Circular dichroism (CD) arises as a consequence of differential absorption of left and right
handed circularly polarized light by an optically active sample. The resultant radiation after
passing through the sample, is elliptically polarized and hence the CD signal is reported in terms
of the ellipticity angle (inverse tangent of the minor axis over major axis of the ellipse).125 A CD
signal originates from electronic transitions from the ground state to the excited state of the
system under study. Thus, the main parameters monitored for a CD band in a spectrum are - the
bandwidth, the wavelength corresponding to maximum ellipticity (max), and the intensity
associated with max. 126
2.1.1 CD spectroscopy in proteins
CD is a widely used technique in protein spectroscopy where electronic transitions occurring in a
protein backbone (amide group), in the far UV region, such as - 1) n→* transition at 220 nm, 2)
→* transition at 190 nm and 3) →* transition at 170 nm, have been used to study the
secondary structure content in polypeptides.127,128 Some of the common secondary protein
structures are α-helices, β-sheets and random coils (disordered structure). Each secondary structure, having different non covalent interactions, yields a distinct protein conformation, which
can then give rise to unique spectral signatures in CD spectroscopy. For instance, the CD
spectrum of a β-sheet contains the following signatures – 1) a positive band at 195 nm, corresponding to a →* transition and 2) a negative band at 216 nm, corresponding to an n→*
transition. Similarly, the n→* transition in α-helices gives rise to a negative signal at 222 nm, while a dipole-dipole coupling between the two →* transitions leads to an exciton splitting in
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α-helices, thus creating two bands, a positive one at 192 nm and a negative band at 208 nm. Additionally, proteins with a disordered structure only have a unique, negative CD band at 200
nm.127,128
The intensity of the CD signals corresponding to these transitions can change depending
on the environmental conditions around a protein, especially upon increasing temperature or
adding denaturants to the solution. Thus, the change in ellipticity of a CD band, at a particular
wavelength, can be utilized to tease out the thermodynamics of the folding process in a protein.
For example, if the ellipticity value of the negative band at 222 nm for an α-helix is monitored
with increasing temperature, then the resultant sigmoidal curve can be fitted to the following
equation corresponding to a two-state folding model.129,130
[𝛳](𝑇) =[𝛳]u(𝑇)+𝐾𝑒𝑞(𝑇)[𝛳]f(𝑇)
1+𝐾𝑒𝑞(𝑇) (2.1)
Here, [𝛳](𝑇) is the mean residue ellipticity or the net CD signal at 222 nm, [𝛳]u(T) and [𝛳]f(T)
are the mean residue ellipticity values of the unfolded state and folded state baselines
respectively, and 𝐾𝑒𝑞(𝑇) is the temperature dependent equilibrium constant. All the mean residue
ellipticity values are temperature dependent and the baselines are considered to be linearly
dependent on temperature as per the equations shown below:
[𝛳]u(𝑇) = a + b𝑇 (2.2)
[𝛳]f(𝑇) = c + d𝑇 (2.3)
Here a, b, c and d are constants.
The equilibrium constant, 𝐾𝑒𝑞(𝑇) can be further expressed in terms of thermodynamic
parameters, 𝛥𝐺 (change in free energy), 𝛥𝐻 (change in enthalpy) and 𝛥𝑆 (change in entropy), at the melting temperature (𝑇𝑚), where 50% of the protein is in an unfolded state. Furthermore, 𝑇𝑚
can be expressed as 𝑇𝑚 = 𝛥𝐻
𝛥𝑆 and 𝛥𝐶𝑃 is referred to as the change in heat capacity for the
17 𝐾𝑒𝑞(𝑇) = e −𝛥𝐺(𝑇) RT (2.4) 𝛥𝐺 (𝑇) = 𝛥𝐻 + 𝛥𝐶𝑃(𝑇 − 𝑇𝑚) − 𝑇{𝛥𝑆 + 𝛥𝐶𝑃𝑙𝑛 ( 𝑇 𝑇𝑚)} (2.5)
Therefore, by fitting the CD thermal melting curves to the two-state model, the melting
temperature of a protein (𝑇𝑚) can be determined.
2.1.2 Coupling between electronic transitions giving rise to CD signals
CD signatures originate from the coupling between electronic transition dipole moments in a
chromohore.126 Each electronic transition has an electric and a magnetic transition dipole
associated with it. While the electric transition dipole arises as a result of a linear displacement of
charge, the magnetic transition dipole exists due to a circular motion of the charge within the
chromophore. Furthermore, whether electronic transitions are allowed or forbidden that depends
on whether the corresponding electrical and magnetic transitions are allowed or not, and this
phenomenon is governed by the symmetry of the system under study. For instance, in simple,
centrosymmetric molecules, a transition can be either electrically allowed (large electric transition
dipole moment) or magnetically allowed (large magnetic transition dipole moment) but not both.
This rule however doesn’t hold for chirotopic molecules responsible for circular dichroism. In fact, both transitions can be responsible for CD bands, since the simplest case involves a helical
displacement of charge that includes both the linear and circular displacement components. The
integrated area under a CD band which can be expressed as the rotational strength of band (𝑅), is therefore directly proportional to the dot product of the electric (𝜇 ⃗⃗⃗ ) and magnetic (𝑚 ⃗⃗⃗⃗ ) transition dipole moment vectors.131
𝑅 ∝ 𝜇 ⃗⃗⃗ . 𝑚 ⃗⃗⃗⃗ (2.6) For large, complex, optically active molecules/chromophores, the CD spectrum can be easily
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interpreted, by dividing the molecule into various groups. Each group has its own set of electronic
transitions which are either electrically allowed (large 𝜇 ⃗⃗⃗⃗ , small 𝑚 ⃗⃗⃗⃗ ) or magnetically allowed (small 𝜇 ⃗⃗⃗⃗ , large 𝑚 ⃗⃗⃗⃗ ) or has significant contributions coming from both dipoles. The transitions across two groups can also undergo coupling, such as the μ-m coupling. This coupling takes place when the dipole moment vectors corresponding to an electrically allowed transition and a
magnetically allowed transition, arising from different groups within the same chromophore
couple to each other. When the coupling is extended to two different chromophores, where one
has a electrical transition dipole moment that predominates and the other has a resultant magnetic
transition dipole moment, then the phenomenon is known as one-electron mixing. Similarly, the
coupling of dipole moments of two chromophores having electrically allowed transitions can also
be envisioned.131 This phenomenon is commonly called exciton coupling and one such scenario
where exciton coupling is observed in proteins, is described in the next section.
2.1.3 Exciton coupling in proteins
For amino acids having aromatic side chains (chromophores A and B), located in close proximity
(8 - 10 Å) and having a specific orientation, their electric transition dipole moments can strongly
interact, thereby splitting the energetically close excited states into two levels. These two levels
are created as a result of the in-phase and out of phase combination of the excited state energies
of the individual chromophores and the phenomenon is called exciton coupling. A bisignate CD
couplet is thus created and the rotational strengths (𝑅𝐴𝐵) associated with the transitions to the
newly formed energy levels are proportional to the distance between the chromophores (𝑟𝐴𝐵) and
their transition dipole moments, that are predominantly electric in nature, 𝜇⃗⃗⃗⃗ 𝐴 and 𝜇⃗⃗⃗⃗ 𝐵.126
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Extinction coefficients (∆𝜀) corresponding to these transitions are directly proportional to
𝑅𝐴𝐵and the splitting (𝑉𝐴𝐵 ) between the two newly formed energy levels.126 Assuming that 𝑉𝐴𝐵
can be expressed as a dipole-dipole interaction potential, the Δε values for the two transitions can then be written in the form of the following equations.
∆𝜀 ∝ ± 𝑉𝐴𝐵 𝑟⃗⃗⃗⃗⃗⃗ . 𝜇𝐴𝐵 ⃗⃗⃗⃗⃗ × 𝜇𝐴 ⃗⃗⃗⃗⃗ 𝐵 (2.8)
∆𝜀 ∝ ± 𝜇𝐴2𝜇𝐵2
𝑟𝐴𝐵2 𝜃(𝑎, 𝑏, 𝑐) (2.9)
In equation (2.9), apart from the electric transition dipole moments, there is an interchromophoric
distance dependent term (𝑟𝐴𝐵2 ) between the two chromophores, and an orientation term θ,
consisting of angles - ‘𝑎’, ‘𝑏’ and ‘𝑐’. While angles ‘𝑎’ and ‘𝑏’ represent the angle between the individual transition dipole moment vectors and 𝑟𝐴𝐵, angle ‘𝑐’ represents the angle between 𝜇⃗⃗⃗⃗⃗ 𝐴
and 𝜇⃗⃗⃗⃗⃗ 𝐵. Now, if the two transition dipole moments are oriented in a way as shown in Figure 2.1,
then it would take a counterclockwise rotation to superimpose the dipole moment in the front on
to the one at the back. This would result in a negative extinction coefficient value for the
maximum wavelength component of the couplet. Thus, if the directions of the transition dipole
moment vectors are known for the interacting aromatic amino acid chromophores, the sign of the
exciton coupling band can be predicted. Additionally, based on the extinction coefficient value, it
is also possible to estimate the distance between the two aromatic amino acids, provided the
values and directions of their transition dipole moments are known.126
The transition dipole moments corresponding to a pair of tryptophan residues in proteins
have been found to couple with each other and form exciton coupling bands. Earlier studies have
shown that cross-strand Trp-Trp interactions can stabilize β-hairpin peptides132 and this
phenomenon has been used to probe short distances and conformational changes in a protein (tear
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