# How do I calculate the isoelectric point of amino acids, each of which has more than two values of pKa?

Chemistry Asked by Andrew Wolf on October 16, 2020

For most amino acids, the $$mathrm{pI}$$ is simply the arithmetic mean of the amino and carboxyl $$mathrm pK_mathrm a$$s. However, for tyrosine and cysteine, which have more than one $$mathrm pK_mathrm a$$ value, this rule of thumb doesn’t apply.

I see that for tyrosine, it’s the $$mathrm pK_mathrm a$$s of the carboxyl and amino groups that are averaged, but for cysteine it’s those of the carboxyl group and the side chain.

I haven’t been able to find an explanation of why this is the case, or what the reasoning behind the calculations is?

Since the $mathrm{pI}$ is the $mathrm{pH}$ at which the amino acid has no overall net charge, you need to average the $mathrm pK_mathrm a$ values relevant to the protonation/deprotonation of the form with no net charge. Here are the acid-base equilibria for tyrosine:

The form with no net charge is in red (+1 and -1 cancel out to give no net charge). It is the $mathrm pK_mathrm a$ values on either side of this form (in blue) that matter, hence the $mathrm{pI}$ of tyrosine is $5.66$ (the average of $2.20$ and $9.11$).

It just so happens that $2.20$ is the carboxyl $mathrm pK_mathrm a$ and $9.11$ is the amino $mathrm pK_mathrm a$. If the side chain $mathrm pK_mathrm a$ were lower than $9.11$, then you should average the carboxyl and side chain $mathrm pK_mathrm a$'s instead.

The same logic applies to cysteine (look up the $mathrm pK_mathrm a$ values and draw out the differently protonated forms). You'll find that since the side chain has a lower $mathrm pK_mathrm a$ than the amino group, you average the carboxyl and the side chain $mathrm pK_mathrm a$'s.

This procedure can of course be extended to the amino acids with acidic side chains (aspartic acid; glutamic acid) and those with basic side chains (lysine; arginine; histidine).

Answered by orthocresol on October 16, 2020