Fluorescence Lifetime of Fluorescent Proteins - Fluorescent Proteins: From Understanding to Design - page 72

spectrum I fl (n) and is used for calculating the centre frequency h n i of the fluo-

3 (3). In a rough approximation, one could
also use the third power of the frequency at the maximum of the fluorescence
spectrum, n max .

rescence spectrum, weighted by n

Ð I fl

fl 1

ðÞ dn

n 3

Ð n 3 I fl

3

¼

dn n

max :

(3)

ðÞ

One caveat has to be mentioned. Although the calculation according to (2) works
reasonably well for good fluorophores, the absorbing ground state S 0 as well as the
emitting excited state S 1 should possess a more or less similar electron distribution.
This is satisfyingly fulfilled for the anionic chromophore species in FPs, i.e., most
GFP (Green Fluorescent Protein), YFP (Yellow Fluorescent Protein) and, likely,
red fluorescent proteins [ 21 ], although also structural changes due to vibrational
relaxation may influence Einstein's relations. Equation (2) certainly fails when
excited-state reactions such as excited-state proton transfer (ESPT) as in wild-
type GFP (wt-GFP) are involved.

1.3 Meaning of Absorption Spectra

According to (2), there seem to be two ways to enhance the radiative rate constant
A 21 . The first approach is to enhance the refractive index n 0 of the surrounding.
Its importance is experimentally proven and is used to map the refractive index
within cells [ 24 - 26 ]. It also influences lifetime measurements at cryogenic tem-
peratures where glycerol or sugars are added as cryoprotectors. Furthermore, the
refractive index influence on A 21 is surely one of the reasons for the, generally
observed, shortened fluorescence lifetime in cells compared to aqueous solutions.
Significantly higher refractive indices than in water were detected for the cytosol
( n 0 ¼

1.45) [ 27 - 29 ]. It is also especially impor-
tant if t Fl is measured close to glass or, via a different mechanism, close to metal
surfaces [ 30 ].
The other appealing approach would be to increase the extinction coefficient
e abs (n). However, the so-called oscillator strength f 12 is given for a chromophoric
system and can be hardly influenced by mutagenesis of the surrounding protein barrel.
f 12 is a dimensionless, molecular quantity for one electronic transition, e.g. absorption
from S 0 to S 1 . It is related to e abs (n) which is experimentally accessible (4).

1.36-1.38) and membranes ( n 0 ¼

ð

4 m e e 0 c
e 2

ln 10
N A

f 12 ¼ e abs ðÞ dn : (4)

The first term contains the electron mass m e , the dielectric permittivity e 0 of the
vacuum and the elementary charge e. The conversion to the molecular quantity is,