www.wiley-vch.de

Mirsky · Yatsim

irsky (Eds.)A

rtifi cial Receptors

for Chem

ical Sensors

The selective binding of a particular compound to another is a lock-and-key principle omnipresent in living organisms and an indispens-able means of information transport and triggering responses. Derived from the biological archetype, synthetic receptors imitate nature‘s idea for tailor-made functionalities such as detection (sensing), signaling, and triggering. This book provides systematically organized informa-tion on all three important aspects of artifi cial receptor design as well as the knowledge on an exceptionally hot and multidisciplinary fi eld of research. Strong emphasis is placed on the methodology for discover-ing artifi cial receptors, with both defi nitions for chemosensitivity as well as experimental setups supplied. Numerous classes of artifi cial receptors are covered, as well as their synthesis, immobilization on surfaces, and quantitative data on their properties. The fi nal chapter with all relevant quantitative data on artifi cial receptors complete this well-rounded book.

Vladimir M. Mirsky is Professor at Lausitz University of Applied Sciences, Senftenberg, Germany. He graduated from Moscow Medical University in Biophysics and went on to study Physical Chemistry and Electrochemistry at the Frum-kin Institute of Electrochemistry of the Soviet Academy of Sciences, obtaining there his PhD in 1986. He subsequently held an Alexander-von-Humboldt Research Fellowship and a research position at the CNRS Centre of Molecular Biology in France prior to joining the Institute of Analytical Chemistry, Chemical Sensors and Biosensors at Regensburg University in 1995. After habilitation he became Professor of Nanobio-technology and moved to Lausitz. He is editor of two recent books, “Ultrathin Electrochemical Chemo- and Biosensors” and “Combinatorial Methods for Chemical and Biological Sensors”. His work has led to about 20 patents and patent applications as well as 120 peer-reviewed scientifi c papers.

Anatoly K. Yatsimirsky is Professor of Chemistry at the National Autonomous University of Mexico in Mexico City. He obtained his PhD and Dr. Sc. degrees from Moscow Lomonosov State University, where he was Professor prior to his move to Mexico in 1992. He spent Visiting Scholar/Pro-fessor stays at Milan University, Italy, in 1980/81 and at the University of California at Santa Barbara in 1998/99. His research is focused on physical organic chemistry and metal complex catalysis and he is the author of 160 peer-reviewed scientifi c publications including a monograph “Principles and Methods in Supramolecular Chemistry” by John Wiley & Sons and further book contributions.

Edited by Vladimir Mirsky and Anatoly Yatsimirsky

Artifi cial Receptors for Chemical Sensors

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Edited by

Vladimir M. Mirsky and

Anatoly K. Yatsimirsky

Artificial Receptors

for Chemical Sensors

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Edited byVladimir M. Mirsky and Anatoly K. Yatsimirsky

Artificial Receptors for Chemical Sensors

The Editors

Prof. Dr. Vladimir M. MirskyLausitz University of Applied SciencesNanobiotechnology - BCVGrossenhainer str. 5701968 SenftenbergGermany

Prof. Dr. Anatoly K. YatsimirskyUniversidad Nacional Autónoma de MéxicoFacultad de Química04510 México D.F.Mexico

CoverDr. N.V. Roznyatovskaya is acknowledgedfor her assistance in the design of thebook cover.

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# 2011 WILEY-VCH Verlag & Co. KGaA,Boschstr. 12, 69469 Weinheim, Germany

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Contents

Preface XIList of Contributors XIII

1 Quantitative Characterization of Affinity Propertiesof Immobilized Receptors 1Vladimir M. Mirsky

1.1 Introduction 11.2 Measurements Under Equilibrium Conditions 31.3 Kinetic Measurements 71.4 Analysis of Temperature Dependencies 101.5 Experimental Techniques 12

References 14

2 Selectivity of Chemical Receptors 17Hans-Jörg Schneider and Anatoly K. Yatsimirsky

2.1 Introduction 172.2 Some General Considerations on Selectivity 182.3 Correlation Between Selectivity and Affinity 212.4 Crown Ether and Cryptand Complexes: Hole Size Fitting

and Other Effects 242.5 Recognition of Transition and Heavy Metal Ions 292.6 Recognition via Ion Pairing 312.7 Hydrogen Bonded Complexes and Solvent Effects 372.8 Lewis Acid Receptors 412.8.1 Associations with Transition Metal Complexes 412.8.2 Associations with Other Lewis Acids 452.9 Complexes with Stacking and van der Waals Interactions 462.10 Multifunctional Receptors for Recognition of Complex

Target Molecules 48

V

2.10.1 Complexation of Amino Acids and Peptides 482.10.2 Complexation of Nucleotides and Nucleosides 542.11 Conclusions 60

References 61

3 Combinatorial Development of Sensing Materials 67Radislav A. Potyrailo

3.1 Introduction 673.2 General Principles of Combinatorial Materials Screening 683.3 Opportunities for Sensing Materials 693.4 Designs of Combinatorial Libraries of Sensing Materials 713.5 Discovery and Optimization of Sensing Materials Using

Discrete Arrays 733.5.1 Radiant Energy Transduction Sensors 733.5.2 Mechanical Energy Transduction Sensors 793.5.3 Electrical Energy Transduction Sensors 843.6 Optimization of Sensing Materials Using Gradient Arrays 923.6.1 Variable Concentration of Reagents 923.6.2 Variable Thickness of Sensing Films 933.6.3 Variable 2D Composition 943.6.4 Variable Operation Temperature and Diffusion Layer Thickness 953.7 Emerging Wireless Technologies for Combinatorial Screening

of Sensing Materials 973.8 Summary and Outlook 102

References 104

4 Fluorescent Cyclodextrins as Chemosensors for MoleculeDetection in Water 113Hiroshi Ikeda

4.1 Introduction 1134.2 Pyrene-Appended Cyclodextrins 1144.2.1 Pyrene-Appended c-Cyclodextrins as Molecule Sensors 1144.2.2 Pyrene-Appended c-Cyclodextrin as a Bicarbonate Sensor 1154.2.3 Bis-Pyrene-Appended c-Cyclodextrins 1164.3 Fluorophore–Amino Acid–CD Triad Systems 1184.3.1 Dansyl-Leucine-Appended CDs 1184.3.2 Dansyl-Valine-Appended and Dansyl-Phenylalanine-Appended

CDs 1224.4 Molecular Recognition by Regioisomers of Dansyl-Appended

CDs 1234.4.1 6-O, 2-O, and 3-O-Dansyl-c-CDs 1234.4.2 6-O, 2-O, and 3-O-Dansyl-b-CDs 1254.5 Turn-On Fluorescent Chemosensors 1254.6 Effect of Protein Environment on Molecule Sensing 1274.7 CD–Peptide Conjugates as Chemosensors 128

VI Contents

4.8 Immobilized Fluorescent CD on a Cellulose Membrane 1304.9 Conclusion 132

References 132

5 Cyclopeptide Derived Synthetic Receptors 135Stefan Kubik

5.1 Introduction 1355.2 Receptors for Cations 1385.3 Receptors for Ion Pairs 1495.4 Receptors for Anions 1505.5 Receptors for Neutral Substrates 1575.6 Conclusion 160

References 161

6 Boronic Acid-Based Receptors and Chemosensors 169Xiaochuan Yang, Yunfeng Cheng, Shan Jin, and Binghe Wang

6.1 Introduction 1696.2 De Novo Design 1726.3 Combinatorial Approaches 1776.4 Template Directed Synthesis 181

References 185

7 Artificial Receptor Compounds for Chiral Recognition 191Thomas J. Wenzel and Ngoc H. Pham

7.1 Introduction 1917.2 Cyclodextrins 1917.2.1 Alkylated Cyclodextrins 1927.2.2 Acylated and Mixed Acylated/Alkylated Cyclodextrins 1947.2.3 Carbamoylated Cyclodextrins 1947.2.4 2-Hydroxypropylether Cyclodextrins 1957.2.5 Tert-butyldimethylsilyl Chloride-Substituted Cyclodextrins 1957.2.6 Anionic Cyclodextrins 1967.2.7 Cationic Cyclodextrins 1977.2.8 Miscellaneous Cyclodextrins 1987.3 Crown Ethers 2007.3.1 1,10-Binaphthalene-Based Crown Ethers 2017.3.2 Carbohydrate-Based Crown Ethers 2027.3.3 Tartaric Acid-Based Crown Ethers 2047.3.4 Crowns Ethers with Phenol Moieties 2067.3.5 Crown Ethers with Pyridine Moieties 2087.4 Calixarenes 2097.5 Calix[4]resorcinarenes 2187.6 Miscellaneous Receptor Compounds 2257.7 Metal-Containing Receptor Compounds 235

References 237

Contents VII

8 Fullerene Receptors Based on Calixarene Derivatives 249Pavel Lhoták and Ondřej Kundrát

8.1 Introduction 2498.2 Calixarenes 2518.3 Solid State Complexation by Calixarenes 2528.4 Complexation in Solution 2578.5 Calixarenes as Molecular Scaffolds 2638.6 Outlook 268

References 269

9 Guanidinium Based Anion Receptors 273Carsten Schmuck and Hannes Yacu Kuchelmeister

9.1 Introduction 2739.2 Instructive Historical Examples 2759.3 Recent Advances in Inorganic Anion Recognition 2839.4 Organic and Biological Phosphates 2879.5 Polycarboxylate Binding 2929.6 Amino Acid Recognition 2979.7 Dipeptides as Substrate 3019.8 Polypeptide Recognition 3039.9 Conclusion 312

References 313

10 Artificial Receptors Based on Spreader-Bar Systems 319Thomas HirschReferences 331

11 Potential of Aptamers as Artificial Receptors in Chemical Sensors 333Bettina Appel, Sabine Müller, and Sabine Stingel

11.1 Introduction 33311.2 Generation and Synthesis of Aptamers 33411.2.1 Selection of Aptamers from Combinatorial Libraries (SELEX) 33411.2.2 SELEX Variations 33611.2.2.1 SELEX Using Modified Oligonucleotide Libraries 33611.2.2.2 PhotoSELEX 33611.2.2.3 Automated SELEX 33711.2.3 Alternative Approaches for Selection of Aptamers

from Combinatorial Libraries 33811.2.3.1 Capillary Electrophoresis Techniques 33811.2.3.2 AFM Techniques 33911.2.4 Synthesis of Aptamers and Stabilization 33911.2.4.1 Chemical Synthesis of Aptamers 33911.2.4.2 Stabilization of Aptamers 34011.3 Aptamer Arrays 34111.4 Techniques for Readout of Ligand Binding to the Aptamer 343

VIII Contents

11.4.1 Conformational Effects 34311.4.2 Aptazymes 34411.4.3 Methods of Sensing 34511.4.3.1 Optical Sensing 34511.4.3.2 Electrochemical Sensing 35011.4.3.3 Acoustic Sensing 35311.4.3.4 Quartz Crystal Microbalance Based Sensing 35411.4.3.5 Cantilever Based Sensing 35411.5 Outlook/Summary 354

References 355

12 Conducting Polymers as Artificial Receptors in Chemical Sensors 361Ulrich Lange, Nataliya V. Roznyatovskaya, Qingli Hao,and Vladimir M. Mirsky

12.1 Introduction 36112.2 Transducers for Artificial Receptors Based on Conducting

Polymers 36212.3 Intrinsic Sensitivity of Conducting Polymers 36612.3.1 Sensitivity to pH Changes 36612.3.2 Affinity to Inorganic Ions 36812.3.3 Affinity to Gases and Vapors 36812.4 Conducting Polymers Modified with Receptor Groups 36912.4.1 Conducting Polymers with Receptor Groups Attached

to the Monomer 36912.4.1.1 Receptors for Ions 36912.4.1.2 Receptors for Organic/Bioorganic Molecules 38112.4.2 Conducting Polymers Doped with Receptor 38212.4.3 Molecular Imprinting of Conducting Polymers 38312.5 Conclusion 383

References 384

13 Molecularly Imprinted Polymers as Artificial Receptors 391Florian Meier and Boris Mizaikoff

13.1 Introduction 39113.2 Fundamentals of Molecular Imprinting 39313.2.1 What are MIPs? 39313.2.2 Approaches toward Molecular Imprinted Polymers 39413.2.2.1 Noncovalent Imprinting (Self-Assembly Approach) 39413.2.2.2 Covalent Imprinting (Preorganized Approach) 39513.2.2.3 Semi-Covalent Imprinting 39513.2.2.4 Advantages and Disadvantages of Different Imprinting

Approaches 39613.2.3 Reagents and Solvents in Molecular Imprinting Technology 39613.2.3.1 Functional Monomers 39613.2.3.2 Crosslinkers 397

Contents IX

13.2.3.3 Radical Initiators 40113.2.3.4 Solvents 40213.2.4 How are MIPs Prepared? 40413.3 Polymer Formats and Polymerization Methods for MIPs 40513.3.1 Bulk Polymers 40513.3.2 Micro- and Nanobeads 40713.3.3 MIP Films and Membranes 40813.3.4 Comparison of MIP Formats Prepared by Different Polymerization

Methods 41213.4 Evaluation of MIP Performance – Imprinting Efficiency 41413.4.1 Binding Capacity and Binding Affinity 41413.4.2 Binding Selectivity 41813.5 MIPs Mimicking Natural Receptors 42013.5.1 Comparison of MIPs and Antibodies 42113.5.2 MIPs as Artificial Antibodies in Pseudo-Immunoassays 42113.5.3 MIPs as Catalysts with Enzymatic Activity 42513.5.4 Quantitative Data on the Binding Properties of MIPs 42713.6 Conclusions and Outlook 427

References 430

14 Quantitative Affinity Data on Selected Artificial Receptors 439Anatoly K. Yatsimirsky and Vladimir M. Mirsky

14.1 Structures of Receptors 449References 458

Index 461

X Contents

Preface

One of the great achievements in modern chemistry is the development of artificialsynthetic receptors, which are typically low molecular weight compounds that per-form selective binding (recognition) of a compound of interest. Such compounds areused for the design and chemically addressed assembly of supramolecular struc-tures. Another important application of these compounds is the development ofchemical sensors. Over the past few few decades affinity assays have been basedmainly on immunological techniques: antibodies are used routinely in clinicalapplications or in food analysis. However, they are expensive, unstable, and cannotbe prepared for some types of analytes. For example, one cannot immunize animalswith highly toxic compounds or with compounds that are present in all animals(such as glucose, sodium ion). The solution is to use artificial receptors. Recent yearshave seen intensive development in this field. Traditional approaches based on thechemical synthesis of small molecules with high affinity have been completed bymolecularly imprinted polymerization and by biotechnological preparation andselection of natural macromolecules with such properties.

Syntheses, structures, and recognition properties of artificial receptors aretouched on in many monographs in the field of supramolecular chemistry. Thebook Functional Synthetic Receptors edited by Thomas Schräder and Andrew D.Hamilton (Wiley-VCHVerlag GmbH, 2005) provides deep insight into fundamentalaspects of the subject. There is little literature, however, discussing artificial recep-tors with the emphasis on their practical applications as components of chemicalsensors and assays. This book intends to fill this gap.

The book starts with two chapters discussing the most relevant quantitativecharacteristics of receptors – binding affinity and selectivity. Chapter 3, on thecombinatorial development of sensing materials, deals with an advanced technolo-gical approach to the discovery of new receptors. Chapters 4–9 discuss particulartypes of receptors (cyclodextrins, cyclopeptides, boronic acids, chiral receptors,calixarenes, and guanidinium derivatives) of significant current importance. Finally,Chapters 10–13 deal with receptors based on organized (spreader-bar approach) orpolymeric (aptamers, conducting polymers, and molecular imprinting) structures.

XI

Chapter 14 provides an extensive compilation of the affinity properties of differentreceptors taken from current literature.We hope that this book will be useful as a handbook for scientists (from uni-

versities and industry) and graduate and post-graduate students working in analy-tical and supramolecular chemistry, chemical sensors and biosensors, and inmaterial science. It will also be of interest to experts and students working/studyingsurface chemistry, physical chemistry, and in some fields of organic chemistry,pharmacology, medical diagnostics, biotechnology, chemical technology, food, andenvironmental monitoring.Finally, we express our gratitude to the authors of this book and hope that readers

also find these contributions enjoyable, interesting, and useful.

February 2010 Vladimir M. Mirsky, SenftenbergandAnatoly K. Yatsimirsky, Mexico City

XII Preface

List of Contributors

XIII

Bettina AppelErnst-Moritz-Arndt UniversitätGreifswaldInstitut für BiochemieFelix-Hausdorff-Str. 417487 GreifswaldGermany

Yunfeng ChengGeorgia State UniversityDepartment of Chemistry and Centerfor Biotechnology and Drug DesignAtlanta, GA 30302-4098USA

Qingli HaoNanjing University of Scienceand TechnologyKey Laboratory of Soft Chemistryand Functional MaterialsMinistry of Education210094 NanjingChina

Thomas HirschUniversity of RegensburgInstitute of Analytical ChemistryChemo- and BiosensorsUniversitätsstraße 3193040 RegensburgGermany

Hiroshi IkedaTokyo Institute of TechnologyGraduate School of Bioscienceand BiotechnologyDepartment of Bioengineering4259-B-44 Nagatsuta-cho, Midori-kuYokohama 226-8501Japan

Shan JinGeorgia State UniversityDepartment of Chemistry and Centerfor Biotechnology and Drug DesignAtlanta, GA 30302-4098USA

Stefan KubikTechnische Universität KaiserslauternFachbereich Chemie - OrganischeChemieErwin-Schrödinger-Strasse67663 KaiserslauternGermany

Hannes Yacu KuchelmeisterUniversity of Duisburg-EssenInstitute for Organic ChemistryUniversitätsstraße 745141 EssenGermany

Ondřej KundrátPrague Institute of ChemicalTechnologyDepartment of Organic ChemistryTechnická 5166 28 Prague 6Czech Republic

Ulrich LangeUniversity of RegensburgInstitute of Analytical Chemistry,Chemo- and BiosensorsUniversitätsstraße 3193040 RegensburgGermany

Pavel LhotákPrague Institute of ChemicalTechnologyDepartment of Organic ChemistryTechnická 5166 28 Prague 6Czech Republic

Florian MeierUniversity of UlmInstitute of Analytical and BioanalyticalChemistryAlbert-Einstein-Allee 1189061 UlmGermany

Vladimir M. MirskyLausitz University of Applied SciencesNanobiotechnology-BCVGrossenhainer str. 5701968 SenftenbergGermany

Boris MizaikoffUniversity of UlmInstitute of Analytical and BioanalyticalChemistryAlbert-Einstein-Allee 1189069 UlmGermany

Sabine MüllerErnst-Moritz-Arndt UniversitätGreifswaldInstitut für BiochemieFelix-Hausdorff-Str. 417487 GreifswaldGermany

Ngoc H. PhamBates CollegeDepartment of ChemistryS. Andrews RoadLewiston, ME 04240USA

Radislav A. PotyrailoGeneral Electric Global ResearchChemical and Biological SensingLaboratoryChemistry Technologies and MaterialCharacterization1 Research CircleNiskayuna, NY 12309USA

Nataliya V. RoznyatovskayaFraunhofer Institute of ChemicalTechnologyJoseph-von-Fraunhofer-Straße 776327 Pfinztal-BerghausenGermany

Carsten SchmuckUniversity of Duisburg-EssenInstitute for Organic ChemistryUniversitätsstraße 545141 EssenGermany

Hans-Jörg SchneiderUniversität des SaarlandesFR Organische Chemie66041 SaarbrückenGermany

XIV List of Contributors

Sabine StingelErnst-Moritz-Arndt UniversitätGreifswaldInstitut für BiochemieFelix-Hausdorff-Str. 417487 GreifswaldGermany

Binghe WangGeorgia State UniversityDepartment of Chemistry and Centerfor Biotechnology and Drug DesignAtlanta, GA 30302-4098USA

Thomas J. WenzelBates CollegeDepartment of ChemistryS. Andrews RoadLewiston, ME 04240USA

Xiaochuan YangGeorgia State UniversityDepartment of Chemistry and Centerfor Biotechnology and Drug DesignAtlanta, GA 30302-4098USA

Anatoly K. YatsimirskyUniversidad Nacional Autónomade MéxicoFacultad de Química04510 México D.F.México

List of Contributors XV

1Quantitative Characterization of Affinity Propertiesof Immobilized ReceptorsVladimir M. Mirsky

1.1Introduction

Affinity as a tendency of molecules (ligands) to associate with another type ofmolecules or polymers (receptor) can be described by a set of kinetic and thermo-dynamic parameters. These parameters include the adsorption (or binding, orassociation) constant, which can be recalculated as the free energy of binding,binding enthalpy and entropy, kinetic adsorption and desorption constants, andactivation energies for binding and for dissociation.

There are several reasons for a quantitative characterization of affinity. The firstis due to possible applications of these receptors in affinity sensors. The sensors areintended to measure volume concentrations of analytes. However, transducers ofaffinity sensors (refractometric, interferometric, mechano-acoustical, capacitive,and others) provide information on the surface concentration of analytes (ligands)on a layer of immobilized receptors (Figure 1.1). Therefore, it is important to obtaina calibration curve – the dependence between volume concentration of an analyte andits surface concentration. Such relations are named in physical chemistry asadsorption isotherms (the binding is usually performed at constant temperature).Several adsorption isotherms can be obtained from simple physical models.A mathematical description of these isotherms allows one not only a better under-standing of binding process but also provides a mathematical basis for interpolationand extrapolation of the calibration curve, which is of importance for analyticalapplications.

The second reason includesmaterial science aspects.Quantitative information canbe used to make an appropriate choice of synthetic receptors for different applica-tions and for prediction of the detection limit and selectivity of analytical devicesbased on these receptors. Additionally, these data can be used as descriptors forcombinatorial optimization and for discovery of new sensing materials (the com-binatorial approach is discussed in Chapter 3) [1–3].

The association canbe investigated in the bulk phase (in the solution or suspensionof the ligand and receptor molecules) or on a surface. Ligand–receptor interactions

j1

can be investigated in a bulk phase by titration and application of any analyticaltechnique that is sensitive to the concentration of free or bound ligands or receptors.For example, the binding of dye molecules can be determined by colorimetry orfluorescence, while ions or redox-active species can be measured by potentiometrictechniques. One of the most commonly used techniques that can be applied forvarious ligand–receptor systems is a NMR titration. Another general approach isbased on isothermal calorimetry; in this case the heat produced during the ligan-d–receptor interaction is measured. This technique has the advantage of providingthe enthalpy of binding in a single titration experiment. Analysis of ligand–receptorbinding in bulk phases is well described in literature [4–7] and, therefore, is notcovered in this chapter.

Applications of artificial receptors for chemical sensors require an immobilizationof these receptors on a surface. In the 1980s to the beginning of 1990s there weremany attempts to induce physical immobilization of chemoreceptors, for example,by using the Langmuir–Blodgett technique or electrostatically driven adsorption.Nowadays, receptor immobilization is performed mainly by formation of chemicalbonds with some surface groups (e.g., peptide bond) or by introduction of surfaceanchoring groups into the receptormolecules. Chemical aspects of covalent receptorimmobilization have been described [8–15]. The most widely used technology ofchemical immobilization is based on the formation of an amide bond throughactivation by either EDC [1-ethyl-3-(3-dimethylaminopropyl)carbodiimide)] [14, 15]or an EDC–NHS (N-hydroxysuccinimide) mixture. The most widely used surfaceanchor group is the thiol group, which forms, spontaneously, an extremely strongbond with gold, silver, palladium, copper, and some other materials [13, 16–19].

Chemical immobilization of a receptor may influence its affinity properties. Thischapter is focused on the characterization of affinity properties of immobilizedreceptors.

Figure 1.1 Transducers of affinity sensors provide information on the surf ace concentration ofbound analytes. For practical applications, information on the volume concentration is required.

2j 1 Quantitative Characterization of Affinity Properties of Immobilized Receptors

1.2Measurements Under Equilibrium Conditions

Binding of a ligand (A) with a receptor (B) leading to the formation of a complex canbe considered using a formal kinetic approach:

AþB ! ABThe rate of association (adsorption onto the receptor layer) is proportional to

the ligand concentration (cL) and to the fraction of uncoated binding sites (1� q),where q is the fraction of occupied binding sites. Therefore, the association rate iskadscL(1� q), where kads is the kinetic adsorption constant (also indicated as thekinetic association constant or kinetic binding constant). The rate of dissociation iskdesq, where kdes is the kinetic constant of desorption (also indicated as the kineticconstant of dissociation). At equilibrium conditions:

kads � cLð1�qeqÞ ¼ kdes � cLqeq ð1:1Þtherefore:

qeq ¼ cLK1þ cLK ð1:2Þ

where:

K ¼ kads=kdes ð1:3ÞThis model, well known as the Langmuir adsorption isotherm, is valid for most

cases of ligand–receptor binding. The model is based on the following assumptions:(i) all binding sites are equivalent; (ii) the ability of a ligandmolecule to bind a bindingsite is independent of the occupation of neighboring sites; (iii) the number of bindingsites is limited; and (iv) there is a dynamic equilibrium between bound moleculesand free molecules in aqueous environment.

At low ligand concentration (cLK� 1) this equation is linearized: q¼ cLK (Henryadsorption isotherm). Physically, it corresponds to binding at low surface coverage.

Analysis of the literature on chemical sensors, biosensors, and supramolecularchemistry demonstrates that the Langmuir adsorption isotherm is valid for mostcases. The main reasons for possible deviations from this simple model are non-homogeneity of binding sites [deviation from postulate (i)] and an influence ofoccupation of binding sites on affinity properties of neighboring sites [deviation frompostulate (ii)].

Non-homogeneity of binding sites is a typical case for artificial receptors formedby molecularly imprinted polymerization (artificial receptors based on molecularlyimprinted polymers are discussed in Chapter 13) [20, 21]. For a receptor layerconsisting of several different types of receptors, the Langmuir adsorption isothermhas the form:

qeq ¼Xi

cicLKi

1þ cLKi ð1:4Þ

1.2 Measurements Under Equilibrium Conditions j3

where ci is the molar fraction of the receptor with binding constant Ki. For acontinuous distribution of binding constants the sum in Eq. (1.4) can be replacedby an integral. In practice, Eq. (1.4) can be applied only for i¼ 2 or 3 and only if thedifference between Ki is at least several-fold. In some cases the heterogeneity of thereceptor properties and distribution through the sensing surface can be describedby fractal geometry [22]. An exponential distribution of energy of the binding sites isdescribed by Freundlich adsorption isotherm:

q ¼ A ffifficBp ð1:5ÞAs a criterion for this isotherm, a linearization versus logarithmic concentration

scale is used.In general, although non-homogeneity of the receptor properties can be explained

and describedmathematically, this leads to serious practical problems in applicationsof such receptors for analytical purposes. In this case the results depend stronglyon the initial occupation of binding states of the receptor layer, and non-completedesorption of ligands leads to a quite different adsorption isotherm.

The distance between receptors immobilized on a surface is usually large enoughto exclude an influence of the occupation of one binding site on the affinity ofneighboring binding sites. However, such effects have been reported in severalstudies. Numerous models have been suggested to describe adsorption under suchconditions. The most widely used is the Frumkin isotherm.

Kc ¼ q1�q exp ð�2aqÞ ð1:6Þ

This is an extension of the Langmuir isotherm, taking into account an interactionof adsorbedmolecules. The interaction is described by parameter a,which is positivefor attraction and negative for repulsion between adsorbed molecules (Figure 1.2).For a¼ 0 the Frumkin isotherm coincides with the Langmuir isotherm.

A signal of affinity sensors (S) is proportional to their surface coverage (q) (thisfact is often considered as a definition of affinity sensors); therefore, for bindingaccording to the Langmuir isotherm the signal has the following dependence onligand concentration:

S ¼ a cLK1þ cLK ð1:7Þ

where a is a proportionality coefficient depending on the type of transducer andon an amplification factor during the signal processing. For small concentrations(cLK� 1) this leads to a linear equation:

S ¼ a cL K ð1:8Þ

The main question in the analysis of experimental data obtained under quasi-equilibrium conditions is the extraction of the binding constant K. In the case ofa linear dependence of the signal of an affinity sensor on concentration [Eq. (1.8)],

4j 1 Quantitative Characterization of Affinity Properties of Immobilized Receptors

such analysis would require information on the coefficient a, which is not alwaysavailable and in general can be different for different receptors. However, even forunknown but constant values of a, a comparison of slopes of the curves measuredat different conditions or for modified receptors provides valuable information oncomparison of binding constants.

Binding curves reaching their saturation range are more informative. An analysisof such dependence can provide information not only on the binding constant butalso on the homogeneity of the binding sites (or on deviations from the Langmuirmodel) and on the value of the proportionality factora corresponding to the saturatedvalue of the signal. The quality of data analysis improves with increasing deviationfrom linear dependence. However, the maximal concentration that can be used forexperimental tests is usually limited (e.g., by solubility or by available amount of theligand).

Principally, the parameters K and a can be extracted from experimental data bydirect nonlinear fitting using Eq. (1.7). Another approach, providing a better

Figure 1.2 Simulated adsorption isothermsaccording to the models of Henry (curve 1),Langmuir (curve 2) and Frumkin (curves 3 and4) for attraction (a¼ þ 1, curve 4) and repulsion

(a¼� 1, curve 3) of adsorbed molecules atdifferent concentration scales (a)–(c) and as asemilogarithmic plot (d). Binding constant in allthe curves is 1/(1 nM).

1.2 Measurements Under Equilibrium Conditions j5

visualization of the type of possible deviation from the Langmuir model, is basedon linearization of this dependence in a double reciprocal plot (Lineweaver–Burk plot):

1S¼ 1

aK1cLþ 1

að1:9Þ

Extrapolation of the line gives information on both parameters of Eq. (1.7)(Figure 1.3a). Although this approach is sometimes considered as a relic of thebefore-computer era, it has several advantages. For example, it may indicate asystematic deviation from the Langmuir model or heterogeneity of binding sites.In this case, n types of binding sites with different affinity give n� 1 breaks of thestraight line. Practically it is applicable only for n¼ 2 or 3 and only when the bindingconstants are very different (about one order or more), and the measurements areperformed over the wide concentration range.

Another approach to obtain the binding constant from experimental data mea-sured before saturation is based on data presentation versus a logarithmic concen-tration scale (Figure 1.2d, curve 2 and Figure 1.3b). In this case the reciprocal bindingconstant corresponds to the concentration at the symmetry point of the curve. Thispoint also corresponds to the maximal slope or to the point of change of the sign ofthe curvature. Therefore, for data measured in a small concentration range, wherethe symmetry point is not clearly visible, it can be also found from analysis of the firstor second derivatives (Figure 1.3b).

The obtained binding constant can be then recalculated into the molar standardGibbs free energy (Gibbs energy) of the binding reaction:

DG0 ¼ �RT lnK ð1:10Þ

The binding constant in Eq. (1.10) characterizes the ratio of activities of corre-sponding species and is therefore a dimensionless value. By application of usualapproximations of activities by concentrations, the concentration values should be

Figure 1.3 Extraction of binding constant by linearization of Langmuir isotherm in doublereciprocal plots (a) and by symmetrization in semilogarithmic plots (b). The symmetry point can befound more exactly from the derivative.

6j 1 Quantitative Characterization of Affinity Properties of Immobilized Receptors

converted into dimensionless ones by normalization of the concentrations to1mol l�1.

In practice, the binding constants of immobilized receptors based on equilibriumbetween volume and surface concentrations are measured under quasi-stationaryconditions, as a response of an affinity sensor with this receptor to stepwiseincreasing ligand concentration. Typically, the measurement is performed10–40min after the concentration increase, when the signal looks constant. Thereis no strong criterion on reaching of equilibrium, and this uncertainty may be areason for a systematic error.

An analysis of binding and selection of an appropriate binding isotherm carrya risk of misinterpretation and require very critical consideration. For example,logarithmic conversion, used for validation of the Freundlich isotherm, leads tostrong compression of the variation range and therefore to some data linearization.A break in the double-reciprocal plot of the Langmuir isotherm for two bindingsites is observed only for a sufficiently high difference of binding constants of thesesites. In addition, data analysis based on a Scatchard plot, which is widely used foraffinity experiments in bulk phase, is often misinterpreted [23, 24]. An uncertaintyin the definition of quasi-equilibrium was discussed above. In many cases,statements on the selection of adsorption models can be checked by numericalsimulations.

1.3Kinetic Measurements

Binding constants can be also obtained from kinetic measurements. Numerousinvestigations have demonstrated that the values obtained from kinetic and equi-librium measurements are almost identical. Kinetic measurements of bindingconstants can be performed much faster than the measurements under quasi-equilibrium conditions. Moreover, for some receptor–ligand pairs the kinetics areso slow that the measurements in quasi-equilibrium conditions are impossible.Another advantage of kinetic measurements is that they provide information notonly on the equilibrium binding constant but also on the kinetic constants of binding(kads) and dissociation (kdes).

As is usual for each surface reaction, a process of ligand to receptor bindingincludes two kinetic steps: diffusion of ligand to the receptor and ligand–receptorbinding. Amodel used for analysis of kineticmeasurements is based on the followingassumptions: (i) the kinetic limiting step of the whole process is the binding and(ii) the binding can be described by the Langmuir isotherm. It is not a rare case whenassumption (i) is not valid. Its validation will be described below.

According to the formal kinetics, the detected adsorption rate dq=dt can bedescribed as an algebraic sum of the rates of adsorption and desorption:

dqdt¼ kadsð1�qÞcL�kdesq ð1:11Þ

1.3 Kinetic Measurements j7

or:

dqdt¼ �q kSþ kadscL ð1:12Þ

and:

dSdt¼ �SkSþ kadscL ð1:13Þ

where:

kS ¼ kadscLþ kdes ð1:14ÞThe solution of the differential equation (1.12) is:

qðtÞ ¼ ½1�exp ð�kStÞ� qeq ð1:15Þ

where qeq is the surface coverage in equilibrium and can, therefore, be found fromEq. (1.2).

The desorption kinetics observed after replacement of the ligand solution by thesolution without ligand can be obtained from the equation:

dqdt¼ �kdesq ð1:16Þ

The solution with the corresponding starting condition is:

qðtÞ ¼ qeqexp ð�kdestÞ ð1:17Þ

It follows fromEq. (1.12) that kS is an apparent kinetic constant of adsorption. Thisvalue can be obtained from experimental data. It is paradoxical that the desorptionconstant is one of the components contributing to the adsorption constant inEq. (1.14).

The dependence of kS on ligand concentration allows one to obtain values of kadsand kdes. The value kS can be obtained by exponential fitting of adsorption kineticswith Eq. (1.15). Instead of nonlinear fitting, the dependence of dS=dt versus S can beanalyzed: a linearity of this dependence verifies the exponential character of thesignal kinetics while its slope gives kS (Figure 1.4). The desorption rate constant kdescan also be extracted from fitting of desorption kinetics with Eq. (1.17). This providesa principal way of obtaining kinetic constants of adsorption and desorption and ofestimating the binding constant from single experiment. However, desorptionkinetics for many receptors are very slow, and kads cannot be measured directly. Inaddition, more reliable data can be obtained by repetition of the measurements atdifferent concentrations and by analysis of the concentration dependence of kSaccording to Eq. (1.14). Values of kads and kdes obtained from kinetic measurementscan be used to calculate the binding constant (K) [Eq. (1.3)]. A deviation of thedependence of kS versus ligand concentration from a linear dependencemay indicatethat the process is not limited by the binding step. The quality of this analysis dependsstrongly on the signal/noise ratio.

8j 1 Quantitative Characterization of Affinity Properties of Immobilized Receptors

As mentioned above, it is not a rare case that the binding process is limited bydiffusion. It is more typical for receptor layers with a three-dimensional matrix.Ignoring this fact and a mechanistic application of the analysis based on theLangmuir model to the diffusion limited processes leads to large errors in thedetermination of kads and kdes and may lead to considerable errors in bindingconstants. Therefore it is important to formulate simple criteria to distinguishdiffusion and reaction control of the binding process. A deviation of the bindingkinetics from mono-exponential dependence is a sign of diffusion limitation;however, it is difficult to provide a reasonable quantitative criterion for this deviation.Moreover, diffusion limited processes can also display a mono-exponential kinetics.

For diffusion controlled processes an adsorption rate depends on the solutionviscosity. The viscosity can be modified by addition of sugar, glycerol, or othercompounds. The influence of viscosity on binding kinetics should be independentof the chemical nature of the viscosity modifier – a criterion that excludes a chemicalinfluence of the viscosity modifier on the binding process.

Another approach to distinguish diffusion and reaction kinetics is based onvariation of thickness of the diffusion boundary layer. It can be performed in devicesthat are similar to the rotating electrodeswidely used in electrochemical experiments.In the case of a reaction limited process, no influence of the rotation rate is expected.For a diffusion limited process, the observed adsorption rate should be increasedwith increasing rotation rate. The thickness of the hydrodynamic equivalent of thediffusion boundary layer (d) depends linearly on the square root of reciprocal rotationrate [25]:

d ¼ 1:61 �D13 g16 v�12 ð1:18Þwhere

D is the diffusion coefficient,g is the solvent viscosity,v is the circular frequency of the electrode rotation.

The diffusion flux is proportional to the reciprocal value of thickness of thediffusion boundary layer. Therefore, for a diffusion controlled process one can expecta linear dependence between the adsorption rate and the square root of the rotationrate. In flow-through cells this approach can be realized by variation of the flow rate.

Figure 1.4 Extraction of kinetic constants of adsorption and desorption.

1.3 Kinetic Measurements j9

In cells without through-flow some variation of the thickness of diffusion layer canbe obtained bymodification of stirring intensity. An application of a rotating receptorsurface in immunoassay has been described [26]. Identification of the limitingkinetic step based on modification of viscosity and on investigation of the depen-dence of binding kinetics on rotation rate of disk electrode has been employed [27];however, such analysis is time consuming and too difficult for routine applications.A simpler test is an investigation of the influence of flow rate on binding kinetics;a quantitative analysis and experimental validation of this approach has beendescribed [28–31].

1.4Analysis of Temperature Dependencies

Affinity properties can be further characterized by investigation of the temperaturedependencies.

Spontaneous adsorption means that the free energy of the process is negative.Adsorption leads to a decrease in freedom. Taking into account that DH¼DG þTDS, thismeans that the enthalpy of adsorption is also negative. Therefore, a bindingof a ligand with a receptor leads to heat production. The entropy production can bedetermined quantitatively by investigation of the temperature dependence of thebinding constant. Substitution of DG¼DH�TDS in Eq. (1.10) leads to the vantHoff relationship, which allows one to obtain the molar enthalpy of the bindingreaction from the temperature dependence of the binding constant:

lnK ¼ 1R

DS0�DH0

T

� �ð1:19Þ

Therefore, a slope of the dependence of the logarithm of the equilibrium constantas a function of reciprocal temperature gives the value of standard reaction enthalpywhile extrapolation to zero value of the reciprocal temperature gives the value ofreaction entropy. A deviation of this dependence was explained by a contribution ofa temperature-dependent heat capacity [32]. Assuming a constant difference in heatcapacity between free and associated ligand and receptor (DCp) in the temperaturerange between the temperature of the standard state T0 (usually 25 �C) and thecurrent temperature T, one can rewrite Eq. (1.19) more exactly:

lnK ¼ 1R

DS0�DH0

TþDCp T�T0T �ln

TT0

� �� �ð1:20Þ

This provides, in principle, the possibility of determining not only the bindingenthalpy and binding entropy but also DCp. However, a numerical simulationdemonstrated that the fitting of experimental data is not very sensitive to thisparameter, and typical values of experimental errors makes quantitative determina-tion of DCp very uncertain [33].

10j 1 Quantitative Characterization of Affinity Properties of Immobilized Receptors

An investigation of temperature dependencies of the kinetic constants of binding(kads) and dissociation (kdes) allows us to obtain activation energies for binding anddissociation, Ea,ads and Ea,des, respectively:

kads � exp ð�Ea;ads=RTÞ; kdes � exp ð�Ea;des=RTÞ ð1:21ÞThe difference between Ea,ads and Ea,des can be interpreted as themolar enthalpy of

the binding reaction (Figure 1.5):

Ea;ads�Ea;des � DH0 ð1:22ÞThe transition state theory developed by Eyring and coauthors [34] provides the

principal means of making a more detailed analysis of the reaction profile and toseparate the contributions of enthalpy and entropy in the activation process. Thistheory gives the following equation for the kinetic constant of binding:

kads ¼ kkBTh exp ð�DH¨0ads =RTÞexp ð�DS¨0ads=RÞ ð1:23Þ

where

the superscript # indicates that the corresponding thermodynamic potentialrefers to an activation process,kB is the Boltzmann constant,h is the Plank constant,k is a transmission factor, which is considered to be between 0.5 and 1.

Linearization in coordinates ln(k/T) versus 1/T (Eyring plots) can be used to extractvalues of standard activation enthalpies and entropies; however, a determination ofentropy requires an assumption on the value of k (usually, as k¼ 1).

The risk of misinterpretation of temperature dependencies of equilibrium andkinetic data is very high. Critical analysis of many aspects of this analysis has beenperformed [33, 35].

Figure 1.5 Activation energies for binding and dissociation (Ea,ads and Ea,des, respectively) allowsus to calculate the molar enthalpy of the binding reaction.

1.4 Analysis of Temperature Dependencies j11

1.5Experimental Techniques

While affinity analysis in the bulk phase can be performedby any analytical techniqueproviding measurements of concentration of free or occupied ligand or receptormolecules, affinity analysis of immobilized receptors requires special methods thatprovide measurements of surface concentrations. Figure 1.6 gives a short review ofthe main label-free techniques.

An application of an impedometric approach to study adsorption phenomenacame into analytical chemistry from classical electrochemistry. This approach is alsoknown as capacitive detection because, usually, an imaginary component of imped-ance is used. Obviously, this approach can be applied only for conducting surfaces.In ideal case, the interface should display pure capacitive properties, that is, shouldblock any charge transfer.

The specific electrical capacitance (C) of an interface coated by some dielectriclayer with relative dielectric constant e and thickness d is:

C ¼ ee0d

ð1:24Þ

where e0 is the dielectric constant of a vacuum. There are twoways to apply capacitivebinding detection: to detect changes of either the layer thickness or dielectricconstant. The first approach has been used, for example, in spreader-bar systems(the spreader-bar technique is described in Chapter 10) [36, 37]: binding of ligands toreceptors leads to an increase of the thickness of the dielectric layer. The secondapproach has been applied formolecularly imprinted polymers (Chapter 13) [38, 39]:

experimental techniques

electrical(electrochemical)

mechano-acoustical optical

capacitive (impedometric)

sensors

quartz crystal microbalance (QMB)

devices based on surface acoustic waves

(SAW)

microcantilevers

refractometers based on surface plasmon resonance

ellipsometers

devices based on ring resonators

devices based on optical fibers

devices based on photonic crystals

Figure 1.6 Main experimental techniques used for investigation of affinity properties ofimmobilized receptors.

12j 1 Quantitative Characterization of Affinity Properties of Immobilized Receptors