Biophotonics_Concepts_to_Applications

temperature), lifetime measurements under a microscope allow the observation of
molecular effects through the spatial variations of thefluorescence lifetimes.
After an acceptor molecule is raised to an excited state, it can dissipate part of the
absorbed energy through interactions with other molecules. This process is called
fluorescence quenching. In this case thefluorescence lifetimeτQbecomes shorter than
τ 0 , as is shown in Fig.9.7. Quenching molecules include oxygen, halogens (bromine,
chlorine, iodine), heavy atoms (iodides, bromides), heavy metal ions (cesium, copper,
lead, nickel, silver), and a variety of organic molecules. For the accurate use of
quenchers in FLIM it is important that thefluorescent quenching rate depends linearly
on the concentration of the quenchers. Thereby the quencher concentration can be
determined directly from the decrease in thefluorescence lifetime [ 13 ].
When a quencher with afluorescence lifetimeτQis added, the intensity decay
becomes a double exponential. This can be expressed as

I(t)¼a 1 expðt=s 0 Þþa 2 expðt=sQÞð 9 : 3 Þ

Here the parametersα 1 andα 2 are called theintensity factors.

Example 9.4Consider the case in which twofluorophores are attached to a

molecule. Suppose thefluorescence lifetimes of thefluorophores are 1 and

5 ns, respectively, and letα 1 =α 2 = 0.5.

(a) What is the expression for thefluorescence intensity?

(b) Make plots of ln I(t) versus t for the two casesfirst whenα 1 = 0 and then

whenα 2 = 0. Let t range from 0 to 8 ns.

(c) Plot the ln I(t) versus t curve for the combinedfluorophores.

Solution: From Eq. (9.3) thefluorescence intensity is given by

I(t)¼ 0 :5 exp(t= 5 Þþ 0 :5 exp(t= 1 Þ

The three curves for parts (b) and (c) are given in Fig.9.8.

Time t (ns)

Intensity (arbitrary units)

13245

Unquenched fluorescence exp[-t/τ 0 ]

0.2

0.4

0.6

0.8

1.0

Quenched fluorescence exp[-t/τQ]

Excitation event

Fig. 9.7 Examples of
fluorescence decay for
fluorophores with lifetimesτ 0
andτQ

268 9 Spectroscopic Methodologies