Circular dichroism (CD) is a form of spectroscopy based on the differential absorption of left- and right-handed circularly polarized light. Spectroscopy was originally the study of the interaction between Radiation and Matter as a function of Wavelength (λ In Electrodynamics, circular polarization (also circular polarisation) of Electromagnetic radiation is a Polarization such that the tip of the Light, or visible light, is Electromagnetic radiation of a Wavelength that is visible to the Human eye (about 400–700 It can be used to help determine the structure of macromolecules (including the secondary structure of proteins and the handedness of DNA). In Biochemistry and Structural biology, secondary structure is the general three-dimensional form of local segments of Biopolymers such as Proteins are large Organic compounds made of Amino acids arranged in a linear chain and joined together by Peptide bonds between the Carboxyl Deoxyribonucleic acid ( DNA) is a Nucleic acid that contains the genetic instructions used in the development and functioning of all known

## Polarized light

Linearly polarized light is polarized in a certain direction (that is, the magnitude of its electric field vector oscillates only in one plane, similar to a sine wave). In circularly polarized light, the electric field vector has a constant length, but rotates about its propagation direction. Hence it forms a helix in space while propagating. If this is a left-handed helix, the light is referred to as left circularly polarized, and vice versa for a right-handed helix. See external links for a demonstrative animation of the different types of electromagnetic waves.

The electric field of a light beam causes a linear displacement of charge when interacting with a molecule, whereas the magnetic field of it causes a circulation of charge. These two motions combined result in a helical displacement when light is impinged on a molecule. Since circularly polarized light itself is "chiral", it interacts differently with chiral molecules. The term chiral (pronounced /ˈkaɪɹ(əl̩/ is used to describe an object that is non- superimposable on its mirror image That is, one of 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 are radiated into a (chiral) solution. One of the two types 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 while propagating.

At a given wavelength,

$\Delta A=A_L-A_R \,$

where ΔA is the difference between absorbance of left circularly polarized (LCP) and right circularly polarized (RCP) light (this is what is usually measured). In Physics wavelength is the distance between repeating units of a propagating Wave of a given Frequency.

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

$\Delta A = (\epsilon_L - \epsilon_R)Cl\,$

where

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

Then

$\Delta \epsilon =\epsilon_L-\epsilon_R\,$

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.
$[\theta] = 3,298.2\Delta \epsilon\,$.

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

$tan \theta = \frac{E_R - E_L}{E_R + E_L} \,$

where

ER and EL are the magnitudes of the electric field vectors of the right-circularly and left-circularly polarized light, respectively. Polarization ( ''Brit'' polarisation) is a property of Waves that describes the orientation of their oscillations In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can

When ER equals EL (when there is no difference in the absorbance of right- and left-circular polarized light), θ is 0° and the light is linearly polarized. In Electrodynamics, linear polarization or plane polarization of Electromagnetic radiation is a confinement of the Electric field vector or When either ER or EL 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. In Electrodynamics, circular polarization (also circular polarisation) of Electromagnetic radiation is a Polarization such that the tip of the

Generally, the circular dichroism effect is small, so tanθ is small and can be approximated as θ in radians. The radian is a unit of plane Angle, equal to 180/ π degrees, or about 57 Since the intensity or irradiance, I, of light is proportional to the square of the electric-field vector, the ellipticity becomes:

$\theta (radians) = \frac{(I_R^{1/2} - I_L^{1/2})}{(I_R^{1/2} + I_L^{1/2})}\,$

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

$I = I_0 e^{-A\ln{10}}\,$

The ellipticity can now be written as:

$\theta (radians) = \frac{(e^{\frac{-A_R}{2}ln10} - e^{\frac{-A_L}{2}ln10})}{(e^{\frac{-A_R}{2}ln10} + e^{\frac{-A_L}{2}ln10})} = \frac{e^{\Delta A \frac{ln10}{2}} - 1}{e^{\Delta A \frac{ln10}{2}} + 1} \,$

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:

$\theta (degrees) = \Delta A \left( \frac {ln10}{4} \right) \left( \frac {180}{\pi} \right)\,$

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

$[\theta] = \frac {100\theta}{Cl}\,$

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

$[\theta]= 100 \Delta \epsilon \left( \frac {ln10}{4} \right) \left( \frac {180}{\pi} \right) = 3,298.2\Delta \epsilon \,$

## Application to biological molecules

In general, this phenomenon will be exhibited in absorption bands of any optically active molecule. In Physics, intensity is a measure of the time-averaged Energy Flux. Irradiance, radiant emittance, and radiant exitance are Radiometry terms for the power of Electromagnetic radiation at a surface per unit In The natural logarithm, formerly known as the Hyperbolic logarithm is the Logarithm to the base e, where e is an irrational In Mathematics, the Taylor series is a representation of a function as an infinite sum of terms calculated from the values of its Derivatives The radian is a unit of plane Angle, equal to 180/ π degrees, or about 57 In Optical rotation or optical activity is the rotation of linearly polarized Light as it travels through certain materials As a consequence, circular dichroism is exhibited by biological molecules, because of the dextrorotary (e. In Chemistry, an enantiomer ( from the Greek ἐνάντιος opposite and μέρος part or portion is one of two Stereoisomers that are nonsuperimposable g. some sugars) and levorotary (e. Sugar is a class of edible Crystalline substances mainly Sucrose, Lactose, and Fructose. Optical rotation or optical activity is the rotation of linearly polarized Light as it travels through certain materials g. some amino acids) molecules they contain. In Chemistry, an amino acid is a Molecule containing both Amine and Carboxyl Functional groups In Biochemistry, this Even more important is that a secondary structure will also impart a distinct CD to its respective molecules. In Biochemistry and Structural biology, secondary structure is the general three-dimensional form of local segments of Biopolymers such as Therefore, the alpha helix of proteins and the double helix of nucleic acids have CD spectral signatures representative of their structures. A common motif in the Secondary structure of Proteins the alpha helix (α-helix is a right-handed coiled conformation resembling a spring, in which In Geometry a double helix (plural helices) typically consists of two congruent helices with the same axis differing by a translation A nucleic acid is a Macromolecule composed of chains of monomeric Nucleotides In Biochemistry these Molecules carry Genetic information

CD is closely related to the optical rotatory dispersion (ORD) technique, and is generally considered to be more advanced. Optical rotatory dispersion is the variation in the Optical rotation of a substance with a change in the Wavelength of Light. CD is measured in or near the absorption bands of the molecule of interest, while ORD can be measured far from these bands. CD's advantage is apparent in the data analysis. Structural elements are more clearly distinguished since their recorded bands do not overlap extensively at particular wavelengths as they do in ORD. In principle these two spectral measurements can be interconverted through an integral transform, if all the absorptions are included in the measurements.

The far-UV (ultraviolet) CD spectrum of proteins can reveal important characteristics of their secondary structure. Ultraviolet ( UV) light is Electromagnetic radiation with a Wavelength shorter than that of Visible light, but longer than X-rays In Biochemistry and Structural biology, secondary structure is the general three-dimensional form of local segments of Biopolymers such as 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. A common motif in the Secondary structure of Proteins the alpha helix (α-helix is a right-handed coiled conformation resembling a spring, in which The β sheet (also β-pleated sheet) is the second form of regular Secondary structure in Proteins consisting of beta strands connected laterally A turn is an element of Secondary structure in proteins According to the most common definition a turn is defined by the close approach of two \mathrm{C^{\alpha}} g. random coil) conformation. A random coil is a Polymer Conformation where the Monomer subunits are oriented randomly while still being bonded to adjacent 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 hydrochloride or urea. Guanidine is a Crystalline compound of strong Alkalinity formed by the Oxidation of Guanine. Urea is an Organic compound with the Chemical formula ( N[[hydrogen H]]22 C[[oxygen O]] In this way it can reveal important thermodynamic information (such as the enthalpy and Gibbs free energy of denaturation) about the molecule that cannot otherwise be easily obtained. In Thermodynamics and molecular chemistry, the enthalpy (denoted as H, h, or rarely as χ) is a quotient or description of In Thermodynamics, the Gibbs free energy ( IUPAC recommended name Gibbs energy or Gibbs function) is a Thermodynamic potential which 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.

The near-UV CD spectrum (>250 nm) of proteins provides information on the tertiary structure. The signals obtained in the 250-300 nm region are due to the absorption, dipole orientation and the nature of the surrounding environment of the phenylalanine, tyrosine, cysteine (or S-S disulfide bridges) and tryptophan amino acids. Unlike in far-UV CD, the near-UV CD spectrum cannot be assigned to any particular 3D structure. Near-UV CD spectra can also provide structural information on the nature of the prosthetic groups in proteins, such as heme groups e. g. 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 X-ray crystallography and protein NMR spectroscopy, for example, which both give atomic resolution data. X-ray crystallography is a method of determining the arrangement of Atoms within a Crystal, in which a beam of X-rays strikes a crystal and scatters Protein nuclear magnetic resonance spectroscopy (usually abbreviated protein NMR) is a field of Structural biology in which NMR spectroscopy is used 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. A solvent is a liquid or gas that dissolves a solid liquid or gaseous Solute, resulting in a Solution. Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature pH is the measure of the acidity or alkalinity of a Solution. Salinity is the Saltiness or dissolved salt content of a body of Water.

CD spectroscopy is usually used to study proteins in solution, and thus it complements methods that study the solid state. Spectroscopy was originally the study of the interaction between Radiation and Matter as a function of Wavelength (λ 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. MembraneA biological membrane or biomembrane is an enclosing or separating Amphipathic layer that acts as a barrier within or around a cell. CD is sometimes measured in thin films.

## 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. Carbohydrates (from ' Hydrates of Carbon ' or saccharides ( Greek σάκχαρον meaning " Sugar " are the most 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 e. A phosphate, an Inorganic chemical, is a salt of Phosphoric acid. In Chemistry, a carbonate is a salt or Ester of Carbonic acid. An acetate, or ethanoate, is either a salt or Ester of Acetic acid. g. in the 10-50 mM range. The TRIS buffer system should be completely avoided when performing far-UV CD. Borate and ammonium salts are often used to establish the appropriate pH range for CD experiments. Borates in Chemistry are Chemical compounds containing Boron bonded to three Oxygen atoms written as B(OR3 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,trifluoroethanol (or TFE). 222-Trifluoroethanol is the Organic compound with the formula CF3CH2OH The latter has the advantage to induce structure formation of proteins, inducing beta-sheets in some and alpha helices in others, which they would not show under normal aqueous conditions. Most common organic solvents such as acetonitrile, THF, chloroform, dichloromethane are however, incompatible with far-UV CD. Acetonitrile (ACN is the Chemical compound with formula CH3CN "THF" redirects here For other uses see THF (disambiguation. Chloroform, also known as trichloromethane and methyl trichloride, is a Chemical compound with formula C[[Hydrogen H]] Cl Dichloromethane ( DCM) or methylene chloride is the Chemical compound with the formula CH2Cl2

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. Oxygen (from the Greek roots ὀξύς (oxys (acid literally "sharp" from the taste of acids and -γενής (-genēs (producer literally begetteris the In practice these spectra are measured not in vacuum but in an oxygen-free instrument (filled with pure nitrogen gas). Nitrogen (ˈnaɪtɹəʤɪn is a Chemical element that has the symbol N and Atomic number 7 and Atomic weight 14

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. A mirror is an object with a surface that has good Specular reflection; that is it is smooth enough to form an Image.

The usual light source in these instruments is a high pressure, short-arc xenon lamp. Xenon (ˈzɛnɒn or) is a Chemical element represented by the symbol Xe. 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. Fused quartz and fused silica are types of Glass containing primarily Silica in amorphous (non- Crystalline form Light from synchrotron sources has a much higher flux at short wavelengths, and has been used to record CD down to 160 nm. A synchrotron is a particular type of cyclic Particle accelerator in which the magnetic field (to turn the particles so they circulate and the electric field (to accelerate Recently the CD spectrometer 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. Geography The city lies roughly at the geographical centre of Denmark on the peninsula of

At the quantum mechanical level, the information content of circular dichroism and optical rotation are identical. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons Optical rotation or optical activity is the rotation of linearly polarized Light as it travels through certain materials