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1. Molecules aligned parallel to the electric field absorb light, molecules aligned perpendicular do not absorb light efficiently. In solution, where molecules tumble rapidly, light absorption is the spatial average of the transition dipole moment.

( ) 20

2222

0 31ˆ EE zyxab µµµµ ++=⋅ΨΨ

2. Without motion, the polarization of the emitted light is parallel to the excitation source. (assuming that the excitation and emission transition dipole moments are parallel)

3. With rapid motion, the emission polarization can either be parallel or perpendicular to the polarization of the excitation source

A - Polarization Anisotropy

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1. The anisotropy indicates the extent to which emission polarization is retained

⊥

⊥

+

−=

IIII

A2||

||

3. I|| + 2I⊥ : the total isotropic fluorescence intensity

Detector

Source

( E and B are ⊥ to direction of propagation)

2. I|| - I⊥ : the difference in the detected intensities of || & ⊥ polarized light

Anisotropy - Definition

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1. What are the Maximum and Minimum Values of A?

a.  AMIN = 0.0 AMAX = 1.0

b.  AMIN = 0.2 AMAX = 0.5

c.  AMIN = 0.0 AMAX = 0.4

d.  AMIN = 0.0 AMAX = 0.5

θ

φ

µ

x

z

y

I|| I⊥

1a. Relative number of excited molecule oriented between θ to θ + dθ and φ to φ + dφ:

φθθθφθφθ ddddP sincos),( 2∝

1b. The fraction of all the excited molecules that are between θ to θ + dθ and φ to φ + dφ:

( ) ( )φθθθ

πφθθθ

φθφθφθφθ ππ dd

dd

ddPddW sincos43

sincos

,, 22

0 0

2

==

∫ ∫

Photoselected Population

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1c. I|| ∝ |µ k|2 and I⊥ ∝ |µ i|2, which are proportional to cos2θ and (sinθcosφ)2, respectively. Integrating over all values of θ and φ

( ) ( ) ( ) ( )53sincos

43,cos

2

0 0

42

0 0

2|| ==∝ ∫ ∫∫ ∫ φθθθ

πφθφθθ

π ππ π

ddddWI

( ) ( ) ( ) ( ) ( ) ( )51sincoscos

43,cossin

2

0 0

3222

0 0

22 ==∝ ∫ ∫∫ ∫⊥ φθθθφπ

φθφθφθπ ππ π

ddddWI

4.052

52535153

2||

||MAX ==

+

−=

+

−=

⊥

⊥

IIII

A

Result:

Spring  2012

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1. Spherical Molecule in Solution à Single Exponential Decay

2. Lower symmetry Molecules à Multi-exponential Decays

cteAtA τ/0)( −=

Anisotropy Decay is Sensitive to Macromolecule Shape and Motional Restrictions

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Decay by Diffusion

( ) ( )tWDdt

tdWRot ,,,, 2 φθ

φθ∇=

by analogy to the one dimensional translational diffusion and random walk equations:

( ) ( )2

2 ,,x

txCDt

txC∂

∂=

∂

∂ Dtx 22 =

Initial Condition:

( ) θθπ

φθ sincos430,, 2=W

Photoselected Population

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Photo-selected Population will Decay by Diffusion to an Isotropic Distribution

…. But the Fluorescence also Decays, as exp(-t/τF). τF = [kF + kic + kis + kq(Q)]-1

( ) FtetW τφθ /,, −

Two time-dependent terms in the anisotropy:

1.  W(θ,φ,t) describes changes in angular distribution of the photoselected population by rotational diffusion

2.  e-t/τ describes fluorescence decay

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FRot ttD eeI τ/6|| 15

431 −−

⎥⎦

⎤⎢⎣

⎡⎟⎠

⎞⎜⎝

⎛+⎟⎠

⎞⎜⎝

⎛=

FRot ttD eeI τ/6

152

31 −−

⊥ ⎥⎦

⎤⎢⎣

⎡⎟⎠

⎞⎜⎝

⎛−⎟⎠

⎞⎜⎝

⎛=

( ) tDRotetA 6

52 −⎟⎠

⎞⎜⎝

⎛= where DRot = kT/fRot = kT/6Vhη

Spring  2012

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Rotational Motion of Membrane Proteins

Kawato et al. 1981. Rotation of cytochrome oxidase in phospholipid vesicles. Investigations of interactions between cytochrome oxidases and between

cytochrome oxidase and cytochrome bc1 complex. J. Biol. Chem. 256:7518-27.

Lipid bilayer

Membrane Protein

Rotational motion can be measured whenever there is a component of the transition dipole in the plane of the membrane