Download Log P

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What is QSAR?
A QSAR is a mathematical relationship
between a biological activity of a molecular
system and its geometric and chemical
characteristics.
QSAR attempts to find consistent relationship
between biological activity and molecular
properties, so that these “rules” can be used
to evaluate the activity of new compounds.
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STERIC PARAMETERS
stearic features of drug markedly effect the drug receptor interactions reflecting the change
In onset and duration of biological action.eg:buprenorphine
As it is more lipophilic it enters CNS more rapidly , rapid onset and duration of action,
because of bulky substituent's it needs time to orient in favorable confirmation and bulky
substituent's also delays detachment of drug from receptor. This leads to late onset and
duration of action.
Various steric parameters in qsar are
1.Tafts steric constant
2.Molecular connectivity index
3.Sterimol
4.parachor
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Taft Equation
The Taft equation is a linear free energy relationship (LFER) used in physical organic chemistry
in the study of reaction mechanisms and in the development of quantitative structure activity
relationships for organic compounds. It was developed by Robert W. Taft in 1952 as a
modification to the Hammett equation. While the Hammett equation accounts for how field,
inductive, and resonance effects influence reaction rates, the Taft equation also describes the
steric effects of a substituent. The Taft equation is written as:
where log(ks/kCH3) is the ratio of the rate of the substituted reaction compared to the
reference reaction
σ* is the polar substituent constant that describes the field and inductive effects of the
substituent,
Es is the steric substituent constant,
ρ* is the sensitivity factor for the reaction to polar effects
δ is the sensitivity factor for the reaction to steric effects.
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Polar Substituent Constants, σ*:
Polar substituent constants describe the way a substituent will influence a reaction through
polar (inductive, field, and resonance) effects.
To determine σ* Taft studied the hydrolysis of methyl esters (RCOOMe).
The hydrolysis of esters can occur through either acid and base catalyzed mechanisms, both
of which proceed through a tetrahedral intermediate.
 In the base catalyzed mechanism the reactant goes from a neutral species to negatively
charged intermediate in the rate determining (slow) step, while in the acid catalyzed
mechanism a positively charged reactant goes to a positively charged intermediate.
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However, because of the difference in charge buildup in the rate determining steps it
was proposed that polar effects would only influence the reaction rate of the base
catalyzed reaction since a new charge was formed. He defined the polar substituent
constant σ* as:
Where
 log(ks/kCH3)B is the ratio of the rate of the base catalyzed reaction compared to
the reference reaction.
 log(ks/kCH3)A is ratio of a rate of the acid catalyzed reaction compared to the
reference reaction.
 ρ* is a reaction constant that describes the sensitivity of the reaction series.
 The factor of 1/2.48 is included to make σ* similar in magnitude to the
Hammett σ values.
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Steric Substituent Constants, Es :
Taft thus assumed that steric effects would influence both reaction mechanisms equally.
Due to this, the steric substituent constant Es was determined from solely the acid
catalyzed reaction, as this would not include polar effects. Es was defined as:
where ks is the rate of the studied reaction and kCH3 is the rate of the reference
reaction (R = methyl).
δ is a reaction constant that describes the susceptibility of a reaction series to steric
effects.
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Polar Sensitivity Factor, ρ* :
Similar to ρ values for Hammett plots, the polar sensitivity factor ρ* for Taft plots will
describe the susceptibility of a reaction series to polar effects. When the steric effects of
substituents do not significantly influence the reaction rate the Taft equation simplifies to a
form of the Hammett equation:
The polar sensitivity factor ρ* can be obtained by plotting the ratio of the measured
reaction rates (ks) compared to the reference reaction (kCH3) versus the σ* values for
the substituents.
•If ρ* > 1, the reaction accumulates negative charge in the transition state and is accelerated by electron
withdrawing groups.
•If 1 > ρ* > 0, negative charge is built up and the reaction is mildly sensitive to polar effects.
•If ρ* = 0, the reaction is not influenced by polar effects.
•If 0 > ρ* > -1, positive charge is built up and the reaction is mildly sensitive to polar effects.
•If -1 > ρ*, the reaction accumulates positive charge and is accelerated by electron donating groups.
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Molar refractivity:
proposed by pauling and pressman.
represents size and polarizibility of molecule or it is measure of both volume of
compound and how it is easily polarized.
it characterizes bulk of molecule or substituent but not shape.
MR can be measured by making use of lorentz-lorentz equation
MR= n2-1/n2+2 . MW/d
MW= molecular weight
N= index of refraction at 200 c
d=density of compound at 200 c
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THE greater the positive MR value of substituent the larger its steric or bulk effect and
substituent binds to polar surface while a negative value indicates steric hinderance at
binding site.
The use of MR terms in some ligand – enzyme interactions could be interpreted with help
of 3D structures in Qsar.
substituent
MR values
H
0.0
CH3
4.7
C2H5
9.4
C6H5
24.3
OH
1.5
NH2
4.2
SO2NH2
11.3
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Molecular connectivity index (χ):
It indicates branching index in the given structure .
MC describes molecular substructures in topological terms.
It is concept based on molecular structure but doesn’t take account of molecular
properties. Since branched isomers of molecule differ in properties with unbranched ones.
Correlation of physicochemical properties with no. of atoms and also upon arrangement of
atoms.
MCI (χ) helps to quantify the effect of size and shape on biological response.
 MCI represents substructure environment, degree of branching, unsaturation, hetero
atoms and their position and presence of cyclic structure.
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For calculation of connectivity index the structural formulae of compound is written as
skeletal formulae without hydrogen atoms which is known as hydrogen supressed graph.
Eg: dimethyl pentane.
1
1
hydrogen supressed graph.
1
3
3
2
1
2,4-dimethyl pentane
The valence no.(δi) of atoms attached to each is indicated. such valence no. of adjacent
atoms are multiplied and bond contribution is calculated by taking reciprocal square root of
product δiδj.
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Parachor:
It is a steric parameter which is defined as molar volume V which has been corrected for
forces of intermolecular attraction by multiplying with the fourth root of surface tension.
P = γ1/4 * M / d
M = molecular weight
d = density
Corections to parachor:
Pr = 0.012 Pr
if to be used for non polar compounds.
Pr = 0.012 Pr – 0.6
if to be used for compounds containing a phenolic OH or
phenolic ether function.
Pr = 0.012 Pr – 1.2
if to be used for compounds containing carbonyl, ester,
amine,nitrile,alcoholic or aliphatic ether functions.
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Minimal Steric Difference:
the most active structure that fits receptor is termed as standard (s). Then the planar
structural formulae's of other molecules are superimposed on standard neglecting small
differences between bond lengths and bond angles then the number of non-superimposable
atoms give MSD value for considered structure since it is the only portion which doesn’t
overlap.
Eg: phenyl and cyclohexyl.
Rules for calculation:
Hydrogen atoms are ignored.
A weighting factor is necessary as atoms of different rows have different vanderwaals radii.
for 2nd period atoms it is 1 (C,Me,N,O,OH etc)
for 3rd period atoms it is 1.5 (S,SH,Cl etc)
for higher period atoms it is 2 (Br,I etc)
different molecules are selected by trial and error method and select the one which yields
higher correlation coefficient for equation.
Ai= α – β(MSD)I where Ai =biological activity
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Lipophilic parameters
include partition coefficient,chromatographic parameters,π substitution constant,
chromatographic parameters.
These parameters define partitioning of compound between the aqueous and non aqueous
phase.2 parameters are commonly used to represent lipophilicity which are
partition coefficient (P): which refers to whole molecule
π substitution constant: refers to substituted groups.
partition coefficient (P): It is ratio of concentration of substance in organic and aqueous
phase under equilibrium conditions It represents drug distribution between an organic and
aqueousphase .
partition coefficient (P):
drug x octanol
P
drug x water
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For easily ionisable drug:
P = [Drug]octanol/[Drug]water * 1/ (1-α)
Where α = degree of ionisation
Generally for the determination of partition coefficient n- octanol --- water system is used
n- octanol is used because of similarity with biological cell membrane system having long
alkyl chain and polar hydroxyl groups.
Having low vapour pressure.
Uv transparent over large range of wavelengths.
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Relation between P and drug activity was given by
Log 1/c = K1 log p + K2
Log (1/C)
Linear Equation
.
.
.
.
.
.
.. .
0.78
3.82
Log P
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log 1/C = – k1 (log p)2 + k2 log p + k3
parabolic equation
Log (1/C)
Log P o
Log P
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If compound is more soluble in water then P < 1 and log p is negative.
 If compound is more soluble in octanol then P > 1 and log p is positive.
more positive log p more lipophilic .
Log p value between 0 and α called log P0 which is called Logarithm of optimum partition
coefficient.
If larger value of P the drug more interacts with lipid phase .if P reaches infinity which
means C12 micelles are formed and drug will not cross aqueous phase.
If P= 0, so water soluble cannot cross lipid phase.
Log p generally ranges between 5-9 carbon atoms.
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π substitution constant or lipophilic substitution constant or hydrophobic substitution
constant :
π is the effect of a given substituent on log p of basic skeleton.
π = log Px – PH
where Px = P of Molecule carrying substituent X.
PH= P of unsubstituted compound.
Eg: π cl = log P chlorobenzene – log P benzene
= 2.84 – 2.13 = o.71
The value of π for the compound is sum of π values of each of separate substituent's.
The π value of specific substituent varies with structural environment of substituent and
they are highly position dependent so that π is different for different positions (O,M and P).
 + ve π value indicates substituent has high lipophilicity than H and drug favours organic
phase.
 – ve π value indicates substituent has low lipophilicity than H and drug favours aqueous
phase.
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Hydrophobic Fragmentation Constant(f) :
According to the π substitution constant the value of hydrogen is zero and no difference
between π CH3 and π CH2 , but the lipophilic contribution of hydrogen atom is not zero hence
rekker suggested a new system called hydrophobic fragmentation constant(f) which is
measure of absolute lipophilicity contribution of corresponding group or substituent.
(f) For some substituents
substituent
(f) aromatic
(f) Aliphatic
H
0.175
0.175
CH3
0.702
0.702
CH2
0.530
0.530
NH2
–0.854
–1.428
COOH
–0.093
–0.954
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Example of calculation of log P
log P of benzene = 2.5 (parent compound)
fi of methyl = 0.6
fi or aromatic fluorine = -0.4
Fi for fluorine atom ortho to a methyl group is -0.3
CH3
F
log P= 2.5 + 0.6 + (-0.4) + (-0.3) = 2.4
n
n
i 1
i j
log P  log Pparent compound   fi   Fij
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Cl
Benzene
(Log P = 2.13)
Chlorobenzene
(Log P = 2.84)
pCl = 0.71
CONH2
Benzamide
(Log P = 0.64)
pCONH 2= -1.49
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Chromatographic parameters:
RM value calculated from RP-TLC as alternative lipophilic parameter in qsar.
RM= log (1/Rf - 1)
Disadvantage:
chromatographic behaviour of drug is not identical to drug partitioning in biological system.
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Hansch analysis:
Two stages of drug action was proposed based on
1.A random walk from point of administration to the site of which involves passage over
series of membranes and is therefore related to partition coefficient.
2. Attachment for the receptor site which depends on
shape of molecule hence stereochemistry of substituent groups
electron density on attachment groups.
He suggested linear and non- linear dependence of biological activity on different
parameters like π,σ and ES.
example of a linear equation where multiple variables are used to obtain a correlation with
biological activity (1/c).
1 
log   k1p  k2  k3
C 
------ linear equation
Where c is molar concentration that elicits a constant biological response

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π= lipophilic substitution constant.
σ= hammet constant.
ES = tafts steraic constant.
BA   k1p  k2 p  k3  k4
2
------ parabolic equation
Example of an extended Hansch Equation where the Taft steric parameter, Es, has been
included.
2
1
2
3
4 S
5
BA   k p  k p  k   k E  k
Practically all the parameters used in hansch analysis are linear free energy related so it is
known as linear free energy approach or extra thermodynamic approach

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Not all parameters are necessarily significant in a qsar model for biological activity. to derive
an equation following rules are formulated by hansch.
 Selection of independent variables like log p,π,σ,MR ,steric parameters should be tried
for obtaining best equation where the inter correlation coefficient should be larger than
0.6-0.7.
 All reasonable parameters must be validated by appropriate statistical procedure by
stepwise regression analysis.
Applications:
 to predict the activity of an as yet unsynthesised compound.
 To give an indication of the importance of influence of parameters on mechanism by
which drug acts.
 Applied to various problems in order to correlate the biological activity with chemical
structure.
 Hansch analysis serves as guide in future testing and synthesis of new compound and to
play roles of hydrophobic, electronic and stearic factors in drug receptor interaction.
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Advantages of Hansch analysis
A) Use of descriptors (p, , Es etc.) from small organic molecules may be applied
to biological systems.
B) Predictions are quantitative and may be evaluated statistically.
C) Quick and easy.
D) Potential extrapolation: conclusions reached may be extended to chemical
substituent's not included in the original analysis.
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Disadvantages of Hansch analysis
A) Descriptors required for substituent's being studied.
B) Large number of compounds required (training set for which physicochemical
parameters and biological activity is available).
C) Limitations associated with using small molecule descriptors, such as steric
factors, on biological systems (i.e. descriptors from physical chemistry).
D) Partial protontation of drugs at physiological conditions (can be included in
mathematical model).
E) Extrapolations beyond the values of descriptors used in the study are limited.
F) Correlation between physical descriptors. For example, the hydrophobicity will
have some correlation with the size and, thus, the Taft steric term.
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Topliss Scheme
Used to decide which substituents to use if optimising compounds one by one (where
synthesis is complex and slow)
Completely non mathematical and non statistical which doesn’t need
computerization of data.
Example: Aromatic substituents
H
4-Cl
L
4-OMe
L
M
E
E
4-CH3
L
M
E
M
3,4-Cl2
L
E
4-But
3-Cl
3-Cl
L
E
M
M
3-CF3-4-Cl
4-CF3
3-CF3-4-NO2
2,4-Cl2
3-NMe2
See Central
Branch
L
2-Cl
4-NMe2
E
M
3-Me-4-NMe2
4-NH2
3-CH3
4-NO2
3-CF3
4-NO2
3,5-Cl2
3-NO2
4-F
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Craig Plot
Craig plot shows values for 2 different physicochemical properties for various substituents
Example:
.
.
. . . ..
. .
.
.
. ..
.
.
.
.
.
.
.
.
.
+
1.0
+ -p
CF3SO 2
.75
CN
CH3SO2
SO 2NH2
NO2
.50
OCF3
.25
CO2H
-2.0
-p
-1.6
-1.2
-.8
-.4
SF5
CF3
CH3CO
CONH2
.4
I
Br
Cl
F
.8
1.2
1.6
CH3CONH
-.25
Me
2.0
+p
Et
t-Butyl
OCH3
OH
+ +p
-.50
NMe 2
NH2
-.75
- -p
-1.0
- +p
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Free-Wilson Approach
Method
•The biological activity of the parent structure is measured and compared with the
activity of analogues bearing different substituents
•An equation is derived relating biological activity to the presence or absence of
particular substituents
BA = μ + Σ aiJ
Where μ =contribution of unsubstituted compounds
Σ aiJ =contribution of substituted compounds
I
=No. of position the substituent occurs
J
=No. of substituent at that position
Activity = k1X1 + k2X2 +.…knXn + Z
•Xn is an indicator variable which is given the value 0 or 1 depending on whether the
substituent (n) is present or not
•The contribution of each substituent (n) to activity is determined by the value of kn
•Z is a constant representing the overall activity of the structures studied
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Free-Wilson Approach
Advantages
•No need for physicochemical constants or tables like π,σ etc
•Useful for structures with unusual substituents
•Useful for quantifying the biological effects of molecular features that cannot be
quantified or tabulated by the Hansch method
Disadvantages
•A large number of analogues need to be synthesised to represent each different
substituent and each different position of a substituent
•It is difficult to rationalise why specific substituents are good or bad for activity
•The effects of different substituents may not be additive
(e.g. intramolecular interactions)
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CADD METHODS:
Quantum mechanics:
It is based on assumption that electrons and all material particles exhibit wave like
properties. the mathematical approach of wave mation is applied to electrons,atomic and
molecular structure.
It is based on Schrödinger wave equation
Hψ = E ψ
E ψ= total potential and kinetic energy of all particles in the same structure.
Ψ= wave function,
H = hamiltonium operatoracting on wave function.
Applications:
Quantum mechanics calculations can be used for energy minimisation studies.
Wave function can be used to calculate a range of chemical properties like
electrondensity,dipolemoment,energies and positions of orbitals.
For calculating bond dissosciation energies,electrostatic potentials,heat of formation for
specific confirmations.
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MOLECULAR MECHANICS:
MAINly for the study of molecular modelling.
Here the position of nuclei is determined by force of attraction and repulsion operating in
that structure.
Total Potential energy of molecule is given by sum of all energies of attractive and
repulsive forces between atoms in structure.
E total = Σ Estretching +ΣEbending+ ΣEtorsion+ ΣEVdW+ ΣEcolumbic
Estretching = ½ k(r – r0)2
Ebending: ½Kθ(θ – θ0)2
r = ideal bond
r0 = standerd bond
K = force constant
θ0= ideal bond length
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Etorsion = ½ K Φ (1+ COS (m( Φ + Φ offset)
Φ = torsion angle
K Φ= energy barrier to the rotation about torsion angle Φ
m= periodicity of rotation
Φ offset = ideal torsion angle.
EVdW = ε [(rmin)12/r – 2 (rmin/r)6]
(rmin/r) 6 = represents attractive force
[(rmin)12/r = represents repulsive force.
r= actual distance between atoms.ε = energy
Ecolumbic = qiqj/Drij
qiqj= point charges on atoms I and j ,
rij = distance between atoms,
D =dielectric constant
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REFERENCE:
comprehensive medicinal chemistry --- volume 4 --- Corwin Hansch.
Principles of medicinal chemistry --- volume 1 --- Kadam.
Medicinal chemistry --- 3rd edition --- Thomas Nogrady.
Organcic chemistry of drug design and drug action --- silverman.
Medicinal chemistry --- volume 2 --- Ilango.
Molecular modeling in drug design ---Berger.
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Thank you
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