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7. Fluorescence microscopy
7.3 FRET microscopy
Radiationless excitation energy transfer
requires interaction between donor and
acceptor

Emission spectrum of donor must
overlap with absorption spectrum of
acceptor.

Several vibronic transitions within
donor have the same energy than in
the acceptor
 Resonant coupling of the transitions
 RET = resonance energy transfer
Resonant transitions
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IPC Friedrich-Schiller-Universität Jena
7. Fluorescence microscopy
7.3 FRET microscopy
Radiationless excitation energy transfer
 Assumption: 2 electrons one at the donor D and one at the acceptor A are
involved in the transition:
 Antisymmetric wavefunction (Fermions) for initially excited state i (D
excited, but not A) and final state f (A excited, but not D):
Overall Hamiltonian:
Interaction energy:
Coulomb term UC
2

Exchange term Uex
IPC Friedrich-Schiller-Universität Jena
7. Fluorescence microscopy
7.3 FRET microscopy
Radiationless excitation energy transfer
Coulomb Interaction (CI)
Exchange Interaction
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IPC Friedrich-Schiller-Universität Jena
7. Fluorescence microscopy
7.3 FRET microscopy
Radiationless excitation energy transfer
 Different interaction mechanism lead to excitation energy transfer:
Dipolar
(Förster)
„Long
Range“
Coulomb
interaction
Multipolar
Singlet
energy transfer
Inter molecular
orbital overlap
Triplet
Energy transfer
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Electron
exchange
(Dexter)
„Short
Range“
Charge
resonance
interaction
IPC Friedrich-Schiller-Universität Jena
7. Fluorescence microscopy
7.3 FRET microscopy
Radiationless excitation energy transfer
 Coulomb interaction dominates for allowed i.e. singlet-singlet-transitions.
 For forbidden transitions i.e. singlet-triplet-transitions exchange-interaction (only
acting for short distances < 10 Å because overlap of orbitals is necessary)
dominates.
 Coulomb interactions appears also for larger distances up to 80 – 100 Å.
 Interaction strength depends on interaction energy (U), energy distance between
D* and A* (E), absorption bandwidth (w) and vibronic bandwidth ().
Strong coupling:
Weak coupling:
Very weak coupling:
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U>>E
U>>E
U<<<<w
U>>w,
w>>U>>
IPC Friedrich-Schiller-Universität Jena
7. Fluorescence microscopy
7.3 FRET microscopy
Förster Resonance Energy Transfer (very weak coupling):
D + hn1
D* + A
A*
 D*
 A* + D
 A + hn2
Absorption
Energy transfer
Emission
The following conditions must hold:
 D must be a fluorophore with sufficiently
long life-time
 Partial spectral overlap between emission
spectrum of D and absorption spectrum of A
 Transition dipole moments D and A must
be oriented properly to each other;
 Distance between D and A shouldn‘t be too
large
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IPC Friedrich-Schiller-Universität Jena
7. Fluorescence microscopy
7.3 FRET microscopy
Förster Resonance Energy Transfer (very weak coupling):
 Coulomb interaction can be developed in a multipole series in which the dipole
term exhibits the term with the longest range
 Energy transfer via dipole-dipole transfer has been first calculated by Förster
and is therefore called Förster process
 Energy transfer rate from molecule D to molecule A at a distance r:
kD = radiative decay rate of donor
tD0 = donor life-time in absence of energy transfer
r-6-dependency as a result of dipole-dipole interaction
R0 = critical distance or Förster-radius (distance at which intensity
decrease caused by energy transfer and spontaneous decay are
equal (
= kD)).
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IPC Friedrich-Schiller-Universität Jena
7. Fluorescence microscopy
7.3 FRET microscopy
Förster Resonance Energy Transfer (very weak coupling):
 R0 can be determined via spectroscopic values:
Overlap between fluorescence of donor and
absorption of acceptor
k2 = orientational factor
F0D = quantum yield of donor in absence of energy transfer
n = average refractive index for wavelength area of spectral overlap
ID(l) = normalized fluorescence spectrum of donor (
)
A(l) = molar absorption coefficient of acceptor.
 For R0 in Å, l in nm, A(l) in M-1 cm-1 (overlap integral in M-1 cm-1 nm4)

 Typical values for Förster-radii R0, i.e. for distances, over which energy transfer is
important lie in the range of 15 -60 Å
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IPC Friedrich-Schiller-Universität Jena
7. Fluorescence microscopy
7.3 FRET microscopy
Förster Resonance Energy Transfer (very weak coupling):
 Transfer efficiency can be expressed by:
 In combination with changed lifetime:
1
D

1
 D0
 k Add D
distance dependency:
 It follows:
D und D0 are excited state life-times of
donor in absence and presence of
acceptor, respectively
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IPC Friedrich-Schiller-Universität Jena
7. Fluorescence microscopy
7.3 FRET microscopy
Förster Resonance Energy Transfer (very weak coupling):
 Besides the distance between the two chromophores also the relative orientation
of the transition dipole moments of the donor D and acceptor A plays a crucial
role for the energy transfer efficiency
 The orientation factor k2 is given by:
A: angle between D-A connecting line and
acceptor transition dipole moment
D: angle between D-A connecting line and
donor transition dipole moment
T: angle between donor and acceptor
transition dipole moment
D
A
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IPC Friedrich-Schiller-Universität Jena
7. Fluorescence microscopy
7.3 FRET microscopy
Förster Resonance Energy Transfer (very weak coupling):
 For systems where the orientation stays constant during the
energy transfer (e.g. usage of highly viscose solvents or
rigid coupling of chromophores to large and stiff molecules)
k2 can reach values between 0 (transition dipole moments
are orthogonal) and 4 (collinear arrangement); k2 = 1, for a
parallel arrangement
 If both acceptor and donor can rotate the orientational factor k2 must be
replaced by an average value:
 In case both chromophores undergo a fast isotropic rotation i.e. the
rotation is considerably faster than the energy transfer rate the average
orientation factor is given by k2 = 2/3
 In case donor and acceptor are freely movable but the rotation is
significantly slower than the energy transfer the orientation factor results
in: k2 = 0.476
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IPC Friedrich-Schiller-Universität Jena
7. Fluorescence microscopy
7.3 FRET microscopy
Förster Resonance Energy Transfer (very weak coupling):
 RET is utilized as „optical nano ruler“ (10 – 100 Å) in biochemistry and cell
biology
 Distance between donor and acceptor should be in the range of:
because R0 is a benchmark for donor-acceptor distances which can be
determined by FRET.
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IPC Friedrich-Schiller-Universität Jena
7. Fluorescence microscopy
7.3 FRET microscopy
Förster Resonance Energy Transfer (very weak coupling):
 RET as „optical nano ruler“ in biochemistry and cell biology
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IPC Friedrich-Schiller-Universität Jena
7. Fluorescence microscopy
7.3 FRET microscopy
Förster Resonance Energy Transfer (very weak coupling):
 RET as „optical nano ruler“ in biochemistry and cell biology
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IPC Friedrich-Schiller-Universität Jena
7. Fluorescence microscopy
7.3 FRET microscopy
Förster Resonance Energy Transfer (very weak coupling):
 RET as „optical nano ruler“ in biochemistry and cell biology
One requires appropriate method to label specific intracellular proteins with
suitable fluorophores (fluorescent proteins genetics):
 Green Fluorescent Protein (GFP) first isolated from the jellyfish Aequorea
victoria
GFP can be combined with just about any other protein
by attaching its gene to the gene of a target protein,
thereby introducing it into a cell. Thus by recording the
GFP fluorescence the spatial and temporal distribution
of this target protein can be directly monitored in living
cells, tissue and organism.
Several GFP mutants with altered fluorescence spectra
exist. These mutants are named according to their color
e.g. CFP (cyan) or YFP (yellow)
Excitation maxima at 395 und 475 nm
Emission wavelength at 509 nm
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IPC Friedrich-Schiller-Universität Jena
7. Fluorescence microscopy
7.3 FRET microscopy
Agar plate of
fluorescent bacteria
colonies
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IPC Friedrich-Schiller-Universität Jena
7. Fluorescence microscopy
7.3 FRET microscopy
Förster Resonance Energy Transfer (very weak coupling):
 RET as „optical nano ruler“ in biochemistry and cell biology :
GFP-mutants
FRET
R0 = 4.7 – 4.9 nm
no FRET
protein folding
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protein-protein interaction
IPC Friedrich-Schiller-Universität Jena