Charge vs pH Curve Calculator

Every group that can gain or lose a proton contributes a step centred on its own pKa, rising for a group that is protonated as pH falls and falling for one that loses its proton. The plotted curve is the arithmetic sum of those steps with the sign each group carries, so the shape of the whole is a readout of how many groups exist and how far apart their pKa values lie. A group whose pKa sits in a region where nothing else sits produces a clean step of its own. Two groups with close pKa values produce one step that looks like a single event and is really two.

That is why the number of visible steps is usually smaller than the number of ionisable groups. The carboxyl groups of a typical peptide sit close enough together to merge, and a reader who counts three steps on the curve and concludes that three groups exist has probably undercounted. The net charge calculator counts the groups explicitly by including every tabulated pKa, which is the more reliable way to establish how many are present. The guide to net charge and Henderson-Hasselbalch sets out the per group arithmetic that these steps come from.

The curve here is sampled at 29 equally spaced pH values across a range of 14, which is one point every half pH unit. That is enough to show where the transitions are and to locate the crossing to within half a sampling interval, that is about a quarter of a pH unit. It is not enough to resolve the profile of a very sharp transition. A step sampled four times can look smooth when the change between adjacent samples is large, and two closely spaced steps can fall entirely between the sample points.

This matters mainly because the plot and the dedicated solver are not equally precise about the same quantity, and a reader comparing them may suspect a fault in one of them. The plot shows the crossing approximately, because it inherits the sampling interval. The isoelectric point calculator does not sample: it brackets the root and halves the interval until the residual charge is negligible, so it returns the crossing to a much finer figure. If the two disagree by more than the sampling interval allows, the sequence is the thing to re-enter rather than the arithmetic to doubt.

The steepness of the curve is informative because it is a direct readout of how much charge is changing per pH unit, which is how many groups are in their sensitive region simultaneously. A single group sitting at its own pKa contributes a peak slope of about 0.58 of a charge per pH unit. Two groups with nearby pKa values add, and the curve steepens beyond anything one group can produce on its own. That steep stretch is the pH range over which the answer on the net charge page is most sensitive to an error in the pH supplied.

The flat stretches are worth reading too. Far from every pKa, adding a tenth of a pH unit changes very little, which makes those regions forgiving and the steep ones unforgiving in exactly the way described above. It also explains the overall tilt: the curve is not symmetric about its centre, because the acidic groups sit low and the basic groups sit high, so the two halves of the range contribute different amounts of charge. That asymmetry is the composition of the sequence showing through, and the explanation of peptide isoelectric points covers the same ground from the pI side.

At the extremes the curve approaches values that are simple to interpret. At very low pH almost every group is protonated, so the charge approaches the number of basic groups the model counts, the N terminus included. At very high pH almost every group has lost its proton, so it approaches the negative of the number of acidic groups, the C terminus included. The vertical span between the two limits is therefore the total number of ionisable groups in the model, and reading it off is a quick check that the sequence is what you believe it to be.

Those limits are approached rather than reached, and 29 samples do not get there. A curve that appears to stop at plus one may simply end at pH 0.0, and the residual at either end is real arithmetic rather than a plotting artefact. The buffer conditions in which a particular point on the curve is realised are a separate question and a separate piece of arithmetic, which is what the buffer dilution calculator is for. The curve describes the molecule; reaching a chosen pH is a practical problem the curve cannot solve.