The `pK_(a)` values of ionisable groups in lysine are 2.18, 8.95 and 10.79 respectively. Find isoelectric point of lysine.

Answer

To find the isoelectric point (pI) of lysine, we will follow these steps:

### Step 1: Understand the pKa values
The pKa values given for lysine are:
- pKa1 = 2.18 (carboxylic group)
- pKa2 = 8.95 (first amino group)
- pKa3 = 10.79 (second amino group)

### Step 2: Identify the relevant pKa values for calculating pI
The isoelectric point (pI) is calculated using the average of the pKa values that correspond to the protonation and deprotonation of the amino acid. For lysine, which has two amino groups and one carboxylic group, we consider the pKa values that are relevant when the molecule is in its zwitterionic form (neutral overall charge).

Since lysine has a basic amino group that will remain protonated at physiological pH, we will use the pKa values of the two basic groups (the first amino group and the second amino group) for the calculation of pI.

### Step 3: Calculate the isoelectric point
The pI is calculated using the formula:
\[ \text{pI} = \frac{\text{pKa2} + \text{pKa3}}{2} \]
Substituting in the values:
\[ \text{pI} = \frac{8.95 + 10.79}{2} \]

### Step 4: Perform the arithmetic
Calculating the sum:
\[ 8.95 + 10.79 = 19.74 \]
Now divide by 2:
\[ \text{pI} = \frac{19.74}{2} = 9.87 \]

### Final Answer
The isoelectric point (pI) of lysine is **9.87**.

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