Isoelectric Point: Zwitterions, pKa and How to Calculate pI

The isoelectric point (pI) is the pH at which a molecule carries no net electrical charge. For an amino acid with no ionisable side chain it is the average of its two backbone pKa values, so glycine (pKa 2.34 and 9.60) has a pI of 5.97. At that pH the dominant form is a zwitterion, with one positive and one negative charge. A peptide’s pI is set the same way by all of its ionisable groups, and it controls where the molecule is least soluble, how it binds ion-exchange columns and where it stops in isoelectric focusing.

This article explains zwitterions and pKa, works through the pI calculation for amino acids and for a real peptide, and shows why pI matters in the laboratory. For the amino acids themselves, see what an amino acid is.

Isoelectric point at a glance

Source: pI values calculated from typical textbook pKa values for free amino acids at 25 °C; peptide prediction per references [1, 2].

What is a zwitterion?

A zwitterion is a molecule that carries a positive charge and a negative charge at the same time, with no net charge overall. Amino acids are the classic case. Each one has a basic amino group and an acidic carboxyl group on the same carbon, and in water they react with each other: the carboxyl group loses a proton (-COO-) and the amino group picks one up (-NH3+).

The numbers show how complete this is. Using glycine’s pKa values, at pH 7 only about 0.002% of carboxyl groups are still protonated, and only about 0.25% of amino groups are uncharged. The form with both groups neutral (H2N-CH2-COOH) is a minor species in water at any pH. That is also why solid amino acids behave like salts, with high melting points and poor solubility in nonpolar solvents.

The zwitterion needs water around it. Ab initio simulations of glycine with small numbers of water molecules by Tripathi and colleagues found that the charge-separated form was the preferred species with ten waters but not with four, reached through a chain of water-mediated proton transfers [3].

pKa and the Henderson-Hasselbalch equation

Each ionisable group has a pKa, the pH at which it is half protonated. The Henderson-Hasselbalch equation links pH, pKa and the ratio of the two forms:

pH = pKa + log10([base form] / [acid form])

One pH unit above the pKa, about 91% of the group is in its base (deprotonated) form. Two units above, about 99%. One unit below, about 91% is protonated. This is the rule of thumb behind every pI calculation: a group is mostly charged or mostly uncharged once the pH is a couple of units away from its pKa.

Source: free amino acid values are typical textbook figures at 25 °C; protein averages from Grimsley, Scholtz and Pace, who tabulated 541 measured pK values from 78 folded proteins [4].

The two columns differ for a reason. In a free amino acid, the alpha-carboxyl and alpha-amino groups sit next to each other and each one’s charge shifts the other’s pKa. In a peptide, the terminal groups are separated by the chain, so the C-terminus is a weaker acid (about 3.3) and the N-terminus a weaker base (about 7.7) than in the free amino acid.

How to calculate the isoelectric point of amino acids

The method is to find the pH where the net charge is zero. For a molecule with only two ionisable groups, that pH is exactly halfway between their pKa values. For a molecule with three, list the pKa values in order, find the neutral form, and average the two pKa values on either side of it.

Source: calculated by Vortex from typical textbook pKa values at 25 °C. Published tables differ slightly, so expect pI values to vary by a few hundredths between sources.

Aspartic acid shows the logic. Below pH 1.88 it carries +1 (amine protonated, both carboxyls neutral). Between 1.88 and 3.65 the alpha-carboxyl has ionised and the net charge is 0. Above 3.65 the side chain ionises too and the net charge is -1. The zero-charge form lives between 1.88 and 3.65, so the pI is their average, 2.77.

Worked example: the isoelectric point of a peptide

A peptide has more groups, but the method is the same. Take the tripeptide Gly-His-Lys (GHK) and, for illustration, a simple pKa set for a short peptide: C-terminus 3.1, histidine 6.0, N-terminus 8.0, lysine 10.5.

1. List the ionisable groups. Positive when protonated: the N-terminal amine, the histidine imidazole and the lysine side chain. Negative when deprotonated: the C-terminal carboxyl.
2. Order the pKa values. 3.1, 6.0, 8.0, 10.5.
3. Track the charge. Below 3.1 the peptide is +3. Between 3.1 and 6.0 it is +2. Between 6.0 and 8.0 it is +1. Between 8.0 and 10.5 it is 0. Above 10.5 it is -1.
4. Average the two pKa values around the neutral form. (8.0 + 10.5) / 2 = 9.25.

Solving the Henderson-Hasselbalch expression for every group numerically gives the same answer, pI 9.25, and the net charge curve below.

Source: calculated by Vortex with the illustrative pKa set above.

The same set gives the following for some well-known sequences:

Source: calculated by Vortex (C-terminus 3.1, Asp 3.9, Glu 4.1, His 6.0, N-terminus 8.0, Cys 8.3, Tyr 10.1, Lys 10.5, Arg 12.5). Other pKa sets will give somewhat different values.

Why calculated pI values disagree

A calculated pI is only as good as the pKa values fed into it, and there is no single correct set. A group’s pKa shifts with its neighbours, with temperature and ionic strength, and with how buried it is in a folded structure. The averages in folded proteins tabulated by Grimsley, Scholtz and Pace come with wide spreads, for example aspartic acid 3.5 ± 1.2 and histidine 6.6 ± 1.0 [4].

Benchmarks put numbers on the problem. Bjellqvist and colleagues measured the focusing positions of 29 polypeptides in narrow immobilised pH gradients under denaturing conditions and found that pI values calculated from sequence matched the experimental values with good accuracy [5]. Shaw and colleagues, working with the protein ribonuclease Sa, showed that pI values estimated from model-compound pK values can be wrong by more than one pH unit [6]. Kozlowski’s 2016 IPC study compared many pKa sets and reported, for its optimised sets, average errors of 0.87 pH units for proteins and 0.25 for peptides [1]. A later version combining deep learning and support vector regression reported prediction errors (RMSD) of 0.848 for proteins and 0.222 for peptides [2].

The practical reading: for a short peptide, a calculated pI is usually close, and the error is often a few tenths of a pH unit. For a folded protein, regard it as an estimate.

Why the isoelectric point matters for solubility

At its pI a molecule has no net charge, so molecules stop repelling each other electrostatically. They can pack together and come out of solution more easily. Shaw and colleagues tested this directly. Ribonuclease Sa is an acidic protein with a pI of 3.5. By swapping surface aspartic and glutamic acid residues for lysine, they made variants with pI values of 6.4 and 10.2, then measured solubility, activity and stability across pH. The pH of minimum solubility moved with the pI of each variant. The pH of maximum activity and the pH of maximum stability did not [6].

For short peptides the same principle applies, with two caveats. Many synthetic peptides are supplied as salts with counter-ions on their charged groups, which changes how a solid behaves when it first meets water. And a peptide’s composition matters as much as its net charge: a strongly hydrophobic sequence can be poorly soluble at any pH. Our explainer on lyophilised peptides covers what else is in a freeze-dried solid besides the peptide.

The isoelectric point in chromatography

Ion-exchange chromatography separates molecules by charge, so pI predicts behaviour. Below its pI a peptide is net positive and binds a cation exchanger. Above its pI it is net negative and binds an anion exchanger. Mant and colleagues review ion-exchange alongside size-exclusion and reversed-phase HPLC as the main modes used for peptides [7]. In a later study they separated six 26-residue peptides with net charges from +5 to +10 by cation-exchange chromatography at pH 6.5, eluting with a salt gradient [8].

Reversed-phase HPLC, the usual method for peptide purity, separates mainly by hydrophobicity, but charge still matters. Typical acidic mobile phases sit near pH 2, well below the pI of most peptides, so basic residues and the N-terminus are protonated and paired with the acid’s counter-ion. Our explainer on HPLC peptide purity covers how those separations are read.

Isoelectric focusing and 2D gels

Isoelectric focusing (IEF) uses the pI directly. A sample is placed in a pH gradient under an electric field. Each molecule migrates toward the electrode of opposite charge until it reaches the pH equal to its pI. There its net charge is zero, it stops moving, and it collects in a sharp band.

Early IEF built the gradient from soluble carrier ampholytes. Bjellqvist and colleagues introduced immobilised pH gradients in 1982, with the buffering groups covalently linked to the polyacrylamide gel. They reported narrow linear gradients anywhere between pH 3 and 10, no cathodic drift, higher resolution and loading capacity, and uniform conductivity and buffering [9].

O’Farrell combined IEF with a second separation by size (SDS electrophoresis) in 1975. The two-dimensional gel resolved 1,100 different components from Escherichia coli and could separate proteins differing by a single charge [10]. Capillary IEF moves the same principle into a narrow capillary, which Righetti and colleagues review for peptide and protein analysis [11].

Whole proteomes show a characteristic pattern. Kiraga and colleagues, analysing 1,784 proteomes, describe the pI distribution as bimodal, splitting proteins into an acidic set and a basic set. The balance between the two sets varied with taxonomy, subcellular location and ecology [12].

Frequently asked questions

What is the isoelectric point?

The isoelectric point (pI) is the pH at which a molecule carries no net electrical charge. Below the pI it is net positive and above it net negative. For glycine the pI is about 5.97.

What is a zwitterion?

A zwitterion is a molecule with both a positive and a negative charge and no net charge. In water, amino acids exist mainly as zwitterions, with a protonated amino group (-NH3+) and a deprotonated carboxyl group (-COO-).

How do you calculate the isoelectric point of an amino acid?

List the pKa values in order, find the form with zero net charge, and average the two pKa values on either side of it. For glycine that is (2.34 + 9.60) / 2 = 5.97. For aspartic acid it is the two lowest values, giving 2.77, and for lysine the two highest, giving 9.74.

Why is a protein least soluble at its isoelectric point?

At the pI the molecules carry no net charge, so they do not repel each other electrostatically and can aggregate more easily. In studies of ribonuclease Sa variants, the pH of minimum solubility moved with the pI of each variant.

Research materials: Vortex supplies peptides as sealed lyophilised research reagents. Browse the catalogue at /shop/. Published lab reports are at /coa/.

References

1. Kozlowski LP. IPC – Isoelectric Point Calculator. Biol Direct. 2016;11(1):55. PMID 27769290. doi:10.1186/s13062-016-0159-9
2. Kozlowski LP. IPC 2.0: prediction of isoelectric point and pKa dissociation constants. Nucleic Acids Res. 2021;49(W1):W285-W292. PMID 33905510. doi:10.1093/nar/gkab295
3. Tripathi R, Durán Caballero L, Pérez de Tudela R, Hölzl C, Marx D. Unveiling zwitterionization of glycine in the microhydration limit. ACS Omega. 2021;6(19):12676-12683. PMID 34056419. doi:10.1021/acsomega.1c00869
4. Grimsley GR, Scholtz JM, Pace CN. A summary of the measured pK values of the ionizable groups in folded proteins. Protein Sci. 2009;18(1):247-51. PMID 19177368. doi:10.1002/pro.19
5. Bjellqvist B, Hughes GJ, Pasquali C, Paquet N, Ravier F, Sanchez JC, Frutiger S, Hochstrasser D. The focusing positions of polypeptides in immobilized pH gradients can be predicted from their amino acid sequences. Electrophoresis. 1993;14(10):1023-31. PMID 8125050. doi:10.1002/elps.11501401163
6. Shaw KL, Grimsley GR, Yakovlev GI, Makarov AA, Pace CN. The effect of net charge on the solubility, activity, and stability of ribonuclease Sa. Protein Sci. 2001;10(6):1206-15. PMID 11369859. doi:10.1110/ps.440101
7. Mant CT, Chen Y, Yan Z, Popa TV, Kovacs JM, Mills JB, Tripet BP, Hodges RS. HPLC analysis and purification of peptides. Methods Mol Biol. 2007;386:3-55. PMID 18604941. doi:10.1007/978-1-59745-430-8_1
8. Mant CT, Byars A, Ankarlo S, Jiang Z, Hodges RS. Separation of highly charged (+5 to +10) amphipathic α-helical peptide standards by cation-exchange and reversed-phase high-performance liquid chromatography. J Chromatogr A. 2018;1574:60-70. PMID 30220427. doi:10.1016/j.chroma.2018.09.003
9. Bjellqvist B, Ek K, Righetti PG, Gianazza E, Görg A, Westermeier R, Postel W. Isoelectric focusing in immobilized pH gradients: principle, methodology and some applications. J Biochem Biophys Methods. 1982;6(4):317-39. PMID 7142660. doi:10.1016/0165-022x(82)90013-6
10. O’Farrell PH. High resolution two-dimensional electrophoresis of proteins. J Biol Chem. 1975;250(10):4007-21. PMID 236308
11. Righetti PG, Sebastiano R, Citterio A. Capillary electrophoresis and isoelectric focusing in peptide and protein analysis. Proteomics. 2013;13(2):325-40. PMID 23180512. doi:10.1002/pmic.201200378
12. Kiraga J, Mackiewicz P, Mackiewicz D, Kowalczuk M, Biecek P, Polak N, Smolarczyk K, Dudek MR, Cebrat S. The relationships between the isoelectric point and: length of proteins, taxonomy and ecology of organisms. BMC Genomics. 2007;8:163. PMID 17565672. doi:10.1186/1471-2164-8-163

Methods note: written by the Vortex Research Editorial Team. Literature was selected from PubMed for chemistry and analytical topics, every PMID was checked against its PubMed record for title, journal and year, and each abstract (where PubMed holds one) was read against the sentence that cites it. pI values and charge curves were calculated by Vortex with the Henderson-Hasselbalch equation and the pKa values stated under each table.

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