Histidine in continuum electrostatics protonation state calculations

Abstract

A modification to the standard continuum electrostatics approach to calculate protein pK(a)s, which allows for the decoupling of histidine tautomers within a two-state model, is presented. Histidine with four intrinsically coupled protonation states cannot be easily incorporated into a two-state formalism, because the interaction between the two protonatable sites of the imidazole ring is not purely electrostatic. The presented treatment, based on a single approximation of the interrelation between histidine's charge states, allows for a natural separation of the two protonatable sites associated with the imidazole ring as well as the inclusion of all protonation states within the calculation.

Figure 1

Schematic diagram of the various charge states of histidine. Top, structural formulas for the deprotonated, neutral tautomers, and protonated forms of the histidine side chain. Bottom, cartoon representation of the approximate charge distribution in each charge state. The approximation of Eq. (5) can be understood qualitatively by superimposing the neutral tautomers. The result is a structure with two peripheral positive charges and two central negative charges. Subtraction of the doubly protonated state charges leaves a single negative charge centered on the imidazole ring.

Figure 2

Titration of histidine in solution with A) N^δ and N^ε treated as equivalent with a model pK_a of 7, and B) N^δ assigned model pK_a of 7 and N^ε assigned model pK_a of 6.6 (N^δ site solid line and N^ε site dashed line). Note in (A) curves are coincident. C) Overall titration behavior/charge for histidine models from (A) small dashed line, (B) large dashed line, and for two non-interacting sites with pK_as of 7 and 14.

Figure 3

HEWL HIS-15 titration curves. A) pKip result with $p{K}_a^{\delta }=14$ and $p{K}_a^{\epsilon }=7$ (N^δ and N^ε equivalent). B) pKip result with $p{K}_a^{\delta }=14$ and $p{K}_a^{\epsilon }=6.6$ (N^δ and N^ε non-equivalent). C) “pseudo independent site” result with $p{K}_a^{\delta }=7$ and $p{K}_a^{\epsilon }=6.6$ <n> is the average proton population of the indicated site; Large dashed line N^δ site, small dashed line N^ε site. Solid curves represent the total titration behavior/charge of the histidine residue.

Figure 4

A) Titrating and B) Non-titrating histidines of myoglobin as determined by the pKip program.

Figure 5

The core of FeS cluster N2, CYS₄[Fe₄S₄]^2−/3−, shown as spheres and the adjacent histidines, ₄HIS-169 (center) and ₄HIS-170 (left), responsible for the redox Bohr effect.

Figure 6

The redox Bohr effect for FeS cluster N2 of complex I. The calculated shift in the midpoint reduction potential, ΔE_m, of N2 calculated with pKip (solid line) and with the “pseudo independent site” model (large-dashed line). The pKip result when the protonation state of ₄HIS-169 is fixed (solid squares) illustrates the loss of redox Bohr activity. Solid circles are the experimentally measured apparent midpoint reduction potentials for N2 from Y. Lipolytica.