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FIGURE 20.7
Two ways in which two fluorescent molecules in a single spot lose their colocalization.
(A) Two spots become colocalized and separated without photobleaching. (B) One of the two
spots is photobleached during colocalization.
20.3.4 Outline of the theory for estimating colocalization lifetimes
This section provides a protocol for correcting colocalization lifetimes with the photo-
bleaching lifetimes of fluorophores. Two fluorescent spots that become colocalized
lose their colocalization in one of the following ways: (1) They become separated after
some time owing to dissociation and independent diffusion ( Fig. 20.7 A), or (2) one of
the two spots is photobleached ( Fig. 20.7 B). We first consider the case in which two-
color fluorescent probes are used and spots with different colors are colocalized. The
dis-colocalization process can be expressed by the differential equation:
d D
½
d t ¼
k b1 D
½
k b2 D
½
k off D
½
(20.1)
where [ D ] indicates the number density of the colocalized fluorescent spots, k b1 and
k b2 are the photobleaching lifetimes for the two fluorescent probes, and k off repre-
sents the off rate for the two colocalized spots (which includes the time needed
for the dissociation of two molecules plus that required for the two molecules to
be separated by more than 240 nm owing to diffusion, but the latter is likely to be
considerably shorter than the former). Eq. (20.1) can readily be solved, giving
½¼
D
D 0 exp
½
ð
k b1 þ
k b2 þ
k off
Þ
t
(20.2)
where D 0 is an integration constant.
Therefore, the apparent rate constant for dis-colocalization, k app , which can be
measured directly with colocalization experiments, can be written as follows:
k app ¼
k b1 þ
k b2 þ
k off
(20.3)
Each rate constant can be related to its associated time constant:
k 1
app
t app ¼
(20.4)
k 1
b1
t b1 ¼
(20.5)
k 1
b2
t b2 ¼
(20.6)
k 1
off
t off ¼
(20.7)
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