Fluorescence Lifetime of Fluorescent Proteins - Fluorescent Proteins: From Understanding to Design - page 76

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:
D n N H ~ 3,300 cm 1 ) but E of GdFP roughly corresponds to D v ¼ 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

to D v ¼ 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

D

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 .

D

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

ð A 21 þ k IC þ k Iso þ k PET þ k FRET þ Þ S½

1
t Fl ¼

! A 21 þ k IC þ k Iso þ k PET þ k FRET þ:

(9)