Biomedical Engineering Reference
In-Depth Information
Another value often seen in the literature that is based on the same principle is
polarization (
P
). Polarization represents the fraction of light that is linearly polarized
and is derived from
I
−
I
⊥
P
=
(9.2)
I
+
I
⊥
Anisotropy and polarization convey similar information, but the relationship
between anisotropy and the fractional concentrations of fluorescent species is more
mathematically tractable and is thus preferred for data analysis. The terms can be
interconverted using the function
2
P
A
=
(9.3)
3
−
P
In practice, the maximum and minimum values of anisotropy (and polarization)
depend on ensemble measurements across populations of molecules. When excited
with polarized light, the probability that a given molecule will be oriented appropri-
ately for excitation is cos
2
q
, where
q
is the angle between the excitation plane and the
transition dipole (Fig.
9.2
). Furthermore, not all the excited molecules will be exactly
parallel to the excitation beam; instead the population will be proportional to sin
q
where
q
is the angle with the vertical axis. Incorporating these two additional pieces
of information, the effective upper and lower limits of anisotropy for most common
fluorophores are 0.4 and 0, respectively (for polarization they are 0.5 and 0) (Jameson
and Ross
2010
). Interestingly, the specific upper limit of polarization/anisotropy
(called the limiting or intrinsic polarization) of a given fluorophore also depends on
the excitation wavelength used in the experiment. This is because excitation can effect
more than one electronic transition in many fluorophores, which in turn may contrib-
ute differentially to emission (Jameson and Ross
2010
; Albinsson et al.
1991
) .
The specific polarization value of a given sample depends on the intrinsic polar-
ization (described above) and the extent of its rotation during the excited state life-
time. The Debye rotational relaxation time is a value that is used to compare molecular
rotations. It is defined as the time required for molecules of a given orientation to
rotate through arccos(
e
−1
) or 68.4°. This value is denoted as
r
0
and is equal to
3
V
RT
h
(9.4)
r
=
0
where
h
is the viscosity of solution,
V
is the effective molar volume of the rotating
unit (which is related to the specific volume of the protein and its hydration
(Lakowicz
1999
; Jameson and Ross
2010
) ,
R
is the gas constant, and
T
is the abso-
lute temperature. When considering the motion of a molecule in solution, the rela-
tionships between the determinants of the Debye rotational relaxation time seem
intuitive: with increasing viscosity and increasing molecular volume, the motion of
a rotating species would be retarded, increasing the relaxation time. By contrast, as
temperature rises, solvents tend to become more fluid and thus permissive of motion.
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