Circular Dichroism spectroscopy– Units

Circular Dichroism Units and Conversions

Circular Dichroism as Differential Absorbance

Circular dichroism (CD) is usually understood and actually measured as the differential absorbance of left (ALCP) and right circularly polarized (ARCP) light, and so can be expressed as:

ΔA= ALCP - ARCP

Taking into account cell pathlength and compound concentration, we can arrive at a Molar circular dichroism (Δε).

Where εLCP and εRCP are the molar extinction coefficients for LCP and RCP light respectively, C= molar concentration, and l = pathlength in centimeters.

Another important unit is mean residue molar circular dichroism ΔεMR. This is a unit specific for proteins, and reports the molar circular dichroism for individual protein residues instead of whole protein molecules. This allows easy comparison of different proteins with vastly different molecule weights. There are two ways to calculate this depending on how much information is known about the protein.

The concentration of protein (C) in molar is multiplied by the number of amino acids (N) in the protein to provide the mean residue concentration (CMR):

CMR = C x N

ΔεMR= ΔA/(CMR x l)

An estimate can be determined for CMR if the sequence of the protein isn't known, using the average amino acid residue weight of 113 daltons, and the concentration of protein (P) in gL-1

CMR = P/113

ΔA and Δε are the most intuitive units for many biochemists, as they are derived from the familiar concept of UV/Vis absorbance spectroscopy, and it is also how modern CD instruments actually measure circular dichroism. CD can also be expressed as degrees of ellipticity (θ), which is a legacy of polarimetry, and such units are frequently used in the literature. In the context of modern CD spectroscopy, these units are archaic and can be confusing. The relationship between ΔA and θ are explained below.

Circular Dichroism as Ellipticity

The description of ellipticity is somewhat more complex than ΔA. Linearly polarized light when passed through a circular dichroic sample will become elliptically polarized. Elliptically polarized light is light that is not fully circular polarized, but instead is elliptical in shape. This is because the circular polarized components of the original linear polarized light are now not of equal magnitudes due to differential absorbance (circular dichroism).

The degree of ellipticity (θ) is defined as the tangent of the ratio of the minor to major elliptical axis, and is illustrated below:

Linear polarized light has 0˚ of ellipticity (θ), while fully LCP or RCP will have + or - 45˚ respectively.

The advantage of circular dichroism ellipticity as a measurement unit is that it is more easily related to optical rotation measurements and polarimetry. Both ellipticity and optical rotation are measurements of changes in polarization state of a linear polarized analyzer beam, and both have the same units and similar amplitudes for a given sample. This similarity aids in comparison of optical rotation and circular dichroism measurements, a useful ability when circular dichroism spectroscopy first started to be widely used, back in the 1960's.

Fortunately it is very easy to inter-convert between θ and ΔA:

ΔA = θ/32.982

Note: Due to the small size of many measurements, θ is often quoted as millidegrees (m˚) or 1/1000 of a degree.

Molar ellipticity can be manipulated in the same way as ΔA. For instance taking into account concentration and cell pathlength according to Beer Lamberts law, we can derive a measurement of molar ellipticity [θ]. Following polarimetric conventions, molar ellipticity is reported in degrees cm2 dmol–1, or degrees M-1 m-1 which are equivalent units as shown below.

Molar ellipticity can be calculated using the following equation:

[θ] = 100xθ/(Cxl)

C is the concentration in molar, and l the cell pathlength in cm. The factor of 100 converts to pathlength in meters.

Molar Circular dichroism and molar ellipticity can be converted directly by:

Δε = [θ]/3298.2

This factor is a hundred fold larger than between raw absorbance and ellipticity due to the conversion between molar extinction defining pathlengths in centimeters and ellipticity having pathlength defined in meters.

Another important unit is mean residue ellipticity [θ]MR. This is a unit specific for proteins, and reports the molar ellipticity for individual protein residues instead of whole protein molecules. This allows easy comparison of different proteins with vastly different molecule weights. There are two ways to calculate this depending on how much information is known about the protein.

The concentration or protein (C) in molar is multiplied by the number of amino acids (N) in the protein to provide the mean residue concentration (CMR).

CMR = C x N

[θ]MR= 100xθ/(CMR x l)

An estimate can be determined for CMR if the sequence of the protein isn't known, using the average amino acid residue weight of 113 daltons, and the concentration of protein (P) in gL-1

CMR = P/113

Fortunately the Pro-Data software for Chirascan systems can convert easily between all these units, with a minimum of user intervention.

TOP