Preface
Progress in molecular biology and studies of small molecule binding to nu-
cleic acids have been inextricably linked. A testament to that fact is the inclusion of
eight papers directly concerned with drug-DNA interactions among the recently
published list of the 100 most cited articles in the
Journal of Molecular Biology.
Few other scientific areas are as well represented on that list. Small molecules have
perhaps taught us more about DNA than DNA has taught us about small molecules.
Watson, for example, notes in the
Molecular Biology of the Gene
that the "fact that
intercalation occurs so readily indicates that it is energetically favored [and] is
additional evidence for the metastability of the double-helical structure its ability
to assume many inherently unstable configurations that normally revert quickly
back to the standard B conformation." From that point of view, intercalation pro-
vided one of the very first indications of the plasticity of DNA, an area that has
blossomed to reveal an incredible diversity of structural forms. Perhaps the most
widespread interest in small molecules that bind to nucleic acids stems from their
potential as useful pharmaceutical agents. Indeed, some of the very best anticancer
drugs are well-documented DNA binders. While interest in drug-DNA interactions
has at times waned, recent advances in chemical synthesis, analytical instrumenta-
tion to measure binding, and structural biology have greatly enhanced the potential
for rational design of new therapeutic compounds. Accordingly, studies on the in-
teraction of small molecules with nucleic acids have taken on new life and have
helped spawn several emergent biotechnology companies dedicated to exploiting
the promise of making new types of pharmaceuticals targeted at nucleic acids.
The aim of this volume is to consolidate key methods for studying ligand-
nucleic acid interactions, both old and new, into a convenient source. Accordingly,
we have solicited from experts in a variety of disciplines articles that concisely
but completely describe useful methods and strategies for studying small molecule
binding to nucleic acids. Techniques that are useful now range from biophysical

and chemical approaches to methods rooted in molecular and cell biology. We hope
that this volume will serve as a useful compendium of methods both to newcomers
entering the field as well as to scientists already actively engaged in research in
this area.
JONATHAN B. CHAIRES
MICHAEL J. WARING
xiii
Contributors to Volume 340
Article numbers are in parentheses following the names of contributors.
Affiliations listed are current.
CHRISTIAN BAILLY (24, 31),
INSERM
U-524, and Laboratoire de Pharmaco-
logie Antitumorale du Centre Oscar
Lambret IRCL, 59045 Lille, France
ALBERT S. BENIGHT (8),
Department
of Chemistry, University of Illinois,
Chicago, Illinois 60607 and DNA Codes
LLC, Chicago, Illinois 60601
LAWRENCE A. BOTTOMLEY (11),
School of
Chemistry and Biochemistry, Georgia In-
stitute of Technology, Atlanta, Georgia
30332
SOPHIA Y. B REUSEGEM (10),
Laboratoryfi~r
Fluorescence Dynamics, Department of
Physics, University of Illinois, Urbana,
Illinois 61801

JONATHAN B. CHAIRES (1, 5, 27),
De-
partment of Biochemistry, University of
Mississippi Medical Center, Jackson,
Mississippi 39216
YEN CHOO (30),
Gendaq Limited, London
NW7 lAD, United Kingdom
BABUR Z. CHOWDHRY (6),
School of Chem-
ical and Life Sciences, University of
Greenwich, London SE18 6PF, United
Kingdom
ROBERT M. CLEGG (10),
Laboratory for
Fluorescence Dynamics, Department of
Physics, University of Illinois, Urbana,
Illinois 61801
DONALD M. CROTHERS (3, 23),
Depart-
ment of Chemistry, Yale University, New
Haven, Connecticut 06520-8107
MARK S. CUBBERLEY (28),
Department of
Chemistry and Biochemistry, University
of Texas, Austin, Texas 78712
CARLEEN M. CULL1NANE (23),
Pharma-
cology and Developmental Therapeutics
Unit, Peter MacCallum Cancer Institute,

Victoria 3002, Australia
SUZANNE M. CUTrS, (23),
Department of
Biochemistry, La Trobe University, Bun-
doora, Victoria 3083, Australia
JAMES C. DABROWIAK (21),
Department of
Chemistry, Center for Science and Tech-
nology, Syracuse University, Syracuse,
New York 13244
TINA M. DAVIS (2),
Department of Chem-
istry, Georgia State University, Atlanta,
Georgia 30303
PETER B. DERVAN (22),
Department of
Chemistry, California Institute of Tech-
nology, Pasadena, California 91125
MAGDALENA ERIKSSON (4),
Department of
Physical Chemistry, Chalmers University
of Technology, Gothenburg SE-41296,
Sweden, and Department of BiD-
chemistry, University of Gothenburg,
Gothenburg SE-40530, Sweden
CHRISTOPHE ESCUDI~ (16),
Laboratoire
de Biophysique, INSERM U201, CNRS
UMR 8646, Museum National d'Histoire
Naturelle, 75231 Paris Cedex 05,

France
IZABELA FOKT (27),
M. D. Anderson Can-
cer Center, University of Texas, Houston,
Texas 77030
KEITH R. Fox (20),
Division of Biochemistry
and Molecular Biology, School of Bio-
logical Sciences, University of Southamp-
ton, Southampton S016 7PX, United
Kingdom
x CONTRIBUTORS TO VOLUME 340
THI~RI~SE GARESTIER (16),
Laboratoire
de Biophysique, 1NSERM U201, CNRS
UMR 8646, Museum National d'Histoire
Naturelle, 75231 Paris Cedex 05, France
JERRY GOOD1SMAN (21),
Department of
Chemistry, Center for Science and Tech-
nology, Syracuse University, Syracuse,
New York 13244
DAVID E. GRAVES (18),
Department of
Chemistry, University of Mississippi,
University, Mississippi 38677
KEITH A. GRIMALDI (17),
CRC Drug-DNA
Interactions Research Group, Royal Free
and University College Medical School,

University College London, London WI P
8BT, United Kingdom
VLAD1M1R M. GUELEV (28),
Department of
Chemistry and Biochemistry, Universi~"
of Texas, Austin, Texas 78712
IHTSHAMUL HAG (6),
Krebs Institute
for Biomolecular Science, Department
of Chemisto, University of Sheffield,
Sheffield $3 7HF, United Kingdom
JOHN
A. HARTLEY (17),
CRC Drug-DNA
Interactions Research Group, Royal Free
and University College Medical School,
University College London, London W1P
8BT, United Kingdom
PAUL B. HOPKINS (19),
Department of
Chemistry, University of Washington,
Seattle, Washington 98195
LAURENCE H. HURLEY (29),
College of
Pharmacy, University of Arizona, Tucson,
Arizona 85721 and Arizona Cancer Cen-
ter, Tucson, Arizona 85724
MARK ISALAN (30),
Gendaq Limited,
London NW7 laD, United Kingdom

BRENT L. IVERSON (28),
Department of
Chemistry and Biochemistry, University
of Texas, Austin, Texas 78712
TERENCE C. JENKINS (6),
Yorkshire Cancer
Research Laboratory of Drug Design,
Cancer Research Group, University of
Bradford, Bradford BD7 1DP, United
Kingdom
BESIK I. KANKIA (7),
Department of
Pharmaceutical Sciences, University ~f
Nebraska Medical Center, Omaha,
Nebraska 68198
ASMITA KUMAR (33),
Department of Bio-
chemistry, University of Mississippi,
Jackson, Mississippi 39216
DONALD
W. KUPKE (7),
Department of
Chemistrry, University of Virginia, Char-
lottesville, Virginia 22901
ANDREW N. LANE (12),
Division of Molecu-
lar Structure, National Institute for Med-
ical Research, London NW7 IAA, United
Kingdom
GREGORY H. LENO (33),

lnfgen Incorpo-
rated, DeForest, Wisconsin 53532
PETER T. LILLEHEI (l l),
School of Chem-
istry and Biochemistry, Georgia Institute
of Technology, Atlanta, Georgia 30332
R. SCOTT LOKEY (28),
Department of
Chemistry and Biochemistr); University
of Texas, Austin, Texas 78712
FRANK G. LOONTIENS (10),
Laboratory
for Biochemistry, WEVIO, University of
Gent, Gent 9000, Belgium
RYAN A. LUCE (19),
Department of Chem-
istr); University of Washington, Seattle,
Washington 98195
CHRISTOPHE MARCHAND (32),
Laboratory
of Molecular Pharmacology, Division
of Basic Sciences, National Cancer In-
stitute, National Institutes of Health,
Bethesda, Maryland 20892
LUIS A. MARKY (7),
Department of
Pharmaceutical Sciences, University of
Nebraska Medical Center, Omaha,
Nebraska 68198
CLAIRE

J. MCGURK (17),
CRC Drug-DNA
Interactions Research Group, Royal Free
and University College Medical School,
University College London, London WI P
8BT, United Kingdom
CONTRIBUTORS TO VOLUME 340 xi
PETER
J. MCHUGH (17),
CRC Drug-DNA
Interactions Research Group, Royal Free
and University College Medical School,
University College London, London W1P
8BT, United Kingdom
MARK P. MCPIKE (21),
Department of
Chemistry, Center for Science and Tech-
nolog); Syracuse University, Syracuse,
New York 13244
MEREDITH M. MURR (28),
Department of
Chemistry and Biochemistry, Universi~
of Texas, Austin, Texas 78712
NOURI NEAMATI (32),
Laboratory of Molec-
ular Pharmacology, Division of Basic
Sciences, National Cancer Institute, Na-
tional Institutes of Health, Bethesda,
Maryland 20892
JAROSLAV NESETI~IL (8),

Department of
Applied Mathematics, Faculty of Math-
ematics and Physics, Charles Universi~,
118 O0 Praha 1, Czech Republic
PETER E. NIELSEN (15),
Department of
Medical Biochemistry and Genetics, The
Panum Institute, University of Copen-
hagen, Copenhagen DK-2200, Denmark
BENGT NORD~N (4),
Department of Phys-
ical Chemistry, Chalmers University
of Technology, Gothenburg SE-41296,
Sweden
RICHARD OWCZARZY (8),
Department
of Chemistry, University of Illinois,
Chicago, Illinois 60607, and Integrated
DNA Technologies, Coralville, Iowa
52241
PETR PAN(~OSKA (8),
Department of Chem-
istry, University of Illinois, Chicago,
Illinois 60607, and Center for Discrete
Mathematics, Applied Computer Science
and Applications DIMAT1A, Charles
University, Prague, Czech Republic, and
DNA Codes LLC, Chicago, Illinois
60601
MARY ELIZABETH PEEK (13),

School of
Chemistry and Biochemistry, Georgia In-
stitute of Technology, Atlanta, Georgia
30332
DON R. PHILLIPS (23),
Department
of Biochemistry, LaTrobe Universit3;
Bundoora, Victoria 3083, Australia
YVES POMMIER (32),
Laboratory of Molec-
ular Pharmacolog); Division of Basic
Sciences, National Cancer Institute, Na-
tional Institutes of Health, Bethesda,
Maryland 20892
JOSl~ PORTUGAL (25, 27),
Departamento de
Biologia Molecular y Celular, lnstituto de
Biologia Molecular de Barcelona, CSIC,
Barcelona 08034, Spain
WALDEMAR PRIEBE (27),
M. D. Ander-
son Cancer Center, University of Texas,
Houston, Texas 77030
TERESA PRZEWLOKA (27),
M. D. Ander-
son Cancer Center, University of Texas,
Houston, Texas 77030
PETER REGENFUSS (10),
Laboratory for
Fluorescence Dynamics, Department of

Physics, Universi~' of Illinois, Urbana,
Illinois 61801
JINSONG REN (5),
Department of Biochem-
istry, University of Mississippi Medical
Center, Jackson, Mississippi 39216
PETER V. RICCELLI (8),
Department
of Chemistry, University of Illinois,
Chicago, Illinois 60607, and DNA Codes
LLC, Chicago, Illinois 60601
RICHARD D. SHEARDY (26),
Department of
Chemistry and Biochemistry, Seton Hall
Universit); South Orange, New Jersey
07079
ANGELA M. SNOW (26),
Memorial High
School, Elmwood Park, New Jersey 07407
CHARLES H. SPINK (9),
Department of
Chemistry, State University of New York,
Cortland, New York 13045
DAEKYU SUN (29),
Institute for Drug De-
velopment, San Antonio, Texas 78245
JIAN-SHENG SUN (16),
Laboratoire de
Biophysique, INSERM U201, CNRS
UMR 8646, Museum National d'Histoire

Naturelle, 75231 Paris Cedex 05,
France
xii CONTRIBUTORS TO VOLUME 340
MICHAEL J. TILBY (17),
Cancer Research
Unit, Medical School, University of New-
castle Upon Tyne, Newcastle NE2 4HH,
United Kingdom
JOHN W. TRAUGER (22),
Department
of Chemistry, California Institute
of Technology, Pasadena, California
91125
JOHN O. TRENT (14, 27),
James Gra-
ham Brown Cancer Center, Department
of Medicine, University of Louisville,
Louisville, Kentucky 40202
PETER M. VALLONE (8),
Department
of Chemistry, University of Illinois,
Chicago, Illinois 60607 and National
Institute of Standards" and Technology,
Biotechnology Division, Gaithersburg,
Mao, land 20899
MICHAEL J. WARING (20, 24),
Department
of Pharmacology, University of Cam-
bridge, Cambridge CB2 IQJ, United
Kingdom

SUSAN E. WELLMAN (9),
Department
of Pharmacology and Toxicolog), Uni-
versity of Mississippi Medical Center,
Jackson, Mississippi 39216
LOREN DEAN WILLIAMS (13),
School of
Chemistry and Biochemistry, Georgia In-
stitute of Technology, Atlanta, Georgia
30332
W. DAVID WILSON (2),
Department of
Chemistry, Georgia State University,
Atlanta, Georgia 30303
HONGZH1 XU (33),
Department of Biochem-
istry, University of Mississippi, Jackson,
Mississippi 39216
STEVEN M. ZEMAN (3),
Department of
Chemistry, Yale University, New Haven,
Connecticut 06520
[1] ANALYSTS OF LIGAND-DNA BINDING ISOTHERMS 3
[1] Analysis and Interpretation of Ligand-DNA
Binding Isotherms
By
JONATHAN B. CHA1RES
Introduction
To attain a reasonable understanding of any ligand-receptor interaction, it is
necessary to answer the questions posed by Scatchard ~ more than 50 years ago:

"How many? How tightly? Where? Why? What of it?" The first two Questions (and
in part the third) can be answered by equilibrium binding studies, and are the pri-
mary focus of this chapter. The remaining questions concisely express the concerns
of structural and functional studies, and may be addressed by X-ray crystallogra-
phy, nuclear magnetic resonance (NMR) techniques, molecular modeling, and a
variety of chemical and molecular biological methods. Macromolecular binding
is a phenomenon of general interest, and the underlying general principles are the
same for ligand binding to proteins or to nucleic acids. A number of excellent
general treatments of macromolecular binding are available that explain the un-
derlying physical chemistry in detail .2-6 What distinguishes the binding of small
molecules to DNA from their binding to proteins is the need to account for behav-
ior arising from the lattice properties of linear DNA molecules. Various neighbor
exclusion models have evolved to cope with that complexity, and are described.
An excellent discussion of the principles of nucleic acid binding interactions is
provided by Bloomfield
et al. 7
Determination of the binding constant K allows the binding free energy change,
AG, to be calculated by the standard Gibbs equation, AG = -
RT
In K, where R
is the gas constant and T is the temperature in degrees Kelvin. From studies of the
temperature dependence of the binding constant, or (preferably) by calorimetric
studies, the binding enthalpy (AH) may be obtained. The binding free energy may
then be partitioned into its enthalpic and entropic components, AG = AH
TAS,
where AS is the entropy change. Knowledge of these thermodynamic parameters
I G. Scatchard,
Ann. N.Y. Acad. Sci.
51,660 (1949).
2 j. T. Edsall and J. Wyman, "Biophysical Chemistry." Academic Press, New York, 1958.

3 j. Wyman and S. J. Gill, "Binding and Linkage." University Science Books, Mill Valley, California,
1990.
41. M. Klotz, "Ligand Receptor Energetics." John Wiley & Sons, New York, 1997.
5 E. diCera, "Thermodynamic Theory of Site-Specific Binding Processes in Biological Macro-
molecules." Cambridge University Press, Cambridge, 1995.
6 G. Weber, "Protein Interactions." Chapman & Hall, New York, 1992.
7 V. A. Bloomfield, D. M. Crothers, and J. Ignacio Tinoco, "Nucleic Acids: Structures, Properties and
Functions," 1st Ed. University Science Books, Sausalito, California, 2000.
Copyright © 2001 by Academic Press
All rights of reproduction in any form reserved.
METHODS IN ENZYMOLOGY, VOL. 340 0076-6879/00 $35.00
4 BIOPHYSICAL APPROACHES
[
11
provides a firm foundation for understanding the molecular forces that govern the
binding reaction, allowing one to begin to address Scatchard's question "Why?"
Details of attempts to parse binding free energies for ligand-DNA interactions in
order to understand the contribution of various molecular forces are described in
publications from this and other laboratories, s- 12
The aim of this chapter is to offer a concise guide for the analysis and interpre-
tation of ligand-DNA binding isotherms. Methods for experimentally obtaining
binding data are not discussed because detailed, practical descriptions of experi-
mental protocols are available. 13 15 In this chapter, examples of binding data are
taken from results obtained in the author's laboratory with the anticancer agent
daunomycin (daunorubicin). Daunomycin is perhaps the best-characterized DNA
intercalator, and its binding to a wide variety of DNA sequences and structures has
been thoroughly investigated. ~ 6,17
Model-Independent Approaches
Figure 1 shows the results from two types of binding experiments, each of
which addresses one of Scatcbard's queries as directly as possible. The method of

continuous variations Is-a1 may be used to construct a so-called Job plot (Fig. 1A).
Binding stoichiometries may be determined from such plots without recourse to
any assumed binding model. For the data shown in Fig. 1A for the interaction
of daunomycin with calf thymus DNA, an inflection near 0.2 mol fraction ligand
indicates a binding stoichiometry of one ligand per 3 or 4 base pairs. The exact
stoichiometry from the inflection at 0.21 mol fraction is (1.0 - 0.21)/0.21 =
3.76 base pairs. This value represents the predominant binding mode, although an
s j. B. Chaires, Anticancer Drug Des. 11,569 (1996).
9 j. B. Chaires, Biopolymers 44, 201 (1997).
l01. Haq, J. E. Ladbury, B. Z. Chowdhry, T. C. Jenkins, and J. B. Chaires, J. Mol. Biol. 271,244 (1997).
II j. Ren, T. C. Jenkins, and J. B. Chaires, Biochemistry 39, 8439 (2000).
12 S. Mazur, F. A. Tanious, D. Ding, A. Kumar, D. W. Boykin, I. J. Simpson, S. Neidle, and W. D.
Wilson, J. Mol. Biol. 300, 321 (2000).
13 X. Qu and J. B. Chaires, Methods Enzymol. 321, 353 (2000).
L4 T. C. Jenkins, in "Drug-DNA Interaction Protocols" (K. R. Fox, ed.), Vol. 90, pp. 195-218. Humana
Press, Totowa, New Jersey, 1997.
15 p. C. Dedon, in "Current Protocols in Nucleic Acid Chemistry" (S. L. Beaucage, D. E. Bergstrom,
G. D. Glick, and R. A. Jones, eds.), Vol. 1, pp. 8.2.1-8.2.8. John Wiley & Sons, New York, 2000.
16 j. B. Chaires, in "Advances in DNA Sequence Specific Agents" (L. H. Hurley, ed.), Vol. 2, pp. 141-
167. JAI Press, Greenwich, Connecticut, 1996.
17 j. B. Chaires, Biophys. Chem. 35, 191 (1990).
18 E Job, Ann. Chim. (Paris) 9, 113 (1928).
19 C. Y. Huang, Methods Enzymol. 87, 509 (1982).
2o A. Waiters, Biomed. Biochim. Acta 44, 132t (1985).
21 E G. Loontiens, E Regenfuss, A. Zechel, L. Dumortier, and R. M. Clegg, Biochemistry 29, 9029
(1990).
[1]
ANALYSIS OF LIGAND-DNA BINDING ISOTHERMS 5
1.0
-200

-400
-600
-800
I I I I I
/
0.0 0.2 0.4 0.6 0.8
Mole Fraction Daunomycin
1.2
,
,
, , , ,
200
0.8
g
t
0.6
0.4
0.2
o.o
• B
,I,I
I I
-20 -18 -16 -14 -12 -t0
In Cf
FIG. I. Daunomycin binding to calf thymus DNA. (A) Job plot obtained from fluorescence titration
studies. A F is the difference in fluorescence emission intensity between solutions of daunomycin alone
and in the presence of DNA. The minimum indicates a binding stoichiometry of 3 or 4 base pairs. (B)
Binding isotherm for the daunomycin calf thymus DNA interaction. The fractional saturation was
calculated assuming a 3-bp binding site. The abscissa is the natural logarithm of the free daunomycin
concentration.

inflection near 0.5-0.6 mol fraction indicates an additional binding mode at higher
drug concentrations. The results shown here, based on fluorescence data, agree well
with data based on absorbance changes. 2° The Job plot thus answers the question
"How many?" directly. In studies of ligand-DNA interactions, this method has
been underutilized and its advantages largely unappreciated. In the case of multiple
binding modes, the method of continuous variations is particularly valuable, and
clearly reveals complexities in the binding process. Published examples for the
groove-binder Hoechst 3325821 and for the bisintercalating anthracycline WP63122
illustrate the value of the method in cases of complicated, multimode binding
interactions.
Figure 1B shows a titration binding isotherm for the daunomycin-calf thymus
DNA interaction. In this form, the fractional occupancy of binding sites is shown as
a function of the natural logarithm of the free daunomycin concentration (Ct-). The
fractional occupancy was calculated from the experimentally determined binding
22 F. Leng, W. Priebe, and J. B. Chaires,
Biochemistry
37, 1743 (1998).
6 BIOPHYSICAL APPROACHES [ 1]
ratio r (moles daunomycin bound per mole base pair) and the binding stoichio-
metry was determined from the Job plot shown in Fig. 1A. The form of the plot
shown in Fig. 1B is regarded by some 3 as the most fundamental representation of
binding data because the logarithm of the free ligand activity is proportional to the
chemical potential of the ligand. For simple binding to identical, noninteracting
sites, titration binding curves should be symmetric about a midpoint located at
a ligand concentration that is the reciprocal of the association binding constant,
and should cover a span of 1.8 lOgl0 units (4.14 In units) in going from 0.1 to 0.9
fractional saturation. 3'4'6 The data shown in Fig. 1B cover a span of 5.4 in units (2.4
log~0 units) and represent an essentially complete binding titration curve. The span
is greater than expected for simple binding, which indicates negative cooperativity,
neighbor exclusion, or heterogeneity of binding sites. Perhaps the main advantage

of the data shown in Fig. 1B is that they may be analyzed in a model-independent
way by using the Wyman concept of median ligand activity. 3'5 The free energy of
ligation (AGx) to go from a state where no ligand is bound to a degree of saturation
of k? is given by Eq. (1):
2
P
AGx = RT Jo In Cfg~" (1)
where RT has its usual meaning. The pronounced advantage of Eq. (1) is that it
provides a free energy estimate to attain any degree of saturation without recourse
to any specific binding model. Numerical integration of the data in Fig. 1 B yields an
estimate of AGx = -7.8 kcal mol I for the full ligation of a daunomycin binding
site. Free energies derived from binding constants obtained by curve fitting to
specific models must agree with this model-independent value if the model is
reasonable.
Neighbor Exclusion Models
Figure 2 shows data for the daunomycin-calf thymus DNA interaction in the
form of a Scatchard plot, J by far the most common representation of binding data
for ligand-DNA interactions. To explain the curvature in such plots, a variety
of neighbor exclusion models were proposed, 23'24 and these have become the
most commonly used models for the interpretation of binding isotherms. Neighbor
exclusion models assume (in their simplest form) that the DNA lattice consists of
an array of identical and noninteracting potential binding sites. The base pair is
commonly defined as the lattice binding site for duplex DNA. Ligand binding
to any one site occludes neighboring sites from binding as defined by the site
size n. As the lattice approaches saturation, the probability of finding a stretch
23 D. M. Crothers, Biopolymers 6, 575 (1968).
24 j. D. McGhee and R H. yon Hippel, J. Mol. Biol. 86, 469 (1974).
[ 1]
ANALYSIS OF LIGAND-DNA BINDING ISOTHERMS 7
8.0x10 5 , , , I , , I

6.0xl 0 s
4.0xl 0 s
G~
C3
2.0x10 5
0.0
"',O •
• o~',~
e~
I I I I I I I
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
r
FIG. 2. Scatchard plot for the daunomycin-calf thymus DNA interaction. The solid line is the best
fit of the neighbor exclusion model [Eq. (2)] to the experimental data yielding the parameters shown
in Table I. The dashed line is the best fit with the exclusion parameter constrained to an integral value
of 3.
of unoccupied DNA n base pairs long decreases, producing the curvature seen
in Fig. 2. The curvature does not result from a decrease in the intrinsic binding
affinity, but rather arises from the decreased probability of finding a free site of the
appropriate size. McGhee and von Hippe124 derived a closed form equation that
embodies the neighbor exclusion model [Eq. (2)]:
r I 1 "r ]°'
= K(1 -
nr)
1
; J
(2)
where K is the association constant for ligand binding to an isolated lattice site, n is
8 BIOPHYSICAL APPROACHES [ 1]
the neighbor exclusion parameter, and r is the binding ratio. Since its publication

in 1974, the McGhee and von Hippel article has been cited more than 1350 times,
and is certainly the most commonly used model for the interpretation of ligand
binding to DNA. It should be noted that Crothers 23 originally derived a neighbor
exclusion model 6 years before McGhee and von Hippel, using the statistical
mechanics matrix method, but did not offer a convenient closed form equation
for use in fitting experimental data. However, starting with Crother's characteristic
equations, 23 it is straightforward to obtain an equation identical to Eq. (2) by simple
algebraic rearrangement. The two models are therefore equivalent.
Equation (2) is commonly used as a fitting function for nonlinear least-squares
analysis of ligand-DNA binding isotherms. 13'25 In fact, Eq. (2) is not appropri-
ate for such purposes, because nonlinear fitting by most methods assumes that
the independent variable is error free, and that all of the experimental uncertainty
resides in the dependent variable. 26 Because the binding ratio r is experimen-
tally determined, it contains error. Worse, the dependent variable
r/Cf
is a derived
quantity so that error in r is propagated into the dependent variable. Nonethe-
less, nonlinear fitting methods are inevitably used to extract K and n value from
experimental data. Two excellent software packages are routinely used in this lab-
oratory for nonlinear curve fitting, FitAll (MTR Software, Toronto, Canada) and
Origin (Microcal, Northampton, MA). FitAll now contains a module for Monte
Carlo analysis z7 of the error in parameter estimates. Origin contains a module for
a rigorous evaluation of parameter error by determination of their upper and lower
bounds at any chosen confidence interval.28 Table I shows the results of fits of the
data shown in Fig. 2 to the neighbor exclusion model. The binding constant, K =
6.6 x 105 M 1, may be used to calculate AG = - 7.8 kcal mol -I. That value
is in excellent agreement with that obtained for the model-independent approach
described above. The exclusion parameter, n = 3.3, agrees well with the estimate
of the site size obtained by the method of continuous variations.
The nonintegral value of the exclusion parameter (n) poses a problem. For

neighbor exclusion models, n should strictly be an integer quantity. A fractional
value makes no physical sense for a DNA lattice composed of identical, noninter-
acting sites] Table I shows, however, that if n is constrained to an integer value
(either 3 or 4), the standard deviation of the fit degrades significantly. Figure 2
shows the best fit obtained with n = 3. Systematic deviation between the fit and
the data are clear, with the data having more curvature than the calculated func-
tion. This results in nonrandom residuals, indicating an inadequate fit of the model
to the data. 28 The fractional values of n that are required to obtain a statistically
25 j. j. Correia and J. B. Chaires,
Methods Enzymol.
240, 593 (1994).
26 M. L. Johnson,
Methods Enzymol.
210, 106 (1992).
27 M. Straume and M. L. Johnson,
Methods Enzymol.
210, 117 (1992).
28 M. L. Johnson and L. M. Faunt,
Methods Enzymol.
210, 1 (1992).
[]] ANALYSIS OF LIGAND-DNA BINDING ISOTHERMS 9
TABLE I
NONLINEAR LEAST-SQUARES FITS OF DAUNOMYCIN BINDING DATA TO
NEIGHBOR EXCLUSION MODELS a
Model
K/IOS(M I) N
(bp)
Standard deviation
McGhee-von Hippel 6.6 ± 0.2 3.3 + 0. l 51,330
n = 3.0 5.9± 0.1 Fixed 56,250

n = 4.0 5.4 i 0.4 Fixed 154,600
Friedman-Manning
7.2+ 0.2 3.1 + 0.1 53,310
n = 3.0 7.0 ± 0.2 Fixed 53,280
n 4.0 7.2 ± 0.5 Fixed 133,300
a
McGhee-von Hippel refers to the neighbor exclusion model speci-
fied by
Eq. (2).
Friedman-Manning refers to the model specified by
Eq. (3). K is
the association constant and n is the neighbor exclusion
parameter expressed in base pairs. The standard deviation is of the
best
fit.
acceptable fit indicate that the neighbor exclusion model is not, in fact, an appro-
priate model for the data. Fundamental assumptions of the model must be violated.
As is discussed below, the most likely assumption that is violated is that sites are
identical, when in fact they are heterogeneous.
An extension of the simple McGhee-von Hippel model incorporates an addi-
tional term to account for ligand-ligand cooperativity. In principle, integral values
of n coupled with negative ligand-ligand cooperativity might adequately fit data
such as are shown in Fig. 2. Unfortunately, we previously have shown that attempts
to incorporate the added cooperativity parameter are statistically unwarranted and
that attempts to force fits to integral values of n are futile. 25
Friedman and Manning derived a variant of the neighbor exclusion model
that incorporates aspects of polyelectrolyte theory. 29'3° Counterion condensa-
tion around DNA is dictated by the spacing of the charged phosphates along the
double helix. 31'32 Counterion release coupled to the binding of a charged lig-
and to DNA provides an energetically favorable contribution to the binding free

energy. For DNA intercalation reactions, a complexity arises that the Friedman-
Manning model addresses. Intercalation results in a separation of the stacked base
pairs in duplex DNA, and increased phosphate spacing. This alters the polyelec-
trolyte properties of the duplex, and results in additional counterion release. As the
DNA lattice is saturated with intercalator, there is an ever-changing increase in the
29 R. A. Friedman and G. S. Manning,
Biopolymers
23, 2671 (1984).
3o R. A. G. Friedman, G. S.
Manning, and
M. A. Shahin,
in
"Chemistry and Physics of
DNA-Ligand
Interactions"
(N. R. Kallenbach, ed.), pp. 37~64.
Adenine Press, Schenectady, New York,
1988.
31 M. T. Record, Jr., C. E
Anderson, and
T. M. Lohman,
Q. Rev. Biophys.
11,
103 (1978).
32 G. S. Manning,
Q. Rev. Biophys.
11,
179 (1978).
10 BIOPHYSICAL
APPROACHES [

1 ]
average phosphate spacing, resulting in a systematic decrease in the polyelectrolyte
contribution to the binding free energy. A closed form equation was derived 29,3° to
embody this model for a univalent intercalator binding to B-form DNA in excess
univalent salt solutions:
r K(2+r]-(2+~)lO_[c~i~2o2,1~+~](l_nr)[ 1-nr ],,-1
C ~ = \2-~-rJ 1 -(n ~l)r
(3)
In Eq. (3) K and n have the same meaning as given above, and the added exponential
terms describe the decrease in polyelectrolyte contribution to the binding free
energy over the course of lattice saturation. The parameter ff 0 is the dimensionless
charge density parameter and is a function of the structure of duplex DNA. Specifi-
cally, ~'0 =
qZ/EkTb,
where q is the charge of an electron, e is the bulk dielectric
constant of the liquid, k is the Boltzmann constant, T is the temperature in degrees
kelvin, and b is the charge spacing on the DNA chain. For standard B-form duplex
DNA, b = 1.7 A, and ~'o = 4.2.
The results of fits of the data shown in Fig. 2 to the Friedman-Manning model
are listed in Table I. In all cases examined, the fits are statistically worse than those
obtained with the simpler McGhee-von Hippel model. The standard deviations of
the fits shown in Table I are all larger for the Friedman-Manning model than for the
McGhee-von Hippel model when both K and n are allowed to vary, even though
the former contains an additional parameter. The curvature imposed on the fitting
function by the added exponential terms in Eq. (3) evidently makes it more difficult
to match the curvature in the data. Statistically, therefore, there is no justification
for use of the Friedman-Manning model instead of the simpler McGhee-von
Hippel neighbor exclusion model. However appealing the underlying theory, the
reality of the experimental data provides the ultimate test of the model. In this
case, the inclusion of added complexity of polyelectrolyte effects is statistically

unwarranted.
Use of the neighbor exclusion model has become the standard practice in stud-
ies of ligand-DNA interactions. The preceding discussion, however, poses some
serious questions about its use. Fractional values for the neighbor exclusion param-
eters are inevitably required to accurately describe the curvature in experimental
data, yet have no meaning in the context of the model because integral values
were assumed in the derivation of the model. Fractional neighbor exclusion values
signify that the model is not an appropriate description of the actual data. The
specific assumption of neighbor exclusion models that is violated is most likely
that lattice sites are homogeneous. Chemical and enzymatic footprinting methods
have shown unambiguously that such is not the case, and that most ligands bind to
DNA sites with a wide distribution of affinities. 33'34 For the specific case of dauno-
mycin, for examples, footprinting studies revealed a strong preference for triplet
binding sites with the sequence 5'-(A/T)GC or 5'-(A/T)CG, where the notation
[1]
ANALYSIS OF LIGAND DNA BINDING ISOTHERMS
11
(A/T) means that either A or T can occupy the position. 35'36 Further, sequences
containing runs of AT base pairs were revealed by footprinting not to bind dauno-
mycin with appreciable affinity. 16 All DNA lattice sites are clearly not identical, in
which case a central tenet of the neighbor exclusion model is violated, vitiating its
use as an appropriate model for the analysis of binding isotherms. This conclusion
was strongly supported in the single example available, where both macroscopic
binding studies and footprinting studies were carried out on the same homoge-
neous fragment, the 165-bp
tyrT
DNA fragment. 37 In that study, the macroscopic
binding isotherm was complex in shape, could not be fit to the neighbor exclusion
model, and clearly revealed a class of high-affinity binding sites whose number
was consistent with the number of high-affinity sites visualized by the companion

footprinting titration study.
The neighbor exclusion principle has also been questioned on other grounds.
Rao and Kollman 38 carried out molecular mechanics and molecular dynamics stud-
ies from which they concluded that there was no stereochemical basis for neighbor
exclusion, at least for the intercalation of 9-aminoacridine into DNA. NMR studies
from the Wilson laboratory 39'4° showed conclusively that actinomycin D can bind
to adjacent 5'-GpC dinucleotide sites within an oligonucleotide, a finding that con-
trasts with the 5- or 6-bp exclusion parameter normally associated with the drug.
While these are limited and perhaps specialized cases, they do raise questions
about the exact physical basis for the neighbor exclusion phenomenon.
Dinucleotide Binding Model
If the neighbor exclusion model is excluded, what model can be used for the
analysis of ligand-DNA binding data? One possibility is to assume heterogeneity
of binding sites at the outset. Crothers in fact introduced an early variant of the
neighbor exclusion model that incorporated simple base pair selectivity, with an
added parameter to account for the relative affinity of GC versus AT base pairs. 23
That simple "two-site" model has not seen wide application. Another, more radical
possibility is to abandon the neighbor exclusion concept entirely and to ascribe
33 j. C. Dabrowiak, A. A. Stankus, and J. Goodisman,
in
"Nucleic Acid Targeted Drug Design C"
(L. Propst and T. J. Perun, eds.). Marcel Dekker, New York, 1992.
34 M. J. Waring and C. Bailly,
J. Mol. Recognir
7, 109 (1994).
35 j. B. Chaires, K. R. Fox, J. E. Henera, M. Britt, and M. J. Waring,
Biochemist~
26, 8227 (1987).
36 j. B. Chaires, J. E. Herrera, and M. J. Waring,
Biochemistry

29, 6145 (1990).
37 C. Bailly, D. Suh, M. J. Waring, and J. B. Chaires,
Biochemistry
37, 1033 (1998).
38 S. N. Rao and P. A. Kollman,
Proc. Natl. Acad. Sci. U.S.A. 84,
5735 (1987).
39 W. D. Wilson, R. L. Jones, G. Zon, E. V. Scott, D. L. Banville, and L. G. Marzilli, J.
Am. Chem. Soc.
108, 7113 (1986).
40 E. V. Scott, R. L. Jones, D. L. Banville, G. Zon, L. G. Marzilli, and W. D. Wilson,
Biochemist~
27,
915 (1988).
12 BIOPHYSICAL
APPROACHES [
11
the curvature in Scatchard plots entirely to heterogeneity. We have explored the
simplest case in this scenario, a model in which a dinucleotide binding site is
assumed. There are 16 possible dinucleotide combinations, 10 of which are unique.
These are (5' -+ 3'): AT, AA ( TT), TA, AC (= GT), CA (= TG), GC, GG
( = CC), CG, GA ( = TC), and AG ( = CT). Because intercalators insert between
adjacent base pairs and make contact with both, dinucleotide selectivity is not an
unreasonable starting point. For binding to dinucleotides (MN), each of which has
a unique affinity (KMN), the binding isotherm is described by
MN fMNKMNCf (4)
rD
1 q'- KMNCf
where the binding ratio ro is now expressed as moles of ligand per mole of di-
nucleotide. The remaining variables are the dinucleotide frequency (fMN) and the

free ligand concentration (C0. Dinucleotide frequencies were experimentally de-
termined and tabulated for a numerous natural DNA samples, 41 and may be fixed
as constants for a given DNA. Because there are 10 unique dinucleotide steps, the
equation has 10 terms, and 10 binding constants must be obtained by nonlinear
least-squares fitting of experimental data. Although at first glance the exercise of
resolving 10 parameters may seem hopeless or even ludicrous, we show that it
can in fact be done with the return of reasonable results. Figure 3 shows the fit
of daunomycin-calf thymus DNA binding data to the dinucleotide model. Note
that the binding ratio is now expressed in terms of total dinucleotide concentration
rather than the usual base pair concentration. The solid line represents the best fit
to the dinucleotide binding model. Estimates of 10 binding constants are obtained,
and are summarized in Fig. 4. The data in Fig. 4 are average values of KMN esti-
mates obtained from fitting daunomycin binding data obtained with eight different
natural DNA samples with known and widely varying dinucleotide frequencies.
These samples ranged from Clostridium perfringens DNA (31% GC content) to
Micrococcus lysodeikticus DNA (72% GC content). Unique KMN values are re-
turned that range over two orders of magnitude. Figure 4 shows that AA, AT, and
TG steps represent low-affinity sites. TA, GC, and CG have intermediate affinity.
High-affinity sites are TC, AC, AG, and GG steps.
Does this analysis make sense? Is it valid? Several observations suggest that the
answer is "yes" to both questions. First, footprinting studies of the daunomycin-
DNA interaction showed that sequences protected from DNase I cleavage by the
bound drug were enriched in the dinucleotides AC, AG, GG, GC, and CG relative
to the tyrT DNA fragment alone that was used for footprinting. 35 These are among
the very dinucleotide steps with the highest KMN values. In contrast, analysis of
unprotected cleavage sites from the footprinting experiments showed that such
41 G. D. Fasman, "Handbook of Biochemistry and Molecular Biology," 3rd Ed. CRC Press, Cleveland,
Ohio, 1976.
[ l ] ANALYSIS OF LIGAND-DNA BINDING ISOTHERMS 1 3
0,75 ]

0.50
t _.t _
0.00
1E-9 1 E-8 1 E-7 1 E-6 1E-5 1E-4
Cf, M
FIG. 3. Binding isotherm for the daunomycin-calf thymus DNA interaction. The binding ratio on the
ordinate is expressed as moles of daunomycin bound per dinucleotide. Free daunomycin concentration
is shown on the abscissa. The solid line represents the best fit to the 10-site, dinucleotide binding model
described in text.
sites were enriched in the dinucleotides AA, AT, and TA. 16'35 Two of these steps
have the lowest measured KMN. Second, KMN values can be used to calculate a
total binding free energy for the loading of the calf thymus DNA lattice that is
in excellent agreement with the model-independent approach described earlier in
this chapter. The total free energy (AGT) is specified by
MN MN
AGT = ~ fMNAGMN = Z fMN(-RT
In KMN) (5)
where
AGMN
is the free energy for binding to the dinucleotide step MN. Using
the known fMN values for calf thymus DNA and the KMN values shown in Fig. 4,
a value of AGT = 7.8 kcal mol I is obtained, in excellent agreement with that
obtained by model-independent analysis. Finally, the binding constants shown in
Fig. 4 may be used in combination with the known dinucleotide frequency of calf
thymus DNA to simulate a binding isotherm, as shown in Fig. 5. If these simulated
data are then fit to the neighbor exclusion model, values ofK = 6.5 x 10 5 M-
I
and n 3.3 bp are obtained. These values are in excellent agreement with those
obtained by fits to actual experimental data (Fig. 2). The key point of this exercise is
14 BIOPHYSICAL

APPROACHES [
1 ]
10 7 I I ! I I I I I I
108 l~,//'~~i,X~ i
10 s
104 t t I t t
AA AT TA TG TC AC AG GG GC CG
Dinucleotide Step
FIG. 4. Affinity profile for the interaction of daunomycin with the 10 unique dinucleotide steps. The
binding constants (K) are average values obtained by fitting of binding isotherms for the interaction
of daunorubicin with eight different DNA samples with widely varying dinucleotide frequencies. The
error bars show standard deviations from the mean values.
that dinucleotide heterogeneity can account entirely for the curvature in Scatchard
plots at least as well as the neighbor exclusion model does.
The model presented in this section is somewhat radical and vitiates the con-
ventional wisdom of the neighbor exclusion model. But because a fundamental
assumption of the neighbor exclusion model (the homogeneity of potential bind-
ing sites) is demonstrably incorrect, the development of other models is manda-
tory. Furthermore, a few studies have questioned the physical basis of neighbor
exclusion. 38-4° The dinucleotide model is consistent with the results of more than
a decade of footprinting studies, which show that ligands inevitably bind with a
wide range of affinities along the DNA lattice. In one sense, we have come full
circle. Early binding isotherms for proflavin 42 were curved and were interpreted in
term of site heterogeneity, namely with two classes of sites later attributed to inter-
calation and "outside" binding. The dinucleotide model assumes a different kind
42 A. R. Peackocke and J. N. H. Skerren,
Trans. Faraday Soc.
52, 261 (1956).
[1] ANALYSIS OF LIGAND-DNA BINDING ISOTHERMS 15
0

5x10 5.
4xl 0 5
3x10 5
2x 10 5
lx10 5
I I I I ~ I
I I I I I
0,05 0.10 0.15 0.20 0.25 0.30
r bound
,-,
FIG. 5. Simulated Scatchard plot for the daunomycin-calf thymus DNA interaction. Dinucleotide
binding constants (Fig. 4) were used in combination with the known dinucleotide frequency for calf
thymus DNA to simulate binding data (solid circles), which were then cast into the form ofa Scatchard
plot. If these simulated data are then fit to the neighbor exclusion model [Eq. (2)], the best fit (solid
line) yields K 6.5 × 105M -1 and n = 3.3 bp.
of heterogeneity involving a larger number of sites derived from a fundamental
property of any DNA, its nearest neighbor dinucleotide frequency.
Coping with Cooperativity
In some cases, ligand-DNA binding isotherms exhibit evidence of positive
cooperativity. In these cases, data cast into the form of a Scatchard plot show
positive slopes at low binding ratios (Figs. 6 and 7). Analysis and interpretation of
such isotherms become even more complicated. McGhee and yon Hippe124 (and
16 BIOPHYSICAL
APPROACHES [
11
4
!3
v 2
4~m
I I I I I

+ %÷÷**~+÷%Q~. •

J. ~ $$
m
I I I I I
0 0.1 0.2 0.3 0.4
r-bound
FIG. 6. Allosteric binding of daunomycin to poly(dA).poly(dT). Binding data were obtained for
the interaction of daunomycin with poly(dA).poly(dT) in buffered 0.2 M NaCI solutions (pH 7.0). The
solid line was calculated for the parameters listed in Table II for the Crothers allosteric binding model.
The -I- + + line shows the best fit to the McGhee-von Hippel Neighbor exclusion model with added
ligand-ligand cooperativity [Eq. (6)].
Crothers earlier 23) presented an extended form of the neighbor exclusion model
that included an additional term to account for ligand-ligand interactions. The
equation for this model is
r K(l_nr)[(2w-1)(l-nr)+r-R]n-l[l-(n+l)r+R]2
C f = Y(~ Ud- n~ 2(1 -
nr)
R = {[1 - (n + l)r] 2 + 4mr(1 -
nr)} 1/2
(6)
where K, n, and r have the same meaning as given above, and co is the cooperativity
parameter, co is defined as the equilibrium constant for moving two ligands bound
at isolated sites into proximity, such that they occupy contiguous lattice sites. If
~o > 1.0, positive cooperativity results and ligands bind preferentially next to one
another. If ~o < 1.0, negative cooperativity results, and ligand binding at adjacent
sites is hampered. A distinctive feature of this model is that the DNA lattice
remains and inert array of identical sites. All cooperativity results from ligand-
ligand interactions of an unspecified nature.
A contrasting model that can account for positive cooperativity is the Crothers

allosteric model. 43 The underlying concept is radically different from the
McGhee-von Hippel model. The allosteric model is analogous to the classic
Monod-Wyman-Changeux model for allostery 44 derived to explain the cooperative
43 N. Dattagupta, M. Hogan, and D. M. Crothers,
Biochemistry
19, 5998 (1980).
44 j. Monod, J. Wyman, and J P. Changeux, Z
Mol. Biol.
12, 88 (1965).
[ l] ANALYSIS OF LIGAND DNA BINDING ISOTHERMS 17
1.2x10 s
1.0xlO s
8.0x10 4
6.0xl 0 4
4.0x10 4
2.0xl
0 4
0.0
I I I I I
Z Form • B Form
"')
I ~ I ~ I ~ I ~ I
0.0
0.1 0.2 0.3 0.4 0.5
r
FIG. 7. Allosteric binding of daunomycin to left-handed Z-DNA. Binding data were obtained for the
interactions of daunomycin with Z-form [poly(dG-dC)]2 in buffered 3.0 M NaCI solutions (pH 7.0). The
solid line was calculated for the parameters listed in Table II for the Crothers allosteric binding model.
At the start of the binding isotherm, the polymer is in the left-handed Z form. Beyond the maximum
near r = 0.3, daunomycin binding has allosterically converted the polymer to the right-hand form.

binding of ligands to proteins, such as the binding of oxygen to hemoglobin.
Crothers built on the basic concept of allostery, but included specific details of the
macromolecular conformational transition and ligand binding that were appropri-
ate for a DNA lattice. The allosteric model assumes that the DNA lattice can exist
in one of two conformational forms (1 and 2). The transition of the lattice between
these forms proceeds by a nucleation step, followed by propagation steps:
O-2S
Nucleation: 111111 < ~ 112111
S
Propagation: 112111 < ~ 112211
The equilibrium constant for nucleation is cr2s and that for propagation is s. The
allosteric model then assumes that ligand can bind to each conformational form
18 BIOPHYSICAL APPROACHES [ 1
]
with unique neighbor exclusion binding parameters, (K1, n l, o~1) and
(K2, t/2,092).
Cooperativity arises when the ligand binds selectively or preferentially to one of the
conformational forms. Binding then drives an allosteric conformational transition
to the form with higher ligand affinity. Eight parameters are needed to compute
binding isotherms. There is no closed form, analytic equation for the allosteric
model. Crothers
et al.
wrote a Fortran program that calculates binding isotherms
according to the derived statistical mechanical model, 43 a program that has seen
modest circulation 45 47 and that has been modified on occasion 4s'49 for easier use.
No nonlinear fitting routine has yet been developed that incorporates the allosteric
model, and users must optimize binding parameters by successive approximation
along with judicious constraint of those selected parameters that can be estimated
by independent methods. 5° Nonetheless, use of the allosteric model is unavoidable
in some cases, as examples will show.

It is important to contrast the key features of the McGhee-von Hippel and
allosteric models. In the McGhee-von Hippel model, positive cooperativity arises
from ligand-ligand interactions while the DNA lattice remains in a single con-
formation. For protein binding to DNA, such ligand-ligand interactions might be
visualized as protein-protein contacts formed when adjacent lattice sites are occu-
pied. For small molecule ligands, although such interactions could also occur, it is
less easy to ascribe a molecular picture to the process. In contrast, positive cooper-
ativity arises in the Crothers allosteric model from an underlying conformational
transition in the DNA lattice to a form with higher ligand binding affinity. The
allosteric model was perhaps the first clear statement of the possibility of struc-
tural selectivity in ligand-DNA interactions. Two examples will illustrate positive
cooperativity in ligand-DNA interactions.
Figure 6 shows the binding of daunomycin to poly(dA) • poly(dT). Independent
studies have shown that poly(dA), poly(dT) undergoes a premelting transition
between two helical forms. 51-53 The binding data in Fig. 6 show a positive slope at
low r values, and pass through a maximum near r = 0.05. Attempts to fit these data
to the extended McGhee-von Hippel model yield unsatisfactory results. The best
fit to that model (with K = 1.4 × 104M -j , n = 2.3 bp, ~o = 2.4) is shown by the
45 j. B. Chaires, J.
Biol. Chem.
261, 8899 (1986).
46 G. Y. Walker, M. E Stone, and T. R. Krugh,
Biochemistry
24, 7462 (1985).
47 G. T. Walker, M. E Stone, and T. R. Krugh,
Biochemistry
24, 7471 (1985).
48 G. T. Walker, Ph.D. Thesis, University of Rochester, 1986.
49 D. Snh, Ph.D. Thesis, University of Mississippi Medical Center, 1993.
5o j. B. Chaires,

J. Biol. Chem.
261, 8899 (1986).
51 j. E. Herrera and J. B. Chaires,
Biochemistry
28, 1993 (1989).
52 S. S. Chan, K. J. Breslauer, M. E. Hogan, D. J. Kessler, R. H. Austin, J. Ojemann, J. M. Passner,
and N. C. Wiles,
Biochemistry
29, 6161 (1990).
53 S. S. Chan, K. J. Breslauer, R. H. Austin, and M. E. Hogan,
Biochemistry
32, 11776 (1993).
[1]
ANALYSIS OF LIGAND-DNA BINDING ISOTHERMS 19
TABLE II
PARAMETER ESTIMATES FOR ALLOSTERIC MODEL "FIT" TO DAUNOMYCIN BINDING TO
POLY(dA).POLY(dT) AND Z-DNA
Parameter Description Poly (dA).Poly(dT) a Z-DNA ~'
o"
s
KI(M -I )
K2(M -I )
K2/KI
?11
n2
Nucleation parameter 0.01 0.00 l
Propagation constant 0.985 0.635
Association constant for binding to form 1 4,800 8,000
Association constant for binding to form 2 21,000 350,000
Ratio of association constants 4.3 44

Neighbor exclusion parameter (form 1) 2.0 2.0
Neighbor exclusion parameter (form 2) 2.0 2.3
a Daunomycin binding to poly(dA).poly(dT) in buffered 0.2 M NaCI solutions (pH 7.0).
Parameters result from analysis of the binding data shown in Fig. 7.
b Daunomycin binding to Z-form [poly(dG-dC)]2 in buffered 3.0 M NaCI solutions (pH 7.0).
Parameters result from analysis of the binding data shown in Fig. 6.
curve with the (+) symbols; no value of ~o can be found that can produce a curve
that matches the steep positive slope at the start of the isotherms. The model, with
an assumed inert DNA lattice, cannot match the experimental data. In contrast,
the allosteric model can match the shape of the binding data well, as shown by
the solid curve in Fig. 6. The best estimates of the parameters for the allosteric
model that describe the binding data are collected in Table II. The key driving
force for the allosteric conversion of poly(dA), poly(dT) is the >4-fold preference
for binding to form 2 of the polynucleotide. A variety of additional physical and
enzymatic tools was used to demonstrate that daunomycin binding was indeed
coupled to a conformational change in poly(dA), poly(dT) 51 the essential feature
of the allosteric model.
Figure 7 shows daunomycin binding to poly(dG-dC) under solution conditions
that initially favor the left-handed Z conformation of the polynucleotide. 45'54 The
allosteric model with the parameters listed in Table II was used to obtain the solid
curve matching the experimental data. In this case, the underlying conformational
transition to which binding is coupled is the Z-to-B conversion. Compared with the
first example of binding to poly(dA) • poly(dT), this system is much more coopera-
tive. The reason for that is the greater preference of daunomycin for the right-hand
form relative to the left-handed form (with
Kz/KI -~
44; Table II), compared with
its preference for the two right-handed helical forms of poly(dA) • poly(dT) (with
K2/KI
= 4; Table II).

54 X. Qu, J. O. Trent, I. Fokt, W. Priebe, and J. B. Chaires,
Proc. Natl. Acad. Sci. U.S.A.
97, 12032
(2O0O).
20 BIOPHYSICAL
APPROACHES [
1 ]
Ligand Binding to Oligonucleotides
Advances in synthetic methods have made it relatively easy to prepare DNA
or RNA oligonucleotides of precisely defined length and sequence, and it is now
fashionable to use such molecules for ligand binding studies. The significant advan-
tage of oligonucleotides is their homogeneity. There are, however, disadvantages.
First, end effects may become a consideration in oligonucleotide studies. Neigh-
bor exclusion models typically assume an "infinite lattice" specifically to avoid
end effects, and therefore such models become inapplicable to oligonucleotide
systems. Polyelectrolyte theory and experiment have shown that significant end
effects exist for oligonucleotides less than about 24 bp in length. 55'56 Second,
problems of appropriate representation of all possible sequence elements may
arise in oligonucleotide systems. There are 10 unique dinucleotide combinations,
as discussed above, and it is rare that a given oligonucleotide is appropriately
designed to contain all possible dinucleotide steps. It is always possible that a
high-affinity interaction may go undetected because the appropriate site is absent
in the oligonucleotide chosen for study. Binding constants may thus be biased by
the choice of sequence unless a large number of oligonucleotides is studied. For
trinucleotides, the situation becomes even worse, because there are 64 possible
triplets, 32 of which are unique. These concerns should not be taken as a call
to abrogate oligonucleotide studies, but rather to acknowledge their appropriate
role. Complete binding studies should be comprehensive and should systemat-
ically move from long natural DNA samples through synthetic polynucleotides
of defined simple repeating sequences to oligonucleotides of precisely defined

sequence. Oligonucleotide systems are of particular value for the study of the
energetics of binding when other experiments have defined the sequence of the
preferred binding site for a given ligand.
Neighbor exclusion models are generally inapplicable for the analysis of ligand
binding to oligonucleotides because they are based on an "infinite lattice" assump-
tion. Binding isotherms in these cases are best analyzed by the classic and simple
stoichiometric binding models that are described in any number of texts and mono-
graphs. 2-4 Figure 8 shows an example of daunomycin binding to a 24-bp duplex
oligonucleotide with the sequence (5'-TGCATGCATGCATGCATGCATGCA)2.
This oligonucleotide was designed and synthesized to contain a repetitive motif
containing the preferred daunomycin binding site that emerged from footprinting
studies [5'-(A/T)GC; where (A/T) means A or T]. Binding data were fit to the
simple expression for multiple identical, noninteracting sites:
~tK Cf
r

(7)
1 +KCf
55 M. C. Olmsted, C. E Anderson, and M. T. Record, Jr.,
Proc. Natl. Acad. Sci. U.S.A.
86, 7766 (1989),
56 M. C. Olmsted, C. E Anderson, and M. T. Record, Jr.,
Biopolymers
31, 1593 (1991).
[ 1]
ANALYSIS OF LIGAND-DNA BINDING ISOTHERMS 21
(D
"O
"5
I1)

E
c-
O
O
t-
o
E3
I I ! I
0
0 2 4 6 8 10
Ct~ee, gM
FIG. 8. Binding of daunomycin to a 24-bp duplex oligonucleotide. Data (solid circles) are presented
as a direct plot, with the best fit to Eq. (7) shown as the solid line.
where r is now expressed as moles of daunomycin bound per mole of oligonu-
cleotide, n is the number of sites, and Kis the association constant. Nonlinear least-
squares fitting of the data yields K = 4.0 (4-0.1) × 106M - 1 and n = 4.3 (-t-0.3).
Evidently only four molecules of daunomycin are binding to each oligonucleotide,
even though there are six potential sites that contain the preferred triplet sequence.
It is possible that the sites near the ends are disfavored, or that there is anticooper-
ativity that disfavors binding to adjacent sites. In the latter case, more complicated
models with added parameters would need to be invoked and implemented. An
excellent example of such an analysis applied to daunomycin binding to hexanu-
cleotide sequences was provided by Rizzo and co-workers. 57
Summary
Binding studies provide information of fundamental and central importance
for the complete understanding of ligand-DNA interactions. Studies of ligand
binding to long natural DNA samples, to synthetic deoxypolynucleotides of simple
repeating sequence, and to oligonucleotides of defined sequence are all needed to
57 V. Rizzo, C. Battistini, A. Vigevani, N. Sacchi, G. Razzano, F. Arcamone, A. Garbesi, E P. Colonna,
M. Capobianco, and L. Tondelli, J. Mol. Recognit. 2, 132 (1989).

22 BIOPHYSICAL APPROACHES [21
begin to understand the interaction in detail. Binding studies provide entry into the
thermodynamics of the DNA interactions, which in turn provides great insight into
the molecular forces that drive the binding process. This chapter summarizes both
model-dependent and -independent approaches for the analysis and interpretation
of binding isotherms, and should serve as a concise guide for handling experimental
data.
Acknowledgment
Work in the author's laboratory was funded by grant CA35635 from the National Cancer Institute.
[2] Surface Plasmon Resonance Biosensor Analysis
of RNA-Small Molecule Interactions
By
TINA M. DAVIS and W. DAVID WILSON
Introduction
Because some of the most devastating human diseases are caused by RNA
viruses, such as human immunodeficiency virus (HIV) and hemorrhagic fever
viruses such as dengue and Ebola, l RNA is an attractive therapeutic target in drug
design. 2-4 The unique structural folds present in RNA, but not DNA, offer the
possibility of much higher recognition specificity by small molecules. Structured
sites in RNA can be targeted with the same specificity with small molecules as
structured binding regions of proteins. Despite the potential advantages of targeting
RNA, few drugs are known that target RNA, and rational design of drugs that
target RNA is in the beginning stages.5-SA summary of some of the RNAs that
have been successfully targeted in drug design and interaction studies is shown in
Table 1. 2,9-26
I M. B. A. Oldstone, "Viurses, Plagues, and History." Oxford University Press, Oxford, 1998.
2 W. D. Wilson and K. Li, Curr. Med. Chem. 7, 73 (2000).
3 K. Michael and Y. Tor, Chem. Eur. J. 4, 2091 (1998).
4 F. Walter, Q. Vicens, and E. Westhof, Curr. Opin. Chem. Biol. 3, 694 (1999).
5 K. Li, M. Fernandez-Saiz, C. T. Rigl, A. Kumar, K. G. Ragunathan, A. W. McConnaughie, D. W.

Boykin, H. J. Schneider, and W. D. Wilson, Bioorg. Med. Chem. 5, 1157 (1997).
6 T. Hermann and W. Westhof, Curt Opinion Biotechnol. 8, 278 (1998).
7 C. Chow and F. M. Bogdan, Chem. Rev. 97, 1489 (1997).
8 M. Afshar, C. D. Prescott, and G. Varani, Curr. Opin. BiotechnoL 10, 59 (1999).
9 M. J. Rogers, Y. V. Bukhman, R. E McCutchan, and D. E. Draper, RNA 3, 815 (1997).
10 G. L. Conn, R. R. Gutell, and D. E. Draper, Biochemistry 37, 11980 (1998).
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