Quantitative Structure Activity Relationships

Introduction.

• Can the biological activity (BA) be expressed as a function of physicochemical properties derived from structure? BA = F (props). First predicted by Crum-Brown/Fraser 1868.
• Overton-Meyer hypothesis and Ferguson's thermodynamic activity can be used to predict activity of structurally non-specific drugs like anesthetics.
• Other physicochemical parameters are required to model drugs which interact with receptors. Directed lead modification requires 'substituent constants', parameters which can be used to predict properties of compounds before they are synthesized.

Hammett sigma constants.

• Louis Hammett, 1933, observed rates of aminolysis of aromatic esters were directly proportional to ionization constants of corresponding carboxylic acids. Reaction rates and equilibrium constants are both related to free energy changes - linear free energy relationship.
• Derivation of the Hammett equation: for a reaction with a linear free energy relationship
  log k = rho log K + c; log (k_X/k_H) = rho.log (K_X/K_H)
• Substituent constant, sigma = log (K_X/K_H), derived from a standard reference reaction (ionization of the acid in water), can  be used to extrapolate the effect of the substituent to other systems.
• Reaction constant can be determined using a few derivatives, and then reaction rates predicted for other derivatives for which the value of sigma is known. Magnitude and sign of rho can give information on reaction mechanism.

Hansch.

• 1951 tried to relate biological activity (log (1/C) to sigma, but without much success.
• Form of the Hammett equation used to relate biological activity to partition coefficient:
  log (1/C) = k₁logP + k₂.
• Parabolic relationship is more usual, works for structurally non-specific drugs, reasonable representation of pharmacokinetic phase.
• Add term in sigma to represent receptor interaction (very limited representation of pharmacodynamic phase):
  log (1/C) = -k₁(logP)² + k₂logP + k₃sigma + k₄

Determination of logP.

• Experiment determination using 1-octanol/aqueous buffer, requires compound.
• Lipophilicity substituent constants, pi, can be determined in the same way as sigma, and used to predict logP.
• Substituent constants are additive, but may be constitutive (require correction factors for certain types of molecular environment).