Arginine: Its pKa value revisited (2025)

Potentiometry

We used potentiometry to measure directly the release of protons by arginine in response to the addition of KOH. The results of these potentiometric titrations are summarized in Table 1 and representative titration curves are shown in Figure 1. The blank used in these experiments consisted of a solution of lysine in water, allowing both calibration of the KOH titrant and control of the ionic strength without requiring the addition of supporting electrolytes. The pK_a values resolved for and attributed to the α-aminium (9.4 ± 0.1) and side chain ζ-aminium (10.9 ± 0.1) groups of free lysine are consistent with accepted data.27, 28

The two titration events in a solution of lysine can be visualized without baseline correction. This is not the case for arginine. With charged α-carboxylate and guanidinium moieties and a neutral α-amine, the arginine titration begins at its isoionic point near pH 11 (i.e., the unadjusted pH of the initially prepared solution). Although masked by the steep rise in pH due to the necessary addition of large quantities of KOH, the guanidinium titration becomes apparent after the lysine/water blank is subtracted. As shown in the inset of Figure 1, inflection points in the difference curve can be seen for each titrating group. Fitting of this curve to a three-site binding isotherm yielded the desired pK_a value of the arginine side chain.

The pK_a value of the arginine guanidinium group obtained by analysis of the difference potentiometric titration curves is, on average, 13.8 ± 0.1 (Table 1). This result is from multiple experiments performed over the course of five months with samples containing 500 mM arginine. Experiments were also carried out with lower concentrations of the free amino acid. Although yielding larger fitting errors due to the proportionally higher water background, a concentration-dependence was observed and a pK_a value of 13.50 ± 0.2 was measured with 125 mM arginine (Table 1). This small variation may be related to ionic strength differences or perhaps to the known propensity of the charged arginine side chain to associate with itself.29 However, for samples of arginine at 10 and 100 mM, similar high pK_a values were obtained by NMR methods.

NMR spectroscopy

In parallel, we attempted to measure with NMR spectroscopy the pK_a value of the arginine side chain in the context of a blocked tripeptide, acetyl-Gly-Arg-Gly-amide. As part of a study to define the pH-dependent chemical shifts of all the common ionizable amino acid side chains, this compound was chosen to mimic a random coil polypeptide and to avoid possible complications due to the deprotonation of the terminal α-aminium and α-carboxylic acid moieties.26 Unfortunately, under highly alkaline conditions, the tripeptide slowly hydrolyzed over the course of the titrations, which required ∼1 day due to detection of ¹³C at natural abundance. A similar hydrolysis problem precluded potentiometric studies of blocked arginine derivatives. As a result, reliable pH-dependent chemical shift changes could only be measured for the arginine side chain ¹³C^ζ and ¹H^δ nuclei in the intact peptide [Fig. 2(A)]. Based on these data, an average pK_a value of 13.8 ± 0.1 was obtained. However, this could be an underestimation as the maximum sample pH value was only 14.5, and thus the plateau chemical shifts of the deprotonated species were not well defined. Also, according to the manufacturer's electrode specifications, interference from the ∼1 M Na⁺ added during the titration may have reduced the apparent sample pH by 0.1 to 0.2 log units.

Subsequently, we monitored via NMR spectroscopy the titration of numerous reporter nuclei in free ¹³C₆/¹⁵N₄-arginine. In this case, KOH was used to reduce possible electrode alkaline errors.30 Also, a higher final pH of 15.25 was attained. As shown in Figure 2(B), two distinct titration events were observed and could be confidently attributed to the α-aminium and guanidinium moieties. Under all pH values examined, the arginine α-carboxylic acid, with a known pK_a value of ∼ 2,27, 31, 32 is unquestionably deprotonated. Based on the individually fit titration curves of these nuclei in data sets recorded with both 10 mM and 100 mM ¹³C₆/¹⁵N₄-arginine, the average pK_a value of the α-aminium in the context of charged α-carboxylate and guanidinium moieties is 9.15 ± 0.05. This is consistent with previously reported pK_a values of 9.0 to 9.3.27, 31, 32 Most importantly, the average of the pK_a values fit individually for several guanidinium reporter nuclei in the presence of a charged α-carboxylate and neutral α-amine is 13.9 ± 0.15. The similarity of results for the acetyl-Gly-Arg-Gly-amide tripeptide and free arginine also indicates that electrode errors (K⁺ versus Na⁺) are minor and that the presence of the negatively charged carboxylate does not significantly increase the pK_a value of the guanidinium group.

Arginine pK_a measurements by potentiometry

Potentiometry is traditionally the method of choice for determining the pK_a values of small molecules because it involves a direct measurement of a pH titration curve. This means that the amplitudes of the titrations determined potentiometrically reflect the number of proton binding sites. However, the resulting pK_a values are macroscopic and, in the absence of any other information, not assignable to specific ionizable groups in the molecule. Furthermore, the standard potentiometry approach involves use of a glass electrode to measure pH values. At high pH, this method is fraught with difficulties caused primarily by the cation error and the sensitivity of the glass surface to these conditions.30 Fortunately, these problems were minimized in this study by using a modern glass electrode designed specifically for work under highly alkaline conditions. Also, a difference titration against a lysine/water blank enabled titrant calibration and, in effect, provided an internal reference for the data fitting. Collectively, this strongly supports the accuracy of the potentiometrically determined pK_a values summarized in Table 1 for the arginine side chain.

Arginine pK_a measurements by NMR spectroscopy

NMR spectroscopy is often the method of choice for measuring polypeptide and protein pKa values because it provides site-specific information in the form of pH-dependent chemical shifts of nuclei associated with constituent ionizable groups.26 However, chemical shift changes may arise from additional ionization events, and the resulting pK_a values are still macroscopic in the sense that they reflect the ensemble average of the pH-independent microscopic equilibria between all possible forms of a protein with a given total protonation level.46 In the case of the free amino acid arginine, the pK_a values of its ionizable functional groups are sufficiently different that it follows one very dominant sequential deprontonation pathway with increasing sample pH (α-carboxylic acid then α-aminium then guanidinium). Thus, the fit pK_a value of 9.15 ± 0.05 can be assigned to arise almost exclusively to the α-aminium group in the context of the charged guanidinium and α-carboxylate moieties, and that of 13.9 ± 0.15 to the guanidinium group in the context of the neutral α-amine and charged α-carboxylate.

The small difference in pK_a values determined by NMR methods for the blocked acetyl-Gly-Arg-Gly-amide tripeptide (13.8 ± 0.1) and free arginine (13.9 ± 0.15) suggests that the ionization equilibrium of the guanidinium group is not substantially perturbed by the presence of the negatively charged α-carboxylate. This is expected given the length of the arginine side chain and the high ionic strength of a solution at pH ∼ 14. Consistent with this observation, a comparison of the ionization equilibria of arginine versus citrulline in solutions of 0.3 − 2 M ionic strength indicated that the pK_a values of the α-carboxylic acid and α-aminium groups are perturbed by only ∼ −0.1 and +0.2 pK_a units, respectively, due to electrostatic interactions with the positively charged guanidinium versus neutral carbamido moieties (i.e., in the directions expected for favorable or unfavorable electrostatic effects).32, 41 Parenthetically, using internal reference compounds for pH calibration, the authors of this study also reported a pK_a value of 13.54 ± 0.01 for the arginine side chain by ¹H-NMR methods.32

pH-dependent chemical shifts

We are unaware of a case in which the pK_a value of an arginine side chain in a protein has been measured unambiguously (although see, for example, Refs. 47] and 48]). Nevertheless, such studies are important to pursue for many reasons, including understanding electrostatic interactions in proteins and testing postulated roles of arginines in catalytic mechanisms and in proton transfer pathways. Therefore, the reference chemical shift data summarized in Figure 3 provide a benchmark for studying the ionization states and pK_a values of arginines in polypeptides and proteins by NMR spectroscopy. In particular, the ¹³C^ζ, ¹⁵N^ε, and ¹⁵N^η nuclei should all report coincident titration curves with Δδ values similar in magnitude and sign to those listed in this figure. This is required to be reasonably confident that any pH-dependent chemical shifts result directly from the deprotonation of the arginine and not indirectly due to structural or electrostatic changes from the deprotonation of other groups, such as amino or phenol moieties, in the protein. Of course, the protein must be confirmed to remain stably folded and well behaved under highly alkaline conditions.

In the absence of any detectable pH-dependent chemical shift changes for reliable reporter nuclei (i.e., ¹³C^ζ, ¹⁵N^ε, or ¹⁵N^η), one cannot a priori conclude whether an arginine is always charged or always neutral over the conditions examined. Of course, given an intrinsic pK_a value of almost 14, one expects (and finds) that the vast majority of arginines are charged in proteins. The observation of chemical shifts within the range of those shown in Figure 3 for the ionized side chain would certainly support this conclusion. In contrast, only the ¹⁵N^η nuclei with dramatically different chemical shifts of ∼71 ppm and 93 ppm in charged versus neutral arginine might serve as an indicator of its ionization state in the absence of any additional information. However, an arginine with an unusually low pK_a value will most certainly be in a very unusual environment, which may also lead to strongly perturbed chemical shifts. Indeed, the guanidino moiety shows substantially smaller chemical shift differences between its charged and neutral forms within nonpolar solvents than in an aqueous environment.49 Unfortunately, this adds a further complication to consider when attempting to determine the ionization states of arginines in proteins by NMR spectroscopy.

Arginine tautomers and a route for pK_a perturbations

In contrast to the planar guanidinium ion, the neutral side chain guanidine moiety is nonplanar and can adopt five possible tautomeric forms, each corresponding to the loss one of the five nitrogen-bonded protons.16 All of these neutral tautomers exist in a pH-independent equilibrium and can interconvert via bond rotations and/or proton transfer. As such, the observed acid dissociation constant of an arginine side chain is actually the sum of the five microscopic acid dissociation constants leading to each of these tautomers.

The observation of degenerate shifts for the two ¹⁵N^η nuclei, as well as similar shifts for the ¹⁵N^ε and ¹⁵N^η nuclei (Figs. 2 and 3), indicates that the neutral arginine tautomers are approximately isoenergetic and interconvert rapidly on the chemical shift timescale (i.e., k_ex > 10³ s⁻1). Otherwise, one would expect significantly different shifts for non-interconverting sp² (CN bonded) and sp³ (CN bonded) hybridized nitrogens.50 However, the microscopic pK_a values associated with each tautomer, and hence their equilibrium population distributions in the neutral form of the arginine side chain, remain uncertain. Based on an extrapolation of temperature-dependent chemical shifts recorded for neutral arginine and methylguanidine analogs in DMSO/H₂O cosolvents, a distribution with ∼2/3 protonated at N^ε has been estimated.51 In contrast, theoretical calculations suggested that the two lowest energy tautomers arise from deprotonation of either the N^ε or one specific N^η.52 Also, the observation that the hydroxide-catalyzed rate constant for hydrogen exchange of the arginine N^εH is two-fold higher than the N^ηH suggests a lower microscopic pK_a value for N^ε deprotonation and hence preferential formation of the tautomer lacking a proton at this nitrogen.53, 54 A caveat to this argument is that steric factors could affect the relative rates of the diffusion-limited exchange reactions.

If a neutral arginine was indeed present in a folded protein, perhaps under highly alkaline conditions, then the relative populations of its tautomeric forms could certainly change in response to structure-dependent intermolecular interactions, such as hydrogen bonding. Moreover, it has been proposed that the pK_a value of an arginine side chain could be perturbed by interactions that twist the guanidinium group towards a nonplanar conformation.6 Such structural-induced perturbations might enable the transient formation of a neutral guanidine moiety to serve, for example, as a general base in an enzymatically catalyzed reaction.

Potentiometric titrations

Solutions of the unmodified amino acids lysine and arginine (Sigma, >99.5% pure) were prepared volumetrically under an N₂ atmosphere (CO₂ free) with deionized water (degassed extensively by boiling under vacuum) made to 100 mM KCl. The stock solutions of lysine and arginine were initially at 500 mM and sealed under an N₂ atmosphere until use. The correct volumes of sample and dilutant were withdrawn with a Hamilton syringe from the sealed containers and injected into the isolated titration vessel, also held under an N₂ atmosphere. The water blanks were prepared in a similar manner. Total volumes used were in the range of 2.0 − 2.5 mL. The saturated KOH solution used as titrant was made from KOH pellets (Fisher), freshly dissolved in 100 mM KCl (prepared with degassed, deionized water).

Direct potentiometric titrations were performed using a glass electrode (pHG2HE8 from Radiometer America) that is inherently insensitive to cation error at pH values as high as 14.30, 55 The electrode chain was completed with a calomel reference electrode (REF401 from Radiometer America) connected to a PHM95 pH meter (Radiometer America). The calibration of electrodes was performed with IUPAC series certified pH 9.180 and 12.45 standards (Radiometer, NIST) just prior to each experiment and rechecked after completion. Between use these buffers were stored in tightly sealed containers at 4 °C. Titrations were performed with a Dosimat E665 (Metrohm) delivering volumes as low as 1 μL. The temperature of the samples was kept at 25 ± 0.1 °C with a water-jacketed titration vessel. Titrations began immediately following initial temperature equilibration, and were monitored continuously with a thermistor probe to ensure re-equilibration after the heating that results from the exothermic dilution of highly concentrated KOH titrant.

Potentiometric titration analysis

The titration of free lysine was used to calibrate the titrants. This involved fitting the pH titration difference curve (titration of a water blank subtracted from the titration of lysine) to a two-site model describing the deprotonation of the α-aminium and side chain ζ-aminium groups. The KOH titrant concentrations were thereby determined to range from 13.7 to 14.5 M. The error in titrant concentration was estimated to be ± 0.3 M, resulting in a propagated error for the fit pK_a values of ± 0.15 if > 12 and ± 0.03 if lower. Titrations were done multiple times to reduce these experimental errors.

NMR-monitored titrations

The blocked tripeptide acetyl-Gly-Arg-Gly-amide (>95% purity by HPLC) was purchased from Biometik. The tripeptide was initially at ∼ 10 mM in 50 mM NaCl with 5% D₂O for lock and 1 mM DSS (4,4-dimethyl-4-silapentane-1-sulfonic acid) as a pH-independent internal reference. The pH adjusted by addition of small aliquots of ∼ 0.1 M, 1 M, or solid NaOH. Uniformly ¹³C₆/¹⁵N₄-labeled l-arginine (Sigma-Aldrich) was initially at 10 mM or 100 mM in 50 mM NaCl with 5% D₂O and 1 mM DSS, and the pH adjusted by addition of 0.1 M, 1 M, or solid KOH. The solid hydroxide was used to obtain the highest pH values. Sample pH values were measured at room temperature (∼20 ^oC) using a Thermal Scientific Orion* 3-Star pH meter and an Orion ROSS micro pH electrode (8220BNWP), calibrated with standard pH 7, 10, and 12.5 (Oakton) reference buffers. According to vendor's specifications, the electrode has a precision of ± 0.01 log units over a pH range of 0 to 14.

Spectra were recorded at 25 ^°C using a cryoprobe-equipped Bruker Avance III 500 MHz spectrometer. The ¹H and ¹³C signals were referenced directly to internal DSS at 0.00 ppm, and ¹⁵N referenced indirectly via magnetogyric ratios.56 Chemical shifts for the unlabeled tripeptide were obtained from standard 1D ¹H-NMR and 2D magnitude-mode ¹³C-HMBC spectra. Chemical shifts for the ¹³C₆/¹⁵N₄-arginine were obtained from 1D ¹³C-decoupled ¹H-NMR, ¹H/¹⁵N-decoupled ¹³C-NMR (with ¹H NOE), and ¹H/¹³C-decoupled ¹⁵N-NMR (with ¹H NOE) spectra. Samples were in 5 mm diameter NMR tubes, except at very high pH and ionic strength conditions, for which 3 mm tubes were used to enable tuning. Also, a 100 mM sample of ¹³C₆/¹⁵N₄-arginine was required for the ¹⁵N-NMR measurements because the Bruker TCI CryoProbe is designed for direct detection of ¹H and ¹³C, but not ¹⁵N signals.

Spectra were processed using Topspin 3. The pH-dependent chemical shifts were fit with GraphPad Prism and Matlab to published equations for one or two sequential titrations in order to obtain pK_a and limiting chemical shift values.46 The standard deviations (fit precision) for the individual titrations shown in Figure 2 were obtained using a Monte Carlo approach with data points randomly varied by assumed standard deviations of 0.05 units for the sample pH, and 0.01/0.05/0.1 ppm for the ¹H/¹³C/¹⁵N chemical shifts. The pK_a values discussed in the text are the averages ± standard deviations of the means of the individually fit values for all nuclei reporting a given titration.