Fluorescence Polarization

CZECH TECHNICAL UNIVERSITY IN PRAGUE

FACULTY OF BIOMEDICAL ENGINEERING

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.

Natural light contains randomly all possible orientations of electric vector

Light propagation direction

Unpolarized (random) light

Polarization

E

BE

cn

B

2EI

an optical component that selects from passing light only the component polarized in a given direction

Unpolarized (random) 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)

PolarizerLinear polarized light

Polarizer

I0 I = I0/2

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 as the mobility of the emitting species

decreased.

Polarization and dipole transitionsAbsorption: The probability of a transition of a molecule between two energetic levels (for example S0 S1) is proportional to cos2, where is the angle between the dipole moment of the transition and the direction of polarization of the excitation light.

Emission of a point dipole is polarized in the direction of the dipole

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.

The emitted intensity is proportional to sin2, where is the angle between the dipole and the direction of propagation of the emitted light

+ -

The polarization state of fluorescence is described by:

Polarization in a fluorescence experiment

Z

Y

X

excitation

detection

I

I

Polarization

Anisotropy

IIII

III

rT 2ll

llll

IIII

Pll

ll

Anisotropy is preferred because it contains the total intensity IT

Polarization in a fluorescence experiment

Z

Y

X

excitation

detection

I

I

IIII

III

rT 2ll

llll

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 fluorophoresfi – fraction of i-th fluorophore

iii rfr

Polarization in a fluorescence experiment

Z

Y

X

excitation

detection

I

I

IIII

r2ll

ll

First we consider the simplest case – a single fluorophore with a fixed position of its transition dipole moment

D

I ≈ cos2

I≈ sin2 sin2

Next we take an ensemble of molecules with random values of

Averaging over : 21sin2 I≈ 1/2 sin2

21cos3 2

Polarization in a fluorescence experiment

Z

Y

X

excitation

detection

I

I

IIII

r2ll

ll

Let us consider random orientation of dipole moments – we have to average over

D

The probability density function of finding an excited molecule with a dipole under the angle :

21cos3 2

2cossin)( p

size of the “cone” for given photoselection

Polarization in a fluorescence experiment

Z

Y

X

excitation

detection

I

I

IIII

r2ll

ll

Let us consider random orientation of dipole moments – we have to average over

D

21cos3 2

2cossin)( p

53

dsincos

dsincos

d)(

d)(cos

cos 2

0

2

2

0

4

2

0

2

0

2

2

p

p

r0 = 0.4

Polarization in a fluorescence experiment

Z

Y

X

excitation

detection

I

I

IIII

r2ll

ll

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 between the two dipoles

Da

De

21cos3

52 2

0

r

r0 P0

0 0.4 0.5

54.7 0 0

90 -0.2 -0.333

Polarization of 2-photon fluorescence

74

21cos3 2

2

pr

Molecules can be excited by a simultaneous absorption of 2 photons. The molecule is excited by energy 2 hexc. The process is nonlinear – probability of excitation is proportional to Iexc

2.

The excitation probability is proportional to cos4 – different photoselection

42 cossin)( pp

75

cos2

hexc

hexc

hem hem > hexc

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 . Changes in are reducing the anisotropy caused by photoselection.

)exp()( 0 trtr

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:

DRTV

61

– viscosity

D – translational diffusion coefficient

For a globular protein: RT

hM

– partial specific volumeh – 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 of anisotropy measured by steady-state fluorescence spectroscopy:

1

1

dexp

dexp

d)(

d)()(

0

00

000

0

0 r

tt

I

ttt

rI

ttI

ttrtI

r

Perrin equation

Perrin, F. 1926. Polarisation de la Lumiere de Fluorescence. Vie Moyene des Molecules Fluorescentes. J. Physique. 7:390-401.

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.

VRT

PP o

1311

311

Perrin-Weber plot

Perrin equation for a spherical molecule expressed in terms of P E1

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

Measuremet of fluorescence anisotropy

Z

Y

X

vertical excitation

detection

I

I

VHVV

HVVV

GIIGII

r2

IVV

IVH

IPA

polarizer analyzer

V … vertical

H … horizontal

IVV = SV I

IVH = SH I

H

V

SS

G

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 !!!

Determination of G factor

Z

Y

X

horizontal excitation

detection

I

IHV

IHH

IPA

polarizer analyzer

V … vertical

H … horizontal

IHV = SV I

IHH = SH I

HH

HV

II

G

I

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 , for which I would contribute to the passing light with a double weight compared to I

22 sincos)( III ll

22 cos2sin

2tan2

74.54 Magic angle

I

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.

Time-resolved fluorescence anisotropy E2

2000 2100 2200 2300 24000

2000

4000

6000

8000

10000

12000

14000

Ph

oto

n c

ou

nts

Channel

IVH

IVV

POPOP

2060 2080 2100 2120 2140 2160 2180 22000,0

0,2

0,4

An

iso

tro

py

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

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).

F

FFF

F F

Hence for a given probe lifetime the polarization (or anisotropy) of the monomer will be less than that of the dimer

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

Lower P Higher P

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-GTPS (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

E3

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

FPIA – Fluorescence Polarization ImmunoAssay E4

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.

High PolarizationAntibody

+

Fluorophore-linked antigen

Unlabeled antigen

+Low Polarization

E4