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Where charge comes from

A peptide has two ionisable termini and one ionisable side chain for every aspartate, glutamate, cysteine, tyrosine, histidine, lysine and arginine in the sequence. Each of those groups is an acid or a base with its own pKa, and each is partly ionised at any given pH.

The net charge is the sum of those fractional contributions. It is not an integer, and treating it as one is the main reason hand estimates disagree with the calculation.

Reading the titration curve

The curve falls monotonically from strongly positive at low pH, where every basic group is protonated and every acid is neutral, to strongly negative at high pH, where the reverse holds. The steepest parts of the curve are where pKa values cluster.

The point where it crosses zero is the isoelectric point. A curve that crosses steeply belongs to a peptide whose charge is sensitive to small pH changes; one that crosses shallowly belongs to a peptide that is relatively forgiving.

What charge predicts

Solubility, first. Charged molecules repel each other, and that repulsion is what keeps them in solution. At the pI the repulsion vanishes and aggregation becomes much more likely, which is why the pI is a pH to avoid rather than a pH to target.

Chromatographic behaviour, second. Cation exchange resins retain positively charged peptides, anion exchange resins retain negatively charged ones, and the pH at which you load determines which. Third, surface interaction: a strongly cationic peptide binds to glass and to negatively charged plastics, which shows up as unexplained loss during handling.

  • •Keep the working pH at least one unit from the pI for solubility.
  • •Load a cation exchange column below the pI, an anion exchange column above it.
  • •Expect adsorptive losses from strongly cationic peptides in standard labware.
  • •Histidine is the one residue whose ionisation changes appreciably across the physiological range, since its pKa sits near 6.

The limits of the model

The calculation treats every ionisable group as independent, which they are not. A lysine next to another lysine finds it harder to hold its proton because of the neighbouring positive charge, so its effective pKa falls. The same effect operates in reverse between opposite charges.

The error is small in long, sparsely charged sequences and largest in short, densely charged ones, which unfortunately describes many research peptides. Treat the output as a good estimate of the shape of the curve and an approximate location for the pI, not as a measurement.

How net charge and pI are calculated

Henderson-Hasselbalch applied once per ionisable group and summed, then a bisection search for the pH at which the sum is zero.

basic group  contributes  + 1 / (1 + 10^(pH - pKa))
acidic group contributes  - 1 / (1 + 10^(pKa - pH))

net charge = SUM over all ionisable groups
pI         = pH where net charge = 0
  1. Enumerate the ionisable groups. The N-terminal amine, the C-terminal acid, and one group per Asp, Glu, Cys, Tyr, His, Lys and Arg. The table lists each with its pKa and its contribution at the current pH.
  2. Compute a fractional charge per group. A group whose pKa equals the pH is half ionised and contributes 0.5. Two units away it is 99 percent ionised or 99 percent neutral.
  3. Sum with sign. Basic groups add, acidic groups subtract. The result is almost never a whole number, which is correct: charge is a population average across many molecules.
  4. Sample the curve. The same sum is evaluated at 141 points from pH 0 to 14 to draw the titration curve, so the shape as well as the value is visible.
  5. Bisect for the isoelectric point. Because net charge falls monotonically with pH, bisection converges reliably. A hundred rounds narrow the interval far below the precision of the pKa values themselves.

What this method cannot tell you

  • •Ionisable groups are treated as independent. Neighbouring charges shift each other's pKa, and the error is largest in short, densely charged peptides.
  • •One published pKa set is used throughout. Other sets differ by up to a pH unit at the termini, which moves the calculated pI by a few tenths.
  • •Ionic strength is not modelled. High salt screens charges and shifts effective pKa values.
  • •Terminal modifications are invisible. An amidated C-terminus and an acetylated N-terminus each remove an ionisable group, which changes the curve substantially in a short peptide.

Where the numbers come from

Peptide charge at pH: frequently asked questions

Sum a fractional charge for every ionisable group, where each fraction comes from the Henderson-Hasselbalch relationship between the pH and that group's pKa.

The groups are the two termini plus one for every Asp, Glu, Cys, Tyr, His, Lys and Arg in the sequence.

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