Peptide Net Charge and pI: A Henderson-Hasselbalch Calculation

The net charge of a peptide at a given pH is the sum of the fractional charges of its ionisable groups, each computed from the Henderson–Hasselbalch relation with a pKa value taken from a stated set: a basic group contributes +1 ÷ (1 + 10^(pH − pKa)) and an acidic group contributes −1 ÷ (1 + 10^(pKa − pH)), each multiplied by the number of such groups in the sequence. The isoelectric point (pI) is the pH at which that sum is zero, found by bisection between a pH where the sum is positive and one where it is negative. The result depends on the pKa set, and the set must be recorded with the figure: published sets differ by up to a pH unit for the same group, and the pI predicted for one sequence can differ by several tenths between calculators for that reason alone 3.

Companion references cover choosing a buffer and converting mass to amount. This page covers the arithmetic that comes before buffer choice. The worked example uses an invented dodecapeptide, ADKHEYRGCKTE, written from N-terminus to C-terminus with free termini and no modifications. It describes no real material.

Which groups ionise: termini and seven side chains

Every unmodified peptide carries an N-terminal α-amino group (a base, positive when protonated) and a C-terminal α-carboxyl group (an acid, negative when deprotonated). Seven side chains ionise within the working pH range: aspartate and glutamate carboxyls, cysteine thiol and tyrosine phenol (acids, negative when deprotonated); histidine imidazole, lysine ε-amino and arginine guanidinium (bases, positive when protonated). Serine, threonine, tryptophan, asparagine, glutamine and the aliphatic residues carry no charge between pH 0 and 14 for this purpose.

Modifications change the count before any arithmetic starts. N-terminal acetylation removes the terminal base. C-terminal amidation removes the terminal acid. A cysteine in a disulfide bridge has no free thiol and is dropped. Phosphoserine, phosphothreonine and phosphotyrosine add an acidic phosphate with two ionisations. A calculation that ignores the modification flags on the supplier's sequence record is wrong before it begins.

Choosing a pKa set and stating it

Two sets are tabulated below. The first is the set of Bjellqvist and colleagues, fitted to the focusing positions of denatured polypeptides in immobilised pH gradients and implemented in several widely used calculators; because it was derived from unfolded chains, it is the more appropriate default for a short synthetic peptide 1. The second is the set of mean values compiled by Grimsley, Scholtz and Pace from measured pK values in folded proteins; the means differ from model-compound values, cysteine most of all, and each carries a standard deviation of roughly a pH unit, which is the spread a residue's environment can impose 2.

Kozlowski compared many published scales against experimentally determined isoelectric points and found that no single scale was best for every dataset, and that the scale chosen shifts the predicted pI of a given sequence by several tenths of a unit 3. The rule for the method file follows: name the set, list the values actually used (implementations alter them), and never mix values from two sets in one calculation.

Fractional charge of an acid and of a base at a given pH

Henderson–Hasselbalch gives pH = pKa + log([A⁻] ÷ [HA]). Rearranged, the fraction of an acidic group that is deprotonated is 1 ÷ (1 + 10^(pKa − pH)), and that fraction carries a charge of −1. For a basic group the charged form is the protonated one, and the protonated fraction is 1 ÷ (1 + 10^(pH − pKa)), carrying +1. Multiply each fraction by the number of groups of that kind, sum the acids and the bases, and the total is the mean net charge per molecule at that pH.

• At pH = pKa the fraction is exactly 0.5.
• One pH unit from the pKa it is 0.909 on one side and 0.091 on the other.
• Two units away it is 0.990 or 0.010; three units away, 0.999 or 0.001.
• A group more than three units from the working pH therefore contributes an integer charge, and only groups within about two units need the calculation.

Worked summation for a generic peptide at four pH values

Sequence ADKHEYRGCKTE. Counting ionisable groups: one N-terminus, one C-terminus, one aspartate, two glutamates, one histidine, one cysteine, one tyrosine, two lysines, one arginine. Alanine, glycine and threonine contribute nothing. Bjellqvist set throughout.

Two cells worked in full. Glutamate at pH 5: −2 ÷ (1 + 10^(4.45 − 5)) = −2 ÷ (1 + 10^(−0.55)) = −2 ÷ (1 + 0.282) = −1.560. Histidine at pH 7: +1 ÷ (1 + 10^(7 − 5.98)) = 1 ÷ (1 + 10.47) = +0.087. Every other cell is the same operation with its own pKa and count.

Reading the bottom row: the peptide is strongly cationic at pH 3, still carries about +1.5 at pH 5, is close to neutral at pH 7 and is anionic at pH 9. The sign change between pH 5 and pH 7 locates the isoelectric point in that interval.

Finding the pI by bisection

Bisection halves an interval that is known to contain the zero. Evaluate the net charge at the midpoint; if it is positive the pI lies above the midpoint, if negative below; keep the half that still contains the sign change and repeat. Starting from the full range 0 to 14 costs a few extra steps but needs no prior guess.

The same sequence with the Grimsley means gives a pI of 6.64, and a net charge at pH 7 of −0.49 rather than −0.16. Almost all of the difference comes from two groups: cysteine, whose pKa drops from 9.0 to 6.8 and so contributes about −0.6 at neutral pH instead of −0.01, and histidine, which rises from 5.98 to 6.6 and contributes +0.29 instead of +0.09 2. The disagreement is not an error in either calculation. It is a difference in the assumed environment of two side chains.

Why calculators disagree: pKa sets, modifications, neighbours

Four causes account for nearly every discrepancy between tools. First, the pKa set, as above; Kozlowski's comparison showed that the scales in common use place the pI of the same sequence across a range of a few tenths, with cysteine and histidine the usual drivers near neutral pH 3. Second, modifications: a tool that does not read an acetyl, amide, disulfide or phosphate flag counts the wrong groups. Third, neighbour effects: adjacent charges and the terminal residue's identity shift pKa values in real molecules, which is why Bjellqvist's method assigns the N-terminal pKa by residue rather than using one value 1; the simple summation ignores every such interaction. Fourth, convention: whether the result is reported as a mean charge or rounded to the nearest integer, and how a value of exactly zero is handled.

What net charge means for solubility, adsorption and CZE

Solubility is usually lowest near the pI, where molecules carry no net charge and nothing electrostatic keeps them apart; the companion references on buffer selection and on aggregation treat the consequences. For the worked sequence, pI about 6.7 means that neutral buffers are the worst choice for dissolution and holding. At pH 4 to 5 the net charge is between +1.5 and +3, which is the direction a mildly acidic default points. This is a calculated expectation, not a measurement; the sequence's actual solubility must be tested.

Adsorption follows the same arithmetic. A net positive peptide is attracted to the negatively charged silanol surface of untreated glass; a net negative one is less so, and may bind more to positively charged or hydrophobic polymer surfaces. Capillary zone electrophoresis separates by charge-to-size ratio, so the calculated charge at the run buffer pH predicts migration order, and a shift of two pH units changes this sequence's charge from −0.16 to −1.74, which is a large change in mobility. Reversed-phase retention is affected indirectly, through the ion-pairing agent.

Recording the calculation in the method file

1. The sequence exactly as supplied, with termini and every modification flag.
2. The count of each ionisable group after modifications are applied.
3. The pKa set by name and source, with the numerical values actually used, including any residue-specific terminal values.
4. The pH values evaluated and the net charge at each, to two decimal places.
5. The pI, the method used to find it, and the final interval reached.
6. Any calculator used, with its version and pKa set, and whether it agreed with the hand calculation within 0.2 units.
7. The working pH chosen and its distance from the pI, with the reason.

The calculation is cheap and its inputs are few. Its value lies in being written down with the set that produced it, so that the next analyst can reproduce the number rather than argue with it.