Circular dichroism

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Circular dichroism (CD), is the differential absorption of left- and right-handed circularly polarized light. It is a form of spectroscopy used to determine the optical isomerism and secondary structure of molecules.

[edit] Derivation of ellipticity

At a given wavelength,

where ΔA is the difference between absorbance of left circularly polarized (LCP) and right circularly polarized (RCP) light (this is what is usually measured).

It can also be expressed, by applying Beer's law, as:

where

ε_L and ε_R are the molar extinction coefficients for RCP and LCP light,

C is the molar concentration

l is the path length in centimeters (cm).

Then

is the molar circular dichroism. This is what is usually meant by the circular dichroism of the substance. Although ΔA is usually measured, for historical reasons most measurements are reported in degrees of ellipticity. Molar circular dichroism and molar ellipticity, [θ], are readily interconverted by the equation:

Elliptical polarized light (purple) is composed of unequal contributions of right (blue) and left (red) circular polarized light.

.

This relationship is derived by defining the ellipticity of the polarization as:

where

E_R and E_L are the magnitudes of the electric field vectors of the right-circularly and left-circularly polarized light, respectively.

When E_R equals E_L (when there is no difference in the absorbance of right- and left-circular polarized light), θ is 0° and the light is linearly polarized. When either E_R or E_L is equal to zero (when there is complete absorbance of the circular polarized light in one direction), θ is 45° and the light is circularly polarized.

Generally, the circular dichroism effect is small, so tanθ is small and can be approximated as θ in radians. Since the intensity or irradiance, I, of light is proportional to the square of the electric-field vector, the ellipticity becomes:

Then by substituting for I using Beer's Law in natural logarithm form:

The ellipticity can now be written as:

Since ΔA<<1, this expression can be approximated by expanding the exponentials in a Taylor series to first-order and then discarding terms of ΔA in comparison with unity and converting from radians to degrees:

The linear dependence of solute concentration and pathlength is removed by defining molar ellipticity as,

Then combining the last two expression with Beer's Law, molar ellipticity becomes:

[edit] Application to biological molecules

In general, this phenomenon will be exhibited in absorption bands of any optically active molecule. As a consequence, circular dichroism is exhibited by biological molecules, because of the dextrorotary (e.g. some sugars) and levorotary (e.g. some amino acids) molecules they contain. Noteworthy as well is that a secondary structure will also impart a distinct CD to its respective molecules. Therefore, the alpha helix of proteins and the double helix of nucleic acids have CD spectral signatures representative of their structures.

CD is closely related to the optical rotatory dispersion (ORD) technique, and is generally considered to be more advanced. CD is measured in or near the absorption bands of the molecule of interest, while ORD can be measured far from these bands. In principle these two spectral measurements can be interconverted through an integral transform, if all the absorptions are included in the measurements.

The ultraviolet CD spectrum of proteins can predict important characteristics of their secondary structure. CD spectra can be readily used to estimate the fraction of a molecule that is in the alpha-helix conformation, the beta-sheet conformation, the beta-turn conformation, or some other (e.g. random coil) conformation. These fractional assignments place important constraints on the possible secondary conformations that the protein can be in. CD cannot, in general, say where the alpha helices that are detected are located within the molecule or even completely predict how many there are. Despite this, CD is a valuable tool, especially for showing changes in conformation. It can, for instance, be used to study how the secondary structure of a molecule changes as a function of temperature or of the concentration of denaturing agents. In this way it can reveal important thermodynamic information about the molecule that cannot otherwise be easily obtained. Anyone attempting to study a protein will find CD a valuable tool for verifying that the protein is in its native conformation before undertaking extensive and/or expensive experiments with it. Also, there are a number of other uses for CD spectroscopy in protein chemistry not related to alpha-helix fraction estimation.

CD gives less specific structural information than e.g. X-ray crystallography or protein NMR spectroscopy, that both give atomic resolution data. However CD spectroscopy is a quick method, that does not require large amounts of proteins and extensive data processing. Thus CD can be used to survey a large number of solvent conditions, varying temperature, pH, salinity and presence of various cofactors.

CD spectroscopy is usually used to study proteins in solution, and thus it complements methods that study the solid state. This is also a limitation, in that many proteins are embedded in membranes in their native state, and solutions containing membrane structures are often strongly scattering. CD is sometimes measured in thin films.

[edit] Experimental limitations

CD has also been studied in carbohydrates, but with limited success due to the experimental difficulties associated with measurement of CD spectra in the vacuum ultraviolet (VUV) region of the spectrum (100-200 nm), where the corresponding CD bands of unsubstituted carbohydrates lie. Substituted carbohydrates with bands above the VUV region have been successfully measured.

Measurement of CD is also complicated by the fact that typical aqueous buffer systems often absorb in the range where structural features exhibit differential absorption of circularly polarized light. Phosphate, sulfate, carbonate, and acetate buffers are generally incompatible with CD unless made extremely dilute. Borate and ammonium salts are often used to establish the appropriate pH range for CD experiments. Some experimenters have substituted fluoride for chloride ion because fluoride absorbs less in the far UV, and some have worked in pure water. Another, almost universal, technique is to minimize solvent absorption by using shorter path length cells when working in the far UV, 0.1 mm path lengths are not uncommon in this work.

It may be of interest to note that the protein CD spectra used in secondary structure estimation are related to the π to π* orbital absorptions of the amide bonds linking the amino acids. These absorption bands lie partly in the so-called vacuum ultraviolet (wavelengths less than about 200 nm). The wavelength region of interest is actually inaccessible in air because of the strong absorption of light by oxygen at these wavelengths. In practice these spectra are measured not in vacuum but in an oxygen-free instrument (filled with pure nitrogen gas).

Once oxygen has been eliminated, perhaps the second most important technical factor in working below 200 nm is to design the rest of the optical system to have low losses in this region. Critical in this regard is the use of aluminized mirrors whose coatings have been optimized for low loss in this region of the spectrum.

The usual light source in these instruments is a high pressure, short-arc xenon lamp. Ordinary xenon arc lamps are unsuitable for use in the low UV. Instead specially constructed lamps with envelopes made from high-purity synthetic fused silica must be used. Light from synchrotron sources has a much higher flux at short wavelengths, and has been used to record CD down to 160 nm.

At the quantum mechanical level, the information content of circular dichroism and optical rotation are identical.

[edit] See also

• Dichroism
• Magnetic circular dichroism
• Optical activity
• Optical isomerism
• Optical rotation
• Polarization

[edit] External links

• Circular Dichroism explained - A commercial supplier's site, but very good information with examples, etc.
• Circular Dichroism at UMDNJ - a good site for information on structure estimation software

[edit] References

1. Fasman, G.D., Circular Dichroism and the Conformational Analysis of Biomolecules (1996) Plenum Press, New York.
2. Hecht, E., Optics 3^rd Edition (1998) Addison Wesley Longman, Massachusetts.