Circular Dichroism (CD)

Theory

Circular dichroism is a chiroptical technique which is similar to optical rotatory dispersion (ORD). These methods measure the wavelength dependence of the ability of an optically active chromophore to rotate plane-polarized light (ORD) and the differential absorption of right and left circularly polarized light (CD). Light is an electromagnetic wave consisting of an oscillating electric (E) field and a magnetic (H) field, both of which can be represented by mutually perpendicular vectors. The plane of polarization is defined as the plane of the E vector. Because a light source usually consists of a collection of randomly oriented emitters, the emitted light is a collection of waves with all possible orientations of the E vectors. Plane-polarized light is usually obtained by passing light through an object that transmits light with only a single plane of polarization.

Suppose that two plane-polarized waves differing in phase by one-quarter wavelength (i.e., when one sine curve crosses the axis of propagation, the other is at a maximum or minimum), whose E vectors are perpendicular to one another, are superimposed. As the waves propagate forward, the result E vector rotates so that its tip follows a helical path. This is also true of the magnetic field vector. Such a light is called circularly polarized and is defined as right circularly polarized if the E vector rotates clockwise to an observer looking at the source.

If a right (R) and a left (L) circularly polarized wave, both of equal amplitude, are superimposed, the result is plane-polarized light, because at any point in space the E vector of each will sum as shown in Figure 3.7A. Similarly, plane-polarized light can be decomposed into R and L components. If the amplitudes of the two circularly polarized waves are not the same, the tip of the resultant E vector will follow an elliptical path and such light is said to be elliptically polarized (Figure 3.7B).

Figure 3.7: Diagrams showing how right and left circularly polarized light combine:(A) if the two waves have the same amplitude, the result is plane-polarized light; and (B) if their amplitudes differ, the result is elliptically polarized light with a and b as their major and minor axes.

A parameter called the ellipticity, , is often used to describe the elliptical polarization. This is the angle whose tangent is the ratio of the minor and major axes of the ellipse shown in Figure 3.7B - that is, When a beam of light (i.e, a propagating electromagnetic field) passes through matter, the electric (E) vector of the propagating wave interacts with the electrons of the component atoms. This interaction has the effect of reducing the velocity of propagation (also called retarding the light) and in decreasing the amplitude of the E vector. Reducing the velocity of propagation is called refraction and is described by the index of refraction, n, and decreasing the amplitude of the E vector is absorption and is described by the molar absorption coefficient, . Both n and depend on wavelength in a way that reflects the electronic structure and geometry of the molecules.

For most substances, simple refraction and absorption are the only detectable result of such an interaction even if the light is polarized. However, the behavior of some molecules is sensitive to the plane of polarization of the incident light. Such a molecule or chromophore is called optically active and is characterized by having distinct indices of refraction, nL and nR, and molar absorption coefficients, and , for left and right circularly polarized light, respectively. The property that determines whether a chromophore is optically active is its asymmetry. If a molecule is asymmetric in the sense that it cannot be superimposed on its mirror image, it is optically active. If a substance retards both L and R equally (i.e., if the indices of refraction for L and R circularly polarized light, nL and nR, are the same), the L and R waves will recombine on leaving the substance to form plane-polarized light, with the plane of the transmitted beam being the same as that of the incident beam. However, if nL and nR are unequal, the transmitted L and R components are each retarded to a different extent so that on leaving the material the phases of the two sine waves differ (Figure 3.8). Henceforth, at any point in space, the E vectors of the L and R waves combine to form a beam of plane-polarized light whose angle differs from that of the plane of polarization of the incident wave; hence, the plane of polarization of the resulting wave will be rotated. For any substance that interacts in this asymmetric way, the extent of the rotation produced by a sample of a given volume depends on the number of chromophores with which the wave interacts - that is, on the concentration of the molecules multiplied by the path length, d, and on the wavelength, , of the light - because n is always a function of .

Figure 3.8: Rotation of the plane of polarization; (A) both right and left circularly polarized light are retarded equally so that the resultant E vector remains in the same plane; (B) the left circularly polarized light is retarded more than the right so that the resultant E vector changes orientation (Because the amount of retardation is proportional to the distance the light travels, the E vector will rotate clockwise with increasing optical pathlength).

So far, only the retardation of R and L waves has been considered, but it is also of interest to know what happens to the intensity of each as these waves pass through matter. If the substance is optically inactive, the absorption of each is equal. If, on the other hand, the material is optically active, then in the range of wavelengths in which absorption occurs, there will be, for each wavelength, differential absorption of L and R circularly polarized light. This difference is usually expressed in terms of the absorption coefficients for L and R light, eL and eR; that is,

eL - eR = (e

in which (e is called the circular dichroism, or CD. It is positive if eL - eR > 0 and negative if eL - eR < 0. If a given optically active molecule has positive CD, then its mirror image will have a negative CD of precisely the same magnitude. It is useful to see the relation between an ordinary dispersion curve (i.e., the index of refraction, n, versus wavelength, l), the ORD curve (which is , in fact, (n = nL - nR versus l), a standard absorption curve (e versus l), and a CD curve ((e = eL - eR

For CD measurements, in principle two light sources are needed, one for L and the other for R circularly polarized light, each provided with a monochromator for wavelength selection. However, L and R light may be generated from a single source by passing plane-polarized light through a crystal that is subjected to an alternating electric field. This crystal (called an electrooptic modulator) has the remarkable property that the polarity of the field determines whether the L or R component of the light is transmitted. Because the field is alternating current, the beam continually modulates from the production of L to the production of R light. This beam then passes through the sample cell followed by a photomultiplier which produces a voltage that is proportional to the ellipticity. The ellipticity q is automatically plotted as a function of wavelength to give the CD spectrum.

The theory of optical activity is not yet capable of yielding the precise structure of a protein from its CD spectrum. The complications are that the chromophore is asymmetrically perturbed by neighbouring groups; the peptide bond (which is the principal element whose spectrum is detected by CD) exists in many conformations depending on its precise location in the protein, and the spectrum is a result of an average of the various conformation parameters.

Hence, in practice, an empirical approach of obtaining an ORD or CD spectrum for molecules whose structure is accurately known from X-ray diffraction is used, and the spectrum is related to the structural features of the molecule. This spectrum is then compared with the spectrum of a protein of unknown structure. Because of the lack of adequate theory, the approach to the elucidation of the secondary structure of a protein has been to determine empirically ORD or CD curves for model polypeptides. (A model polypeptide has only a single conformation and its structure is known from X-ray scattering). Then an attempt is made to construct from these 'standard' curves a weighted sum that is the same as the observed curve of the sample. For proteins, the principal standards are three forms of poly-L-lysine: a-helix, b-sheet, and the random coil. The concept of using poly-L-lysine was first demonstrated by Holzwarth and Doty (1965). Yang and coworkers developed computational methods for fitting the entire spectrum of a protein to a weighted sum of the three major secondary structure spectra based on a poly-L-lysine reference set (Yang et al., 1986). While this method provides good estimates of secondary structure, it ignores the contributions of other chiral components of proteins, such as the aromatic amino acids, that contribute to the far UV CD spectrum. For this reason several groups have developed reference sets based on the CD spectra of proteins whose secondary structure is well known from crystallographic data. Chen and Yang (1971), developed a reference set based on five proteins, while Chang et al. (1978) used a total of 15 proteins to develop their reference spectra. The use of a protein based reference set provides slightly better estimates of secondary structure for globular proteins, and has the added advantage of allowing one to estimate beta turn content as well as the three major secondary structural types. Figures 3.9 and 3.10 show the major CD spectra associated with various secondary structures.

Figure 3.9: CD spectra associated with various secondary structures: a-helix( ___ ), anti-parallel b-sheet (----), b-turn type I (......), left handed extended 31-helix (-l-l-), irregular structure (----). Redrawn from Brahms and Brahms (1980); Drake et al. (1988).

Figure 3.10: The major secondary structure classes and their associated CD spectra.


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