A pKa is never read off an instrument. A potentiometric titration produces a set of cell potentials as a function of added titrant, and the constants are parameters of a model fitted to that curve. Almost every failure mode in the experiment lives in the gap between the two: the electrode may not be reporting the quantity your model assumes, the titrant may not be what the bottle says, and the model may carry more adjustable parameters than the data can distinguish. For a peptide with four or five ionisable groups, the last of these is usually the one that bites.
The cell, and what it is actually reporting
The experiment is a proton mass balance. A known amount of peptide is dissolved in a background electrolyte of fixed composition, acidified with standard strong acid until every group of interest is protonated, then titrated with standardised strong base in small increments while the potential of a glass electrode against a reference half-cell is recorded after each addition. Fitting proceeds by writing mass-balance equations for the peptide and for protons, expressing them in terms of trial constants, and minimising the residual between calculated and observed potential.
That fitting is done in concentrations. The constants you extract are stoichiometric constants valid at the ionic strength you worked at, and they mean what you think only if the electrode reading is proportional to hydrogen ion concentration rather than activity. Calibrating a glass electrode against standard pH buffers does not deliver that. Irving, Miles and Pettit examined the errors introduced into acid dissociation constants determined by potentiometric titration and showed that unknown junction potentials can arise when a glass electrode paired with a saturated calomel reference is calibrated against a standard buffer solution; they demonstrated the magnitude of the influence of those unknown potentials and recommended an experimental procedure that gives meaningful results [1]. The practice that follows is to calibrate the whole cell in the medium you will actually use, by titrating a known strong acid with a known strong base.
Treat that calibration titration as an experiment in its own right, because it returns more than a slope and an intercept. The GLEE program calibrates a glass electrode by means of a strong acid–strong base titration and returns the pseudo-Nernstian standard potential and slope of the electrode, an estimate of the carbonate contamination of the base, and optionally the concentration of the base and pKw [2]. Each of those is a quantity your peptide fit would otherwise have to assume. A slope that has drifted from the ideal value, or a pKw carried over from a different medium rather than determined in the one you are using, propagates straight into the alkaline end of the peptide curve — which is exactly where lysine, tyrosine and cysteine titrate.
Fix the background electrolyte and state it. The peptide reference values the field leans on were obtained by potentiometric titration of alanine pentapeptides with appropriately blocked termini, in 0.1 M KCl at 25 °C [3]. A constant reported without its medium and its temperature cannot be compared with them.
Carbonate, and the other contents of the titrant
Hydroxide solutions absorb atmospheric CO2, and the carbonate that forms is itself a diprotic base. It consumes titrant, and it does so across a pH range that overlaps the region where amino and phenolic groups titrate, so it does not merely displace the curve — it changes its shape. That a purpose-built calibration program reports carbonate contamination of the base as one of its fitted outputs [2] is a fair measure of how routinely this happens.
The countermeasures are procedural rather than computational: prepare base from a carbonate-free stock, store and deliver it under an inert atmosphere, blanket the titration vessel with nitrogen or argon so that CO2 cannot re-enter through the headspace over the course of a run, and re-standardise on a schedule rather than on suspicion. The carbonate estimate returned by each calibration titration then becomes a running quality check on the titrant rather than a diagnosis performed after a peptide dataset has already failed to fit.
From a curve to a set of constants
The intuition that each ionisable group produces its own inflection, and that you read a pKa off each one, fails as soon as groups titrate close together. Ullmann analysed the relation between protonation constants and titration curves in polyprotic acids and concluded that inflection points of total and individual titration curves, and the pH at which a binding site is half protonated (pK1/2), are generally not identical with the pKa values of a polyprotic acid; they are a first good guess for further fitting, but only fitting titration curves to proper thermodynamic expressions leads to the pKa values associated with the reaction free energy [4].
The reason is interaction between sites. Onufriev, Case and Ullmann showed that a set of N interacting titratable sites can be mapped onto N independent, non-interacting quasi-sites, each characterised by its own pK'a; the individual site titration curves are then weighted sums of Henderson–Hasselbalch curves, while the total protonation curve is the unweighted sum of those same curves [5]. This is the formal statement of why a constant extracted from a total titration curve belongs to the molecule rather than to a residue: the constants that reproduce the whole curve are quasi-site constants, and the mapping from them back onto individual sites is not one-to-one.
Resolution is therefore a signal-to-noise question, not a matter of eyeballing plateaux. Meloun and colleagues tested how reliably two regression programs recover four dissociation constants for a small molecule with five variously protonated forms and heavily overlapping absorption bands, and found, in synthetic spectra carrying a deliberately pre-selected noise level, the bias in the fitted constants negligible once that imposed error was below 0.5 mAU, with all four constants still sufficiently accurate across an imposed error range of 0.1 to 1.0 mAU; goodness-of-fit was the most effective diagnostic for deciding whether the fitted parameters were justified by the data [6]. That work is spectrophotometric and on a small molecule, so neither the thresholds nor the program names transfer to a potentiometric peptide titration. What transfers is the structure of the problem: the number of constants you can resolve is set by the precision of the primary observable, and a fit diagnostic rather than visual inspection is what licenses a two-constant model over a one-constant model.
In practice, fit the entire curve to a model with a defined number of protonation steps, compare models differing in that number, and report the standard deviations the fit returns. Expect two carboxylates separated by a few tenths of a log unit to come back as two macroscopic constants with correlated and inflated uncertainties. The model is not wrong; the second constant is simply barely determined, and quoting it to two decimals overstates what the experiment established.
Macroscopic constants are not site constants
This is where a single reported pKa for a peptide becomes actively misleading. A macroscopic constant describes the equilibrium between two protonation levels of the molecule — species carrying n and n−1 protons — summed over every arrangement of those protons among the available sites. A microscopic constant describes one specified site changing state while the states of all other sites are fixed. When a molecule carries several groups of similar intrinsic basicity, the microconstants proliferate relative to the macroconstants, and no amount of curve fitting on a total titration curve recovers them.
Glutathione makes the arithmetic concrete. Mirzahosseini, Somlyay and Noszál characterised the thiol and disulfide forms of this tripeptide by 1H NMR–pH titration and quantified their acid–base properties in terms of 128 microscopic protonation constants, the first complete set of such parameters for the pair, together with 12 interactivity parameters [7]. A potentiometric titration of the same molecule returns a handful of macroscopic constants. Both descriptions are correct; only the microscopic set tells you which group is charged at a given pH.
Site-specific numbers require a site-specific observable. McDougal and colleagues followed the two histidines of the peptide α-conotoxin MII by 1H NMR across pH and found that the E11A substitution does not significantly perturb the pKa of either His9 or His12, whereas the triple variant N5R:E11A:H12K produces a significant decrease in the pKa of His9; constant-pH molecular dynamics reproduced the NMR-derived values with a mean absolute deviation from experiment of 0.3 pKa units [8].
The practical consequence is blunt. If your peptide carries two glutamates, or a histidine and a free N-terminus within the same pH window, a potentiometric titration will tell you how many protons leave and over what pH range, and will not tell you which residue lost them. Writing “the histidine pKa is 6.4” on the strength of potentiometry alone records an assignment you have not made.
Ionic strength and temperature belong to the number
Because the fitted constants are stoichiometric, they are functions of the medium. Nagai, Kuwabara and Carta determined apparent dissociation constants of eight amino acids at 283.1 K, 298.1 K, 313.1 K and 333.1 K at various ionic strengths by potentiometric titration, using the Davies equation to extrapolate to zero ionic strength [9]. Their temperature result is the one to carry into peptide work: the pK of the carboxylic acid attached to the α-carbon, and that of the glutamic acid side-chain carboxyl, were almost independent of temperature, while the pK values of α-amino groups and of the side-chain amino groups of the basic amino acids varied substantially with temperature, with van 't Hoff plots linear enough to indicate constant standard enthalpies of reaction over that range [9].
The asymmetry is mechanistic and follows from the van 't Hoff relation itself: a constant that barely moves with temperature is one whose reaction enthalpy is near zero, which is the case for carboxylate protonation, while amine protonation carries a substantial enthalpy and its constant moves accordingly. So a thermostatted vessel matters far more for the basic end of a peptide curve than for the acidic end, and a value measured at ambient temperature and compared against a 25 °C reference will disagree mostly in the lysine and N-terminal region.
Ionic strength acts through activity coefficients and shifts constants in a charge-dependent way, so transferring a value between media is not free. Cigala and co-workers determined the acid–base properties of glutathione by potentiometry in a range of salt solutions and ionic strengths, measured activity coefficients by distribution methods and calculated Specific Ion Interaction Theory coefficients, so that the resulting speciation could be defined in aqueous media containing Na+, K+, Mg2+ and Ca2+ [10]. Absent that modelling effort, the rule is simply to choose a medium and ionic strength, hold both constant across the whole study, and report them with the temperature.
When there is not enough material
Potentiometry is a bulk stoichiometric method. The observable is titrant consumed by the entire solution, so the peptide's proton uptake has to stand out against that of water, the background electrolyte and any residual carbonate. That is the structural reason a synthesis-limited or poorly soluble sample resists titration, and it is not fixed by a better electrode.
Spectrophotometric titration lifts the constraint when the analyte carries a chromophore whose spectrum responds to the ionisation of interest. Allen and colleagues acquired UV spectra with a fibre-optic dip probe, light source and photodiode array detector while a titrator manipulated pH and ionic strength, then applied target factor analysis to the multiwavelength absorbance data; the pKa values obtained for five ionisable small molecules agreed with those from conventional pH-metric titration, and the approach worked even when the absorption spectra of the reacting species were very similar [11]. Those were small molecules, not peptides, but the instrumental argument carries over: absorbance is an intensive observable and does not require the analyte to dominate the solution's buffer capacity.
NMR titration is the other route, and it is site-resolved rather than merely sensitive. Platzer, Okon and McIntosh measured the pH-dependent 1H, 13C and 15N chemical shifts of nearly all nuclei in the seven common ionisable amino acids within the blocked tripeptide acetyl-Gly-X-Gly-amide, with alanine amide and N-acetyl alanine as models of the N- and C-termini, producing an essentially complete set of intra-residue and nearest-neighbour reference shifts [12]. Those references are what let you judge whether a shift observed in your peptide reflects a genuinely perturbed pKa or a nearest-neighbour effect you would have seen in an unstructured chain.
Two cautions attach to NMR titration. First, a constant measured in D2O is not the aqueous constant. Krężel and Bal determined a linear correlation between pH-meter readings in equivalent D2O and H2O solutions and derived the recalculation pKH = 0.929 pKH* + 0.42 [13]. Second, the methods are close but not identical. Pálla and colleagues compiled 417 records covering 112 compounds from 43 studies and compared protonation constants from potentiometry against those from NMR titration, finding NMR-determined values tending to be higher by an average of 0.056 log units across the whole compiled set before outlier removal, with much of the bias attributable to variance-related issues in the data and particularly to potentiometric measurement error at extreme pKa values; they conclude that the two methods can be used interchangeably in the intermediate pKa range and that outside the range 2 to 10, NMR titration with in situ pH indicators is preferable [14]. In their framing pH/potentiometric titration remains the gold standard for acid/base constants, with the spectroscopic techniques as alternatives for specific analytical challenges that also report on the structure and site of protonation [14].
A computed pKa is a starting hypothesis
Sequence-based pKa tables exist because they are useful, not because they are right about your peptide. The reference values have themselves moved. The blocked alanine pentapeptide measurements gave 3.67 ± 0.03 for the α-carboxyl, 3.67 ± 0.04 for Asp, 4.25 ± 0.05 for Glu, 6.54 ± 0.04 for His, 8.00 ± 0.03 for the α-amino group, 8.55 ± 0.03 for Cys, 9.84 ± 0.11 for Tyr and 10.40 ± 0.08 for Lys, and several of these differ from the Nozaki and Tanford values still widely quoted: Asp 3.67 against 4.0, His 6.54 against 6.3, α-amino 8.00 against 7.5, Cys 8.55 against 9.5, Tyr 9.84 against 9.6 [3].
Those are model-compound values in an unstructured chain. Where structure intervenes the spread widens sharply: Grimsley, Scholtz and Pace tabulated 541 measured pK values for the Asp, Glu, His, Cys, Tyr and Lys side chains and the C and N termini of 78 folded proteins, averaging Asp 3.5 ± 1.2, Glu 4.2 ± 0.9, His 6.6 ± 1.0, Cys 6.8 ± 2.7, Tyr 10.3 ± 1.2, Lys 10.5 ± 1.1, C-terminus 3.3 ± 0.8 and N-terminus 7.7 ± 0.5 [15]. That is a folded-protein data set and a short flexible peptide should sit nearer the model values, but a disulfide-constrained, helical or self-associating peptide has no guarantee of doing so.
The consequence for the isoelectric point is direct, because a sequence-derived pI is not a measurement at all — it is a computation over a chosen pKa set, and the choice propagates. Kozlowski built the Isoelectric Point Calculator around exactly that dependence, estimating pI from several dissociation constant sets including two computationally optimised ones, and reported that the new sets outperform previous algorithms by at least 14.9% for proteins and 0.9% for peptides, with average errors of pI estimation of 0.87 and 0.25 pH units for proteins and peptides respectively [16].
Read that last figure the right way. A quarter of a pH unit is close enough to select an ion-exchange buffer or bracket a focusing run, and loose enough that the sign of the net charge is genuinely uncertain within a quarter-unit of the predicted pI — which is precisely the region where solubility minima and aggregation windows sit. Where that matters, the calculated value is the hypothesis and a titration is the test: potentiometric if you have the material and the solubility, spectrophotometric if you have a responsive chromophore, NMR-monitored if you need to know which residue is doing it.