# How can I properly calculate the isoelectric point (pI) of amino acids?

The following amino acid is called lysine. I was asked to calculate its isoelectric point, with the given $$\mathrm pK_\mathrm a$$ values.

I've searched a lot, and the most helpful post that I found was How do I calculate the isoelectric point of amino acids with more than two pKa's? According to orthocresol's answer:

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.

Let's call the ends $$e_1, e_2$$ and $$e_3$$ (from left to right).

# Approach $$\#1$$

• deprotonate $$e_3$$ (i.e., carboxyl group)
• deprotonate $$e_1$$ or $$e_2$$ [neutral point]

So, $$\mathrm pK_\mathrm a$$'s of $$e_1$$ and $$e_2$$ are relevant.

$$\Rightarrow \mathrm{pI} = \frac{10.53 + 8.95}{2} = 9.74$$

But, is there some limit to number of protonations/deprotonations or some procedures to follow?

For instance,

# Approach $$\#2$$

• deprotonate $$e_1$$
• deprotonate $$e_3$$ [neutral point]
• deprotonate $$e_2$$ and protonate $$e_1$$ [neutral point]

This time, $$\mathrm pK_\mathrm a$$'s of $$e_3$$ and $$e_1$$ are relevant. But, the calculated $$\mathrm{pI}$$ isn't correct.

So, how can I validate the approaches?

Problem source: FIITJEE study material

$$\mathrm pK_\mathrm a$$ and $$\mathrm{pI}$$ values table for amino acids: https://www.anaspec.com/html/pK_n_pl_Values_of_AminoAcids.html

• The first approach I'd say is the correct one. It's obvious that the isoelectric point will be between e1 and e2 because lysine is a dibasic aminoacid, therefore the two amino groups will have a bigger influence on the pI than the acidic group, thus rendering the pI basic. In these cases, as far as I know, you have to find the average of 2 pKa-values that are going to have the biggest influence on the pI. In this case, since there are 3 pKa-values of which 2 are basic, the pI will be the arithmetic mean of those values. Jul 18 '20 at 14:21
• Related: Various pI calculators for proteins give different results: ExPASy (8.75), isoelectric.org (9.04), and Prot pi (8.475). Jul 19 '20 at 12:53

Isoelectric point of an amino acid is the $$\mathrm{pH}$$ at which the molecule carries no net charge[1]. It can be calculated by the average of the relevant $$\mathrm pK_\mathrm a$$ values as you have mentioned.

Your confusion seems to stem from choosing the relevant $$\mathrm pK_\mathrm a$$ values. For this we should refer to the titration curve of the amino acid.

For a neutral amino acid[2]:

From the curve we can infer that the $$\mathrm{pI}$$ is simply the average of the two $$\mathrm pK_\mathrm a$$ values of the carboxylic acid and the amino group.

For a basic amino acid[2]:

From the curve we can infer that the $$\mathrm{pI}$$ is simply the average of the two $$\mathrm pK_\mathrm a$$ values of the two amino groups. The $$\mathrm pK_\mathrm a$$ of the carboxylic acid group is not relevant.

For an acidic amino acid[3]:

From the curve we can infer that the $$\mathrm{pI}$$ is simply the average of the two $$\mathrm pK_\mathrm a$$ values of the two carboxylic acid groups. The $$\mathrm pK_\mathrm a$$ of the amino group is not relevant.

Here are examples for all three cases:

References: