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Janaky Narayanan PC 5213 AY 2004-05/Semester 2
55
II.3 CIRCULAR DICHROISM
Light is an electromagnetic wave which oscillates periodically in both time and space. In
the wave, the electric and magnetic vectors, which are proportional to each other in
magnitude, are mutually perpendicular and also perpendicular to the direction of
propagation. Non-polarized light consists of vibrations in many different polarization
directions. In other words, the plane containing the oscillating electric vector and the
propagation direction keeps changing with time. In linearly polarized light the sinusoidal
oscillations of the electric vector are confined to one plane. In circularly polarized light,
the magnitude of the electric vector remains constant, but it traces out a helix as a
function of time. It is useful to apply the principle of superposition to analyze the state of
polarization of a light beam. Circularly polarized light can be represented as the sum of
two orthogonal linearly polarized light in which the amplitudes are equal and the phases
are shifted by ± π/2.
Superposition of two Simple Harmonic Motions (SHM) at right angles to each other
Let the vibrations be given by
x = a sin t
y = b sin (t +)
(1)
(2)
where a and b are the amplitudes of the two SHM of same frequency, , executed in
perpendicular directions and  is their phase difference.
Now, y/b = sin (t + ) = sin t cos + cost sin.
From (1)
x
= sint and
a
 x2 
1  2   cos ωt ( cos2  + sin2 = 1)
 a 
Substituting in (3),
y x
x2
 cos   1 - 2 sin 
b a
a
or
1-
(3)
x2
y x
sin   - cos
2
a
b a
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Squaring,
 x2  2
y2 2xy
x2
1  2  sin δ  2 cosδ  2 cos 2δ
b
ab
a
 a 
Rearranging the terms,
y 2 2xy
x2
sin2 = 2 cosδ  2 (cos 2   sin 2  )
b
ab
a
2
2
y 2xy
x
i.e.,
General equation for an ellipse.
cosδ  2  sin 2   0 (4)
2
b
ab
a
Special cases:
y 2 2xy x 2
If
 = 0;

0
b 2 ab a 2
2
y x
or
 -  0
b a
or
b
y   x
a
If
 b
 = ; y   -  x
 a
If
 = /2 or 3/2;
Equation of a straight line through origin with + slope
Equation of a straight line through origin with – slope.
y2 x 2

1
b2 a 2
If  = /2 or 3/2 and a = b; y2 + x2 = a2
Equation to a standard ellipse.
Equation to a circle.
Thus two perpendicular vibrations of equal amplitude and phase difference /2 or 3/2
on superposition will form circular vibration.
If  = /2, and a = b, equations (1) and (2) can be written as
x = a sint and
y = a sin(t + /2), or, y = a cost,
Resultant is circular vibration in clock-wise direction (right circular).
Similarly if  = 3/2, and a = b,
x = a sint, and
y = a sin(t + 3/2) or y = -a cost,
Resultant is circular vibration in counter clock-wise direction (left circular).
Adding right and left circular vibrations of equal amplitudes, the resultant is
Y = (a sint + a cost) + (a sint – a cost) = 2a sint
linear vibration
 Sum of two circular vibrations of equal amplitudes one clockwise and the other
counterclockwise will give linear vibration.
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Stereochemistry and Chirality
The three dimensional spatial arrangement of the atoms of a molecule is termed its
stereochemistry. A molecule may be identified first by its chemical formula, then by its
chemical structure, and finally by its molecular structure. For example, C2H6O is the
chemical formula of ethyl alcohol. CH3-CH2-OH is the chemical structure of ethyl
alcohol. The molecular structure is determined by the three dimensional arrangement of
the atoms in space. The word “conformation” describes the different arrangements of
atoms that are obtained when parts of the molecule are rotated about one of the bonds. A
change in the conformation necessarily does not involve any breaking of covalent bonds.
Groups that are connected by a single bond can undergo rotation leading to different
relative orientations with respect to each other. For example, in ethyl alcohol, depending
on the angle of rotation about the C-C bond, the relative orientations of hydrogen atoms
and the hydroxyl group will vary.
In some molecules the differences in the arrangement of the atoms may not affect many
of the physical properties of the molecules such as melting point, density, refractive
index, etc., but may affect the interaction of the molecules with polarized light. Such
molecules are said to be optically active and are called optical isomers. Optically active
molecules rotate the plane of polarization of the plane polarized light incident on them in
different directions. Levorotatory molecules rotate the plane towards left and
dextrorotatory molecules rotate the plane towards right. Levorotation is designated as () and dextrorotation is denoted by (+). These optically active molecules may differ in
their biological behavior. For example, only one of the optical isomers of aspargine is
sweet to taste. Louis Pasteur showed that the difference in action between two optical
isomers is due to the difference in molecular architecture, i.e. due to the differences in the
arrangement of the atoms in space. The two alanine molecules shown in figure have the
same number of atoms but differ in the stereochemistry and hence are known as
stereoisomers.
D-alanine
L-alanine
A molecule or other object that is different from its own mirror image, i.e., nonsuperimposable on its mirror image is chiral (eg. a pair of shoes, hands). Molecules that
are identical to their mirror image are achiral. A chiral molecule and its mirror image
molecules are enantiomers. Thus pairs of isomers which are non-superimposable images
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of each other are called enantiomers. Most chiral molecules contain one or more chiral
centers. A chiral center is an atom in tetrahedral hybridization with four all–different
groups bonded to it. Thus compounds with four substitutions at a carbon atom (Cabcd)
will exhibit optical activity. Such a carbon atom is generally is known as an asymmetric
carbon and a molecule containing such an atom is a chiral molecule (eg. -carbon atom
in alanine). A mixture of two isomers, which have optical activity opposite to each other,
is on the whole optically inactive since the effect of one is annulled by the other. Such a
mixture is known as a racemic mixture. A combination of equal amounts of enantiomers
is a racemic mixture. A pair of enantiomers may display distinct toxicity to humans with
one enantiomer being toxic and the other non-toxic. Eg, thalidomide – one of the
enantiomers of this drug was responsible for the deformity of the limbs in babies born in
1950’s. Stereoisomers not related to each other as enantiomers are called
diastereoisomers. Diastereoisomerism will occur in molecules with more than one chiral
center. Other than carbon, atoms like silicon with a valency of four can also act as chiral
centers. Living systems almost exclusively synthesize one of the possible two
enantiomorphous forms (either the D or L compound). Proteins for example, contain only
L-amino acids. Most monosaccharides are D-enantiomers; D-2-deoxyribose and D-ribose
form part of the nucleotides used in the synthesis of DNA and RNA respectively. All the
major biological molecules, like amino acids, proteins, DNA, sugars and lipids, are
optically active. Optical activity and life seem to be inseparable.
Optical Activity
Nearly all molecules synthesized by living organisms are optically active, i.e., they rotate
the plane of polarized light. Optical activity arises from chirality of the molecules. Most
of the biomolecules are chiral due to the presence of asymmetric carbon atoms or because
the supramolecular structure such as a helix winds in either right or left handed fashion.
This property is used to explore the amount of coil, helix and -sheet in a
macromolecule.
For any compound, the extent of optical rotation depends on the number of molecules in
the path of the polarized light, i.e., on the solution concentration and on the path length of
the beam through it. It also depends on the wavelength of the radiation and the
temperature. Optical activity is quantified by the specific rotation, , given by
deg ree

in

lc
dm.(g / cm 3 )
where  is the angle of rotation of the plane of polarization, l is the path length (in
decimeter) and c is the concentration (in g/cm3). The optical rotation, , as a function of
wavelength is called the Optical Rotatory Dispersion (ORD).
Light passing through a chromophore solution may interact with the sample in two main
ways. The light may be refracted on passage through the solution or it may be absorbed.
Refraction is quantitated by the refractive index, n, of the solution while absorption is
quantitated by the molar extinction coefficient, . If the light is plane polarized and the
sample is optically active, each enantiomer may interact differently with the left and right
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circularly polarized components of the light beam. Optical rotation arises from the fact
that there is a specific refractive index for left (nL) and right (nR) circularly polarized light
and nL  nR. This is called circular birefringence. The difference in refractive index at
any wavelength may be expressed as n. An ORD spectrum is a plot of n or  against
wavelength (). Similarly, optically active samples have distinct molar extinction
coefficients for left (L) and right (L) circularly polarized light. L  R. The difference in
absorbance of the two components, is a measure of Circular Dichroism (CD). i.e.,
CD = AL – AR
The difference between L and R may be expressed as . From Beer-Lambert Law the
difference in the absorbance of left and right circularly polarized light A, can be given
by, A =cl. If  or A or ellipticity (see below) is plotted against wavelength (), a
CD spectrum may be obtained. The CD spectrum of one enantiomer is a mirror image of
that of the other and is related to the corresponding ORD spectrum (and vice versa) by a
mathematical transformation called the general Kronig-Kramers transformation. Both
ORD and CD spectra are evidence for optical activity in the sample and both reflect
structure of molecules in the sample, especially of chiral biopolymers such as proteins
and nucleic acids. In practice, ORD has now largely been superseded by CD
spectroscopy.
Thus there are at least four ways in which an optically active sample can alter the
properties of transmitted light: Optical Rotation, Ellipticity, Circular Dichroism, and
Circular Birefringence. They are inter-related as explained in detail below.
Consider plane polarized light. An observer looking along the direction of propagation

(z-axis, perpendicular to the plane of paper) will see the electric vector E oscillate


sinusoidally in the xy plane, say along x direction. Let E  i E 0 sin t where iˆ is a unit
vector in the x direction and  = 2 is the circular frequency of the light. After passing
through an optically active absorbing sample, the maximal amplitude of the electric
vector is no longer confined to a plane, but traces out an ellipse. The ellipticity of the
light is a measure of optical activity. Ellipticity is defined as the arc tangent of the ratio of
the minor axis to the major axis of the ellipse. i.e.,  = tan-1(b/a), where a and b are the
semi-major and semi-minor axes of the ellipse. For example, an ellipse with a
minor/major axial ratio of 1/100 will have an ellipticity of 0.57 degree. The major axis of
the ellipse is not parallel to the direction of polarization of the incident light. If the
absorption of the light is negligibly small, then the minor axis of the ellipse will be very
small compared to the major axis. The emerging light will be equivalent to planepolarized light. In this case, we simply say that the plane of polarization is rotated
through an angle (). The orientation of the ellipse corresponds to optical rotation. The
optical rotation of a sample can be measured at any wavelength, i.e., also outside the
absorption bands. This is the main advantage of ORD over CD.
A plane polarized light can be considered as equivalent to two equal-amplitude
components of opposite circular polarization:
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
1
E R  (î E 0 sin ωt  ĵE 0 cos ωt)
2

1
E L  (î E 0 sin ωt  ĵE 0 cos ωt)
2
ˆ
where j is a unit vector in the y direction. If these two components are added at each
time point, the result is simply plane-polarized light, polarized in the y-direction.
In an optically active medium the absorbance of left circularly polarized light (A L) is
different from the absorbance of right circularly polarized (AR). After passing through the
sample, each component is still circularly polarized, but the radii of the circles traced out
by the electric vector of each (i.e., the amplitudes of the electric vectors) are now
different.
When these two opposite circularly polarized light waves are combined, the result will be
elliptically polarized light because the two components have different amplitudes. The
ellipticity, , is proportional to the difference in absorbance of the two components, A L –
AR. Thus, CD is equivalent to ellipticity.
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

In an optically active material, the electric vectors E R and E L rotate at different speeds.
This results in a net rotation in the direction of polarization of the emergent beams. Since
the two circularly polarized components propagate with different speeds, the index of
refraction (n) for the two components will be different. This effect is called circular
birefringence (CB). The result is a phase shift between the two components, ,
proportional to the refractive index difference, nL–nR. Actually,  = (2/)l(nL–nR). When
the two components are combined, the phase shift results in a permanent rotation of the
long axis (major axis) of the elliptically polarized light. In fact,  = /2 = (/)l(nL–nR).
Thus circular birefringence is equivalent to optical rotation. Since the refractive
index is always dependent on the wavelength, the angle of rotation is also wavelength
dependent.
The relationships between CD and ellipticity () and between the circular birefringence
and the optical rotation () are given by
 = 180l(nL – nR) / 
 = 2.303(AL – AR)180/4 = 33.0 (AL – AR) = 33.0 A
and
where l is the sample length and  and  are measured in degree.
The circular birefringence, i.e., (nL – nR ) usually is a very small number, so it is far more
convenient to measure  directly. For typical protein or nuclei acid solutions at 10-4 M
chromophore concentrations, the plane of polarized light will be rotated by 0.01 to 0.1
degree for a 1 cm sample. Current instruments can detect rotations as small as 10-4
degree. CD, i.e., (AL – AR) can be measured easily by exposing a sample alternately to
left-hand and right-hand circularly polarized light and detecting just the differential
absorption. This difference typically is about 0.03% to 3% of the total absorption. This
difference can be determined quite accurately with modern instrumentation. The
ellipticity, , is very small (~ 10-4 deg) and would be difficult to measure directly.
However, it can be calculated from CD.
For comparison of results from different samples it is necessary to consider molarity.
M 
100 cl
Molar rotation
[ ] 
Molar ellipticity
[θ] 
M θ
100 cl
in
deg ree.cm 2
decimol
in
deg ree. cm 2
decimol
Here M designates the molecular weight; c is in g/cm3 and l in decimeter.
[] and [] are related to each other by a set of integrals called the Kronig-Kramers
transforms.


2 [ (λ ' )]λ '
- 2 [ (' )]
and
[ ( )]   2 '2 dλ '
[ ( )] 
d '
π 0 λ -λ
 0 2 - '2
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The ORD and CD of a sample depend strongly on the wavelength of light used to
perform the measurement. For absorbing samples, one typically determines the ORD or
CD over the same wavelength range used to record an absorption spectrum. The resulting
optical activity spectra are called ORD and CD spectra. If the sample contains only
strongly allowed electronic transitions (such as   *), the shape of the CD spectrum
(often called a Cotton effect) is related to the absorption spectrum in a very simple way.
Outside the regions of absorption, [] = 0. This is reasonable because []  (AL – AR),
and both AL and AR are zero. In absorbing regions, [] has the same shape as the
absorption spectrum. However, it can have a positive or a negative sign. Both the sign
and the integrated intensity of each CD band are sensitive functions of molecular
structure. In the ORD spectra there is a point of zero optical rotation (the crossover point)
that is coincident with each CD maximum or minimum. The limiting form ( ≠ 0),
called a Drude equation, is [(()] = A0/(2 - λ 20 ), where A0 is a constant related to the
intensity of the corresponding CD spectrum, and 0 is the crossover wavelength.
However, the ORD spectra die off quite slowly at wavelengths outside the absorption
band. The form of the Drude equation shows why molecules such as sucrose can
demonstrate substantial optical rotation with visible light, even though they cannot absorb
this light.
Absorption spectrum
CD (solid line) and ORD
(dashed line) for a positive
Cotton effect
CD (solid line) and ORD
(dashed line) for a negative
Cotton effect
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Equipment Used in CD
CD spectra are measured in a special type of spectrophotometer called a CD
spectropolarimeter.
CD spectropolarimeter
Since CD depends on differential absorbance, a means of selectively exposing sample to
left and right circularly polarized light is necessary. This is achieved by passing a beam
of plane polarized light through a photoelastic modulator which is normally quartz
piezoelectric crystal subjected to an oscillating electric field. The effect of this is to vary
the circular polarization of the beam passing through the modulator alternately from left
to right with a frequency of some 50 kHz while maintaining a constant light intensity.
Differential absorption of left and right circularly polarized light is detected at a
photomultiplier and converted into ellipticity,  which has units of millidegrees. In a CD
spectropolarimeter, the two light beams are not in fact recombined but a photomultiplier
detector converts incident light intensity into an electric current composed partly of
alternating current (AC) and partly of direct current (DC) components. The DC
component is related to total light absorption by the sample while the AC component is a
direct measure of CD. This arrangement facilitates separate absorption measurements of
the right and left circularly polarized components of plane polarized light. Samples which
are achiral or composed of racemic mixtures would give no detectable spectrum in this
system. (i.e. A = AL – AR = 0 for all  values).
Applications of CD
The CD spectrum of a polymer is different from that of a monomer, the difference
reflecting the three dimensional arrangement. CD therefore is immensely useful to study
three-dimensional structures of biopolymers such as proteins and nucleic acids.
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The synthetic homopolymer poly-L-lysine adopts a random coil structure at neutral and
acid pH values. However, at high pH values, a mainly -helical conformation is adopted
which may be converted to predominantly antiparallel -sheet by gentle heating. Each of
these three forms of poly-L-lysine gives a characteristic CD spectrum in the range 190 250 nm as shown in figure. The fact that similar spectra are obtained for homopolymers
of other amino acids
suggest that they arise
predominantly
from
asymmetry
of
the
polypeptide
backbone.
CD spectra of proteins
and peptides of unknown
secondary structure are
often compared with
homopolypeptides
to
estimate empirically the
percentage of common
secondary
structural
features. Since the effect
of side chains is ignored,
these estimates are not as
accurate
as
direct
structural determination
using X-ray diffraction or
NMR. However, CD
technique requires very
low sample concentration and is a fast method for comparison as well as following the
changes in secondary structure conformation.
For proteins the aim is to analyze the CD spectrum to obtain secondary structural features
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such as the percentage of  helical regions or -sheet regimes or random coil regions. CD
signal is strong for - helix and weak for -sheets. It is very reliable for monitoring
changes in the conformation of proteins under different conditions. In the unfolded state
CD is nearly zero in the region 210-220 nm, which corresponds to the absorption band of
peptide bond. Hence protein folding/unfolding can be conveniently followed by CD
spectroscopy. Since absorption takes place in 10-15 s, any structural change taking place
due to ligand binding etc can be followed using CD spectroscopy.
In the wavelength range 190-250 nm, the protein CD spectrum is dominated by the
polypeptide backbone chromophores and the effects of the side chains are usually
negligible. It can be considered as a linear combination of the spectra of each of the
regular secondary structural regions such as -helix, -sheet and random coil. One may
thus write
[()] = k[(()] + k[()] + k[()]
where [()] is the measured ellipticity; k, k and k are the fractional compositions of
-helix,  -sheet and random coil regions respectively, and [()], [()] and [()]
are the measured CD of polypeptides in the conformation indicated. This equation can be
used to estimate k, k and k for an unknown protein, provided [()], [()] and
[()] are known.
The second major class of biopolymers which have been studied by CD are the nucleic
acids. Of the structural components of which nucleotides are composed, only the pentose
sugar is chiral. Mainly as a result of the presence of this sugar, nucleotides are
intrinsically chiral structures and give measurable, albeit weak, CD spectra. As the level
of structural order increases however (e.g. polymerization of nucleotides into
polynucleotides followed by assembly into duplex structures such as double stranded
DNA and tRNA), the symmetry of the system and hence the strength of the CD spectrum
obtained also increases. CD is therefore a useful measure of structure in nucleic acids.
Differences are observed in CD spectra due to variation of nucleotide sequence, GC
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composition, stacking of bases in different forms of DNA, formation of macromolecular
assemblies such as ribosomes and nucleosomes and ligand binding to DNA.
Many chromophores associated with biomacromolecules are themselves chiral and CD
measurements of their spectra can give information on their interactions with proteins,
DNA or macromolecular complexes.
Summary:
Circular dichroism spectroscopy is used to gain information about the secondary structure
of proteins and polypeptides in solution.
Benefits: Uses very little sample (200l of 0.5 mg/ml solution in standard cells). It is a
non-destructive method. Relative changes due to influence of environment on sample
(pH, denaturants, temperature etc.) can be monitored very accurately.
Drawbacks: Due to interference with solvent absorption in the UV region, only very
dilute, non-absorbing buffers allow measurements below 200 nm. Absolute
measurements are subject to a number of experimental errors, average accuracy of fits
about ± 10%. A CD spectropolarimeter is relatively expensive.
Seminar Topic:
(1) Circular Dichroism studies of structural stability of tetrameric p53 (tumour suppressor
protein)
Ref: David Sheehan, Physical Biochemistry: Principles and Applications, p.93
Johnson et al., Biochemistry 34, 5309, 1995.
(2) CD of Biopolymers
Ref: David Sheehan, 3.5.5
Cantor and Schimmel, Biophysical Chemistry II, Ch. 8, pp 425-432.
II.4 LINEAR DICHROISM
(a)
(b)
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The absorbances A1 = A2 in case (a) i.e., random orientation.
A1 ≠ A2 in case (b) i.e., oriented sample
Several molecules have elongated shapes such as ellipsoidal, rod-like etc. When they are
dissolved in an aqueous solvent they are randomly oriented and hence the sample will
give the same absorption spectrum regardless of the direction of polarization of a beam of
incident light. If the molecules were all orientated in a single direction, different
absorption spectra would be obtained depending on the direction of polarization of the
light beam. In linear Dichroism this fact is exploited by exposing orientated samples to
plane polarized light.
In LD spectroscopy, samples are orientated in a single axis relative to the incident
linearly polarized light. Let the molecules be oriented parallel to their longer axis (say, zaxis). Let A|| be the absorbance of light polarized parallel to z-axis and A be the
absorbance of light polarized perpendicular to the z-axis. Linear Dichroism (LD) is the
differential absorbance given by,
LD = A|| - A
It is often convenient to express the result as a dichroic ratio, d:
d = (A|| - A)/ (A|| + A)
A wide variety of physico-chemical means of achieving the orientation of molecules are
available. In the stretched polymer technique, orientation is achieved by absorbing
sample onto a polymer (e.g. polyvinyl alcohol) and stretching it in a particular direction.
The long axis of the sample molecule aligns in the stretch direction. Other popular
techniques include flow orientation, electric field orientation and squeezed gel
orientation.
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In flow orientation, the sample is placed in the
gap between the cylinders. The inner cylinder
is rotated causing the sample to flow by
viscous drag in the direction shown by arrows.
The long axis of sample molecules aligns in
the direction of flow.
An electric field is created around the sample by
parallel electrodes to align the molecules. Excessive
heating of sample can be avoided by the use of pulsed
fields.
Sample is embedded in a gel mixture which is
mechanically squeezed. This results in a rectangular
or square squeezed gel with oriented molecules.
LD of Biomolecules
LD spectroscopy is well suited to the study of certain
sample molecules such as fibrous proteins and DNA
since these posses a high axial ratio and are readily orientated in a particular direction.
Information has been obtained from such studies about the relative orientation of DNA
bases, intercalation of agents such
as ethidium bromide into DNA,
binding of drugs at the major and
minor DNA grooves and flexibility
of DNA.
Example: Flow LD spectrum of
DNA
The decrease in LD in the DNA
absorption region in the presence
of transition metal supramolecular
helicate [Fe2L3]Cl4 means reduced
DNA orientation. This indicates
that [Fe2L3]Cl4 helicate is kinking
the DNA.
(Alison Rodger et al., from website www.warwick.ac.uk)
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A limitation of LD in the study of biomolecules is the necessity for orientated samples.
Globular proteins are particularly difficult to orientate and LD has not been as widely
used in investigations of such samples. However, membrane proteins in the
photosynthetic reaction center have been studied using LD spectroscopy. LD has also
been used in studies of binding of proteins to DNA.
Seminar topic: LD study of DAPI binding to DNA
Ref: David Sheehan, Physical Biochemistry, p. 96
Eriksson et al., Biochemistry (1993) 32, 2987.