Tautomerism and Apparent pKa in Property Assignment

Why Tautomerism Matters for pKa Assignment

A molecular structure file usually shows one arrangement of atoms and bonds. In solution, however, a drug may occupy several tautomeric forms: structures with the same molecular formula that differ in the placement of a proton and associated bonds. Those forms can have different proton affinities. If protonation or deprotonation also changes the relative abundance of the tautomers, the pKa measured for the whole solution need not equal the pKa associated with any one drawn structure.

This distinction matters when assigning physicochemical inputs for PBPK models. A pKa is often used to represent pH-dependent charge-state fractions, but a molecular structure is also used to describe properties that may differ among microstates. Treating one drawn tautomer as the only species can therefore give an inaccurate account of which forms are present, even when the reported apparent pKa itself is measured correctly.

The key is to distinguish a microstate, one specified molecular form, from a macroscopic protonation level, which groups together all microstates with the same number of bound protons. An experimentally determined apparent pKa generally describes an equilibrium between such groups, not necessarily a single pair of structures.

Aggregating Tautomer-Specific Equilibria

Consider a simplified acid with two neutral tautomers, \(N_1\) and \(N_2\), and two corresponding deprotonated tautomers, \(A_1^-\) and \(A_2^-\). Assume all four forms interconvert rapidly enough to reach equilibrium, and that the two neutral forms belong to the same protonation level, as do the two anionic forms. Write their total concentrations as \(C_N=[N_1]+[N_2]\) and \(C_A=[A_1^-]+[A_2^-]\).

Define the tautomer ratios \(K_t=[N_2]/[N_1]\) and \(K_t^-=[A_2^-]/[A_1^-]\). Let the microscopic acid dissociation constants for the two corresponding paths be \(K_{a1}\) and \(K_{a2}\), with \(K_{a1}=[H^+][A_1^-]/[N_1]\) and \(K_{a2}=[H^+][A_2^-]/[N_2]\). These are conditional concentration-based expressions for a fixed solution medium; thermodynamic definitions use activities. The overall, or macroscopic, dissociation constant is defined using the total concentrations at each protonation level.

The last expression follows by substituting the tautomer ratios into the totals. Since \(C_N=[N_1](1+K_t)\) and \(C_A=[A_1^-](1+K_t^-)\), their ratio is \([A_1^-]/[N_1]\) multiplied by \((1+K_t^-)/(1+K_t)\). Multiplication by \([H^+]\) gives the stated result. Equilibrium around the cycle also requires \(K_{a2}/K_{a1}=K_t^-/K_t\); the constants cannot be assigned independently if these species interconvert.

This result makes the source of the apparent value explicit: it reflects both the microscopic deprotonation tendency and how the neutral and charged tautomer pools are distributed. The apparent pKa is \(pK_{a,\mathrm{app}}=-\log_{10}(K_{a,\mathrm{app}})\). It can differ from either microscopic pKa.

From Apparent pKa to Microstate Fractions

For a single aggregate acid equilibrium at fixed conditions, the total deprotonated-to-protonated ratio is \(10^{\mathrm{pH}-pK_{a,\mathrm{app}}}\). This relation describes the two pools; it does not by itself divide either pool among its tautomers. To obtain microstate fractions, combine the pool fractions with the tautomer ratios within each pool.

A corresponding aggregation applies when there are more than two protonation levels. For each level, sum the concentrations of its microstates; a macroscopic stepwise pKa relates the totals at adjacent levels. Tautomers can occur within one level, and protonation at different sites can produce distinct microstates at another. Coupling among these forms affects the aggregate constants as well as the detailed distribution within each level.

Choosing a Representation for Property Assignment

There are three practical levels of representation. Their suitability depends on the model question and on what data are available.

For calculations requiring only aggregate charge-state fractions, an appropriate apparent pKa can be more useful than a microscopic pKa attached to an arbitrarily selected drawing. If different tautomers have meaningfully different properties relevant to the model, however, an aggregate pKa alone does not supply enough information. An explicit microstate treatment may be warranted, provided its equilibrium and property inputs can be supported.

A reported pKa should therefore be interpreted with its conditions and definition in mind. The value may be a macroscopic equilibrium constant or a conditional apparent value inferred under particular solution conditions. A pKa tied to a specified microstate is not interchangeable with an aggregate value. This distinction is especially important when a property-assignment workflow takes a single structure as input: the structure is a representation, not proof that only that tautomer exists in solution.

Diagnostics and Common Mistakes

Several checks help reveal when a single-structure assignment may be inadequate. Look for more than one chemically plausible proton location, multiple likely ionization sites, or a reported pKa that cannot be reconciled with the microstate-specific value assigned to the chosen structure. If a predicted speciation curve disagrees with measured aggregate behavior, check whether the calculation used a microscopic constant in place of a macroscopic one. Also check that the tautomer ratios and pKa values refer to compatible solution conditions.

A useful internal check is to confirm that calculated microstate fractions are nonnegative and sum to 1, and that summing them within each protonation level reproduces the aggregate fractions. For a coupled network, equilibrium constants around any closed cycle must also be consistent: multiplying the equilibrium ratios along a cycle must give the same result in either direction. Failure of this check signals inconsistent constants or definitions, not a new chemical effect.

• Mistake: “The structure file shows \(N_1\), so the measured pKa must be the pKa of \(N_1\).”
  Correction: The measurement may describe the total pools of several tautomers. A single structure does not identify the scope of the measured equilibrium.
• Mistake: “The apparent pKa gives the fraction of every individual tautomer.”
  Correction: It gives the ratio of aggregate protonation-level pools. Within-pool tautomer ratios are additional information.
• Mistake: “If two forms have the same molecular formula, their pKa and other properties must be identical.”
  Correction: Tautomers can differ in proton affinity and other properties. Their contributions to aggregate behavior depend on their equilibrium populations.

A dominant-tautomer approximation can be reasonable when one form overwhelmingly dominates under the relevant conditions and the omitted forms do not materially affect the target prediction. It is not justified merely because a drawing convention, database entry, or input file displays one structure. Conversely, using an explicit network is not automatically superior: poorly supported microstate constants may make the apparent detail misleading. Choose the simplest representation that captures the distinctions required by the PBPK application.