Isoelectric Point (pI) Calculator

A pI does not belong to a peptide on its own. It belongs to the peptide and to the table of pKa values used to reason about it, and those two things are separable. Change the pKa set and the same sequence gives a different answer, not a slightly different answer but a different number, because the zero crossing moves with the curve it sits on. Published scales are not interchangeable, and no attempt is made here to reconcile them. Two tools that report disagreeing pI values are usually not disagreeing about the chemistry. They are feeding different constants into the same definition.

That is also the honest reason to treat a pI as approximate even when it is reported to several places. The definition itself is exact within the model, and the model is only as good as its constants. The tabulated pKa values were measured under particular conditions, and the spread between published values for the same group is of the order of a fraction of a pH unit. The explanation of peptide isoelectric points covers what the definition does and does not pin down, and is worth reading before a figure is quoted to more precision than the method supports.

There is no closed form for the pH at which a sum of many logistic terms crosses zero. Each group contributes a rational function of ten raised to a power, and a sum of several such terms cannot be inverted algebraically. What can be done is to notice that the sum decreases monotonically as pH rises, so it crosses zero at most once, so any sign change brackets a unique root. Bracketing and then halving the interval is therefore sufficient, and it is the method used here.

Bisection is chosen instead of a derivative based method for a simple reason: it cannot diverge. A step size derived from a slope can overshoot and leave the bracket, after which the search has to be restarted. Halving never leaves the bracket, never widens the interval, and converges at a rate known in advance, so the number of passes needed to reach a tolerance can be stated before the search starts. On a function that is smooth and monotone, the dull method is the right one. The net charge calculator supplies the function being solved.

A pI reported to four decimal places is a precise solution of an approximate function, and the two descriptions should not be allowed to run together. Bisection will drive the residual charge to within a tolerance far below any meaningful size, because tightening the tolerance costs nothing but extra iterations. The pKa values feeding it are tabulated constants, and the real disagreement between published values for the same group is a fraction of a pH unit. A result quoted to four places therefore describes the arithmetic exactly and the chemistry to about one.

In practice that means the last three digits are arithmetic residue rather than information. Two decimal places is already generous for most uses, and one is usually the precision that a buffer formulation, a supplier figure or a chromatographic method will act on. Reporting more is not more accurate, only more precise. If a downstream figure is going to be computed from a pI, carry it at one decimal place and let the rounding happen early, rather than propagating four places into the next calculation.

The composition of the chain decides the answer more than most readers expect. When a sequence has few or no basic side chains, the only positive charge available is the N terminus, and the zero crossing is set by the region where the carboxyl groups are still partly protonated. That is why peptides with no lysine, arginine or histidine legitimately return a pI near 3, and why a value that low is a structural result rather than an error. The charge versus pH calculator shows the same thing as a curve, with the crossing sitting between two closely spaced steps.

The same sensitivity runs in the other direction. Capping a terminus removes a whole charge, which moves the crossing far more than any plausible change to the rest of the chain, and the terminal modification calculator is the place to establish what a given cap does to the mass before that effect is reasoned about. A pI also says nothing about solubility or about migration speed. It is the pH at which the charge vanishes, which is one fact and not a general description of how a peptide behaves around it. Working out the buffer conditions that produce a particular pH is separate arithmetic, handled by the buffer dilution calculator .