The Isoelectric Point
A single amino acid dissolved in water carries a net charge. This charge depends entirely on the pH of its surroundings. There exists exactly one pH at which that charge sums to zero. This pH is the isoelectric point, pI. It is not a fixed property of the molecule the way molecular weight is. Instead, it is a computed consequence of the Titration Curves of Amino Acids. These curves describe every ionizable group hanging off the backbone. Get the pI wrong and you get the wrong prediction. You'll mispredict how a protein migrates in an electric field. You'll also misjudge whether it precipitates out of a buffer. And you'll misjudge which chromatography resin will bind it. The isoelectric point matters because net charge, not molecular identity, is what an electric field or a charged surface actually senses. Isoelectric focusing, ion-exchange chromatography, protein crystallization screens, and even the design of buffers for enzyme assays all hinge on this. They depend on knowing where a given amino acid or protein sits relative to its pI. A protein at its pI has minimum solubility in most cases. This happens because there is no net electrostatic repulsion to keep molecules apart. So they aggregate and precipitate — a fact exploited daily in protein purification. The big picture is that pI is computed from pKa values. It is not measured directly as an independent constant. For a simple amino acid with only an α-carboxyl and an α-amino group, the pI is the arithmetic mean of the two flanking pKa values. These bracket the neutral (zwitterionic) species. For amino acids with ionizable side chains — aspartate, glutamate, histidine, cysteine, tyrosine, lysine, arginine — the rule generalizes. Average the two pKa values that bracket the pH range. Over this range, the molecule carries zero net charge. This article builds that rule from first principles. It uses the Henderson–Hasselbalch framework and explicit proton-inventory bookkeeping. What follows is a rigorous derivation of the pI formula. It covers both simple and side-chain-bearing amino acids. It also includes two fully worked mechanistic derivations. These show exactly why the "average of two pKa's" recipe works. Three worked numerical examples span glycine, glutamate, and histidine. A survey follows of how pI governs electrophoretic mobility and solubility in real biochemical practice. It sets up the chemistry needed to understand The Peptide Bond and Its Formation. There, these same ionizable groups are consumed one by one. This happens as residues are linked into a chain.
- The isoelectric point pI is the pH at which an amino acid or protein has net charge exactly zero.
- For a simple amino acid (no ionizable side chain), pI = (pKa1 + pKa2)/2, averaging the groups flanking the neutral zwitterion.
- For amino acids with ionizable side chains, pI averages the two pKa values that bracket the pH range of the zero-net-charge species — not simply "all pKa's averaged."
- Below pI a molecule is net positive and migrates toward the cathode; above pI it is net positive... reversed — net negative and migrates toward the anode.
- Solubility of a protein is typically minimal at its pI because there is no net charge to enforce electrostatic repulsion between molecules.
- Isoelectric focusing separates proteins by pI in a stationary pH gradient, independent of size.
- Key idea: pI is not a property of a single ionization but the midpoint between the two pKa's that border the zero-net-charge species on a titration curve.
The isoelectric point is the pH where the average charge state of every ionizable group sums to zero; it is found by locking onto the neutral species on a titration curve and averaging the pKa immediately below it and the pKa immediately above it — never by averaging all pKa's indiscriminately.
Where this lives today
Isoelectric focusing (IEF) remains a cornerstone analytical technique: proteins are loaded into a gel containing a stable, continuous pH gradient (established by ampholyte carrier molecules) and subjected to an electric field. Each protein migrates until it reaches the exact pH position equal to its own pI, at which point it stops moving — net charge is zero there, so the electric force vanishes. This gives extraordinarily sharp bands, resolving proteins differing in pI by as little as 0.01 pH units, and forms the first dimension of two-dimensional gel electrophoresis (2D-PAGE), the workhorse technique for proteomic separation prior to mass spectrometry identification. In protein purification, pI dictates the choice of ion-exchange resin and buffer pH: a target protein is loaded onto a cation exchanger at a pH below its pI (where it is net positive, binding the negatively charged resin) or an anion exchanger above its pI (net negative, binding a positively charged resin), while contaminant proteins with different pI values flow through or elute at different salt concentrations. Crystallization screens for structural biology routinely include buffer conditions near a target protein's calculated pI, since minimum solubility at pI promotes the ordered aggregation needed for crystal nucleation — though this must be balanced against the risk of disordered precipitation rather than useful crystal growth. Industrially, isoelectric precipitation is used to purify casein from milk (casein's pI ≈ 4.6 is why milk curdles when acidified, as in cheese-making — souring the milk with bacterial lactic acid production or added acid drives pH down to casein's pI, causing coagulation) and to recover soy and other plant proteins during food processing. In pharmaceutical formulation, monoclonal antibody therapeutics are characterized by their pI (typically 6–9, controlling charge-based aggregation propensity and determining optimal formulation buffer pH for shelf stability). In renal physiology, the pI of serum albumin (≈ 4.7) relative to physiological pH (7.4) explains why albumin is strongly net-negative in blood and normally repelled by the negatively charged glomerular basement membrane, a key part of why healthy kidneys prevent albuminuria; loss of this charge-selective barrier is a hallmark of certain kidney diseases.
Ask the tutor: How would the pI calculation change for a peptide (rather than a free amino acid) once the α-amino and α-carboxyl groups of internal residues are consumed by peptide bond formation?
The physical picture — thorough prose
Every amino acid free in solution exists as an equilibrium mixture of protonation states, not as one fixed structure. The α-carboxyl group (pKa typically 1.8–2.4) and the α-amino group (pKa typically 8.8–10.8) are always present; side chains contribute additional ionizable groups only in seven of the twenty proteinogenic amino acids. At any instant, a huge ensemble of molecules exists in various states, and what electrophoresis or a pH meter reports is the population-averaged net charge — the mean charge weighted by the fractional occupancy of each protonation state, given by the Henderson–Hasselbalch equation applied group by group. Consider glycine, the simplest case. Fully protonated at very low pH, it is , net charge +1. As pH rises past the carboxyl pKa (≈ 2.34), the carboxyl deprotonates, giving the zwitterion , net charge 0. This zwitterion persists over a wide pH plateau until the amino group's pKa (≈ 9.60) is approached, where deprotonation gives , net charge −1. The isoelectric point is the pH that sits exactly in the "trough" of this titration curve — the pH at which the population is essentially all zwitterion, and the small amounts of +1 and −1 species that do exist are present in exactly equal concentration, so they cancel and the ensemble-averaged charge is precisely zero. This equal-cancellation condition, not merely "the zwitterion dominates," is the operational definition of pI, and it is what forces the averaging rule. At pH = pI, the concentration of the +1 species (protonated carboxyl, protonated amine) equals the concentration of the −1 species (deprotonated carboxyl already accounted for, deprotonated amine) by symmetry of two consecutive equilibria sharing a common intermediate — the zwitterion. Because the same neutral species is the product of the first deprotonation and the reactant for the second, the mathematics of two coupled acid-base equilibria forces the point of exact charge cancellation to be the arithmetic mean of the two flanking pKa's, a result derived rigorously below. For amino acids carrying an ionizable side chain, the same population-averaging logic applies, but there are now three (or more) ionizable groups and hence three (or more) plateaus separated by pKa "steps" on the titration curve. The zero-net-charge species is still a single, specific protonation state — but it may not sit at the midpoint of the entire titration range. Instead, pI is the average of whichever two pKa's flank that particular zero-charge species, and the other pKa (or pKa's) play no role in the pI calculation at all. This is the single most common site of error in applying the concept, and it is addressed explicitly in the worked examples.
The core ideas — the governing equations
For any ionizable group, the Henderson–Hasselbalch relation gives the ratio of deprotonated to protonated form:
where: — pH is the solution pH, — p is the acid dissociation constant of the specific ionizable group, — [A⁻] and [HA] are the equilibrium concentrations of deprotonated and protonated forms of that group.
Reading: at pH = pKa exactly, the group is 50% deprotonated; one pH unit above pKa, the ratio is 10:1 favoring deprotonated; one unit below, 10:1 favoring protonated. Each ionizable group in a molecule obeys its own independent version of this equation (to good approximation, ignoring electrostatic coupling between nearby groups). The general pI formula, valid once the correct flanking pKa's have been identified, is:
where: — p(acid below) is the dissociation constant of the group that, upon losing a proton, creates the neutral (zero-net-charge) species, — p(acid above) is the dissociation constant of the group that, upon losing a proton, destroys the neutral species (converts it to the next more negative species).
Reading: the neutral species sits on a titration curve between two dissociation steps; pI is simply the horizontal midpoint between those two steps, in pH units — not an average over every ionizable group present in the molecule. For a simple amino acid (glycine, alanine, valine, etc.):
For an acidic side chain amino acid (Asp, Glu), the neutral zero-charge species is the one with both carboxyls ionized and the amino group still protonated cancelling to net zero is impossible with three groups unless read carefully — the correct zero-charge species has the α-carboxyl ionized (−1), the side-chain carboxyl still protonated (0), and the amino group protonated (+1), summing to 0:
For a basic side chain amino acid (Lys, Arg, His), the neutral species has the α-carboxyl ionized (−1), α-amino protonated (+1), and side-chain group still protonated but not yet net-charged past neutrality; the flanking pKa's are the α-amino group and the side-chain basic group:
Goal. Show rigorously, from the Henderson–Hasselbalch equation applied to each group independently, that the pH at which net charge is exactly zero for glycine-type amino acids equals (pKa1 + pKa2)/2 — and that this is exact, not approximate, when the two equilibria are independent.
Step 1 — Define the three species and their fractional populations. Let H₂A⁺ denote the fully protonated form (both α-COOH and α-NH₃⁺ protonated, charge +1), HA the zwitterion (COO⁻, NH₃⁺, charge 0), and A⁻ the fully deprotonated form (COO⁻, NH₂, charge −1). Two independent equilibria connect them:
Step 2 — Write Henderson–Hasselbalch for each step.
Step 3 — Impose the isoelectric condition. Net charge is the population-weighted sum , where are the mole fractions of H₂A⁺, HA, A⁻. Net charge is zero exactly when , i.e. .
Step 4 — Solve the two Henderson–Hasselbalch equations for the two ratios. Rearranging Step 2:
Step 5 — Multiply the two ratios to eliminate [HA].
Step 6 — Apply the isoelectric condition [A⁻] = [H₂A⁺], which forces the left side to equal 1.
Conclusion. The averaging rule is an exact algebraic consequence of two independent, consecutive acid-base equilibria sharing a common neutral intermediate — no approximation was made beyond treating the two ionizations as independent (a good approximation when pKa1 and pKa2 differ by several units, as they do for glycine: 2.34 vs 9.60, a separation of 7.26 units, making cross-coupling negligible).
Go deeper · Derivation B · 2 minGeneralizing to a triprotic amino acid: why only two of the three pKa's enter pI
Goal. For glutamate (three ionizable groups: α-COOH, side-chain γ-COOH, α-NH₃⁺), show that the isoelectric pH depends only on pKa1 (α-COOH, 2.19) and pKaR (γ-COOH, 4.25), and derive why pKa2 (α-NH₃⁺, 9.67) drops out.
Step 1 — Enumerate all four protonation states and their charges. Label the states by (α-COOH, γ-COOH, α-NH₃⁺) protonation status:
- State I: all protonated → COOH, COOH, NH₃⁺ → net charge +1
- State II: α-COOH ionized, γ-COOH protonated, NH₃⁺ protonated → COO⁻, COOH, NH₃⁺ → net charge 0
- State III: both COOH ionized, NH₃⁺ protonated → COO⁻, COO⁻, NH₃⁺ → net charge −1
- State IV: both COOH ionized, NH₂ deprotonated → COO⁻, COO⁻, NH₂ → net charge −2
These four states are connected by three sequential equilibria, governed by pKa1 = 2.19 (I→II, the more acidic α-COOH ionizes first), pKaR = 4.25 (II→III, side-chain carboxyl ionizes second because carboxylic acid pKa's near a charged ammonium are somewhat elevated relative to isolated acetic acid), and pKa2 = 9.67 (III→IV, the amino group).
Step 2 — Identify the neutral (net-charge-zero) species. Only State II has net charge exactly zero. It is bounded below by the pKa1 equilibrium (I⇌II) and above by the pKaR equilibrium (II⇌III).
Step 3 — Set up the isoelectric condition in terms of adjacent charge states. The isoelectric pH is where the total positive charge contribution equals the total negative charge contribution across the whole ensemble. Because State II carries zero charge, it contributes nothing to either side of the balance regardless of how much of it is present. The condition becomes: population of State I (charge +1) equals population of State III (charge −1), with State IV's contribution assumed negligible near this pH (justified below).
Step 4 — Apply Henderson–Hasselbalch to the I⇌II and II⇌III steps exactly as in the diprotic derivation.
Multiplying:
Setting [III] = [I] (charge balance, State II charge-neutral so uninvolved):
Step 5 — Justify neglecting State IV. At pH ≈ 3.22, State IV requires the α-amino group (pKa2 = 9.67) to have lost a proton — this requires pH near 9.67, some 6.45 units above 3.22. The fraction of molecules in State IV at pH 3.22 is smaller than of the total population (from ), utterly negligible compared to State I and State III populations, which are comparable in magnitude near pI. This confirms pKa2 correctly drops out of the pI calculation — not because the amino group doesn't matter chemically, but because it is essentially fully protonated (contributing a constant +1 wherever it appears) throughout the entire pH range relevant to the acid-base equilibrium that sets pI.
Conclusion. The rule "average the two pKa's flanking the neutral species" is not a memorized shortcut — it is the exact solution of the charge-balance equation once distant equilibria are shown to be negligibly populated in the relevant pH window, which is routinely true when pKa's are separated by more than about 3–4 units.
Worked examples
Example 1 — Foundational: glycine. Glycine's two relevant pKa values are pKa1(α-COOH) = 2.34 and pKa2(α-NH₃⁺) = 9.60. There is no side chain, so the simple formula applies directly:
Check at pH = 5.97: the ratio [zwitterion]/[cation] = , so essentially all molecules that are not zwitterion and are charged sit in the cationic +1 state or the anionic −1 state in equal, tiny amounts; explicitly, , confirming exact charge cancellation. Limiting case check: if pKa1 and pKa2 were equal (a hypothetical, non-physical case), pI would equal that common value exactly — consistent with the formula degenerating correctly, though no real amino acid has such closely spaced pKa's.
Example 2 — Applied: glutamate at physiological pH, relevant to protein purification. Using pKa1 = 2.19 (α-COOH), pKaR = 4.25 (γ-COOH), pKa2 = 9.67 (α-NH₃⁺), the neutral species is bounded by pKa1 and pKaR (both carboxyls flank the zero-charge state as derived above), so:
At physiological pH 7.4, since 7.4 ≫ pI = 3.22, glutamate carries a net charge of essentially −2 (both carboxyls ionized, amino group still protonated, since 7.4 is well below pKa2 = 9.67). This is exactly why glutamate residues in proteins are negatively charged at physiological pH and why, in ion-exchange chromatography at pH 7.4, an anion exchanger (positively charged resin) retains glutamate-rich proteins strongly while a cation exchanger would not bind them. Limiting case check: far above pI, net charge saturates toward −2 as pH → high values below pKa2; only as pH approaches pKa2 = 9.67 does the charge become more negative than −2 (approaching −3 as the amino group also deprotonates), confirming the −2 plateau is bounded, not indefinite.
Example 3 — Exam/competition level: histidine, where the flanking groups are non-adjacent in the conventional listing. Histidine has three ionizable groups: α-COOH (pKa1 = 1.82), imidazole side chain (pKaR ≈ 6.00), and α-NH₃⁺ (pKa2 = 9.17). Unlike glutamate, histidine's side chain is basic (imidazole, protonated/positive form is the acid), so the states are:
- State I: COOH, ImH⁺, NH₃⁺ → net charge +2
- State II: COO⁻, ImH⁺, NH₃⁺ → net charge +1
- State III: COO⁻, Im (neutral), NH₃⁺ → net charge 0
- State IV: COO⁻, Im, NH₂ → net charge −1
The neutral species is State III, flanked below by the imidazole ionization (pKaR = 6.00, State II→III) and above by the α-amino ionization (pKa2 = 9.17, State III→IV). Note that pKa1 (the α-carboxyl) is not one of the flanking values here — it governs the much lower-pH I→II transition and is essentially fully ionized (contributing a constant −1) throughout the pH range relevant to pI. Applying the same charge-balance logic as in the second derivation (populations of State II and State IV must be equal, since State III is charge-neutral):
This matches the well-known value that histidine's pI (≈ 7.6) sits close to physiological pH, which is precisely why histidine side chains in proteins are potent physiological buffers and often serve as general acid/base catalysts in enzyme active sites — at pH 7.4 the imidazole is roughly half-protonated. Limiting-case check: verify by symmetry that if instead one mistakenly averaged pKa1 and pKaR (1.82 and 6.00, giving 3.91), the predicted pI would fall far below the experimentally observed isoelectric focusing band for histidine (~7.6), confirming that identifying the correct flanking pair — not merely "the two lowest" or "the two highest" pKa's — is essential.
Limiting cases, scope & common traps
| Situation | Correct treatment | Common error |
|---|---|---|
| Simple amino acid, no side chain (Gly, Ala, Leu, Val, Ile, Ser, Thr, Cys, Met, Phe, Trp, Pro, Asn, Gln, Tyr) | pI = (pKa1 + pKa2)/2 using only α-COOH and α-NH₃⁺ | Forgetting Cys and Tyr have weakly ionizable side chains (pKa ≈ 8.3 and 10.5) that in principle shift pI slightly upward from the naive two-group average |
| Acidic side chain (Asp, Glu) | Average the two lowest pKa's (both carboxyls) | Averaging pKa1 with pKa2 (amino group) instead of pKaR |
| Basic side chain (Lys, Arg, His) | Average the two highest pKa's (α-amino and side-chain base) | Averaging pKa1 (carboxyl) with pKa2, ignoring the side chain entirely |
| Protein (many ionizable groups) | pI computed from the full charge-vs-pH curve summing Henderson–Hasselbalch contributions of every group, set to zero | Assuming pI is simply the average of "acidic" and "basic" residue pKa's without weighting by actual counts and burial/environment effects |
| At pH = pI | Net charge is exactly zero; solubility often minimal; no net migration in electrophoresis | Assuming zero individual ionization — in fact groups are still substantially ionized, just symmetrically so |
| pH ≪ pI | Net charge strongly positive; migrates to cathode | Confusing direction of migration with sign convention inconsistently |
| pH ≫ pI | Net charge strongly negative; migrates to anode | Same confusion, reversed |
The chemist behind it
The isoelectric point concept traces to the broader development of acid-base equilibrium theory and colloid chemistry in the late nineteenth and early twentieth centuries, but its rigorous application to amino acids and proteins is most closely associated with Lawrence Joseph Henderson and the physical chemists who extended the Brønsted-Lowry framework to biological macromolecules, alongside Karl Landsteiner's and Leonor Michaelis's pioneering studies of protein electrophoretic behavior in the 1900s–1920s, which first demonstrated experimentally that a protein's mobility in an electric field reverses sign as pH crosses a specific characteristic value — the isoelectric point. Michaelis, working in Berlin, systematically measured how proteins and amino acids behaved in electrophoretic and solubility experiments across pH, establishing the practical definition of pI used in biochemistry laboratories to this day. The theoretical scaffolding — Henderson–Hasselbalch equilibrium bookkeeping applied to polyprotic acids — was formalized by Lawrence Henderson (thermodynamics and blood buffering) and Karl Albert Hasselbalch (who cast Henderson's mass-action relations into the now-familiar logarithmic form).
Origins · 1 minLeonor Michaelis and how this was discovered
Michaelis trained as a physician in Berlin and became one of the founders of quantitative enzyme kinetics — his name is permanently attached to the Michaelis-Menten equation for enzyme catalysis. Less widely celebrated is his parallel, foundational work on protein and amino acid electrochemistry: he developed rigorous methods for measuring how proteins migrate in electric fields as a function of pH, establishing the experimental basis for isoelectric point determination and demonstrating that solubility minima and electrophoretic mobility reversal both occur at the same characteristic pH for a given protein. Forced to emigrate from Nazi Germany in 1922 (initially to Japan, then to the United States in 1926), Michaelis continued this work at the Rockefeller Institute, linking oxidation-reduction potentials, pH buffering, and protein charge behavior into a unified physical-chemical picture of biological macromolecules that underlies modern protein purification technology.
Is pI a measured constant like a melting point, or is it always calculated?
For small molecules like free amino acids, pI is calculated from independently measured pKa values using the averaging rule, though it can also be measured directly via electrophoresis (finding the pH at which mobility is zero) or isoelectric focusing (finding the stationary band position). For proteins, pI is most reliably measured experimentally by IEF, because side-chain pKa's inside a folded protein are perturbed by the local electrostatic and hydrogen-bonding environment, sometimes shifting by more than a full pH unit from their free-amino-acid values. Calculated pI (from primary sequence, summing Henderson–Hasselbalch contributions of each ionizable residue) gives a useful estimate but is often only approximately correct for folded proteins, especially those with buried ionizable groups or unusual local environments such as active-site residues with perturbed pKa's.
Why do Asp and Glu use the two lowest pKa's while Lys, Arg, and His use the two highest?
The rule always picks the two pKa's that flank the neutral (net-charge-zero) species specifically. For acidic side chains, the neutral species already has the α-carboxyl ionized (−1) balanced against the protonated amino group (+1), with the side chain still protonated (0) — this neutral state sits between the low-pH carboxyl ionizations, so pKa1 and pKaR flank it, and the α-amino pKa (which governs an even higher-pH transition to −2) is irrelevant. For basic side chains, the neutral species requires the side-chain base to be fully protonated (+1) balanced against an ionized α-carboxyl (−1), with the α-amino group also eventually needing to lose its charge — so the neutral species sits between the α-amino and side-chain ionizations, both at relatively high pH, making the α-carboxyl pKa irrelevant. The position of the neutral species on the ladder of ionization states, not any fixed rule about "highest" or "lowest," is what actually matters — it just happens to correlate with high or low pKa's depending on whether the side chain is acidic or basic.
How does pI relate to buffering capacity — is a solution best buffered at its pI?
Not necessarily. Buffering capacity is maximal at each individual pKa, where a group is 50% ionized and small pH changes are strongly resisted by proton absorption/release. The pI, by contrast, is the midpoint between two pKa's (for a simple amino acid) — precisely the point where buffering capacity from either individual group is relatively weak, since neither group is at its own 50% point. Glycine buffers best near pH 2.34 or pH 9.60, not at its pI of 5.97, where it actually has quite poor buffering capacity. This is a subtlety students often miss: pI marks charge neutrality, not buffering optimum.
Can two different amino acids or proteins share the same pI, and does that cause problems in purification?
Yes, and this is a real practical limitation. Any two molecules with the same net charge behavior across pH will co-migrate in isoelectric focusing and will not be separable by charge-based methods (ion exchange, IEF) at a single pH, regardless of differences in size or other properties. In practice, this is why purification protocols combine multiple orthogonal methods — size-exclusion chromatography, hydrophobic interaction chromatography, affinity chromatography — with ion-exchange or IEF steps, since pI-based separation alone cannot resolve co-isoelectric species. Two-dimensional gel electrophoresis specifically pairs IEF (first dimension, by pI) with SDS-PAGE (second dimension, by size) precisely to resolve species that happen to share a pI but differ in molecular weight.
Does temperature or ionic strength change the isoelectric point?
Yes, though the effect is usually modest for small-molecule amino acids and can be more significant for proteins. pKa values themselves are temperature-dependent (via the van't Hoff relationship connecting pKa to the enthalpy of ionization), so pI, being an average of two pKa's, shifts somewhat with temperature — carboxyl pKa's are relatively temperature-insensitive while amino group pKa's can shift by several tenths of a pH unit over a 20–30 °C range because ammonium ionization has a larger enthalpy of ionization. Ionic strength affects activity coefficients of charged species, subtly shifting apparent pKa's (and hence apparent pI) measured in different salt concentrations — this is why published pI values are always specified alongside standard conditions (typically 25 °C, low ionic strength), and why measured pI in a specific experimental buffer may differ slightly from tabulated reference values.
Why does histidine's pI (~7.6) matter so much biologically compared to, say, valine's pI (~6.0)?
Histidine's imidazole side chain has a pKa (≈ 6.0) unusually close to physiological pH (7.4), meaning it is substantially protonated and substantially deprotonated simultaneously in living systems — this is precisely the condition for maximal buffering capacity at physiological pH, and it is why histidine residues are the single most important amino acid for physiological pH buffering in proteins and why they so often serve as general acid/general base catalytic residues in enzyme active sites (as in the catalytic triad of serine proteases). Valine has no ionizable side chain at all, so its pI reflects only the generic α-carboxyl/α-amino averaging and carries no special physiological buffering significance — the comparison highlights that pI is chemically meaningful (predicting net charge and electrophoretic behavior) but the side-chain pKa itself, not pI per se, is what confers special catalytic or buffering roles.
How would you calculate the pI of a full protein rather than a single amino acid?
In principle, sum the Henderson–Hasselbalch fractional charge contribution of every ionizable group in the protein (N-terminal α-amino, C-terminal α-carboxyl, and every Asp, Glu, His, Cys, Tyr, Lys, and Arg side chain) as a function of pH, using tabulated or experimentally determined pKa's, and numerically solve for the pH where the sum equals zero. This is exactly what pI-prediction software (such as the Expasy Compute pI/Mw tool) does, using standard reference pKa tables. The result is only an estimate because folded proteins perturb individual pKa's from their free-amino-acid reference values — buried ionizable groups, hydrogen bonding, and nearby charges can shift a given side-chain pKa by a full pH unit or more, so computed pI values should always be treated as first approximations to be confirmed experimentally by isoelectric focusing when precision matters.