How the Isoelectric Point of a Peptide Is Calculated

What the isoelectric point is

A peptide carries several groups that can gain or lose a proton: the free amine at the N-terminus, the free carboxylic acid at the C-terminus, and the side chains of up to seven amino acids. Each group has its own pKa, the pH at which it is half protonated. As the pH of the solution changes, these groups switch between charged and uncharged forms, and the net charge of the peptide changes with them.

At very low pH every group is protonated: amines and guanidines carry a positive charge, carboxylic acids are neutral, and the peptide is strongly positive. At very high pH every group is deprotonated and the peptide is negative. Somewhere between the two the positive and negative charges balance exactly. That pH is the isoelectric point.

At its pI a peptide still carries charged groups. What disappears is the net charge, and with it the electrostatic repulsion between molecules. This is why pI matters in practice: it predicts where a peptide stops moving in an electric field, and where it is most likely to aggregate or precipitate.

The ionisable groups

Only nine kinds of group contribute to the charge of an unmodified peptide. They fall into two families. Basic groups are positive when protonated and neutral when not. Acidic groups are neutral when protonated and negative when not.

The side-chain values are the classic textbook figures measured on free amino acids. The terminal values (8.0 and 3.1) are lower and higher, respectively, than the α-amino and α-carboxyl pKa values of free amino acids (about 9.5 and 2.2). That is deliberate: in a peptide the termini are no longer next to each other, so they no longer influence each other's ionisation as strongly.

Cys and Tyr are often forgotten because they are neutral at physiological pH. They still matter above pH 8, and a Cys residue that is part of a disulfide bond has no thiol left to ionise at all.

How the calculation works

The fraction of each group that carries a charge at a given pH follows the Henderson–Hasselbalch equation. For a basic group the positive charge is:

and for an acidic group the negative charge is:

At pH = pKa either expression gives exactly half a charge. One pH unit away the group is 91% in one form; two units away it is 99%. The net charge of the peptide is simply the sum over every ionisable group, counting each residue separately. A peptide with three lysines has three lysine terms.

The net charge always decreases as pH rises, so there is exactly one pH where it equals zero. Calculators find it numerically, usually by bisection: start with the interval 0–14, evaluate the charge at the midpoint, keep the half in which the sign changes, and repeat. Thirty iterations locate the pI to better than 0.0001 pH units. The pI calculator on this site works exactly this way.

Worked example: angiotensin II (DRVYIHPF)

Angiotensin II is the eight-residue vasoconstrictor peptide of the renin–angiotensin system. Its ionisable groups are the two termini, Asp1, Arg2, Tyr4 and His6. At pH 7.4 each contributes:

The net charge is slightly negative, so the pI must lie below 7.4. Repeating the sum at other pH values brackets the zero crossing, which falls at pH 7.00.

A shortcut you can do by hand

For simple peptides the pI can be estimated without a computer. List the pKa values in ascending order and track the net charge of the fully protonated molecule as each group loses its proton in turn:

The pI lies halfway between the two pKa values that flank the neutral form. The shortcut is exact only when those two pKa values are far from all the others. When several groups have similar pKa values, as happens with multiple Asp and Glu residues, their charges overlap and the numerical method is needed.

Reading the charge–pH curve

Plotting net charge against pH gives a descending curve with a step near each pKa. The pI is where the curve crosses zero. The shape of the curve near that point is at least as informative as the pI itself.

Where the curve crosses zero steeply, as it does for glutathione between its carboxyl groups, the pI is well defined and small errors in pKa move it only slightly. Where the curve is flat near zero, as for angiotensin II between His and the N-terminus, the peptide stays close to neutral over a wide pH range. There, small changes in any pKa shift the calculated pI a long way, which is exactly what the next section shows.

Glutathione is an instructive case for another reason. Its glutamate is linked through the side-chain γ-carboxyl rather than the α-carboxyl, so the sequence ECG does not describe an ordinary peptide. The set of ionisable groups is still the same (two carboxyls, one amine, one thiol), so the calculated charge curve remains valid.

Why different calculators give different pI values

There is no single correct pKa table. Values measured on free amino acids, on short model peptides and on folded proteins all differ, and each popular tool has adopted its own set. Some of the best known are:

The ExPASy implementation of the Bjellqvist method also adjusts terminal pKa values according to the terminal residue; the table shows its default values. Running the same peptides through each set gives:

Two patterns stand out. Short peptides are more sensitive than long ones, because the termini make up a large share of their ionisable groups and the terminal pKa values differ most between sets. And angiotensin II, with its flat curve near neutrality, shows the largest spread of all: a full pH unit. Longer peptides with several acidic and basic residues, such as the 30-residue insulin B chain, vary less.

None of these sets is "right" for every peptide. The practical conclusion is to treat a calculated pI as accurate to about ±0.5 units, and to quote the tool or pKa set whenever a pI appears in a report or publication.

Modifications change the pI more than anything else

A calculation from sequence assumes a free N-terminal amine, a free C-terminal acid and free Cys thiols. Change any of these and the set of ionisable groups changes with it:

• C-terminal amidation removes the C-terminal carboxyl, a negative charge above pH 3.
• N-terminal acetylation removes the N-terminal amine, a positive charge below pH 8.
• Disulfide bonds remove two Cys thiols.
• Phosphorylation adds an acidic group with two ionisations: one near pH 1–2 and a second around pH 5.5–6.5.
• Pyroglutamate formation at an N-terminal Gln or Glu removes the N-terminal amine.

Worked example: oxytocin

Entered as the linear sequence CYIQNCPLG, oxytocin has a calculated pI of 5.37. Its acidic groups are the C-terminus and two Cys thiols; its only basic group is the N-terminus.

The native hormone, however, is C-terminally amidated and has a disulfide bond between Cys1 and Cys6. Both modifications remove acidic groups. What remains is the N-terminal amine (pKa 8.0) and the Tyr phenol (pKa 10.07), and the pI moves to about 9.0, halfway between them. The peptide changes from slightly acidic to basic, which affects everything from its solubility to its retention in ion-exchange chromatography.

Limits of the calculation

The Henderson–Hasselbalch approach treats every group as independent and fully exposed to water. Real peptides deviate from this in predictable ways:

• Neighbouring charges shift pKa values. A carboxyl next to a positively charged residue gives up its proton more easily; two adjacent carboxyls make each other's second ionisation harder.
• Structure buries some groups and shields others. In folded proteins, measured pKa values scatter widely around the textbook values. A 2009 survey of hundreds of measurements (Grimsley, Scholtz and Pace) found average values of 3.5 for Asp, 4.2 for Glu, 6.6 for His, 6.8 for Cys, 10.3 for Tyr and 10.5 for Lys, each with a spread of about one pH unit.
• The arginine pKa is probably higher than most tables assume. A careful NMR study in 2015 put it near 13.8, which barely affects most peptides but explains why arginine is almost never found deprotonated.
• Ionic strength and temperature also shift pKa values slightly. Tables usually refer to 25 °C and low salt.

For short, unstructured peptides these effects are modest, and calculated pI values are usually within half a unit of measured ones. For peptides that form stable helices or hairpins, or that contain clusters of like charges, experimental measurement by isoelectric focusing or capillary IEF is the only reliable answer.

Using pI in the lab

Dissolving peptides

Solubility is lowest near the pI, so the standard strategy is to dissolve a peptide at a pH well away from it. Basic peptides (pI above 7) usually dissolve in water or dilute acetic acid. Acidic peptides (pI below 7) usually dissolve in water or dilute ammonium bicarbonate or aqueous ammonia. Peptides with pI values close to the pH of the intended buffer, and very hydrophobic peptides, may need a small amount of organic co-solvent first.

Ion-exchange chromatography

Below its pI a peptide is positive and binds a cation exchanger; above its pI it is negative and binds an anion exchanger. A buffer 1–2 units from the pI gives firm binding; elution then uses a salt gradient or a pH shift towards the pI. The net charge at the working pH, which the calculator reports directly, is a better guide than the pI alone.

Isoelectric focusing

In a pH gradient under an electric field each molecule migrates until it reaches the pH equal to its pI, where it stops. IEF is the first dimension of classic 2D gel electrophoresis and the basis of capillary IEF, used to characterise charge variants of peptide and protein drugs.

Common mistakes

1. Ignoring terminal modifications and disulfides. As the oxytocin example shows, these can move the pI by several units.
2. Comparing pI values from different tools without checking which pKa set each used.
3. Quoting pI to two decimals as though it were a measured value. One decimal, with the method named, is more honest.
4. Forgetting Cys and Tyr when working at high pH, for example in ammonium bicarbonate buffers around pH 8.
5. Assuming pI alone determines solubility. Hydrophobicity, length and aggregation propensity matter as much; see the hydropathy guide.

Frequently asked questions

References

• Bjellqvist B, Hughes GJ, Pasquali C, et al. (1993) The focusing positions of polypeptides in immobilized pH gradients can be predicted from their amino acid sequences. Electrophoresis 14:1023–1031.
• Grimsley GR, Scholtz JM, Pace CN (2009) A summary of the measured pK values of the ionizable groups in folded proteins. Protein Science 18:247–251.
• Kozlowski LP (2016) IPC – Isoelectric Point Calculator. Biology Direct 11:55.
• Fitch CA, Platzer G, Okon M, García-Moreno B, McIntosh LP (2015) Arginine: its pKa value revisited. Protein Science 24:752–761.

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