pKa values, or the enzyme must lower the intrinsic barrier. It may do both. 

A thermochemical method for comparing pKa values of weak acids in DMSO has been described by Arnett et al. (1973). A linear relationship is observed between AGf and AHf for 30 weak acids in DMSO over a range of 20 pKa units. Thus AHf, the enthalpy of ionization in DMSO, is a useful guide to relative acid/base strength (Arnett and Scorrano, 1976). The relationship implies, of course, that AS° is linearly related to AHf. Correlations have been drawn between acidities in DMSO and intrinsic gas-phase acidities (Arnett et al., 1975 Bordwell et al., 1975). 

Fig. 17 shows the pH-solubility profile for cocrystal plotted according to Eq. (34) with cocrystal K p values of 1 X 10 and 1 x 10 and acidic ligand pKa = 5. The pH-solubility profile of a cocrystal with one component that is a weak acid is similar to that of a weak acid. At pH < pKa, the cocrystal solubility is at its lowest intrinsic solubility value, given by K pf-. At pH = pKa, the cocrystal solubility is 1.4 times higher, and at pH > pKa, the solubility increases exponentially. Also, increasing the K p value increases the intrinsic solubility of cocrystal as observed in Fig. 17. The K p value is characteristic of the cocrystal of an API with a specific ligand. Therefore, if multiple cocrystals exist for the same API, determination and comparison of the K p and values enables one to select the cocrystal with the desired solubility pH dependence.

If all acidic functional groups in a molecule are absolutely identical and are physically so far apart that there are no electrostatic effects on pKa values, the titration curve of a polyprotic acid can be represented by the titration curve of a suitable monoprotic acid whose Ka value is the statistically corrected intrinsic K for the polyprotic acid. For instance, in the previous example, if there were no electrostatic effects to be considered and A and B were identical, then Ka would equal Kc - The thermodynamic con-... 

The result of this charging effect on inhibiting dissociation is that the apparent pAa of polyprotic organic acids can only be compared directly with the pA, of monoprotic organic acids when the polyprotic acid is undissociated (a = 0). Thus, the pKa value at a = 0 is called the intrinsic pKa of the humic material. The relationship of the apparent pA to the intrinsic pKa is given by... 

The acidity of a alumina in the binary mixture must go to zero at zero mixture ratio. The extended dashed line for a pKa of —1.5 is employed to indicate that the acidity was indeed greater than zero for all ru > 0 at this pK, (as demonstrated by the indicator color). The intrinsic acidity values of a alumina are achieved at r = 1.0. 

FIGURE 2.9 Dissociation of acids as function of pH. (a) Calculated degree of dissociation (a) of a fatty acid (intrinsic pKa — 4.7) at very small ionic strength, (b) Titration curves, i.e., experimentally determined degree of neutralization (a ) by KOH of citric acid and phosphoric acid the intrinsic pK i values are indicated by vertical dashes. 

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