Circular dichroism

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Circular dichroism (CD) is

d transitions.[2] Vibrational circular dichroism, which uses light from the infrared energy region, is used for structural studies of small organic molecules, and most recently proteins and DNA.[5]

Physical principles

Circular polarization of light

Electromagnetic radiation consists of an electric and magnetic field that oscillate perpendicular to one another and to the propagating direction,[7] a transverse wave. While linearly polarized light occurs when the electric field vector oscillates only in one plane, circularly polarized light occurs when the direction of the electric field vector rotates about its propagation direction while the vector retains constant magnitude. At a single point in space, the circularly polarized-vector will trace out a circle over one period of the wave frequency, hence the name. The two diagrams below show the electric field vectors of linearly and circularly polarized light, at one moment of time, for a range of positions; the plot of the circularly polarized electric vector forms a helix along the direction of propagation . For left circularly polarized light (LCP) with propagation towards the observer, the electric vector rotates counterclockwise.[2] For right circularly polarized light (RCP), the electric vector rotates clockwise.

Interaction of circularly polarized light with matter

When circularly polarized light passes through an absorbing optically active medium, the speeds between right and left polarizations differ () as well as their wavelength() and the extent to which they are absorbed (). Circular dichroism is the difference .

translation and rotation and their associated operators. The experimentally determined relationship between the rotational strength
of a sample and the is given by

The rotational strength has also been determined theoretically,

We see from these two equations that in order to have non-zero , the electric and magnetic dipole moment operators ( and ) must transform as the same irreducible representation. and are the only

point groups
where this can occur, making only chiral molecules CD active.

Simply put, since circularly polarized light itself is "chiral", it interacts differently with chiral molecules. That is, the two types of circularly polarized light are absorbed to different extents. In a CD experiment, equal amounts of left and right circularly polarized light of a selected wavelength are alternately radiated into a (chiral) sample. One of the two polarizations is absorbed more than the other one, and this wavelength-dependent difference of absorption is measured, yielding the CD spectrum of the sample. Due to the interaction with the molecule, the electric field vector of the light traces out an elliptical path after passing through the sample.

It is important that the chirality of the molecule can be conformational rather than structural. That is, for instance, a protein molecule with a helical secondary structure can have a CD that changes with changes in the conformation.

Delta absorbance

By definition,

where (Delta Absorbance) is the difference between absorbance of left circularly polarized (LCP) and right circularly polarized (RCP) light (this is what is usually measured). is a function of wavelength, so for a measurement to be meaningful the wavelength at which it was performed must be known.

Molar circular dichroism

It can also be expressed, by applying

Beer's law
, as:

where

and are the molar extinction coefficients for LCP and RCP light,
is the molar concentration,
is the path length in centimeters (cm).

Then

is the molar circular dichroism. This intrinsic property is what is usually meant by the circular dichroism of the substance. Since is a function of wavelength, a molar circular dichroism value () must specify the wavelength at which it is valid.

Extrinsic effects on circular dichroism

In many practical applications of circular dichroism (CD), as discussed below, the measured CD is not simply an intrinsic property of the molecule, but rather depends on the molecular conformation. In such a case the CD may also be a function of temperature, concentration, and the chemical environment, including solvents. In this case the reported CD value must also specify these other relevant factors in order to be meaningful.

In ordered structures lacking two-fold rotational symmetry, optical activity,

extrinsic 3d chirality
is associated with the mutual orientation of light beam and structure.

Molar ellipticity

Although is usually measured, for historical reasons most measurements are reported in degrees of ellipticity. Molar ellipticity is circular dichroism corrected for concentration. Molar circular dichroism and molar ellipticity, , are readily interconverted by the equation:

Elliptical polarized light (violet) 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

and are the magnitudes of the
vectors
of the right-circularly and left-circularly polarized light, respectively.

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

Generally, the circular dichroism effect is small, so is small and can be approximated as in radians. Since the intensity or irradiance, , 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 , this expression can be approximated by expanding the exponentials in a Taylor series to first-order and then discarding terms of 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:

The units of molar ellipticity are historically (deg·cm2/dmol). To calculate molar ellipticity, the sample concentration (g/L), cell pathlength (cm), and the molecular weight (g/mol) must be known.

If the sample is a protein, the mean residue weight (average molecular weight of the amino acid residues it contains) is often used in place of the molecular weight, essentially treating the protein as a solution of amino acids. Using mean residue ellipticity facilitates comparing the CD of proteins of different molecular weight; use of this normalized CD is important in studies of protein structure.

Mean residue ellipticity

Methods for estimating secondary structure in polymers, proteins and polypeptides in particular, often require that the measured molar ellipticity spectrum be converted to a normalized value, specifically a value independent of the polymer length. Mean residue ellipticity is used for this purpose; it is simply the measured molar ellipticity of the molecule divided by the number of monomer units (residues) in the molecule.

Application to biological molecules

Upper panel: Circular dichroism spectroscopy in the ultraviolet wavelength region (UV-CD) of MBP-cytochrome b6 fusion protein in different detergent solutions. It shows that the protein in DM, as well as in Triton X-100 solution, recovered its structure. However the spectra obtained from SDS solution shows decreased ellipticity in the range between 200 and 210 nm, which indicates incomplete secondary structure recovery.
Lower panel: The content of secondary structures predicted from the CD spectra using the CDSSTR algorithm. The protein in SDS solution shows increased content of unordered structures and decreased helices content.[12]

In general, this phenomenon will be exhibited in absorption bands of any

nucleic acids
have CD spectral signatures representative of their structures. The capacity of CD to give a representative structural signature makes it a powerful tool in modern biochemistry with applications that can be found in virtually every field of study.

CD is closely related to the

Kramers–Kronig relation
), if all the absorptions are included in the measurements.

The far-UV (

beta-turn conformation, or some other (e.g. random coil) conformation.[13][14][15][16] 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, e.g. Guanidinium chloride or urea. In this way it can reveal important thermodynamic information about the molecule (such as the enthalpy and Gibbs free energy of denaturation) 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. Moreover, CD spectroscopy has been used in bioinorganic interface studies. Specifically it has been used to analyze the differences in secondary structure of an engineered protein before and after titration with a reagent.[17]

The near-UV CD spectrum (>250 nm) of proteins provides information on the

disulfide bridges) and tryptophan amino acids. Unlike in far-UV CD, the near-UV CD spectrum cannot be assigned to any particular 3D structure. Rather, near-UV CD spectra provide structural information on the nature of the prosthetic groups in proteins, e.g., the heme groups in hemoglobin and cytochrome c
.

Visible CD spectroscopy is a very powerful technique to study metal–protein interactions and can resolve individual d–d electronic transitions as separate bands. CD spectra in the visible light region are only produced when a metal ion is in a chiral environment, thus, free metal ions in solution are not detected. This has the advantage of only observing the protein-bound metal, so pH dependence and stoichiometries are readily obtained. Optical activity in transition metal ion complexes have been attributed to configurational, conformational and the vicinal effects. Klewpatinond and Viles (2007) have produced a set of empirical rules for predicting the appearance of visible CD spectra for Cu2+ and Ni2+ square-planar complexes involving histidine and main-chain coordination.

CD gives less specific structural information than

protein NMR spectroscopy, for example, which both give atomic resolution data. However, CD spectroscopy is a quick method that does not require large amounts of proteins or extensive data processing. Thus CD can be used to survey a large number of solvent conditions, varying temperature, pH, salinity
, and the 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.

CD spectroscopy has also been done using semiconducting materials such as TiO2 to obtain large signals in the UV range of wavelengths, where the electronic transitions for biomolecules often occur.[18]

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.

Onium compounds
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.

In addition to measuring in aqueous systems, CD, particularly far-UV CD, can be measured in organic solvents e.g. ethanol, methanol,

are however, incompatible with far-UV CD.

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

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. In 2010 the CD spectrophotometer at the electron storage ring facility ISA at the University of Aarhus in Denmark was used to record solid state CD spectra down to 120 nm.[19] At the

Optical rotary dispersion and circular dichroism share the same quantum information
content.

See also

References

  1. .
  2. ^ . Retrieved 29 April 2011.
  3. ^ Introduction to Quantum Theory 2ED David Park Sec 2.2 Pg32 "...the polarization of a beam of light is exactly the same kind of thing as the spin of a beam of electrons, the differences of terminology reflecting only the accidents of the historical order of discovery."
  4. . Retrieved 29 April 2011.
  5. ^ . Retrieved 29 April 2011.
  6. .
  7. . Retrieved 29 April 2011.
  8. .
  9. .
  10. .
  11. .
  12. .
  13. (PDF) from the original on 2022-10-09.
  14. .
  15. .
  16. .
  17. ^ Bioinorganic Interface: Mechanistic Studies of Protein-Directed Nanomaterial Synthesis. (2016, May 5). Retrieved March 1, 2019, from https://pubs.acs.org/doi/pdf/10.1021/acs.jpcc.6b02569
  18. ^ Sarkar, Sumant, Ryan Behunin, and John G. Gibbs. "Shape-Dependent, Chiro-Optical Response of UV-Active, Nanohelix Metamaterials." Nano letters (2019). https://pubs.acs.org/doi/10.1021/acs.nanolett.9b03274
  19. ]

External links