24.5 Biological Amines and the Henderson–Hasselbalch Equation

Biological Amines

Biological amines like neurotransmitters, amino acids, and hormones are everywhere in your body. Whether they're protonated or neutral at a given pH determines how they behave: whether they cross membranes, bind receptors, or dissolve in blood. The Henderson–Hasselbalch equation is the tool you use to figure out which form dominates.

Acid-Base Equilibria and Dissociation Constants

Before diving into calculations, make sure you're solid on the constants involved.

• $K_a$ (acid dissociation constant) measures how readily an acid donates a proton. $pK_a = -\log(K_a)$. A lower $pK_a$ means a stronger acid.
• $K_b$ (base dissociation constant) measures how readily a base accepts a proton. $pK_b = -\log(K_b)$. A lower $pK_b$ means a stronger base.
• For a conjugate acid-base pair in water: $pK_a + pK_b = 14$

This relationship lets you convert freely between the acid and base perspectives, which matters because amines are bases but you'll often be given (or need) the $pK_a$ of their conjugate acid.

Protonation States Using the Henderson–Hasselbalch Equation

The core equation for acids and their conjugate bases is:

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

For amines specifically, you can write the equivalent base form:

$pOH = pK_b + \log\left(\frac{[B]}{[BH^+]}\right)$

Here, $[B]$ is the neutral (free base) amine and $[BH^+]$ is the protonated form.

To find the protonation state of an amine at physiological pH (7.4):

1. Look up (or calculate) the $pK_b$ of the amine. If you're given the $pK_a$ of the conjugate acid, convert: $pK_b = 14 - pK_a$.

2. Convert pH to pOH: $pOH = 14 - 7.4 = 6.6$

3. Rearrange to isolate the ratio: $\log\left(\frac{[B]}{[BH^+]}\right) = pOH - pK_b$

4. Solve: $\frac{[B]}{[BH^+]} = 10^{(pOH - pK_b)}$

The resulting ratio tells you directly how much neutral amine exists relative to protonated amine at that pH.

You can also work entirely in the $pK_a$ framework. For the conjugate acid $BH^+$:

$pH = pK_a + \log\left(\frac{[B]}{[BH^+]}\right)$

If $pH < pK_a$, the protonated form $BH^+$ dominates. If $pH > pK_a$, the neutral form $B$ dominates. Most biogenic amines have conjugate acid $pK_a$ values around 9–11, well above 7.4, so the protonated form wins at physiological pH.

Protonated Form of Cellular Amines

Most cellular amines (amino acids, dopamine, serotonin, histamine) have $pK_b$ values that place them solidly in the protonated camp at pH 7.4. Their conjugate acids typically have $pK_a$ values of 9–11, meaning physiological pH sits well below the $pK_a$. That makes $BH^+$ the dominant species.

This is why you'll see cellular amines drawn in their protonated form ($-NH_3^+$) in biochemistry. It's not just convention; it reflects what actually exists in the cell. The positive charge also matters functionally: protonated amines are water-soluble and can't easily cross lipid membranes, which is relevant for drug design and neurotransmitter compartmentalization.

Calculating Neutral vs. Protonated Percentages

Once you have the $[B]/[BH^+]$ ratio, you can calculate exact percentages. Here's the process:

1. Define total concentration: $C_T = [B] + [BH^+]$

2. Let $x = [B]$, so $[BH^+] = C_T - x$

3. From your Henderson–Hasselbalch calculation, you already know the ratio $[B]/[BH^+] = R$

4. Substitute: $\frac{x}{C_T - x} = R$, then solve for $x = \frac{R \cdot C_T}{1 + R}$

5. Calculate percentages:

   • $\%B = \frac{x}{C_T} \times 100\% = \frac{R}{1 + R} \times 100\%$
   • $\%BH^+ = \frac{1}{1 + R} \times 100\%$

Example: Suppose an amine has $pK_b = 4.0$ and you want the protonation state at pH 7.4.

• $pOH = 14 - 7.4 = 6.6$
• $\log([B]/[BH^+]) = 6.6 - 4.0 = 2.6$
• $[B]/[BH^+] = 10^{2.6} \approx 398$
• $\%B = \frac{398}{399} \times 100\% \approx 99.7\%$

This amine is almost entirely in its neutral form. Compare that to an amine with $pK_b = 10.0$:

• $\log([B]/[BH^+]) = 6.6 - 10.0 = -3.4$
• $[B]/[BH^+] = 10^{-3.4} \approx 0.0004$
• $\%BH^+ = \frac{1}{1.0004} \times 100\% \approx 99.96\%$

This amine is almost entirely protonated. Most biologically relevant amines fall into this second category at pH 7.4.