Notes on Log P and Log D in Pharmacology

PKA (874) and PHRM 6201: Physical Pharmacy - Week 10 Notes

Organic compounds distribute between two immiscible liquid phases:
- Examples: Organic solvent vs. water, Oil vs. water.
Distribution reaches equilibrium:
- A solute is soluble in both phases and distributes (partitions) according to the chemical potential in each phase:
  C1 imes P = C2

Partitioning between 1-Octanol and water:
- 1-Octanol serves as the organic phase mimicking lipid membranes.
- Note: 1-Octanol has both polar and non-polar regions. Lipophilic properties mimic cell membranes.

Defined as the ratio of solute concentrations in 1-Octanol and water phases at equilibrium:
- Log P = Log rac{C{octanol}}{C{water}}
- Indicator of an organic compound's lipophilicity:
- Higher log P = More lipophilic.
- Lower log P = More hydrophilic.
Relation to pharmacological and biopharmaceutic properties:
- Lipophilicity is dependent on drug structures.

Log D accounts for both ionized and non-ionized forms in the system;
- Lipophilicity and biological effectiveness of quinine derivatives are correlated with Log D. Optimal activity is noted at intermediate log D.
Observations:
- Too hydrophilic results in poor membrane permeability and less access to parasite sites.
- Too lipophilic can lead to poor aqueous solubility and potential nonspecific binding.
- Physiological pH significantly affects lipophilicity.

Regression analysis on relationship between log D and efficacy:
- Equation: y = -0.6007x + 2.0021, with R^2 = 0.7755, P < 0.01.
- Data range indicates concentrations of benzoic acid in both aqueous and organic phases.

Emulsion preparation:
- Mixing oil and water (buffer solution) with high shear stirring stabilized by surfactants.
- Lipophilic drugs partition into oil droplets increasing overall solubility.

Molecules in the organic phase must be in monomeric form; dimers or trimers are not viable for partitioning.
Concentration relationships in octanol phase and aqueous phase:
- For weak electrolytes, only non-ionized forms can partition into the aqueous phase.

Certain polar compounds self-associate reducing polarity.
- Concentrations in the octanol phase must reflect those of monomers to maintain log P.

Distribution of benzoic acid in benzene and buffer at 25°C, considerations of dimer formation in the organic phase.
- Summary of concentration data illustrating the relationship between concentrations in both phases.

Example of extraction using 11 grams of benzoic acid (pKa = 4.2) in 0.1 N HCl:
- Equilibrium calculations in the presence of an organic solvent with presumed log P.

The necessity for non-ionized forms to partition into octanol phase is emphasized in acidic and basic drugs.
- The presence of both ionized and non-ionized forms alters the degree of partitioning.

Distribution coefficient (D) expressed as log D:
- Log D incorporates effective lipophilicity at given pH and the degree of ionization.
Relationships:
- D = rac{[HA]{octanol}}{[HA]{water}} + rac{[A^-]{water}}{[B]{octanol} + [BH^+]_{water}}
- Log D influences the efficacy of acidic and basic drugs at varying pHs, providing a practical understanding of drug behavior in physiological contexts.

Fundamental relationships outlined for calculating changes in log D:
- For acidic drugs:
- log D = log P - log(1 + 10^{(pH - pKa)})
- For basic drugs:
- log D = log P - log(1 + 10^{(pKa - pH)})
Effect of pH on ionization, demonstrating its impact.

Calculation of Log D for given drugs at specific pH values (Diclofenac and Desipramine) using provided Data.

Analysis of drugs based on partitioning coefficients and pKa values to predict the highest human milk to plasma concentration ratio.