Net Charge Calculator

Every ionisable group is a conjugate acid and base pair sitting in equilibrium, and mass action fixes the ratio between the two forms. Raising the pH favours the deprotonated form, and the ratio of protonated to deprotonated populations equals ten to the power of pH minus pKa. Solving that relationship for the fraction rather than for the ratio gives the two terms this page adds up: a positive expression for a group that is basic and a negative one for a group that is acidic. Nothing here is fitted or tuned. The shape of each contribution is imposed by the equilibrium, and the pKa is simply the pH at which the two forms are equally abundant.

That is also why the two expressions are mirror images rather than two different formulas, and why every contribution is bounded by plus or minus one. A group cannot carry more than a single charge either way, because it holds one proton or none of them. Summing them produces a number that is usually not a whole number, and that is not a defect. It is an expectation: the average charge per molecule across a population in which each group sits at its equilibrium fraction, not a count of charged positions. The guide to net charge and Henderson-Hasselbalch works through the same derivation with a fuller curve.

The sensitivity of a group to pH is not constant across the range. It is greatest at exactly its own pKa, where the group is half protonated, and it falls away on either side. Differentiating the fraction gives a peak slope of about 0.58 of a charge per pH unit for a single group sitting at its pKa, and effectively zero well away from it. One tenth of a pH unit is therefore worth a great deal when it lands near a pKa and almost nothing when it lands on a flat stretch. Error in a quoted pH is not uniformly damaging, and where it lands decides how damaging.

This is the practical reason a buffer matters more than its molarity suggests. A tenth of a pH unit placed beside a histidine or a carboxyl group moves that group by around six percent of a charge, and with several groups sharing a pH the total moves further still. The same tenth placed near pH 9.7, in a stretch where nothing is changing, moves the answer by almost nothing. The charge versus pH calculator draws the whole function, so the distance between your working pH and the nearest step becomes visible rather than something to be inferred.

The model counts every group carrying a pKa in the tabulated set, which includes cysteine and tyrosine. Both are treated as ionisable, and at neutral pH both contribute very little, which is why their effect is usually invisible at pH 7 and becomes noticeable in alkaline conditions. Cysteine also carries a charge of an entirely different kind when it forms a disulfide, and that change is not modelled at all. Caps that remove a terminal charge belong with the terminal modification calculator , not here.

The two termini are always counted and are never optional. On a long chain they are a rounding error beside the side chains. On a chain of four or five residues they can be half of every ionisable position in the molecule, and removing one by amidation or acetylation moves the answer by a full unit. That is also why the charged residue fraction on its own is a poor guide to charge on a short peptide: it counts side chains only, leaving the two ends out of both the numerator and the denominator.

This number is a thermodynamic model of protonation equilibria in solution. It is not mobility, and mobility is not charge. Electrophoretic behaviour additionally depends on ionic strength, on the counter ions present, on any specific interaction with a support or a membrane, and on shape. None of those appear in the sum, and a peptide carrying a charge of minus one can migrate very differently from another with the same charge if their friction coefficients differ.

Nor does it describe one particular molecule. The result is an average across a population, which is what makes it fractional, and any real sample sits somewhere on that distribution rather than exactly at its middle. Where the answer is close to zero, it is worth asking what pH would be needed to change the sign, because that pH is the isoelectric point and it is a far more stable quantity to quote than a charge at an arbitrary pH. Getting to a chosen pH in the first place is separate arithmetic, and the buffer dilution calculator is where that begins.