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| '''Circular dichroism (CD)''' refers to the differential [[Absorption (electromagnetic radiation)|absorption]] of left and right [[circular polarization|circularly polarized]] [[light]].<ref>{{cite book|author=P. Atkins and J. de Paula|title= Elements of Physical Chemistry, 4th ed.|publisher=Oxford University Press|year=2005|isbn=0-7167-7329-5}}</ref><ref name="E. I. Solomon and A. B. P. Lever 2006 78">{{cite book|author1=Edward I. Solomon|author2=A. B. P. Lever|title=Inorganic electronic structure and spectroscopy|url=http://books.google.com/books?id=C7KaQgAACAAJ|accessdate=29 April 2011|date=3 February 2006|publisher=Wiley-Interscience|isbn=978-0-471-97124-5|page=78}}</ref> This phenomenon was discovered by [[Jean-Baptiste Biot]], [[Augustin Fresnel]], and [[Aimé Cotton]] in the first half of the 19th century.<ref>{{cite book|author=Gerald D. Fasman|title=Circular dichroism and the conformational analysis of biomolecules|url=http://books.google.com/books?id=ivc0FaowEYMC&pg=PA3|accessdate=29 April 2011|year=1996|publisher=Springer|isbn=978-0-306-45142-3|pages=3–}}</ref> It is exhibited in the [[absorption (electromagnetic radiation)|absorption bands]] of [[optical activity|optically active]] [[chirality (chemistry)|chiral]] molecules. CD [[spectroscopy]] has a wide range of applications in many different fields. Most notably, [[Ultraviolet|UV]] CD is used to investigate the [[secondary structure]] of proteins.<ref name=b1>{{cite book|author1=Kōji Nakanishi|author2=Nina Berova|author3=Robert Woody|title=Circular dichroism: principles and applications|url=http://books.google.com/books?id=aNWjQgAACAAJ|accessdate=29 April 2011|year=1994|publisher=VCH|isbn=978-1-56081-618-8|page=473}}</ref> UV/Vis CD is used to investigate [[charge-transfer complex|charge-transfer transitions]].<ref>{{cite journal|first=Neidig|last=Solomon| coauthors=A. T. Wecksler, G. Schenk, and T. R. Holman|title= Kinetic and Spectroscopic Studies of N694C Lipoxygenase: A Probe of the Substrate Activation Mechanism of a Non-Heme Ferric Enzyme| journal=J. Amer. Chem. Soc.| volume=129|pages=7531–7537|year=2007|doi=10.1021/ja068503d|pmc=2896304|pmid=17523638|issue=24}}</ref> [[Near-infrared]] CD is used to investigate [[molecular structure|geometric]] and [[electronic structure]] by probing [[transition metal|metal]] [[D orbital|d]]→[[D orbital|d]] transitions.<ref name="E. I. Solomon and A. B. P. Lever 2006 78"/> [[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.<ref name=b1/>
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| ==Physical principles==
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| ===Circular polarization of light===
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| {{main|Circular polarization}}
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| [[Electromagnetic radiation]] consists of an electric (E) and magnetic (B) field that oscillate perpendicular to one another and to the propagating direction.,<ref>{{cite book|author1=Alison Rodger|author2=Bengt Nordén|title=Circular dichroism and linear dichroism|url=http://books.google.com/books?id=THeKGC99hJcC|accessdate=29 April 2011|year=1997|publisher=Oxford University Press|isbn=978-0-19-855897-2}}</ref> a [[transverse wave]]. While [[Polarization (waves)|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 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 (k). For left circularly polarized light (LCP) with propagation towards the observer, the electric vector rotates counterclockwise.<ref name="E. I. Solomon and A. B. P. Lever 2006 78"/> For right circularly polarized light (RCP), the electric vector rotates clockwise.
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| [[File:Linearly pol.png]] [[File:Circularly pol.png]]
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| ===Interaction of circularly polarized light with matter===
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| When circularly polarized light passes through an absorbing optically active medium, the speeds between right and left polarizations differ (c<sub>L</sub>{{unicode| ≠}} c<sub>R</sub>) as well as their [[wavelength]] ({{unicode|λ}}<sub>L</sub>{{unicode| ≠ λ}}<sub>R</sub>) and the extent to which they are absorbed ({{unicode|ε}}<sub>L</sub>{{unicode|≠ε}}<sub>R</sub>). ''Circular dichroism'' is the difference {{unicode|Δε ≡ ε}}<sub>L</sub>- {{unicode|ε}}<sub>R</sub>.<ref name=b1/> The electric field of a light beam causes a linear displacement of charge when interacting with a molecule ([[electric dipole]]), whereas the magnetic field of it causes a circulation of charge ([[magnetic dipole]]). These two motions combined cause an excitation of an [[electron]] in a helical motion, which includes [[translation (physics)|translation]] and [[rotation]] and their associated [[Operator (mathematics)|operators]]. The experimentally determined relationship between the [[rotational strength]] (R) of a sample and the {{unicode|Δε}} is given by
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| :<math>R_{exp} = \frac{3hc10^{3} ln(10)}{32\pi^{3}N_A} \int \frac{\Delta\epsilon}{\nu} d{\nu}</math>
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| The rotational strength has also been determined theoretically,
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| :<math>R_{theo} = \frac{1}{2mc} Im \int \Psi_g \widehat{M}_{(elec. dipole)} \Psi_e d\tau \bullet \int \Psi_g \widehat{M}_{(mag. dipole)} \Psi_e d\tau </math>
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| We see from these two equations that in order to have non-zero <math>\Delta\epsilon</math>, the electric and magnetic dipole moment operators (<math>\widehat{M}_{(elec. dipole)}</math> and <math>\widehat{M}_{(mag. dipole)}</math>) must transform as the same [[group theory|irreducible representation]]. <math>C_n</math> and <math>D_n </math> are the only [[point groups]] where this can occur, making only chiral molecules CD active.
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| Simply put, since circularly polarized light itself is "chiral", it interacts differently with [[chirality (chemistry)|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.
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| 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 [[Protein secondary structure|secondary structure]] can have a CD that changes with changes in the conformation.
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| ====Delta absorbance====
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| By definition,
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| :<math>\Delta A=A_L-A_R \,</math>
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| where ΔA (Delta Absorbance) is the difference between absorbance of left circularly polarized (LCP) and right circularly polarized (RCP) light (this is what is usually measured). ΔA is a function of [[wavelength]], so for a measurement to be meaningful the wavelength at which it was performed must be known.
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| ====Molar circular dichroism====
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| It can also be expressed, by applying [[Beer-Lambert law|Beer's law]], as:
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| :<math>\Delta A = (\epsilon_L - \epsilon_R)Cl\,</math>
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| where
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| :ε<sub>L</sub> and ε<sub>R</sub> are the molar extinction coefficients for LCP and RCP light,
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| :''C'' is the molar concentration
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| :''l'' is the path length in centimeters (cm).
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| Then
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| :<math> \Delta \epsilon =\epsilon_L-\epsilon_R\,</math>
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| is the molar circular dichroism. This intrinsic property is what is usually meant by the circular dichroism of the substance. Since <math> \Delta \epsilon</math> is a function of wavelength, a molar circular dichroism value (<math> \Delta \epsilon</math>) must specify the wavelength at which it is valid.
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| ====Extrinsic effects on circular dichroism====
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| 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.
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| ====Molar ellipticity====
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| Although ΔA is usually measured, for historical reasons most measurements are reported in degrees of ellipticity.
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| Molar ellipticity is circular dichroism corrected for concentration. Molar circular dichroism and molar ellipticity, [''θ''], are readily interconverted by the equation:
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| [[File:Electric Vectors 1.png|thumb|Electric_Vectors|200px|right|Elliptical polarized light (violet) is composed of unequal contributions of right (blue) and left (red) circular polarized light.]]
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| :<math> [\theta] = 3298.2\,\Delta \varepsilon.\, </math>
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| This relationship is derived by defining the [[polarization (waves)|ellipticity of the polarization]] as:
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| :<math> \tan \theta = \frac{E_R - E_L}{E_R + E_L} \,</math>
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| where
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| :E<sub>R</sub> and E<sub>L</sub> are the magnitudes of the [[electric field]] [[vector (geometry)|vectors]] of the right-circularly and left-circularly polarized light, respectively.
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| When E<sub>R</sub> equals E<sub>L</sub> (when there is no difference in the absorbance of right- and left-circular polarized light), θ is 0° and the light is [[linear polarization|linearly polarized]]. When either E<sub>R</sub> or E<sub>L</sub> is equal to zero (when there is complete absorbance of the circular polarized light in one direction), θ is 45° and the light is [[circular polarization|circularly polarized]].
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| Generally, the circular dichroism effect is small, so tanθ is small and can be approximated as θ in [[radian]]s. Since the [[Radiant intensity|intensity]] or [[irradiance]], I, of light is proportional to the square of the electric-field vector, the ellipticity becomes:
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| :<math> \theta (\text{radians}) = \frac{(I_R^{1/2} - I_L^{1/2})}{(I_R^{1/2} + I_L^{1/2})}\,</math>
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| Then by substituting for I using [[Beer–Lambert law|Beer's law]] in [[natural logarithm]] form:
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| :<math> I = I_0 e^{-A\ln 10}\,</math>
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| The ellipticity can now be written as:
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| :<math> \theta (\text{radians}) = \frac{(e^{\frac{-A_R}{2}\ln 10} - e^{\frac{-A_L}{2}\ln 10})}{(e^{\frac{-A_R}{2}\ln 10} + e^{\frac{-A_L}{2}\ln 10})} = \frac{e^{\Delta A \frac{\ln 10}{2}} - 1}{e^{\Delta A \frac{\ln 10}{2}} + 1} \,</math>
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| 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 [[radian]]s to degrees:
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| :<math> \theta (\text{degrees}) = \Delta A \left( \frac {\ln 10}{4} \right) \left( \frac {180}{\pi} \right)\, </math>
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| The linear dependence of solute concentration and pathlength is removed by defining molar ellipticity as,
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| :<math> [\theta] = \frac {100\theta}{\text{Cl}}\, </math>
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| Then combining the last two expression with [[Beer–Lambert law|Beer's law]], molar ellipticity becomes:
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| :<math> [\theta]= 100 \,\Delta \varepsilon \left( \frac {\ln 10}{4} \right) \left( \frac {180}{\pi} \right) = 3298.2\,\Delta \varepsilon \,</math>
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| The units of molar ellipticity are historically (deg·cm<sup>2</sup>/dmol). To calculate molar ellipticity, the sample concentration (g/L), cell pathlength (cm), and the molecular weight (g/mol) must be known.
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| If the sample is a protein, the mean residual weight (average molecular weight of the amino acids it contains) is used in place of the molecular weight, essentially treating the protein as a solution of amino acids.
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| ====Mean residue ellipticity====
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| 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.
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| ==Application to biological molecules==
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| In general, this phenomenon will be exhibited in absorption bands of any [[optical activity|optically active]] molecule. As a consequence, circular dichroism is exhibited by biological molecules, because of their [[dextrorotary]] and [[levorotary]] components. Even more important 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. 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.
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| 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. 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 ([[Kramers–Kronig relation]]), if all the absorptions are included in the measurements.
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| The far-UV ([[ultraviolet]]) CD spectrum of proteins can reveal 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.<ref name="pmid17896349">{{cite journal |author=Whitmore L, Wallace BA |title=Protein secondary structure analyses from circular dichroism spectroscopy: methods and reference databases |journal=Biopolymers |volume=89 |issue=5 |pages=392–400 |year=2008|pmid=17896349 |doi=10.1002/bip.20853}}</ref><ref name="pmid17406547">{{cite journal |author=Greenfield NJ |title=Using circular dichroism spectra to estimate protein secondary structure |journal=Nature protocols |volume=1 |issue=6 |pages=2876–90 |year=2006 |pmid=17406547 |doi=10.1038/nprot.2006.202 |pmc=2728378}}</ref> 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. [[Guanidine|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.
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| 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 bond|disulfide bridges]]) and tryptophan [[amino acid]]s. 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]]. | |
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| 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 Cu<sup>2+</sup> and Ni<sup>2+</sup> square-planar complexes involving histidine and main-chain coordination.
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| CD gives less specific structural information than [[X-ray crystallography]] and [[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.
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| 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 [[biological membrane|membranes]] in their native state, and solutions containing membrane structures are often strongly scattering. CD is sometimes measured in thin films.
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| ==Experimental limitations==
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| {{Refimprove|date=March 2010}}
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| 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.
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| 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.g. in the 10–50 mM range. The TRIS buffer system should be completely avoided when performing far-UV CD. [[Borate]] and [[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.
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| In addition to measuring in aqueous systems, CD, particularly far-UV CD, can be measured in organic solvents e.g. ethanol, methanol, [[trifluoroethanol]] (TFE). 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.
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| 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 bond]]s linking the amino acids. These absorption bands lie partly in the ''so-called'' [[Vacuum_ultraviolet#Vacuum_UV|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).
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| 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 [[Mirror#Instruments|aluminized mirrors]] whose coatings have been optimized for low loss in this region of the spectrum.
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| The usual light source in these instruments is a high pressure, short-arc [[Xenon arc lamp|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.
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| Light from [[synchrotron]] sources has a much higher flux at short wavelengths, and has been used to record CD down to 160 nm. 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.<ref>{{cite journal|author= U. Meierhenrich, J.J. Filippi, C. Meinert, J. H. Bredehöft, J. Takahashi, L. Nahon, N. C. Jones, S. V. Hoffmann|title=Circular Dichroism of Amino Acids in the Vacuum-Ultraviolet Region| journal=Angewandte Chemie Int. Ed.| volume=49|pages=7799–7802|year=2010|pmid= 20845349| doi=10.1002/anie.201003877|issue=42}}</ref>
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| At the [[quantum mechanics|quantum mechanical]] level, the information content of circular dichroism and [[optical rotation]] are identical.
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| ==See also==
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| {{colbegin|3}}
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| *[[Circular polarization in nature]]
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| *[[Dichroism]]
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| *[[Linear dichroism]]
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| *[[Magnetic circular dichroism]]
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| *[[Optical activity]]
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| *[[Optical isomerism]]
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| *[[Optical rotation]]
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| *[[Optical rotatory dispersion]]
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| *[[Vibrational circular dichroism]]
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| *[[Protein circular dichroism data bank]]
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| {{colend}}
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| ==References==
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| {{reflist}}
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| ==External links==
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| *[http://www.ap-lab.com/circular_dichroism.htm Circular Dichroism explained]
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| *[http://www.enzim.hu/~szia/cddemo/edemo1.htm Electromagnetic waves] – Animated electromagnetic waves. The Emanim program is a teaching resource for helping students understand the nature of electromagnetic waves and their interaction with birefringent and dichroic samples
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| * A step by step tutorial on [https://perswww.kuleuven.be/~u0052493/English/RechercheT3a.htm Circular Dichroism]
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| *[http://www.photophysics.com/tutorials/circular-dichroism-cd-spectroscopy An Introduction to Circular Dichroism Spectroscopy] – a very good tutorial on circular dichroism spectroscopy
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| *[http://www.avactaanalytical.com/analytical-services/technical-capabilities/circular-dichroism-spectroscopy Circular Dichroism] - Interesting information on the applications of CD and links to addition papers
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| {{Protein structure determination}}
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| {{DEFAULTSORT:Circular Dichroism}}
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| [[Category:Polarization (waves)]]
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| [[Category:Physical quantities]]
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| [[Category:Protein structure]]
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