Quantitative Structure Activity
Relationship (QSAR)
Advanced Medicinal
Chemistry
(Pharm 5219):
Section A
Ref.: An Introduction to Medicinal Chemistry, 3rd ed. 2005, G.L.Patrick, Oxford University press
Drug design: QSAR as a strategy
Some – involve in a change in shape in order to have better fit for its
target binding site.
Others – involve in a change in functional group or substituent in order
to improve pharmacokinetics or binding site interactions.
These involve in synthesis of analogues with substituents on aromatic
or heteroaromatic rings or accessible functional groups.
Number of possible analogues could be infinite.
So, a need of rational approach in deciding useful substituents.
To tackle this problem,
QSAR is extremely useful.
QSAR approach
To identify and quantify physicochemical properties of a drug
To see if any property has effect on drug’s biological activity.
Then an equation is drawn up to quantify the relationship and
the role of the property in pharmacokinetics & mechanism
of action of drug.
Also predict to calculate in advance the biological activity of a
novel analogue.
Graphs & equations
A range of compounds – synthesized
Vary one physicochemical property (log P) and test biological activity (log 1/C)
Plot biological activity on y-axis and physicochemical property on x-axis
Graphs & equations
How to draw the best possible line?
Done by ‘linear regression analysis by the least square method’
Draw arbitrary lines through points, draw vertical lines from each point
Verticals – measure, square and add up to get a total (sum of squares)
Best line is one where this total is minimum.
Now, done using relevant software.
Graphs & equations
How to see whether the relationship is meaningful?
1. by observing ‘goodness of fit’
Regression or correlation coefficient (r) tells how well the equation
explains the variance in activity in terms of physicochemical
parameters (usually quoted as r2)
If r=1, a perfect fit (observed=calculated activity), impossible in reality
If r>0.9 or r2>0.8, a good fit (acceptable)
‘r2 multiplied by 100’ indicates % variation in activity accounting for
physicochemical parameters. For example, r2 = 0.85
Graphs & equations
How to see whether the relationship is meaningful?
2. by calculating ‘standard error of estimate/standard deviation (s)’
Ideally s=0, if no experimental error in experiment or parameters.
In reality, ‘s’ should be small.
Necessary to know whether ‘s’ is acceptably low.
Number of compounds (n) influences value of ‘s’.
Graphs & equations
How to see whether the relationship is meaningful?
3. by using statistical tests e.g., Fisher’s F-test
y = k 1x + k2
To assess significance of coefficients for each parameter
Normally, p values (obtained from F-test)  0.05 (to be significant)
If not, the parameter – excluded from QSAR equation.
Physicochemical properties
QSAR approach: many physical, structural and chemical properties
Most common – hydrophobic, electronic & steric properties (as possible
to quantify).
QSAR studies –
carried out on compounds of same general structure with varied
substituents on aromatic rings or functional groups.
Consider how the hydrophobic, electronic and steric properties of
substituents affect biological activity.
Hydrophobicity
Crucial to how easily a drug crosses cell membrane and also, in
receptor interactions.
Hydrophobicity character of a drug – measured experimentally by
testing relative distribution in oil-water mixture.
Hydrophobic molecules dissolve preferably in oily layer.
Hydrophilic molecules dissolve preferably in aqueous layer.
Relative distribution is known as partition coefficient (p),
p=
Conc. Of drug in oily phase
Conc. Of drug in aqueous phase
Hydrophobicity
Hydrophobic compounds – high p value
Hydrophilic compounds – low p value
Varying substituents on lead compounds produce series of analogues
with different hydrophobicity & different p values.
Plot p values vs biological activity of these analogues, see if there is
any relationship between these 2 properties.
Biological activity is expressed as 1/C, where C is conc. of drug
required to achieve a level of activity.
More active drugs achieve a biological activity at lower concentration.
Hydrophobicity
A straight line would be obtained with the equation:
An example: Binding of drugs to serum albumin is determined by
hydrophobocity. A study of 42 compounds resulted in the following
equation:
(n=42, r=0.96, s=0.159)
Serum albumin binding increases as log p increases.
Hydrophobic drugs bind more strongly to s. albumin than hydrophilic drugs
Hydrophobicity
By knowing strength of binding with s. albumin, estimate effective
dose for that drug.
When serum albumin bound, drug cannot bind to receptor & so,
dose level depends on unbound (free) drug in circulation.
The equation helps to calculate binding strength of drugs of similar
structure to s. albumin.
Also, an indication of availability of free drugs to interact receptors.
r=0.96 (close to 1), the line is a good fit.
r2 = 92%, i.e., 8% variation due to experimental error & 92% due to
difference in hydrophobicity of tested drugs.
Hydrophobicity
However, increasing hydrophobicity increases biological activity in
other ways.
Drugs – cross hydrophobic barriers (e.g., cell membranes) to reach
their targets.
- interact with a target (e.g., enzyme or receptor)
(hydrophobic)
Therefore, increasing hydrophobocity helps in crossing
hydrophobic barriers and in binding to target sites.
Hydrophobicity
However,
Increasing log p should not increase biological activity ad infinitum
Reasons…….
 Drug may become poorly soluble in aqueous phase
 Drugs may be trapped in fat deposits and never reach to
site of action
 Hydrophobic drugs are more susceptible to metabolism
and elimination
Hydrophobicity
normally,
A straight-line relationship between log p and biological activity
Because, the range of log p values are relatively narrow.
In previous serum albumin binding example…….
• Log p values in the range of 0.78 to 3.82
• If extended to include very high log p values, parabolic curve.
Hydrophobicity
Parabolic curve can be expressed by the equation:
 (log p)2 has a minus sign
 If P is small, (log p)2 is very small & equation dominated by log
p term, representing first part of the graph.
 If P is large, (log p)2 is more significant & overwhelms log p
term, representing last part of the graph where activity drops
with increasing P.
 k1, k2 & k3 are constants and determined by software program.
Hydrophobicity
Few drugs –related to log p only
Tend to operate in cell membrane (hydrophobicity is !!!!)
Example: general anesthesia
• Function by entering CNS and dissolving into cell membrane
• No specific drug-receptor interaction
• Mechanism of action solely depends on ability to enter cell
membrane (i.e., hydrophobicity)
Hydrophobicity
General anesthetic activity of a range of ethers – fit the following
parabolic equation:
Anesthetic activity increases with increasing P.
The relationship is parabolic and there is a log p0 beyond which
increasing hydrophobicity decreases anesthetic activity.
Possible to predict anesthetic activity of other compounds from
their partition coefficients.
But the equation is only for anesthetic ethers and not applicable
to other structural types of anesthetics. (drawback of QSAR)
Hydrophobicity
QSAR study of other structural types of general anesthetics – each
case a parabolic curve.
Although constants are different, optimum hydrophobicity (log p0)
– close to 2.3.
Suggesting that all general anesthetics – act in a similar fashion
(also, depend on hydrophobicity of structure)
log p value of any anesthetics gives an idea of potency.
For example, p values of ether, chloroform & halothane are 0.98,
1.97 & 2.3; activity increases in same order.
Hydrophobicity
General anesthetics –
simple M/A based on efficiency to enter CNS
So, log p value – indication of how easily a drug enters CNS
Compounds having a log p value close to 2 enter CNS efficiently
So, drugs targeted for CNS should have log p value close to 2
Accordingly, drugs targeted to act elsewhere should have log p
value different from 2 (to avoid CNS side effects e.g.,
drowsiness)
Hydrophobicity
To get P, synthesize compounds and Experimentally measure
-(a lot of work and maximum would be in vain!!)
Otherwise, calculate P theoretically and decide whether a compound
is worth synthesizing (to target most promising-looking structure)
Substituent hydrophobicity constant (π):
- calculate contribution of various substituents to hydrophobicity.
- a measure of how hydrophobic, a substituent is (w.r.t. hydrogen).
Hydrophobicity
How to calculate π?
P – measured experimentally for a standard compound (H) with &
without a substituent (X).
πX = Hydrophobicity constant for the substituent (X)
PH = Partition coefficient for the standard compound
PX = Partition coefficient for standard compound with substituent
Positive π value – substituent more hydrophobic
Negative π value – substituent less hydrophobic
Hydrophobicity
An exercise:
log p: benzene = 2.13, chlorobenzene = 2.84 & benzamide = 0.64;
calculate theoretical log p for metachlorobenzamide.
Benzene is the parent compound,
Substituent constants for Cl and CONH2 are 0.71 and -1.49 respectively.
Calculated log p is referred to as Clog p.
The observed log p for metachlorobenzamide is 1.51.
Electronic effect
Electronic effects of various substituents influence a drug’s ionization
or polarity – affect how easily a drug passes through cell
membrane or how strongly it interacts with binding site.
For substituents on aromatic rings,
Hammett substituent constant (σ): a measure
of electron-withdrawing or electron-donating ability of
substituents; determined by measuring dissociation of series
of substituted benzoic acids and comparing with dissociation
of benzoic acid itself.
Electronic effect
Benzoic acid – a weak acid, partially ionizes in water.
An equilibrium is set up between ionized and non-ionized forms.
The relative proportions of these forms = equilibrium/dissociation
constant, KH.
If substituent is present, equilibrium is affected
Electron-withdrawing groups (e.g., nitro group) shift equilibrium to
ionized form with larger K value.
Electron-donating groups (e.g., alkyl group) shift equilibrium to left with
smaller K value (weaker acid).
Electronic effect
Hammett substituent constant (σX) for a particular substituent (X)
is defined by:
(KH for benzoic acid)
Electron-withdrawing substituents on benzoic acid – larger KX;
so (+)ve σX, e.g., Cl, CN, CF3, etc.
Electron-donating substituents on benzoic acid – smaller KX;
so (-)ve σX, e.g., Me, Et, t-Bu, etc.
σX for H is zero.
Electronic effect
σX takes into account both resonance & inductive effects.
So, σX depends on whether the substituent is meta or para.
In meta position, electron-withdrawing is due to inductive effect.
In para position, it is due to both inductive & resonance effects.
Electronic effect
Most studies – consider σX & if more than 1 substituent, use ∑σ
σ – a measure of substituent’s inductive & resonance effects
With detailed studies, inductive (F) and resonance effect (R) –
considered separately
Electronic effect
Limitations to electronic constants:
σ cannot be measured for ortho substituent
very few drugs – activity is solely depended on electronic effect
Constants (σ, R & F) – only useful for aromatic substituents.
Electronic effect
Aliphatic electronic substituent constants:
Obtained by measuring rates of hydrolysis for a series of ester
Methyl ethanoate – parent ester; rate of hydrolysis varies with
substituent X.
Extent to which rate of hydrolysis is affected is a measure of
substituent’s electronic effect at site of action.
Electronic effect is purely inductive and denoted as σ1.
Electron-donating group reduces the rate and has negative
value of σ1.
Electron-withdrwing group increases the rate and has negative
value of σ1.
Steric factors
Size & shape of a drug influence how easily it approaches and
interacts with binding site.
Bulky substituent acts like a shield and hinders interaction;
alternatively, helps to orientate a drug properly for binding.
More difficult to quantify steric properties than hydrophobic
or electronic properties.
Steric factors
1. Taft’s steric factor (Es) – obtained by comparing rates of hydrolysis of
substituted aliphatic esters with standard ester under acidic
condition.
Es = log kx – log k0
kx represents rate of hydrolysis of aliphatic ester bearing substituent X
k0 represents rate of hydrolysis of reference ester.
Substituents such as H and F (smaller than methyl group) – result in a
faster rate of hydrolysis (kx>k0); so, (+)ve Es.
Substituents larger than methyl group – reduce the rate; so, (-)ve Es.
Steric factors
2. Molar refractivity (MR)
- volume occupied by an atom or group of atoms
n
= index of refraction
MW = molecular weight
d
= density
 MR is particularly significant with substituents having π electrons
or lone pair of electrons.
Steric factors
3. Verloop steric parameters
- involves computer program called Sterimol
- calculates steric substituent values from bond angles,
van der Waals radii, bond lengths and possible
conformation for substituent.
- can be measured for any substituent
For example, parameters for carboxylic acid group.
(see figure 13.10 from book)
L = length of substituent
B1 - B4 = radii of group in different dimensions
Other physicochemical parameters
Other properties – also considered
- including dipole moments, hydrogen bonding,
conformations, interatomic distance, etc.
Quantifying these properties are difficult.
Several formulae – developed based on highest occupied
and/or lowest unoccupied orbitals of test compounds.
Calculation of these orbitals –carried out using semi-empirical
quantum mechanical methods and also, indicative
variables.
Hansch equation
Biological activity of most drugs
– related to combination of physical properties.
Hansch equation – relate biological activity to most commonly
used physicochemical properties (log p, π, σ, or a steric factor)
If hydrophobicity values – limited to small range, linear equation:
If hydrophobicity values – spread over a large range, parabolic
equation:
Craig plot
Tables of π & σ factors for different substituents are available.
However, easier to visualize relative properties by considering a plot
with y-axis for σ & x-axis for π which is called Craig plot.
For example, Craig plot for para-aromatic substituents
Craig plot
 Shows no relationship between σ & π.
 Possible to tell at a glance which substituent has (+)ve or (-)ve σ or π.
 Easy to find substituent with similar σ or π value.
 Used in planning which substituent to study in QSAR.
 Hansch equation tells whether (+)ve or (-)ve σ or π values are needed
to get good biological activity, concentrate on the right quadrant on
Craig plot.
Topliss scheme
Sometimes, synthesis of large range of structure is difficult. So, few
structures are synthesized, test them for biological activity and use
these results to determine next analogues to be synthesized.
A Topliss scheme is a flow diagram which allows such a procedure to be
followed.
2 Topliss schemes:
1 for aromatic substituents, and
1 for aliphatic side chain substituents
Topliss scheme
Topliss scheme for aromatic substituents
Topliss scheme
Topliss scheme for aliphatic side chain substituents
Bioisosters
Knowledge of substituent constants - to identify bioisosters.
CN, NO2 & COMe have similar hydrophobic, electronic and steric factors
and are potential bioisoters
But groups can be bioisosters in some situations but not in others.
For example,