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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
A timely, accessible survey of the multidisciplinary field of bioanalytical chemistry
- Provides an all in one approach for both beginners and experts, from a broad range of backgrounds, covering introductions, theory, advanced concepts and diverse applications for each method
- Each chapter progresses from basic concepts to applications involving real samples
- Includes three new chapters on Biomimetic Materials, Lab-on-Chip, and Analytical Methods
- Contains end-of-chapter problems and an appendix with selected answers
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Veröffentlichungsjahr: 2016
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Contents
Cover
Title Page
Copyright
Preface to Second Edition
Preface to First Edition
Acknowledgments
1: Quantitative Instrumental Measurements
1.1 Introduction
1.2 Optical Measurements
1.3 Electrochemical Measurements
1.4 Radiochemical Measurements
1.5 Surface Plasmon Resonance
1.6 Calorimetry
1.7 Automation: Microplates, Multiwell Liquid Dispensers and Microplate Readers
1.8 Calibration of Instrumental Measurements
1.9 Quantitative and Semi-Quantitative Measurements
Suggested Reading
Problems
2: Spectroscopic Methods for the Quantitation of Classes of Biomolecules
2.1 Introduction
2.2 Total Protein
2.3 Total DNA
2.4 Total RNA
2.5 Total Carbohydrate
2.6 Free Fatty Acids
References
Problems
3: Enzymes
3.1 Introduction
3.2 Enzyme Nomenclature
3.3 Enzyme Commission Numbers
3.4 Enzymes in Bioanalytical Chemistry
3.5 Enzyme Kinetics
3.6 Enzyme Activators
3.7 Enzyme Inhibitors
3.8 Enzyme Units and Concentrations
Suggested Reading
References
Problems
4: Quantitation of Enzymes and Their Substrates
4.1 Introduction
4.2 Substrate Depletion or Product Accumulation
4.3 Direct and Coupled Measurements
4.4 Classification of Methods
4.5 Instrumental Methods
4.6 High-Throughput Assays for Enzymes and Inhibitors
4.7. Assays for Enzymatic Reporter Gene Products27-30
4.8 Practical Considerations for Enzymatic Assays
Suggested Reading
References
Problems
5: Immobilized Enzymes
5.1 Introduction
5.2 Immobilization Methods
5.3 Properties of Immobilized Enzymes
5.4 Immobilized Enzyme Reactors
5.5 Theoretical Treatment of Packed-Bed Enzyme Reactors34-37
Suggested Reading
References
Problems
6: Antibodies
6.1 Introduction
6.2 Structural and Functional Properties of Antibodies
6.3 Polyclonal and Monoclonal Antibodies
6.4 Antibody-Antigen Interactions
6.5 Analytical Applications of Secondary Antibody-Antigen Interactions
Suggested Reading
References
Problems
7: Quantitative Immunoassays with Labels
7.1 Introduction
7.2 Labeling Reactions
7.3 Heterogeneous Immunoassays
7.4 Homogeneous Immunoassays
7.5 Evaluation of New Immunoassay Methods33,34
Suggested Reading
References
Problems
8: Biosensors
8.1 Introduction
8.2 Biosensor Diversity and Classification
8.3 Recognition Agents
8.4 Response of Enzyme-Based Biosensors5
8.5 Examples of Biosensor Configurations
8.6 Evaluation of Biosensor Perfomance
8.7 In VIVO Applications of Biosensors
Suggested Reading
References
Problems
9: Directed Evolution for the Design of Macromolecular Reagents
9.1 Introduction
9.2 Rational Design and Directed Evolution
9.3 Generation of Genetic Diversity
9.4 Linking Genotype and Phenotype
9.5 Identification and Selection of Successful Variants
9.6 Examples of Directed Evolution Experiments
Suggested Reading
References
Problems
10: Image-Based Bioanalysis
10.1 Introduction
10.2 Magnification and Resolution
10.3 Optical Microscopy
10.4 Electron Microscopy
10.5 Scanning Tunneling Microscopy
10.6 Atomic Force Microscopy (AFM)
10.7 Scanning Electrochemical Microscopy (SECM)
Suggested Reading
References
Problems
11: Principles of Electrophoresis
11.1 Introduction
11.2 Electrophoretic Support Media
11.3 Effect Of Experimental Conditions Onelectrophoretic Separations
11.4 Electric Field Strength Gradients
11.5 Pulsed Field Gel Electrophoresis (PFGE)
11.6 Detection of Proteins and Nucleic Acids After Electrophoretic Separation
Suggested Reading
References
Problems
12: Applications of Zone Electrophoresis
12.1 Introduction
12.2 Determination of Protein Net Charge and Molecular Weight Using Page1
12.3 Determination of Protein Subunit Composition and Subunit Molecular Weights2
12.4 Molecular Weight of DNA By Agarose Gel Electrophoresis5
12.5 Identification of Isoenzymes
12.6 Diagnosis of Genetic (Inherited) Disorders
12.7 DNA Fingerprinting and Restriction Fragment Length Polymorphism10
12.8 DNA Sequencing With the Maxam-Gilbert Method14
12.9 Immunoelectrophoresis16
Suggested Reading
References
Problems
13: Isoelectric Focusing and 2D Electrophoresis
13.1 Introduction
13.2 Carrier Ampholytes
13.3 Modern IEF With Carrier Ampholytes
13.4 Immobilized pH Gradients (IPGs)9
13.5 Two-Dimensional Electrophoresis12
13.6 Difference Gel Electrophoresis (DIGE)
Suggested Reading
References
Problems
14: Capillary Electrophoresis
14.1 Introduction
14.2 Electroosmosis
14.3 Elution of Sample Components
14.4 Sample Introduction2
14.5 Detectors for Capillary Electrophoresis
14.6 Capillary Polyacrylamide Gel Electrophoresis (C-PAGE)12
14.7 Capillary Isoelectric Focusing (CIEF)14
Suggested Reading
References
Problems
15: Centrifugation Methods
15.1 Introduction
15.2 Sedimentation and Relative Centrifugal g Force
15.3 Centrifugal Forces in Different Rotor Types
15.4 Clearing Factor (k)
15.5 Density Gradients
15.6 Types of Centrifugation Techniques
15.7 Harvesting Samples
15.8 Analytical Ultracentrifugation
15.9 Selected Examples
Suggested Reading
References
Problems
16: Chromatography of Biomolecules
16.1 Introduction
16.2 Units and Definitions
16.3 Plate Theory of Chromatography1
16.4 Rate Theory of Chromatography2
16.5 Size Exclusion (Gel Filtration) Chromatography
16.6 Stationary Phases for Size Exclusion Chromatography
16.7 Affinity Chromatography
16.8 Ion-Exchange Chromatography
Suggested Reading
References
Problems
17: Mass Spectrometry of Biomolecules
17.1 Introduction
17.2 Basic Description of the Instrumentation
17.3 Interpretation of Mass Spectra
17.4 Biomolecule Molecular Weight Determination
17.5 Protein Identification
17.6 Protein-Peptide Sequencing
17.7 Nucleic Acid Applications
17.8 Bacterial Mass Spectrometry
17.9 Mass Spectrometry Imaging
Suggested Reading
References
Problems
18: Micro-TAS, Lab-on-a-Chip, and Microarray Devices
18.1 Introduction
18.2 Device Fabrication Materials and Methods
18.3 Microfluidics
18.4 Detectors
18.5 Examples of Bioanalytical Devices
Suggested Reading
References
Problems
19: Validation of New Bioanalytical Methods
19.1 Introduction
19.2 Precision and Accuracy
19.3 Mean and Variance
19.4 Relative Standard Deviation and Other Precision Estimators
19.5 Estimation of Accuracy
19.6 Qualitative (Screening) Assays
19.7 Examples of Validation Procedures
Suggested Reading
References
Answers to Selected Problems
Index
End User License Agreement
List of Tables
Table 2.1
Table 3.1
Table 3.2
Table 3.3
Table 3.4
Table 4.1
Table 5.1
Table 5.2
Table 6.1
Table 6.2
Table 7.1
Table 7.2
Table 8.1
Table 8.2
Table 9.1
Table 9.2
Table 9.3
Table 11.1
Table 11.2
Table 12.1
Table 12.2
Table 12.3
Table 12.4
Table 13.1
Table 13.2
Table 14.1
Table 14.2
Table 14.3
Table 15.1
Table 15.2
Table 16.1
Table 16.2
Table 16.3
Table 16.4
Table 16.5
Table 16.6
Table 16.7
Table 16.8
Table 17.1
Table 17.2
Table 17.3
Table 17.4
Table 17.5
Table 17.6
Table 17.7
Table 17.8
Table 17.9
Table 17.10
Table 19.1
Table 19.2
Table 19.3
Table 19.4
Table 19.5
Table 19.6
List of Illustrations
Figure 1.1
Figure 1.2
Figure 1.3
Figure 2.1
Figure 2.2
Figure 2.3
Figure 2.4
Figure 2.5
Figure 2.6
Figure 2.7
Figure 2.8
Figure 2.9
Figure 3.1
Figure 3.2
Figure 3.3
Figure 3.4
Figure 3.5
Figure 3.6
Figure 3.7
Figure 3.8
Figure 3.9
Figure 3.10
Figure 3.11
Figure 3.12
Figure 3.13
Figure 3.14
Figure 3.15
Figure 4.1
Figure 4.2
Figure 4.3
Figure 4.4
Figure 4.5
Figure 4.6
Figure 5.1
Figure 5.2
Figure 5.3
Figure 5.4
Figure 5.5
Figure 5.6
Figure 5.7
Figure 5.8
Figure 5.9
Figure 5.10
Figure 5.11
Figure 5.12
Figure 5.13
Figure 5.14
Figure 6.1
Figure 6.2
Figure 6.3
Figure 6.4
Figure 6.5
Figure 6.6
Figure 6.7
Figure 6.8
Figure 6.9
Figure 7.1
Figure 7.2
Figure 7.3
Figure 7.4
Figure 7.5
Figure 7.6
Figure 7.7
Figure 7.8
Figure 7.9
Figure 7.10
Figure 7.11
Figure 7.12
Figure 7.13
Figure 7.14
Figure 7.15
Figure 8.1
Figure 8.2
Figure 8.3
Figure 8.4
Figure 8.5
Figure 8.6
Figure 8.7
Figure 8.8
Figure 8.9
Figure 8.10
Figure 8.11
Figure 8.12
Figure 8.13
Figure 8.14
Figure 8.15
Figure 8.16
Figure 8.17
Figure 8.18
Figure 8.19
Figure 8.20
Figure 8.21
Figure 8.22
Figure 8.23
Figure 8.24
Figure 8.25
Figure 8.26
Figure 9.1
Figure 9.2
Figure 9.3
Figure 9.4
Figure 9.5
Figure 9.6
Figure 9.7
Figure 9.8
Figure 9.9
Figure 10.1
Figure 10.2
Figure 10.3
Figure 10.4
Figure 11.1
Figure 11.2
Figure 11.3
Figure 11.4
Figure 11.5
Figure 11.6
Figure 11.7
Figure 11.8
Figure 11.9
Figure 11.10
Figure 11.11
Figure 11.12
Figure 11.13
Figure 11.14
Figure 11.15
Figure 11.16
Figure 11.17
Figure 11.18
Figure 11.19
Figure 12.1
Figure 12.2
Figure 12.3
Figure 12.4
Figure 12.5
Figure 12.6
Figure 12.7
Figure 12.8
Figure 12.9
Figure 12.10
Figure 12.11
Figure 12.12
Figure 12.13
Figure 12.14
Figure 12.15
Figure 13.1
Figure 13.2
Figure 13.3
Figure 13.4
Figure 13.5
Figure 13.6
Figure 13.7
Figure 13.8
Figure 13.9
Figure 13.10
Figure 13.11
Figure 13.12
Figure 13.13
Figure 14.1
Figure 14.2
Figure 14.3
Figure 14.4
Figure 14.5
Figure 14.6
Figure 14.7
Figure 14.8
Figure 14.9
Figure 14.10
Figure 14.11
Figure 14.12
Figure 14.13
Figure 14.14
Figure 15.1
Figure 15.2
Figure 15.3
Figure 15.4
Figure 15.5
Figure 15.6
Figure 15.7
Figure 15.8
Figure 15.9
Figure 15.10
Figure 15.11
Figure 15.12
Figure 15.13
Figure 16.1
Figure 16.2
Figure 16.3
Figure 16.4
Figure 16.5
Figure 16.6
Figure 16.7
Figure 16.8
Figure 16.9
Figure 16.10
Figure 16.11
Figure 16.12
Figure 17.1
Figure 17.2
Figure 17.3
Figure 17.4
Figure 17.5
Figure 17.6
Figure 17.7
Figure 17.8
Figure 17.9
Figure 17.10
Figure 17.11
Figure 17.12
Figure 17.13
Figure 17.14
Figure 17.15
Figure 17.16
Figure 17.17
Figure 17.18
Figure 18.1
Figure 18.2
Figure 18.3
Figure 18.4
Figure 18.5
Figure 19.1
Figure 19.2
Figure 19.3
Figure 19.4
Figure 19.5
Figure 19.6
Figure 19.7
Figure 19.8
Figure 19.9
Guide
Cover
Table of Contents
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Chapter 1
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Bioanalytical Chemistry
Second Edition
Susan R. Mikkelsen
Eduardo Cortón
Copyright © 2016 by John Wiley & Sons, Inc. All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey.
Published simultaneously in Canada.
No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission.
Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.
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Library of Congress Cataloging-in-Publication Data:
Names: Mikkelsen, Susan R., 1960- | Cortón, Eduardo, 1962-Title: Bioanalytical chemistry / Susan R. Mikkelsen, Eduardo Cortón.
Description: Second edition. | Hoboken, New Jersey : John Wiley & Sons, Inc., [2016] | Includes index.
Identifiers: LCCN 2015041460 (print) | LCCN 2015043820 (ebook) | ISBN 9781118302545 (cloth) | ISBN 9781119057703 (pdf) | ISBN 9781119057635 (epub)
Subjects: LCSH: Analytical biochemistry. | Chemistry, Analytic.
Classification: LCC QP519.7 .M54 2016 (print) | LCC QP519.7 (ebook) | DDC 612/.01585–dc23
LC record available at http://lccn.loc.gov/2015041460
Preface to Second Edition
The success of our first edition, with reader feedback, has encouraged us to produce an expanded and updated second edition of Bioanalytical Chemistry. Over the past decade, we have both read, in the primary literature, about enormous advances in certain areas, including imaging and microfluidic devices. It had also been suggested that an introductory chapter involving instrumental measurement principles and methods would be helpful to readers. New chapters were warranted, and we have included these in our second edition.
Traditional areas of bioanalytical chemistry, such as electrophoresis, chromatography and immunoassay, have also seen surprising and significant developments. An enormous development in 2D electrophoresis, involving the simultaneous separation of two or more cell lysates on a single gel, has provided a quantum leap for proteomic studies. Nanoparticles, quantum dots and new polymers have seen many applications to biomolecule separation and quantitation. We have attempted to provide an introduction, as well as leading references, to these areas in our second edition.
The Argentine-Canadian collaboration of the authors began in the mid-1990s as a result of mutual interests in bioanalytical chemistry research and teaching. Over the years, despite the advantages of modern telecommunications technology, we have found that travel is both necessary and beneficial, especially when the final stages of manuscript preparation are underway. With the north-south travel, we have found that the climate is always pleasant somewhere.
Susan R. MikkelsenEduardo CortónBuenos Aires, ArgentinaAugust 2015
Preface to First Edition
The expanding role of bioanalytical chemistry in academic and industrial environments has made it important for students in chemistry and biochemistry to be introduced to this field during their undergraduate training. Upon introducing a bioanalytical chemistry course in 1990, I found that there was no suitable textbook that incorporated the diverse methods and applications in the depth appropriate to an advanced undergraduate course. Many specialized books and monographs exists that cover one or two topics in detail, and some of these are suggested at the end of each chapter as sources of further information.
This book is intended for use as a textbook by advanced undergraduate chemistry and biochemistry students, as well as bioanalytical chemistry graduate students. These students will have completed standard introductory analytical chemistry and biochemistry courses, as well as instrumental analysis. We have assumed familiarity with basic spectroscopic, electrochemical and chromatographic methods, as they apply to chemical analysis.
The subject material in each chapter has generally been organized as a progression from basic concepts to applications involving real samples. Mathematical descriptions and derivations have been limited to those that are believed essential for an understanding of each method, and are not intended to be comprehensive reviews. Problems given at the end of each chapter are included to allow students to assess their understanding of each topic; most of these problems have been used as examination questions by the authors.
As research in industrial, government and academic laboratories moves toward increasingly interdisciplinary programs, the authors hope that this book will be used to facilitate, and to prepare students for, collaborative scientific work.
Susan R. MikkelsenEduardo CortónWaterloo, CanadaJuly 2003
Acknowledgments
The support of our colleagues at the University of Waterloo and Universidad de Buenos Aires, during the preparation of this book, is gratefully acknowledged.
We also acknowledge the patience and support of our families and friends, who understood the time commitments that were needed for the completion of this project.
Susan R. MikkelsenEduardo CortónBuenos Aires, Argentina, andWaterloo, Canada
Chapter 1Quantitative Instrumental Measurements
1.1 Introduction
This chapter introduces the basic principles underlying many common methods of signal transduction. This term is used to describe the conversion of one type of energy to another. Generally, analytical specialists use the term transducer to describe the conversion of a concentration (or mass) into a useful electronic signal, which is ultimately almost always a voltage. This voltage is related to the concentration (or mass) of the analyte, or species of interest, in the original sample. The species that can be measured by one or more of these methods is not always the analyte itself; for example, if the analyte is an enzyme or other catalytic species, the depletion of reactants or accumulation of products is assessed based on their own unique properties.
Transduction can be accomplished in many different ways, and the choice of the best method depends on which of many possible physical properties are exhibited by the measured species. In this chapter, we consider the three main types of transduction that are widely used in instrumental methods in bioanalytical chemistry. The conversion of light into current is performed by photodiodes or photomultipliers, and this current is then electronically converted into a voltage that is proportional to the intensity of the light. Electrochemical and surface plasmon resonance transducers convert chemical energy into a measured voltage or into a current that is subsequently converted to a voltage. Scintillation counters, used in many radiochemical methods, first convert beta-particle radioactivity to light, and the light is detected using photodiodes or photomultipliers. Thermal transducers, used for calorimetry, convert heat into current (and then voltage).
Considerations for the choice of a transduction method include the uniqueness of the various measurable properties of the measured species, since it is often present in a complicated sample matrix. The matrix is the surrounding environment, and includes all other components present in the sample. Matrix components can interfere with measurements in direct or indirect ways: a matrix component may exhibit a similar physical property to the analyte, and interfere with analyte measurement; also, a matrix component may interact with the analyte, changing the nature of its physical property and/or the magnitude of its resulting signal.
This chapter is intended as an introduction and brief review of common transduction methods used in bioanalytical chemistry. More detailed descriptions of applications and instrumental variations will be found within specific chapters of this book, where more specialized adaptations are described for specific assay methods.
The reader is referred to two excellent analytical chemistry textbooks for greater depth of coverage of most of the basic descriptions given in this chapter, as well as two excellent review articles for more information on thermal measurement methods, listed at the end of the chapter.
1.2 Optical Measurements
The majority of quantitative optical methods make use of light that is either absorbed or emitted in the ultraviolet and visible regions of the electromagnetic spectrum. These regions formally correspond to wavelengths of 1.0 × 10-8 to 7.8 × 10-7 m, and are more commonly expressed in nm units (10 to 780 nm). The far UV region, also called the vacuum UV region, is generally not analytically useful, but the near UV and the visible regions are widely used.
The colours that surround us result mainly from wavelength-selective visible light absorption by molecules present in the items that we see. However, differences between species, and between individuals within a species, cause the wavelength range of visible light, and the colours within this range, to be perceived differently. Common examples are bumblebees, that have blue-shifted visible ranges, and hummingbirds, that have red-shifted ranges. For this reason, standard wavelength ranges have been defined for the different colours of the visible spectrum. For example, blue light is defined as the 440–470 nm range, and if blue light is absorbed, its complementary colour, orange, is observed. Similarly, if green light (500–520 nm) is absorbed, purple is the observed colour. Many compounds absorb light at multiple wavelengths, and it is the combination of complementary colours that we observe.
The relationship between wavelength, frequency and energy of light is shown below:
where E is the energy of the light, h is Planck's constant (6.626 × 10−34 J·s), υ is the frequency of the light (s−1), λ is the wavelength of the light (m), and c is the speed of light (2.998 × 108 m/s in a vacuum, and this number is divided by the refractive index n for any other medium). This relationship connects the two key concepts that light is both a particle (a photon with energy E) and a wave, with frequency υ and wavelength λ.
In the visible and near UV regions of the spectrum, molecules absorb and emit light as their electronic configurations change. For example, electrons convert between paired and unpaired states, or between bonding and non-/antibonding orbitals. These conversions are accompanied by energy gains or losses as the molecule absorbs or emits a photon. Depending on molecular structure, as well as many other factors including solvent, pH and temperature, fixed electronic energy levels exist, and only photons of particular energies (wavelengths) can be absorbed or emitted. Associated with each electronic energy level are vibrational and rotational energy levels, which are separated by much smaller energy differences. Isolated vibrational or rotational transitions can be made to occur using infrared or microwave radiation, which have much lower energy. But the electronic transitions that occur in the UV-visible region are accompanied by vibrational and rotational transitions, and this means that a range of wavelengths can be absorbed by molecules, shown in Eq. 1.2:
where, for a given electronic transition, the total energy ΔET of the photons absorbed is the sum of the energy required for the electronic transition itself, ΔEElec, which is fixed, plus the energy changes associated with multiple possible vibrational and rotational transitions, ΔEVib and ΔERot. This means that, for any given electronic transition, molecules absorb or emit a fairly wide range of wavelengths, centered on a wavelength of maximal absorption or emission. For molecules absorbing or emitting light in the near UV and visible regions, the range of wavelengths can be as large as 100 nm for a given electronic transition, because of these accompanying vibrational and rotational transitions.
1.2.1 UV-Visible Absorbance
A simple spectrophotometer, an instrument for measuring absorbance, consists of a light source, a monochromator (or filter), a sample compartment and a light detector, all of which are enclosed to prevent interference from ambient light. These components are shown as a block diagram in Figure 1.1. Typically, the light source is a tungsten filament lamp (for the visible region) and/or a deuterium lamp (for the UV region); both of these sources emit continuous radiation over a wide range of wavelengths. Wavelength selection can be accomplished using filters, for repetitive fixed-wavelength measurements, or a monochromator containing a diffraction grating or prism, that allows adjustment of wavelength as well as wavelength scanning. The quality of the filter or monochromator determines the width of the wavelength range in the light beam that exits the device and is directed into the sample. Analyte solutions are contained in a cuvette (or cell) made of a material that is transparent to the wavelength(s) of interest, such as quartz, glass or polystyrene. Light detection may be accomplished using a photomultiplier tube, a photodiode, or a photodiode array (in which the spatial distribution of light of different wavelengths allows nearly instantaneous acquisition of a complete spectrum).
Figure 1.1 Block diagram of a simple UV-Vis absorption spectrophotometer.
Many variations of this simple design have been introduced for specialized applications. For example, dedicated instruments may employ an inexpensive light-emitting diode as the light source, a combination of absorption and interference filters for wavelength selection, or a flow cell in which a solution continuously flows past the light beam. In all cases, the instruments are designed to measure the absorption of light by an analyte.
The intensity, or power, of the incident monochromatic beam of light is given the symbol PO, and the light intensity that exits the sample compartment has the symbol P. Commonly, PO is measured using a reagent blank solution, i.e. a solution containing all of the components of the sample solution except the analyte. Transmittance, T, is the ratio of these values (P/PO), and may be expressed as this simple ratio, with a value between zero and one, or as a percentage that ranges from zero to one hundred.
As the concentration of the analyte in the sample cell is increased, the transmittance decreases, but the dependence of transmittance on concentration is not linear. For quantitative purposes, transmittance values are converted to absorbance (A) values as follows:
Absorbance increases linearly as analyte concentration is increased. It also increases linearly with the distance through which the light beam travels in the sample; this is called the path length and is given the symbol b. The Beer-Lambert Law (Eq. 1.4), also called Beer's Law, is the most important relationship in quantitative spectrophotometry.
In this relationship, absorbance A depends linearly on analyte concentration c with two proportionality constants: b, the path length, and ɛ, the molar absorptivity of the analyte. Absorbance is unitless, and so the units of ɛ are generally M-1cm-1, when analyte concentration is in molar units and path length is expressed in cm.
Absorbance is additive. If there is more than one absorbing species present in a solution, the total absorbance at a given wavelength is the sum of the absorbances of the individual species at that wavelength. This property is analytically useful for the quantitation of multiple absorbing species, if the molar absorptivities are known at multiple wavelengths. The concentrations of two components, for example, can be determined by measuring absorbances at two wavelengths, at which the molar absorptivities of the two components are known.
Absorbance spectra, plots of absorbance against wavelength, are used to determine the best wavelengths for analyte quantitation. A maximum, or peak, in this plot indicates the wavelength at which ɛ has its highest value, and at this wavelength, the slope of the calibration curve of A vs. c (the sensitivity) will be maximal. There may be several peaks in an absorption spectrum; the choice of the best wavelength to use for quantitation depends on both the molar absorptivities at the peaks and the likelihood of interfering species absorbing light at the chosen wavelength.
Most bioanalytical methods focus on analytes that are present in aqueous solutions, and most of these analytes have charge states that are pH dependent. Absorption spectra can change quite dramatically as pH is varied, because the electronic energy levels change with the protonation state of the molecule. Molecules containing carboxylic acid and amine groups, for example, exhibit pH-dependent absorption spectra. Some of the most dramatic examples of this effect are found in small molecules that are used as visible indicators in pH titrations. Control of the pH of the analyte and standard solutions is thus critical.
Molar absorptivity also depends on temperature, ionic strength and solvent. Its value, if needed, is commonly determined from the slope of a plot of absorbance against concentration, using a calibrated cuvette with a known path length.
1.2.2 Turbidimetry (Light-Scattering)
These methods employ the same instruments used for absorbance spectrophotometry. They are applied to turbid solutions, meaning that the solutions appear cloudy due to suspensions of particulate matter. The particles can be cells or precipitates formed by reactions. An apparent absorbance value is measured, for which the scattering, rather than the absorption of light is the cause. Often the term “optical density” is used rather than absorbance. Light scattering tends to increase as the wavelength decreases toward the UV region of the spectrum, but absorbance, rather than scattering, also increases at lower wavelengths. Turbidity is typically measured at a wavelength near 540 nm, where absorbance is rare. Optical density depends on particle size, and, for a constant particle size and low concentrations, is linearly related to particle concentration.
Cells in suspension are often quantitated by turbidimetry. Calibration is required for each species, by correlation with plate counts, or colony-forming units. A second area of wide application involves latex particles that are surface-modified to react with a soluble analyte. This causes clumping of the particles, or a growth in average particle size, allowing the quantitation of the soluble analyte by turbidimetry. These latex agglutination tests are discussed in more detail in Chapter 6.
1.2.3 Fluorescence
The instruments used for fluorescence spectroscopy are more complicated than those used for absorbance measurements. They use a very high-intensity light source, such as a xenon arc lamp, and they require two monochromators, as shown in Figure 1.2. Incident monochromatic radiation is used to excite the analyte, i.e. to change its energy from the ground to an excited electronic state. This incident light is directional, meaning that a beam of light is directed through the sample. During the lifetime of the excited state, which is typically 0.01–100 μs, the molecule rotates and can lose vibrational and rotational energy through radiationless deactivation. Emission of a photon then allows the molecule to return to the ground electronic state. Emitted photons are generally of lower energy (longer wavelength) because of radiationless deactivation. The difference between the excitation and the emission wavelengths is called the Stokes shift. For instruments that are used only for fluorimetry, P is not measured, and this light is simply absorbed by the flat black internal walls of the instrument housing. In some instruments, Po is measured as a reference signal (in case of fluctuations in lamp intensity) using a beam splitter and a reference light detector; with this configuration, the sample emission is related to Po, and this provides improved precision.
Figure 1.2 Block diagram of a simple spectrofluorimeter.
From a quantitative perspective, the finite lifetime of the excited state is very significant. Excited state molecules rotate randomly, and when photons are emitted by fluorescent molecules in solution, they are emitted in all directions. This means that emitted light can be collected at right angles to the incident excitation beam, and this is the common detection geometry for stand-alone fluorescence instruments. This collection geometry minimizes background light that reaches the detector. This geometry has important analytical implications: for fluorescent molecules, quantitation by fluorescence can be as much as 1000-fold more sensitive than quantitation by absorbance.
The appropriate fixed wavelengths for the two monochromators are chosen by sequentially scanning wavelengths with each device to obtain excitation and emission spectra. An excitation spectrum is obtained by monitoring the emission at a fixed wavelength, and scanning the excitation wavelengths; it is a plot of emission intensity against excitation wavelength. A maximum in the excitation spectrum indicates the appropriate fixed wavelength to use in order to obtain the emission spectrum. The emission spectrum is acquired by fixing the excitation wavelength and scanning the emission wavelength; it is a plot of emission intensity against emission wavelength. For a new analyte, an absorbance spectrum may be acquired initially, to aid in the selection of an appropriate excitation wavelength.
Once these wavelengths have been determined, the monochromators are fixed at these values, and a calibration is performed. At low concentrations of fluorescing species, fluorescence intensity is directly proportional to concentration. The proportionality constant (or the slope of the calibration curve) depends on many factors including molar absorptivity and quantum yield of the analyte, as well as a number of instrumental parameters that determine how much light is collected and how monochromatic it is when it is detected.
A molecule's quantum yield is the ratio of the number of molecules that emit a photon to the number of molecules that are in the excited state. The value lies between zero and one, with one representing the most fluorescence. Structurally rigid, aromatic molecules and functional groups (and some amino acid side chains) tend to exhibit strong fluorescence. Factors such as solvent, pH, dissolved oxygen concentration and temperature also affect fluorescence.
Self-absorption is a phenomenon that occurs when the concentration of the fluorescent species is high. Under these conditions, emitted light is absorbed by nearby fluorescent molecules that are not already in an excited state. Calibration curves that extend to high concentrations generally exhibit a linear region, at low concentration, followed by a maximum and then a continuous decrease in fluorescence intensity as concentration increases.
Quenching of fluorescence can occur when a different molecular species is able to absorb photons that are emitted by a fluorescent molecule. This concept has been used in a number of important bioanalytical methods and devices that are described in later chapters.
Specialized fluorescence measurement methods include time-resolved fluorescence and fluorescence polarization, and are largely employed when fluorescent labels are used in homogenous immunoassays. In these methods, the persistence of fluorescence with time, or the polarization of the light emitted after excitation by polarized light, is measured. For certain useful labels, these properties change significantly when the fluorescently-labelled molecule interacts with its binding partner.
1.2.4 Chemiluminescence and Bioluminescence
Excited-state molecules can be generated as products of chemical or biochemical reactions. When the excited-state reaction products return to their ground states, photons are emitted at characteristic wavelengths. A well-known example of bioluminescence involves the firefly: the enzyme luciferase generates an excited-state product, and when the product molecules emit photons, the fireflies glow in the dark.
The instrumentation needed for these measurements is very simple: a housing painted flat black on the inside, containing a sample compartment, light collection optics and a light detector such as a photomultiplier tube or photodiode. Filters and monochromators are possible, but are generally not needed for bioanalytical measurements.
The signal obtained from chemi- and bioluminescence measurements is fundamentally different from that obtained from fluorescence measurements. Instead of the continuous absorption and emission of photons, as occurs in fluorescence, photons are produced stoichiometrically, as products of the (bio)chemical reaction. For this reason, a limited number of photons are produced, and can be detected, with these methods, and when the reaction has proceeded to completion, no further photons will be produced.
Instruments used for these measurements generally allow the integration of the signal from the light detector. When signal integration is performed for a fixed time interval following the start of the reaction, these integrated signals are proportional to the reaction rate and thus to the concentrations of reactants.
1.3 Electrochemical Measurements
This family of measurement methods is based on reduction-oxidation (redox) reactions in which one or more electrons are stoichiometrically transferred from a reduced species to an oxidized species. These types of reactions are widespread in biological and biochemical systems, and are the basis of respiration in living organisms. Aerobic organisms, after a long series of enzyme-catalyzed redox reactions, ultimately transfer electrons to molecular oxygen, reducing it to water.
An overall, or net, electron transfer reaction can also be made to occur through an external circuit that separates two containers, each containing one of the two reactants. An electrode, made of an inert material such as platinum or carbon, is placed in each container, and if these two electrodes are connected with, e.g. a copper wire, electrons will flow from the container containing the reduced form to the one containing the oxidized reactant. The circuit is completed by a salt bridge that allows the movement of ions from the container with the oxidized reactant to that with the reduced reactant, to compensate for electron flow and maintain electroneutrality. Thus, electrons flow through the external circuit, while ions flow between the solutions. The transduction event, the conversion of ion current into electronic current, occurs at the surfaces of the two electrodes, where electrons are either accepted from or donated to the reacting species in the solutions.
In each of these two containers, a half-reaction (either an oxidation or a reduction) occurs. When the two reactions are balanced for the number of electrons transferred, and then summed, a net, or overall cell reaction is obtained. The standard reduction potential, Eo, and the formal reduction potential, Eo', of each of the two half reactions are thermodynamic properties that indicate the propensity of the reactant to either accept or donate electrons. The standard reduction potential value applies to unit activities of the reacting species, and is not widely used for biological systems. The formal reduction potential, however, is widely used, and values are based on specified conditions of pH, temperature and ionic strength. These values are widely available in tables.
For analytical purposes, we are generally interested in only one of the two half-reactions, but the second half-reaction is needed to complete the circuit to allow the measurement to occur. The second half-reaction can be made to occur under constant conditions in a reference half-cell, also called a reference electrode, that is contained in, typically, a small glass tube that is separated from the analyte solution by a porous glass frit, which acts as a salt bridge, allowing the movement of ions. Various geometric options exist for the manufacture of electrochemical cells, including screen-printing of both electrodes/half cells onto flat plastic, disposable substrate materials that are very useful for the measurement of blood glucose and lactate levels when a drop of blood is placed onto the surface, connecting the two electrodes via the mainly aqueous liquid.
The key equation for most electrochemical measurements is the Nernst Equation (Eq. 1.5), which, when constants are evaluated for 25 °C and collected into one term, simplifies to Eq. 1.6:
where R is the Rydberg constant, T is absolute temperature, F is Faraday's constant and n is the number of electrons involved in the reduction of the oxidized species, O, to the reduced form, R:
Strictly, activities, rather than concentrations, exist in the Nernst Equation; the activity coefficients are also collected into the Constant term of Eq. 1.6. In these expressions, E (on the left side) represents the net cell potential, in volts, and this is the driving force for the overall reaction. It is important to note that E is related to the logarithm of the concentration ratio.
Typically, in biochemical or organic chemical redox reactions, protons, as well as electrons are involved in half-reactions:
where m is the stoichiometric factor for protons in the reaction, and often, m has the same value as n. Because of this pH dependence, and because standard conditions involve unit activity of reactants (i.e. 1 M acid, or a pH of zero), formal reduction potentials, Eo', are used, and are determined by measurements made when [O] = [R], under specified conditions of pH, temperature and ionic strength. Buffers are used to maintain constant pH, and thus pH-related terms in the Nernst Equation are collected into the value of the Constant shown in Eq. 1.6.
For analytical purposes, it is generally unnecessary to know the exact values of Eo' or Eref, as long as they are constant, since calibration curves are generated.
1.3.1 Potentiometry
Potentiometric methods employ a high-impedance voltmeter to measure the value of E while preventing the overall cell reaction from occurring to any significant extent.
The most widely familiar example of potentiometric measurement involves the combination pH electrode. In this device, two reference half cells are incorporated into a single probe, using concentric tubes. The half cells are connected by a porous glass frit, exposed to the external solution. The key element in the pH electrode is a glass membrane that separates one of the reference half-cells from the external (analyte or calibration) solution. The glass membrane allows the selective transport of protons (hydronium ions) and thus incorporates an ion-selective connection between the two reference electrodes. The ionic or solution connection is thus from one reference electrode, through the glass membrane, through the analyte solution, through the glass frit (salt bridge) into the second reference electrode compartment. If the two reference electrodes are identical, any difference in proton concentration (pH) on the two sides of the glass membrane generates a measurable, nonzero potential difference that is calibrated to the pH of standard solutions.
The glass membrane of a pH electrode can be covered with a gas-only-permeable membrane, trapping a thin layer of weakly buffered solution between the two membranes. With this arrangement, dissolved gas present in the analyte solution can cross into the thin layer. Due to their acid-base equilibria, both ammonia (NH3/NH4+) and carbon dioxide (CO2/HCO3-) can be quantitated using these devices, in which the measurement of the pH of the thin layer of solution is calibrated against the concentration of the dissolved gas in the analyte solution.
Various other ion-selective membrane materials have been developed to allow potentiometric measurements of anions and cations. With all ion-selective electrodes, calibration curves are constructed as plots of measured potential against the logarithm of the ion concentration. At 25 °C, the slopes of these calibration curves are equal to 0.05916/z V/decade, where z is the charge on the ion (e.g. ±1, ±2). Thus, a Ca2+ ion-selective electrode will produce a slope of +0.02958 V/decade, while a Cl- electrode will yield a slope of −0.05916 V/decade.
1.3.2 Amperometry
Amperometric measurements involve the application of a potential E to the cell (Eq. 1.6), to control the [R]/[O] ratio at the surface of the working, or indicator electrode (where the reaction of interest occurs). If this dictated ratio is different from the ratio existing in the solution, current flows, and current is the measured parameter. The reactions only occur at the electrode surfaces, and not in the bulk of the solution, so transport of the analyte to the working electrode surface is a key factor in determining the magnitude of the current that is measured. Flowing or stirred solutions can be used to enhance mass transport.
Electrodes used for amperometry are good conductors, such as platinum, gold or different forms of carbon. They may be thinly coated with a blocking agent to prevent the adsorption of reactants, products or other constituents present in the analyte solution that would cause fouling of the electrodes and thus decreased currents.
When the applied potential is sufficiently extreme, all analyte that reaches the working electrode surface reacts. Under these conditions, the measured current is directly proportional to analyte concentration. Current may also be integrated for a defined period of time, to provide the total charge consumed during this integration time. Charge is also directly proportional to analyte concentration.
One widely-used application of amperometry involves the Clark oxygen electrode. This small, self-contained device contains two electrodes, one of which converts molecular oxygen to hydrogen peroxide. An inner solution is separated from the external analyte solution using a gas-permeable membrane, allowing only dissolved gases to cross into the inner solution. The applied potential is controlled to allow mass-transport-limited reduction of oxygen, and the resulting current is proportional to dissolved oxygen concentration in the external solution. Many enzymatic reactions that consume oxygen (e.g. the oxidases) have been studied with the aid of the Clark electrode.
1.3.3 Impedimetry
In bioanalytical chemistry, impedance measurements can be used to monitor changes in the ionic strength, or conductivity of a solution as a result of a (bio)chemical reaction. In weakly-buffered solutions, reactions that produce or consume ions can be monitored by impedimetry.
With these methods, a small, alternating (sinusoidal) voltage is applied across two electrodes that are present in the solution. This alternating waveform is centered on zero volts, and its small peak-to-peak magnitude (≤50 mV) and high frequency (kHz) prevent redox reactions from occurring at the electrode surfaces. Instead, it is the movement of ions present in the solution that provides the basis for the measurement. Ions migrate toward the oppositely-charged electrode, changing direction when the polarity of that electrode changes. The magnitude and phase of this alternating ion current are measured, and often just the ac magnitude is used for quantitation.
Fundamental relationships exist between solution conductivity and ion type and concentration; however, these are not used in practical quantitative methods. Calibrations are performed, and it is generally the change in alternating current magnitude that occurs during a defined reaction time, rather than its absolute value, that is used for quantitation.
1.4 Radiochemical Measurements
Radioactive isotopes of the elements contain unstable nuclear configurations due to their numbers of neutrons, and undergo radioactive decay, to form more stable products. Many radioactive elements have been used as labels in bioassays, including isotopes of iodine, carbon, phosphorus, sulphur and hydrogen. While the use of radioisotopes has been decreasing with the introduction of alternative, less hazardous labels, radioisotopes are still used in a number of methods.
Radioactivity is characterized by the type of decay as well as the half-life of the radioactive element. The major types of radiation are called alpha (α), beta (β) and gamma (γ). Of these, the emitted β and γ forms of radiation are useful, due to the elements used in bioassays. Isotopes of carbon (C14), phosphorus (P32), sulphur (S35) and hydrogen (H3) emit β radiation, which consists of high-energy electrons. These electrons are detected by scintillation counting. Radioactive iodine (I125) is also used as a tracer in bioassays and metabolic studies; it emits γ radiation, which has no mass or charge, but is detectable using a Geiger counter.
The half-life of a radioisotope is the time required for half of the atoms to decay to their more stable products, and this value is a characteristic constant for each radioisotope. For the elements of interest in bioassays, the half-lives are: 5715 years (C14), 14.3 days (P32), 87.2 days (S35), 12.3 years (H3) and 59.9 days (I125).
1.4.1 Scintillation Counting
This method involves the capture of β particles in a liquid or solid scintillator. The function of the scintillator is to convert these high energy electrons into light that is detected using a photomultiplier tube or photodiode. Liquid scintillators are solutions that usually contain more than one organic species that can both absorb the energy of the β particle and then emit light at a characteristic maximum wavelength. Solid scintillators consist of these types of molecules dispersed in an otherwise transparent solid block.
Depending on their energies, β particles can penetrate a few centimetres to several metres into a surrounding medium, and their capture results in the excitation of scintillator molecules, which release this energy as photons, as they return to their ground states.
Modern instruments for scintillation counting employ coincidence detection, in which two light detectors are used. The detectors are placed in different locations near the scintillator, and a signal is registered only when both detectors simultaneously provide a nonzero signal. This arrangement has greatly improved both the sensitivities and the detection limits of scintillation-based bioassays, since random non-analyte signals are minimized.
1.4.2 Geiger Counting
Geiger counters are used to detect γ radiation, which has a lot of energy, but no mass or charge. This device, called a Geiger-Mueller tube, consists of a housing that contains polarized inner electrodes, an anode and a cathode. The tube is filled with a mixture of ionizable gases such as argon and neon. The cathode is a hollow metal cylinder of large area, while the anode is typically a wire located in the centre of the cylindrical cathode.
The γ radiation penetrates the housing of the tube and collides with the glass or metal walls or electrodes, causing the ejection of electrons that collide with the gas molecules, causing their ionization due to the loss of outlying electrons. These reactions result in the formation of cations and electrons in the gas phase, and because of their positive and negative charges, migrate to and are captured by the electrodes. This results in a measurable current in an external circuit. These devices are very sensitive, and produce current spikes as random collections of individual events are detected. The amplified audio version of these current spikes are the common experience of those familiar with these devices.
Different Geiger counter designs are used for detection of γ radiation in air and for immersion in liquid samples.
1.5 Surface Plasmon Resonance
This method is used to detect and follow binding reactions that occur on a surface. It is largely used for research on the thermodynamic and kinetic properties of association/dissociation reactions, but practical applications to quantitative binding assays and biosensors have been suggested.
This is an optical detection method, in which the angle of reflection of a polarized and generally monochromatic light beam is influenced by the refractive index of a very thin layer of material bound to a very thin (≈50 nm) layer of a metal, which is often gold. The surface-bound layer is on one side of this thin, planar film, while a glass prism is present on the other side.
The principles of SPR are illustrated in Figure 1.3. Light is directed onto one side of the prism. It refracts at the air-glass interface, partially reflects off of the gold film, and travels out the other side of the prism, refracting once again at the glass-air interface. A position-sensitive light detector, such as a photodiode array or a CCD camera, is used to monitor both the intensity and angle of the exiting light beam.
Figure 1.3 Instrumental principles for simple surface plasmon resonance measurements.
The surface plasmon phenomenon involves the excitation of electrons present at the interface between the conducting material (the gold film) and an insulating layer bound to the surface opposite the prism. As the incident light angle is varied, a critical angle is reached at which light is absorbed at the interface, creating surface plasmons. At this surface plasmon resonance angle, a minimum is detected in the intensity of reflected light. The angle at which the minimum occurs is dependent upon the refractive index of the layer of surface-bound material.
As the incident light angle is scanned, light intensity is measured, and data are plotted as intensity against incident angle. From these data, the resonance angle is determined. Since the resonance angle depends on the refractive index of the surface-bound layer, and this depends on what is bound to the surface, any change in angle indicates a change in the nature of the layer.
Association/dissociation reactions, with one binding partner immobilized on the gold surface (often with the aid of a thin polymer coating to allow covalent binding of one reactant), have been studied using this method. The change in resonance angle can be of the order of 0.1 degree, but instruments are able to measure changes as small as ten microdegrees. Because the resonance angle is sensitive to potentially fluctuating experimental parameters such as temperature and flow rate, a second complete flow cell with a second chip and detection system is used to provide a reference measurement, and the differences between the sample and reference measurements are recorded.
These sensor chips, as they are called, are often employed with a specially designed flow cell, to allow the continuous flow of buffer containing introduced quantities of the solution-phase binding partner across the surface opposite the prism. Binding reversal, and regeneration of the original surface conditions, allows multiple measurements using the same chip.
Challenges with this method include the need for strict temperature control and the elimination of nonspecific binding (adsorption) of solution-phase species that do not interact with the surface-bound binding partner, but stick to the surface of the chip. Another present obstacle involves the expense of the chips, but manufacturing advances may occur to lower these costs, making this transduction method more practical for routine assays.
1.6 Calorimetry
Calorimetry involves the measurement of heat. Bio(chemical) reactions may be either exothermic or endothermic, and involve the release or absorption of heat. These reactions result in an increase or decrease in the temperature of the reaction medium. The rate of change of temperature with time is proportional to the rate of the reaction. Two possibilities exist for measurement: temperature change can be monitored as a function of time, using a thermally-jacketed reaction cell, or the reaction medium can be maintained at constant temperature with measurement of the energy required to do this, again as a function of time.
These methods can be used to study protein-ligand interactions, protein unfolding and denaturation, DNA denaturation, DNA/protein/lipid-drug interactions, drug-delivery agents, the incorporation of drugs into nanoparticles, lipid phase transitions, antimicrobial drug mechanisms of action as well as drug purity and thermal stability. Their introduction into the bioanalytical fields has resulted from improvements in sensitivities and detection limits, because limited quantities of biomolecules are commonly available for these studies.
1.6.1 Differential Scanning Calorimetry (DSC)
Older DSC instruments used adiabatic measurements, meaning that heat transfer between samples and their environments was absent or at least minimized by thermal jackets. Since then, it has been shown that non-adiabatic systems can be used to improve baseline stability and reproducibility.
Modern DSC instruments employ microcells such as capillaries, so that no temperature gradients exist across a sample (large surface area/volume ratio), and employ a power compensation method to monitor the difference in power required to maintain sample and reference cells at the same temperature. Temperature is scanned and, since equilibrium conditions are implied by the equations used for subsequent calculations, slower scan rates are preferred (a very slow scan rate for DSC is 0.1 °C/min). There is a tradeoff, however, since slower scan rates yield smaller signals and require more sensitive measurements. Some instruments can simultaneously monitor multiple samples against the same reference solution.
The difference in power required to maintain sample and reference solutions at the same temperature is used to calculate the excess heat capacity of the sample over the reference solutions, as a function of temperature, as temperature is scanned. The excess heat capacity is plotted against temperature in a thermogram (or thermoanalytical curve). The thermogram exhibits a negative-going peak for an exothermic reaction, and a positive-going peak for an endothermic process.
Simple two-state transitions, with no cooperativity, yield flat baselines with symmetric peaks in their DSC thermograms. The peak maximum occurs at Tm, the transition midpoint temperature, and the area under the peak yields the enthalpy of the transition (ΔH). Because, at Tm, the Gibbs free energy (ΔG) of the transition is zero, and since ΔG = ΔH − TmΔS, entropy (ΔS) can also be calculated as the ratio of ΔH/Tm.
Most biological systems exhibit sloped baselines with asymmetric peaks, due to multiple states during the transition and/or cooperative association/dissociation processes. Many studies have investigated the deconvolution of the resulting thermograms, and some have applied the peak width at half-height, ΔT1/2
