Protein Dynamics and Interactions - Single Molecule Dynamics in Life Science - page 196

Typical lifetimes of singlemolecule uorophores are 1 - 4 ns. In order to see emission
from the fluorophores, it is important to maximize k r versus k nr . This is quanti ed as
the quantum yield of uorescence,
Q r ¼ k r =ð k r þ k nr þ k ISC þ k bl Þ k r =ð k r þ k nr Þ: ð 9 : 2 Þ

One important feature of fluorescence is the Stokes shift, where the emission is
red-shifted compared to the absorption. This is caused by the vibronic energy levels.
In either S 0 or S 1 , the uorophore remains within an energy k B Tof the lowest vibronic
state. Within 1 ps, any excitation into another vibronic state quickly relaxes down to

the lowest vibronic states. However, the density of vibronic states is much greater
above the lowest vibronic states. This means that it is much easier to excite the
fluorophore from S 0 to a high vibronic of S 1 than to the lowest vibronic state of S 1 .
Also, the state S 1 tends to uoresce such that the fluorophore de-excites into a higher
vibronic state of S 0 . The vibronic energy levels increase the energy of the photon
required to ef ciently excite the fluorophore, and decrease the energy of the emitted
photons. This shift in the excitation and emission photons, or Stokes shift, allows the
emission photons to be ef ciently separated from the excitation photons (using a

fluorescence that allows for
single-molecule spectroscopy by exclusion of background laser scattering.
At the single-molecule level, the process of

filter). This is one of the most important features of

fluorescence involves repeated cycling
of the uorophore through the energy levels shown in Figure 9.1. The jumps between
states occur at random time intervals, with rates as outlined above. The waiting times
to jumps follow Poisson statistics (exponential distributions), with rates as outlined
above. If at time t 0, the fluorophore is in the ground state, then the time to a jump

to S 1 has a probability of P(t)

¼

k e t). At time t 0 after the excitation to S 1 , the
fluorophore usually decays back to the ground state with a probability of P 0 (t 0 )

¼ k e exp (

¼ exp

t 0 / ( was de ned above. The probability that the fluorophore emits a

photon upon de-excitation is the quantum yield Q. At this point the uorophore
repeats the cycle. It is in this repeated cycling that the slow processes such as inter-
system crossing and photobleaching become important. After many cycles, on
average (k r þ

t )/ t , where t

k bl )/k ISC , the fluorophore will undergo intersystem
crossing to T1. Since k Ph is much slower than uorescence, the fluorophore remains
in the triplet state for a comparatively long time. If the excitation is high, as is the case
in single-molecule studies, these excursions to the triplet state will be interspersed
among the emitted fluorescence photons as dark periods. Also, eventually the
fluorophore will photobleach after on average (k r

k nr þ k ISC þ

þ k nr þ k ISC þ k bl )/k bl cycles, and

stop emitting altogether.

9.2.2
Point Emission-Localization Measurements

Fluorophores are in general very small ( 0.5 nm), much smaller than the wavelength

of light they emit, and thereforemay be considered as point sources of light. Repeated
excitation of the fluorophore causes emission from the same point. This is a simple
observation, but it has important consequences. The position of the uorophore

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