Microscopic Ionization Constants

Here k f k2f and kare microscopic ionization constants defined in section 4.6. From this it was possible to calculate and plot variation in Dnoh with pH for pentazocine as shown in Figure 2. The fourth partition coefficient was obtained by structural group contribution to the measured partition coefficient of a reference compound (morphine). This was done following the Hansch approach. 

This sort of problem underlines the need for an unequivocal determination of microscopic ionization constants. As already mentioned, the rate-limiting step in catalysis is controlled by an ionization with a pKa of 7. Cruickshank and Kaplan (30) used a-chymotrypsin as a test enzyme and estimated the pKa of its two histidine residues from the pH dependence of their reaction with trace amounts of tritiated l-fluoro-2,4-dinitro-benzene. From their data, a pKa of 6.8 was assigned to His-57 and 6.7 to His-40, which is not involved in catalysis. This data is consistent with deprotonation of His-57 being the critical ionization for catalysis. 

At appreciable ionic strength these microscopic constants should be written in terms of activities rather than concentrations. The constants are normally estimated by spectral means. There are three microscopic ionization constants for the loss of the first proton, six for the loss of the second, and three for the loss of the last. In Table 3-2 the subscripts 1, 2, and 3 denote the carboxyl, sulfhydryl, and ammonium protons thus 32 is the microscopic constant for the ion formed by loss of the sulfhydryl proton from the species that has already lost the ammonium proton. 

C.d. spectroscopy has been used to study the interaction of tri-N-acetylchito-triose with human lysozymes at various pH values. The binding constants for the trisaccharide and diiferent microscopic protonated forms of lysozyme were estimated using the binding constants determined at various pH values and the microscopic ionization constants of the catalytic carboxylic acid groups (Glu-35 and Asp-52). Unlike hen and turkey lysozymes, all four species of human lysozyme showed similar binding with tri-N-acetylchitotriose. 

The carboxyl ionization [pK]) is low and easily identified. However, the ammonium and thiol groups have similar pK values (compare methylamine with methyl mercaptan, Table 2.1) and so an uncertainty exists as to which group ionizes first. Ki, K2, and K3 represent macroscopic ionization constants determined experimentally from a titration curve. K2 and are the composite of four microscopic ionization constants. Once the proton is lost from the carboxyl group, one of two ionization pathways may be followed ... 

The ionization constants pK% pKg, etc. refer to the entire active site of the free enzyme or its complex with the substrate. Therefore, they are called molecular ionization constants. The molecular ionization constants are connected to the microscopic ionization constants, that is, ionization constants of particular titratable groups in the protein, as illustrated by Figure 5 and the following equations. 

Figure 5 Schematic representation of ionization of a dibasic acid with microscopic ionization constants and concentrations of each form.

Fig. 11.3 Macroscopic and microscopic ionization constants of malic acid...

Recall that the behavior of polyacids depends on macroscopic and microscopic ionization constants. The former can be determined experimentally. They globally quantify the more or less simultaneous ionization of several acid functions. Their value cannot be assigned in totality to only one acidity constant if the initial acid is dissymmetric. Let us consider malic acid (Fig. 11.1). It exhibits two different microscopic ionization methods (Fig. 11.3). 

Fig. 11.6 Estimated values of the microscopic ionization constants of lysine and ...

The concept of apparent values is very useful, and it appears in other phenomena, such as in pKa values (section L3). Quite often, a pKa value does not represent the microscopic ionization of a particular group but is a combination of this value and various equilibrium constants between different conformational states of the molecule. The result is an apparent pKa which may be handled titri-metrically as a simple pKa. This simple-minded approach must not be taken too far, and, when one is considering the effects of temperature, pH, etc., on an apparent Km, one must realize that the rate-constant components of this term are also affected. The same applies to kcat values. The literature contains examples in which breaks in the temperature dependence of kcat have been interpreted as indicative of conformational changes in the enzyme, when, in fact, they are due to a different temperature dependence of the individual rate constants in cal, e.g., k2 and k2 in equation 3.22. 

Fig. 10. The eight microscopic forms of tyrosine and the twelve ionization constants which interrelate them. Parentheses enclose symbols indicating the charge on each of the ionizing groups, in the sequence carboxyl, phenolic hydroxyl, amino. (Martin el al., 1958 redrawn with permission.)...

This chapter provides an introductory overview of the approaches used to predict ionization states of titratable residues in proteins, based on the assumption that the difference in protonation behavior of a given group isolated in solution, for which the ionization constant is assumed to be known, and the protonation behavior in the protein environment is purely electrostatic in origin. Calculations of the relevant electrostatic free energies are based on the Poisson-Boltzmann (PB) model of the protein-solvent system and the finite difference solution to the corresponding Poisson-Boltzmaim equation. We also discuss some relevant pH-dependent properties that can be determined experimentally. The discussion is limited to models that treat the solvent and the solute as continuous dielectric media. Alternative approaches based on microscopic simulations, which can be useful for small molecules (e.g., see Refs. 19-24) are not covered here because they are, in general, too time intensive for proteins. The present treatment is intended to be simple and pedagogic. 

Principle of enzymatic peptide synthesis, (a) Synthesis under thermodynamic control is based on microscopic reversibility. The overall equilibrium constant will be strongly dependent on ionization constants of the different species and the reaction pH. 

Previous theoretical kinetic treatments of the formation of secondary, tertiary and higher order ions in the ionization chamber of a conventional mass spectrometer operating at high pressure, have used either a steady state treatment (2, 24) or an ion-beam approach (43). These theories are essentially phenomenological, and they make no clear assumptions about the nature of the reactive collision. The model outlined below is a microscopic one, making definite assumptions about the kinematics of the reactive collision. If the rate constants of the reactions are fixed, the nature of these assumptions definitely affects the amount of reaction occurring. 

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