A peptide’s net charge at a given pH is the sum of every ionizable group’s Henderson-Hasselbalch charge contribution: 1 / (1 + 10^(pH - pKa)) for a basic group, and -1 / (1 + 10^(pKa - pH)) for an acidic one. This post walks through that per-group sum, the Henderson-Hasselbalch equation it rests on, and what it deliberately leaves out.
The Henderson-Hasselbalch equation, per group
For any group that can gain or lose a proton, the fraction of that group that is protonated at a given pH, relative to its own pKa, follows a sigmoidal curve derived from the Henderson-Hasselbalch relationship. For a basic group (protonated form is positively charged), the contribution to net charge is:
charge contribution = 1 / (1 + 10^(pH - pKa))For an acidic group (deprotonated form is negatively charged):
charge contribution = -1 / (1 + 10^(pKa - pH))Both expressions produce a value between 0 and 1 (or 0 and -1) that shifts smoothly from fully charged to fully neutral as pH crosses the group’s pKa, rather than switching abruptly.
How do you calculate peptide net charge at a given pH?
A peptide has ionizable groups at both ends (the free N-terminal amine, basic, and the free C-terminal carboxyl, acidic) plus whichever side chains in the sequence can ionize: aspartate and glutamate (acidic), cysteine and tyrosine (weakly acidic at high pH), and histidine, lysine and arginine (basic). Net charge at a given pH is the sum of every one of these terms:
net charge(pH) = N-terminus term + C-terminus term + sum(side chain terms)The net charge calculator computes exactly this sum for a supplied sequence and pH. Every pKa value in the sum, for both terminal groups and every ionizable side chain, comes from a single published source: Bjellqvist et al. 1993, the same scale ExPASy’s tools use. The N-terminus is fixed at pKa 9.69 and the C-terminus at pKa 2.34 on this scale; side chain pKa values vary by residue.
pI is the same sum, solved rather than evaluated
The isoelectric point is the pH where this same net charge sum equals zero. Because there is no closed-form solution when several differently-weighted sigmoid terms are summed, it is found by numerically narrowing in on the crossing point rather than solved algebraically. That numerical method, and why the same Bjellqvist scale underlies it, is covered in full in peptide isoelectric point, explained, which this post’s charge equation is built on directly.
The isoelectric point calculator and the charge vs. pH curve calculator both use this same underlying net charge function, the first solving for where it crosses zero, the second sampling it across the full pH range to show the shape of the curve rather than a single point on it.
Why this is an approximation
Two things limit how literally to read a Henderson-Hasselbalch net charge figure. First, it treats every ionizable group as independent, with a fixed pKa regardless of what else is nearby in the folded structure; real electrostatic environments can shift an individual group’s effective pKa in ways a linear-sequence calculation cannot capture. Second, the Bjellqvist pKa scale used here is one of several published scales (others exist, measured or fitted under different conditions), and different scales predict somewhat different net charge and pI values for the same sequence. This calculation is the standard, widely used method, not a claim of a single universally agreed-upon number.
Related, simpler summaries
Net charge and pI describe a continuous function of pH. Two other calculators describe related composition facts that do not depend on pH at all. The charged residue fraction calculator reports what percentage of a sequence’s residues are acidic or basic, independent of what net charge that produces at any particular pH. The aromaticity calculator reports the percentage of aromatic residues (phenylalanine, tryptophan, tyrosine), which matters separately for extinction coefficient and hydrophobicity calculations rather than for charge. Neither is a substitute for a net charge or pI calculation, but both are useful quick reads on a sequence’s composition before working through the full pH-dependent math.
In short, peptide net charge at any pH is the sum of each ionizable group’s Henderson-Hasselbalch contribution, and the isoelectric point is simply the pH where that sum crosses zero.
Primary scientific literature and citations
- Henderson, L. J. (1908). Concerning the relationship between the strength of acids and their capacity to preserve neutrality. American Journal of Physiology, 21(2), 173-179. DOI: 10.1152/ajplegacy.1908.21.2.173. The original mathematical description of acid-base equilibrium and buffer neutralization capacity.
- Hasselbalch, K. A. (1916). Die Berechnung der Wasserstoffzahl des Blutes aus der freien und gebundenen Kohlensaeure desselben, und die Sauerstoffbindung des Blutes als Funktion der Wasserstoffzahl. Biochemische Zeitschrift, 78, 112-144. Expressed Henderson’s equation in logarithmic format using Sorenson’s pH notation.
- Bjellqvist, B., Hughes, G. J., Pasquali, Ch., Paquet, N., Ravier, F., Sanchez, J. Ch., Frutiger, S., & Hochstrasser, D. (1993). The focusing positions of polypeptides in immobilized pH gradients can be predicted from their amino acid sequences. Electrophoresis, 14(1), 1023-1031. PubMed PMID: 8125050. Source of the standard polypeptide terminal and side-chain pKa constants used in the multi-group net charge calculation.
- IUPAC Compendium of Chemical Terminology (Gold Book). Acidity constant and pH entries. Pure and Applied Chemistry, 1997. International standards for dissociation equilibrium constants and electrochemical pH definitions.