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 & equationsHow 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 = k1x + 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 compoundPX = Partition coefficient for standard compound with substituent

Positive π value – substituent more hydrophobicNegative 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 refractionMW = molecular weightd = 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 plotTables 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,