Quantitative Structure-Activity Relationships (QSAR)

 Attempts to identify and quantitate physicochemical properties of a drug in relation to its biological activity or binding

  Studies hydrophobic, electronic, and steric properties--either whole molecule or pieces

med chemist draws up an equation that quantifies the med chemist draws up an equation that quantifies the relationship & allows one to predict (to some extent) relationship & allows one to predict (to some extent) the biological activitythe 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

P = [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 The more active drugs require lower concs. more active drugs require lower concs.

Log P (partition coefficient)

Hydrophobicity• Plot log 1/C vs. log P•  • Typically over a small range of log P, e.g. 1-4, a

straight line is obtained  e.ge.g. log 1/C = 0.75 log P + 2.30. log 1/C = 0.75 log P + 2.30

• If graph is extended to very high log P values, then get a parabolic curve. Reasons:

 poorly soluble in aqueous phase   trapped in fat depots• more susceptible to metabolism

Log P: Hydrophobicity

Log P

Parabolic curveParabolic 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: Uses

With these equations for anesthetics (ethers only), it is possible to predict activity if log P known (doesn’t work if structure very different)

ether chloroform halothane

0.98 1.97 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 don’t want possible CNS side effects

Example: decreased CNS side effects

P vs.  •P measures drug’s overall hydrophobicity & measures drug’s transportability

measures the hydrophobicity of a specific region on the drug--hydrophobic bonding to a receptor

substituent hydrophobicity constant, substituent hydrophobicity constant,

• Possible to calculate the substituent hydrophobicity constant ()

• A measure of how hydrophobic relative to H

• Measure P experimentally for a standard compound with and without a substituent (X). Use this equation:

•  

x = log Px - log PH

x = log Px - log PH

•H is for standard compound

•positive = substituent more hydrophobic than H

•negative = less hydrophobic than H

values for various substituents on aromatic rings

CH3 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 + for Cl

= 2.13 + 0.71 = 2.84

values for various substituents on aromatic rings

CH3 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 + for Cl + for CONH2

= 2.13 + 0.71 - 1.49 = 1.35= 1.35

Tables of

•See 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 MOST QSAR equations have contribution from either P or either P or or both or both

Electronic Effects: The Hammett Constant

Hammett constant (1940) Measure e-withdrawing or e-donating effects (compared to benzoic acid & how affected its ionization) 

Electronic Effects: The Hammett Constant

Electron Withdrawing Groups:

Equilibrium shifts Right & Kx > Kbenzoic

Since x = log Kx – log Kbenzoic, then will be positive .

x = log (Kx/Kbenzoic)

Electronic Effects: The Hammett Constant

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

Hammett Constants

Hammett constant takes into account both takes into account both resonance and resonance and inductiveinductive effects; thus, the value depends on whether the effects; thus, the value depends on whether the substituent is substituent is para or metapara or meta substituted 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

Uses

Only 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 – 0.348

Steric Effects

        much harder to quantitate

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

Putting it all together

For 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 - 0.223 (n=30, s=0.519, r= 0.629)

Log (1/C) = 0.492 Es - 0.585 - 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 + k3 + k4Es + k5

Hansch Analysis

• Look at size and sign for each component of the equation.

• Values of r <<0.9 indicate equation not reliable

• Accuracy depends on using enough analogs, accuracy of data, & choice of parameters.

Craig Plots

• Plots of one parameter against another.

• For example, vs.

• Used to quickly decide which analogs to synthesize if the Hansch equation is known.

Hansch equations

log 1/C = 1.22 – 1.59 + 7.89 (n=22; s=0.238; r= 0.918

log 1/C = 0.398 + 1.089 + 1.03 Es + 4.541 (n=9; r= 0.955)

log Cb = 0.765 = 0.540 2 + 1.505

log 1/c = 1.78 – 0.12 + 1.674