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Fig. 4 Experimental isotope effect on the basis of the energy-gap law. (a) The longer component
of the fluorescence decay in Gold fluorescent Protein (GdFP) [ 35 ] prolongs from t Fl
¼ 2.7 ns to
t Fl
¼ 4.2 ns upon H 2 O/D 2 O exchange. The decay faster component is, probably, a result of the
structural heterogeneity of GdFP. (b) The prolongation can be explained by the energy-gap law:
n N H ~ 3,300 cm 1 ) but
E of GdFP roughly corresponds to
5 quanta of an N-H vibration (
n N D ~ 2,300 cm 1 ). Calculations on the model of Fig. 3a,
b and (8) ( inset ; wavefunctions are only half depicted) yield a reduction of k IC by a factor 400 upon
isotope exchange which is then too slow to compete with k rad
7 quanta of an N-D vibration (
structural analyses that the more planar a chromophore is in the crystallographic
structure the longer is t Fl .
One-dimensional potential curves as depicted in Fig. 3 are only a rough approxi-
mation of the real circumstances of complex potential energy surfaces (PES). Even
the chromophore itself exhibits a conformational space with more than 40 degrees
of freedom. Displacements along some combinations of the underlying normal
coordinates q i lead to close approaches of the S 0 and S 1 PES, i.e.,
E is small and
efficient IC can occur. Even crossings of the different PES can exist in so-called
conical intersections (CIs). However, isotope effects are unexpected for
E ~0,
and only quantum-mechanical treatments can give evidence for the corresponding
radiationless transition from S 1 to S 0 [ 37 ]. It should be emphasized that only the
knowledge of the coordinates q i , i.e., geometric changes of the chromophore after
excitation, gives a basis for the suppression of these movements and, thus, the
fundament for a rational design of FPs with prolonged t Fl .
1.5 Other Mechanisms Which Compete with Fluorescence
There are other mechanisms which can lead to a reduction of
t Fl . They are
accounted for in (9) as additional rate constants.
d S ½
d t ¼
A 21 þ
k IC þ
k Iso þ
k PET þ
k FRET þ
t Fl ¼
A 21 þ
k IC þ
k Iso þ
k PET þ
k FRET þ:
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