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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5319_Библиотеки_им_академика_М_И_Перельмана.pdf
. • Synopsis
developed the Feature-Trees method, which can search
large databases using topological criteria. However, it
does not compare the connectivity of chemical formulas. Rather, the database entries are rst classied by the
topological sequences of certain features, such as the
presence of an H-bond donor group or ahydrophobic
cyclic molecular building block. In this way, molecules
can be compared and candidates with pharmacophore
properties in acomparable topological connectivity can
be found extremely quickly.
Databases that contain 3D molecular geometries allow the search for the spatial pattern of the pharmacophore. For example, the Cambridge Structural Database of crystal structures of small organic molecules
(Sect.13.9) can be used for such asearch. Molecules are
found with experimentally determined geometries that
satisfy the pharmacophore. In the search for ligands for
HIV protease (Sect.24.3), apharmacophore pattern was
derived from the known crystal structure of the enzyme,
and the Cambridge Database was searched for molecules
that match this pattern. The results of this search are
presented in Sect.24.4 (. Fig.24.16) in detail. It inspired
the researchers at Dupont–Merck with rst ideas that led
to the development of an entirely new class of nonpeptidic HIV protease inhibitors.
Today, databases containing 3D structures of molecules generated from 2D structural formulas are commonly used alongside experimental structural databases.
In other approaches, the spatial structure of candidate
molecules is generated on the y during the search
(Sect.15.2). Here, as with most entries in the Cambridge
Database, each molecule exists in only one conformation. However, molecules can adopt many different conformations (Chap.16). It is usually the exception rather
than the rule that aexible molecule will be stored in the
“correct” conformation required for the search. Therefore, conformational exibility must be taken into account during the search. An exhaustive search, such as
the “active analog approach,” would require too much
computational time. Therefore, fast algorithms have been
developed to identify whether certain pharmacophoric
groups on the molecules could fall within predened distance ranges. It is sufcient to estimate the minimum or
maximum achievable distances. This concept has been
realized, for example, in the program UNITY from the
company Tripos. It is possible to start from adatabase
that contains several precalculated conformers. In this
case, it is very important that the distribution of the conformers in the conformational space is as representative
as possible (Sect.16.6). The individual conformers will
then be checked to see whether they t the dened pharmacophore pattern. This concept has been implemented
in the database search engine Catalyst from Accelrys.
Asimilar concept is followed by the program Ligand-
Scout of Thierry Langer in Vienna, Austria and Gerhard
Wolber in Berlin, Germany.
Such database searches are not expected to immediately yield candidates for clinical testing. However,
as agenerator of ideas, they can lead drug discovery
scientist to new lead structures and take his or her synthesis plans down completely different paths. Database
searches are now widely used as part of virtual screening
(Sect.7.6). This involves screening proprietary collections of compounds or searching compilations of commercially available compounds. John Irwin and Brian
Shoichet at UCSF in San Francisco, USA, have taken the
initiative to continuously store commercially available
compounds in the ZINC database and make them available for database searching. Preset lters help to extract
the desired subset from the collection of several million
compounds for the user’s own search. Hits found in this
way can be obtained commercially and tested experimentally in an assay. Many candidates for new lead structures
have already been discovered through this lead discovery
by shopping (for an example, see Sect.21.7).
17.12 Synopsis
The structure of the binding pocket determines which
-
functional groups are necessary on the ligand side for
successful protein binding. Either the ligand or the
protein structure can be used as the starting point
from which apharmacophore is derived.
The superposition of active and inactive small-mole-
-
cule ligands from aseries of related compounds can
be used to dene the allowed and forbidden areas in
ahypothetical binding pocket. Logical operations of
volume differences are indicative for the design of op-
timized ligands.
Flexible molecules that can adopt different conforma-
-
tions present aspecial challenge in the mutual super-
positions. The molecules must be energy-minimized
as part of the superposition procedure or, alterna-
tively, multiple conformations must be evaluated.
Alternatively, aset of molecules can be superimposed
-
by assigning pharmacophoric groups, and through
systematic rotations about all open-chain single
bonds acommon alignment is found in the “active
analog approach.”
Care must be taken to not be deceived by molecules
-
that look similar with respect to their chemical for-
mulas. Instead, the interacting functional groups are
important for the molecular recognition at the bind-
ing pocket and not the scaffold itself. The role of wa-
ter in the binding must not be underestimated.
Molecular recognition properties can also be consid-
-
ered to mutually superimpose molecules.
The synthesis of a structurally rigid analogue (or
-
analogues) can help to dene and validate the phar-
macophore assignment and the determination of the
biologically active conformation.
Chapter • Pharmacophore Hypotheses and Molecular Comparisons
1
17
Binding “hot spots” can be found by examining the
-
protein by mapping the binding pocket with small
molecules or molecular probes with different properties. These give some ideas as to what sort of molecule
might successfully bind to the target protein.
The Cambridge Database of crystal structures pro-
-
vides valuable insights into preferred interaction
geometries and motifs. Such information is of high
relevance for protein–ligand complexes because the
forces that are responsible for crystal packing are the
same as for nonbonding interactions between active
substances and proteins.
A variety of databases are available that can be
-
screened by using a3D pharmacophore as asearch
query. Usually, commercially available compounds
are screened rst. If they show activity on acertain
protein of interest, they can be purchased and tested,
and will hopefully provide astarting point for further
lead discovery.
Bibliography and Further Reading
General Literature
T. Langer and R. D. Hoffmann, Pharmacophores and Pharmacophore
Searches (Vol. 32 in Methods and Principles in Medicinal Chemistry, R. Mannhold, H. Kubinyi and G. Folkers, Eds.), Wiley-VCH,
Weinheim (2006)
G. R. Marshall, Computer-Aided Drug Design, in: Computer-Aided
Molecular Design, W. G. Richards, Ed., IBC Technical Services
Ltd, London, pp. 91–104 (1989)
G. Klebe, Structural Alignment of Molecules, in: 3D-QSAR in Drug
Design. Theory, Methods and Application, H. Kubinyi, Ed., ESCOM, Leiden, pp. 173–199 (1993)
Y. C. Martin, 3D Database Searching in Drug Design, J. Med. Chem.,
35, 2145–2154 (1992)
Special Literature
C. G. Wermuth, C. R. Ganellin, P. Lindberg, L. A. Mitscher, Glossary
of terms used in medicinal chemistry (IUPAC Recommendations
1998), Pure Appl. Chem., 70, 1129–1143 (1998)
W. E. Klunk, B. L. Kalman, J. A. Ferrendelli and D. F. Covey, Com-
puter-Assisted Modeling of the Picrotoxinin and γ-Butyrolactone
Receptor Site, Mol. Pharmacol., 23, 511–518 (1983)
M. F. Mackay and M. Sadek, The Crystal and Molecular Structure of
Picrotoxinin, Austr. J. Chem., 36, 2111–2117 (1983)
G. R. Marshall, C. D. Barry, H. E. Bossard, R. A. Dammkoehler and
D. A. Dunn, The Conformational Parameter in Drug Design: The
Active Analog Approach, in: Computer-Assisted Drug Design,
ACS Symp. Series 112, E. C. Olson and R. E. Christoffersen, Eds.,
Amer. Chem. Soc., Washington DC., pp. 205–226 (1979)
D. Mayer, C. B. Naylor, I. Motoc and G. R. Marshall, A Unique Ge-
ometry of the Active Site of Angiotensin-Converting Enzyme
Consistent with Structure-Activity Studies, J. Comput.-Aided Mol.
Design, 1, 3–16 (1987)
D. J. Kuster and G. R. Marshall, Validated Ligand Mapping of ACE
Active Site, J. Comput.-Aided Mol. Design, 19, 609–615 (2005)
J. T. Bolin, D. J. Filman, D. A. Matthews, R. C. Hamlin and J. Kraut,
Crystal Structure of Eschericha coli and Lactobacillus casei Dihydrofolate Reductase Rened at 1.7 Å Resolution, J. Biol. Chem.,
257, 13650–13662 (1982)
S. K. Kearsley and G. M. Smith, An Alternative Method for the Align-
ment of Molecular Structures: Maximizing Electrostatic and Steric
Overlap, Tetrahedron Comput. Methodol., 3, 615–633 (1990)
P. C. D. Hawkins, A. G. Skillman and A. Nicholls. Comparison of
shape-matching and docking as virtual screening tools. J. Med.
Chem., 50, 74–82 (2007) https://www.eyesopen.com/rocs (Last ac-
cessed Nov. 18, 2024)
C. Lemmen, T. Lengauer and G. Klebe, FlexS: A Method for Fast Flex-
ible Ligand Superposition, J. Med. Chem., 41, 4502–4520 (1998)
https://www.biosolveit.de/wp-content/uploads/2021/01/FlexS.pdf
(Last accessed Nov. 18, 2024)
G. Klebe, T. Mietzner and F. Weber, Different Approaches Toward an
Automatic Structural Alignment of Drug Molecules: Applications
to Sterol Mimics, Thrombin and Thermolysin Inhibitors, J. Com-
put.-Aided Mol. Design, 8, 751–778 (1995)
W. Seidel, H. Meyer, L. Born, S. Kazda and W. Dompert, Rigid Cal-
cium Antagonists of the Nifedipine-Type: Geometric Require-
ments for the Dihydropyridine Receptor, in: QSAR as Strategies
in the Design of Bioactive Compounds, J. K. Seydel, Ed., VCH,
Weinheim, pp. 366–369 (1984)
P. Goodford, Drug design by the method of receptor t, J. Med. Chem.,
27, 557–564 (1984) https://www.moldiscovery.com/software/grid/
(Last accessed Nov. 18, 2024)
I. J. Bruno, J. C. Cole, J. P. Lommerse, R. S. Rowland, R. Taylor and
M. L. Verdonk, IsoStar: a library of information about nonbonded
interactions, J. Comput.-Aided Mol. Design, 11, 525–537 (1997)
IsoStar: https://www.ccdc.cam.ac.uk/solutions/software/isostar/ (Last
accessed Nov. 18, 2024)
M. L. Verdonk, J. C. Cole, R. Taylor, SuperStar: A Knowledge-based
Approach for Identifying Interaction Sites in Proteins, J. Mol.
Biol., 289, 1093–1108 (1999)
SuperStar: https://www.ccdc.cam.ac.uk/solutions/software/superstar/
(Last accessed Nov. 18, 2024)
G. Klebe, The Use of Composite Crystal-Field Environments in Molec-
ular Recognition and the “De-Novo” Design of Protein Ligands,
J. Mol. Biol., 237 212–235 (1994)
R. Taylor and P. A. Wood, A Million Crystal Structures: The Whole
Is Greater than the Sum of Its Parts, Chem. Rev., 119, 9427–9477
(2019)
H. Gohlke, M. Hendlich and G. Klebe, Knowledge-based Scoring
Function to Predict Protein-Ligand Interactions, J. Mol. Biol., 295,
337–356 (2000) https://www.fz-juelich.de/en/ibg/ibg-4/expertise/da-
tabases-softwares-and-webservers-in-the-gohlke-group/drugscore
(Last accessed Nov. 18, 2024)
A. Caisch, A. Miranker, and M. Karplus, Multiple copy simultaneous
search and construction of ligands in binding sites: application
to inhibitors of HIV-1 aspartic proteinase, J. Med. Chem., 36,
2142–2167 (1993)
D. Joseph-McCarthy, J. M. Hogle and M. Karplus, Use of the multiple
copy simultaneous search (MCSS) method to design a new class of
picornavirus capsid binding drugs, Proteins, Struct, Funct, Bioin-
form., 29, 32–58 (1997)
M. Rarey and J. S. Dixon, Feature trees: A new molecular similarity
measure based on tree matching, J Comput.-Aided Mol. Des.,
12, 471–490 (1998) https://www.biosolveit.de/wp-content/up-
loads/2022/03/FTrees.pdf (Last accessed Nov. 18, 2024)
G. Wolber and T. Langer, LigandScout: 3-D pharmacophores derived
from protein-bound ligands and their use as virtual screening l-
ters, J. Chem. Inf. Model., 45, 160–169 (2005) https://ligandscout.
software.informer.com/ (Last accessed Nov. 18, 2024)
J.J. Irwin and B.K. Shoichet, ZINC—A Free Database of Commer-
cially Available Compounds for Virtual Screening, J. Chem. Inf.
Model., 45, 177–182 (2005) https://zinc15.docking.org/ (Last ac-
cessed Nov. 18, 2024)
Quantitative Structure–
Activity Relationships
Contents
18.1 How It All Began: Structure–Activity
Relationships of Alkaloids – 274
18.2 From Richet, Meyer, and Overton
to Hammett and Hansch – 274
18.3 The Determination and Calculation of Lipophilicity – 275
18.4 Lipophilicity and Biological Activity – 275
18.5 The Hansch Analysis and the Free–Wilson Model – 276
18.6 Structure–Activity Relationships of Molecules in Space – 278
18.7 Structural Alignment as aPrerequisite for the
Relative Comparison of Molecules – 278
18.8 Binding Anities as Compound Properties – 278
18.9 How Is aCoMFA Analysis Performed? – 279
18.10 Molecular Fields as Criteria of aComparative Analysis – 280
18.11 3D-QSAR: Correlation of Molecular Fields
with Biological Properties – 280
18.12 Results of aComparative Molecular Field Analysis
and Their Graphical Interpretation – 282
18.13 Scope, Limitations, and Possible Expansions
of the CoMFA Analysis – 283
18.14 A Glimpse Behind the Scenes: Comparative Molecular
Field Analysis of Carbonic Anhydrase Inhibitors – 284
18.15 Synopsis – 287
Bibliography and Further Reading – 288
© The Author(s), under exclusive license to Springer-Verlag GmbH, DE, part of Springer Nature 2024
G. Klebe, Drug Design, https://doi.org/10.1007/978-3-662-68998-1_18
18
Chapter • Quantitative Structure–Activity Relationships
Quantitative structure–activity relationships, QSAR
(usually pronounced [′kyü:sar]), attempt to describe and
quantify the correlation between chemical structure and
biological activity. The investigated substances should
come from achemically uniform series and must interact
with the same biological target. They should also display the same mode of action. For example, structurally
analo gous inhibitors of aparticular protein can be compared among themselves, but not different blood pressure
lowering drugs that have diverse modes of action on different target proteins. The correlation between biological
activity and physicochemical properties is always related
to relative potency in atest model, but not to different
modes of action.
The basis for quantitative correlations between chemical structure and biological effect is the entirely reasonable assumption that the differences in physicochemical
properties are responsible for the relative potency of the
interactions of the drug with biological macromolecules.
In arst approximation, these are assumed to contribute additively to the afnity of adrug for its receptor.
The concept of describing the biological activity of substances with mathematical models is derived from this
approach.
For the system under investigation, it can be assumed
that the simpler it is, the more likely it is that aquantitative structure–activity relationship can be derived. To
acertain extent, this is true for in vitro systems, such as
enzyme inhibition or receptor binding, where the assay
records only the binding of acompound to aprotein.
The more complex the system, e.g., effects on the central
nervous system of an animal after oral administration,
the more different processes have to be considered. In this
case, absorption, distribution, blood–brain barrier penetration, transport to the target tissue, metabolism, and
excretion overlap with one another and with the actual
effect at the receptor. In principle, an individual structure–activity relationship is required for each of these
events. In order to establish valid and relevant models for
each of these steps, appropriate test systems are needed
to study the different steps separately. In favorable cases,
it may be possible to characterize acomplex multistep
process by asingle equation. This will only be feasible if
one step, e.g., the penetration of the blood–brain barrier,
dominates the entire structure–activity relationship.
18.1 How It All Began: Structure–Activity
Relationships of Alkaloids
The South American arrow poison tubocurarine
(Sect.6.2) was the rst therapeutic principle for which
the exact mode of action was elucidated. In 1852, Claude
Bernard realized that this quaternary alkaloid causes
muscle paralysis, but that both the nerve and the muscle remain independently excitable. Curare must, there-
. Fig. 18.1 The protonation of atertiary amine depends on the pH
value of the medium (left). On the other hand, the quaternization of
anitrogen atom leads to apermanently positively charged compound
(right)
fore, act on the coupling between nerve and muscle. The
Scottish pharmacologists Alexander Crum-Brown and
Thomas Fraser studied in more detail whether the quaternization of the nitrogen atom of various alkaloids
(. Fig.18.1) inuences their biological effects. In 1868,
on the basis of very different effects observed before and
after the transformation of alkaloids, they formulated
ageneral equation to describe structure–activity relationships (Eq.18.1).
(18.1)
This equation is ingeniously simple, but it says only
thatΦ, the biological activity, is a function ofC, the
chemical structure. At that time, the tetrahedral structure of the carbon atom had not been elucidated, and
the composition of many organic compounds, especially
complex natural products, was completely unknown.
18.2 From Richet, Meyer, and Overton
to Hammett and Hansch
In 1893, Charles Richet published astudy on the toxicity
of organic compounds. Comparing the water solubility
of ethanol, diethyl ether, urethane, paraldehyde, amyl
alcohol, and absinthe extract(!) to the lethal dose in the
dog, he concluded plus ils sont subles, moins ils sont tox-
iques, that is, the better the solubility, the less the toxicity.
This was the rst evidence of alinear inverse relationship
between water solubility and biological activity.
At the turn of the last century, the pharmacologist
Hans Horst Meyer and the botanist Charles Ernest Over
ton independently established the lipid theory of anesthe-
sia, which combines three important statements:
All chemically unreactive substances that are lipo-
-
philic and can be distributed in biological systems
have anesthetic effects.
The biological effect occurs in nerve cells because fats
-
play an important role in their function.
The relative potency of anesthetics depends on their
-
partition coefcient (Sect.19.2) in amixture of fats
and water.
-
R−X
−log K
R−H
−log P
−H
. • Lipophilicity and Biological Activity
The work of Crum-Brown, Fraser and Richet or the
contribution of Meyer and Overton can be considered
as the origin of quantitative structure–activity relationships. In fact, after the formulation of the anesthetic
theory, numerous other linear and later nonlinear dependencies on the lipophilicity, the “fat afnity” of drugs,
were found. However, these were all relatively unspecic
“membrane” effects.
In the mid-1930s, Louis P. Hammett formulated
arelationship between the electronic properties of substituents and the reactivity of aromatic compounds. According to this relationship, the relative contributions of
electron-withdrawing and electron-donating substituents
to the electron density of the aromatic ring are always
constant. They are determined by the electronic parameter of the substituent, the Hammett constant,σ. Electron-accepting substituents with positive σvalues are,
among others, the nitro group, the cyano group, and the
halogens. Electron-donating substituents with negative
σvalues are hydroxyl and amino groups, the methoxy
group, and alkyl substituents. Acceptor substituents
enhance the acidity of benzoic acids and phenols, they
reduce the basicity of anilines, and they accelerate the
basic hydrolysis of benzoic ethers. Electron-donating
substituents exert an opposite inuence.
However, an individual reaction constantρ must be
applied for each reaction type of aromatic compounds.
By using Eq.18.2, later generally called the Hammett
equation, the equilibrium constantK for an arbitrary
reaction can be calculated fromρ andσ. R–X and R–H
represent the relevant aromatic compounds substituted
with the groupX, or unsubstituted, respectively.
(18.2)
Acceptor and donor substituents inuence the electron
density on the heteroatoms and reduce or increase the ability to form hydrogen bonds. This explains, among other
things, the electronic inuence of aromatic substituents
on the biological activity of drug molecules. The Hammett equation has, therefore, been seen as achallenge for
medicinal chemists and biologists to derive quantitative
structure–activity relationships from this concept. Many
groups have attempted to nd relationships between biological activity and the Hammet constantsσ, or betweenσ
and/or ρ-analogous substituents, and to derive test parameters for biological systems. Despite some interesting
results, no general concept could be established.
It was Corwin Hansch and Toshio Fujita who published apaper in 1964 that laid the foundation for quan-
titative structure–activity relationships. In it they describe:
The denition of alipophilicity parameterπ, analo-
-
gous to the electronic termσ in the Hammett equation.
The combination of several parameters in one model.
-
The formulation of a parabolic model to describe
-
nonlinear lipophilicity–activity relationships.
18.3 The Determination and Calculation
of Lipophilicity
Corwin Hansch had previously studied the structure–
activity relationship of phenoxyacetic acids, which have
growth-stimulating effects in plants. In addition to their
biological activity, he was particularly interested in their
lipophilicity, which can be measured by the partition coefcient in an octanol/water system (Sect.19.1). While
analyzing the data, he realized that lipophilicity is an
additive molecular parameter. The logarithm of the octanol/water partition coefcientP is given by the sum of
the group contributions of each part of the molecule.
Hansch dened alipophilicity parameterπ (Eq. 18.3)
analogous to the Hammett equation. R–X and R–H have
the same meaning as in Eq.18.2. The absence of areaction-specic ρterm in Eq.18.3 results from relating the
πvalues to asingle distribution system, the two-phase
mixture of n-octanol and water.
R−X
n-Octanol was chosen for theoretical and practical reasons. It has along aliphatic chain and ahydroxyl group
that is an H-bond donor as well as an acceptor. Its
structure, therefore, resembles the membrane lipids to
some extent. It dissolves alarge number of organic compounds, it has alow vapor pressure, but can nonetheless
be easily removed. Its UV transparence over an extremely
wide range is particularly advantageous.
With the help of the lipophilicity parameterπ, the
logP values of new compounds, and therefore their lipophilicity, can be calculated. For this, the lipophilicity
of the basic scaffold and the πvalues of the substituents
must be known. In this way, the biological activity can
be correlated without the tedious experimental measurements of each individual partition coefcient. In addition to the πvalues of all important substituents, avery
large number of experimentally determined octanol/
water partition coefcients are available in the literature.
18.4 Lipophilicity and Biological Activity
Lipophilicity plays an overwhelming role in describing
the dependence of biological effects on chemical structure and, therefore, explains many quantitative structure–
activity relationships. This is easily understood because
biological systems consist of aqueous phases separated
by lipid membranes. The transport and distribution of
small molecules in such systems must, therefore, depend
on their lipophilicity. For polar substances, the lipid
membrane is an insurmountable barrier. Only substances
with moderate lipophilicity have agood chance of “migrating” into both the aqueous and lipid phases to reach
the target tissue in adequate concentrations (Chap.19).
(18.3)
R
1
.log P/2+ k2log P + k3 + :::k
Chapter • Quantitative Structure–Activity Relationships
18
Although soluble proteins carry predominantly polar
amino acid residues on their surface, the more or less
buried binding sites for ligands are composed of polar
and nonpolar regions. The hydrophobic parts of the ligand bind to the hydrophobic parts of these pockets. The
size of these hydrophobic surfaces is always limited. The
size and shape of the lipophilic part of the ligand must
t the hydrophobic surfaces in the binding pocket. Since
the natural ligands normally bound in these pockets are
themselves sufciently water soluble, the lipophilic regions in the binding pockets are of limited size. This fact
is another explanation for the complex, generally nonlinear, lipophilicity–activity relationships.
Many linear and nonlinear lipophilicity–activity
relationships describe relatively unspecic biological
. Table 18.1 The biological activity of meta- and para-sub-
stituents of phenethylamines 18.1 (i.v. application in the rat;
Cin mol/kg rat)
meta para log 1/C
H H 7.46
H F 8.16
H Cl 8.68
H Br 8.89
H I 9.25
H Me 9.30
F H 7.52
Cl H 8.16
Br H 8.30
I H 8.40
Me H 8.46
Cl F 8.19
Br Cl 8.57
Me F 8.82
Cl Cl 8.89
Br Cl 8.92
Me Cl 8.96
Cl Br 9.00
Br Br 9.35
Me Br 9.22
Me Me 9.30
Br Me 9.52
effects, such as anesthetic, bactericidal, fungicidal, and
hemolytic effects. They will not be discussed further here.
Other relationships describe the transport and distribution in abiological system. Such structure–activity relationships are discussed in Chap.19.
18.5 The Hansch Analysis and
the Free–Wilson Model
In 1964 Corwin Hansch and Toshio Fujita derived
amathematical model more intuitively than theoretically that can quantitatively describe structure–activity
relationships, the Hansch analysis (Eq.18.4).
(18.4)
In Eq.18.4, C is amolar concentration that produces
aparticular biological effect. When related to aseries of
substances, it is the equieffective molar dose. LogP is the
logarithm of the octanol/water partition coefcientP,
and σis the Hammett constant. The square of the logP
term allows the quantitative description of nonlinear lipophilicity–activity relationships. This term is omitted when
the dependence is linear. Other terms such as polarizability
and steric parameters can additionally occur.
The coefcients k1, k2,… andk are determined using
the method of regression analysis. The Hansch analysis,
therefore, establishes ahypothetical model for quantitative relationships between biological activity and physicochemical parameters. Biological data are awed, and
the same is true for physicochemical properties. Despite
this, the reliability of the latter parameters is usually
greater than those of the biological data. The result of
acalculation is judged by the squared differences between
the measured biological data and the values that were
calculated from the model. The sum must be as small
as possible over all the compounds investigated. It is an
important criterion for judging the quality of amodel
or for comparing different models of different quality.
The quantitative structure–activity relationship
of the antiadrenergic effect of N,N-dimethyl-β-bro-
mophenethylamines 18.1 (. Table18.1) is considered
as an example. According to their structure, these compounds more or less reverse the agonistic effect of an
adrenaline dose. The valueC is the dose of an antagonist
that blocks the adrenaline effect by 50%. The data can be
described using the Hansch model shown in . Fig.18.2.
The entire dataset can be described by amathematical model using the derived equations. When bromine is
cleaved, acarbocation is formed and the substances bind
irreversibly to the adrenergic receptor. Accordingly, the
+
σ
term is found in the Hansch equation (. Fig.18.2),
which describes this type of reaction particularly well.
Lipophilic substituents increase the biological activity
(positive π term) and electron withdrawing substitu-
. • The Hansch Analysis and the Free–Wilson Model
. Fig. 18.2 A QSAR equation delivers individual parameters
for aquantitative model for the prediction of biological activity,
in this case from substituted N,N-dimethyl-β-bromophenethylamines (. Table18.1)
ents decrease it (negative σ+ term). Therefore, lipophilic
electron-donating substituents, such as large alkyl substituents, should be optimal for activity. Second, within
certain limits, the effect of other compounds can be predicted. Interpolations (i.e., conclusions based on very
similar substituents) are generally much more reliable
than attempts at extrapolations (i.e., predictions made
outside the parameter space, e.g., for considerably more
lipophilic, more polar, or larger substituents). As arst
approximation for the statistical parametersr, s, andF
(. Fig.18.2), it can be said that the correlation coefcientr should have values close to 1.00, the standard
deviations should be as small as possible, and the Fvalue
should be as large as possible. The better these criteria
are met, the better the quantitative model will be, in other
words, the better the agreement between the experimental and calculated values.
Also in 1964, and independent of Hansch and Fu
jita, S.R. Free and J.W. Wilson developed acompletely
different model for structure–activity analysis. Since the
original approach is confusingly formulated and difcult
to use, only avariant, which was later proposed by Fujita and T.Ban, will be discussed here, the Free–Wilson
analysis. The Free–Wilson analysis assumes that within
aset of chemically related substances, areference compound, usually the unsubstituted parent compound,
per se makes aspecic contributionμ to the biological
effect. Each substituent on this scaffold makes an “additive and constitutive” contribution ai to the biological
activity (. Fig.18.3)—additive, because there is no consideration of structural variation at other positions in
the molecule, and constitutive, because it matters where
in the molecule the specic structural change is made.
Despite these relatively simple assumptions, Free–Wilson analysis provides good quantitative models for many
structure–activity relationships.
In contrast to the Hansch analysis, which compares
properties, the Free–Wilson analysis is areal “structure–
. Fig. 18.3 The Free–Wilson analysis uses the additive nature of the
group contributions to describe the biological activity. Accordingly,
the biological activity in the displayed equation is made up of the activityμ of the basic scaffold and the constant group contributions ai
of the substituents X
activity analysis,” because the parameter that codes for
the structural information (1for present, 0for absent)
correlates with biological effects. It is easily carried out,
but the structures and the biological data must be known.
-
Unfortunately, the Free–Wilson analysis also has disadvantages:
The structural variation must be present on at least
-
two different substitution sites, because otherwise
there will not be enough degrees of freedom to use
statistical methods.
The usually large number of variables diminishes the
-
predictive value and reliability of the analyses.
Predictions are only possible for combinations of
-
substituents that have already been considered in the
analysis, and not for new substituents.
When the Free–Wilson analysis is applied to the above
example of the antiadrenergic phenethylamine, the values for the scaffold and substituent contributions shown
in . Table18.2 are obtained. At rst glance, an increase
in the values fromF to Cl and from Br toI, i.e., the inuence of lipophilicity, is obvious. Despite having almost
the same lipophilicity, the methyl and chloro substituents are different. This is due to their different electronic
properties. Differences in the meta and para positions on
i
Chapter • Quantitative Structure–Activity Relationships
18
. Table 18.2 Free–Wilson group contributions for
phenethylamines
Atom type
Position
meta
para
µ = 7.82
(n = 22; r = 0.97; s = 0.19)
a
For an explanation of these values see . Fig.18.2
H F Cl Br I Me
0.00 −0.30 0.21 0.43 0.58 0.45
0.00 0.34 0.77 1.02 1.43 1.26
a
the electronic inuence can also be followed. Therefore,
the Free–Wilson analysis indeed has advantages for the
analysis of substituent effects.
18.6 Structure–Activity Relationships of
Molecules in Space
As shown in the previous section, an attempt is made
to correlate structure–activity relationships with compound-specic parameters. These parameters, such as
volume, polarizability, or lipophilicity, are properties
that are calculated or measured for the entire molecule
or for specic groups of substituents. The 3D structure
of the molecules is only conditionally taken into account
by these descriptors. Therefore, in the context of increasing knowledge of the spatial structure of protein–ligand
complexes, QSAR methods focus on parameters that can
be derived from the 3Dstructure. In general, the goal
of these approaches is to calculate binding afnity. The
techniques can also be used to describe other biological
properties such as bioavailability, toxicity, or metabolic
reactivity (Chap.19). To distinguish them from the classical QSAR techniques described above, they are referred
to as 3D-QSAR methods.
Ideally, parameters that can be read directly from the
3D structure of acompound and used to infer its binding
afnity would be desirable. However, the interplay between these parameters and activity is very complex and
still far from being fully understood. In addition, there
are many other biological systems to which one would
like to apply 3D-QSAR methods, but the structures of
the relevant target proteins are unknown. Many pharmacologically relevant receptors are membrane-bound
and their structure determination has proven to be extremely difcult. However, the knowledge of their structures is aprerequisite for areasonable estimation of the
binding afnity of a ligand from the geometry of the
formed complex (Chap.4). Therefore, instead of trying
to calculate the absolute values of the binding afnities
from these incomplete data, we will focus on the relative
afnity differences between compounds in adataset. The
gradual changes in the compound-specic parameters
are then correlated with the biological data.
18.7 Structural Alignment as
aPrerequisite for the Relative
Comparison of Molecules
Assumptions about the spatial structure of molecules are
already taken into account in classical QSAR techniques.
Different positions of substituents, e.g., in the meta or
para position of an aromatic ring, are often described by
individual parameters. In this form, they are considered
in the Hansch equation as well as in the Free–Wilson
analysis (Sect.18.5). Furthermore, in classical QSAR
models, indicator variables are dened for different congurations of substituents, e.g., the conguration of
stereoisomers. The use of these parameters assumes an
analogous orientation of the molecules in ahypothetical
binding pocket. For example, in aseries of ortho-substi-
tuted derivatives, it is assumed that all ortho substituents
are oriented towards the “same side.” Structure–activity
relationships that correlate biological activity with properties of the 3D structure require aspatial superposition
of the compounds. This superposition should approximate the relative orientation in the binding pocket as
closely as possible. Methods for calculating these spatial
superpositions were discussed in Chap.17.
18.8 Binding Affinities as Compound
Properties
What compound-specic properties can be used to correlate the properties of the 3D structure with the binding afnity? As discussed in Chap.4, binding afnity is
composed of enthalpic and entropic components. The
former includes everything that depends on direct energetic interactions. These are mainly of steric (van der
Waals potentials, Sect.15.4) or electrostatic (Coulomb
potentials) nature. The second contribution focuses on
the degree of order and the distribution of energy over
the different degrees of freedom of the system under investigation. The ligands as well as the binding pockets
of aprotein are solvated by water molecules in the uncomplexed state. Upon complex formation, the enthalpic interactions to these water molecules are lost. They
are replaced by direct interactions between the ligand
and the protein. Since only relative differences between
the molecules of adataset are of interest, effects that
are the same for all ligands are not considered. This includes all inuences that affect the protein. This omission is certainly an oversimplication, since the protein
changes its degree of solvation upon ligand binding and
is polarized differently by ligands. Water molecules are
displaced from the binding site. Ligand-induced adapta-
. • How Is aCoMFA Analysis Performed?
tions of side chains in the binding pocket or changes in
the rotational degrees of freedom of methyl groups and
side chains (Sect.4.10) are conceivable. These effects are
either not considered or are assumed to be the same for
all molecules in the dataset. This assumption is probably valid in many cases. However, many recent investigations clearly show that changes affecting the protein or
the dynamics of the ligand are often not constant within
aseries of compounds. This is where the methods fail.
Initially, only the steric and electrostatic interactions
of acompound in the binding pocket should be considered. How can these properties be compared for aset
of ligands? Arst approach has been the hypothetical
interaction models developed by Hans-Dieter Höltje
and LemontB. Kier. Akey assumption of these models
was the selection and spatial positioning of amino acid
side chains around the ligands. When the molecules are
embedded in alattice and systematically scanned with
an interaction probe, these assumptions are no longer
necessary. Richard Cramer and M.Milne proposed such
amodel in 1978 (DYLOMMS). It took another 10years
before the generally applicable CoMFA (comparative mo-
lecular eld analysis) method was established. Despite
many theoretical and practical shortcomings in its application, the method was quickly accepted. Today, it is
applied in many different variations.
Before performing such an analysis in practice, some
basic considerations should be made. Do steric and electrostatic interactions account for all contributions to
ligand binding that ultimately lead to acorrect relative
ranking of binding afnities? As mentioned above, binding afnity is composed of enthalpic and entropic contributions. Sampling properties via probes to map interactions certainly provides ameasure of how well amolecule
can undergo energetically favorable interactions. But how
well are the entropic contributions accounted for? Asignicant part of this is due to solvation and desolvation
processes (Sect.4.6). In the dissolved state, in the im-
mediate vicinity of the hydrophobic surface portion of
aligand, the water structure must assume amore ordered
state compared to the bulk water phase. The transfer of
such aligand from water to the protein-binding pocket,
thus, requires that acertain number of water molecules
in the water phase change to asignicantly less ordered
state. This increases the entropy of the system and favors the spontaneous occurrence of the binding event.
The number of water molecules involved in this process
depends on the size of the hydrophobic surface of the
ligand. Furthermore, the displacement of bound water
molecules out of the binding pocket by the ligand to be
accommodated increases the disorder of the system under consideration and, thus, also the entropy of the system. In the approximation discussed above, it is assumed
that these effects are the same for all molecules in the
dataset and are not important in arelative comparison.
In addition, rotational, translational, and internal con-
formational degrees of freedom are frozen. As aresult,
the entropy of the system decreases. For the afnities to
be correctly considered, all these effects would have to be
taken into account.
In 2019, Tobias Hüfner in Marburg performed MD
simulations on enzyme complexes using the GIST method
(Sect.15.4) to predict binding afnities considering enthalpic and entropic solvation contributions. He made
avery interesting observation. Aset of crystal structures
of different ligands with atarget protein was used. All
the structures were superimposed in their experimentally
observed geometry. Thus, the problem of ligand alignment, which is essential for performing aCoMFA analysis, could be solved using experimental data. Tobias Hüfner then used different mathematical models to calculate
the GIST contributions to the dataset. He also analyzed
adataset in which only the ligands were considered, but
in their protein-bound conformations. In this way, the
ligands are practically sampled for their potential interactions with water molecules using an MD simulation.
The calculated solvation contributions have been deposited on alattice surrounding all ligands. Accordingly, the
result is very similar to aCoMFA analysis. Surprisingly,
this simulation, performed with only the ligands, gave an
excellent afnity prediction for the ligands. How can this
be understood? It is possible that asignicant part of
the relative differences in binding afnities is already accounted for by the desolvation properties of the ligands.
Contributions due to the properties of the protein and
its desolvation seem to cancel each other out to arst approximation in the relative comparison. Certainly, there
are water molecules in the binding pockets whose enthalpic and entropic properties are very different from those
in asurrounding water phase. Apparently, alarge part of
these differences in the individual desolvation contributions required to displace the water molecules from the
binding site are in turn compensated for by the individual
functional groups of the ligands binding to these sites
and achieving comparably graded binding contributions
with the residues of the protein. Therefore, simply scanning the ligands with their different functional groups
in the correct bound geometry with awater probe already provides arelevant picture to reasonably predict
the relative differences in the afnity data. Perhaps this
is aclue as to why comparative eld analysis works so
surprisingly well.
18.9 How Is aCoMFA Analysis Performed?
The most important and widely used 3D structure–activity method is the CoMFA method. The rst step in
performing aCoMFA study is to select adataset of
suitable compounds. This dataset should contain about
50–100 compounds with related overall geometry. It
should also be ensured that all compounds bind to the
Chapter • Quantitative Structure–Activity Relationships
18
same protein at the same site and that a binding afnity is known for all of them. The ligands must have
acertain diversity of their structural variation. Their
binding afnities should be spread over at least three
orders of magnitude. Conformations are generated for
all molecules (Chap.16) and superimposed using one
of the techniques discussed in Chap.17. In general, one
refers to the spatial structure of the target protein, if
available, and ts the ligands of interest into the binding
pocket. Of course, it will be optimals if acrystal structure with the protein is available for many, if not all,
bound ligands. Finally, the superimposed molecules are
embedded in alattice (. Fig.18.4) that surrounds them
by asufciently large margin. The intersections of the
lattice should have aspacing of 1 or 2 Å. Aprobe, this
is an atom with the properties of hydrogen, carbon, or
oxygen, or aparticle with aformal charge, is placed at
each of the lattice intersections. The interaction energies
between this probe and each molecule in the dataset are
calculated. The collective interaction contributions on
the lattice are referred to as the interaction eld of the
molecule. This is where the name of the method comes
from. Finally, the elds of the molecules in the dataset
are compared. With abox size of 10–20 Å and agrid
spacing of 1–2 Å, there are many thousands of eld
values per molecule in the dataset to be processed. This
huge amount of data means that eld evaluation can be
computationally rather intensive.
18.10 Molecular Fields as Criteria of
aComparative Analysis
Steric and electrostatic interactions are described by
aLennard-Jones or Coulomb potential (. Fig.18.5) in
force elds (Sect.15.4). As the distance between aprobe
and an atom of the molecule approaches zero, the Len-
nard-Jones and Coulomb potentials increase towards in-
nity. For like-charged particles, the Coulomb potential
approaches innity; for oppositely charged particles, it
approaches negative innity. These values reach extremely
high eld contributions at grid points near the surface or
inside amolecule. They must be avoided in aCoMFA
analysis. Therefore, the eld contributions above and
below acertain threshold are set to apredened cut-off
value. Following these procedures, aLennard-Jones or
Coulomb potential can be calculated. For example, aliphatic carbon atoms can be used as probes. These probes
are given apositive or negative charge to study the electrostatic properties of the molecules. The program GRID
by Peter Goodford was introduced in Sect.17.10. With
this program, molecular elds can be calculated for numerous probes describing different functional groups. For
each predened probe, there are regions in space where
favorable or unfavorable interactions between the probe
and the studied molecule are expected.
In addition, other elds can be dened besides those
that probe the steric and electrostatic properties of molecules. It was discussed in Sect.18.8 that the hydrophobic
surface of amolecule is ameasure of the entropic contribution, especially in the transition from the bulk water phase. In the group of Donald Abraham, at Virginia
Commonwealth University, Richmond, USA, molecular
elds have been developed which allow the hydrophobic
properties of molecules (program HINT) to be studied.
These are calculated using avery similar distance-dependent function. The resulting molecular eld describes the
lipophilicity distribution on the surface of amolecule.
18.11 3D-QSAR: Correlation of Molecular
Fields with Biological Properties
Let us assume that multiple molecular elds have been
calculated for each molecule in adataset, and a correlation of their differences with binding afnity is attempted. How are these differences expressed? For this,
we will consider three hypothetical examples of substituted phenyl derivatives.
First, all substituents on the phenyl ring in aseries
-
of compounds should be varied so that increasingly
larger eld contributions occur in the vicinity of the
substituent when scanned with apositively charged
probe. If the binding afnities increase as the eld
contributions increase, this will be reected in the
quantitative analysis. They indicate that ligands with
increasingly negatively charged groups in this region
of the molecule lead to more potent compounds.
This is explained by the fact that the more negatively
charged groups interact better with the positively
charged probe.
The second example is abit different. Now the sub-
-
stituents on the phenyl ring are given positive or neg-
ative partial charges. Their variation has no inuence
on the potency of the compounds. The quantitative
analysis shows that the changes in the electrostatic
eld contributions have no correlation with the bi-
ological activity. A possible explanation could be
that this effect and another property, e.g., the size of
the substituents, cancel each other out. It could also
be that the biological activity is inuenced by other
properties of the substituents, such as their hydropho-
bic character.
In the third case, the electrostatic properties of the
-
substituents that are important for binding to the re-
ceptor should not vary much at the examined position.
There may be different substituents present, but they
all have comparable partial charges. The model that
analyzes the eld contributions in the vicinity of these
groups does not recognize differences and, therefore,
does not nd acorrelation with binding afnity. It
may be that aclass of substituents at aparticular posi-