Quantitative Structure-Activity Relationships (QSAR)y Attempts to identify and quantitate physicochemical properties of a drug in relation to its biological activity or binding y Studies hydrophobic, electronic, and steric properties--either whole molecule or pieces med chemist draws up an equation that quantifies the relationship & allows one to predict (to some extent) the biological activity

Quantitative Structure-Activity Relationships (QSAR) %dv fewer compounds may need to be made ,oweverif compound does not fit the equation, then chemist knows they need to modify the equation

Log P (partition coefficient) Hydrophobicity yP = [drug] in octanol / [drug] in water Vary log P & see how this affects the biological activity. Biological activity normally expressed as 1/C, where C = [drug] required to achieve a defined level of biological activity. The more active drugs require lower concs.

Log P (partition coefficient) Hydrophobicity

Log P: Hydrophobicity

Log PParabolic curve: curve: log 1/C = - k1 (log P)2 + k2 log P + k3

When P small, dominated by log P term When P large, log P squared dominates & so activity decreases

Log P

Note that one is not always measuring biological activity, sometimes binding!

*RELATIVELY FEW DRUGS EXIST WHOSE ACTIVITY IS RELATED TO LOG P ALONE!!! --those that do are the general anesthetics--partition into cell membranes, & thereby affect membrane structure & nerve function --no specific drug-receptor interactions

Log P Values: UsesWith these equations for anesthetics (ethers only), it is possible to predict activity if log P known (doesnt work if structure very different) ether 0.98 chloroform 1.97 halothane 2.3

(anesthetic activity increases in same order) Drugs with Log P values close to 2 should be able to enter the CNS efficiently e.g. barbiturates have log P values close to 2 also; want to make sure log P value is much lower if you dont want possible CNS side effects

Example: decreased CNS side effects

P vs. TP measures drugs overall hydrophobicity & measures drugs transportability T measures the hydrophobicity of a specific region on the drug--hydrophobic bonding to a receptor

substituent hydrophobicity constant, T

T Possible to calculate the substituent hydrophobicity constant (T) A measure of how hydrophobic relative to H Measure P experimentally for a standard compound with and without a substituent (X). Use this equation: Tx = log Px - log PH

TTx = log Px - log PH H is for standard compound positive T = substituent more hydrophobic than H negative T = less hydrophobic than H

T values for various substituents on aromatic ringsCH3 t-Bu OH CONH2 CF3 Cl Br F

0.52 1.68 -0.67 -1.49

1.16 0.71 0.86 0.14

Theoretical Log P for chlorobenzene = log P for benzene + T for Cl = 2.13 + 0.71 = 2.84

T values for various substituents on aromatic ringsCH3 t-Bu OH CONH2 CF3 Cl Br F

0.52 1.68 -0.67 -1.49

1.16 0.71 0.86 0.14

Theoretical Log P for meta-chlorobenzamide = log P for benzene + T for Cl + T for CONH2 = 2.13 + 0.71 - 1.49 = 1.35

Tables of TSee Table 2.5 Many tables exist for all sorts of different structures. Note that values will be different when using different solvent systems.

MOST QSAR equations have contribution from either P or T or both

Electronic Effects: The Hammett Constant WHammett constant (1940) W Measure e-withdrawing or e-donating effects (compared to benzoic acid & how affected its ionization)

Electronic Effects: The Hammett Constant W Electron Withdrawing Groups:

Equilibrium shifts to Right & Kx > Kbenzoic Since Wx = log Kx log Kbenzoic, then W will be positive . Wx = log (Kx/Kbenzoic)

Electronic Effects: The Hammett Constant W

e-withdrawing groups stabilize the carboxylate ion: larger Kx, and have positive W values e.g. Cl, CN, CF3 e-donating groups (e.g. alkyl) equilibrium shifts left (favoring unprotonated): lower Kx and negative W values

Hammett ConstantsHammett constant takes into account both resonance and inductive effects; thus, the value depends on whether the substituent is para or meta substituted --ortho not measured due to steric effects In some positions only inductive effects effect & some both resonance & inductive effects play a part

aliphatic electronic substituent constants are also available

UsesOnly one known example where just Hammett constants effectively predict activity (insecticides, diethyl phenyl phosphates. These drugs do not have to pass into or through a cell membrane to have activity). Log (1/C) = 2.282 W 0.348

Steric Effectsy

much harder to quantitate

Examples are: y Tafts steric factor (Es) (~1956), an experimental value based on rate constants y Molar refractivity (MR)--measure of the volume occupied by an atom or group--equation includes the MW, density, and the index of refraction-y Verloop steric parameter--computer program uses bond angles, van der Waals radii, bond lengths

Putting it all togetherFor a group of antihistamines, Log (1/C) = 0.440 Es 2.204 (n=30, s=0.307, r= 0.886) Log (1/C) = 2.814 W - 0.223 (n=30, s=0.519, r= 0.629) Log (1/C) = 0.492 Es - 0.585 W- 2.445 (n=30, s= .301, r= 0.889)

Hansch Analysis Proposed that drug action could be divided into 2 stages: 1) Transport & 2) Binding Log 1/C = k1P = k2P2 + k3W + k4Es + k5

Hansch Analysis Look at size and sign for each component of the equation. Values of r