Principal Burger's Medicinal Chemistry and Drug Discovery. Drug Discovery

Burger's Medicinal Chemistry and Drug Discovery. Drug Discovery

Medicinal chemistry provides medical researchers with knowledge about chemical structures, chemical reactions, reaction mechanisms, and biochemical mechanisms of therapeutic agents. This tried and true comprehensive source of information for medicinal chemists has been thoroughly updated and improved under new dynamic editorial leadership.
Categories: Chemistry
Volume: Volume 1
Año: 2003
Edición: 6th edition
Idioma: english
Páginas: 932
File: RAR, 234.21 MB
Descarga (rar, 234.21 MB)

Most frequently terms




Sixth Edition 

Volume 1: Drug Discovery 

Edited by 

Donald J. Abraham 
Department of Medicinal Chemistry 

School of Pharmacy 
Vir - r  m- 

. . 

Burger's Medicinal Chemistry and Drug Discovery 
is  available Online in full color at 

A John Wiley and Sons, Inc., Publication 


The Sixth Edition of Burger's Medicinal 
Chemistry and Drug Discovery is being desig- 
nated as a Memorial Edition. Professor Alfred 
Burger was born in Vienna, Austria on Sep- 
tember 6, 1905 and died on December 30, 
2000. Dr. Burger received his Ph.D. from the 
University of Vienna in 1928 and joined the 
Drug Addiction Laboratory in the Department 
of Chemistry at the University of Virginia in 
1929. During his early years at UVA, he syn- 
thesized fragments of the morphine molecule 
in an attempt to find the analgesic pharma- 
cophore. He joined the UVA chemistry faculty 
in 1938 and served the department until his 
retirement in 1970. The chemistry depart- 
ment at UVA became the major academic 
training ground for medicinal chemists be- 
cause of Professor Burger. 

Dr. Burger's research focused on analge- 
sics, antidepressants, and chemotherapeutic 
agents. He is one of the few academicians to 
have a drug, designed and synthesized in his 

laboratories, brought to market [Parnate, 
which is the brand name for tranylcypromine, 
a monoamine oxidase (MAO) inhibitor]. Dr. 
Burger was a visiting Professor at the Univer- 
sity of Hawaii and lectured throughout the 
world. He founded the Journal of Medicinal 
Chemistry, Medicinal Chemistry Research, 
and published the first major reference work 
"Medicinal Chemistry" in two volumes in 
1951. His last published work, a book, was 
written at age 90 (Understanding Medica- 
tions: What the Label Doesn't Tell You, June 
1995). Dr. Burger received the Louis Pasteur 
Medal of the Pasteur Institute and the Amer, 
ican Chemical Society Smissman Award. Dr. 
Burger played the violin and loved classical 
music. He was married for 65 years to Frances 
Page Burger, a genteel Virginia lady who al- 
ways had a smile and an open house for the 
Professor's graduate students and postdoc- 
toral fellows. 



The Editors, Editorial Board Members, and 
John Wiley and Sons have worked for three 
and a half years to update the fifth edition of 
Burger's Medicinal Chemistry and Drug Dis- 
covery. The sixth edition has several new and 
unique features. For the first time, there will 
be an online version of this major reference 
work. The online version will permit updating 
and easy access. For the first time, all volumes 
are structured entirely according to content 
and published simultaneously. Our intention 
was to provide a spectrum of fields that would 
provide new or experienced medicinal chem- 
ists, biologists, pharmacologists and molecu- 
lar biologists entry to their subjects of interest 
as well as provide a current and global per- 
spective of drug design, and drug develop- 

Our hope was to make this edition of 
Burger the most comprehensive and useful 
published to date. To accomplish this goal, we 
expanded the content from 69 chapters (5 vol- 
umes) by approximately 50% (to over 100 
chapters in 6 volumes). We are greatly in debt 
to the authors and editorial board members 
participating in this revision of the major ref- 
erence work in our field. Several new subject 
areas have emerged since the fifth edition ap- 
peared. Proteomics, genomics, bioinformatics, 
combinatorial chemistry, high-throughput 
screening, blood substitutes, allosteric effec- 
tors as potential drugs, COX inhibitors, the 
statins, and high-throughput pharmacology 
are only a few. In addition to the new areas, we 
have filled in gaps in the fifth edition by in- 
cluding topics that were not covered. In the 

sixth edition, we devote an entire subsection 
of Volume 4 to cancer research; we have also 
reviewed the major published Medicinal 
Chemistry and Pharmacology texts to ensure 
that we did not omit any major therapeutic 
classes of drugs. An editorial board was consti- 
tuted for the first time to also review and sug- 
gest topics for inclusion. Their help was 
greatly appreciated. The newest innovation in 
this series will be the publication of an aca- 
demic, "textbook-like" version titled, "Bur- 
ger's Fundamentals of Medicinal Chemistry." 
The academic text is to be published about a 
year after this reference work appears. It will 
also appear with soft cover. Appropriate and 
key information will be extracted from the ma- 
jor reference. 

There are numerous colleagues, friends, 
and associates to thank for their assistance. 
First and foremost is Assistant Editor Dr. 
John Andrako, Professor emeritus, Virginia 
Commonwealth University, School of Phar- 
macy. John and I met almost every Tuesday 
for over three years to map out and execute 
the game plan for the sixth edition. His contri- 
bution to the sixth edition cannot be under- 
stated. Ms. Susanne Steitz, Editorial Program 
Coordinator at Wiley, tirelessly and meticu- 
lously kept us on schedule. Her contribution 
was also key in helping encourage authors to 
return manuscripts and revisions so we could 
publish the entire set at once. I would also like 
to especially thank colleagues who attended 
the QSAR Gordon Conference in 1999 for very 
helpful suggestions, especially Roy Vaz, John 
Mason, Yvonne Martin, John Block, and Hugo 

Kubinyi. The editors are greatly indebted to 
Professor Peter Ruenitz for preparing a tem- 
plate chapter as a guide for all authors. My 
secretary, Michelle Craighead, deserves spe- 
cial thanks for helping contact authors and 
reading the several thousand e-mails gener- 
ated during the project. I also thank the com- 
puter center at Virginia Commonwealth Uni- 
versity for suspending rules on storage and 
e-mail so that we might safely store all the 
versions of the author's manuscri~ts where 
they could be backed up daily. ~ r $ t  and not 
least, I want to thank each and every author, 
some of whom tackled two chapters. Their 
contributions have ~rovided our-field with a 


sound foundation of information to build for 
the future. We thank the many reviewers of 
manuscripts whose critiques have greatly en- 
hanced the presentation and content for the 
sixth edition. Special thanks to Professors 
Richard Glennon, William Soine, Richard 
Westkaemper, Umesh Desai, Glen Kel- 
logg, Brad Windle, Lemont Kier, Malgorzata 


Dukat, Martin Safo, Jason Rife, Kevin Reyn- 
olds, and John Andrako in our Department 
of Medicinal Chemistry, School of Pharmacy, 
Virginia Commonwealth University for sug- 
gestions and special assistance in reviewing 
manuscripts and text. Graduate student 
Derek Cashman took able charge of our web 
site, http:l/, an- 
other first for this reference work. I would es- 
pecially like to thank my dean, Victor 
Yanchick, and Virginia Commonwealth Uni- 
versity for their support and encouragement. 
Finally, I thank my wife Nancy who under- 
stood the magnitude of this project and pro- 
vided insight on how to set up our home office 
as well as provide John Andrako and me 
lunchtime menus where we often dreamed of 
getting chapters completed in all areas we se- 
lected. To everyone involved, many, many 

Midlothian, Virginia 


Dr. Alfred Burger 

ltograph of Professor Burger followed by his comments to the American Chemical Society 26th Medicinal 
,mistry Symposium on June 14, 1998. This was his last public appearance a t  a meeting of medicinal 
mists. As general chair of the 1998 ACS Medicinal Chemistry Symposium, the editor invited Professor 
ger to open the meeting. He was concerned that the young chemists would not know who he was and he 
ht have an attack due to his battle with Parkinson's disease. These fears never were realized and his 
.ments to the more than five hundred attendees drew a sustained standing ovation. The Professor was 93, 
it was Mrs. Burger's 91st birthday. 

Opening Remarks 

ACS 26th Medicinal Chemistry Symposium 

June 14, 1998 
Alfred Burger 

University of Virginia 

It has been 46 years since the third Medicinal Chemistry Symposium met at the University of 
Virginia in Charlottesville in 1952. Today, the Virginia Commonwealth University welcomes 
you and joins all of you in looking forward to an exciting program. 

So many aspects of medicinal chemistry have changed in that half century that most of the 
new data to be presented this week would have been unexpected and unbelievable had they 
been mentioned in 1952. The upsurge in biochemical understandings of drug transport and 
drug action has made rational drug design a reality in many therapeutic areas and has made 
medicinal chemistry an independent science. We have our own journal, the best in the world, 
whose articles comprise all the innovations of medicinal researches. And if you look at the 
announcements of job opportunities in the pharmaceutical industry as they appear in 
Chemical & Engineering News, you will find in every issue more openings in medicinal 
chemistry than in other fields of chemistry. Thus, we can feel the excitement of being part of 
this medicinal tidal wave, which has also been fed by the expansion of the needed research 
training provided by increasing numbers of universities. 

The ultimate beneficiary of scientific advances in discovering new and better therapeutic 
agents and understanding their modes of action is the patient. Physicians now can safely look 
forward to new methods of treatment of hitherto untreatable conditions. To the medicinal . 
scientist all this has increased the pride of belonging to a profession which can offer predictable 
intellectual rewards. Our symposium will be an integral part of these developments. 




C. D. Selassie 
Chemistry Department 
Pomona College 
Claremont, California 


A. Tropsha 
University of  North Carolina 
Laboratory for Molecular Modeling 
School of Pharmacy 
Chapel Hill, North Carolina 


Garland R. Marshall 
Washington University 
Center for Computational Biology 
St. Louis, Missouri 

Denise D. Beusen 
Tripos, Inc. 
St. Louis, Missouri 


Peter A. Kollman 
University of California 
School of Pharmacy 
Department of Pharmaceutical 
San Francisco, California 

David A. Case 
The Scripps Research Institute 
Department of Molecular Biology . 
La Jolla, California 


Jonathan S. Mason 
Pfizer Global Research & 
Sandwich, United Kingdom 

Stephen D. Pickett 
GlmoSmithKline Research 
Stevenage, United Kingdom 


xiv Contents 


Ingo Muegge 
Istvan Enyedy 
Bayer Research Center 
West Haven, Connecticut 


Christoph Sotriffer 
Gerhard Klebe 
University of Marburg 
Department of Pharmaceutical 
Marburg, Germany 

Martin Stahl 
Hans-Joachim Bohm 
Discovery Technologies 
F. Hoffmann-La Roche AG 
Basel, Switzerland 


David J. ParrySmith 
ChiBio Informatics 
Cambridge, United Kingdom 


Douglas R. Henry 
MDL Information Systems, Inc. 
San Leandro, California 

DESIGN, 417 

Larry W. Hardy 
Aurigene Discovery Technologies 
Lexington, Massachusetts 

Martin K. Safo 
Virginia Commonwealth University 
Richmond, Virginia 

Donald J. Abraham 
Virginia Commonwealth University 
Richmond, Virginia 


Douglas A. Livingston 
Sean G. Buchanan 
Kevin L. D'Amico 
Michael V. Milburn 
Thomas S. Peat 
J. Michael Sauder 
Structural GenomiX 
San Diego, California 


David J. Craik 
Richard J. Clark 
Institute for Molecular Bioscience 
Australian Research Council 
Special Research Centre for 
Functional and Applied Genomics 
University of  Queensland . 
Brisbane, Australia 


Richard B. van Breemen 
Department of Medicinal Chemistry 
and Pharmacognosy 
University of Illinois at Chicago 
Chicago, Illinois 


Richard Henderson 
Medical Research Council 
Laboratory of Molecular Biology 
Cambridge, United Kingdom 


Timothy S. Baker 
Purdue University 
Department of Biological Sciences 
West Lafayette, Indiana 

DESIGN, 633 

M. Angels Estiarte 
Daniel H. Rich 
School of Pharmacy-Department of 
University of Wisconsin-Madison 
Madison, Wisconsin 


Joseph G. Cannon 
The University of Iowa 
Iowa City, Iowa 


Michael J. McLeish 
George L. Kenyon 
Department of Medicinal Chemistry 
University of Michigan 
Ann Arbor, Michigan 


Alistair G. Draffan 
Graham R. Evans 
James A. Henshilwood 
Celltech R&D Ltd. 
Granta Park, Great Abington, 
Cambridge, United Kingdom 

AGENTS, 827 

Herbert S. Rosenkranz 
Department of Biomedical Sciences 
Florida Atlantic University 
Boca Raton, Florida 


A. D. Buss 
MerLion Pharmaceuticals 
Singapore Science Park, 

B. Cox 
Medicinal Chemistry 
Respiratory Diseases Therapeutic 
Novartis Pharma Research Centre 
Horsham, United Kingdom 

R. D. Waigh 
Department of Pharmaceutical . 
University of Strathclyde 
Glasgow, Scotland 

INDEX, 901 


A N D  


History of Quantitative 
structure-~ctivity Relationships 

Chemistry Department 
Pomona College 
Claremont, California 


1 Introduction, 2 
1.1 Historical Development of QSAR, 3 
1.2 Development of Receptor Theory, 4 

2 Tools and Techniques of QSAR, 7 
2.1 Biological Parameters, 7 
2.2 Statistical Methods: Linear 

Regression Analysis, 8 
2.3 Compound Selection, 11 

3 Parameters Used in QSAR, 11 
3.1 Electronic Parameters, 11 
3.2 Hydrophobicity Parameters, 15 

3.2.1 Determination of Hydrophobicity by 
Chromatography, 17 . 

3.2.2 Calculation Methods, 18 
3.3 Steric Parameters, 23 
3.4 Other Variables and Variable Selection, 25 
3.5 Molecular Structure Descriptors, 26 

4 Quantitative Models, 26 
4.1 Linear Models, 26 

4.1.1 Penetration of ROH into 
Phosphatidylcholine Monolayers (1841, 

4.1.2 Changes in EPR Signal of Labeled 
Ghost Membranes by ROH (185),27 

4.1.3 Induction of Narcosis in Rabbits by 
ROH (184), 27 

4.1.4 Inhibition of Bacterial Luminescence 
by ROH (185),27 

4.1.5 Inhibition of Growth of Tetrahymena 
pyriformis by ROH (76, 1861, 27 

4.2 Nonlinear Models, 28 
4.2.1 Narcotic Action of ROH on Tadpoles, 28 
4.2.2 Induction of Ataxia in Rats by ROH, 29 

Burger's Medicinal Chemistry and Drug Discovery 4.3 Free-Wilson Approach, 29 
Sixth Edition, Volume 1: Drug Discovery 4.4 Other QSAR Approaches, 30 
Edited by Donald J. Abraham 5 Applications of QSAR, 30 
ISBN 0-471-27090-3 O 2003 John Wiley & Sons, Inc. 5.1 Isolated Receptor Interactions, 31 

History of Quantitative Structure-Activity Relationships 

5.1.1 Inhibition of Crude Pigeon Liver 
DHFR by Triazines (202),31 

5.1.2 Inhibition of Chicken Liver DHFR by 
3-X-Triazines (207),31 

5.1.3 Inhibition of Human DHFR by 3-X- 
Triazines (208), 32 

5.1.4 Inhibition of L1210 DHFR by 3-X- 
Triazines (2091, 32 

5.1.5 Inhibition of P. carinii DHFR by 3-X- 
Triazines (210), 32 

5.1.6 Inhibition of L. major DHFR by 3-X- 
Triazines (211),33 

5.1.7 Inhibition of T. gondii DHFR by 3-X- 
Triazines, 33 

5.1.8 Inhibition of Rat Liver DHFR by 2,4- 
Diamino, 5-Y, 6-Z-quinazolines (213), 

5.1.9 Inhibition of Human Liver DHFR by 
2,4-Diamino, 5-Y, 6-Z-quinazolines 
(214), 34 

5.1.10 Inhibition of Murine L1210 DHFR by 
(2141, 34 

5.1.11 Inhibition of Bovine Liver DHFR by 
(215), 34 

5.1.12 Binding of X-Phenyl, N-Benzoyl-L- 
alaninates to a-Chyrnotqpsin in 
Phosphate Buffer, pH 7.4 (203),35 

5.1.13 Binding of X-Phenyl, N-Benzoyl-L-ala- 
ninates to a-Chymotrypsin in 
Pentanol(203), 35 

5.1.14 Binding of X-Phenyl, N-Benzoyl-L- 
alaninates in Aqueous Phosphate 
Buffer (218),35 

5.1.15 Binding of X-Phenyl, N-Benzoyl-L- 
alaninates in Pentanol(218), 35 

5.1.16 Inhibition of 5-a-Reductase by 4-X, 
ones, I, 36 

5.1.17 Inhibition of 5-a-Reductase by 170- 
drost-4-ene-3-ones, II,36 


It has been nearly 40 years since the quantita- 
tive structure-activity relationship (QSAR) 
paradigm first found its way into the practice 
of agrochemistry, pharmaceutical chemistry, 
toxicology, and eventually most facets of 
chemistry (1). Its stayingpower may be attrib- 
uted to the strength of its initial postulate that 
activity was a function of structure as de- 

5.1.18 Inhibition of 5-a-Reductase by 17P- 
(N-( 1-X-phenyl-cycloalky1)carbamoyl)- 
6-azaandrost-4-ene-3-ones, 111, 36 

5.2 Interactions at the Cellular Level, 37 
5.2.1 Inhibition of Growth of L1210/S by 3- 

X-Triazines (209), 37 
5.2.2 Inhibition of Growth of L1210lR by 

3-X-Triazines (209), 37 
5.2.3 Inhibition of Growth of Tetrahymena 

pyriformis (40 h), 37 
5.2.4 Inhibition of Growth of T. pyriformis 

by Phenols (using a) (22'71, 38 
5.2.5 Inhibition of Growth of T. pyriformis 

by Electron-Releasing Phenols (2271, 

5.2.6 Inhibition of Growth of T. pyriformis 
by Electron-Attracting Phenols (2271, 

5.2.7 Inhibition of Growth of T. pyriformis 
by Aromatic Compounds (229), 38 

5.3 Interactions In Viuo, 38 
5.3.1 Renal Clearance of P-Adrenoreceptor 

Antagonists, 38 
5.3.2 Nonrenal Clearance of P- 

Adrenoreceptor Antagonists, 39 
6 Comparative QSAR, 39 

6.1 Database Development, 39 
6.2 Database: Mining for Models, 39 

6.2.1 Incidence of Tail Defects of Embryos 
(235), 40 

6.2.2 Inhibition of DNA Synthesis in CHO 
Cells by X-Phenols (236),40 . 

6.2.3 Inhibition of Growth of L1210 by X- 
Phenols, 40 

6.2.4 Inhibition of Growth of L1210 by 
Electron-Withdrawing Substituents 
(af > 0),41 

6.2.5 Inhibition of Growth of L1210 by 
Electron-Donating Substituents (at < 
O), 41 

6.3 Progress in QSAR, 41 
7 Summary, 42 

scribed by electronic attributes, hydrophobic- 
ity, and steric properties as well as the rapid 
and extensive development in methodologies 
and computational techniques that have en- 
sued to delineate and refine the many vari- 
ables and approaches that define the para- 
digm. The overall goals of QSAR retain their 
original essence and remain focused on the 
predictive ability of the approach and its re- 
ceptiveness to mechanistic interpretation. 

1 Introduction 

Rigorous analysis and fine-tuning of indepen- 
dent variables has led to an expansion in de- 
velopment of molecular and atom-based de- 
scriptors, as well as descriptors derived from 
quantum chemical calculations and spectros- 
copy (2). The improvement in high-through- 
put screening procedures allows for rapid 
screening of large numbers of compounds un- 
der similar test conditions and thus minimizes 
the risk of combining variable test data from 
many sources. 

The formulation of thousands of equa- 
tions using QSAR methodology attests to a 
validation of its concepts and its utility in 
the elucidation of the mechanism of action of 
drugs at the molecular level and a more com- 
plete understanding of physicochemical phe- 
nomena such as hydrophobicity. It is now 
possible not only to develop a model for a 
system but also to compare models from a 
biological database and to draw analogies 
with models from a physical organic data- 
base (3). This process is dubbed model min- 
ing and it provides a sophisticated approach 
to the study of chemical-biological interac- 
tions. QSAR has clearly matured, although 
it still has a way to go. The previous review 
by Kubinyi has relevant sections covering 
portions of this chapter as well as an exten- 
sive bibliography recommended for a more 
complete overview (4). 

1.1 Historical Development of QSAR 

More than a century ago, Crum-Brown and 
Fraser expressed the idea that the physiologi- 
cal action of a substance was a function of its 
chemical composition and constitution (5). A 
few decades later, in 1893, Richet showed that 
the cytotoxicities of a diverse set of simple or- 
ganic molecules were inversely related to their 
corresponding water solubilities (6). At the 
turn of the 20th century, Meyer and Overton 
independently suggested that the narcotic (de- 
pressant) action of a group of organic com- 
pounds paralleled their olive oiVwater parti- 
tion coefficients (7, 8). In 1939 Ferguson 
introduced a thermodynamic generalization 
to the correlation of depressant action with 
the relative saturation of volatile compounds 
in the vehicle in which they were administered 
(9). The extensive work of Albert, and Bell and 
Roblin established the importance of ioniza- 

tion of bases and weak acids in bacteriostatic 
activity (10-12). Meanwhile on the physical 
organic front, great strides were being made in 
the delineation of substituent effects on or- 
ganic reactions, led by the seminal work of 
Hammett, which gave rise to the "sigma-rho" 
culture (13, 14). Taft devised a way for sepa- 
rating polar, steric, and resonance effects and 
introducing the first steric parameter, Es (15). 
The contributions of Hammett and Taft to- 
gether laid the mechanistic basis for the devel- 
opment of the QSAR paradigm by Hansch and 
Fujita. In 1962 Hansch and Muir published 
their brilliant study on the structure-activity 
relationships of plant growth regulators and 
their dependency on Hammett constants and 
hydrophobicity (16). Using the octanoVwater 
system, a whole series of partition coefficients 
were measured, and thus a new hydrophobic 
scale was introduced (17). The parameter a, 
which is the relative hydrophobicity of a sub- 
stituent, was defined in a manner analogous to 
the definition of sigma (18). 

P, and P, represent the partition coefficients 
of a derivative and the parent molecule, re- 
spectively. Fujita and Hansch then combined 
these hydrophobic constants with Hammett's 
electronic constants to yield the linear Hansch 
equation and its many extended forms (19). 

Hundreds of equations later, the failure of lin- 
ear equations in cases with extended hydro- 
phobicity ranges led to the development of the 
Hansch parabolic equation (20): 

Log 1IC = a . log P 

- b(l0g P y  + C U  + k 

The delineation of these models led to explo- 
sive development in QSAR analysis and re- 
lated approaches. The Kubinyi bilinear 
model is a refinement of the parabolic model 
and, in many cases, it has proved to be supe- 
rior (21). 

History of Quantitative Structure-Activity Relationships 

Log 1IC = a . log P 

Besides the Hansch approach, other method- 
ologies were also developed to tackle struc- 
ture-activity questions. The Free-Wilson ap- 
proach addresses structure-activity studies in 
a congeneric series as described in Equation 
1.5 (22). 

BA is the biological activity, u is the average 
contribution of the parent molecule, and ai is 
the contribution of each structural feature; xi 
denotes the presence Xi = 1 or absence Xi = 0 
of a particular structural fragment. Limita- 
tions in this approach led to the more sophis- 
ticated Fujita-Ban equation that used the log- 
arithm of activity, which brought the activity 
parameter in line with other free energy-re- 
lated terms (23). 

In Equation 1.6, u is defined as the calculated 
biological activity value of the unsubstituted 
parent compound of a particular series. Gi rep- 
resents the biological activity contribution of 
the substituents, whereasxi is ascribed with a 
value of one when the substituent is present or 
zero when it is absent. Variations on this ac- 
tivity-based approach have been extended by 
Klopman et al. (24) and Enslein et al. (25). 
Topological methods have also been used to 
address the relationships between molecular 
structure and physical/biological activity. The 
minimum topological difference (MTD) 
method of Simon and the extensive studies on 
molecular connectivity by Kier and Hall have 
contributed to the development of quantita- 
tive structure propertylactivity relationships 
(26,271. Connectivity indices based on hydro- 
gen-suppressed molecular structures are rich 
in information on branching, 3-atom frag- 
ments, the degree of substitution, proximity of 
substituents and length, and heteroatom of 
substituted rings. A method in its embryonic 
state of development uses both graph bond 

distances and Euclidean distances among at- 
oms to calculate E-state values for each atom 
in a molecule that is sensitive to conforma- 
tional structure. Recently, these electrotopo- 
logical indices that encode significant struc- 
tured information on the topological state of 
atoms and fragments as well as their valence 
electron content have been applied to biologi- 
cal and toxicity data (28). Other recent devel- 
opments in QSAR include approaches such as 
HQSAR, Inverse QSAR, and Binary QSAR 
(29-32). Improved statistical tools such as 
partial least square (PLS) can handle situa- 
tions where the number of variables over- 
whelms the number of molecules in a data set, 
which may have collinear X-variables (33). 

1.2 Development of Receptor Theory 

The central theme of molecular pharmacol- 
ogy, and the underlying basis of SAR studies, 
has focused on the elucidation of the structure 
and function of drug receptors. It is an en- 
deavor that proceeds with unparalleled vigor, 
fueled by the developments in genomics. It is 
generally accepted that endogenous and exog- 
enous chemicals interact with a binding site 
on a specific macromolecular receptor. This in- 
teraction, which is determined by intermolec- 
ular forces, may or may not elicit a pharmaco- 
logical response depending on its eventual site 
of action. 

The idea that drugs interacted with specific 

receptors began with Langley, who studied the 
mutually antagonistic action of the alkaloids, 
pilocorpine and atropine. He realized that 
both these chemicals interacted with some re- 
ceptive substance in the nerve endings of the 
gland cells (34). Paul Ehrlich defined the re- 
ceptor as the "binding group of the protoplas- 
mic molecule to which a foreign newly intro- 
duced group binds" (35). In 1905 Langley's 
studies on the effects of curare on muscular 
contraction led to the first delineation of crit- 
ical characteristics of a receptor: recognition 
capacity for certain ligands and an amplifica- 
tion component that results in a pharmacolog- 
ical response (36). 

Receptors are mostly integral proteins em- 
bedded in the phospholipid bilayer of cell 
membranes. Rigorous treatment with deter- 
gents is needed to dissociate the proteins from 
the membrane, which often results in loss of 

1 Introduction 

integrity and activity. Pure proteins such as 
enzymes also act as drug receptors. Their rel- 
ative ease of isolation and amplification have 
made enzymes desirable targets in structure- 
based ligand design and QSAR studies. Nu- 
cleic acids comprise an important category of 
drug receptors. Nucleic acid receptors (apta- 
mers), which interact with a diverse number 
of small organic molecules, have been isolated 
by in vitro selection techniques and studied 
(37). Recent binary complexes provide insight 


into the molecular recognition process in 
these biopolymers and also establish the im- 
portance of the architecture of tertiary motifs 
in nucleic acid folding (38). Groove-binding li- 
gands such as lexitropsins hold promise as po- 
tential drugs and are thus suitable subjects for 
focused QSAR studies (39). 

Over the last 20 years, extensive QSAR 
studies on ligand-receptor interactions have 
been carried out with most of them focusing 
on enzymes. Two recent developments have 
augmented QSAR studies and established an 
attractive approach to the elucidation of the 
mechanistic underpinnings of ligand-receptor 
interactions: the advent of molecular graphics 
and the ready availability of X-ray crystallog- 
raphy coordinates of various binary and ter- 
nary complexes of enzymes with diverse li- 
gands and cofactors. Early studies with serine 
and thiol proteases (chymotrypsin, trypsin, 
and papain), alcohol dehydrogenase, and nu- 
merous dihydrofolate reductases (DHFR) not 
only established molecular modeling as a pow- 
erhl  tool, but also helped clarify the extent of 
the role of hydrophobicity in enzyme-ligand 
interactions (40-44). Empirical evidence indi- 
cated that the coefficients with the hydropho- 
bic term could be related to the degree of de- 
solvation of the ligand by critical amino acid 
residues in the binding site of an enzyme. To- 
tal desolvation, as characterized by binding in 
a deep crevice/pocket, resulted in coefficients 
of approximately 1.0 (0.9 -1.1) (44). An exten- 
sion of this agreement between the mathemat- 
ical expression and structure as determined by 
X-ray crystallography led to the expectation 
that the binding of a set of substituents on the 
surface of an enzyme would yield a coefficient 
of about 0.5 (0.4-0.6) in the regression equa- 
tion, indicative of partial desolvation. 

Probing of various enzymes by different li- 
gands also aided in dispelling the notion of 
Fischer's rigid lock-and-key concept, in which 
the ligand (key) fits precisely into a receptor 
(lock). Thus, a "negative" impression of the 
substrate was considered to exist on the en- 
zyme surface (geometric complementarity). 
Unfortunately, this rigid model fails to ac- 
count for the effects of allosteric ligands, and 
this encouraged the evolution of the induced- 
fit model. Thus, "deformable" lock-and-key 
models have gained acceptance on the basis of 
structural studies, especially NMR (45). 

I t  is now possible to isolate membrane- 
bound receptors, although it is still a challenge 
to delineate their chemistry, given that sepa- 
ration from the membrane usually ensures 
loss of reactivity. Nevertheless, great ad- 
vances have been made in this arena, and the 
three-dimensional structures of some mem- 
brane-bound proteins have recently been elu- 
cidated. To gain an appreciation for mecha- 
nisms of ligand-receptor interactions, it is 
necessary to consider the intermolecular 
forces at play. Considering the low concentra- 
tion of drugs and receptors in the human body, 
the law of mass action cannot account for the 
ability of a minute amount of a drug to elicit a 
pronounced pharmacological effect. The driv- 
ing force for such an interaction may be attrib- . 
uted to the low energy state of the drug- 
receptor complex: KD = [Drug] [Receptor]/ 
[Drug-Receptor Complex]. Thus, the biological 
activity of a drug is determined by its affinity 
for the receptor, which is measured by its K,,, 
the dissociation constant at equilibrium. A 
smaller KD implies a large concentration of 
the drug-receptor complex and thus a greater 
affinity of the drug for the receptor. The latter 
property is promoted and stabilized by mostly 
noncovalent interactions sometimes aug- 
mented by a few covalent bonds. The sponta- 
neous formation of a bond between atoms re- 
sults in a decrease in free energy; that is, AG is 
negative. The change in free energy AG is re- 
lated to the equilibrium constant K,,. 

Thus, small changes in AG" can have a pro- 
found effect on equilibrium constants. 

6 History of Quantitative Structure-Activity Relationships 

Table 1.1 Types of Intermolecular Forces 

Bond Strength 
Bond Type (kcallmol) Example 

1. Covalent 40-140 CH3CH20-H 

2. Ionic (Electrostatic) 5 + - I 1  R 4 N ~ ~ ~ ~ ~ ~ ~ ~ O - C -  

3. Hydrogen 

5. van der Wads 

6.  Hydrophobic 

In the broadest sense, these "bonds" would 
include covalent, ionic, hydrogen, dipole-di- 
pole, van der Wads, and hydrophobic interac- 
tions. Most drug-receptor interactions consti- 
tute a combination of the bond types listed in 
Table 1.1, most of which are reversible under 
physiological conditions. 

Covalent bonds are not as important in 
drug-receptor binding as noncovalent interac- 
tions. Alkylating agents in chemotherapy tend 
to react and form an immonium ion, which 
then alkylates proteins, preventing their nor- 
mal participation in cell divisions. Baker's 
concept of active site directed irreversible in- 
hibitors was well established by covalent for- 
mation of Baker's antifolate and dihydrofolate 
reductase (46). 

Ionic (electrostatic) interactions are formed 
between ions of opposite charge with energies 
that are nominal and that tend to fall off with 
distance. They are ubiquitous and because 
they act across long distances, they play a 
prominent role in the actions of ionizable 
drugs. The strength of an electrostatic force is 
directly dependent on the charge of each ion 
and inversely dependent on the dielectric con- 
stant of the solvent and the distance between 
the charges. 

Hydrogen bonds are ubiquitous in nature: 
their multiple presence contributes to the sta- 

bility of the (ahelix and base-pairing in DNA. 
Hydrogen bonding is based on an electrostatic 
interaction between the nonbonding electrons 
of a heteroatom (e.g., N, 0, S) and the elec- 
tron-deficient hydrogen atom of an -OH, SH, 
or NH group. Hydrogen bonds are strongly 
directional, highly dependent on the net de- 
gree of solvation, and rather weak, having en- 
ergies ranging from 1 to 10 kcal/mol(47,48). 
Bonds with this type of strength are of critical 
importance because they are stable enough to 
provide significant binding energy but weak 
enough to allow for quick dissociation. The 
greater electronegativity of atoms such as ox- 
ygen, nitrogen, sulfur, and halogen, compared 
to that of carbon, causes bonds between these 
atoms to have an asymmetric distribution of 
electrons, which results in the generation of 
electronic dipoles. Given that so many func- 
tional groups have dipole moments, ion-dipole 
and dipole-dipole interactions are frequent. 
The energy of dipole-dipole interactions can 
be described by Equation 1.8, where p is the 
dipole moment, 0 is the angle between the two 
poles of the dipole, D is the dielectric constant 
of the medium and r is the distance between 
the charges involved in the dipole. 

2 Tools and Techniques of QSAR 

Although electrostatic interactions are 
generally restricted to polar molecules, there 
are also strong interactions between nonpolar 
molecules over small intermolecular dis- 
tances. Dispersion or Londonlvan der Wads 
forces are the universal attractive forces be- 
tween atoms that hold nonpolar molecules to- 
gether in the liquid phase. They are based on 
polarizability and these fluctuating dipoles or 
shifts in electron clouds of the atoms tend to 
induce opposite dipoles in adjacent molecules, 
resulting in a net overall attraction. The en- 
ergy of this interaction decreases very rapidly 
in proportion to llr6, where r is the distance 
separating the two molecules. These van der 
Wads forces operate at a distance of about 
0.4-0.6 nm and exert an attraction force of 
less than 0.5 kcallmol. Yet, although individ- 
ual van der Wads forces make a low energy 
contribution to an event, they become signifi- 
cant and additive when summed up over a 
large area with close surface contact of the 

Hydrophobicity refers to the tendency of 
nonpolar compounds to transfer from an 
aqueous phase to an organic phase (49, 50). 
When a nonpolar molecule is placed in water, 
it gets solvated by a "sweater" of water mole- 
cules ordered in a somewhat icelike manner. 
This increased order in the water molecules 
surrounding the solute results in a loss of en- 
tropy. Association of hydrocarbon molecules 
leads to a "squeezing out" of the structured 
water molecules. The displaced water becomes 
bulk water, less ordered, resulting in a gain in 
entropy, which provides the driving force for 
what has been referred to as a hydrophobic 
bond. Although this is a generally accepted 
view of hydrophobicity, the hydration of apo- 
lar molecules and the noncovalent interac- 
tions between these molecules in water are 
still poorly understood and thus the source of 
continued examination (5 1-53). 

Because noncovalent interactions are gen- 
erally weak, cooperativity by several types of 
interactions is essential for overall activity. 
Enthalpy terms will be additive, but once the 
first interaction occurs, translational entropy 
is lost. This results in a reduced entropy loss in 
the second interaction. The net result is that 
eventually several weak interactions combine 
to produce a strong interaction. One can safely 

state that it is the involvement of myriad in- 
teractions that contribute to the overall selec- 
tivity of drug-receptor interactions. 


2.1 Biological Parameters 

In QSAR analysis, it is imperative that the 
biological data be both accurate and precise to 
develop a meaningful model. It must be real- 
ized that any resulting QSAR model that is 
developed is only as valid statistically as the 
data that led to its development. The equilib- 
rium constants and rate constants that are 
used extensively in physical organic chemistry 
and medicinal chemistry are related to free 
energy values AG. Thus for use in QSAR, stan- 
dard biological equilibrium constants such as 
Ki or K, should be used in QSAR studies. 
Likewise only standard rate constants should 
be deemed appropriate for a QSAR analysis. 
Percentage activities (e.g., % inhibition of 
growth at certain concentrations) are not ap- 
propriate biological endpoints because of the 
nonlinear characteristic of dose-response rela- 
tionships. These types of endpoints may be 
transformed to equieffective molar doses. 
Only equilibrium and rate constants pass 
muster in terms of the free-energy relatioA- 
ships or influence on QSAR studies. Biological 
data are usually expressed on a logarithmic 
scale because of the linear relationship be- 
tween response and log dose in the midregion 
of the log dose-response curve. Inverse loga- 
rithms for activity (log 1/C) are used so that 
higher values are obtained for more effective 
analogs. Various types of biological data have 
been used in QSAR analysis. A few common 
endpoints are outlined in Table 1.2. 

Biological data should pertain to an aspect 
of biological/biochemical function that can be 
measured. The events could be occurring in 
enzymes, isolated or bound receptors, in cellu- 
lar systems, or whole animals. Because there 
is considerable variation in biological re- 
sponses, test samples should be run in dupli- 
cate or preferably triplicate, except in whole 
animal studies where assay conditions (e.g., 
plasma concentrations of a drug) preclude 
such measurements. 

History of Quantitative Structure-Activity Relationships 

Table 1.2 Types of Biological Data Utilized 
in QSAR Analysis 

Source of Activity Biological Parameters 

1. Isolated receptors 
Rate constants Log k& Log k,,& Log k 
Michaelis-Menten Log 1 /K, 

Inhibition constants Log l/Ki 
Affinity data P&; PA, 

2. Cellular systems 
Inhibition constants Log 1/1C,, 
Cross resistance Log CR 
In vitro biological data Log 1IC 
Mutagenicity states Log T b  

3. "In vivo" systems 
Biocencentration factor Log BCF 
In vivo reaction rates Log I (Induction) 
Pharmacodynamic Log 2' (total clearance) 


It is also important to design a set of mole- 
cules that will yield a range of values in terms 
of biological activities. It is understandable 
that most medicinal chemists are reluctant to 
synthesize molecules with poor activity, even 
though these data points are important in de- 
veloping a meaningful QSAR. Generally, the 
larger the range (>2 log units) in activity, the 
easier it is to generate a predictive QSAR. This 
kind of equation is more forgiving in terms of 
errors of measurement. A narrow range in bi- 
ological activity is less forgiving in terms of 
accuracy of data. Another factor that merits 
consideration is the time structure. Should a 
particular reading be taken after 48 or 72 h? 
Knowledge of cell cycles in cellular systems or 
biorhythms in animals would be advanta- 

Each single step of drug transport, binding, 
and metabolism involves some form of parti- 
tioning between an aqueous compartment and 
a nonaqueous phase, which could be a mem- 
brane, serum protein, receptor, or enzyme. In 
the case of isolated receptors, the endpoint is 
clear-cut and the critical step is evident. But in 
more complex systems, such as cellular sys- 
tems or whole animals, many localized steps 
could be involved in the random-walk process 
and the eventual interaction with a target. 

Usually the observed biological activity is re- 
flective of the slow step or the rate-determin- 
ing step. 

To determine a defined biological response 
(e.g., IC,,), a dose-response curve is first es- 
tablished. Usually six to eight concentrations 
are tested to yield percentages of activity or 
inhibition between 20 and 80%, the linear por- 
tion of the curve. Using the curves, the dose 
responsible for an established effect can easily 
be determined. This procedure is meaningful 
if, at the time the response is measured, the 
system is at equilibrium, or at least under 
steady-state conditions. 

Other approaches have been used to apply 
the additivity concept and ascertain the bind- 
ing energy contributions of various substitu- 
ent (R) groups. Fersht et al. have measured 
the binding energies of various alkyl groups to 
aminoacyl-tRNA synthetases (54). Thus the 
AG values for methyl, ethyl, isopropyl, and 
thio substituents were determined to be 3.2, 
6.5, 9.6, and 5.4 kcal/mol, respectively. 

An alternative, generalized approach to de- 
termining the energies of various drug-recep- 
tor interactions was developed by Andrews et 
al. (55), who statistically examined the drug- 
receptor interactions of a diverse set of mole- 
cules in aqueous solution. Using Equation 1.9, 
a relationship was established between AG 
and Ex (intrinsic binding energy), ED,, (energy' 
of average entropy loss), and the A S , ,  (energy 
of rotational and translational entropy loss). 

Ex denotes the sum of the intrinsic binding 
energy of each functional group of which nx 
are present in each drug in the set. Using 
Equation 1.9, the average binding energies for 
various functional groups were calculated. 
These energies followed a particular trend 
with charged groups showing stronger inter- 
actions and nonpolar entities, such as sp2, sp3 

carbons, contributing very little. The applica- 
bility of this approach to specific drug-receptor 
interactions remains to be seen. 

2.2 Statistical Methods: Linear 
Regression Analysis 
The most widely used mathematical tech- 
nique in QSAR analysis is multiple regression 

2 Tools and Techniques of QSAR 

analysis (MRA). We will consider some of the Expanding Equation 1.15, we obtain 
basic tenets of this approach to gain a firm 
understanding of the statistical procedures n 
that define a QSAR. Regression analysis is a SS = 2 (Yo,: - YobsaXi - YObsb 
powerful means for establishing a correlation i = l  
between independent variables and a depen- 
dent variable such as biological activity (56). - Yob&Xi + a2Xi2 + aXib (1.16) 

Taking the partial derivative of Equation 1.14 
Certain assumptions are made with regard with respect to b and then with respect to a, 
to this procedure (57): results in Equations 1.17 and 1.18. 

1. The independent variables, which in this 
dSS n case usually include the physicochemical - = 2 - 2(Yobs - b - ax i )  

parameters, are measured without error. db 

i = l  
Unfortunately, this is not always the case, 
although the error in these variables is dSS n 
small compared to that in the dependent -- da - 2 - 2Xi(Yobs - b - ax i )  (1.18) variable. i = l  

2. For any given value of X, the Y values are 
independent and follow a normal distribu- SS can be minimized with respect to b and a 
tion. The error term Ei possesses a normal and divided by -2 to yield the normal Equa- 
distribution with a mean of zero. tions 1.19 and 1.20. 

3. The expected mean value for the variable 
Y, for all values of X, lies on a straight line. 

4. The variance around the regression line is 
constant. The "best" straight line for 
model Yi = b + aZi + E is drawn through 
the data points, such that the sum of the 
squares of the vertical distances from the 
points to the line is minimized. Y repre- 
sents the value of the observed data point 
and Y,,,, is the predicted value on the line. 
The sum of squares SS = 2: (Y,,, - Yc,,)2. 

These "normal equations" can be rewritten as 

2 Ei2 = C A2 = SS 
i = l  

The solution of these simultaneous equa- 
tions yields a and b. More thorough analyses 

= 2 ( yobs - YcaIc) of these procedures have been examined in 
detail (19, 58-60). The following simple ex- 

n ample, illustrated by Table 1.3, will illus- 
Thus, SS = 2 (Yobs - axi  - b)2 (1.15) trate the nuances of a linear regression anal- 

i = l  ysis. 

Table 1.3 Antibacterial Activity 
of N'-(R-pheny1)sulfanilamides 

Compound u(X) Observed BA (Y) 

1. 4-CH3 -0.17 4.66 
2. 4-H 0 4.80 
3. 4 4 1  0.23 4.89 
4. 241 0.23 5.55 
5. 2-NO2 0.78 6.00 
6. 4-NO, 0.78 6.00 

k = no. of variables = 1 
n = no. of data points = 6 
X X = 1.85 
Z Y = 31.90 
Z X2 = 1.352 
Z Y2 = 171.45 
Z XY = 10.968 

For linear regression analysis, Y = ax + b 

The correlation coefficient r, the total vari- 
ance SS,, the unexplained variance SSQ, 
and the standard deviation, are defined as 

x A2 = SSQ = 2 (Yobs - YcdJ2 (1.25) 

History of Quantitative Structure-Activity Relationships 

The correlation coefficient r is a measure of 
quality of fit of the model. It constitutes the 
variance in the data. In an ideal situation one 
would want the correlation coefficient to be 
equal to or approach 1, but in reality because 
of the complexity of biological data, any value 
above 0.90 is adequate. The standard devia- 
tion is an absolute measure of the quality of fit. 
Ideally s should approach zero, but in experi- 
mental situations, this is not so. It should be 
small but it cannot have a value lower than the 
standard deviation of the experimental data. 
The magnitude of s may be attributed to some 
experimental error in the data as well as im- 
perfections in the biological model. A larger 
data set and a smaller number of variables 
generally lead to lower values of s. The F value 
is often used as a measure of the level of sta- 
tistical significance of the regression model. It 
is defined as denoted in Equation 1.27. 

A larger value of F implies a more significant 
correlation has been reached. The confidence 
intervals of the coefficients in the equation r& 
veal the significance of each regression term in 
the equation. 

To obtain a statistically sound QSAR, it is 
important that certain caveats be kept in 
mind. One needs to be cognizant about col- 
linearity between variables and chance corre- 
lations. Use of a correlation matrix ensures 
that variables of significance and/or interest 
are orthogonal to each other. With the rapid 
proliferation of parameters, caution must be 
exercised in amassing too many variables for a 
QSAR analysis. Topliss has elegantly demon- 
strated that there is a high risk of ending up 
with a chance correlation when too many vari- 
ables are tested (62). 

Outliers in QSAR model generation 
present their own problems. If they are badly 
fit by the model (off by more than 2 standard 
deviations), they should be dropped from the 
data set, although their elimination should be 
noted and addressed. Their aberrant behavior 

3 Parameters Used in QSAR 

may be attributed to inaccuracies in the test- 
ing procedure (usually dilution errors) or un- 
usual behavior. They often provide valuable 
information in terms of the mechanistic inter- 
pretation of a QSAR model. They could be par- 
ticipating in some intermolecular interaction 
that is not available to other members of the 
data set or have a drastic change in mecha- 

2.3 Compound Selection 

In setting up to run a QSAR analysis, com- 
pound selection is an important angle that 
needs to be addressed. One of the earliest 
manual methods was an approach devised by 
Craig, which involves two-dimensional plots of 
important physicochemical properties. Care is 
taken to select substituents from all four 
quadrants of the plot (63). The Topliss opera- 
tional scheme allows one to start with two 
compounds and construct a potency tree that 
grows branches as the substituent set is ex- 
panded in a stepwise fashion (64). Topliss 
later proposed a batchwise scheme including 
certain substituents such as the 3,4-Cl,, 441, 
4-CH,, 4-OCH,, and 4-H analogs (65). Other 
methods of manual substituent selection in- 
clude the Fibonacci search method, sequential 
simplex strategy, and parameter focusing by 
Magee (66 - 68). 

One of the earliest computer-based and sta- 
tistical selection methods, cluster analysis was 
devised by Hansch to accelerate the process 
and diversity of the substituents (1). Newer 
methodologies include D-optimal designs, 
which focus on the use of det (X'X), the vari- 
ance-covariance matrix. The determinant of 
this matrix yields a single number, which is 
maximized for compounds expressing maxi- 
mum variance and minimum covariance (69 - 
71). A combination of fractional factorial de- 
sign in tandem with a principal property 
approach has proven useful in QSAR (72). Ex- 
tensions of this approach using multivariate 
design have shown promise in environmental 
QSAR with nonspecific responses, where the 
clusters overlap and a cluster-based design ap- 
proach has to be used (73). With strongly clus- 
tered data containing several classes of com- 
pounds, a new strategy involving local 
multivariate designs within each cluster is de- 
scribed. The chosen compounds from the local 

designs are grouped together in the overall 
training set that is representative of all clus- 
ters (74). 


3.1 Electronic Parameters 

Parameters are of critical importance in deter- 
mining the types of intermolecular forces that 
underly drug-receptor interactions. The three 
major types of parameters that were initially 
suggested and still hold sway are electronic, 
hydrophobic, and steric in nature (20,751. Ex- 
tensive studies using electronic parameters 
reveal that electronic attributes of molecules 
are intimately related to their chemical reac- 
tivities and biological activities. A search of a 
computerized QSAR database reveals the fol- 
lowing: the common Hammett constants (a, 
u+, up) account for 700018500 equations in 
the Physical organic chemistry (PHYS) data- 
base and nearly 1600/8000 in the Biology 
(BIO) database, whereas quantum chemical 
indices such as HOMO, LUMO, BDE, and po- 
larizability appear in 100 equations in the BIO 
database (76). 

The extent to which a given reaction re- 
sponds to electronic perturbation constitutes 
a measure of the electronic demands of that 
reaction, which is determined by its mecha- , 
nism. The introduction of substituent groups 
into the framework and the subsequent alter- 
ation of reaction rates helps delineate the 
overall mechanism of reaction. Early work ex- 
amining the electronic role of substituents on 
rate constants was first tackled by Burckhardt 
and firmly established by Hammett (13, 14, 
77, 78). Hammett employed, as a model reac- 
tion, the ionization in water of substituted 
benzoic acids and determined their equilib- 
rium constants K,. See Equation 1.28. This 
led to an operational definition of u, the sub- 
stituent constant. It is a measure of the size of 
the electronic effect for a given substituent 
and represents a measure of electronic charge 
distribution in the benzene nucleus. 

Electron-withdrawing substituents are thus 



characterized by positive values, whereas elec- 
tron-donating ones have negative values. In 
an extension of this approach, the ionization 
of substituted phenylacetic acids was mea- 

The effect of the 4-C1 substituent on the ion- 
ization of 4 4 1  phenylacetic acid (PA) was 
found to be proportional to its effect on the 
ionization of 4-C1 benzoic acid (BA). 

K' a 

then log--,= p e a  
K H 

p (rho) is defined as a proportionality or reac- 
tion constant, which is a measure of the sus- 

History of Quantitative Structure-Activity Relationships 

ceptibility of a reaction to substituent effects. 
A positive rho value suggests that a reaction is 
aided by electron withdrawal from the reac- 
tion site, whereas a negative rho value implies 
that the reaction is assisted by electron dona- 
tion at the reaction site. Hammett also drew 
attention to the fact that a plot of log KA for 
benzoic acids versus log k for ester hydrolysis 
of a series of molecules is linear, which sug- 
gests that substituents exert a similar effect in 
dissimilar reactions. 

kx Kx log - log - = p - a (1.32) 

Although this expression is empirical in na- 
ture, it has been validated by the sheer volume 
of positive results. It is remarkable because 
four different energy states must be related. 

A correlation of this type is clearly mean- 
ingful; it suggests that changes in structure 
produce proportional changes in the activa- 
tion energy AG* for such reactions. Hence, the 
derivation of the name for which the Hammett 
equation is universally known: linear free en- 
ergy relationship (LFER). Equation 1.32 has 
become known as the Hammett equation and 
has been applied to thousands of reactions 
that take place at or near the benzene ring 
bearing substituents at the meta and para po- 
sitions. Because of proximity and steric ef- 
fects, ortho-substituted molecules do not al- 
ways follow this maxim and are subject to 
different parameterizations. Thus, an ex- 
panded approach was established by Charton 
(79) and Fujita and Nishioka (80). Charton 
partitioned the ortho electronic effect into its 
inductive, resonance, and steric contribu- 
tions; the factors a, p, and X are susceptibility 
or reaction constants and h is the intercept. 

Log k = aa, + paR + Xr, + h (1.33) 

Fujita and Nishioka used an integrated ap- 
proach to deal with ortho substituents in data 
sets including meta and para substituents. 

Log k = p a  + GEsodhO + fFOrth, + C (1.34) 

For ortho substituents, para sigma values 

3 Parameters Used in QSAR 

were used in addition to Taft's Es values and 
Swain-Lupton field constants F,,,,. 

The reason for employing alternative treat- 
ments to ortho-substituted aromatic mole- 
cules is that changes in rate or ionization con- 
stants mediated by meta or para substituents 
are mostly changes in (@ or AiT because sub- 
stitution does not affect AS* or AS". Ortho 
substituents affect both enthalpy and entropy; 
the effect on entropy is noteworthy because 
entropy is highly sensitive to changes in the 
size of reagents and substituents as well as 
degree of solvation. Bolton et al. examined the 
ionization of substituted benzoic acids and 
measured accurate values for AG, AH, and A S  
(81). A hierarchy of different scenarios, under 
which an LFER operates, was established: 

1. AIP is constant and A S  varies for a series. 
2. AS" is constant and AH varies. 
3. AiT and AS" vary and are shown to be lin- 

early related. 
4. Precise measurements indicated that cate- 

gory 3 was the prevalent behavior in ben- 
zoic acids. 

Despite the extensive and successful use in 
QSAR studies, there are some limitations to 
the Hammett equation. 

1. Primary a values are obtained from the 
thermodynamic ionizations of the appro- 
priate benzoic acids at 25°C; these are reli- 
able and easily available. Secondary values 
are obtained by comparison with another 
series of compounds and are thus subject to 
error because they are dependent on the 
accuracy of a measured series and the de- 
velopment of a regression line using statis- 
tical methods. 

2. In some multisubstituted compounds, the 
lack of additivity needs to be noted. Proxi- 
mal effects are operative and tend to distort 
electronic contributions. For example, 

2 aCdc(3 ,4,5- trichlorobenzoic acid) 
= 0.97; 

thatis, 2 a M +  up or 2(0.37) + 0.23 

aObs(3 ,4,5-trichlorobenzoic acid) = 0.95 

Sigma values for smaller substituents are 
more likely to be additive. However, in the 
case of 3-methyl, 4-dimethylaminobenzoic 
acid, the discrepancy is high. For example, 

2 acdc(3-CH,, 4-N(CH3), benzoic acid) 

2 uobs(3-CH3, 4-N(CH3)2 benzoic acid) 

The large discrepancy may be attributed to 
the twisting of the dimethylamino substitu- 
ent out of the plane of the benzene ring, 
resulting in a decrease in resonance. Exner 
and his colleagues have critically examined 
the use of additivity in the determination of 
a constants (82). 

3. Changes in mechanism or transition state 
cause discontinuities in Hammett plots. 
Nonlinear plots are often found in reac- 
tions that proceed by two concurrent path- 
ways (83,84). 

4. Changes in solvent may lead to dissimilar- 
ities in reaction mechanisms. Thus extrap- 
olation of u values from a polar solv'ent 
(e.g., CH,CN) to a nonpolar solvent such as 
benzene has to be approached cautiously. 
Solvation properties will differ consider- 
ably, particularly if the transition state is 
polar andlor the substituents are able to - 
interact with the solvent. 

5. A strong positional dependency of sigma 
makes it imperative to use appropriate val- 
ues for positional, isomeric substituents. 
Substituents ortho to the reaction center 
are difficult to describe and thus one must 
resort to a Fujita-Nishioka analysis (80). 

6. Thorough resonance or direct conjugation 
effects cause a breakdown in the Hammett 
equation. When coupling occurs between 
the substituent and the reaction center 
through the pi-electron system, reactivity 
is enhanced, diminished, or mitigated by 
separation. In a study of X-cumyl chlorides, 
Brown and Okamoto noticed the strong 
conjugative interaction between lone-pair, 

para substituents and the vacant p-orbital 
in the transition state, which led to devia- 
tions in the Hammett plot (85). They de- 
fined a modified LFER applicable to this 

Log- = ( p + ) ( a + )  

k H 

a+ was a new substituent constant that ex- 
pressed enhanced resonance attributes. A 
similar situation was noticed when a strong 
donor center was present as a reactant or 
formed as a product (e.g., phenols and mi-  
lines). In this case, strong resonance interac- 
tions were possible with electron-withdrawing 
groups (e.g., NO, or CN). A scale for such sub- 
stituents was constructed such that 

One shortcoming of the benzoic acid sys- 
tem is the extent of coupling between the car- 
boxyl group and certain lone-pair donors. In- 
sertion of a methylene group between the core 
(benzene ring) and the functional group 
(COOH moiety) leads to phenylacetic acids 
and the establishment of a0 scale from the ion- 
ization of X-phenylacetic acids. A flexible 
method of dealing with the variability of the 
resonance contribution to the overall elec- 
tronic demand of a reaction is embodied in the 
Yukawa-Tsuno equation (86). It includes nor- 

and enhanced resonance contributions to 

Log - = p[a + r(a+ - a)]  (1.37) 


where r is a measure of the degree of enhanced 
resonance interaction in relation to benzoic 
acid dissociations (r = 0) and cumyl chloride 
hydrolysis (r = 1). 

Most of the Hammett-type constants per- 
tain to aromatic systems. In evaluating an 
electronic parameter for use in aliphatic sys- 
tems, Taft used the relative acid and base hy- 
drolysis rates for esters. He developed equa- 
tion 1.38 as a measure of the inductive effect 

History of Quantitative Structure-Activity Relationships 

(a*) of a substituent R' in the ester R' COOR, 
where B and A refer to basic and acidic hydro- 
lysis, respectively. 

The factor of 2.48 was used to make a* equi- 
scalar with Hammett a values. Later, a aI 
scale derived from the ionization of 4-X- 
bicyclo[2.2.2]octane-1-carboxylic acids was 
shown to be related to a* (87, 88). I t  is now 
more widely used than a*. 

Ionization is a function of the electronic 
structure of an organic drug molecule. Albert 
was the first to clearly delineate the relation- 
ship between ionization and biological activity 
(89). Now, pKa values are widely used as the 
independent variable in physical organic reac- 
tions and in biological systems, particularly 
when dealing with transport phenomena. 
However, caution must be exercised in inter- 
preting the dependency of biological activity 
on pKa values because pKa values are inher- 
ently composites of electronic factors that are 
used directly in QSAR analysis. 

In recent years, there has been a rapid 
growth in the application of quantum chemi- 
cal methodology to QSAR, by direct derivation 
of electronic descriptors from the molecular 
wave functions (90). The two most popular 
methods used for the calculation of quantum 
chemical descriptors are ab initio (Hartree- 
Fock) and semiempirical methods. As in other 
electronic parameters, QSAR models incorpo- 
rating quantum chemical descriptors will in- 
clude information on the nature of the inter- 
molecular forces involved in the biological 
response. Unlike other electronic descriptors, 
there is no statistical error in quantum chem- 
ical computations. The errors are usually 
made in the assumptions that are established 
to facilitate calculation (91). Quantum chemi- 
cal descriptors such as net atomic changes, 
highest occupied molecular orbitalllowest un- 
occupied molecular orbital (HOMO-LUMO) 
energies, frontier orbital electron densities, 
and superdelocalizabilities have been shown 

3 Parameters Used in QSAR 

to correlate well with various biological activ- 
ities (92). A mixed approach using frontier or- 
bital theory and topological parameters have 
been used to calculate Hammett-like substitu- 
ent constants (93). 

In Equation 1.40, AN represents the extent 
of electron transfer between interacting ac- 
id-base systems; AE is the energy decrease in 
bimolecular systems underlying electron 
transfer; DXDH (EAH/EAx) corresponds to 
electron affinity and distance terms; and 
OS, factors the electrotopological state in- 
dex, whereas E a is the number of all a-elec- 
trons in the functional group. Observed 
principal component analysis (PCA) cluster- 
ing of 66 descriptors derived from AM1 cal- 
culations was similar to that previously re- 
ported for monosubstituted benzenes (94, 
95). The advantages of quantum chemical 
descriptors are that they have definite 
meaning and are useful in the elucidation of 
intra- and intermolecular interactions and 
can easily be derived from the theoretical 
structure of the molecule. 

3.2 Hydrophobicity Parameters 

More than a hundred years ago, Meyer and 
Overton made their seminal discovery on the 
correlation between oiltwater partition coeffi- 
cients and the narcotic potencies of small or- 
ganic molecules (7,8). Ferguson extended this 
analysis by placing the relationship between 
depressant action and hydrophobicity in a 
thermodynamic context; the relative satura- 
tion of the depressant in the biophase was a 
critical determinant of its narcotic potency (9). 
At this time, the success of the Hammett equa- - 
tion began to permeate structure-activity 
studies and hydrophobicity as a determinant 
was relegated to the background. In a land- 
mark study, Hansch and his colleagues de- 

vised and used a multiparameter approach 
that included both electronic and hydrophobic 
terms, to establish a QSAR for a series of plant 
growth regulators (16). This study laid the ba- 
sis for the development of the QSAR paradigm 
and also firmly established the importance of 
lipophilicity in biosystems. Over the last 40 
years, no other parameter used in QSAR has 
generated more interest, excitement, and con- 
troversy than hydrophobicity (96). Hydropho- 
bic interactions are of critical importance in 
many areas of chemistry. These include en- 
zyme-ligand interactions, the assembly of lip- 
ids in biomembranes, aggregation of surfac- 
tants, coagulation, and detergency (97-100). 
The integrity of biomembranes and the ter- 
tiary structure of proteins in solution are de- 
termined by apolar-type interactions. 

Molecular recognition depends strongly on 
hydrophobic interactions between ligands and 
receptors. Excellent treatises on this subject 
have been written by Taylor (101) and Blokzijl 
and Engerts (51). Despite extensive usage of 
the term hydrophobic bond, it is well known 
that there is no strong attractive force be- 
tween apolar molecules (102). Frank and 
Evans were the first to apply a thermodynamic 
treatment to the solvation of apolar molecules 
in water at room temperature (103). Their 
"iceberg" model suggested that a large en- 
tropic loss ensued after the dissolution of apo- 
lar compounds and the increased structure of 
water molecules in the surrounding apolar sol- 
ute. The quantitation of this model led to the 
development of the "flickering" cluster model 
of NBmethy and Scheraga, which emphasized 
the formation of hydrogen bonds in liquid wa- 
ter (104). The classical model for hydrophobic 
interactions was delineated by Kauzmann to 
describe the van der Waals attractions be- 
tween the nonpolar parts of two molecules im- 
mersed in water. Given that van der Waals 
forces operate over short distances, the water 
molecules are squeezed out in the vicinity of 
the mutually bound apolar surfaces (49). The 
driving force for this behavior is not that al- 
kanes "hate" water, but rather water that 
"hates" alkanes (105, 106). Thus, the gain in 
entropy appears as the critical driving force 
for hydrophobic interactions that are primar- 
ily governed by the repulsion of hydrophobic 

16 History of Quantitative Structure-Activity Relationships 

solutes from the solvent water and the limited 
but important capacity of water to maintain 
its network of hydrogen bonds. 

Hydrophobicities of solutes can readily be 
determined by measuring partition coeffi- 
cients designated as P. Partition coefficients 
deal with neutral species, whereas distribu- 
tion ratios incorporate concentrations of 
charged andlor polymeric species as well. By 
convention, P is defined as the ratio of concen- 
tration of the solute in octanol to its concen- 
tration in water. 

It was fortuitous that octanol was chosen as 
the solvent most likely to mimic the biomem- 
brane. Extensive studies over the last 35 years 
(40,000 experimental P-values in 400 different 
solvent systems) have failed to dislodge octa- 
no1 from its secure perch (107,108). 

Octanol is a suitable solvent for the mea- 
surement of partition coefficients for many 
reasons (109, 110). It is cheap, relatively non- 
toxic, and chemically unreactive. The hy- 
droxyl group has both hydrogen bond acceptor 
and hydrogen bond donor features capable of 
interacting with a large variety of polar 
groups. Despite its hydrophobic attributes, it 
is able to dissolve many more organic com- 
pounds than can alkanes, cycloalkanes, or ar- 
omatic hydrocarbons. It is UV transparent 
over a large range and has a vapor pressure 
low enough to allow for reproducible measure- 
ments. It is also elevated enough to allow for 
its removal under mild conditions. In addition, 
water saturated with octanol contains only 

M octanol at equilibrium, whereas octa- 
no1 saturated with water contains 2.3 M of 
water. Thus, polar groups need not be totally 
dehydrated in transfer from the aqueous 
phase to the organic phase. Likewise, hydro- 
phobic solutes are not appreciably solvated by 
the M octanol in the water phase unless 
their intrinsic log P is above 6.0. Octanol be- 
gins to absorb light below 220 nm and thus 
solute concentration determinations can be 
monitored by W spectroscopy. More impor- 
tant, octanol acts as an excellent mimic for 
biomembranes because it shares the traits of 

amphiphilicity and hydrogen-bonding capabil- 
ity with phospholipids and proteins found in 
biological membranes. 

The choice of the octanollwater partition- 
ing system as a standard reference for assess- 
ing the compartmental distribution of mole- 
cules of biological interest was recently 
investigated by molecular dynamics simula- 
tions (111). It was determined that pure l-oc- 
tan01 contains a mix of hydrogen-bonded 
"polymeric" species, mostly four-, five-, and 
six-membered ring clusters at 40°C. These 
small ring clusters form a central hydroxyl 
core from which their corresponding alkyl 
chains radiate outward. On the other hand, 
water-saturated octanol tends to form well-de- 
fined, inverted, micellar aggregates. Long hy- 
drogen-bonded chains are absent and water 
molecules congregate around the octanol hy- 
droxyls. "Hydrophilic channels" are formed by 
cylindrical formation of water and octanol hy- 
droxyls with the alkyl chains extending out- 
ward. Thus, water-saturated octanol has cen- 
tralized polar cores where polar solutes can 
localize. Hydrophobic solutes would migrate 
to the alkyl-rich regions. This is an elegant 
study that provides insight into the partition- 
ing of benzene and phenol by analyzing the 
structure of the octanollwater solvation shell 
and delineating octanol's capability to serve as 
a surrogate for biomembranes. 

The shake-flask method, so-called, is most 
commonly used to measure partition coeffi- 
cients with great accuracy and precision and 
with a log P range that extends from -3 to +6 
(112, 113). The procedure calls for the use of 
pure, distilled, deionized water, high-purity 
octanol, and pure solutes. At least three con- 
centration levels of solute should be analyzed 
and the volumes of octanol and water should 
be varied according to a rough estimate of the 
log P value. Care should be exercised to ensure 
that the eventual amounts of the solute in 
each phase are about the same after equilib- 
rium. Standard concentration curves using 
three to four known concentrations in water 
saturated with octanol are usually estab- 
lished. Generally, most methods employ a UV- 
based procedure, although GC and HPLC may 
also be used to quantitate the concentration of 
the solute. 

3 Parameters Used in QSAR 

Generally, 110-mL stopped centrifuge tubes or 
2WmL centrifuge bottles are used. They are in- 
verted gently for 2-3 min and then centrifuged at 
1000-2000 g for 20 min before the phases are an- 
alyzed. Analysis of both phases is highly recom- 
mended, to minimize errors incurred by adsorp 
tion to glass walls at low solute concentration. For 
highly hydrophobic compounds, the slow stirring 
procedure of de B d j n  and Hermens is recom- 
mended (114). The filler probe extractor system of 
Tornlinson et al. is a modified, automated, shake 
flask method, which is efficient, fast, reliable, and 
flexible (115). 

Partition coefficients from different sol- 
vent systems can also be compared and con- 
verted to the octanollwater scale, as was sug- 
gested by Collander (116). He stressed the 
importance of the following linear relation- 
ship: log P, = a log P, + b. This type of rela- 
tionship works well when the two solvents are 
both alkanols. However, when two solvent sys- 
tems have varying hydrogen bond donor and 
acceptor capabilities, the relationship tends to 
fray. A classical example involves the relation- 
ship between log P values in chloroform and 
octanol(ll7, 118). 

Log Po,,, = 1.012 log P,, - 0.513 (1.42) 

Only 66% of the variance in the data is ex- 
plained by this equation. However, a separation 
of the various solutes into OH bond donors, ac- 
ceptors, and neutrals helped account for 94% of 
the variance in the data. These restrictions led 
Seiler to extend the Collander equation by incor- 
porating a corrective term for H-bonding in the 
cyclohexane system (119). Fujita generalized 
this approach and formulated Equation 1.43 as 
shown below (120). 

log P2 = a log P,  + 2 bi. HBi + C (1.43) 
P, is the reference solvent and HB, is an H- 

bonding parameter. Leahy et al. suggested that 
a more sophisticated approach incorporating 
four model systems would be needed to ade- 
quately address issues of solute partitioning in 
membranes (121). Thus, four distinct solvent 
types were chosen-apolar, amphiprotic, proton 

donor, and proton acceptor-and they were rep- 
resented by alkanes, odanol, chloroform, and 
propyleneglycol dipelargonate (PGDP), respec- 
tively. The demands of measuring four partition 
coefficients for each solute has slowed progress 
in this particular area. 

3.2.1 Determination of Hydrophobicity by 
Chromatography. Chromatography provides 
an alternate tool for the estimation of hydro- 
phobicity parameters. R, values derived from 
thin-layer chromatography provide a simple, 
rapid, and easy way to ascertain approximate 
values of hydrophobicity (122,123). 

Other recent developments in chromatogra- 
phy techniques have led to the development . ~ 
of powerful tools to rapidly and accurately 
measure octanol/water partition coefficients. 
Countercurrent chromatography is one of 
these methods. The stationary and mobile 
~hases  include two nonmiscible solvents (wa- 

ter and octanol) and the total volume of the 
liquid stationary phase is used for solute par- 
titioning (124,125). Log P,,, values of several 
diuretics including ionizable drugs have been 
measured at different pH values using coun- 
tercurrent chromatography; the log P values 
ranged from -1.3 to 2.7 and were consistknt 
with literature values (126). 

Recently, a rapid method for the determi- 
nation of partition coefficients using gradient 
reversed phasehigh pressure liquid chroma- 
tography (RP-HPLC) was developed. This 
method is touted as a high-throughput hydro- 
phobicity screen for combinatorial libraries 
(127, 128). A chromatography hydrophobicity 
index (CHI) was established for a diverse set of 
compounds. Acetonitrile was used as the mod- 
ifier and 50 mm ammonium acetate as the mo- 
bile phase (127). A linear relationship was es- 
tablished between Clog P and CHIN for 
neutral molecules. 

Clog P = 0.057 CHIN - 1.107 (1.45) 

A more recent study using RP-HPLC for the 
determination of log P (octanol) values for 

neutral and weakly acidic and basic drugs, 
revealed an excellent correlation between 
log Po,, and log Kw values (129). Log Po,, 
values determined in this system are re- 
ferred to as Elog Po,,. They were expressed 
in terms of solvation parameters. 

In this equation, R, is the excess molar re- 
fraction; ,rr,H is the dipolarity/polarizability; 
2 aZH and 2 p,O are the summation of hydro- 
gen bond acidity and basicity values, respec- 
tively; and V, is McGowan's volume. 

3.2.2 Calculation Methods. Partition coef- 
ficients are additive-constitutive, free energy- 
related properties. Log P represents the over- 
all hydrophobicity of a molecule, which 
includes the sum of the hydrophobic contribu- 
tions of the "parent" molecule and its sub- 
stituent. Thus, the .rr value for a substituent 
may be defined as 

% is set to zero. The n-value for a nitro 
substituent is calculated from the log P of ni- 
trobenzene and benzene. 

An extensive list of T-values for aromatic 
substituents appears in Table 1.4. Pi values 
for side chains of amino acids in peptides have 
been well characterized and are easily avail- 
able (130-132). Aliphatic fragments values 
were developed a few years later. For a more 
extensive list of substituent value constants, 
refer to the extensive compilation by Hansch 
et al. (133). Initially, the T-system was applied 
only to substitution on aromatic rings and 
when the hydrogen being replaced was of in- 
nocuous character. It was apparent from the 

History of Quantitative Structure-Activity Relationships 

beginning that not all hydrogens on aromatic 
systems could be substituted without correc- 
tion factors because of strong electronic inter- 
actions. It became necessary to determine .rr 
values in various electron-rich and -deficient 
systems (e.g., X-phenols and X-nitroben- 
zenes). Correction factors were introduced for 
special features such as unsaturation, branch- 
ing, and ring fusion. The proliferation of 
T-scales made it difficult to ascertain which 
system was more appropriate for usage, par- 
ticularly with complex structures. 

The shortcomings of this approach pro- 
vided the impetus for Nys and Rekker to de- 
sign the fragmental method, a "reductionist" 
approach, which was based on the statistical 
analysis of a large number of measured parti- 
tion coefficients and the subsequent assign- 
ment of appropriate values for particular mo- 
lecular fragments (118, 134). Hansch and Leo 
took a "constructionist" approach and devel- 
oped a fragmental system that included cor- 
rection factors for bonds and proximity effects 
(1, 135). Labor-intensive efforts and inconsis- 
tency in manual calculations were eliminated 
with the debut of the automated system 
CLOGP and its powerful SMILES notation 
(136-138). Recent analysis of the accuracy of 
CLOGP yielded Equation 1.48 (139). . 

MLOGP = 0.959 CLOGP + 0.08 (1.48) 

The Clog P values of 228 structures (1.8% 
of the data set) were not well predicted. It 
must be noted that Starlist (most accurate val- 
ues in the database) contains almost 300 
charged nitrogen solutes (ammonium, pyri- 
dinium, imidazolium, etc.) and over 2200 in 
all, which amounts to 5% of Masterfile (data- 
base of measured values). CLOGP adequately 
handles these molecules within the 0.30 stan- 
dard deviation limit. Most other programs 
make no attempt to calculate them. For more 
details on calculating log Po, from structures, 
see excellent reviews by Leo (140, 141). 

The proliferation of methodologies and 
programs to calculate partition coefficients 
continues unabated. These programs are 
based on substructure approaches or whole- 
molecule approaches (142, 143). Substructure 

3 Parameters Used in QSAR 19 

Table 1.4 Substituent Constants for QSAR Analysis 

No. Substituent Pi MR L B1 B5 S-P S-M 

+ NH, 
C H , O ( N H , )  
N H O ( N H , )  

20 History of Quantitative Structure-Activity Relationships 

Table 1.4 (Continued) 



N H M ( C F , )  
N H M ( 0 E t )  

3 Parameters Used in QSAR 

Table 1.4 (Continued) 


C H 2 M ( C F 3 )  
4 - w d y l  

C H d H 2  


Table 1.4 (Continued) 

History of Quantitative Structure-Activity Relationships 


3 Parameters Used in QSAR 

Table 1.4 (Continued) 


C 6 H 4 1 ~  


methods are based on molecular fragments, 
atomic contributions, or computer-identified 
fragments (1, 106, 107, 144-147). Whole-mol- 
ecule approaches use molecular properties or 
spatial properties to predict log P values (148- 
150). They run on different platforms (e.g., 
Mac, PC, Unix, VAX, etc.) and use different 
calculation procedures. An extensive, recent 
review by Mannhold and van de Waterbeemd 
addresses the advantages and limitations of 
the various approaches (143). Statistical pa- 
rameters yield some insight as to the effective- 
ness of such programs. 

Recent attempts to compute log P calcula- 
tions have resulted in the development of sol- 
vatochromic parameters (151, 152). This ap- 
proach was proposed by Kamlet et al. and 
focused on molecular properties. In its sim- 
plest form it can be expressed as follows: 

hydrogen bond donor strength, respectively; 
and e is the intercept. An extension of this 
model has been formulated by Abraham and 
used by researchers to refine molecular de: 
scriptors and characterize hydrophobicity 
scales (153-156). 

3.3 Steric Parameters 

The quantitation of steric effects is complex at 
best and challenging in all other situations, 
particularly at the molecular level. An added 
level of confusion comes into play when at- 
tempts are made to delineate size and shape. 
Nevertheless, sterics are of overwhelming im- 
portance in ligand-receptor interactions as 
well as in transport phenomena in cellular sys- 
tems. The first steric parameter to be quanti- 
fied and used in QSAR studies was Taft's Es 
constant (157). Es is defined as 

V is a solute volume term; T* represents 
the solute polarizability; P,  and a ,  are mea- 
sures of hydrogen bond acceptor strength and 

where k ,  and k ,  represent the rates of acid 
hydrolysis of esters, XCH,COOR and CH,COOR, 

History of Quantitative Structure-Activity Relationships 

respectively. To correct for hyperconjuga- 
tion in the a-hydrogens of the acetate moi- 
ety, Hancock devised a correction on Es such 

In Equation 1.51, n represents the num- 
ber of a-hydrogens and 0.306 is a constant 
derived from molecular orbital calculations 
(158). Unfortunately, the limited availabil- 
ity of Es and Es

C values for a great number 
of substituents precludes their usage in 
QSAR studies. Charton demonstrated a 
strong correlation between Es and van der 
Waals radii, which led to his development of 
the upsilon parameter y, (159). 

where r ,  and r ,  are the minimum van der 
Waals radii of the substituent and hydrogen, 
respectively. Extension of this approach 
from symmetrical substituents to nonsym- 
metrical substituents must be handled with 

One of the most widely used steric param- 
eters is molar refraction (MR), which has 
been aptly described as a "chameleon" pa- 
rameter by Tute (160). Although it is gener- 
ally considered to be a crude measure of 
overall bulk, it does incorporate a polariz- 
ability component that may describe cohe- 
sion and is related to London dispersion 
forces as follows: MR = 47rNd3, where N is 
Avogadro's number and a is the polarizabil- 
ity of the molecule. I t  contains no informa- 
tion on shape. MR is also defined by the 
Lorentz-Lorenz equation: 

MR is generally scaled by 0.1 and used in bio- 
logical QSAR, where intermolecular effects 
are of primary importance. The refractive in- 
dex of the molecule is represented by n. With 
alkyl substituents, there is a high degree of 
collinearity with hydrophobicity; hence, care 

must be taken in the QSAR analysis of such 
derivatives. The MR descriptor does not dis- 
tinguish shape; thus the MR value for amyl 
(-CH2CH2CH2CH2CH,) is the same as that 
for [-C(Et)(CH,),]: 2.42. The coefficients 
with MR terms challenge interpretation, al- 
though extensive experience with this param- 
eter suggests that a negative coefficient im- 
plies steric hindrance at that site and a 
positive coefficient attests to either dipolar in- 
teractions in that vicinity or anchoring of a 
ligand in an opportune position for interaction 

The failure of the MR descriptor to ade- 
quately address three-dimensional shape is- 
sues led to Verloop's development of STERI- 
MOL parameters (162), which define the 
steric constraints of a given substituent along 
several fixed axes. Five parameters were 
deemed necessary to define shape: L, B1, B2, 
B3, and B4. L represents the length of a sub- 
stituent along the axis of a bond between the 
parent molecule and the substituent; B1 to B4 
represent four different width parameters. 
However, the high degree of collinearity be- 
tween B1, B2, and B3 and the large number of 
training set members needed to establish the 
statistical validity of this group of parameters 
led to their demise in QSAR studies. Verloop 
subsequently established the adequacy of jqst 
three parameters for QSAR analysis: a slightly 
modified length L, a minimum width B1, and a 
maximum width B5 that is orthogonal to L 
(163). The use of these insightful parameters 
have done much to enhance correlations with 
biological activities. Recent analysis in our 
laboratory has established that in many cases, 
B1 alone is superior to Taft's Es and a combi- 
nation of B1 and B5 can adequately replace Es 

Molecular weight (MW) terms have also 
been used as descriptors, particularly in cellu- 
lar systems, or in distributionltransport stud- 
ies where diffusion is the mode of operation. 
According to the Einstein-Sutherland equa- 
tion, molecular weight affects the diffusion 
rate. The Log MW term has been used exten- 
sively in some studies (159-161) and an exam- 
ple of such usage is given below. In correlating 
permeability (Perm) of noneledrolytes through 
chara cells, Lien et al. obtained the following 
QSAR (168): 

3 Parameters Used in QSAR 25 

Log Perm 

= 0.889 log P* - 1.544 log MW (1.54) 

In QSAR 54, Log P* represents the olive oil/ 
water partition coefficient, MW is the molec- 
ular weight of the solute and defines its size, 
and Hb is a crude approximation of the total 
number of hydrogen bonds for each mole- 
cule. The molecular weight descriptor has 
also been an omnipresent variable in QSAR 
studies pertaining to cross-resistance of var- 
ious drugs in multidrug-resistant cell lines 
(169). was used because it most 
closely approximates the size (radii) of the 
drugs involved in the study and their inter- 
actions with GP-170. See QSAR 1.55. 

Log CR = 0.70 w 
- 1.01 l0g(Ps 10 + 1) 

- 0.10 log P + 0.381 

log /3 = -6.851 optimum = 7.21 

3.4 Other Variables and Variable Selection 

Indicator variables ( I )  are often used to high- 
light a structural feature present in some of 
the molecules in a data set that confers un- 
usual activity or lack of it to these particular 
members. Their use could be beneficial in 
cases where the data set is heterogeneous and 
includes large numbers of members with un- 
usual features that may or may not impact a 
biological response. QSAR for the inhibition of 
trypsin by X-benzamidines used indicator 
variables to denote the presence of unusual 
features such as positional isomers and vinyl/ 
carbonyl-containing substituents (170). A re- 
cent study on the inhibition of lipoxygenase 
catalyzed production of leukotriene B4 and 
5-hydroxyeicosatetraenoic from arachidonic 

acid in guinea pig leukocytes by X-vinyl cat- 
echols led to the development of the following 
QSAR (171): 

Log 11C 

Log Po = 4.61(?0.49) Log P = -4.33 

The indicator variables are D2 and D3; for 
simple X-catechols, D2 = 1 and for X-naphtha- 
lene diols, D3 = 1. The negative coefficients 
with both terms (D2 and D3) underscore the 
detrimental effects of these structural fea- 
tures in these inhibitors. Thus, discontinuities 
in the structural features of the molecules of 
this data set are accounted for by the use of 
indicator variables. An indicator variable may 
be visualized graphically as a constant that 
adjusts two parallel lines so that they are su- 
perimposable. The use of indicator variables 
in QSAR analysis is also described in the fol- 
lowing example. An analysis of a comprehen- . 
sive set of nitroaromatic and heteroaromatic 
compounds that induced mutagenesis in TA98 
cells was conducted by Debnath et al., and 
QSAR 1.57 was formulated (172). 

Log TA9 8 

Log Po = 4.93(%0.35) Log P = -5.48 

TA98 represents the number of revertants per 
nanomole of nitro compound. E,,,, is the 
energy of the lowest unoccupied molecular or- 

History of Quantitative Structure-Activity Relationships 

bital and I, is an indicator variable that signi- 
fies the presence of an acenthrylene ring in the 
mutagens. I, is also an indicator variable that 
pertains to the number of fused rings in the 
data set. It acquires a value of 1 for all conge- 
ners containing three or more fused rings and 
a value of zero for those containing one or two 
fused rings (e.g., naphthalene, benzene). 
Thus, the greater the number of fused rings, 
the greater the mutagenicity of the nitro con- 
geners. The EL,,, term indicates that the 
lower the energy of the LUMO, the more po- 
tent the mutagen. In this QSAR the combina- 
tion of indicator variables affords a mixed 
blessing. One variable helps to enhance activ- 
ity, whereas the other leads to a decrease in 
mutagenicity of the acenthrylene congeners. 
In both these QSAR, Kubinyi's bilinear model 
is used (21). See Section 4.2 for a description of 
this approach. 

3.5 Molecular Structure Descriptors 

These are truly structural descriptors because 
they are based only on the two-dimensional 
representation of a chemical structure. The 
most widely known descriptors are those that 
were originally proposed by Randic (173) and 
extensively developed by Kier and Hall (27). 
The strength of this approach is that the re- 
quired information is embedded in the hydro- 
gen-suppressed framework and thus no exper- 
imental measurements are needed to define 
molecular connectivity indices. For each bond 
the Ck term is calculated. The summation of 
these terms then leads to the derivation of X, 
the molecular connectivity index for the mol- 

S is the count of formally bonded carbons and 
h is the number of bonds to hydrogen atoms. 

'X is the first bond order because it considers 
only individual bonds. Higher molecular con- 
nectivity indices encode more complex at- 
tributes of molecular structure by considering 
longer paths. Thus, 2X and 3X account for all 
two-bond paths and three-bond paths, respec- 

tively, in a molecule. To correct for differences 
in valence, Kier and Hall proposed a valence 
delta (6") term to calculate valence connectiv- 
ity indices (175). 

Molecular connectivity indices have been 
shown to be closely related to many physico- 
chemical parameters such as boiling points, 
molar refraction, polarizability, and partition 
coefficients (174, 176). Ten years ago, the E- 
State index was developed to define an atom- 
or group-centered numerical code to represent 
molecular structure (28). The E-State was es- 
tablished as a composite index encoding both 
electronic and steric properties of atoms in 
molecules. It reflects an atom's electronegativ- 
ity, the electronegativity of proximal and dis- 
tal atoms, and topological state. Extensions of 
this method include the HE-State, atom-type 
E-State, and the polarity index Q.  Log P 
showed a strong correlation with the Q index 
of a small set (n = 21) of miscellaneous com- 
pounds (28). Various models using electroto- 
pological indices have been developed to delin- 
eate a variety of biological responses 
(177-179). Some criticism has been leveled at 
this approach (180, 181). Chance correlations 
are always a problem when dealing with such 
a wide array of descriptors. The physico- 
chemical interpretation of the meaning of 
these descriptors is not transparent, although 
attempts have been made to address thi's 
issue (27). 


4.1 Linear Models 

The correlation of biological activity with 
physicochemical properties is often termed an 
extrathermodynamic relationship. Because it 
follows in the line of Hammett and Taft equa- 
tions that correlate thermodynamic and re- 
lated parameters, it is appropriately labeled. 
The Hammett equation represents relation- 
ships between the logarithms of rate or equi- 
librium constants and substituent constants. 
The linearity of many of these relationships 
led to their designation as linear free energy 
relationships. The Hansch approach repre- 
sents an extension of the Harnmett equation 
from physical organic systems to a biological 
milieu. It should be noted that the simplicity 

4 Quantitative Models 

of the approach belies the tremendous com- 
plexity of the intermolecular interactions at 
play in the overall biological response. 

Biological systems are a complex mix of het- 
erogeneous phases. Drug molecules usually tra- 
verse many of these phases to get from the site of 
administration to the eventual site of action. 
Along this random-walk process, they perturb 
many other cellular components such as or- 
ganelles, lipids, proteins, and so forth. These in- 
teractions are complex and vastly different from 
organic reactions in test tubes, even though the 
eventual interaction with a receptor may be 
chemical or physicochemical in nature. Thus, 
depending on the biological system involved- 
isolated receptor, cell, or whole animal-one ex- 
pects the response to be multifactorial and com- 
plex. The overall process, particularly in vitro or 
in vivo, studies a mix of equilibrium and rate 
processes, a situation that defies easy separation 
and delineation. 

Meyer and Overton were the first to attempt 
to get a grasp on biological responses by noting 
the relationship between oillwater partition co- 
efficients and their narcotic activity. Ferguson 
recognized that equitoxic concentrations of 
small organic molecules was markedly influ- 
enced by their phase distribution between the 
biophase and exobiophase. This concept was 
generalized in the form of Equation 1.60 and 
extended by Fylita to Equation 1.61 (182,183). 

Log 1/C = m Log(1lA) + constant (1.61) 

C represents the equipotent concentration, k 
and m are constants for a particular system, 
and A is a physicochemical constant represen- 
tative of phase distribution equilibria such as 
aqueous solubility, oillwater partition coeffi- 
cient, and vapor pressure. In examining a 
large and diverse number of biological systems, 
Hansch and coworkers defined a relationship 
(Equation 1.62) that expressed biological ac- 
tivity as a function of physicochemical param- 
eters (e.g., partition coefficients of organic 
molecules) (19). 

Model systems have been devised to elucidate 

the mode of interactions of chemicals with bi- 
ological entities. Examples of linear models 
pertaining to nonspecific toxicity are de- 
scribed. The effects of a series of alcohols 
(ROH) have been routinely studied in many 
model and biological systems. See QSAR 1.63- 

4.1.1 Penetration of ROH into Phosphati- 
dylcholine Monolayers (1 84) 

Log 1/C = 0.87(?0.01)logP 
(1.63) + 0.66(&0.01) 

4.1.2 Changes in EPR Signal of Labeled 
Ghost Membranes by ROH (185) 

Log 1/C = 0.93(?0.09)logP 

4.1.3 Induction of Narcosis in Rabbits by 
ROH (184) 

Log 1/C = 0.72(?0.16)logP 

4.1.4 lnhibition of Bacterial Luminescence 
by ROH (1 85) 

Log 1/C = 1.10(+0.07)logP 
(1.66) + 0.16(20.12) 

4.1.5 lnhibition of Growth of Tetrahymena 
pyriformis by ROH (76, 186) 

Log 1/C = 0.82(+0.04)clog P 

In all cases, there is a strong dependency on 

Octanol phase n f7 Bio phase 
Water phase Aqueous phase 

Figure 1.1. Log Pohno, mirrors Log Pbio. 

log P,, because all these processes involve 
transport of alcohols through membranes. 
The low intercepts speak to the nonspecific 
nature of the alcohol-mediated toxic interac- 
tion. An equilibrium-pseudoequilibrium mod- 
eled by log P can be defined as shown in Fig. 

The Hammett-type relationship for this 
conceptual idea of distribution is 

Log Pbio = a . log Po-o1 + b (1.68) 
This postulate assumes that steric, hydropho- 
bic, electronic, and hydrogen bonding factors 
that affect partitioning in the biophase are 
handled by the octanollwater system. Given 
that the biological response (log 1/C) is propor- 
tional to log P,,, then it follows that 

Log 1IC = a . log + constant (1.69) 
Hansch and coworkers have amply demon- 
strated that Equation 1.69 applies not only to 
systems at or near phase distribution equilib- 
rium but also to systems removed from equi- 
librium (184, 185). 

4.2 Nonlinear Models 

Extensive studies on development of linear 
models led Hansch and coworkers to note that 
a breakdown in the linear relationship oc- 
curred when a greater range in hydrophobic- 
ity was assessed with particular emphasis 
placed on test molecules at extreme ends of the 
hydrophobicity range. Thus, Hansch et al. 
suggested that the compounds could be in- 
volved in a "random-walk" process: low hydro- 
phobic molecules had a tendency to remain in 
the first aqueous compartment, whereas 
highly hydrophobic analogs sequestered in the 
first lipoidal phase that they encountered. 
This led to the formulation of a parabolic 
equation, relating biological activity and hy- 
drophobicity (187). 

History of Quantitative Structure-Activity Relationships 

Log 1/C = -a(log P)* + b + log P 
+ constant (1.70) 

In the random-walk process, the compounds 
partition in and out of various compartments 
and interact with myriad biological compo- 
nents in the process. To deal with this conun- 
drum, Hansch proposed a general, compre- 
hensive equation for QSAR 1.71 (188). 

Log 1/C = -a(log P)' + b log P 
(1.71) + p u  + SEs + constant 

The optimum value of logP for a given system 
is log Po and it is highly influenced by the 
number of hydrophobic barriers a drug en- 
counters in its walk to its site of action. 
Hansch and Clayton formulated the following 
parabolic model to elucidate the narcotic ac- 
tion of alcohols on tadpoles (189). 

4.2.7 Narcotic Action of ROH on Tadpoles 

This is an example of nonspecific toxicity 
where the last step probably involves parti- 
tioning into a hydrophobic membrane. Log Po 
represents the optimal hydrophobicity (as de- 
fined by logP) that elicits a maximal biological 

Despite the success of the parabolic equa- 
tion, there are a number of worrisome limita- 
tions. This approach forces the data into a 
symmetrical parabola, with the result that 
there are usually deviations between the ex- 
perimental and parabola-calculated data. Sec- 
ond, the ascending slope is curved and incon- 
sistent with the observed linear data. Thus, 
the slope of a linear model cannot be compared 
to the curved slope of the parabola. In 1973 
Franke devised a sophisticated, empirical 

4 Quantitative Models 

model consisting of a linear ascending part 
and a parabolic part (190). See Equations 1.73 
and 1.74. 

Log 1/C = a . l o g P +  c 

(if log P < log Px) 

Log 1/C = -a(log P)' + b . log P + c 

(if log P > log Px) 

The binding of drugs to proteins is linearly 
dependent on hydrophobicity up to a limited 
value, log P,, after which steric hindrance 
causes the linear dependency to alter to a non- 
linear one. The major limitation of this ap- 
proach involves the inclusion of highly hydro- 
phobic congeners that tend to cause 
systematic deviations between experimental 
and predicted values. 

Another cutoff model, which deals with 
nonlinearity in biological systems, is one de- 
fined by McFarland (191). It attempts to elu- 
cidate the dependency of drug transport on 
hydrophobicity in multicompartment models. 
McFarland addressed the probability of drug 
molecules traversing several aqueous lipid 
barriers from the first aqueous compartment 
to a distant, final aqueous compartment. The 
probability Po,, of a drug molecule to access 
the final compartment n of a biological system 
was used to define the drug concentration in 
this compartment. 

LogCR= a - l o g P  - 2a.log(P+ 1) 

+ constant (1.75) 

The ascending and descending slopes are 
equal (= 1) and linear. However, a major draw- 
back of this model is that it forces the activity 
curves to maximize at log P = 0. These studies 
were extended by Kubinyi, who developed the 
elegant and powerful bilinear model, which is 
superior to the parabolic model and is exten- 
sively used in QSAR studies (192). 

Log 1/C= a . l o g P  - b- log(p.P + 1) 
+ constant (1.76) 

where p is the ratio of the volumes of the or- 

ganic phase and the aqueous phase. An impor- 
tant feature of this model lies in the symmetry 
of the curves. For aqueous phases of this