Physico-chemical properties which influence drugs' activity
Solubilities, lipophilicity, hydrophobicity
Water solubility
●needed for dissolution of a drug from a solid drug form to the gastrointestinal tract (GIT)
content, for transport of a drug (d.) by body liquids
●a small solubility suffices for oral administration; a saturated solution of d. is generated in
GIT, a compound is continually absorbed through the mucose layer and the dissolution
continues until d. is completely absorbed (there are 2 dynamic equilicbria: drug form – GIT
liquid; GIT liquid – mucose (→ blood plasma))
●similarly for intramuscular (i.m.) and subcutaneous (s.c.) administration because of gradual
liberation from a “pool” in a muscle or under the skin which is generated by means of such
administration
●intravenous (i.v.) administration however needs satisfactory water solubility (therefore
preparation of salts, hydrophilic prodrugs, incorporation into β-cyclodextrine cavity, cocrystals,
molecular complexes etc.)
●solubility expressed i.g. in g/100 ml water, g/l water, mmol/l water etc. (but do not commute
for concentration – solubility is mostly the amount of a compound in some volume of a pure
solvent, but read your particular resource carefully); for comparative exactly defined
expressing see the Pharmacopoeia (e.g. PhEur 6).
© Oldřich Farsa 2011
Solubility in lipids
●needed for permeation of d. through barriers of the organism
●hydrophobic interactions are also involved in binding of a d. molecule to a receptor or enzyme
active site
●absolute solubility in lipids or a lipophilic solvent is rarely determined; it can have some
processing meaning in pharmaceutics (e. g. salicylic acid is practically insoluble in petrolatum,
castor oil can be used for its solubilization)
●(hydro)lipofilicity or hydrofobicity much often expressed
Lipophilicity or hydrophobicity of a compound
●nearly synonyms
●express “affinity” of d. to aqueous or lipidic phase on their interface
●quantification of lipophilicity: most commonly partition coefficient P, mostly often as log P
to eliminate a difference of several orders among values of particular d.
W
L
c
c
P =
CL
, Cw
– equilibrium concentrations in lipidic and water phase respectively; lipids
are in most substituted with some suitable organic solvent
●commonly used systems: octanol/water (octanol mimics properties of biological
membranes), most often in pharmacy or medicinal chemistry respectively; for acids
and bases usually set pH of aquaeous phase (strong acid or base, buffer)
●procedure of determination: shaking in dividing funnel or other suitable vessel
ideally until equilibrium (necessary to repeatedly determine) but in most only for
limited preliminarily estimated time; then log P´ (= apparent partition coefficient );
ratio of volumes of both phases has to be choiced in order that the concentration in
one of phases can be determined by means of a selected analytical method
●non-dissociated form of dissociable compounds is the most lipophilic one (see
further)
Examples of influence of lipophilicity on penetration of a d. through organism barriers
●blood-brain barrier (BBB): log Po/w
in range 1.5 to 2.7 with a maximum at 2.1 is optimal
for penetration of d. by passive diffusion
Blood-brain barrier (a section through a
brain capillary)
Buccal, intestinal and skin barriers
Comparison of structure of the skin, oral cavity mucosa and small intestine mucosa
●the skin and buccal mucosa are covered by a stratified squamous epithelium, whereas the
surface of the small intestine consists of a simple columnar epithelium
●oral cavity mucosa is keratinized in some places whereas the skin everywhere (stratum
corneum); permeation through the keratinized layer demands increased lipophilicity
Transport ways of d. through the buccal mucosa in comparison with the small intestine mucosa
small intestine buccal mucosa
●comparatively hydrophilic compounds penetrate through the paracellular way
whereas hydrophobic ones prefer transcellular way; increased lipophilicity is needed
for penetration through the buccal mucosa
Examples of drugs spontaneously penetrating through the skin barrier into the blood circulation
O
O
O
O2
N
NO2
O2
N CH3
OH
OH
H
H
H
OH
O
O
O
N
CH3
H
H
H
H
N
CH3
N
CH3
N
O
N
glycerol trinitrate
log P = 1.62
- also buccaly
Nitroglycerin-Slovakofarma orm tbl buc
oestradiol
log P = 4.01
Climara drm emp tdr
scopolamine
log P = 0.98
nicotine
log P = 1.17
Nicopatch drm emp tdr
- also buccaly (chewing gums)
phentanyl
log P = 4.05
Durogesic drm emp tdr
- also buccaly
Effentora orm tbl buc
Acidobasic properties
● many d. are weak acids or bases
● strength of an acid or a base is quantified by dissociation constant Ka
or Kb
respectively, negative logarithms pK = -log K (= “dissociation exponents”) are
often used
For acids
)(
10
][
][
][
][
log
][
][
log
][
][
log]log[log
][
]][[
apKpH
a
a
aa
a
HA
A
pKpH
HA
A
HA
A
pHpK
HA
A
HKpK
HA
AH
K
−
−
−
−
−
+
−+
=
−=
−=
−−=−=
=
HA H
+
A+
Henderson-Hasselbach equation
thus for the ratio of dissociated and non-dissociated form can be written
An example: ibuprophene in blood plasma
pKa
= 4,91 pH = 7,4
%68.999968.0
03.310
03.309
1:03.30903.3091010
][
][ 49.2)91.44.7(
==⇒⇒=== −
−
HA
A
For bases
pH
B
BH
pK
H
B
BH
HB
BH
pK
HB
BH
K
b
b
b
−−=
−−−=−−=
=
+
+
+
+
+
+
+
][
][
log
])log[0(
][
][
log
][
1
log
][
][
log
]][[
][
B H
+
BH
+
+
Henderson-Hasselbach equation
●pKa
s of the conjugated acids are often presented in bases, the equation is valid for them
14=+ ba pKpK
●then the higher pKa
the stronger base
●then ratio (fraction) of dissociated and non-dissociated form is defined
An example – calculation of fraction of dissociated form of morphine in stomach
pH =1
pKa
=7.87
)(
10
][
][ pHpKa
B
BH −
+
=
%:
[B]
][BH )(
9999865.99999999865.0
413.7413103
413.7413102
1413.7413102413.741310210 187.7
==⇒⇒== −
+
Relationship between dissociation and lipophilicity
●the most lipophilic form is the non-dissociated one
●compouns cross barriers including GIT mucosa best in the most lipophilic form
●
⇒ acids are preferably absorbed from acid medium of stomach, bases from basic
medium of the small intestine
●distribution coefficient D, more often log D, is log P at given pH thus it
characterizes a d. from points of view of lipophilicity and acidobasic properties
together
An example - ciprophloxacine
logD -1.80 pH 1
logD -1.79 pH 2
logD -1.78 pH 3
logD -1.75 pH 4
logD -1.54 pH 5
logD -1.07 pH 6
logD -0.85 pH 7
logD -0.95 pH 8
logD -1.47 pH 9
logD -2.14 pH 10
N
O
N
F
OH
O
NH
QSAR = QUANTITATIVE STRUCTURE – ACTIVITY
RELATIONSHIPS
We are searching for a relationship where a quantified biological activity is a function of structure or
parameters which are connected with structure respectively
A= f (structure)
2 basic approaches of classical QSAR
●regression analysis – searches for a mathematical description of the function in most using linear or other
regression
●empirical methods – search only for extremes (maxima or minima) of a given function without recognizing
of its mathematical description thus the function remains a “black box”
Regression analysis
searches for an equation in form A = a0
+ a1
x1
+ a2
x2
+…an
xn
,
where A is a quantified biological activity, x are parameters or descriptors derived from compounds´
structure, a , b are regression coefficients (a0
…absolute term) acquired by calculation. In case of so called
Hansch method, x are physico-chemical descriptors derived from the structure, in case of so called FreeWilson
approach x parameters express simple presence or non-presence of a particular substituent or
structural fragment in the molecule.
Hansch method of regression analysis
A = a0
+ a1
x1
+ a2
x2
+…an
xn
A … a quantified biological activity, often in reciprocal or in logarithm in order to get linearity of equation
Examples:
●1/MIC … reciprocal minimal inhibition concentration in antimicrobial compounds
● log ED50
... logarithm of a dose which causes a desired effect in 50 % of testing subjects
● log LD50
... a parameter of acute toxicity; logarithm of a dose which causes death in 50 % of testing
animals
●IC50
… a concentration of studied compound which lowers enzyme activity to its 50%
●log BB … express the ability of a compound cross the blood-brain barrier
● … etc.
a1
... an
... regression coefficients i.e. coefficients acquired by calculation using e.g. linear regression
“Classical” parameters x1
... xn
●hydrophobic
●electronic
●steric
a) Hydrophobic parameters – in an equation often in square – they express ratio of solubility of a
compound in lipids and in water; they often fundamentally impact compound activity particularly penetration
through barrier systems of an organism e.g. log P(octanol/water), log P(cyclohexane/water) etc.,
parameter Rm from partition thin layer chromatography (TLC) on so called reversed phase (stacionary phase
is lipophilic, mobile phase hydrophilic):
further logarithm of capacity factor log k´ from gas chromatography (GC) or reversed phase highperformance
liquid chromatography (RP-HPLC)
where tr is retention time of a studied compound and and t0 so called dead time of a column i.e. retention
time of a compound which is not retained at the column (e.g. sodium nitrite is used in RP-HPLC on
octadecylated silica gel)
Rm=log
1
Rf
−1 ,
log k ´=log
tr−t0
t0
,
further (Hansch) lipofilicity parameter π − for series of compounds which contain various substituents on
the same structural fragment (mostly often benzene ring)
where PX
is partition coefficient of the substituted compound and PH
partition coefficient of the unsubstituted
one.
Calculated hydrophobic parameters
Except experimentally determined hydrophobic parameters are recently used estimations of such
parameters acquired by means of calculations according to various algorithms. Among them, probably
procedures for estimation of log P (octanol/water) by means of sum of log P increments belong to the
simpliest ones, e.g. the formula of Rekker and Nyss
where fi
called the fragment constant is log P of the particular fragment and ai
je is the count of occurrence
of such fragment,
=log
PX
PH
=log PX −log PH
log P=∑
i
ai f i ,
or more precious estimation according to Hansch (and Leo) defined by formula
where fi
is the fragment constant, fj
is the correction factor which tries to respect the placement of a particular
fragment in a moleule and its neighborhood and ai
and bj
are counts of occurrence of a given parameter.
However, much more complex procedures are recently used. They need computers and suitable software
which in most enables also optimization of structure by means of molecular mechanics methods and
calculations of some additional parameters for QSAR calculations (for PC e.q. Molgen, HyperChem). The
conformity of calculated log P estimation with experimentally determined value is very different for various
computing algorithms although a linear relationship between experimental and computed values suffices in
many cases.
logP=∑
i
ai f i∑
j
bj f j ,
An example of a QSAR relationship with a hydrophobic parameter only
Effect of some phenols as apoptose inductors in cancer cells
Hansch, C. et al.: Bioorg. Med. Chem. 11, 617 (2003)
log 1/C = 0,67(±0,21)ClogP + 0.37(±0.63)
n = 8, r2
= 0,910, s = 0,201, q2
= 0,863
OH
OH
CH3
HH
H
estradiol (1)
CH3
CH3
OH
OH
diethylstilbestrol (8)
b) Electronic parameters
-directly or indirectly linked with the electronic coat of a particular molecule
●
Hammet constants σ - for m- a p-substituted benzene; they express electron-donor (+M, +I) or
elektron-accepting (-M, -I) properties of a substituent; derived constants: σm
, σi
, σ∗
, similar SwainLupton
constants ℱ, ℜ
●
parameters from spectra and other physical measurements – chemical shifts δ from NMR,
wavelength of absorbtion maximum λmax
from UV-VIS spectra, wavemumber ν of a significant
absorption band in IR spectra, half-wave potential E1/2
from polarography etc.; values must be
significantly different for every member of a studied series
● calculated electronic parameters: polarity, polarizability, partial charge at a particular atom etc.
c) Steric parameters
- express “overall bulkiness” of a molecule or preferably of a particular substituent on a common
skeleton
●van der Waals radii vF
●Taft steric constant Es
derived by means of rate constants of alkanoic acids esters hydrolysis
where kx
is the rate constant of hydrolysis of an ester of a particular alkanoic acid RCOOR´ and kh
obdobná the same constant for the corresponding acetic acid ester CH3
COOR´- a standard. Es
is not a
purely steric parameter because it partially includes also electronic influnce (+I).
Es
(CH3
) = 0, for more bulky substituents Es
< 0, for less bulky ones Es
> 0
Es=log
kx
kh
,
● Verloop steric parameters
– for particular substituents
– derived (measured) from computed molecule geometry (Sterimol)
– L represents the length of the substituent and B1
– B4
designate the radii
(i.e. longitudinal and horizontal)
(An example of carboxylic moiety in benzoic acid molecule)
Other parameters used in QSAR
➢in most computed
➢in most characterize the whole molecule
➢often include 2 or 3 types of influence (hydrophobic+ electronic + steric)
“Classical”
●parachor
where γ is surface tension, M molar weight and d density.
●molar refraction (= molekular refractivity) MR (also CMR); definition formula is known as Lorentz-Lorenz
equation
where n is refractivity index.
“Non-classical”
●solvation energy – if it is for water then hydration energy ∆GO
w
●molecule surface areas of various kind: – polar van der Waals, non-polar, water accessible, dynamic
polar (DPSA), topologic polar (TPSA) etc.
●molecule volumes – polar, water accessible etc.
MR=n2
−
1
n2

2M
d
=
n
2
−1
n2
2
M
d
,
Pr=
M
d

1/4
Free- Wilson method of regression analysis
● searches for a relationship between a biological activity and presence or non-presence of some
substituents or structural fragments in a molecule. Exactly it is statistic separation of activity
into contributions of particular parts of a molecule i.e. aditivity of influence of substituents or other
molecular fragments is assumed. Such a method leads to solution of equation systems of higher
number of unknowns which are in simple cases to solve by means of matrix arithmetic otherwise
by statistic software enabling multilinear regression (MLR).
●both Hansch and Free-Wilson methods could also be combined. A part of autonomous
variables then express physico-chemical properties of compounds and other ones which are
called “indicator variables” (symbol I) express presence or non-presence of particular
molecular fragments. Usually there is only small count of indicator variables, often only one.
Empirical methods of QSAR
●preferred to use there where the mathematical description of the function A = f(structure) is not easily to
find
●search only for extremes (maxims and/or minims) of given function; its mathematical description remains a
“black box”
● while applied a synthetic chemist choices compounds to synthesize according to biological evaluation of
previous ones
Optimization according one structural parameter: Fibonacci optimization
This method is based on the Fibonacci progression part of which is expressed in the Table. Compounds
are ordered in accordance with the increasing value of a structural parameter which is assumed to
influence the activity significantly. The number of compounds must conform to the number of points in
some Fibonacci interval (see Table. If it is not so one of marginal compounds which are not probable to be
the most active is excluded or on the contrary a fictive marginal compound is added. Compounds, which
have numbers listed in the column C of the Table in a particular interval, are selected for synthesis. Their
biological activities are determined and, in dependence of its results, the part of the given interval from one
of marginal points to the less active compound is excluded. The resulted set of compounds is the next
Fibonacci interval. Such selection is repeated until the most active compound is reached. This method
enables to decrease the number of synthesized and tested compounds significantly e.g. instead of 589
compounds which were necessary to prepare and test to find the most active one, only 13 compounds are
sufficient to synthesize and evaluate (see column C of the Table).
Table: Fibonacci optimization
Legend: A … number of compounds of a particular Fibonacci interval
B … order of compounds selected for synthesis and evaluation in a
particular interval
C … total number of compounds needed for optimization
A B C A B C A B C
2 l and 2 2 20 8 and 13 6 143 55 and 89 10
4 2 and 3 3 33 13 and 21 7 222 89 and 144 11
7 3 and 5 4 54 21 and 34 8 366 144 and 233 12
12 5 and 8 5 88 34 and 55 9 589 233 and 377 13
Optimization according more structure parameters
Simplex method
Every compound can be characterized as a particular point in n-dimensional space in which
the first coordinate is a biological activity and additional coordinates belong to physical
and physico-chemical properties which are assumed to influence the activity. If we work in
classical three-dimensional space i.e. if we optimize only two parameters we can perform
such optimization also graphically on a chart paper. In fact we work in the projection into the
plane of properties. Three compounds which are not far from themselves in the plane of
properties are selected for (synthesis and) evaluation. Ideally their coordinates form an
equilateral triangle. We compare activities of such three compounds. Now we draw a half-line
from the point which belongs to the compound of the least activity through the center of join of
two points of higher activities (alternatively through the point originated by division of this joint
in reversal ratio of activities) and at the line we find the point which has the same distance
from the joint to the point of the least activity but the opposite orientation. If no compound
belong to thus found point we select for evaluation the nearest one. This point and two
previous ones give us the next triangle which is put to the same optimization procedure. This
procedure is repeated as long as the activity increases. Once the activity begins to decrease
the compound with the highest reached activity can be recognized as the most active one.
Simplex method
π
σ
A
0,5
B
0,7 C
0,9
D
0,8
E
1,0
F
1,2
G
1,4
H
1,1
Optimization according more structure parameters
Optimization schemes
● sequences of rational intellectual processes of an medicinal chemist
● they have regard for hydrophobic, electron and steric parameters
●they are not universal: a novel one could be needed to formulate for a particular type of
modifications of a particular structure
Scheme of modifications on phenyl (Topliss 1972):
●an active compound (= lead compound) having a moiety necessary for the activity (= a
pharmacophore) bond on the unsubstituted benzene ring
● a pharmacophore cannot be modified unless the activity is lost but we can modify the
benzene ring by any arbitrary substitution
Scheme of modifications on phenyl (Topliss 1972)
Legend: E – equally active L – less active M – more active
Commentary to the scheme of modifications of substituents on phenyl
At first the unsubstituted compound and its 4-chloro derivative are synthesized. Chlorine
substitution lowers electron density in position one where the pharmacophore is bond and
simultaneously increases lipophilicity (4-Cl: σ = 0.23; π = 0.71); if the 4-chloro derivative is more
active both lipohilicity and electron-accepting properties can be further increased by further
chlorine substitution. If the 4-chloro derivative is less active we can assume that electron density
decrease influenced the activity negatively and 4-methoxy derivative is prepared. It has almost
the same lipophilicity as the unsubstituted compound but electron density in position one is
higher (4-OCH3
: σ = -0.27, π = 0.02). If there is no significant difference between activities of
unsubstituted compound and its 4-chloro derivative we can suppose that influences of electron
density and lipophilicity act against each other and 4-methyl derivative which has increased
both is prepared (4-CH3
: σ = -0.17, π = 0.56). If activities of all compounds substituted in position
4 are lower than that of unsubstituted compound then there is evident that substitution in
position 4 is sterically disadvantageous and compounds substituted in positions 2 and 3 can be
prepared. Particular branches of this scheme can be continued until the compound with the
optimal activity is reached.