Histidine is an amino acid with three ionizable functional groups: the carboxyl group (pKa ~ 2.2), the amino group (pKa ~ 9.2), and the side chain imidazole group (pKa ~ 6.0).
1. **Equilibrium equations for ionizations**:
a) Carboxyl group:
\[ \text{Histidine} \underset{\text{acid}}{\rightleftharpoons} \text{H}^+ + \text{Histidine}^- \]
b) Amino group:
\[ \text{Histidine}^+ \underset{\text{base}}{\rightleftharpoons} \text{H}^+ + \text{Histidine} \]
c) Imidazole group:
\[ \text{Histidine} \underset{\text{acid}}{\rightleftharpoons} \text{H}^+ + \text{Histidine}^- \]
2. **Net charge on histidine molecule at different pH values**:
- At pH 1 (very acidic), all three ionizable groups will be protonated, so the net charge will be +1.
- At pH 4, the carboxyl group will be protonated, but the amino group and the imidazole group will be deprotonated, so the net charge will be 0.
- At pH 8, both the carboxyl group and the amino group will be deprotonated, but the imidazole group will be protonated, so the net charge will be 0.
- At pH 12 (very basic), all three ionizable groups will be deprotonated, so the net charge will be 0.
3. **Direction of migration in an electric field**:
- At pH 1 (positively charged), histidine will move towards the cathode (negative electrode) because positively charged ions migrate towards the negative electrode (cathode) in an electric field.
- At pH 4 (neutral), histidine will not migrate because it is neutrally charged.
- At pH 8 (neutral), histidine will not migrate because it is neutrally charged.
- At pH 12 (negatively charged), histidine will move towards the anode (positive electrode) because negatively charged ions migrate towards the positive electrode (anode) in an electric field.