Circular dichroism (CD) units and conversions

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

ΔA= A_LCP - A_RCP

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

Δε =ε_LCP -ε_RCP = ΔA/(C x l)

Where ε_LCP and ε_RCP 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 Δε_MR. 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 (C_MR):
C_MR = C x N

Δε_MR= ΔA/(C_MR x l)

An estimate can be determined for C_MR 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

C_MR = 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.

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

Circular dichroism as ellipticity- the orange cuboid represents the sample.

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 polarised light has 0 degrees of ellipticity (θ), while fully LCP or RCP will have + or - 45 degrees 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 polarisation state of a linear polarised 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 (C_MR):
C_MR = C x N

[θ]_MR = 100xθ/(C_MR x l)

An estimate can be determined for C_MR 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

C_MR = P/113

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

<<Previous Page

Introduction to Circular Dichroism Understanding circular dichroism: the basics of polarisation Chiral molecules: the origin of optical activity Chirality and biology Principle of operation of a circular dichroism spectrometer Performance of a circular dichroism spectrometer Circular dichroism signatures of secondary structural elements CD units and conversions