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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
"As will be seen, there is not much missing here. I thought that the sections were well balanced, with rarely too much or too little on a given topic...This is a text to be welcomed by both teachers and students." BIOCHEMISTRY & MOLECULAR BIOLOGY EDUCATION (on the first edition)
The second edition of this successful textbook explains the basic principles behind the key techniques currently used in the modern biochemical laboratory and describes the pros and cons of each technique and compares one to another. It is non-mathematical, comprehensive and approachable for students who are not physical chemists.
- A major update of this comprehensive, accessible introduction to physical biochemistry.
- Includes two new chapters on proteomics and bioinformatics.
- Introduces experimental approaches with a minimum of mathematics and numerous practical examples.
- Provides a bibliography at the end of each chapter.
Written by an author with many years teaching and research experience, this text is a must-have for students of biochemistry, biophysics, molecular and life sciences and food science.
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Veröffentlichungsjahr: 2013
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Contents
Preface
Chapter 1 Introduction
1.1 Special Chemical Requirements of Biomolecules
1.2 Factors Affecting Analyte Structure and Stability
1.3 Buffering Systems Used in Biochemistry
1.4 Quantitation, Units and Data Handling
1.5 The Worldwide Web as a Resource in Physical Biochemistry
1.6 Objectives of this Volume
Chapter 2 Chromatography
2.1 Principles of Chromatography
2.2 Performance Parameters Used in Chromatography
2.3 Chromatography Equipment
2.4 Modes of Chromatography
2.5 Open Column Chromatography
2.6 High Performance Liquid Chromatography (HPLC)
2.7 Fast Protein Liquid Chromatography
2.8 Perfusion Chromatography
2.9 Membrane-Based Chromatography Systems
2.10 Chromatography of a Sample Protein
Chapter 3 Spectroscopic Techniques
3.1 The Nature of Light
3.2 The Electromagnetic Spectrum
3.3 Ultraviolet/Visible Absorption Spectroscopy
3.4 Fluorescence Spectroscopy
3.5 Spectroscopic Techniques Using Plane-Polarized Light
3.6 Infrared Spectroscopy
3.7 Nuclear Magnetic Resonance (NMR) Spectroscopy
3.8 Electron Spin Resonance (ESR) Spectroscopy
3.9 Lasers
3.10 Surface Plasmon Resonance
Chapter 4 Mass Spectrometry
4.1 Principles of Mass Spectrometry
4.2 Mass Spectrometry of Proteins/Peptides
4.3 Interfacing MS With other Methods
4.4 Uses of Mass Spectrometry in Biochemistry
Chapter 5 Electrophoresis
5.1 Principles of Electrophoresis
5.2 Nondenaturing Electrophoresis
5.3 Denaturing Electrophoresis
5.4 Electrophoresis in DNA Sequencing
5.5 Isoelectric Focusing (IEF)
5.6 Immunoelectrophoresis
5.7 Agarose Gel Electrophoresis of Nucleic Acids
5.8 Pulsed Field Gel Electrophoresis
5.9 Capillary Electrophoresis
5.10 Electroblotting Procedures
5.11 Electroporation
Chapter 6 Three-Dimensional Structure Determination of Macromolecules
6.1 The Protein-Folding Problem
6.2 Structure Determination by NMR
6.3 Crystallization of Biomacromolecules
6.4 X-Ray Diffraction by Crystals
6.5 Calculation of Electron Density Maps
6.6 Other Diffraction Methods
6.7 Comparison of X-Ray Crystallography with Multi-Dimensional NMR
6.8 Structural Databases
Chapter 7 Hydrodynamic Methods
7.1 Viscosity
7.2 Sedimentation
7.3 Methods for Varying Buffer Conditions
7.4 Flow Cytometry
Chapter 8 Biocalorimetry
8.1 The Main Thermodynamic Parameters
8.2 Isothermal Titration Calorimetry
8.3 Differential Scanning Calorimetry
8.4 Determination of Thermodynamic Parameters by Non-Calorimetric Means
Chapter 9 Bioinformatics
9.1 Overview of Bioinformatics
9.2 Sequence Databases
9.3 Tools for Analysis of Primary Structures
9.4 Tertiary Structure Databases
9.5 Programs for Analysis and Visualization of Tertiary Structure Databases
9.6 Homology Modelling
Chapter 10 Proteomics
10.1 Electrophoresis in Proteomics
10.2 Mass Spectrometry in Proteomics
10.3 Chip Technologies in Proteomics
10.4 Post-Translational Modification Proteomics
Appendix 1 SI Units
Appendix 2 The Fourier Transform
Index
This edition first published 2009, © 2009 John Wiley & Sons Ltd
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Library of Congress Cataloging-in-Publication Data
Sheehan, David, 1958–
Physical biochemistry : principles and applications / David Sheehan. – 2nd ed.
p. ; cm.
Includes bibliographical references and index.
ISBN 978-0-470-85602-4 (hb) – ISBN 978-0-470-85603-1 (pb) 1. Physical biochemistry. I. Title. [DNLM: 1. Biophysics. 2. Biochemistry. 3. Chemistry, Phisical. QT 34 S541p 2008]
QD476.2.S42 2009
572′.43–dc22
2008046672
ISBNs: 9780470856024 (HB)
9780470856031 (PB)
A catalogue record for this book is available from the British Library.
First Impression 2009
To the memory of my father, Patrick Sheehan (1917–2003)
Preface
The first edition of Physical Biochemistry: Principles and Applications set out to describe the physical basis and some examples of applications of key physically-based techniques used in Biochemistry and other areas of molecular life science research. In the last decade there has been a noticeable renaissance in some traditional techniques such as X-ray diffraction, ultracentrifugation and electrophoresis in a variety of formats. In the same time-frame ‘hyphenated’ techniques (e.g. LC-tandem MS) have become much more mainstream and some instrumentation has become available in desktop formats making quite sophisticated analysis possible even in the nonspecialist lab. The emphasis was on a largely nonmathematical treatment at a level appropriate to students in the penultimate year of a Biochemistry course with a view to making these techniques comprehensible and accessible to a level intermediate between a general Biochemistry textbook and a specialist text. The feedback I have had from many readers is that this goal was largely achieved.
My task with this second edition was to retain as much as possible of the description of physical principles whilst updating and integrating new material into a reasonably compact volume. The first edition was strongly influenced by the effects of the then-recent completion of the Human and other large-scale genome sequencing projects. At the time Proteomics and other ‘-omics’ technologies were still relatively new paradigms and bioinformatics approaches largely the province of the specialist. It is remarkable how quickly these technologies have now become embedded in many areas of biochemical research so that they are now perceived as part of the mainstream. In the second edition I have dedicated new chapters to proteomics and bioinformatics, respectively, to reflect this changed situation and to emphasize how interconnected physical and computational techniques have now become.
The second edition required choices to be made and these are inevitably influenced by one’s perception of what is needed and useful for students to know at the start of their scientific journey into molecular life science. In making these choices I have continued to be guided by what I perceive to be the most generally-used and helpful techniques but I accept that specialists in one or more technique may disagree.
In preparing this second edition I had help from many of the colleagues listed in the preface to the First Edition. In addition, I must thank Dr Rebecca Green, School of Pharmaceutical Sciences, University of Nottingham, UK, for her invaluable comments on surface plasmon resonance (Chapter 3). I am also indebted to the excellent staff at Wiley’s especially my editors, Celia Carden and Fiona Woods for their unfailing encouragement and understanding. However, any errors in the text are my own. I earnestly hope that the reader will find something interesting and thought-provoking in this volume and be encouraged to explore these very powerful approaches in their work.
Prof David Sheehan
University College Cork
June 2008
Chapter 1
Introduction
This volume describes a range of physical techniques which are now widely used in the study both of biomolecules and of processes in which they are involved. There will be a strong emphasis throughout on biomacromolecules such as proteins and nucleic acids as well as on macromolecular complexes of which they are components (e.g. biological membranes, ribosomes, chromosomes). This is because such chemical entities are particularly crucial to the correct functioning of living cells and present specific analytical problems compared to simpler biomolecules such as monosaccharides or dipeptides. Biophysical techniques, give detailed information offering insights into the structure, dynamics and interactions of biomacromolecules.
Life scientists in general and biochemists in particular have devoted much effort during the last century to elucidation of the relationship between structure and function and to understanding how biological processes happen and are controlled. Major progress has been made using chemical and biological techniques which, for example, have contributed to the development of the science of molecular biology. However, in the last decade physical techniques which complement these other approaches have seen major development and these now promise even greater insight into the molecules and processes which allow the living cell to survive. For example, a major focus of life science research currently is the proteome as distinct from the genome. This has emphasized the need to be able to study the highly-individual structures of biomacromolecules such as proteins to understand more fully their particular contribution to the biology of the cell. For the foreseeable future, these techniques are likely to impact to a greater or lesser extent on the activities of most life scientists. This text attempts to survey the main physical techniques and to describe how they can contribute to our knowledge of biological systems and processes. We will set the scene for this by first looking at the particular analytical problems posed by biomolecules.
1.1 SPECIAL CHEMICAL REQUIREMENTS OF BIOMOLECULES
The tens of thousands of biomolecules encountered in living cells may be classified into two general groups. Biomacromolecules (e.g. proteins; nucleic acids) are characterized by high molecular mass (denoted throughout this text as relative molecular mass, Mr) and are generally unstable under extreme chemical conditions where they may lose structure or break down into their chemical building blocks. Low molecular weight molecules are smaller and more chemically robust (e.g. amino acids; nucleotides; fatty acids). Within each group there is displayed a wide range of water-solubility, chemical composition and reactivity which is determined by complex interactions between physicochemical attributes of the biomolecule and solvent. These attributes are the main focus for the techniques described in this volume and reflect the highly individual function which each molecule performs in the cell (Tables 1.1 and 1.2).
Notwithstanding the great range of form and structure, we can nonetheless recognize certain attributes as common to all biomolecules. The first and most obvious is that all of these molecules are produced in living cells under mild chemical conditions of temperature, pressure and pH. Biomacromolecules are built up from simpler building block molecules by covalent bonds formed usually with the elimination of water. Moreover, biomolecules are continuously synthesized and degraded in cells in a highly regulated manner. It follows from this that many biomolecules are especially sensitive to extremes of temperature and pH which may present a problem in their handling prior to and during any biophysical analysis. Since biomolecules result from a long process of biological evolution during which they have been selected to perform highly specific functions, a very close relationship has arisen between chemical structure and function. This means that, even at pH and temperature values under which the molecule may not be destroyed, it may function suboptimally or not at all.
Table 1.1. Some important physical attributes of biomolecules amenable to study by biophysical techniques
Table 1.2. Some important chemical attributes of biomolecules which may be used in study by biophysical techniques
These facts impose limitations on the chemical conditions to which biomolecules may be exposed during extraction, purification or analysis. In most of the techniques described in this volume, sample analytes are exposed to a specific set of chemical conditions by being dissolved in a solution of defined composition. Whilst other components in the solution may also be important in individual cases as will be discussed below (Section 1.3.2), three main variables govern the makeup of this solution which are discussed in more detail in the following section.
1.2 FACTORS AFFECTING ANALYTE STRUCTURE AND STABILITY
In practice, most of the biophysical procedures described in this volume use conditions which have been optimized over many years for thousands of different samples. These robust conditions will normally maintain the sample in a defined structural form facilitating its separation and/or analysis. However, some procedures (e.g. chromatography, capillary electrophoresis, crystallization) may require case-by-case optimization of conditions. Before embarking on a detailed analysis of a biomolecule using biophysical techniques it is often useful to know something about the stability of the sample to chemical variables, especially pH, temperature and solvent polarity. This knowledge can help us to design a suitable solvent or set of chemical conditions which will maximize the stability of the analyte for the duration of the experiment and may also help us to explain unexpected results. For example, we sometimes find loss of enzyme activity during column chromatography which may be partly explained by the chemical conditions experienced by the protein during the experiment. Moreover, many of the techniques described in this volume are actually designed to be suboptimal and to take advantage of disruption of the normal functional structure of the biomolecule to facilitate separation or analysis (e.g. electrophoresis, HPLC, MS).
A good indication of the most stabilizing conditions may often be obtained from knowledge of the biological origin of the biomolecule. It is also wise to assess the structural and functional stability of the analyte over the range of experimental conditions encountered in the experiment during its likely time-span.
We can distinguish two main types of effects as a result of variation in the chemical conditions to which biomolecules are exposed. Structural effects reflect often irreversible structural change in the molecule (e.g. protein/nucleic acid denaturation; hydrolysis of covalent bonds between building blocks of which biopolymers are composed). Functional effects are frequently more subtle and may be reversible (e.g. deprotonation of chemical groups in the biomolecule resulting in ionization; partial unfolding of proteins). A detailed treatment of these effects on the main classes of biomolecules is outside the scope of the present volume but a working knowledge of the likely effects of these conditions can be very useful in deciding conditions for separation or analytical manipulation.
1.2.1 pH Effects
pH is defined as the negative log of the proton concentration:
(1.1)
Because both the H+ and OH− concentrations of pure water are 10–7 M, this scale runs from a maximum of 14 (strongly alkaline) to a minimum of 0 (strongly acidic). As it is a log scale, one unit reflects a 10-fold change in proton concentration. Most biomacromolecules are labile to alkaline or acid-catalyzed hydrolysis at extremes of the pH scale but are generally stable in the range 3–10. It is usual to analyse such biopolymers at pH values where they are structurally stable and this may differ slightly for individual biopolymers. For example, proteins normally expressed in lysosomes (pH 4) are quite acid-stable while those from cytosol (pH 7) may be unstable near pH 3. Aqueous solutions in which sample molecules are dissolved usually comprise a buffer to prevent changes in pH during the experiment. These are described in more detail in Section 1.3 below.
Many biomolecules are amphoteric in aqueous solution that is they can accept or donate protons. Some chemical groups such as inorganic phosphate or acidic amino acid side-chains (e.g. aspartate) can act as Brønsted acids and donate protons:
(1.2)
Other groups such as the imidazole ring of histidine or amino groups can act as Brønsted bases and accept protons
(1.3)
The position of equilibrium in these protonation/ deprotonation events may be described by an equilibrium constant, Ka:
(1.4)
pKa (–logKa) is the pH value at which 50% of the acid is protonated and 50% is deprotonated. The Henderson–Hasselbach equation describes variation of concentrations of A− and AH as a function of pH:
(1.5)
Functional groups present as structural components of biomolecules (e.g. amino acid side-chains of proteins; phosphate groups of nucleotides) will have distinct Ka values which may differ slightly from the value found in other chemical circumstances (e.g. the Ka values of amino acid side-chains in polypeptides differ from those in the free amino acid). Some biomolecules can contain both acidic and basic groups within their structure (e.g. proteins) while particular chemical structures found in biomolecules may be polyprotic, that is capable of multiple ionizations (e.g. phosphate). Such biomolecules may undergo a complex pattern of ionization resulting in varying net charge on the molecule. pH titration curves for biomolecules allow us to identify pKa values (Figure 1.1).
Since protonation-deprotonation effects are responsible for the charges on biomacromolecules which maintain their solubility in water, their solubility is often lowest at their isoelectric point, pI, the pH value at which the molecule has no net charge. These can also be determined by titration using methods described in Chapter 5 (Section 5.5.3; Figure 5.24).
While the pH scale reflects the situation in aqueous solution, many microenvironments encountered in living cells are quite nonpolar (see below). Good examples include biological membranes and water-excluding regions of proteins (e.g. some enzyme active sites). In these environments, protonation/deprotonation properties of chemical groups may deviate widely from those observed in aqueous solution. For example, catalytic residues of many enzymes frequently display pKa values which are perturbed far from those normal for that residue in water-exposed regions of proteins.
1.2.2 Temperature Effects
Three main effects of temperature on biomolecules are important for the biophysical techniques described in this volume. These are effects on structure, chemical reactivity and solubility. Heat can disrupt noncovalent bonds such as hydrogen bonds which are especially important in the structure of biomacromolecules. This can lead to denaturation of proteins and DNA or to disruption of multimolecular complexes in which they may be involved. Moreover, since covalent bonds linking building block molecules (e.g. peptide bonds; glycosidic bonds; 3′, 5′-phosphodiester bonds) have generally lower bond energies than bonds within such building blocks, extensive heating can result in disintegration of the covalent structure of biomacromolecules. Thus proteins can break down into component peptides or nucleic acids into smaller polynucleotide fragments as a result of exposure to heat.
Figure 1.1. pH titration curves, (a) Lysine. Four protonation states are possible for lysine as shown. Three pKa values are evident from this at pH values of 2.18, 8.95 and 10.53. The pI of lysine is 9.74. (b) Glycine. Note that only three protonation states exist for glycine compared to four for lysine. pKa values are at pH values of 2.34 and 9.6 which differ slightly from the corresponding ionisations in (a). Glycine has a pI of 5.97
Secondly, all chemical reaction processes obey the Arrhenius relationship:
(1.6)
where k is the rate constant for the process, A is a constant, Ea is the activation energy of the reaction, R is the Universal gas constant and T is absolute temperature. This relationship arises from large changes in the number of activated molecules available for reaction as a result of change in temperature. The exponential dependence on temperature means that small changes in T can result in large effects on the rate constant, k.
Thirdly, temperature usually increases the solubility of molecules in a solvent as well as the rate of diffusion through the solvent. This is because heat increases the average kinetic energy of solvent molecules. In the case of water, this is accompanied by extensive breakdown of water-water hydrogen bonds which increases the solute capacity of a given volume of water. Thus, for example 8M urea is soluble at 30 °C while the limit of solubility is closer to 5 M at 4 °C. Kinetic energy effects are also important in situations involving biological membranes because the phospholipid bilayer of which they are composed becomes increasingly fluid at higher temperature.
Temperature is therefore usually tightly controlled during biophysical experiments. In dealing with biomacromolecules in particular, it is generally not possible to use temperatures higher than 80 °C and, in most cases, much lower temperatures are used. Moreover, samples such as proteins or nucleic acids are normally stored under refrigerated conditions to maximize their stability. This is achieved with the aid of liquid nitrogen (–196 °C) or with refrigerators set at –80 or –20 °C. Particular care must be taken in handling crude biological extracts since hydrolases such as proteases and nucleases present in these will be active in the range 18–37 °C and result in extensive degradation of proteins and nucleic acids. This can be avoided by maintaining low temperatures near 4 °C during manipulation of sample and by cooling buffer solutions before dissolving biological samples.
Most biomolecules are optimally active at temperatures similar to those experienced in the biological source from which they were obtained. For example, proteins from thermophilic bacteria are especially heat stable compared to corresponding proteins from mesophilic bacteria while mammalian proteins are optimally active around 37 °C.
1.2.3 Effects of Solvent Polarity
Polarity arises from unequal affinity of atoms bonded together for shared electrons called electronegativity. Apart from fluorine (with an electronegativity value of 4), oxygen is the most electronegative element in the periodic table (electronegativity value of 3.5) leading, for example, to oxygens of –OH groups tending to be partially negatively charged (δ−) while hydrogens tend to be partially positively charged (δ+). Water (which is itself polar) interacts ionically with polar functional groups such as –OH by hydrogen bonding (Figure 1.2). Organic molecules composed mainly of carbon and hydrogen, however, tend to be nonpolar as these atoms have similar electronegativities (2.5 and 2.1, respectively). In general, polar biomolecules dissolve readily in polar solvents such as water while those which are nonpolar dissolve in nonpolar solvents (e.g. trichloromethane).
Biomolecules lacking strongly electronegative elements such as oxygen and nitrogen and consisting mainly of carbon and hydrogen tend to be principally nonpolar (e.g. fatty acids; sterols; integral membrane proteins). Conversely, those containing oxygen, sulfur and nitrogen tend to be mainly polar (e.g. monosaccharides; nucleotides). Biomacromolecules often contain distinct structural regions some of which may be polar while others may be nonpolar.
Since water is the main biological solvent, most biomolecules (or parts of biomolecules) have been selected by evolution to interact with it in particular ways either by attraction or repulsion. Polar regions strongly attracted to water are called hydrophilic while nonpolar regions which are repulsed by water are called hydrophobic. In the living cell, biomolecules adopt a structure determined to a large degree by the extent to which they are hydrophobic/hydrophilic. For example, biological membranes are made up of phospholipid bilayers which spontaneously form when phospholipid molecules are dissolved in water. The polar heads of phospholipids are on the exterior in contact with water while the nonpolar fatty acid components are on the interior of the bilayer protected from water. Cytosolic proteins express hydrophilic groups on their surface whilst folding in such a manner that hydrophobic groups are protected from exposure to water in the interior of the protein (Chapter 6). Membrane-bound proteins such as hormone receptors expose hydrophobic groups to the interior of biological membranes and hydrophilic groups to the exterior.
In extracting, analyzing and purifying biomolecules these intricate structural interactions are often lost which can result in aggregation, precipitation or loss of structure and, hence, of biological activity. If it is desired to retain biological activity we use aqueous solutions to handle largely hydrophilic biomolecules, nonpolar solvents to dissolve mainly hydrophobic samples and detergent solutions for molecules which possess both classes of groups. Many of the individual techniques described in this volume use specific solvent systems of distinct polarity/nonpolarity but it may occasionally be necessary to design individual solvent systems to take account of the requirements of particular biomolecules. Examples include column chromatography (Chapter 2), spectroscopy (Chapter 3) and capillary electrophoresis (Chapter 5).
Figure 1.2. Hydrogen bonding. Water molecules hydrogen bond because of partial charge-differences arising from the different electronegativities of oxygen and hydrogen. Hydrogen bonds (dashed lines) are shown both in bulk water and between water and amino acid side-chains of glutamic acid and serine residues of a polypcptidc. Such ionic interactions maintain a solvation shell of water around the surface of globular proteins and other hydrated biomacromolecules
1.3 BUFFERING SYSTEMS USED IN BIOCHEMISTRY
A buffer is an aqueous solvent system designed to maintain a given pH. In the context of biochemical work, the main function of buffers is to resist any tendency for pH to rise or drop during the experiment. This can happen during any process which might release or absorb protons from solution such as, for example, during an enzyme-catalyzed reaction or as a result of electrochemical processes such as electrophoresis. A secondary but often crucial role for a buffer is to maximize the stability of biomolecules in solution. Frequently, additional molecules are dissolved in the buffer to help it to do this and these are discussed in more detail below.
1.3.1 How Does a Buffer Work?
Any aqueous solution containing both A− and AH (Section 1.2 above) is, in principle, capable of resisting change in pH. This is because, if protons are generated in the solution, they can be neutralized by A−:
(1.7)
Conversely, if alkali is generated in the solution (which would tend to remove protons), it can be neutralized by AH:
(1.8)
In practice, most buffers consist of mixtures either of a weak acid and its salt or of a weak base and its salt.
Of course, the ability of a buffer to resist change in pH is finite, especially if the number of protons involved is especially large. This limit is represented by the buffering capacity of the buffer, β. This is defined as the number of moles of [H+] which must be added to a liter of the buffer to decrease the pH by one unit. It can be mathematically calculated from the following equation:
(1.9)
1.3.2 Some Common Buffers
A selection of buffers commonly used in biochemistry is given in Table 1.3. Some of these buffer components are of biological origin (e.g. glycine; histidine; acetate). Good’s buffers were developed by N.E. Good to facilitate buffering in the pH range 6–10.5. Because of their complicated chemical names, these buffers are more usually known by abbreviations (e.g. Pipes; Hepes; Mops). Inspection of Table 1.3 shows that buffers are available which span the range of interest for physical studies of biomolecules (i.e. pH 3–10). When preparing buffers, it is essential that both the concentration and pH are correct since these are the two variables critical to buffering capacity (Equation (1.7)).
A number of problems can arise with particular buffers which can limit their use in specific cases. For example, several buffers interact with divalent metals (e.g. phosphate binds Ca2+; Tris reacts with Cu2+ and Ca2+) and should be avoided in cases where this is important to interpretation of the experiment. Tris buffers are especially sensitive to temperature which can result in the same buffer giving a slightly different pH at different temperatures. Phosphate buffers are particularly susceptible to bacterial contamination if stored for long periods of time (although this can be avoided by including a low concentration of sodium azide as a preservative). Some buffer components (e.g. EDTA) may give high absorbance readings which can affect detection during processes such as chromatography. Volatile buffer components (e.g. formic acid; bicarbonate; triethanolamine) can be lost from the buffer over time leading to a gradual change in pH and buffering capacity.
1.3.3 Additional Components Often Used in Buffers
In addition to buffer components such as weak acids/bases and their salts, buffers frequently contain a range of other components of which a selection is shown in Table 1.4. These may be necessary to maintain stability of the biomolecule, to control levels of metal ions, to ensure reducing/oxidizing conditions or to keep the biomolecule dissolved and/or denatured. We will observe that some of the agents tabulated in Table 1.4 are used in more than one of the techniques described in this book and therefore represent generally useful tools for the manipulation of chemical conditions to which biomolecules are exposed.
Table 1.3. Some common buffers used in biochemistry
1.4 QUANTITATION, UNITS AND DATA HANDLING
1.4.1 Units Used in the Text
Physical measurements usually result in quantification of some property of a molecule or system such as those tabulated in Table 1.1. Various systems of internationally-agreed units have been used historically to record these measurements but, throughout this book, the Systeme Internationale (SI) system, the most currently-agreed scientific quantification system will be used. The main units are tabulated in Appendix 1. This system has the advantage of great internal consistency which removes any need for conversion factors. For example, units of distance (meters) readily relate to units of velocity (meters/second).
Table 1.4. Additional reagents sometimes added to buffers
In addition to SI units, some measurements used are operational measurements commonly employed in the life science literature. These are units which have gained wide acceptance in the international science community but which are not strictly part of the SI system. Relative molecular mass (Mr) is expressed as Daltons (Da) or multiples thereof (e.g. kDa) with 12 Da being equivalent to twelve atomic mass units (i.e. the mass of 12C). In the case of nucleic acids, base pairs (bp) or multiples thereof (e.g. kbp, Mbp) are used as units of mass. Interatomic distances such as bond-lengths are generally given as angstroms (Å) with 1 Å corresponding to 10–10 m (i.e. 0.1 nm).
Concentrations are given mainly in molarity (1 M solution being Avogadro’s Number of molecules dissolved in 11 of solvent) although occasionally they are expressed as percentages of weight/weight (% w/w) or weight/volume (% w/v). Thus, 10% (w/v) would represent a solution of 10 g per 100 ml while 10% (v/v) would represent a solution of 10 ml per 100 ml.
The most commonly used temperature scale in the text is the Celsius scale although absolute temperatures (in units of Kelvin, K) are specifically referred to by T (e.g. Equation (1.6) above).
1.4.2 Quantification of Protein and Biological Activity
Most of the techniques described in this text are used to separate or analyse biomolecules or mixtures containing them. In carrying out this kind of experimentation it is crucial to know exactly how much sample is being applied since most of the systems described are highly loading-sensitive. In the case of pure samples this may not be a problem but many samples encountered in biochemistry may be quite crude and heterogeneous. A common strategy for quantifying such samples is to estimate their protein content (e.g. by the Bradford method, Figure 3.18, or by one of the other methods mentioned in the bibliography at the end of this chapter) and to load a standard amount of protein. Since the ratio of protein to the other components of the mixture is fixed, this normally ensures uniform loading. Similarly, when quantifying the biological activity of a sample (e.g. enzyme activity, antibody content, antiviral activity) it is often useful to express this as specific activity that is units/mg protein. This is a measure which is independent both of sample volume and sample concentration.
The majority of the approaches described measure relative properties of biomolecules rather than absolute properties. Examples of this would include Mr estimation by mass spectrometry, gel filtration and electrophoresis, pI estimation by isoelectric focusing, secondary structure estimation of proteins by circular dichroism and determination of chemical shifts in NMR spectroscopy. For this reason, a common strategy found in many of the techniques is to compare the sample being analysed to a series of well-characterized standard molecules using well-established procedures which have been optimized for that particular method. It is important to understand that measurements obtained in this way are therefore highly dependent on standard measurements being of good quality and that this may vary somewhat from method to method.
1.5 THE WORLDWIDE WEB AS A RESOURCE IN PHYSICAL BIOCHEMISTRY
1.5.1 The Worldwide Web
The worldwide web was originally devised as a distributed computer network for the military capable of withstanding nuclear attack! In the last decade, it has grown to include millions of individual entries called web pages containing information on almost every conceivable subject. These web pages exist on a computer somewhere in the world but can in principle be accessed by other computers through the web. At the time of writing, (March, 2008) it is estimated that 20% (1320 million) of the Earth’s 6606 million population have access to the web (http://www.internetworldstats.com/stats). We can connect to web pages on the web with an appropriate browser such as Internet Explorer. However, due to the sheer mass of material being constantly added to and changed on the web, we normally use a search engine to find pages on specific named topics. Google is a good example of a general purpose search engine. It should be remembered that no search engine gives 100% coverage so results from a search could represent as few as 25% of the total possible pages on a given topic.
The ‘address’ of a particular web page is given by a uniform resource locator (URL). Examples of URLs include http://www.google.com for google and http://alta-vista.com for altavista. The prefix http:// is to tell the receiving computer that it can expect a communication in hypertext transfer protocol – the most common format allowing one computer to communicate with another. The rest of the URL defines a location, that is a computer containing the relevant file. The ending .html which often occurs in URLs signifies hypertext markup language, the language in which web pages are written.
1.5.2 Web-Based Resources for Physical Biochemistry
The web provides several resources of use in Physical Biochemistry. Individual web pages are available which describe various experimental techniques thus complementing published work such as review articles and textbooks. There are also databases which are archives of one particular category of information. Examples would include sequence databases, databases of NMR spectra, the three dimensional structure database and databases of two-dimensional electrophoresis patterns. The best databases are curated (i.e. they are looked after and regularly updated by some reputable body) and they are annotated (which means each entry contains extra information such as literature citations, references to other related entries, etc.). These features make databases part of the daily life of modern molecular life scientists. Even though many resources on the web are not peer-reviewed in the way that say research articles are, most authoritative databases achieve the same result by maintaining a close link with the peer-reviewed literature. Conversely, it is becoming increasingly common for research articles to be submitted to journals in electronic format and for peer-reviewed articles to appear on the web long before the paper version. A third set of very useful resources on the web is made possible by the availability, often as freeware (i.e. for free!) of computer programs which help us to analyse or represent our data differently. Examples would include graphics programs which allow us to view the three dimensional structures of biomacromolecules encoded in protein databank (PDB) files (Chapters 6 and 9) or hydropathy plots which allow us to identify hydrophobic regions of amino acid sequences (Chapter 9).
The ever-closer links between molecular life sciences and information technology (IT) is represented in the relatively new discipline of bioinformatics which is introduced in Chapter 9. In this book relevant URLs for web-based resources are given at the end of each chapter.
In addition to text and programs, the wordwide web can be searched for images or videos using the standard search engines. A word of caution about using this type of searching in an academic context. The fact that material is on the web does not absolve us as scientists from respecting copyright law so permission should always be obtained to reproduce images, text or videos obtained from the web just as we would in using such content from a published source. Secondly, we should always take care to refer back to the primary literature as this is the bedrock of modern science and is likely to remain so as long as rigorous peer-review prevails.
1.6 OBJECTIVES OF THIS VOLUME
All of the techniques mentioned in this book merit one or more volumes to describe fully their potential for the future of life science research. In the bibliography at the end of each chapter the reader will find a list of such specialist texts and it is hoped that the present book will act as a general introduction to specialist biophysical techniques. In addition, recent review articles are cited which will bring the reader more up-to-date on specific applications of individual techniques. It is not the intention of the text to supplant such specialist literature but rather to guide students towards a greater understanding of the potential of biophysical approaches to biochemistry.
A chapter is devoted to each technique or group of techniques which describes the physical basis, advantages, limitations and opportunities it offers. This is presented in a generally nonmathematical way to maximize its accessibility (more detailed treatments may be found in the specialist texts). Moreover, the relationship between techniques is strongly emphasized because several combinations of individual techniques often offer advantages over single experimental approaches. In particular, recent advances have seen the combination of techniques such as mass spectrometry, chromatography, electrophoresis and spectroscopy as hyphenated or multi-dimensional analytical techniques. Care has also been taken to emphasize how biophysical approaches often complement biological and chemical experimentation to give a fuller understanding of biochemical systems.
Specific examples of applications of the approaches described are given in boxes throughout the text. These are meant to give a flavour of their versatility and power for the solving of many different types of problems in biochemistry. The bibliography contains many more examples such as, for example, applications in clinical laboratories and in industry. Articles and books (e.g. laboratory manuals) containing practical hints to novices contemplating using these techniques are also cited.
Finally, it is hoped that this book will furnish the student with sufficient understanding to allow them to understand and grasp as-yet undeveloped biophysical approaches which may appear in the next decade or so by noticing the common factors underlying the methods described as well as their diversity.
REFERENCES
Buffers and pH
Voit, E.O. and Ferreira, A.E.N. (1998) Buffering in models of integrated biochemical systems. Journal of Theoretical Biology, 191, 429–37. A description of the effects of including buffers in modelling of biochemical systems.
Good, N.E. and Izawa, S. (1972) Hydrogen ion buffers for photosynthesis research. Methods in Enzymology, XXIV, 53–68. A description of Good’s buffers.
Grady, J.K., Chasteen, N.D. and Harris, D.C. (1988) Radicals from Good’s buffers. Analytical Biochem., 173, 111–5. Further reading on Good’s buffers.
Units and quantities
Kotyk, A. (ed.) (1999) Quantities, Symbols, Units and Abbreviations in the Life Sciences. Humana Press, Totowa, NJ, USA. A guide to standard usage of units and quantities in the life sciences.
Methods for protein estimation
Bradford, M. (1976) A rapid and sensitive method for the quantitation of microgram quantities of protein utilizing the principle of protein-dye binding. Analytical. Biochem., 72, 248–54. Original description of the Bradford method.
Hartree, E.F. (1972) Determination of protein: A modification of the Lowry method that gives a alinear photometric response. Analytical Biochem., 48, 422–7. A later modification of the Lowry method.
Lowry, O., Rosebrough, A., Farr, A. and Randall, R. (1951) Protein measurement with the Folin phenol reagent. J. Biol. Chem., 193, 265–75. Original description of the Lowry method.
Williams, G.A., Macevilly, U., Ryan, R. and Harrington, M.G. (1995) Semiautomated protein assay using microtitre plates – some practical considerations. British Journal of Biomedical Science, 52, 230–1. Description of problems encountered in miniaturising protein assays with microtitre plates.
Bioinformatics
Roberts, E., Eargle, J., Wright, D. and Luthey-Schulten, Z. (2006) MultiSeq: Unifying sequence and structure data for evolutionary analysis. BMC Bioinformatics, 7, Art. No 382. This on-line journal article introduces MultiSeq, a tool for combining sequence and structure data for proteins including an excellent general discussion of current bioinformatic issues.
Lesk, A. (2005) Introduction to Bioinformatics, 2nd edn, Oxford University Press, Oxford, UK. An excellent, comprehensive and clear description of modern bioinformatics.
Some useful web sites
The SI system at National Institute of Standards and Technology (USA): http://www.physics.nist.gov/cuu/Units/.
An illustrated site in “chemguide” on ionization and acid-base chemistry by Jim Clark: http://www.chemguide.co.uk/physical/acideqiamenu.html.
Aquasol solubility database: http://www.pharm.arizona.edu/aquasol/index.html.
Useful bioinformatics sites: National Library of Medicine (USA): http://www.ncbi.nlm.nih.gov/.
European Bioinformatics Institute (UK): www.ebi.ac.uk.
Uniprot site (US/Europe): http://www.ebi.uniprot.org/index.shtml.
Chapter 2
Chromatography
Thephysical basisof chromatography.Thechemical basisof the principal chromatography methods used in biochemistry.Performance criteriawhich can be used to compare chromatography systems.The range of differentchromatography formatsused in biochemistry.How one might approachdesign of a purification protocol,for example to purify a specific protein of interest.
Living cells contain hundreds of thousands of distinct chemical species. These include large molecules like proteins, nucleic acids, lipids as well as lower molecular weight molecules which act as building blocks for biopolymers or as components of complex metabolic pathways. Some of these molecules are present in only trace amounts (e.g. intermediates in enzyme mechanisms) whilst others are present in abundance (e.g. structural proteins). Moreover, some components are present only at certain stages of the cell-cycle, whilst others are present at approximately constant levels. Study of individual chemical components of cells can, therefore, give us an insight into many fundamental cellular processes and help us to understand the dynamics of cell composition and function.
One approach to the study of individual chemical species is to separate them from each other by analytical or preparative chromatography. Originally, this technique was used by Tswett (1903) in the separation of plant pigments (chromatography comes from the Greek, chroma, meaning colour) but we now know that it is applicable to all chemical species, whether coloured or not. Because of the large range of size, shape and hydrophobicity found in biomolecules, it is to be expected that no one chromatography technique will suffice for all separations. In this chapter, the basic principles of chromatography will be described to explain why different molecules are separable. Some examples of the main chromatographic techniques used in Biochemistry are then given to illustrate how biomolecules are separated in practice.
2.1 PRINCIPLES OF CHROMATOGRAPHY
2.1.1 The Partition Coefficient
When applied to any two-phase system (e.g. liquid–liquid, liquid–solid), a molecule may partition between the phases (Figure 2.1). The precise ratio of concentration achieved is ultimately determined by inherent thermodynamic properties of the molecule (in turn, a function of its chemical structure) and of the phases. In the case of a liquid–liquid system, the relative solubility of the molecule in each liquid will be very important in determining partitioning. In a liquid–solid system, different sample molecules may adsorb to varying degrees on the solid phase. Both partition and adsorption phenomena are possible in a column system and this is called column chromatography. In column chromatography, one phase is maintained stationary (the stationary phase) while the other (the mobile phase) may flow freely over it. We can express the concentration ratio in such a system as the partition coefficient, K:
(2.1)
where Cs and Cm are the sample concentrations in the stationary and mobile phases, respectively. When a mixture made up of several components is applied to such a two-phase system, each component will have its own individual partition coefficient. As a result, each will interact slightly differently with the stationary phase and, because of different partitioning between phases, will migrate through the column at different rates. Since K will be directly affected by the precise experimental conditions (e.g. temperature, solvent polarity) the chromatographer may vary these to optimize separation. In column chromatography, we therefore exploit what are often tiny differences in the partitioning behaviour of sample molecules to achieve their efficient separation.
Figure 2.1. Partitioning of biomolecules in a two-phase system. Two components are represented by circles and squares, respectively. The two phases could be an aqueous buffer and a solid stationary phase. The two samples have very different partition coefficients in this experimental system.
2.1.2 Phase Systems Used in Biochemistry
In chromatographic systems used in biochemistry the stationary phase is made up of solid particles or of solid particles coated with liquid. In the former case, chemical groups are often covalently attached to the particles and this is called bonded phase liquid chromatography. In the latter case, a liquid phase may coat the particle and be attached by noncovalent, physical attraction. This type of system is called liquid–liquid phase chromatography. A good example of liquid–liquid phase chromatography is silica coated with a nonpolar hydrocarbon (e.g. C-18 reverse phase chromatography; Section 2.4.3). Commonly, the particles are composed of hydrated polymers such as cellulose or agarose. Such particles may be immobilized in a column (Section 2.3.1) and washed with mobile phase. They offer good flow characteristics and possess sufficient mechanical strength and chemical inertness for the chromatography of biomolecules. Because biomolecules have evolved to function in an aqueous environment, it is usually necessary to use aqueous buffers as the mobile phase if we require the molecule to retain its native structure (e.g. in the purification of active enzymes). If the native structure is not required, however, then it is possible to use more ‘nonbiological’ conditions such as organic solvents (e.g. in purification of peptides by reverse phase chromatography; Section 2.4.3).
liquid–solid or liquid–liquid phases are the most common phase systems used in biochemistry. However, in specialized situations other phases may be used. For example, gas-solid and gas-liquid phases are used in gas chromatography (GC; Section 2.1.4). Regardless of the precise phase composition, chromatographic separation is a direct result of the different K values of each sample component.
2.1.3 Liquid Chromatography
To minimize loss of biological activity, separations are often carried out in aqueous buffers below room temperature. Low temperatures are especially important in the chromatography of cell extracts during, for example, protein purification. This reduces protease activity which might otherwise destroy the protein of interest. Chromatography with liquid mobile phases is called liquid chromatography (LC).
LC uses an experimental system outlined in Figure 2.2. Separation takes place in a column which contains the stationary phase. The volume and shape of the column will depend on the amount of sample to be separated and on the mode of chromatography to be used. Buffer is stored in a reservoir and is pumped through tubing onto the column. Appropriate valves allow the convenient injection of sample into this flow or the formation of gradients with a second buffer if required. The stationary phase is packed in the column and, as the sample passes through the bed of stationary phase, separation occurs. In partition chromatography modes, the sample separates into individual components as it passes through the stationary phase (e.g. gel filtration; Section 2.4.2). In adsorption chromatography modes, however, it is necessary first to load the entire sample and later to fractionate it. A good example of adsorption chromatography is ion exchange chromatography where the sample components are eluted by means of a gradient of competing salt counterions after all the sample has been loaded onto and washed completely through the column (Sections 2.3.4 and 2.4.1). Separated sample components elute from the column and are detected. A typical LC separation is shown in Figure 2.3.
Figure 2.2. A typical liquid chromatography system. The direction of flow is shown by arrows. Sample is loaded via injection through a valve. If a large number of samples are required an autosampler may be used to reload the column repetitively after each chromatography.
2.1.4 Gas Chromatography
Many biomolecules are sensitive to high temperatures that can lead to destruction of structure and function (see Section 1.2.2). However, some molecules of importance in biochemistry may be converted to derivatives that are structurally stable, though volatile, in the temperature range 200–250°C. Good examples are trimethylsilated sterols and carbohydrates (esterified at their hydroxyl groups), and methylated esters of fatty acids. A second category of molecules (e.g. ethanol) is stable and volatile at somewhat lower temperatures without derivatization. Both of these groups of molecules may be analysed by gas chromatography (GC, also sometimes called gas-liquid chromatography; GLC). This is a form of partition chromatography in which a volatile sample is carried in an inert gas mobile phase (the carrier gas) such as nitrogen, helium or argon and applied to a narrow column (0.1 to 0.5 cm diameter) ranging in length from one to thirty meters that contains a liquid stationary phase. Sample is introduced to the system by injection from a syringe through a rubber septum into an injection port. This port is held approx. 10 °C above the column temperature to ensure efficient volatilization. The column is located in an oven that maintains a high temperature. Control of the temperature in this oven is crucial to successful chromatography and gradients of temperature may be used to achieve good separation. Because the sample components partition differently between the phases and because the column is so long, they separate efficiently from each other. The column may either be packed with solid particles coated with a liquid phase or it may be a capillary column in which the inner wall of the column itself is coated with liquid. The latter have much smaller inner diameters (e.g. 25 μm) and are generally longer (10–100 m) than packed columns.
Figure 2.3. A typical liquid chromatography experiment. This shows separation of a group of isoenzymes by ion exchange chromatography. A 0–100mM NaCl gradient (dashed line) is used with detection at 280 nm. This wavelength is often used to detect proteins. Note that peak 1 contains unbound material while proteins in peaks 2 to 4 are bound with progressively greater affinity.
Sample components may be detected using flame ionization, flame photometry or thermal conductivity detectors. In flame photometry detectors, the sample is combusted to produce electrons and other ions that produce an electric current while in flame photometry detectors the change in conductivity of a wire is altered by the sample. As with the injection port, detectors are held approx. 10°C above the temperature of the column. If the separated sample components are to be collected for further analysis (or for an interfaced method such as mass spectrometry; see Section 4.4.3), the carrier gas flow may be split before it enters the flame ionization detector.
Varying column temperature, gas flow and type of column may optimize GC separations.
2.2 PERFORMANCE PARAMETERS USED IN CHROMATOGRAPHY
Varied types (e.g. GC, LC) and modes (e.g. gel filtration, ion exchange) of chromatography are used in biochemistry. It is therefore very useful to be able to compare and quantify separations so that we can optimize them for a particular purpose. For example, in an analytical HPLC separation, we might wish to replace a particular column with one from a different manufacturer or with a slightly different stationary phase. The question would then arise, how effective is the new column compared to the old one? The yardsticks that allow us to make such comparisons we will call performance parameters.
2.2.1 Retention
When chromatography is carried out as described in Figures 2.2 and 2.3, the various sample components separate on the column because they are retained to different extents. We can describe this retention in terms of time (taking zero as the time of sample injection) or volume (calculated from volume at sample injection). These are called retention time (tR) and retention volume, (VR) respectively (seeFigure 2.4). We can interconvert these terms using Equation (2.2):
(2.2)
where tR is the retention time (min), VR the retention volume (ml) and f is the flow rate (ml/min). Under a single set of experimental conditions (temperature, column composition and dimensions, etc.), each component of the sample will have a characteristic retention (i.e. tR or VR) that can often be used to identify it in different samples. In general, retention is proportional to the length of the column used and is inversely proportional to the flow rate. Moreover, because the response of the detector usually relates to the concentration of the sample components, we can quantify each component by measuring their peak areas.
Figure 2.4. Retention in column chromatography. A typical chromatography trace showing the separation of two components; 1 and 2. The retention volumes of the components are shown by V1 and V2, respectively, while the base peak widths are denoted by W1 and W2. The void volume is denoted by V0.
Sample components move through the column more slowly than does mobile phase. We can therefore define a retardation factor (R.F.) for each component as follows:
(2.3)
where V denotes rate of movement.
Even if the sample did not adsorb onto or partition into the stationary phase, it would take a finite amount of time before it eluted from the column. The volume required for the injected solvent merely to pass, unretained, through the column and to be eluted is called the void or excluded volume (V0, seeFigure 2.4). This is the contained volume of the column, plus that of injection valve and tubing, minus the volume of the polymeric component of the column packing. Retention volumes greater than V0 are said to occur in the included volume and it is here that the sample may be fractionated.
2.2.2 Resolution
A sample chromatographic separation of two components of a mixture, 1 and 2, is shown in Figure 2.4. As the two peaks are ‘resolved’ from each other, we use the term resolution, R, to describe their separation. This important performance parameter in chromatography allows us to compare how effective a given column is in separating a mixture. R has a definite mathematical meaning (Equation (2.4)) that may be calculated from the trace shown in Figure 2.4:
(2.4)
W is the base width of the peak of each sample component of retention volume, V. It is clear from this equation that the best resolution chromatographies are those in which the peaks are narrow (i.e. small W) and well separated (e.g. large V2 – V1).
2.2.3 Physical Basis of Peak Broadening
If a sample of a single component is applied to a chromatography system in a small volume, it might be expected to elute in a very sharp peak of similar volume. This is not usually observed, however, due to a phenomenon called band broadening, that is the sample elutes in a much larger volume than that in which it was applied. The considerations summarized in Equation (2.4) indicate that this is a major factor in determining the R-value of a given chromatography column. To understand why some chromatography experiments achieve separation while others do not, it is necessary to understand the physical basis of band broadening. The applied sample may interact with the stationary phase, resulting in diffusion of the sample or it may become involved in mass transfer phenomena within the mobile or stationary phase. These are represented diagrammatically in Figure 2.5.
Eddy diffusion arises from a tendency of the mobile phase to experience eddies or local regions of circular flow similar to that observed in whirlpools. Mobile phase passes through channels in the stationary phase (usually composed of small particles) that will vary somewhat in size, some being wide and some narrow. Circular flow in narrow channels is generally slower than that in wide channels. Since sample will diffuse through a variety of channel sizes, it will be gradually distributed between fast-flowing, wide channels and slow-flowing, narrow channels. As a band of sample moves through the stationary phase it is broadened as a result of this diffusion.
Mass transfer phenomena arise from distribution of sample molecules within either the mobile or stationary phases. Mobile phase mass transfer occurs because mobile phase adjacent to the particle moves more slowly than mobile phase in the middle of the channel. This is due to frictional resistance to flow of the mobile phase by the particle.
Stagnant mobile phase mass transfer arises because different sample components enter channels that are not orientated in the same direction as the main flow through the column. These molecules are retained for varying amounts of time in the stagnant mobile phase in these channels. Therefore, the sample will be retained to varying extents. It is also possible for mass transfer to occur within the stationary phase in stationary phase mass transfer (i.e. for sample to enter the surface of the stationary phase).
2.2.4 Plate Height Equation
One way to envisage the chromatographic separation of a sample is mentally to divide the column into very thin, horizontal sections that we call theoretical plates. If we take a simple example of a two-component mixture in which the components have partition coefficients of 1 and 0.1, respectively, and follow how it behaves as it moves through a small number of succeeding plates we can easily see how separation depends on the difference in component partition coefficients (Example 2.1). The theoretical plate number, N, is an important performance indicator of a chromatography column and is directly related to the surface area of the particles of which the stationary phase is composed. It may be calculated from the relationship between a chromatography peak’s retention time, tR and width at its base, W, using Equation (2.5):
(2.5)
Figure 2.5. Physical causes of band broadening. (a) Eddy diffusion, (b)Mobile phase mass transfer, (c) Stagnant mobile phase mass transfer, (d) Stationary phase mass transfer. All of these may simultaneously contribute to broadening of the comparatively narrow initial bandwidth of applied sample.
The higher the value of N, the better the chromatographic performance we can expect to obtain from a column. This number may be compared between different columns and may even be used to compare bioseparations achieved in other types of experimental systems (e.g. electrophoretic separations; see Section 5.9.1). In practice, it may be difficult to measure W accurately so an alternative relationship may be used in which the peak width at half the peak height, Wh, is used (Equation (2.6)):
(2.6)
Two chromatography columns of different length (e.g. 15 and 30 cm) might contain the same number of theoretical plates (e.g. a typical 15 × 0.46 cm C-8 reverse phase column contains approx. 13 000 theoretical plates). Clearly, the shorter column would be regarded as giving better chromatographic performance. We can express the number of theoretical plates as a function of column length with the plate height number, H, also sometimes known as the height equivalent to a theoretical plate, HETP (Equation (2.7)):
(2.7)
where L is column length. The better the chromatographic performance of a column, the smaller this number should be. In our example of columns of 15 and 30 cm length, the H value of the former (1.15 μm) will be half that of the latter (2.3 μm).
