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[2] Optical spectroscopy: General principles and overview
[2]
OVERVIEW
OF OPTICAL
SPECTROSCOPY
13
[2] O p t i c a l S p e c t r o s c o p y : G e n e r a l P r i n c i p l e s a n d O v e r v i e w By IGNACIO TINOCO, JR. Introduction In this volume Section I focuses on the use of the absorbance and fluorescence of light to learn about structures and dynamics of biological macromolecules. Native states of proteins and nucleic acids can be distinguished from denatured states by measurement of the absorbance of unpolarized light. The ultraviolet absorbance of a double-stranded, or triplestranded, polynucleotide can be 20-30% less than that of the single strands. Helical polypeptides absorb significantly less in the amide absorbance region than coil polypeptides. This is the well-known hypochromicity caused by induced dipole-induced dipole interactions among the stacked bases of the nucleic acids, or among the helical array of the peptide bonds. Interactions among transition dipoles, which give rise to the hypochromicity, will be a recurring theme throughout this section. The absorbance of linearly polarized light reveals the orientation of chromophores and the interactions among them. Molecules can be partially oriented by flow, stretched films, compressed gels, or electric or magnetic films. Linear dichroism measures the orientation of the molecules and the arrangement of chromophores relative to the orientation axis. Alternatively, an unoriented sample can be prepared in an anisotropic state by excitation with a linearly polarized light pulse. The transient linear dichroism produced can reveal transfer of excitation among transition moments. This is especially useful for macromolecular structures with several similar chromophores, such as photosynthetic pigments. If right and left circularly polarized light is used, and the differential absorbance--the circular dichroism--is measured, the circular dichroism spectrum provides a very sensitive measure of conformation. Secondary structure elements, such as helices,/3 sheets, and turns in proteins, or double strands and loops in nucleic acids, can be quantitatively assessed. In nucleic acids, not only can one-, two-, and three-stranded structures be distinguished, but different conformations for each can be identified. The right-handed B-form typical of duplex DNA and the right-handed A-form typical of duplex RNA are easily distinguished. The left-handed Z-forms of both RNA and DNA have very different circular dichroism spectra from the right-handed forms. In general, circular dichroism is a very convenient way of following conformational changes in nucleic acids METHODS IN ENZYMOLOGY, VOL. 246
Copyright © 1995 by Academic Press, Inc. All rights of reproduction in any form reserved.
14
ULTRAVIOLET/VISIBLE SPECTROSCOPY
[9.]
as a function of base sequence and environmental conditions such as temperature, pH, and solvent. For proteins, circular dichroism in the amide absorption region from 230 to 180 nm is used to determine percent o~ helix, /3 sheet, /3 turns, and other. In addition to the amides, other chromophores in proteins, such as phenylalanine, tyrosine, tryptophan, and cystine, serve as specific probes for studying the folding of particular domains in a protein. Non-amino acid ligands which are part of the active site of a protein, or are cofactors in an enzymatic reaction, can also introduce useful chromophores into a protein. Only chiral structures--those different from their mirror images--differentially absorb circularly polarized light. However, in the presence of an external magnetic field all matter becomes chiral. Right and left circularly polarized light incident parallel to a magnetic field is differentially absorbed by all materials. This is magnetic circular dichroism; it can be especially helpful for studying transitions which involve magnetic moments in the ground or excited states. The kinetics and mechanisms of reactions can be studied by absorption and circular dichroism. Disappearance of reactants and formation of products provides rates and rate constants, but spectra of transient intermediates give valuable clues about mechanisms. Combination of rapid scanning spectroscopy with stopped-flow kinetic methods can characterize steps in enzyme-catalyzed reactions which occur on the millisecond time scale. Faster reactions (femtoseconds to nanoseconds) which occur, for example, in the first steps of visual excitation can be studied with pump-probe methods. A short pulse of light starts the reaction; a probe pulse detects and characterizes the time dependence of intermediates. Hole-burning spectroscopy in which a sharp laser pulse is used to excite a specific transition and thus remove a narrow region of an absorption spectrum can also be used to study kinetics of fast chemical and physical processes. As a complement to using fast detection methods for studying kinetics, the rates of reactions can be slowed by lowering the temperature. Thus, low temperature spectroscopy is a useful addition to the methods for characterizing biological reactions. Fluorescence adds a very powerful set of spectroscopic parameters to relate to structure and dynamics. The excitation spectrum (the absorption spectrum which leads to fluorescence at a chosen wavelength) and the fluorescence emission spectrum can identify and characterize fluorophores in complex mixtures. Time-resolved fluorescence spectra provide greater discrimination by introducing time as another variable. Fluorescence energy transfer measures the efficiency of transfer of excitation from a donor group to an acceptor group. The efficiency of transfer decreases with the inverse sixth power of the distance between
[2]
OVERVIEW OF OPTICAL SPECTROSCOPY
15
the groups. This clearly provides a sensitive and selective method of measuring distances in macromolecules. Often only qualitative information is very useful. For example, the kinetics of cleavage or ligation of a bond in a protein or nucleic acid can be monitored by the presence or absence of energy transfer. Use of polarized light to excite fluorescence, and measurement of the state of polarization of the emitted light introduce another set of measurable parameters that can characterize structures and dynamics of molecules. The anisotropy of the polarization of fluoresence after excitation by linearly polarized light provides the rotational diffusion coefficient, or rotational correlation time, of the fluorophore. When there is fluorescence energy transfer, analysis of the anisotropy of both donor and acceptor can reveal the relative orientation, and the relative motion. Measurement of fluorescence after excitation by circularly polarized light provides the fluorescence-detectedcircular dichroism. This measurement characterizes the chiral environment of the ground state of the fluorophore. If the circular polarization of the fluorescence is measured, the circularly polarized luminescence is obtained. This measurement characterizes the chirality of the excited state. Methods that use ultraviolet and visible light to learn about structures, dynamics, and therefore functions of biological molecules are presented in this section. The general theories are given, experimental methods are described, and specific applications are given to provide a good understanding of the wide range of methods available. Absorption and Circular Dichroism The application of absorption and circular dichroism spectra to the study of nucleic acids is discussed by Gray et al. [3]. Examples of the advantages of circular dichroism spectra over absorption spectra in analysis of the stoichiometry and structure of DNA, RNA, and hybrid duplexes and triplexes are given. Woody [4] defines circular dichroism and circular intensity differential scattering and describes the instrumentation to measure them. He relates the experimental properties to the rotational strength, namely, the product of the electric dipole transition moment and the magnetic dipole transition moment. The main applications are to secondary and tertiary structures of proteins, protein folding, and protein-ligand interactions. The special problems of proteins in membranes are assessed. Applications not considered by Gray et al. in [3] to nucleic acids, such as binding of small molecule ligands and protein-nucleic acid complexes, are also discussed.
16
U L T R A V I O L E T / V I S I BSPECTROSCOPY LE
[2]
Solomon et al. [5] consider the application of the spectroscopic methods described in this book to metalloproteins. The emphasis is on understanding function by determining metal ion geometry and electronic structure, particularly in d n electronic configurations. The fundamentals of crystal field theory (electrostatic interactions between the d orbitals and the ligands) and ligand field theory (including all types of interactions) are reviewed first. This provides a theoretical basis for understanding the geometry of a complex in the ground state, and for interpreting the d d transitions. The mechanism of the nonheme iron enzyme metapyrocatechase, which catalyzes the oxidation of catechol, is discussed. Circular dichroism, magnetic circular dichroism, electron paramagnetic resonance, and M6ssbauer studies are used to establish the structure of the metal site and to understand its interaction with various ligands. The theory and practice of magnetic circular dichroism is presented by Sutherland [6]. Natural circular dichroism, which requires a chiral structure, is most useful for studying the overall conformation of a protein or nucleic acid. Magnetic circular dichroism is most useful in studying the individual peptides, amino acid chromophores, or nucleic acid bases. Instrumentation and applications are described for each region of the spectrum from the infrared to the X-ray (10/zm to 10 nm). Metalloproteins in general and those containing porphyrins in particular are the most usually studied. Interpretations of the magnetic circular dichroism spectra in terms of their shapes compared to the absorption spectra are described. A method which can be used to give complementary information about conformations and kinetics is low temperature spectroscopy described by Austin and Shyamsunder [7]. Experimental methods for measuring absorption and fluorescence, theoretical principles involved in their interpretation, and recombination kinetics of carbon monoxide and other ligands with the heme iron in myoglobin are discussed. Transient Absorption and Kinetics Measurements of absorption as a function of time can provide a wide range of useful information. Brzovid and Dunn [8] describe instrumentation for measuring the time dependence of absorption spectra after rapid mixing of reactants. Several rapid-scanning stopped-flow instruments are commercially available; reactions that take place in a millisecond or longer can be studied. Enzyme-catalyzed reactions with natural chromophores, such as NADH, are discussed, and the substitution of a colored metal center [Co(II)] for a colorless one [Zn(II)] are also described. Detailed mechanistic conclusions for horse liver alcohol dehydrogenase (LADH) are given. Van Amerongen and van Grondelle [9] describe pump-probe methods
[2]
OVERVIEW OF OPTICAL SPECTROSCOPY
17
for studying processes that occur in the range of femtoseconds or slower. After an intense short pulse of light (the pump) is incident on the sample, the changes in absorption can be followed by probe pulses. These changes are due to loss of ground state species, production of excited state species, production of new molecules, or the influence of the excitation on neighboring chromophores. Instrumentation for slow (nano- to millisecond) and fast (femto- to nanosecond) time regimes are described. Study of the efficient transfer of excitation from antenna pigments to the photosynthetic reaction center, where charge separation occurs, represents a useful application of transient absorption measurements. Hole burning, reviewed by Friedrich [ 10], is the decrease in absorbance in a narrow wavelength region of a spectrum caused by an intense laser pulse. As in the pump-probe experiments, the change in absorbance can be caused by the depletion of a ground state species. In a broad spectrum caused by chromophores in slightly different environments, that is, an inhomogeneously broadened spectrum, one of the chromophores can be specifically excited, causing a sharp dip in the broad spectrum. Friedrich discusses the theoretical and experimental aspects of the method and concentrates on two applications: photosynthesis and protein physics. The first conclusive evidence for the presence of coherent, exciton-like states in the antenna pigments of photosynthetic species came from holeburning experiments. Coherent and incoherent energy transfer are both very important in photosynthesis. The many conformational states that a protein can exit in at equilibrium means that the free energy minimum is actually a broad, rough trough with many local minima. Hole burning is an excellent way of detecting these slightly different conformations, and of measuring rates of interconversion. Linear Dichroism and Fluorescence Van Amerongen and Struve [11] give a thorough theoretical analysis of spectroscopy using linearly polarized light. They consider unoriented samples which are prepared in an anisotropic excited state by absorption of linearly polarized light. The state can be investigated by a polarized probe pulse or by the polarization of emitted fluorescent light. Samples that are partially oriented by compression or expansion of gels, by stretching of films, or by external electric or magnetic fields can also be studied by polarized absorption and emission. The linear dichroism and fluorescence anisotropy methods reveal the orientations of ground state and excited state transition moments, and the interactions among them. Coherent and incoherent states are possible; their properties are very different. With geland film-oriented samples the orientation of transition dipoles relative to molecular shapes are obtained. The permanent dipole vector, the electric
18
ULTRAVIOLET/VISIBLE SPECTROSCOPY
[2]
polarizability tensor, and the magnetic susceptibility tensor are key for orientation by electric and magnetic fields. Clearly, a vast amount of useful data can be obtained about macromolecules and macromolecular assemblies. Applications of fluorescence anisotropy to study macromolecular interactions is described by Jameson and Sawyer [12]. The measured anisotropy defined as r = Itl - I± Iii + 2 I .
where Ill is the intensity of fluorescent light parallel to incident polarization and Iz is the intensity of fluorescent light perpendicular to incident polarization, is independent of concentration. This greatly simplifies the analysis of mixtures of species because the measured anisotropy is a weighted sum of the contribution from each component. Binding isotherms for use in Scatchard plots, for example, are directly obtained. Studies of interactions of proteins with small ligands, peptides, other proteins, and nucleic acids have been done. Nucleic acids can be studied if extrinsic fluorophores are added. Hydrodynamic properties in the form of diffusion coefficients of the molecules and their complexes can be obtained from the magnitudes of the anisotropies. Selvin [13] reviews fluorescence resonance energy transfer and its use as a molecular ruler. He provides a thorough discussion of the theory with emphasis on understanding the concepts. The effect of each molecular variable on the apparent donor-acceptor distance is assessed; this leads to the conclusion that the method is best for relative distances. Criteria for choosing dyes for the fluorescence energy measurement are given. The advantages and disadvantages of the various methods which have been used to measure transfer efficiency are discussed. The methods include decreases in fluorescence, lifetime, or photobleaching of the donor and increases in fluorescence of the acceptor. A wide range of applications is described including the structure of four-way junctions in DNA, the kinetics of protease cleavage of a vital human immunodeficiency virus (HIV) protein, and the measurement of translational diffusion rates. Holzwarth [14] describes techniques for measuring and analyzing timeresolved fluorescence; he discusses applications to dynamics of proteins, nucleic acids, and membranes. Time-resolved two-dimensional microscopic images show promise of revealing detailed information about the location and motions of fluorophores in ceils. The article by Waggoner [15] is pertinent for everyone who uses fluorescence in research. It describes criteria for choosing a fluorophore for labeling a biomolecule, and gives detailed protocols for labeling proteins and nucleic acids.
OVERVIEW
OF OPTICAL
SPECTROSCOPY
13
[2] O p t i c a l S p e c t r o s c o p y : G e n e r a l P r i n c i p l e s a n d O v e r v i e w By IGNACIO TINOCO, JR. Introduction In this volume Section I focuses on the use of the absorbance and fluorescence of light to learn about structures and dynamics of biological macromolecules. Native states of proteins and nucleic acids can be distinguished from denatured states by measurement of the absorbance of unpolarized light. The ultraviolet absorbance of a double-stranded, or triplestranded, polynucleotide can be 20-30% less than that of the single strands. Helical polypeptides absorb significantly less in the amide absorbance region than coil polypeptides. This is the well-known hypochromicity caused by induced dipole-induced dipole interactions among the stacked bases of the nucleic acids, or among the helical array of the peptide bonds. Interactions among transition dipoles, which give rise to the hypochromicity, will be a recurring theme throughout this section. The absorbance of linearly polarized light reveals the orientation of chromophores and the interactions among them. Molecules can be partially oriented by flow, stretched films, compressed gels, or electric or magnetic films. Linear dichroism measures the orientation of the molecules and the arrangement of chromophores relative to the orientation axis. Alternatively, an unoriented sample can be prepared in an anisotropic state by excitation with a linearly polarized light pulse. The transient linear dichroism produced can reveal transfer of excitation among transition moments. This is especially useful for macromolecular structures with several similar chromophores, such as photosynthetic pigments. If right and left circularly polarized light is used, and the differential absorbance--the circular dichroism--is measured, the circular dichroism spectrum provides a very sensitive measure of conformation. Secondary structure elements, such as helices,/3 sheets, and turns in proteins, or double strands and loops in nucleic acids, can be quantitatively assessed. In nucleic acids, not only can one-, two-, and three-stranded structures be distinguished, but different conformations for each can be identified. The right-handed B-form typical of duplex DNA and the right-handed A-form typical of duplex RNA are easily distinguished. The left-handed Z-forms of both RNA and DNA have very different circular dichroism spectra from the right-handed forms. In general, circular dichroism is a very convenient way of following conformational changes in nucleic acids METHODS IN ENZYMOLOGY, VOL. 246
Copyright © 1995 by Academic Press, Inc. All rights of reproduction in any form reserved.
14
ULTRAVIOLET/VISIBLE SPECTROSCOPY
[9.]
as a function of base sequence and environmental conditions such as temperature, pH, and solvent. For proteins, circular dichroism in the amide absorption region from 230 to 180 nm is used to determine percent o~ helix, /3 sheet, /3 turns, and other. In addition to the amides, other chromophores in proteins, such as phenylalanine, tyrosine, tryptophan, and cystine, serve as specific probes for studying the folding of particular domains in a protein. Non-amino acid ligands which are part of the active site of a protein, or are cofactors in an enzymatic reaction, can also introduce useful chromophores into a protein. Only chiral structures--those different from their mirror images--differentially absorb circularly polarized light. However, in the presence of an external magnetic field all matter becomes chiral. Right and left circularly polarized light incident parallel to a magnetic field is differentially absorbed by all materials. This is magnetic circular dichroism; it can be especially helpful for studying transitions which involve magnetic moments in the ground or excited states. The kinetics and mechanisms of reactions can be studied by absorption and circular dichroism. Disappearance of reactants and formation of products provides rates and rate constants, but spectra of transient intermediates give valuable clues about mechanisms. Combination of rapid scanning spectroscopy with stopped-flow kinetic methods can characterize steps in enzyme-catalyzed reactions which occur on the millisecond time scale. Faster reactions (femtoseconds to nanoseconds) which occur, for example, in the first steps of visual excitation can be studied with pump-probe methods. A short pulse of light starts the reaction; a probe pulse detects and characterizes the time dependence of intermediates. Hole-burning spectroscopy in which a sharp laser pulse is used to excite a specific transition and thus remove a narrow region of an absorption spectrum can also be used to study kinetics of fast chemical and physical processes. As a complement to using fast detection methods for studying kinetics, the rates of reactions can be slowed by lowering the temperature. Thus, low temperature spectroscopy is a useful addition to the methods for characterizing biological reactions. Fluorescence adds a very powerful set of spectroscopic parameters to relate to structure and dynamics. The excitation spectrum (the absorption spectrum which leads to fluorescence at a chosen wavelength) and the fluorescence emission spectrum can identify and characterize fluorophores in complex mixtures. Time-resolved fluorescence spectra provide greater discrimination by introducing time as another variable. Fluorescence energy transfer measures the efficiency of transfer of excitation from a donor group to an acceptor group. The efficiency of transfer decreases with the inverse sixth power of the distance between
[2]
OVERVIEW OF OPTICAL SPECTROSCOPY
15
the groups. This clearly provides a sensitive and selective method of measuring distances in macromolecules. Often only qualitative information is very useful. For example, the kinetics of cleavage or ligation of a bond in a protein or nucleic acid can be monitored by the presence or absence of energy transfer. Use of polarized light to excite fluorescence, and measurement of the state of polarization of the emitted light introduce another set of measurable parameters that can characterize structures and dynamics of molecules. The anisotropy of the polarization of fluoresence after excitation by linearly polarized light provides the rotational diffusion coefficient, or rotational correlation time, of the fluorophore. When there is fluorescence energy transfer, analysis of the anisotropy of both donor and acceptor can reveal the relative orientation, and the relative motion. Measurement of fluorescence after excitation by circularly polarized light provides the fluorescence-detectedcircular dichroism. This measurement characterizes the chiral environment of the ground state of the fluorophore. If the circular polarization of the fluorescence is measured, the circularly polarized luminescence is obtained. This measurement characterizes the chirality of the excited state. Methods that use ultraviolet and visible light to learn about structures, dynamics, and therefore functions of biological molecules are presented in this section. The general theories are given, experimental methods are described, and specific applications are given to provide a good understanding of the wide range of methods available. Absorption and Circular Dichroism The application of absorption and circular dichroism spectra to the study of nucleic acids is discussed by Gray et al. [3]. Examples of the advantages of circular dichroism spectra over absorption spectra in analysis of the stoichiometry and structure of DNA, RNA, and hybrid duplexes and triplexes are given. Woody [4] defines circular dichroism and circular intensity differential scattering and describes the instrumentation to measure them. He relates the experimental properties to the rotational strength, namely, the product of the electric dipole transition moment and the magnetic dipole transition moment. The main applications are to secondary and tertiary structures of proteins, protein folding, and protein-ligand interactions. The special problems of proteins in membranes are assessed. Applications not considered by Gray et al. in [3] to nucleic acids, such as binding of small molecule ligands and protein-nucleic acid complexes, are also discussed.
16
U L T R A V I O L E T / V I S I BSPECTROSCOPY LE
[2]
Solomon et al. [5] consider the application of the spectroscopic methods described in this book to metalloproteins. The emphasis is on understanding function by determining metal ion geometry and electronic structure, particularly in d n electronic configurations. The fundamentals of crystal field theory (electrostatic interactions between the d orbitals and the ligands) and ligand field theory (including all types of interactions) are reviewed first. This provides a theoretical basis for understanding the geometry of a complex in the ground state, and for interpreting the d d transitions. The mechanism of the nonheme iron enzyme metapyrocatechase, which catalyzes the oxidation of catechol, is discussed. Circular dichroism, magnetic circular dichroism, electron paramagnetic resonance, and M6ssbauer studies are used to establish the structure of the metal site and to understand its interaction with various ligands. The theory and practice of magnetic circular dichroism is presented by Sutherland [6]. Natural circular dichroism, which requires a chiral structure, is most useful for studying the overall conformation of a protein or nucleic acid. Magnetic circular dichroism is most useful in studying the individual peptides, amino acid chromophores, or nucleic acid bases. Instrumentation and applications are described for each region of the spectrum from the infrared to the X-ray (10/zm to 10 nm). Metalloproteins in general and those containing porphyrins in particular are the most usually studied. Interpretations of the magnetic circular dichroism spectra in terms of their shapes compared to the absorption spectra are described. A method which can be used to give complementary information about conformations and kinetics is low temperature spectroscopy described by Austin and Shyamsunder [7]. Experimental methods for measuring absorption and fluorescence, theoretical principles involved in their interpretation, and recombination kinetics of carbon monoxide and other ligands with the heme iron in myoglobin are discussed. Transient Absorption and Kinetics Measurements of absorption as a function of time can provide a wide range of useful information. Brzovid and Dunn [8] describe instrumentation for measuring the time dependence of absorption spectra after rapid mixing of reactants. Several rapid-scanning stopped-flow instruments are commercially available; reactions that take place in a millisecond or longer can be studied. Enzyme-catalyzed reactions with natural chromophores, such as NADH, are discussed, and the substitution of a colored metal center [Co(II)] for a colorless one [Zn(II)] are also described. Detailed mechanistic conclusions for horse liver alcohol dehydrogenase (LADH) are given. Van Amerongen and van Grondelle [9] describe pump-probe methods
[2]
OVERVIEW OF OPTICAL SPECTROSCOPY
17
for studying processes that occur in the range of femtoseconds or slower. After an intense short pulse of light (the pump) is incident on the sample, the changes in absorption can be followed by probe pulses. These changes are due to loss of ground state species, production of excited state species, production of new molecules, or the influence of the excitation on neighboring chromophores. Instrumentation for slow (nano- to millisecond) and fast (femto- to nanosecond) time regimes are described. Study of the efficient transfer of excitation from antenna pigments to the photosynthetic reaction center, where charge separation occurs, represents a useful application of transient absorption measurements. Hole burning, reviewed by Friedrich [ 10], is the decrease in absorbance in a narrow wavelength region of a spectrum caused by an intense laser pulse. As in the pump-probe experiments, the change in absorbance can be caused by the depletion of a ground state species. In a broad spectrum caused by chromophores in slightly different environments, that is, an inhomogeneously broadened spectrum, one of the chromophores can be specifically excited, causing a sharp dip in the broad spectrum. Friedrich discusses the theoretical and experimental aspects of the method and concentrates on two applications: photosynthesis and protein physics. The first conclusive evidence for the presence of coherent, exciton-like states in the antenna pigments of photosynthetic species came from holeburning experiments. Coherent and incoherent energy transfer are both very important in photosynthesis. The many conformational states that a protein can exit in at equilibrium means that the free energy minimum is actually a broad, rough trough with many local minima. Hole burning is an excellent way of detecting these slightly different conformations, and of measuring rates of interconversion. Linear Dichroism and Fluorescence Van Amerongen and Struve [11] give a thorough theoretical analysis of spectroscopy using linearly polarized light. They consider unoriented samples which are prepared in an anisotropic excited state by absorption of linearly polarized light. The state can be investigated by a polarized probe pulse or by the polarization of emitted fluorescent light. Samples that are partially oriented by compression or expansion of gels, by stretching of films, or by external electric or magnetic fields can also be studied by polarized absorption and emission. The linear dichroism and fluorescence anisotropy methods reveal the orientations of ground state and excited state transition moments, and the interactions among them. Coherent and incoherent states are possible; their properties are very different. With geland film-oriented samples the orientation of transition dipoles relative to molecular shapes are obtained. The permanent dipole vector, the electric
18
ULTRAVIOLET/VISIBLE SPECTROSCOPY
[2]
polarizability tensor, and the magnetic susceptibility tensor are key for orientation by electric and magnetic fields. Clearly, a vast amount of useful data can be obtained about macromolecules and macromolecular assemblies. Applications of fluorescence anisotropy to study macromolecular interactions is described by Jameson and Sawyer [12]. The measured anisotropy defined as r = Itl - I± Iii + 2 I .
where Ill is the intensity of fluorescent light parallel to incident polarization and Iz is the intensity of fluorescent light perpendicular to incident polarization, is independent of concentration. This greatly simplifies the analysis of mixtures of species because the measured anisotropy is a weighted sum of the contribution from each component. Binding isotherms for use in Scatchard plots, for example, are directly obtained. Studies of interactions of proteins with small ligands, peptides, other proteins, and nucleic acids have been done. Nucleic acids can be studied if extrinsic fluorophores are added. Hydrodynamic properties in the form of diffusion coefficients of the molecules and their complexes can be obtained from the magnitudes of the anisotropies. Selvin [13] reviews fluorescence resonance energy transfer and its use as a molecular ruler. He provides a thorough discussion of the theory with emphasis on understanding the concepts. The effect of each molecular variable on the apparent donor-acceptor distance is assessed; this leads to the conclusion that the method is best for relative distances. Criteria for choosing dyes for the fluorescence energy measurement are given. The advantages and disadvantages of the various methods which have been used to measure transfer efficiency are discussed. The methods include decreases in fluorescence, lifetime, or photobleaching of the donor and increases in fluorescence of the acceptor. A wide range of applications is described including the structure of four-way junctions in DNA, the kinetics of protease cleavage of a vital human immunodeficiency virus (HIV) protein, and the measurement of translational diffusion rates. Holzwarth [14] describes techniques for measuring and analyzing timeresolved fluorescence; he discusses applications to dynamics of proteins, nucleic acids, and membranes. Time-resolved two-dimensional microscopic images show promise of revealing detailed information about the location and motions of fluorophores in ceils. The article by Waggoner [15] is pertinent for everyone who uses fluorescence in research. It describes criteria for choosing a fluorophore for labeling a biomolecule, and gives detailed protocols for labeling proteins and nucleic acids.