Quantitative Structure Activity Relationship
• Change
in physico-chemical properties will affect the ADME
• QSAR
approach help in deciding which substituents to be used
• Identify
and quantify the physic-chemical properties which can influence the drug action
• Derive
a mathematical equation
• It
allows the medicinal chemist for some level of prediction
• Has
two advantages- shortlist the compounds
• If
analogue is not fitting the equation, implies that some other feature is
important
• What
are physic-chemical features?
• Refers
to any structural, physical or chemical property of a drug
• Any
drug will have infinite properties to calculate
• Difficult
task to quantify and relate them to biological activity
• Simple
and more practical approach is to consider one or two physico-chemical
properties
• Its
not possible always
• Simple
example for LogP vs Log(1/C)
• Draw
the best possible line through the data points on the graph
• Linear
regression analysis by the least squares method
• If
we draw a line through a set of data points, most of the points will be
scattered on either side of the line
• Best
line will be the one closest to the data points
• To
measure how close the data points are, vertical lines are drawn from each point
• Verticals
are measured and then squared in order to eliminate the negative values
• Squares
are then added up to give a total
• Best
line through the points will be the line where this total is a minimum
• Equation
of the straight line will be y = k1x + k2 where k1 and k2
are constants
• For
a perfect fit, r^{2} = 1. Good fits generally have r^{2} values
of 0.95 or above
Physicochemical properties
• Many
physical, structural, and chemical properties which have been studied by the
QSAR approach
• Most
commonly studied are hydrophobic, electronic, and steric
• Possible
to quantify easily
• Hydrophobic
properties can be easily quantified for complete molecules or for individual
substituents
• Electronic
and steric properties are more difficult to quantify, and
• Quantification
is only really feasible for individual substituents
Hydrophobicity
• Hydrophobic
character of a drug is crucial to how easily it crosses cell membranes
• May
also be important in receptor interactions
• Changing
substituents on a drug may well have significant effects on its hydrophobic
character and hence its biological activity
• Partition
coefficient (P)
• Hydrophobic
character of a drug can be measured experimentally by testing the drug’s
relative distribution in an octanol/water mixture
• Hydrophobic
molecules will prefer to dissolve in the octanol layer
• Hydrophilic
molecules will prefer the aqueous layer
• Relative
distribution is known as the partition coefficient
• Hydrophobic
compounds will have a high P value
• Hydrophilic
compounds will have a low P value
• Varying
substituents on the lead compound will produce a series of analogues having
different hydrophobicities and therefore different P values
• Plotting
these P values against the biological activity of these drugs
• Possible
to see if there is any relationship between the two properties
• Biological
activity is normally expressed as 1/C
• where
C is the concentration of drug required to achieve a defined level of
biological activity
• Reciprocal
of the concentration (1/C) is used, since more active drugs will achieve a
defined biological activity at lower concentration
• Graph
is drawn by plotting log (1/C) versus log P
• Relationship
between hydrophobicity and biological activity
• Binding
of drugs to serum albumin is determined by their hydrophobicity
• Equation
shows that serum albumin binding increases as log P increases
• Hydrophobic
drugs bind more strongly to serum albumin than hydrophilic drugs
• Knowing
how strongly a drug binds to serum albumin can be important in estimating
effective dose levels for that drug
• When
bound to serum albumin, the drug cannot bind to its receptor
• Straight-line
relationship between logP and biological activity is observed in many QSAR
studies
• General
anaesthetics have a simple mechanism of action based on the efficiency with
which they enter the central nervous system (CNS)
• Most
potent barbiturates for sedative and hypnotic activity are found to have logP
values close to 2
• Drugs
which are to be targeted for the CNS should have a log P value of
approximately 2
• Drugs
which are designed to act elsewhere in the body should have logP values
significantly different from 2 in order to avoid possible CNS side-effects
• Cardiotonic
agent is producing bright visions in some patients, entering CNS
• log
P value of the drug was 2.59
• 4-OMe
group was replaced with a 4-S(O)Me group
• Particular
group is approximately the same size as the methoxy group, but more hydrophilic
• logP
value of the new drug (sulmazole) was found to be 1.17
Hydrophobicity
constant (Π)
• hydrophobicity
of a compound can be quantified by using the partition coefficient P
• It
would be much better if we could calculate P theoretically and decide in
advance whether the compound is worth synthesizing
• QSAR
would then allow us to target the most promising looking structures
• For
example, planning to synthesize a range of barbiturate structures
• calculate
log P values for them all and concentrate on the structures which had logP
values closest to the optimum logP0 value for barbiturates
• partition
coefficients can be calculated by knowing the contribution that various
substituents make to hydrophobicity
• contribution
is known as the substituent hydrophobicity constant (Π)
• measure
of how hydrophobic a substituent is, relative to hydrogen
• Partition
coefficients are measured experimentally for a standard compound with and
without a substituent (X)
• hydrophobicity
constant (Π_{X}) for the substituent (X) is then obtained using the
following equation
• P_{H}
is the partition coefficient for the standard compound, and Px is the partition
coefficient for the standard compound with the substituent
• positive
value indicates that the substituent is more hydrophobic than hydrogen
• negative
value indicates that the substituent is less hydrophobic
• can
be used to calculate how the partition coefficient of a drug would be affected
by adding these substituents
• consider
the log P values for benzene (log P = 2.13), Chlorobenzene (logP = 2.84), and
benzamide (logP = 0.64)
• benzene
is the parent compound, the substituent constants for Cl and CONH_{2}
are 0.71 and —1.49
• it
is now possible to calculate the theoretical logP value for
meta-chlorobenzamide and observed is 1.51
• It
should be noted that TT values for aromatic substituents are different from
those used for aliphatic substituents
• accurate
only for the structures from which they were derived
P vs Π
• Both
are not exactly equivalent
• different
equations would be obtained with different constants
• partition
coefficient P is a measure of the drug’s overall hydrophobicity
• Π factor measures the
hydrophobicity of a specific region on the drug’s skeleton
• Most
QSAR equations will have a contribution from P or from TT or from both
• study
on antimalarial drugs showed very little relationship between antimalarial
activity and hydrophobic character
• these
drugs are acting in red blood cells
Electronic
effects
• electronic
effects of various substituents will clearly have an effect on a drug’s
ionization or polarity
• In
turn may have an effect on how easily a drug can pass through cell membranes or
how strongly it can bind to a receptor
• measure
used is known as the Hammett substitution constant which is given the symbol σ
• measure
of the electron withdrawing or electron donating ability of a substituent and
has been determined by measuring the dissociation of a series of substituted
benzoic acids compared to the dissociation of benzoic acid itself
Hammett substitution constant (σ)
• Benzoic
acid is a weak acid and only partially ionizes in water
• When
a substituent is present on the aromatic ring, this equilibrium is affected
• Electron
donating and electron withdrawing substituents
• If
the substituent X is an electron donating group such as an alkyl group, then
the aromatic ring is less able to stabilize the carboxylate ion
• equilibrium
shifts to the left and a weaker acid is obtained with a smaller Kx value
• Hammett substituent constant for a
particular substituent (X) is defined by the following equation
• Value
of σ x for an electron donating substituent will be negative
• Hammett
substituent constant for H will be zero
• Hammett
constant takes into account both resonance and inductive effects
• value
of σ for a particular substituent will depend on whether the substituent is meta
or para
• Indicated
by the subscript m or p after the a symbol
• For
example, the nitro substituent has σp = 0.78 and σm = 0.71
• At
the para position inductive and resonance both play a part and so the σp
value is greater
• At
the meta position, the influence is inductive and electron withdrawing
• At
the para position, the electron donating influence due to resonance is
more significant
• Tables
of constants are available which quantify a substituent’s inductive effect (F)
and its resonance effect (R)
• There
are limitations to the electronic constants
• Hammett
Substituent Constants cannot be measured for ortho substituents
• Substituents
have an important steric, as well as electronic, effect
• Above
all is only suitable for drugs containing aromatic rings
• A
series of aliphatic electronic substituent constants are available
• Obtained
by measuring the rates of hydrolysis for a series of aliphatic esters
• Methyl
ethanoate is the parent ester and it is found that the rate of hydrolysis is
affected by the substituent X
• Electronic
effect is purely inductive
• Electron
donating groups reduce the rate of hydrolysis and have negative values
• Electron
withdrawing groups increase the rate of hydrolysis and have positive values
• Values
for methyl, ethyl, and propyl are —0.04, —0.07, and -0.36 respectively
• Values
for NMe_{3}^{+} and CN are 0.93 and 0.53 respectively
• Inductive
effect is not the only factor affecting the rate of hydrolysis
• May
also have steric effect
• Bulky
substituent may ‘shield’ the ester from attack and lower the rate of hydrolysis
Steric factors
• For
a drug to interact with an enzyme or a receptor, it has to approach, then bind
to a binding site
• Bulk,
size, and shape of the drug may have an influence on this process
• Bulky
substituent may act like a shield and hinder the ideal interaction between drug
and receptor
• Alternatively,
a bulky substituent may help to orientate a drug properly for maximum receptor
binding and increase activity
• Quantifying
steric properties is more difficult than quantifying hydrophobic or electronic
properties
Taft’s steric factor (E_{s})
• Highly
unlikely that a drug’s biological activity will be affected by steric factors
alone
• Attempts
have been made to quantify the steric features of substituents by using Taft’s
steric factor
• Number
of substituents which can be studied by this method is restricted
• Can
be calculated similar to Electronic effects
Molar refractivity (MR)
• Measure
of the volume occupied by an atom or group of atoms
• Obtained
from the following equation
• n
is the index of refraction,
• M
W is the molecular weight, and
• d
is the density.
• Term
MW/d defines a volume, while the (n^{2} — l)/(n^{2}
+ 2) term provides a correction factor by defining how easily the substituent
can be polarized
Verloop steric parameter
• Measuring
the steric factor involves a computer programme called STERIMOL
• Calculates
steric substituent values from standard bond angles, van der Waals radii, bond
lengths, and possible conformations for the substituent
• Can
be measured for any substituent
Key points
Hydrophobicity |
Hydrophobic compounds have high P value and Hydrophilic compounds have low P value Hydrophobicity constant (Π)- Positive value- hydrophobic; negative value- hydrophilic |
Electronic effects |
Hammett substitution constant (σ) Aromatic compounds- electron withdrawing groups- positive Aromatic compounds- electron donating groups- negative Both resonance and inductive effect is considered Cannot be measured for ortho substituents |
Steric factors |
Taft’s steric factor (E_{s}) Molar refractivity Verloop steric parameter |
Hansch analysis
• If
biological activity is related to one property, simple equation be drawn up
• Biological
activity of most drugs is related to a combination of physicochemical
properties
• Hansch
equations- relate biological activity to the most commonly used physicochemical
properties
• If
the range of hydrophobicity values is limited to a small range then the
equation will be linear as follows
• If
the P values are spread over a large range then the equation will be parabolic
for the same reasons
• Constants
k1-k5 are determined by computer in order to get the best fitting line
• Not
all the parameters will necessarily be significant
• For
example, the adrenergic blocking activity of β-halo-(β-arylamines)
was related to Π and a and did not include a steric factor
• Equation
tells us that biological activity increases if the substituents have a positive
Π value and a negative σ value
• Substituents
should be hydrophobic and electron donating
• For
example, a series of 102 phenanthrene aminocarbinols were tested for
antimalarial activity and found to fit the following equation
• Equation
tells us that antimalarial activity increases very slightly as the
hydrophobicity of the molecule (P) increases
• Constant
of 0.14 is low and shows that the increase is slight
• (logP)^{2}
term shows that there is an optimum P value for activity
• Also
shows that activity increases significantly if hydrophobic substituents are
present on ring X and in particular on ring Y
• Could
be taken to imply that some form of hydrophobic interaction is involved at
these sites
• Electron
withdrawing substituents on both rings are also beneficial to activity, more so
on ring Y than ring X.
• It
is important to choose the substituents carefully to ensure that the change in
biological activity can be attributed to a particular parameter
• For
example, drugs which contain an amine group
• Most
common reaction is N-alkylation
• If
activity increases with the chain length of the substituent, is it due to
increasing hydrophobicity or to increasing size or to both?
• Π and MR are not related much here
and suitable for varied substituents
What are descriptors?
Includes
molecular weight,
Lipophilicity
Hydrogen
bonding donors & acceptors
Molecular
connectivity
Molecular
topology
Molecular
geometry
Stereochemistry
Good
descriptors should characterize molecular properties important for molecular
interactions
Literature
suggests that more than 2000 molecular descriptors can be calculated
QSAR
• Success of any QSAR model greatly depends on the
a) choice of molecular descriptors and
b) ability to generate the appropriate
mathematical relationship between the descriptors and the biological activity
of interest