Limiting Values of the one-bond C–H Spin-Spin Coupling Constants of the Imidazole Ring of Histidine at High-pH

Summary

Assessment of the relative amounts of the forms of the imidazole ring of Histidine (His), namely the protonated (H⁺) and the tautomeric N^ε2-H and N^δ1-H forms, respectively, is a challenging task in NMR spectroscopy. Indeed, their determination by direct observation of the ¹⁵N and ¹³C chemical shifts or the one-bond C–H, ¹J_CH, Spin-Spin Coupling Constants (SSCC) requires knowledge of the “canonical” limiting values of these forms in which each one is present to the extent of 100%. In particular, at high-pH, an accurate determination of these “canonical” limiting values, at which the tautomeric forms of His coexist, is an elusive problem in NMR spectroscopy. Among different NMR-based approaches to treat this problem, we focus here on the computation, at the DFT level of theory, of the high-pH limiting value for the ¹J_CH SSCC of the imidazole ring of His. Solvent effects were considered by using the polarizable continuum model approach. The results of this computation suggest, first, that the value of ¹J_Cε1H = 205 ± 1.0 Hz should be adopted as the canonical high-pH limiting value for this SSCC; second, the variation of ¹J_Cε1H SSCC during tautomeric changes is minor, i.e., within ±1Hz; and, finally, the value of ¹J_Cδ2H SSCC upon tautomeric changes is large (15 Hz) indicating that, at high-pH or for non-protonated His at any pH, the tautomeric fractions of the imidazole ring of His can be predicted accurately as a function of the observed value of ¹J_Cδ2H SSCC.

Graphical abstract

Introduction

The role of Histidine (His) in many biological functions and activities is very well documented [1–4], and the reason for such versatility can be found in three distinctive properties of the His amino acid residue: (i) existence of two neutral, chemically-distinct forms (N^δ1–H and N^ε2–H tautomers, also known as π and τ tautomers, respectively [5], and a charged H⁺ form, shown in Figure 1), with one form favored over the other by the protein environment and pH [6]; (ii) the only ionizable residue (the charged form) that titrates around neutral pH has a pK° of 6.6 [7] and (iii) appearance of a population of ~50% in all enzyme active sites [8].

Figure 1.

Ball and stick representation of the forms of the imidazole ring of His, namely the: (a) N^ε2-H, or τ tautomer [5], (b) N^δ1-H, or π tautomer [5], and (c) H⁺ form, respectively.

Despite these well-known facts, the physical properties of neutral His are difficult to characterize experimentally [9], making a proper determination of the fractions of the tautomeric forms of the imidazole ring of His a challenging problem in NMR spectroscopy. Among the experimental methods in current use, are those based on the observed: (a) ¹⁵N chemical shifts [10–12]; (b) ¹³C^γ and ¹³C^δ2 chemical shifts [6,13]; and (c) ¹J_CH Spin-Spin Coupling Constant (SSCC) of the imidazole ring of His [13–15]. As with any experimental method, all these mentioned approaches possess shortcomings: (i) the tautomeric fractions obtained by the ¹⁵N-based method may differ significantly depending on the adopted canonical limiting values of the ¹⁵N chemical shift [16]; (ii) the ¹³C^γ and ¹³C^δ2 chemical shifts cannot always be observed. In fact, only 106 ¹³C^γ, versus 4,703 ¹³C^δ2, chemical shifts of the imidazole ring of histidine have been deposited in the Biological Magnetic Resonance data Bank (BMRB) [17]. Hence, problems in the determination of the chemical shifts for these nuclei, such as that for the ground state of His 40 in the protein Im7 [14], often prevent the use of this methodology; and (iii) the observed one bond C–H SSCC value at the high-pH limit is ambiguous, as will be discussed below.

It should be noted, from Figure 1, that there are only two one-bond C–H’s, ¹J_CH, SSCC’s of the imidazole ring of Histidine, namely the ¹³C^ε1–H, ¹J_Cε1H, and the ¹³C^δ2–H, ¹J_Cδ2H, SSCC, respectively. Absences of an accurate value for each of these SSCC’s, at the high-pH limit, gives rise to two different kinds of problems as explained below.

The first problem pertains to the use of ¹J_Cε1H SSCC to determine the protonation fraction of His, e.g., to detect sparsely populated, short-lived, protein states [14]. In detail, the low-pH limiting value for ¹J_Cε1H SSCC appears to be quite well defined (221 ± 1.0 Hz [14]), for the ¹J_Cε1H SSCC pH-dependence of four titrating His residues (His 6, His 13, His 26, His 87) of the PLCCγ SH2 protein domain [14,18]. However, the observed high-pH limit for ¹J_Cε1H SSCC differs among five His residues, of the PLCCγ SH2 protein domain, by up to ~6Hz [14], i.e., four titrating His residues converge to a high-pH limiting value of 207 ± 1.0 Hz while the remaining one (His 57), which is the only non-titrating His residue, shows an almost flat, pH-independent, value of 203 ± 1.0 Hz [14]. The existence of two possible high-pH limiting values for ¹J_Cε1H SSCC, namely 207 ± 1.0 Hz or 203 ± 1.0 Hz [14], is a source of ambiguity. A similar ambiguity is found for four non-titrating His residues of subtilisin BPN′ having ¹J_Cε1H SSCC in the range of ~205Hz to ~209Hz [19].

The second problem pertains to a potential contradiction between an assumption [15] and existing evidence about the variation of ¹J_Cδ2H SSCC upon tautomeric change [13]. Platzer et al. [15] had proposed that the variations of ¹J_Cδ2H SSCC should be independent of the forms of the His tautomer, as for ¹J_Cε1H SSCC. On the other hand, there is experimental evidence for L-histidine at pH 12 in 80% d6-ethanol/20% H₂O at −55 °C [13], showing the existence of a large, rather than a small change, of ¹J_Cδ2H SSCC upon changes of the tautomeric forms.

As can be inferred from the above, a common problem, in both ¹J_CH SSCC’s and the ¹⁵N-based methods, is the need for accurate knowledge of the “canonical” limiting values of the imidazole ring of His in which each form of His, namely the protonated (H⁺) and the tautomeric N^ε2-H and N^δ1-H forms, respectively, is present to the extent of 100%. In this regard, the canonical limiting values of the ¹⁵N chemical shift have already been analyzed [16] and, hence, here we will determine the high-pH limiting values for both ¹J_CH SSCC’s of the imidazole ring of His. By doing this, we will be able to: (i) eliminate any possible ambiguity about the actual value of ¹J_Cε1H SSCC; and, (ii) resolve a possible contradiction associated with the variations of ¹J_Cδ2H SSCC upon changes in the relative amounts of the tautomeric forms.

Materials and Methods

Calculations details

All DFT-calculations of the two ¹J_CH SSCC’s, of the imidazole ring of His in the Ac-His-NMe molecule, were carried out by using the Gaussian 09 suite of programs [20]; the Keywords used in Gaussian 09 (listed here for assessing the reproducibility of the calculations) were: “NMR=Mixed”, with the options “CPHF=Conv=10” and “Int=ultrafine” [21]. Additional Keywords, such as “Readatoms”, were also tested (see Results and Discussion section).

There are four contributions to the NMR coupling constants [22], namely, the Fermi Contact (FC), the Spin Dipolar (SD), the Paramagnetic Spin-Orbit (PSO), and the Diamagnetic Spin-Orbit (DSO) contribution, respectively. All four are known as the Ramsey contributions. For this reason, in each of the Tables, we have listed: (i) the sum (Σ) of all four Ramsey contributions to each DFT-computed ¹J_CH SSCC, as computed with the Gaussian 09 suite of programs; and (ii) the predicted values for the ¹J_CH SSCC’s, listed in the last column of each Table, are obtained after adding an ad-hoc contribution of 5Hz, to the Σ term, due to the Zero Point Vibrational Contribution [23].

All the results in Table 1 correspond to gas-phase DFT calculations, while the ones in Tables 2–4 include DFT-calculations in both gas-phase and in the presence of solvent (see Solvent Effects section below). For the latter, all the results obtained with solvent are highlighted in italics and bold face.

Table 1.

Test of functionals for the DFT computations of ¹J_Cε1H SSCC of the N^ε2-H tautomer^a

Functional	Σ{FC,SD,PSO,DSO} (Hz)	1JCε1H (Hz)
OPW91	199.02	~204
B3LYP	231.65	~237
B3P86	215.54	~220
OPBE	198.10	~203
B972	212.57	~218
BP86	211.35	~216

^aAll gas-phase DFT calculations of ¹J_Cε1H SSCC were carried out on Ac-His-NMe by using the Gaussian 09 suite of programs [20]; the chosen ϕ, ψ, ω, χ1 and χ2 torsional angles for His correspond to a local-minimum of the ECEPP force-field [25] in the α-helical region of the Ramachandran map: −73.563°, −35.197°, −179.856°, 66.389° and −62.607°, respectively; for each functional we used an “aug-cc-pVTZ-J” basis set [37] on all nuclei of the imidazole ring of His, and a “6-31G” basis set on the remaining nuclei of Ac-His-NMe. The total (Σ) is a sum over the four Ramsey contributions [22], as given by the output of the Gaussian 09 suite of programs [20], namely, the Fermi Contact (FC), the Spin Dipolar (SD), the Paramagnetic Spin-Orbit (PSO), and the Diamagnetic Spin-Orbit (DSO) contribution, respectively; the last column lists the predicted value for the one-bond ¹J_Cε1H SSCC after adding 5 Hz to the Σ term (second column), due to the Zero Point Vibrational Contribution [23].

Table 2.

High-pH limiting value for ¹J_Cε1H SSCC of the N^ε2-H tautomer^a

Σ{FC,SD,PSO,DSO} (Hz)	1JCε1H (Hz)
199.20	~204b
199.29	~204c
199.10	~204d
199.02	~204e
198.91	~204f
199.12	~204g
198.62	~204h
201.26	~206i
201.78	~207j

^aAll gas-phase DFT calculations of ¹J_Cε1H SSCC, unless otherwise noted, for which see items i–j below, were carried out for Ac-His-NMe by using the Gaussian 09 suite of programs [20]; the chosen ϕ, ψ, ω, χ1 and χ2 torsional angles for His correspond to a local-minimum of the ECEPP force-field [25] in the α-helical region of the Ramachandran map: −73.563°, −35.197°, −179.856°, 66.389° and −62.607°, respectively, unless otherwise noted, for which see items f–h below; the total (Σ) is a sum over the four Ramsey contributions (see footnote a of Table 1) [22]; column 2 lists the predicted values for the one-bond ¹J_Cε1H SSCC after adding 5 Hz to the Σ term (in column 1), due to the Zero Point Vibrational Contribution [23].

^bResult obtained by using a uniform basis set “aug-cc-pVTZ-J” [37] for all the nuclei of Ac-His-NMe.

^cResult obtained by using an “aug-cc-pVTZ-J” basis set for the ¹³C^ε1, ¹H^ε1, N^δ1, N^ε2 and H^ε2 nuclei of the imidazole ring of His and a “3-21G” basis set for all the remaining nuclei of Ac-His-NMe, i.e., by using a “locally-dense” basis set approximation [41].

^dSame as (c) with a “6-31G” rather than a “3-21G” basis set.

^eResult obtained by using an “aug-cc-pVTZ-J” basis set for all nuclei of the imidazole ring of His, and a “6-31G” basis set for the remaining nuclei of Ac-His-NMe, i.e., by using a “locally-dense” basis set approximation.

^fSame as (e) with the ϕ, ψ, ω, χ1 and χ2 torsional angles of His from a local-minimum, of the ECEPP force-field [25], in the extended region of the Ramachandran map: −142.183°, 153.652°, −179.870°, −58.886° and 113.207°, respectively.

^gSame as (e) with the ϕ, ψ, ω, χ1 and χ2 torsional angles of His from a local-minimum, of the ECEPP force-field,²⁵ in the extended region of the Ramachandran map: −156.922°, 159.176°, 179.634°, 60.066° and 96.365°, respectively.

^hSame as (e) with the ϕ, ψ, ω, χ1 and χ2 torsional angles of His from a local-minimum, of the ECEPP force-field [25], in the extended region of the Ramachandran map: −154.460°, 157.818°, −178.614°, −152.343° and −67.537°, respectively.

ⁱSame as (c) with solvent effects computed by using the PCM [31,32] approach with D_i = 6.5.

^jSame as (i) with D_i = 25.5

Table 4.

High-pH limiting value for ¹J_Cδ2H SSCC^a

Tautomer	Σ{FC,SD,PSO,DSO} (Hz)	1JCδ2H (Hz)
Nε2-H	158.54	~164b
	159.87	~165c
	160.08	~165d
Nδ1-H	176.14	~181b
	175.38	~180c
	175.07	~180d

^aAll gas-phase DFT calculations of ¹J_Cδ2H SSCC, unless otherwise noted, for which see items c–d below, were carried out on Ac-His-NMe by using the Gaussian 09 suite of programs [20]; the chosen ϕ, ψ, ω, χ1 and χ2 torsional angles for the N^ε2-H and N^δ1-H tautomers of His correspond to a local-minimum in the α-helical region of the Ramachandran map, and are given in footnote a of Tables 2 and 3, respectively; the total (Σ) is a sum over the four Ramsey [22] contributions (see item a of Table 1); column 3 list the predicted values for the one-bond ¹J_Cδ2H SSCC after adding 5 Hz to the Σ term (in column 2), due to the Zero Point Vibrational Contribution [23].

^bResult obtained by using an “aug-cc-pVTZ-J” basis set [37] for all nuclei of the imidazole ring of His and “6-31G” on the remaining nuclei of Ac-His-NMe.

^cSame as (b) with solvent effects computed by using the PCM [31,32] approach with D_i = 6.5

^dSame as (c) with D_i = 25.5

Structural geometry of His

All the ¹J_CH SSCC calculations, at the DFT level of theory, were carried out by using the histidine geometry as defined in the Empirical Conformational Energy Program for Peptides and Proteins (ECEPP) in which their bond-lengths and bond-angles were parameterized by Momany et al. [24] and updated by Némethy et al. [25] by using a high-resolution (R = 0.037) X-ray crystal structure of histidine. In this regard, (i) less than 10% of more than 500,000 crystal structures deposited in the Cambridge Structural Database have an R-factor < 0.04 [26]; and (ii) a comparison between DFT-computed and observed ¹³C^α chemical shifts of two different structures of Ubiquitin [27], one that possesses non-regular geometry which has been obtained by X-ray diffraction at 1.8 Å resolution (PDB id 1UBQ [29]) and the other structure with regularized ECEPP geometry [27], 1UBQ_reg, with both, in terms of rmsd, leading to 3.28 ppm and 2.38 ppm, respectively. Supplementary analysis of the agreement between these structures with the deposited electron density data of 1UBQ, in terms of the R-factor, leads to 19.2% and 23.1% for 1UBQ and 1UBQ_reg, respectively, while the all-heavy-atom rmsd between these two structures is only 0.142 Å.

Overall, the better agreement, in terms of ¹³C^α chemical-shifts, obtained with 1UBQ_reg, rather than 1UBQ, is consistent with the well-known recognition that the bond lengths and bond angles of both X-ray and NMR-derived structures of proteins are not defined as highly accurately as in studies of small molecules [29] with which the ECEPP geometry has been parameterized [24,25].

Solvent effects

It is well known that sizable solvent effects are important for the computation of ⁿJ_CH SSCC only for n = 1 [30], with n being the number of intervening bonds between the Carbon and the Hydrogen. Consequently, dielectric solvent effects were taken into account during the DFT-calculations by using a Polarizable Continuum Model (PCM) [31,32] as implemented in the Gaussian package [20]. Because we are interested primarily in proteins in water, we decided to model the dielectric medium of such a system by using theoretical evidence [23] indicating that the average dielectric constants (D_i) inside and at-the-surface of a protein are around 6–7 and 20–30, respectively. Hence, the dielectric solvent effects on the DFT-computation of the ¹J_CH SSCC for the imidazole ring of His were computed by using the PCM approach with an effective D_i of 6.5 and 25.5, respectively.

It is worth noting that there is a direct and an indirect contribution of the solvent effects on the ¹J_CH SSCC [30], and both effects were taken into account here. The direct contribution, due to the polarization of the molecular electronic structure by the solvent, was considered here by using the PCM approach which, during the calculation of ¹J_CH SSCC, takes into account the induced surface charges derived from the boundary conditions at the cavity surface. The indirect effect, caused by the change of the molecular geometry due to the solvent, was also considered here because we used a high-resolution X-ray crystal structure of histidine and, as is well known, the crystals contain, on average, ~50% of solvent [34].

Determination of the factors affecting the computation of ¹J_CH SSCC

Among the factors affecting the computation of the four Ramsey contributions to ¹J_CH SSCC, we first analyzed their dependence on the functionals and on the basis sets chosen for the DFT calculations. This dependence is discussed below.

Selecting the functional

Maximoff et al. [35] ranked 20 functionals for their ability to reproduce the observed ¹J_CH SSCC of 31 chemical compounds containing 11 aromatic molecules. Among all the 20 functionals, we selected only those showing a mean absolute error < 3Hz (see Table 1). In Table 1, we highlight in bold face the results from those functionals giving closer predictions to the observed ¹J_Cε1H SSCC for the non-titrating His 57 of the PLCCγ SH2 protein domain, namely ~203Hz [14]. These selected best functionals, namely, OPW91 and OPBE, are in agreement with the conclusion reached by Maximoff et al. [35] after testing 20 functionals. To decide which one of these two functionals should be adopted for our DFT calculations, the following complementary analysis was carried out. There is only one aromatic group (C₄H₄N₂), among 11 tested by Maximoff et al., [35] possessing a C–H between 2 nitrogen atoms, in a similar chemical arrangement as that of ¹³C^ε1 of the imidazole ring of His (see Figure 1). For this particular aromatic group (C₄H₄N₂), the results obtained by Maximoff et al. [35] with the OPW91 (0.2Hz) and the OPBE (2.4 Hz) functionals, in terms of the difference, Δ, between the observed and DFT-computed ¹J_CH SSCC, show that OPW91 matches the experimental data better than OPBE (see Supporting Information in Table 1 from Maximoff et al. [35]). This result indicates that OPW91 is the best functional with which to predict the observed values of ¹J_CH SSCC for the C₄H₄N₂ aromatic group and, hence, OPW91 rather than OPBE was chosen for the DFT calculations in this work.

Selecting a basis set

It is well known that ¹J_CH SSCC calculations are dominated by the Fermi-Contact (FC) contribution which depends strongly on the electron density close to the nuclei and, hence, demands high quality of the basis set chosen [36]. Consequently, all the DFT-calculations in this work were carried out by using the “aug-cc-pVTZ-J” basis set [37] which is specially designed to study NMR properties. In addition, there is an important consensus that this basis set gives satisfactory close agreement between observed and computed ¹J_CH SSCC [21,35,36,38,39,40].

A locally-dense basis set approximation [41] was also used to sense the response of the DFT-computed ₁J_CH SSCC to the basis set distribution chosen, i.e., different combinations of “aug-cc-pVTZ-J” basis sets on the nuclei of interest of the imidazole ring of His, and a “6-31G” or “3-21G” basis set on the remaining nuclei of the Ace-His-NMe molecule, were tested here; the results are shown in Tables 2 and 3.

Table 3.

High-pH limiting value for ¹J_Cε1H SSCC of the N^δ1-H tautomer^a

Σ{FC,SD,PSO,DSO} (Hz)	1JCε1H (Hz)
197.98	~203b
198.02	~203c
197.84	~203d
19787	~203e
199.32	~204f
199.66	~205g

^aAll gas-phase DFT calculations of ¹J_Cε1H SSCC, unless otherwise noted, for which see items f–g below, were carried out for Ac-His-NMe by using the Gaussian 09 suite of programs [20]; the total (Σ) is a sum over the four Ramsey contributions (see footnote a of Table 1); the chosen ϕ, ψ, ω, χ1 and χ2 torsional angles for His correspond to a local-minimum of the ECEPP force-field [25] in the α-helical region of the Ramachandran map: −74.737°, −39.192°, 179.928°, −67.874°, and 28.534°, respectively; column 2 lists the predicted values for the one-bond ¹J_Cε1H SSCC after adding 5 Hz to the Σ term (in column 1), due to the Zero Point Vibrational Contribution [23].

^bResult obtained by using a uniform basis set “aug-cc-pVTZ-J” [37] for all the nuclei of Ac-His-NMe.

^cResult obtained by using an “aug-cc-pVTZ-J” basis set for the ¹³C^ε1, ¹H^ε1, N^δ1, N^ε2 and H^ε2 nuclei of the imidazole ring of His, and a “3-21G” basis set for all the remaining nuclei of Ac-His-NMe, i.e., by using a “locally-dense” basis set approximation [41].

^dSame as (c) with “6-31G” rather than a “3-21G” basis set.

^eResult obtained by using an “aug-cc-pVTZ-J” basis set for all nuclei of the imidazole ring of His, and a “6-31G” basis set on the remaining nuclei of Ac-His-NMe, i.e., by using a “locally-dense” [41] basis set approximation.

^fSame as (e) with solvent effects computed by using the PCM [31,32] approach with D_i = 6.5.

^gSame as (f) with D_i = 25.5.

Results and Discussion

In general, the gas-phase results from Tables 2 and 3 enable us to conclude that the computed ¹J_Cε1H SSCC with a locally-dense basis set approximation is indistinguishable from the one obtained by using a uniform basis set distribution, i.e., a “aug-cc-pVTZ-J” basis set on all the nuclei of the Ac-His-NMe molecule, but with a considerable reduction in computational time. In addition, a comparison of the DFT-computed ¹J_Cε1H SSCC values, from rows 4–7 of Table 2, shows that the results do not depend on the ϕ, ψ, χ1 and χ2 torsional angles of His. It is worth noting that, for a given basis set distribution, the use of the keyword “Readatoms”, that focuses the computation of ¹J_CH SSCC on the chosen pair of nuclei, can speed up the calculation by up to ~7 times.

Consideration of solvent effects, by using the PCM approach with two D_i, namely 6.5 and 25.5, increases the gas-phase results for ¹J_Cε1H SSCC on the N^ε2-H and the N^δ1-H tautomers by up to ~3Hz (see the highlight in italics in rows 8–9 and 5–6 of Tables 2 and 3, respectively). In view of all the assumptions and round off made, the most accurate DFT-computed value for ¹J_Cε1H SSCC is 205Hz ± 1.0Hz. Without doubt, within ±1 Hz, the values of ¹J_Cε1H SSCC for the tautomers of the imidazole ring of His, are indistinguishable. This likely high-pH limiting value (205Hz ± 1.0Hz) for ¹J_Cε1H SSCC is within the range of the lowest high-pH limiting value observed from non-titrating His on both the subtilisin BPN′ and the PLCCγ SH2 protein domain, explicitly ~205Hz and 203 ± 1.0 Hz, respectively. Moreover, it is also in very good agreement with the observed values (~205Hz for each of the His tautomers) obtained from NMR experiments for L-histidine at pH 12 in 80% d6-ethanol/20% H₂O at −55 °C [13].

The computed ¹J_Cδ2H SSCC in the gas-phase and in the presence of solvent, by using the PCM approach, with an “aug-cc-pVTZ-J” basis set on all nuclei of the imidazole ring of His and a “6-31G” basis set on the remaining nuclei of the Ac-His-NMe molecule, are listed in Table 4 for both the N^ε2-H and the N^δ1-H tautomer, respectively. In the presence of solvent effects (highlighted in italics in Table 4) the most remarkable of the results obtained for ¹J_Cδ2H SSCC, is the existence of a large difference between His tautomers, namely 15Hz. This result is counter to the assumption made by Platzer et al. [15] that ¹J_Cδ2H SSCC should behave like ¹J_Cε1H SSCC upon tautomeric changes, i.e., showing minimal or no difference. Even more important, our result for the difference between tautomers, in terms of ¹J_Cδ2H SSCC, is in excellent agreement with existing NMR-based evidence on L-histidine at pH 12 in 80% d6-ethanol/20% H₂O at −55 °C [13], showing that the difference in ¹J_Cδ2H SSCC between His tautomers is indeed 15Hz.

Despite the excellent agreement mentioned above, there is a conflict between the observed and the DFT-computed value for ¹J_Cδ2H SSCC for each of the tautomeric forms of the neutral His, i.e., the computed values in the presence of solvent for the N^ε2-H and the N^δ1-H tautomer are, as shown in Table 4, 165Hz and 180Hz, respectively, while the observed values are in the reverse order, namely, 180Hz and 165Hz, respectively (see Table 2S of Sudmeier et al. [13]). An irrefutable test to resolve this discrepancy would be to repeat the NMR experiments on L-histidine at pH 12 in 80% d6-ethanol/20% H₂O at −55 °C. However, this is beyond the scope of this work. For this reason, and in order to validate that the predictions in Table 4 actually belong to the referred His tautomer, the following analyses were carried out, first a validation in terms of the observed chemical shifts, second, a computation of the difference in the ¹J_Cδ2Cγ SSCC values (Δ_Cδ2Cγ) upon tautomeric changes and, third, a computation of the ¹J_CδΝε2 the and ²J_CδΝδ1 SSCC in the N^ε2-H and in the N^δ1-H tautomers, respectively.

The ¹³C^γ and ¹³C^δ2 shieldings for each tautomer of the imidazole ring of His, mentioned in Table 5, were computed at the DFT-level of theory because these nuclei are very sensitive probes with which to confirm the tautomeric forms of His accurately [6,11]. Chemical shifts are related to shieldings as differences with respect to a reference shielding. Hence, from Table 5, we can straightforwardly infer the following chemical-shifts inequalities:

$${\left({ }^{13}{\mathrm{C}}^{\mathrm{\gamma }}\right)}_{\text{Nε}2-\mathrm{H}}\gg {\left({ }^{13}{\mathrm{C}}^{\mathrm{\gamma }}\right)}_{\text{Nδ}1-\mathrm{H}}\text{and}{\left({ }^{13}{\mathrm{C}}^{\mathrm{\delta }2}\right)}_{\text{Nδ}1-\mathrm{H}}\gg {\left({ }^{13}{\mathrm{C}}^{\mathrm{\delta }2}\right)}_{\text{Nε}2-\mathrm{H}}$$ (1)

Table 5.

Chemical shieldings for the ¹³C^δ2 and ¹³C^γ nuclei^a

Nucleus	Nε2-H tautomer Shielding (ppm)	Nδ1-H tautomer Shielding (ppm)
13Cγ	42.1	61.9
13Cδ2	78.1	60.8

^aAll gas-phase DFT-calculations were computed, by using the Gaussian 09 suite of programs [20], for Ace-His-NMe with the OB98 functional [6] and a “6-311+G(2d,p)” basis set [6] for all the nuclei of His and a “6-31G” basis set on the remaining nuclei of the molecule, i.e., by using a “locally-dense” basis set approximation.⁴¹

The chemical-shift inequalities between tautomers given by Eq. (1) are in full agreement with both the observed chemical shifts (see Table 2S of Sudmeier et al. [13]) and the DFT-computed shielding values in model peptides for the tautomeric forms of the imidazole ring of histidine (see Figure 1 of Vila et al. [6]).

The computation, at the DFT-level of theory, of the difference (Δ_Cδ2Cγ) for the ¹J_Cδ2Cγ SSCC upon tautomeric changes, viz., with Δ_Cδ2Cγ = (¹J_Cδ2Cγ|^ε2 − ¹J_Cδ2Cγ|^δ1), where ¹J_Cδ2Cγ|^λ with λ = ε2 or δ1 represents the computed ¹J_Cδ2Cγ SSCC value for the N^ε2-H and the N^δ1-H tautomers, respectively, was carried out by using the His structures, the functional (OPW91) and the basis-set described in Table 4. The computed difference, Δ_Cδ2Cγ = +2.6 Hz, is in good agreement, but opposed in sign, with the observed difference, Δ_Cδ2Cγ = −3.0 Hz (see Table 2S of Sudmeier et al. [13]). Although no effort was made to optimize the functional and basis set for the computed one-bond C–C, ¹J_CC, SSCC, an analyses with all the functionals shown in Table 1, with a locally-dense basis set distribution mentioned in Table 4, shows consistency with the result obtained with OPW91, namely Δ_Cδ2Cγ = +1.8 Hz, +2.0 Hz, +2.6 Hz, +1.8 Hz and +1.9 Hz, for the B3LYP, B3P86, OPBE, B972 and PB86 functionals, respectively.

For a long time, it has been recognized that the Carbon–Nitrogen spin-spin coupling constants (J_CN) can be used for an accurate determination of the tautomeric forms of His [8,42]. For this reason, and despite the fact that no effort was made to optimize the functional or the basis set with which to compute the one- and two-bond C–N, J_CN, an analysis of the computed J_CN values was carried out by using the His structures, the functional (OPW91), and the basis set described in Table 4. Among all possible C–N SSCC of the imidazole ring of His, we focused the calculations on both the ¹J_Cδ2Nε2 and the ²J_Cδ2Nδ1 because these SSCC were suggested as the probes of choice with which to determine the ratio of the N^ε2-H and the N^δ1-H tautomers, accurately [8]. Consequently, the results obtained here for ¹J_Cδ2Nε2 (13.2 Hz), in the N^ε2-H tautomer (see Figure 1a), and ²J_Cδ2Nδ1 (4.7 Hz), in the N^δ1-H tautomer (see Figure 1b), show the same trend as that of the observed absolute values for these tautomers, namely ~13 Hz and ~5 Hz, respectively [8,42]. Even though this analysis does show internal consistency with the previous calculations of both the chemical shifts and ¹J_Cδ2H SSCC, the validation of the theoretical results remains elusive without farther experimental evidence.

Overall, under the only condition that His must be non-protonated and, assuming the correctness of the theoretical predictions for ¹J_Cδ2H SSCC of the N^ε2-H and the N^δ1-H tautomers, it is possible to determine the fraction of the N^δ1-H tautomeric form of the imidazole ring of His, f^δ1, as a function of the observed ¹J_Cδ2H SSCC value. So, assuming that $J^{\mathit{\text{obs}}}=f^{\mathrm{\epsilon }2}{J}_{\mathit{\text{high}}-pH}^{\epsilon 2}+f^{\mathrm{\delta }1}{J}_{\mathit{\text{high}}-pH}^{\delta 1}$, and f^ε2+f^δ1 = 1 the following equation can be used for this purpose:

$$f^{\delta 1}=\frac{J^{\mathit{\text{obs}}}-J_{\mathit{\text{high}}-pH}^{\epsilon 2}}{J_{\mathit{\text{high}}-pH}^{\delta 1}-J_{\mathit{\text{high}}-pH}^{\epsilon 2}}=\frac{J^{\mathit{\text{obs}}}-165}{15}$$ (2)

where J refers to ¹J_Cδ2H SSCC, “obs” is the value observed, $J_{\mathit{\text{high}}-pH}^{\epsilon 2}$ and $J_{\mathit{\text{high}}-pH}^{\delta 1}$ refer to ¹J_Cδ2H SSCC obtained, at the high-pH limiting value, from the N^ε2-H and N^δ1-H His tautomers, respectively; as shown in Table 4, “165” is the value for the $J_{\mathit{\text{high}}-pH}^{\epsilon 2}$ SSCC of the N^ε2-H tautomer, and “15” is the difference, 180–165, between the computed ¹J_Cδ2H SSCC for the tautomeric forms of His at the high-pH limit. Naturally, the fraction of the N^ε2-H tautomeric forms is given by: f^ε2 = 1− f^δ1.

It is worth noting that, even if the Sudmeier et al. [13] observations were confirmed Equation (2) will still be valid after the substitution δ1 → ε2.

Conclusions

The main results obtained for ¹J_CH SSCC in the N^ε2-H and N^δ1-H tautomers of the imidazole ring of His indicate that: (i) ¹J_Cε1H = 205 ± 1.0 Hz should be adopted as the canonical high-pH limiting value for this SSCC; (ii) ¹J_Cε1H SSCC is not sensitive enough to be used as a probe with which to determine the tautomeric states of the imidazole ring of His; and (iii) ¹J_Cδ2H SSCC shows a large difference (~15Hz) between tautomers and, hence, this SSCC emerges as a very sensitive probe with which to identify the tautomeric fractions of non-protonated His.

Overall, the theoretical confirmation showing that ¹J_Cε1H SSCC is not sensitive upon tautomeric change means that the use of this SSCC will enable us to predict the protonation fraction of His, as a function of the pH, accurately, because the prediction will not depend on the fraction of the tautomeric forms. In addition, the fraction of the tautomeric forms of the imidazole ring of His, at either high-pH or for non-protonated buried His, can be predicted accurately by using Equation (2) for ¹J_Cδ2H SSCC.

Highlights.

• The ¹J_CH SSCC of the imidazole ring of His was computed at the DFT-level of theory.

• Solvent effects (polarizable continuum model approach) were considered.

• The Zero Point Vibrational Contribution was included.

• ¹J_Cε1H SSCC shows a slight difference (~1 Hz) between tautomers.

• ¹J_Cδ2H SSCC shows a large difference (~15Hz) between tautomers.