Chemistry Reference
In-Depth Information
begins with the identi
cation of these bursts. Burst search algorithms are essentially
a region-of-interest selection as described above, but in the time domain (see for
example [54]). Rather than identi
cation of full transits of molecules diffusing
through the optically isolated detection volume it is possible to threshold-analyze
time traces on a bin-by-bin basis, without a burst search [55, 56].
Once a single-molecule signal is identi
ed, time traces, time correlations, and
various quantities describing the molecule can be calculated and analyzed to provide
information on the molecule.
9.3.5.4 Histogram-based Analysis (Including Correlation Analysis)
Before going on to describe the analysis of identi
ed single molecules, we will
describe another way to analyze single-molecule data. This involves the formation of
histograms and correlations from the data without
first identifying regions contain-
ing single molecules. Techniques in this category include
fluorescence correlation
spectroscopy (FCS) [5], photon counting histogram (PCH) [57],
fluorescence inten-
sity distribution analysis (FIDA) [58], photon arrival-time interval distribution
(PAID) [59], and time-integrated
fluorescence cumulant analysis (TIFCA) [60] with
all subsequent additions and variations. The main bene
t of these techniques is that
the effects of the single-molecule identi
cation threshold are eliminated, allowing for
easier mathematical modeling. In addition, there is less potential for biasing the
results that may occur during the single-molecule identi
cation process.
In PCHand FIDA and their variations, a
xed time bin width is used for analysis of
photons. The number of photons counts per channel is calculated over the time bin. A
one- or two-dimensional histogram is formed, where the axis or axes are the number
of photons counted. Each point in the histogram counts the number of time bins in
the experiment with the speci
ed number of photon counts. Fitting functions have
been obtained that allow for the concentration, molecular brightness, and back-
ground to be obtained for one or more
fluorescent species. Extensions of FIDA and
PCH to two channels, to include temporal or
fluorescence lifetime information have
been demonstrated.
In FCS, a time-correlation function is formed. The temporal cross-correlation
function is de
ned as C
AB
(
t
)
h
I
A
(t)I
B
(t
þ t
)
i
/
h
I
A
(t)
ih
I
B
(t
þ t
)
i
, where I
A
(t) and
I
B
(t) are the detected intensities for channels A and B, and t and
are continuous time
and time lag variables. The correlation function decay is used to determine the time
scales of
uorescence
fluctuations, which is key for monitoringmolecular dynamics.
Often, correlations are calculated using hardware correlators, and only the correla-
tions are kept. For experiments at the single-molecule level, signal amplitudes are not
high enough to make this bene
cial. Recording photon events allows
flexibility to
performother types of analysis, and, with proper algorithms [61
-
63], the correlations
can be calculated quickly. Extensions of FCS include the use of cross-correlations [64].
PAID extends FCS to include information about brightness, similar to the informa-
tion obtained from PCH and FIDA [59].
Generally, these methods are very useful for obtaining quantitative, unbiased
values for brightness and concentrations of
fluorescent analytes. This is particularly
true for determining stoichiometry of binding partners (for example see [65]).
t
