58
Circular Dichroism in Protein Analysis
E
L
E
R
q
a
B
A
(a)
(b)
Fig. 1
(a) shows linearly polarized light
with equally intense left- and
right-polarized components (
E
L
and
E
R
). (b) Shows circularly polarized light
with unequal left- and right-circularly
polarized components.
θ
is the ellipticity
and is the ratio of the minor axis to the
major axis of the ellipse
(
A
/
B
)
;
α
is
called the
optical rotation
.
where
c
is the concentration in mg ml
1
;
MRW
is the mean residue weight, which
is equal to molecular mass/(
N
1);
N
is
the number of amino acid units and is
typically one more than the number of
peptide bonds, giving rise to the factor
of
N
1. The mean residue ellipticity
is independent of the pathlength and
concentration.
Although optical rotation is a dispersive
measurement requiring the measurement
over the complete spectrum, experimen-
tally the measurements are conFned to
a relatively narrow wavelength range. In
principle, CD can be measured with any
frequency of electromagnetic radiation.
However, in practice, most CD spec-
tra are recorded in the ultraviolet–visible
(UV–vis) region arising from electronic
transitions. Since the early 1980s, new
developments in optical and electronic
technology have enabled optical activity
measurements to be extended into the
vibrational spectrum using both infrared
and Raman techniques. We will focus on
electronic CD, which is more commonly
used, and will give only a brief description
of vibrational optical activity.
2
Electronic Circular Dichroism
CD spectra arise from transitions that
are electrically and magnetically allowed.
When an electron of a molecule is ex-
cited from the ground state to a higher
energy state, there is a change in the
electric Feld of the radiation or the mag-
netic Feld or both. The change of the
electric Feld causes a linear rearrange-
ment of the electrons. The net linear
displacement of charge during the transi-
tion is called the
electric transition dipole
moment
,
µ
. The magnetic Feld change
induces a circular rearrangement of elec-
tron density. The net circulation of charge
is termed the
magnetic transition dipole
moment
,
m
. In electronic absorption spec-
troscopy, bands arise from transitions that
are either electrically allowed and magnet-
ically forbidden or magnetically allowed
and electrically forbidden. The oscilla-
tor strength,
f
, is proportional to the
square of the electric transition dipole mo-
ment,
µ
2
, and corresponds to the area
under a band in an electronic absorp-
tion spectrum. The rotational strength of
a band in a CD spectrum is analogous
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