26.2 Amino Acids and the Henderson–Hasselbalch Equation: Isoelectric Points

Amino Acids and Isoelectric Points

Amino acids are the building blocks of proteins, and each one carries ionizable groups that gain or lose protons depending on the surrounding pH. The isoelectric point (pI) is the specific pH at which an amino acid (or protein) carries no net electrical charge. Understanding pI is essential for predicting how amino acids behave in solution and for separating proteins using techniques like electrophoresis.

Isoelectric Point Calculation

The pI is the pH where an amino acid's positive and negative charges exactly balance out, giving a net charge of zero. You calculate it by averaging the two pKa values that flank the zwitterionic (neutral) form of the amino acid.

For amino acids with non-ionizable side chains (Ala, Val, Leu, Ile, Met, Phe, Trp, Pro, Gly, Ser, Thr, Asn, Gln, Cys):

Only the $\alpha$-carboxyl and $\alpha$-amino groups ionize, so you average those two pKa values:

$pI = \frac{pK_{a1}(COOH) + pK_{a2}(NH_3^+)}{2}$

For amino acids with ionizable side chains, the side chain introduces a third pKa. The trick is to identify which two pKa values bracket the zwitterionic form:

• Acidic side chains (Asp, Glu): The zwitterion sits between the two lowest pKa values (both carboxyl-type deprotonations), so:

$pI = \frac{pK_{a1}(COOH) + pK_{a}(side\ chain)}{2}$

• Basic side chains (Lys, Arg, His): The zwitterion sits between the two highest pKa values (both involve losing a proton from a positively charged nitrogen), so:

$pI = \frac{pK_{a}(side\ chain) + pK_{a2}(NH_3^+)}{2}$

Worked example: Alanine has $pK_{a1} = 2.34$ and $pK_{a2} = 9.69$. Since it has no ionizable side chain:

$pI = \frac{2.34 + 9.69}{2} = 6.01$

At pH 6.01, alanine exists almost entirely as the zwitterion ($^+H_3N\text{-}CHR\text{-}COO^-$) with no net charge.

Amino Acid Forms at Different pH

The Henderson–Hasselbalch equation lets you figure out the protonation state of each ionizable group at any given pH:

$pH = pK_a + \log\frac{[A^-]}{[HA]}$

Here, $[HA]$ is the protonated form and $[A^-]$ is the deprotonated form. The pKa is the pH at which the group is exactly half-protonated.

Three key rules to remember:

• pH < pKa: The protonated form ($HA$) predominates. More $H^+$ in solution pushes the equilibrium toward protonation.
• pH > pKa: The deprotonated form ($A^-$) predominates. The basic conditions favor loss of the proton.
• pH = pKa: The group is exactly 50% protonated and 50% deprotonated ($[HA] = [A^-]$).

To determine the overall charge on an amino acid at a given pH, compare the pH to each group's pKa individually:

• Groups with pKa well below the pH will be fully deprotonated
• Groups with pKa well above the pH will be fully protonated
• The group with pKa closest to the pH will be partially protonated/deprotonated

Worked example: Glutamic acid (Glu) has $pK_{a1} = 2.19$, $pK_a(side\ chain) = 4.25$, and $pK_{a2} = 9.67$. At pH 7.0:

• $\alpha$-Carboxyl group (pKa 2.19): fully deprotonated → $-COO^-$ (charge: $-1$)
• Side chain carboxyl (pKa 4.25): fully deprotonated → $-CH_2CH_2COO^-$ (charge: $-1$)
• $\alpha$-Amino group (pKa 9.67): fully protonated → $-NH_3^+$ (charge: $+1$)
• Net charge at pH 7.0 = $+1 + (-1) + (-1) = -1$

This makes sense: pH 7.0 is well above glutamic acid's pI of $\frac{2.19 + 4.25}{2} = 3.22$, so the molecule carries a net negative charge.

Amino Acid Properties

Amino acids are amphoteric, meaning they can act as both acids and bases. At low pH they accept protons (acting as bases), and at high pH they donate protons (acting as acids). This is why every amino acid exists as a zwitterion at physiological pH: the carboxyl group has donated its proton ($COO^-$) while the amino group has accepted one ($NH_3^+$).

The net charge on an amino acid depends entirely on the pH of its environment relative to the pKa values of its ionizable groups. Factors like the ionic strength of the solution can also influence amino acid behavior by screening charges and affecting electrostatic interactions between molecules.

Electrophoresis and Isoelectric Points

Protein Separation by Electrophoresis

Electrophoresis separates proteins by placing them in an electric field, where they migrate based on their net charge (and, in some setups, their size). The net charge a protein carries depends on the relationship between the buffer pH and the protein's pI:

• pH < pI: The protein has a net positive charge and migrates toward the cathode (negative electrode)
• pH > pI: The protein has a net negative charge and migrates toward the anode (positive electrode)
• pH = pI: The protein has zero net charge and does not migrate

Isoelectric focusing (IEF) is a specialized form of electrophoresis that exploits these charge differences using a pH gradient:

1. A gel is prepared with a continuous pH gradient (e.g., pH 3 to 10)
2. A protein mixture is loaded and voltage is applied
3. Each protein migrates through the gradient until it reaches the zone where pH equals its pI
4. At that point, the protein's net charge drops to zero and it stops moving
5. Proteins with different pI values accumulate at different positions along the gradient

Example: A mixture contains three proteins with pI values of 5, 7, and 9, run on a pH 3–10 gradient. The pI 5 protein stops in the acidic region, the pI 7 protein stops at the center, and the pI 9 protein stops in the basic region. Each forms a distinct band at its characteristic pH.

After separation, protein bands are visualized using staining methods such as Coomassie Brilliant Blue (detects ~0.1 µg protein) or silver stain (more sensitive, detects ~1 ng protein).