3.1: Physicochemical Properties of Drugs

3.1: Physicochemical Properties of Drugs

Solubility and Dissolution Kinetics (Noyes-Whitney)

In biopharmaceutics, a clear distinction must be made between solubility (a thermodynamic property representing the maximum concentration of solute that dissolves in a given solvent at equilibrium) and dissolution rate (a kinetic property describing the speed at which a solute dissolves). For an orally administered solid dosage form, the rate-limiting step for systemic absorption is often the dissolution of the drug in the aqueous fluids of the gastrointestinal (GI) tract, particularly for drugs belonging to Class II (low solubility, high permeability) and Class IV (low solubility, low permeability) of the Biopharmaceutics Classification System (BCS).

The dissolution of solid drugs is mathematically described by the Noyes-Whitney equation:

$\frac{dC}{dt} = \frac{D \cdot A \cdot (C_s - C)}{h}$

Where:

• $\frac{dC}{dt}$ is the rate of drug dissolution.
• $D$ is the diffusion coefficient of the drug in the dissolution medium.
• $A$ is the effective surface area of the drug particles available for dissolution.
• $C_s$ is the saturation solubility of the drug in the stagnant diffusion layer surrounding the solid particle.
• $C$ is the concentration of the drug in the bulk dissolution medium at time $t$.
• $h$ is the thickness of the stagnant diffusion layer.

Under physiological conditions, sink conditions are typically maintained because the drug is rapidly absorbed across the intestinal mucosa into the mesenteric circulation, meaning that the bulk concentration $C$ is much smaller than the saturation solubility ($C \ll C_s$). The equation then simplifies to:

$\frac{dC}{dt} \approx \frac{D \cdot A \cdot C_s}{h}$

Clinical and Formulation Strategies to Modify Dissolution

1. Particle Size Reduction (Micronisation): Decreasing the particle size increases the effective surface area ($A$), thereby increasing the dissolution rate. This is clinically relevant for drugs like digoxin, spironolactone, and griseofulvin, where micronisation improves bioavailability and reduces dosage requirements.
2. Solvent and Surfactant Co-administration: Surfactants (e.g., sodium lauryl sulfate, polysorbates) reduce the contact angle between the solid drug and the dissolution medium, enhancing wetting and effective surface area ($A$).
3. Increasing Saturation Solubility ($C_s$): This can be achieved by utilizing salt forms, amorphous states, or solid dispersions, which present higher thermodynamic activity.

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Ionization, pKa, and the Henderson-Hasselbalch Equation

Most therapeutic agents are organic molecules that behave as either weak acids or weak bases. Consequently, they exist in a pH-dependent equilibrium between their unionized (uncharged) and ionized (charged) forms. The relationship between the pH of the medium, the acid dissociation constant ($pK_a$) of the drug, and the ratio of ionized to unionized species is described by the Henderson-Hasselbalch equation.

For Weak Acids (e.g., Aspirin, Ibuprofen, Salicylic Acid):

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

Rearranging this to solve for the fraction or percentage of ionized drug: $\% \text{ Ionized} = \frac{10^{pH - pK_a}}{1 + 10^{pH - pK_a}} \times 100\%$

For Weak Bases (e.g., Amitriptyline, Morphine, Diazepam):

$\text{BH}^+ \rightleftharpoons \text{H}^+ + \text{B}$ $pH = pK_a + \log\left(\frac{[\text{B}]}{[\text{BH}^+]}\right) = pK_a + \log\left(\frac{[\text{Unionized}]}{[\text{Ionized}]}\right)$

Rearranging for the percentage of ionized drug: $\% \text{ Ionized} = \frac{10^{pK_a - pH}}{1 + 10^{pK_a - pH}} \times 100\%$

Worked Clinical Example: Ionization Profile of Aspirin

Consider aspirin (acetylsalicylic acid), a weak acid with a $pK_a$ of 3.5. Let us calculate its ionization state in the stomach (pH 1.5) versus the upper small intestine (pH 5.5).

• In the Stomach (pH 1.5): $1.5 = 3.5 + \log\left(\frac{[\text{Ionized}]}{[\text{Unionized}]}\right)$ $-2.0 = \log\left(\frac{[\text{Ionized}]}{[\text{Unionized}]}\right) \implies \frac{[\text{Ionized}]}{[\text{Unionized}]} = 10^{-2} = 0.01$ This means for every 1 ionized molecule, there are 100 unionized molecules. $\% \text{ Unionized} = \frac{100}{101} \times 100\% \approx 99\%$
• In the Duodenum (pH 5.5): $5.5 = 3.5 + \log\left(\frac{[\text{Ionized}]}{[\text{Unionized}]}\right)$ $2.0 = \log\left(\frac{[\text{Ionized}]}{[\text{Unionized}]}\right) \implies \frac{[\text{Ionized}]}{[\text{Unionized}]} = 10^2 = 100$ This means for every 100 ionized molecules, there is only 1 unionized molecule. $\% \text{ Ionized} = \frac{100}{101} \times 100\% \approx 99\%$

The pH-Partition Hypothesis

According to the pH-partition hypothesis, biological membranes behave as lipoidal barriers that are permeable only to the unionized, lipid-soluble form of a drug. Therefore, absorption occurs primarily when the drug is in its unionized state.

However, clinical practice often presents a paradox: although aspirin is 99% unionized in the stomach, the bulk of its absorption takes place in the small intestine. This is because the small intestine possesses an enormous surface area (microvilli) and a highly vascularized mucosal layer, which overrides the unfavorable ionization state.

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Partition Coefficient (logP) and Distribution Coefficient (logD)

Lipophilicity is a key determinant of a drug's pharmacokinetic profile, affecting its ability to cross biological barriers (like the blood-brain barrier) and its affinity for metabolic enzymes and plasma proteins.

Partition Coefficient (logP)

The partition coefficient ($P$) is the ratio of the concentration of the unionized drug in a non-polar solvent (typically 1-octanol) to its concentration in an aqueous phase at a state of equilibrium:

$P = \frac{[\text{Unionized drug}]_{\text{octanol}}}{[\text{Unionized drug}]_{\text{water}}}$

• $\log P > 0$: Lipophilic drug (prefers octanol).
• $\log P < 0$: Hydrophilic drug (prefers water).
• Optimal Range: For optimal oral absorption, a $\log P$ value between 1 and 3 is generally desired. Drugs with very high $\log P$ (e.g., $>5$) are highly lipophilic, showing poor aqueous solubility and high plasma protein binding, which limits their free concentration. Drugs with low $\log P$ (e.g., $<0$) are highly hydrophilic, exhibiting poor passive transcellular permeability.

Distribution Coefficient (logD)

Because $\log P$ only measures the partitioning of the unionized species, it does not account for ionization at physiological pH levels. The distribution coefficient ($D$) represents the ratio of the sum of the concentrations of all species (ionized + unionized) in the octanol phase to that in the aqueous phase at a specific pH:

$D = \frac{[\text{Unionized}]_{\text{octanol}} + [\text{Ionized}]_{\text{octanol}}}{[\text{Unionized}]_{\text{water}} + [\text{Ionized}]_{\text{water}}}$

For a weak acid: $\log D_{\text{acid}} = \log P - \log(1 + 10^{pH - pK_a})$

For a weak base: $\log D_{\text{base}} = \log P - \log(1 + 10^{pK_a - pH})$

At physiological pH (7.4), $\log D_{7.4}$ is the most biochemically relevant parameter for predicting in vivo permeability, volume of distribution ($V_d$), and renal clearance.

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Salt Forms and Their Clinical Significance

Approximately 50% of all small-molecule drugs are administered as salt forms. Salt selection is a critical formulation strategy used to modify solubility, dissolution rates, stability, and organoleptic properties without altering the pharmacological activity of the active pharmaceutical ingredient (API).

Mechanism of Enhanced Dissolution

When a salt of a weak acid (e.g., sodium, potassium, calcium salt) or a weak base (e.g., hydrochloride, mesylate, sulfate salt) is introduced into an aqueous environment, it dissolves and dissociates. The counterions released create a microenvironment pH around the dissolving solid core that is different from the bulk pH:

• A sodium salt of a weak acid (e.g., diclofenac sodium) will raise the microenvironment pH (making it more alkaline). This shift increases the local saturation solubility ($C_s$), accelerating the overall dissolution rate according to Noyes-Whitney, even in the acidic environment of the stomach.
• A hydrochloride salt of a weak base (e.g., metformin hydrochloride) will lower the microenvironment pH (making it more acidic), facilitating faster dissolution.

Salt Factor (S)

The Salt Factor represents the proportion of the salt form that consists of the active drug moiety. In clinical calculations, the salt factor value must be used to ensure correct dosing when switching between salt forms or free forms:

$\text{Dose of active drug} = \text{Dose of salt} \times \text{Salt Factor}$

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Clinical Practice Context and Pitfalls

Drug-Drug Interactions (Gastric pH Modification)

Weakly basic drugs require an acidic gastric pH to dissolve. The co-administration of proton pump inhibitors (PPIs, e.g., esomeprazole), $H_2$-receptor antagonists (e.g., famotidine), or antacids raises the gastric pH from ~1.5 to $>4$. This dramatic increase in pH shifts weak bases into their unionized, highly insoluble form, reducing $C_s$ and preventing dissolution.

• Clinically significant examples: Atazanavir, ketoconazole, itraconazole, and ledipasvir.
• Management: Counsel patients to take these medications with an acidic beverage (e.g., cola) or separate administration times if possible (refer to the Australian Medicines Handbook for specific drug guidelines).

Urinary Ion Trapping in Overdose

The principles of Henderson-Hasselbalch are utilized in toxicology to enhance the renal clearance of certain toxins.

• Salicylate (Aspirin) Overdose: Salicylic acid is a weak acid ($pK_a \approx 3.0$). By administering intravenous sodium bicarbonate, the urine is alkalinised (pH increased to 7.5–8.0). At this higher pH, the salicylic acid in the renal tubules becomes highly ionized ($A^-$). Because ionized species cannot cross the lipophilic tubular membrane, the drug is "trapped" in the urine and excreted, preventing reabsorption into systemic circulation.