Introduction to Macromolecular Binding Equilibria

259 Pages·2007·8.769 MB·English

by  Charles P. Woodbury

Introduction to
MACROMOLECULAR
BINDING EQUILIBRIA
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Introduction to
MACROMOLECULAR
BINDING EQUILIBRIA
Charles P. Woodbury
Boca Raton London New York
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Library of Congress Cataloging-in-Publication Data
Woodbury, Charles P.
Introduction to macromolecular binding equilibria / author, Charles P.
Woodbury Jr.
p. ; cm.
“A CRC title.”
Includes bibliographical references and index.
ISBN-13: 978-1-4200-5298-5 (hardcover : alk. paper)
ISBN-10: 1-4200-5298-5 (hardcover : alk. paper)
1. Binding sites (Biochemistry) 2. Ligand binding (Biochemistry) 3.
Macromolecules. I. Title.
[DNLM: 1. Binding Sites. 2. Ligands. 3. Macromolecular Substances. 4.
Models, Molecular. QU 34 W884i 2008]
QP517.B42W66 2008
572’.33--dc22 2007020733
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
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Dedication
To my beloved aunt, Martha Ann Woodbury.
Thank you for sharing your love of books.
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Contents
Chapter 1 Binding Sites ........................................................................................1
1.1 The Importance and Complexity of Macromolecular Binding ........................1
1.1.1 Different Types of Multiple Equilibria
in Macromolecular Binding ..................................................................1
1.2 Generating Affinity and Specificity with Weak Interactions ...........................4
1.2.1 Weak Interactions and Reversible Binding ...........................................4
1.2.2 Binding Specificity and Multiple Simultaneous Weak
Interactions ...........................................................................................5
1.2.3 The Strength of Binding .......................................................................7
1.2.4 Enthalpy-Entropy Compensation ..........................................................7
1.3 Size, Shape, and Functional Complementarity Determine
Recognition .....................................................................................................10
1.3.1 Exposed Surfaces and Binding ...........................................................10
1.3.1.1 Accessible Surface Area .......................................................10
1.3.2 Convergence of Functional Groups ....................................................11
1.3.2.1 The Proximity or Chelate Effect ..........................................11
1.3.2.2 Clefts as a Structural Motif for Binding Sites ......................15
1.3.3 Conformational Flexibility .................................................................15
1.3.3.1 Microstates ...........................................................................15
1.3.3.2 Hydration and Flexibility .....................................................19
1.3.3.3 Time and Distance Scales ....................................................19
1.4 Binding Sites on Proteins ...............................................................................21
1.4.1 Macromolecular Structures and the Protein Data Bank.....................21
1.4.2 Small Molecule Sites ..........................................................................22
1.4.3 Protein-Protein Interfaces ...................................................................23
1.4.4 Binding ‘Hot Spots’ ............................................................................24
1.4.5 Protein Surfaces That Bind DNA .......................................................27
1.5 Binding Sites on Nucleic Acids ......................................................................28
1.5.1 Nucleic Acids as Polyanions: Salt Effects in Ligand
Binding ...............................................................................................30
1.5.2 Nucleic Acid Double Helices: Contacts in the Grooves .....................30
1.5.3 Intercalative Binding ..........................................................................31
1.5.4 Sequence-Specific Binding .................................................................33
1.5.4.1 Sequence Recognition via the Major Groove .......................33
1.5.4.2 Site-Specific Binding in the Minor Groove .........................36
1.5.5 Nonspecific Binding and Ligand Sequestration .................................37
References ................................................................................................................38
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Chapter 2 Binding Isotherms ..............................................................................47
2.1 Some Definitions and Conventions on Notation .............................................47
2.1.1 The Two Partners: Ligand and Macromolecule..................................47
2.1.2 Concentrations of Components ...........................................................48
2.1.3 The Amount Bound: Binding Density and Degree
of Saturation ......................................................................................48
2.1.4 Notation for Binding Constants ..........................................................50
2.2 Connecting the Binding Density < r > with the Free Ligand
Concentration [L] ............................................................................................51
2.2.1 Describing Binding at the Phenomenological Level ..........................53
2.2.2 The Binding Isotherm as a Plot of < r > versus [L] ............................55
2.2.3 An Effective Binding Constant: The Concentration of Free
Ligand at Half Saturation ...................................................................56
2.2.4 The Question of Binding Stoichiometry .............................................58
2.3 Simple Isotherm Models via the Binding Polynomial ....................................59
2.3.1 Binding Free Energy Changes and the Binding
Polynomial ..........................................................................................59
2.3.2 The Langmuir Isotherm Model: Binding to Equal Independent
Sites .....................................................................................................61
2.3.3 Multiple Classes of Independent Sites ................................................62
2.4 Graphical Methods .........................................................................................67
2.4.1 Virtues and Weaknesses of the Direct Plot ........................................68
2.4.2 Linearized Plots ..................................................................................68
2.4.3 Some Common Errors of Experimental Design
and Interpretation ...............................................................................71
2.4.3.1 Neglecting Corrections for Ligand Depletion
and for Nonspecific Binding ................................................71
2.4.3.2 Misinterpreting Slopes and Intercepts .................................73
References ................................................................................................................77
Chapter 3 Binding Linkage, Binding Competition, and Multiple
Ligand Species ...................................................................................79
3.1 The Binding Polynomial and Linked Binding Equilibria ..............................81
3.1.1 Positive Linkage, Negative Linkage, and No Linkage
between Species ..................................................................................81
3.1.2 Binding Competition ..........................................................................83
3.1.3 A Single Class of Binding Sites and Two Competing
Ligand Species ....................................................................................84
3.1.3.1 Constant Concentration of One Species ...............................84
3.1.3.2 Multiple Identical Sites .........................................................85
3.1.4 IC Values and Competition Assays ..................................................86
50
3.1.4.1 Comparing Calcium Channel Blockers by
Displacement Assay .............................................................87
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3.1.5 Competitive Inhibition of an Enzyme ................................................89
3.1.5.1 The Cheng-Prusoff Relations ...............................................89
3.1.5.2 Validating the Use of the Cheng-Prusoff Relations .............91
3.1.6 Further Considerations in Competition Assays ..................................91
3.2 Linkage and “Piggy-Back” Binding ...............................................................92
3.2.1 Basic Theory for Piggy-Back Systems ...............................................93
3.2.2 Hydrogen Ion as a Piggy-Back Ligand: Theory for pH Effects .........95
3.2.2.1 Titration of a Single Residue on the Ligand .........................95
3.2.2.2 Comparison to Titration of a Single Residue
on the Receptor.....................................................................97
3.2.3 pH Effects in RNase-Inhibitor Binding ..............................................97
3.3 Linkage Effects on Macromolecular Associations
and Conformational Changes .........................................................................98
3.3.1 Linkage and an A←→B Equilibrium ............................................99
3.3.2 Ligand-Ligand Linkage and an A+B←→CEquilibrium ...........101
3.3.3 General Expression for the Salt Dependence of K .........................102
obs
3.3.4 Applications of Log-Log Plots ..........................................................104
3.3.4.1 Salt Effects in a-Chymotrypsin Dimerization ...................105
3.3.4.2 Water Activity and Chloride Ion Binding in the
Oxygenation of Hemoglobin ..............................................107
3.3.5 Uptake of L by a Macromolecule Partially Saturated with L ........108
2 1
3.4 Linkage Involving Weak and Nonstoichiometric Binding ...........................110
3.4.1 Preferential Interaction .....................................................................111
3.4.2 Preferential Interaction and Macromolecular Equilibria .................116
References ..............................................................................................................120
Chapter 4 Cooperativity ....................................................................................123
4.1 The Phenomenon of Binding Cooperativity .................................................123
4.1.1 Cooperative Binding in the Oxygenation
of Hemoglobin ..................................................................................123
4.1.2 Cooperativity in Enzyme Action ......................................................125
4.2 Terminology for Cooperative Interactions ...................................................127
4.3 Criteria for Cooperativity in Ligand Binding ...............................................128
4.3.1 Statistical Effects in Multisite Binding .............................................129
4.3.2 The All-or-None Model and the Hill Plot ........................................130
4.3.3 An Operational Definition for Cooperativity ...................................135
4.3.4 Linkage Relations and Binding Cooperativity .................................138
4.4 Structural Models of Cooperative Binding ..................................................140
4.4.1 The Concerted Monod-Wyman-Changeux
(MWC) Model ..................................................................................141
4.4.1.1 Heterotropic Effectors in the MWC Model .......................143
4.4.2 The Sequential Koshland-Nemethy-Filmer (KNF)
Model ................................................................................................144
4.4.2.1 Heterotropic Effectors in the KNF Model .........................145
4.4.3 Comparison of the KNF and MWC Models ....................................146
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4.4.4 Oxygenation of Hemoglobin .............................................................148
4.4.5 Nesting ..............................................................................................152
4.5 Aggregation and Cooperativity ....................................................................153
4.5.1 Aggregation of Ligand as a Source of Binding
Cooperativity ....................................................................................154
4.5.2 Aggregation of Receptor as a Source of Cooperativity ....................156
4.5.3 Ligand Dimerization Driven by a Piggy-Back Ligand .....................158
4.6 Negative Cooperativity .................................................................................160
4.6.1 Negative Cooperativity in the Titration of Ethylene
Diamine ............................................................................................162
4.6.2 Glyceraldehyde 3-Phosphate Dehydrogenase and Negative
Cooperativity ....................................................................................163
References ..............................................................................................................166
Chapter 5 Binding to Lattices of Sites ..............................................................171
5.1 Linear Lattices of Binding Sites ...................................................................171
5.1.1 Redefining the Binding Density for Linear Systems ........................172
5.1.2 The McGhee-von Hippel Treatment [1] ............................................175
5.1.3 Extensions of the Model: Oriented Lattices and Ligands ................182
5.1.4 Site-Exclusion in DNA-Polyamine Binding .....................................185
5.1.5 Site-Exclusion and Positive Cooperativity
in DNA-Protein Binding ...................................................................186
5.1.6 Site-Exclusion and Lattice Conformational Change ........................187
5.1.6.1 Ethidium/DNA Interactions ...............................................190
5.1.7 Piggy-Back Binding and DNA-Protein Interactions ........................192
5.2 Binding to Two-Dimensional Lattices ..........................................................195
5.2.1 Heuristic Treatment of Site Exclusion in Two Dimensions ..............196
5.2.1.1 The Stankowski Model.......................................................196
5.2.2 Application to Membrane Binding ...................................................200
References ..............................................................................................................201
Chapter 6 Choosing a Method and Analyzing the Data ...................................205
6.1 Considerations when Choosing a Method ....................................................205
6.1.1 Possible Assay Interference from Binding Kinetics .........................206
6.1.1.1 The Rate of Association .....................................................207
6.1.1.2 The Dissociation Rate ........................................................208
6.1.1.3 Further Kinetic Considerations ..........................................208
6.1.2 Direct versus Indirect Methods of Measuring the
Equilibrium .......................................................................................209
6.2 Designing The Experiment ...........................................................................210
6.2.1 Nonideal Behavior: Salt and Crowding Effects ................................211
6.2.2 Choosing Working Concentrations in Relation to K.........................213
6.2.3 Some General Precautions to Consider ............................................215
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6.3 Model-Free Analyses of Binding Signals .....................................................216
6.3.1 Assumptions and Notation ................................................................217
6.3.2 Signal from the Ligand .....................................................................218
6.3.3 Signal from the Macromolecule .......................................................220
6.4 Statistical Analysis of Binding Data .............................................................223
6.4.1 Errors in Dependent and Independent Variables ..............................223
6.4.2 Computerized Fitting of Data ...........................................................224
6.4.2.1 Nonlinear Curve Fitting .....................................................225
References ..............................................................................................................231
Appendix: The Sequence-Generating Function Method .................................235
Index ......................................................................................................................245
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Preface
This book is based on my experience in teaching biophysical chemistry to graduate
students in the medicinal chemistry, pharmaceutics, and bioengineering programs at
the University of Illinois at Chicago. The course was designed to give these students
an adequate background in biophysical chemistry for research in drug discovery and
development, and the course has had a strong emphasis on macromolecular solva-
tion and ligand binding. The role of hydration in binding phenomena, along with the
effects of salt and pH, is increasingly emphasized in the literature, so these students
need a somewhat deeper background in preferential interaction concepts and in link-
age thermodynamics than might students in biochemistry, pharmacology, or physi-
ology programs. Of course, the students also need to learn about new techniques
for characterizing macromolecular complexes with small molecules, such as surface
plasmon resonance and fluorescence polarization, but there are certain underlying
concepts in binding theory they need to grasp firmly so that they can interpret the
results of assays that use these new methods.
This book tries to give that necessary theoretical background. It is certainly not
a complete exposition of macromolecular binding, only an introduction that empha-
sizes some selected fundamental topics. The analytical methods of assaying mac-
romolecular binding I have mainly left aside, though I do present what I hope will
be some useful general advice on designing binding assays and how to interpret
them. I also have summarized qualitative features of binding sites on proteins and
nucleic acids, an area that is now referred to as “molecular recognition”. But my
main purposes have been to show how to use the binding polynomial approach in
model building and interpretation, and to show how linkage thermodynamics can tie
together disparate binding observations. Whenever possible, I have tried to tie the
theory to concrete examples drawn from the research literature. I have also included
a substantial number of references to the original literature, for those who might
wish to pursue further any of the topics presented.
I would like to acknowledge the support given me by the Department of Medici-
nal Chemistry and Pharmacognosy at the University of Illinois at Chicago, and by
my colleagues in that department. And of course, I welcome comments and sugges-
tions from readers for improvement of this book.
Charles Woodbury
University of Illinois at Chicago
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