The amino group (NH3+) is 9.74, the pKa of the carboxyl group (COOH) is 2.2, and the pKa of the side chain amino group (NH2) is 10.8.

To calculate the isoelectric point (pI), we need to determine the pH at which the net charge of lysine is zero. We can do this by comparing the pKa values of the different ionizable groups in lysine and identifying the pH at which each group is either protonated or deprotonated.

At a pH below the pKa of the amino group (NH3+), the amino group will be protonated and positively charged (+1). The carboxyl group (COOH) will also be protonated and negatively charged (-1). The side chain amino group (NH2) will also be protonated and positively charged (+1).

As the pH increases above the pKa of the amino group (NH3+), the amino group will start to deprotonate and become neutral (0). At a pH around 9.74, the amino group will be fully deprotonated and neutral (0). The carboxyl group (COOH) will still be protonated and negatively charged (-1). The side chain amino group (NH2) will also be protonated and positively charged (+1).

As the pH increases further above the pKa of the side chain amino group (NH2), the side chain amino group will start to deprotonate and become neutral (0). At a pH around 10.8, the side chain amino group will be fully deprotonated and neutral (0). The amino group (NH3+) will still be deprotonated and neutral (0). The carboxyl group (COOH) will still be protonated and negatively charged (-1).

Therefore, the isoelectric point (pI) of lysine can be calculated as the average of the pKa values of the amino group and the side chain amino group:

pI = (pKa of NH3+ + pKa of NH2) / 2
pI = (9.74 + 10.8) / 2
pI = 10.27

Therefore, the isoelectric point (pI) of lysine is approximately 10.27. This means that at a pH of 10.27, lysine will have a net charge of zero and will be electrically neutral.