Biochemistry - Chemical Reactions in Living Cells, Volume 1 - D. Metzler 1980

How molecules bind to each other
Quantitative evaluation of binding affinity
Tautomerism and proton binding

The two monoprotonated forms of pyridoxine constitute a tautomeric pair [see equation (2-3)]. The tautomeric ratio

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is a pH-independent Equilibrium Constant equal to 0.796/0.204 = 3.9 at 25 °C [7]. It should be noted that in order to evaluate the microscopic constants characterizing proton binding to molecules containing non-equivalent groups, it is necessary to know the tautomeric ratio (or ratios, if more than two binding centers are involved). In the case of pyridoxine, the value of R was determined spectrophotometrically.

Using equation (4-20), where [PX]_A and [PX]_B represent the concentrations of the two tautomeric forms of pyridoxine, The values of the microscopic constants can be calculated.

It can be seen that K₁ is simply the sum of the two microscopic constants for the protonation processes leading to The formation of the two tautomeric forms PX(A) and PX(B). Similarly, it can be shown that K₂ is directly related to the microscopic constants characterizing the binding of the second molecule of X [equations (4-21) and (4-22)]¹:

Since the tautomeric ratio R equals [PX]_A/[PX]_B, equations (4-20) and (4-22) can be written as follows:

Spectrophotometric measurements have shown that for pyridoxine, log K₁ = 8.89 and log K₂ = 4.94. These values, combined with the experimentally determined tautomeric ratio R, made it possible to determine the microscopic constants.

¹ In chemical literature, dissociation constants are most commonly used rather than binding (association) constants. For instance, if X is a proton, the arrows in equation (4-21) are reversed. In this case, the microscopic dissociation constants of PH₂ are denoted as K_a and K_b, and the dissociation constant characterizing the step of the removal of the first proton is denoted as K₁.

Since determining tautomeric ratios is usually quite difficult, microscopic constants are approximated by binding constants measured for analogous compounds in which one of the basic groups is methylated, esterified, or blocked in some other way. Let us consider the protonation of the two tautomeric forms of the very weak base 1-methyluracil:

The apparent constants (log K_i) for the protonation of the two dimethylated derivatives shown below were measured [8]. In both cases, cations similar to those in equation (4-25) are formed.

It is entirely reasonable to assume that the obtained pK_a values are approximately equal to log K^*_c and log K^*_d (as indicated above). Hence, using equation (4-24), we find that log R ≈ 0.65 + 3.25 = 3.9. This means that the majority of 1-methyluracil molecules [equation (4-25)] exist in the tautomeric form A¹.

Along with the Tautomerism accompanying the binding of protons and other small ligands to Proteins [10, 11], biochemists have always been interested in the tautomerism of the monoprotonated forms of Cysteine, Glutathione, and Other Amino Acids and Peptides [9, 9a].

¹ This result suggests that, within experimental error, the pK_a value (log K₂) for 1-methyluracil is equal to log K^*_c, specifically —3.25. Although it indeed turned out to be close to this value (—3.40), it was not close enough to be reliably used for an exact quantitative estimation of R. The authors of [8] also determined the value of R by an independent method.