Transcript Polarization of fluorescence

Fluorescence Polarization
Polarization
Light is a harmonic electromagnetic wave. When considering its interaction with
matter we can in most cases neglect the magnetic part. The plain in which the
electric vector E oscillates defines the polarization of light.
B
B
E
n
E
c
I  E2
Natural light contains randomly all possible orientations of electric vector
Unpolarized
(random) light
Polarizer
an optical component that selects from passing light only the component polarized
in a given direction
I0
I = I0/2
Polarizer
Unpolarized (random) light
Linear polarized light
Common polarizers:
• double refracting (birefrigent) calcite (CaCO3) crystals- which refract components
of light polarized in two perpendicular planes under different angles
• filters, which effectively absorb one plane of polarization (e.g., Polaroid type-H
sheets based on stretched polyvinyl alcohol impregnated with iodine)
In 1920, F. Weigert discovered that the fluorescence from solutions of
dyes was polarized. Specifically, he looked at solutions of fluorescein,
eosin, rhodamine and other dyes and noted the effect of temperature
and viscosity on the observed polarization. Wiegert discovered that
polarization increased with the size of the dye molecule and the
viscosity of the solvent, yet decreased as the temperature increased.
He recognized that all of these considerations meant that fluorescence
polarization increased
decreased.
as the mobility
of
the emitting
species
Polarization and dipole transitions
Absorption: The probability of a transition of a molecule between two energetic
levels (for example S0  S1) is proportional to cos2f, where f is the angle between
the dipole moment of the transition and the direction of polarization of the excitation
light.
+
-
potential dipole orientation
probability of excitation
Photoselection: The phenomenon of anisotropic distribution of orientation of
molecules in excited state in the sample caused by the properties of excitation light.
Emission of a point dipole is polarized in the direction of the dipole
The emitted intensity is proportional to sin2x,
where x is the angle between the dipole and the
direction of propagation of the emitted light
Polarization in a fluorescence experiment
Z
excitation
I
X
detection
I
Y
The polarization state of fluorescence is described by:
Polarization
Anisotropy
Ill  I
P 
Ill  I
Ill  I
Ill  I
r 

IT
Ill  2I
Anisotropy
is
preferred
because it contains the
total intensity IT
Polarization in a fluorescence experiment
Z
Ill  I
Ill  I
r 

IT
Ill  2I
excitation
I
X
detection
I
Y
Why is the total intensity IT equal to I + 2 I ???
For the reason of symmetry the component polarized in the X direction
and Y direction have the same intensity I, but in the given geometry we
detect only the one polarized in X direction.
Note: anistropy of a mixture of fluorophores
fi – fraction of i-th fluorophore
r 
f
i
i
ri
Polarization in a fluorescence experiment
Z
Ill  I
3 cos2 q  1
r 

Ill  2I
2
D
q
excitation
I ≈ cos2q
I
X
detection
f
I
I≈ sin2f sin2q
Y
First we consider the simplest case – a single fluorophore with a
fixed position of its transition dipole moment
Next we take an ensemble of molecules with random values of f
Averaging over f:
sin2 f  1 2
I≈ 1/2 sin2q
Polarization in a fluorescence experiment
Z
Ill  I
3 cos2 q  1
r 

Ill  2I
2
D
q
excitation
I
X
detection
f
I
Y
Let us consider random orientation of dipole moments – we have
to average over q
The probability density function of finding an excited molecule with a dipole
under the angle q:
p(q )  sinq cos2 q
size of the “cone” for given q
photoselection
Polarization in a fluorescence experiment
Z
Ill  I
3 cos2 q  1
r 

Ill  2I
2
D
q
r0 = 0.4
excitation
I
X
detection
f
I
p(q )  sinq cos2 q
Y
Let us consider random orientation of dipole moments – we have
to average over q
 2
 cos q p(q ) dq
 2
2
cos2 q 
0
 2
 p(q ) dq
0

4
cos
q sinq dq

0
 2
2
cos
q sinq dq

0

3
5
Polarization in a fluorescence experiment
Z
Da
De
excitation
q
a
I
X
f
I
r 
Ill  I
Ill  2I
a
r0
P0
0
0.4
0.5
54.7
0
0
90
-0.2
-0.333
Y
detection
The derivation was true for molecules with collinear transition dipole
moments of absorption and emission, that is however not a general
situation. Let us consider an angle a between the two dipoles
2  3 cos2 a  1 

r0  
5
2

Polarization of 2-photon fluorescence
Molecules can be excited by a simultaneous absorption of 2 photons.
The molecule is excited by energy 2 hnexc. The process is nonlinear –
probability of excitation is proportional to Iexc2.
hnexc
hnem
hnem > hnexc
hnexc
The excitation probability is proportional to cos4q – different
photoselection
p2p(q )  sinq cos4 q
cos2 q 
r2 p
5
7
3 cos2 q  1 4


2
7
Polarization of multiphoton fluorescence
Anisotropy and molecular motion
So far we have considered “frozen” molecules. However, in reality
the molecules are mobile and their rotation changes the
orientation of the dipole q. Changes in q are reducing the
anisotropy caused by photoselection.
r(t )  r0 exp( t )
Where  is the rotational correlation time (Debye rotational relaxation time)
which is the time for a given orientation to rotate through an angle given by the
arccos e-1 (68.42o).
For a spherical molecule:
For a globular protein:
V
1
 

RT 6D
 
M   h
RT
 – viscosity
D – translational diffusion
coefficient
 – partial specific volume
h – degree of hydration
Temporal decay of anisotropy
The temporal decay of anisotropy due to molecular rotations can be
investigated by time-resolved fluorescence spectroscopy (like fluorescence
lifetimes – TCSPC, frequency domain)
It also influences the value
fluorescence spectroscopy:

r 
 I(t ) r(t ) dt
0

 I(t ) dt
0
of
anisotropy
measured
by
steady-state

 t t
I
r
exp
0 0 0       dt
1


r
0


 t
1

0 I0 exp    dt

Perrin equation
Perrin, F. 1926. Polarisation de la Lumiere de Fluorescence. Vie Moyene des
Molecules Fluorescentes. J. Physique. 7:390-401.
Perrin equation for a spherical molecule expressed in terms of P
1 1  1 1 
RT 
    1 
 
P 3  Po 3 
V 
E1
Perrin-Weber plot
A plot of 1/P - 1/3 versus T/ predicts a straight line, the intercept and slope of
which permit determination of Po and the molar volume (if the lifetime is known).
Shown below is such a plot (termed a Perrin-Weber plot) for protoporphyrin IX
associated with apohorseradish peroxidase - the viscosity of the solvent is varied
by addition of sucrose.
Measuremet of fluorescence anisotropy
Z
IPA
polarizer
analyzer
V … vertical
vertical
excitation
H … horizontal
IVV
I
X
detection
I
IVV = SV I
IVH = SH I
Y
IVH
The plane defined by the direction of excitation and detection (XY) is called
horizontal (it is usually horizontal in the experiment). The measured intensities
are identified by two indices describing the orientations of the excitation polarizer
and analyzer (the polarizer in the detection channel). We have to account for
different sensitivities S of detection of individual polarizations
r 
IVV  GIHV
IVV  2GIVH
G
SV
SH
Determination of G factor
Z
IPA
polarizer
analyzer
V … vertical
horizontal
excitation
H … horizontal
IHV
I
X
detection
I
IHV = SV I
IHH = SH I
Y
IHH
In the case of horizontal excitation (excitation light polarized in Y direction), the
light polarized in Z and X direction, which we detect are both I !!!
G
IHV
IHH
Magic angle
If we place no analyzer in the detection pathway, we measure I + I. That is,
however, not the total intensity IT = I + 2 I . The fluorescence intensity decays
measured in that way may be, therefore, distorted due to anisotropy decay.
• We can either measure separately I and I and calculate IT.
• or we can measure with an analyzer oriented under an angle x, for which I
would contribute to the passing light with a double weight compared to I
I(x )  Ill cos2 x  I sin2 x
I
sin2 x  2 cos2 x
tan2 x  2
x
x  54.74
Magic angle
I
Note: Even unpolarized excitation causes photoselection, because the light
transversally polarized. In that case the maximal anisotropy (for collinear transition
dipole moments) r0MAX = 0.2.
E2
Time-resolved fluorescence anisotropy
POPOP
0,4
14000
IVH
8000
IVV
Photon counts
10000
Anisotropy
12000
6000
0,2
4000
2000
0
2000
2100
2200
Channel
2300
2400
0,0
2060
2080
2100
2120
2140
2160
2180
Channel
Note: Scattered light can cause higher anisotropy, because it is completely
polarized (rsc = 1). It is necessary to minimize scattering for accurate anisotropy
measurement
2200
Polarization methods are ideally suited to study the aggregation state of proteins.
Consider, for example, the case of a protein dimer - monomer equilibrium.
F
F
Following either intrinsic protein fluorescence (if possible) or by labeling the
protein with a suitable probe one would expect the polarization of the system to
decrease upon dissociation of the dimer into monomers since the smaller
monomers will rotate more rapidly than the dimers (during the excited state
lifetime).
Lower P
Higher P
Hence for a given probe lifetime the polarization (or anisotropy)
of the monomer will be less than that of the dimer
E3
The polarization/anisotropy approach is also very useful to study
protein-ligand interactions in general.
The first application of fluorescence polarization to monitor the binding of small
molecules to proteins was carried out by D. Laurence in 1952 using Gregorio
Weber’s instrumentation in Cambridge. Specifically, Laurence studied the binding
of numerous dyes, including fluorescein, eosin, acridine and others, to bovine
serum albumin, and used the polarization data to estimate the binding constants.
E3
A typical plot of polarization versus ligand/protein ratio is
shown below:
In this experiment, 1 micromolar mant-GTPS (a fluorescent, non-hydrolyzable GTP
analog) was present and the concentration of the GTP-binding protein, dynamin, was
varied by starting at high concentrations followed by dilution. The binding curve was
fit to the anisotropy equation (in this case the yield of the fluorophore increased
about 2 fold upon binding). A Kd of 8.3 micromolar was found
FPIA – Fluorescence Polarization ImmunoAssay
E4
Among the first commercial instruments designed to use a fluorescence
polarization immunoassay for clinical diagnostic purposes was the Abbott TDx –
introduced in 1981.
The basic principle of a polarization immunoassay is to:
1.
Add a fluorescent analog of a target molecule – e.g., a drug – to a solution
containing antibody to the target molecule
2.
Measure the fluorescence polarization, which corresponds to the fluorophore
bound to the antibody
3.
Add the appropriate biological fluid, e.g., blood, urine, etc., and measure
the decrease in polarization as the target molecules in the sample fluid bind
to the antibodies, displacing the fluorescent analogs.
E4
+
Antibody
Fluorophore-linked
antigen
High Polarization
Unlabeled antigen
Low Polarization
+