Chapter 3 — Case Study 2: pH, pKa, and Why Drugs Get Where They Need to Go

The quiet chemistry that decides whether a pill works.

1. The pharmacokinetic problem

Suppose you swallow an aspirin tablet for a headache. The aspirin must:

1. Survive the acidic environment of the stomach (pH ~1–2).
2. Cross the stomach lining or the wall of the small intestine (pH ~6–7) into the bloodstream (pH 7.4).
3. Travel through the bloodstream without being rapidly cleared by the liver and kidneys.
4. Cross from the bloodstream into the target tissue (usually the site of inflammation).
5. Bind to its target protein (cyclooxygenase, in the case of aspirin).

Every one of these steps depends on the drug's protonation state — which in turn depends on its $pK_a$ and the local pH. A drug that is the right chemistry but the wrong $pK_a$ will fail, sometimes spectacularly. Drug designers think about $pK_a$ constantly.

This case study walks through the chemistry, using three example drugs — aspirin, codeine, and morphine — to show how the same principles play out very differently depending on the drug's acid-base character.

2. The Henderson-Hasselbalch equation

The relationship between pH, $pK_a$, and the ratio of protonated to deprotonated forms of a weak acid is given by the Henderson-Hasselbalch equation:

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

Rearranging:

$$\frac{[A^-]}{[HA]} = 10^{pH - pK_a}$$

Three useful special cases:

• pH = $pK_a$: Exactly 50:50 protonated:deprotonated.
• pH = $pK_a$ + 2: 99:1 deprotonated:protonated (the acid is almost entirely in its conjugate-base form).
• pH = $pK_a$ − 2: 1:99 deprotonated:protonated (the acid is almost entirely in its neutral form).

For a weak base, the analogous equation uses $pK_{aH}$ (the $pK_a$ of the protonated form):

$$\frac{[\text{base}]}{[\text{base-H}^+]} = 10^{pH - pK_{aH}}$$

3. Aspirin (pKa of carboxylic acid = 3.5)

Aspirin is a weak acid — its carboxylic-acid proton has $pK_a \approx 3.5$. What fraction is neutral (protonated) vs. ionized (deprotonated) at different pH values?

• Stomach, pH 1.5: $10^{1.5 - 3.5} = 10^{-2}$. Ratio of deprotonated:protonated = 1:100. So 99% of aspirin in the stomach is in its neutral form, with the $COOH$ intact.
• Intestine, pH 6.5: $10^{6.5 - 3.5} = 10^3$. Ratio = 1000:1 deprotonated. So 99.9% of aspirin in the intestine is the anionic carboxylate form.
• Blood, pH 7.4: $10^{7.4 - 3.5} = 10^{3.9}$. Virtually all anionic.

This matters for absorption. Cell membranes are lipid bilayers, and neutral (uncharged) molecules cross them much more easily than charged ones. The neutral form of aspirin crosses the stomach wall relatively well; the anionic form does not. So most aspirin absorption happens in the stomach — a small but historically important observation, because it explains why aspirin can irritate the stomach lining (it stays protonated and crosses into stomach tissue, where it also inhibits protective prostaglandin synthesis locally).

Modern enteric-coated aspirin tablets are designed specifically to survive the stomach intact and dissolve only in the small intestine. This sacrifices some absorption rate for reduced stomach irritation — a direct pharmacokinetic consequence of $pK_a$.

4. Codeine (basic amine with pKaH ≈ 8.2)

Codeine is a weak base — an alkaloid structurally related to morphine, with a tertiary amine ($pK_{aH}$ of the ammonium ~8.2). At different pH:

• Stomach, pH 1.5: deprotonated:protonated = $10^{1.5 - 8.2} = 10^{-6.7}$. Essentially all protonated (cationic form).
• Intestine, pH 6.5: $10^{6.5 - 8.2} = 10^{-1.7}$. Ratio ~1:50, so still ~98% protonated.
• Blood, pH 7.4: $10^{7.4 - 8.2} = 10^{-0.8}$. Ratio ~1:6, so ~85% protonated.

Codeine is cationic (protonated amine) almost everywhere in the body. Yet codeine is absorbed reasonably well by the small intestine and distributes throughout the body. How?

The answer: codeine is not entirely protonated. At pH 7.4, about 15% is neutral — and it is that 15% that crosses membranes. Because the reaction between the protonated and neutral forms is fast (a proton transfer with water, effectively instantaneous), the protonated population is continuously replenishing the neutral population as the neutral form crosses the membrane. The entire pool of codeine eventually distributes, even though only a small fraction is membrane-crossing at any moment.

This is an important general principle: for a weak base with $pK_{aH}$ near 8–10, partial protonation at physiological pH allows reasonable membrane permeability. A drug designer aiming for good oral absorption often targets $pK_{aH}$ in the 7–9 range for basic amines, because much lower ($pK_{aH}$ of 5 means always neutral, no solubility in water) or higher ($pK_{aH}$ of 12 means always protonated, no membrane crossing) would cause problems.

5. Morphine (phenol pKa ≈ 10, amine pKaH ≈ 9)

Morphine is more complicated. It has both a phenol ($pK_a \approx 9.85$) and a tertiary amine ($pK_{aH} \approx 8.0$). At physiological pH, it can exist as four distinct protonation states:

• Fully neutral (phenol protonated, amine neutral): uncommon.
• Zwitterionic (phenol deprotonated, amine protonated): common, especially at high pH.
• Cationic (phenol protonated, amine protonated): dominant at low pH.
• Dianionic (phenol deprotonated, amine neutral): uncommon, requires very high pH.

At pH 7.4:

• Phenol: $10^{7.4 - 9.85} = 10^{-2.45}$ → ~0.4% deprotonated.
• Amine: $10^{7.4 - 8.0} = 10^{-0.6}$ → about 20% neutral (80% protonated).

The dominant form (~80%) is the mono-cation (phenol protonated, amine protonated). The remaining ~20% is a mix of zwitterionic and other neutral forms.

Morphine's absorption is modest — only about 30% of an oral dose reaches the bloodstream unchanged (the rest is metabolized in the intestinal wall and liver). The mixed protonation state is part of the reason. Drug designers have been trying to improve morphine for a century, with mixed success: heroin (diacetylmorphine) crosses the blood-brain barrier much more rapidly than morphine because both of morphine's hydroxyls are masked as esters (less polar, more membrane-permeable). But heroin is deacetylated back to morphine once inside the brain — so heroin's effect is simply a much-faster-acting morphine, which is precisely what makes it so addictive.

6. The "rule of 5" and drug design

In 1997, Christopher Lipinski at Pfizer analyzed which drug candidates in the company's pipeline succeeded and which failed in clinical trials. He found a simple empirical rule for predicting oral bioavailability, now called the Lipinski "rule of five":

A drug is likely to have poor oral absorption if it has:

1. More than 5 hydrogen-bond donors (OH + NH groups).
2. More than 10 hydrogen-bond acceptors (N + O atoms).
3. A molecular weight greater than 500 Da.
4. A calculated log P (partition coefficient, octanol/water) greater than 5.
5. Charge at physiological pH (implicit — charged species fail).

The rules are guidelines, not laws (some successful drugs violate one or more rules), but they encode a remarkable amount of $pK_a$ and polarity intuition. A drug with the wrong $pK_a$ is likely to be charged at physiological pH, which triggers rule violations.

Modern drug designers use computational prediction of $pK_a$ and log P to filter millions of virtual compounds before making any of them in a lab. The filtering is a $pK_a$-aware selection — favoring compounds with protonation states amenable to membrane crossing at pH 7.4.

7. The lesson

Drug development is $pK_a$ development. Every compound that becomes a marketed pharmaceutical went through hundreds of small chemical adjustments aimed, in part, at getting the $pK_a$ values right.

A drug that has the right pharmacology but the wrong $pK_a$ may never cross a membrane, never reach its target, and never become a drug. The history of medicinal chemistry is littered with compounds that had beautiful in vitro activity and abysmal in vivo pharmacokinetics. The gap between "works in a test tube" and "works in a patient" is often a $pK_a$ problem.

Chapter 3's framework is how drug designers think. The $pK_a$ of a functional group determines which form the drug is in at which pH. The pH-dependent distribution determines membrane crossing. Membrane crossing determines whether the drug gets to its target. And target engagement determines whether the drug works.

From $pK_a$ to patient — the chain of consequences is direct.

Further reading. Lipinski, C. A. et al. (2001). Experimental and computational approaches to estimate solubility and permeability in drug discovery and development settings. Advanced Drug Delivery Reviews, 46, 3–26. The paper that introduced the rule of five. Manallack, D. T. (2007). The pKa distribution of drugs. Perspectives in Medicinal Chemistry, 1, 25–38.