In Section 13.1.3 we have already seen that electromagnetic radiation oscillates in all possible directions and that it is possible to preferentially select waves oscillating in a single plane, as applied for fluorescence polarisation. The phenomenon first known as mutarotation (described by Lowry in 1898) became manifest in due course as a special property of optically active isomers allowing the rotation of plane-polarised light. Optically active isomers are compounds of identical chemical composition and topology, but whose mirror images cannot be superimposed; such compounds are called chiral.
Polarimetry and Optical Rotatory Dispersion
Polarimetry essentially measures the angle through which the plane of polarisation is changed after linearly polarised light is passed through a solution containing a chiral substance. Optical rotatory dispersion (ORD) spectroscopy is a technique that measures this ability of a chiral substance to change the plane-polarisation as a function of the wavelength. The angle α between the plane of the resulting linearly polarised light against that of the incident light is dependent on the refractive index for left ( nleft ) and right ( nright ) circularly polarised light (Figure 1). The refractive index can be calculated as the ratio of the speed of light in vacuo and the speed of light in matter. After normalisation against the amount of substance present in the sample (thickness of sample/cuvette length d , and mass concentration ρ*), a substance-specific constant [α] is obtained that can be used to characterise chiral compounds.
Fig1. (a) Linearly polarised light can be thought of consisting of two circularly polarised components with opposite ‘handedness’. The vector sum of the left- and right-handed circularly polarised light yields linearly polarised light. The angle α defi nes the angle between the plane of the incident light and the plane of the resulting polarised light (a consequence of the phenomenon of optical rotatory dispersion). (b) If the amplitudes of left- and right-handed polarised components differ, the resulting light is elliptically polarised. The composite vector will trace the ellipse shown in grey. The ellipse is characterised by a major and a minor axis. The ratio of minor and major axis yields tan Θ, where Θ is called the ellipticity.
Circular Dichroism
In addition to changing the plane of polarisation, an optically active sample also shows unusual absorption behaviour. Left- and right-handed polarised components of the incident light are absorbed differently by the sample, which yields a difference in the absorption coefficients ∆ε = ε left − ε right . This difference is called circular dichroism (CD). The difference in absorption coefficients ∆ε (i.e. CD) is measured in units of dm3 mol–1 cm−1, and is the observed quantity in CD experiments. Frequently, results from protein CD experiments are reported as ellipticity θ ( Figure1). Normalisation of θ similar to the ORD yields the molar ellipticity:
It is common practice to display graphs of CD spectra with the molar ellipticity θ in units of 1° cm2 dmol−1 = 10° cm2 mol−1 on the abscissa (Figure 2). Three important conclusions can be drawn:
1. ORD and CD are the manifestation of the same underlying phenomenon
2. If an optically active molecule has a positive CD, then its enantiomer will have a negative CD of exactly the same magnitude
3. The phenomenon of CD can only be observed at wavelengths where the optically active molecule has an absorption band.
Fig2. Circular dichroism spectra for three standard secondary structures according to Fasman. An α-helical peptide is shown in turquoise, a peptide adopting β-strand (extended) structure in magenta, and a random coil peptide in green.
The Chromophores of Protein Secondary Structure
In Section 13.2.1 , we saw that the peptide bond in proteins possesses UV absorption bands in the area of 190–220 nm. The carbon atom vicinal to the peptide bond (the Cα atom) is asymmetric and a stereogenic centre in all amino acids except glycine. This chirality induces asymmetry into the peptide bond chromophore. Because of the serial arrangement of the peptide bonds making up the backbone of a protein, the individual chromophores couple with each other. The (secondary) structure of a poly peptide thus induces an ‘overall chirality’ which gives rise to the CD phenomenon of a protein in the wavelength interval 190–260 nm.
With protein circular dichroism, the molar ellipticity θ is typically normalised further with respect to the number of residues to yield the mean residue ellipticity θ res (also called MRE), owing to the fact that the chromophores responsible for the chiral absorption phenomenon are the peptide bonds. Therefore, the number of chromophores of a polypeptide in this context is equal to the number of residues less one. Because of the Beer–Lambert law, the number of chromophores is proportional to the magnitude of absorption, i.e. in order to normalise the spectrum of an individual polypeptide for reasons of comparison, the CD has to be scaled by the number of peptide bonds.
