Biophotonics_Concepts_to_Applications

Example 9.6Figure9.9shows a spheroid with the radii of the equatorial and

polar axes being 0.3 and 2.0μm, respectively. What is the volume of the

spheroid?

Solution: The volume of a spheroid is found from the equation (4π/3)a^2 c.

Herea is the equatorial radius andc is the polar radius. Thus the volume is

V ¼ð 4 p= 3 Þð 0 : 3 lmÞ^2 ð 2 : 0 lmÞ¼ 0 : 75 lm^3 ¼ 0 :75 fL

The analysis procedure of FCS for determining molecular processes is made
through a statistical analysis of thefluorescence signalfluctuations. This analysis
uses a Poisson distribution, which describes the statisticalfluctuations of particle
occupancy. In a Poisson system the variance is proportional to the average number
offluctuating species. This is carried out by means of an autocorrelation function G
(τ) of thefluctuations in thefluorescence intensity emission. Note that in statistics
theautocorrelationof a random process describes the correlation between values of
the process at different times. An example of this is given in Fig.9.10where
measurements are made at two different observation times t 1 and t 2 in time intervals
τ. Then theautocorrelation functionG(τ)isdefined by

a = 0.3 μm

c = 2.0 μm

FCS spheroid

detection

volume

Fig. 9.9 Example detection
volume of a confocal
microscope in FCS
procedures

Average

intensity

<I(t)>

Time-varying

intensity

Time

Intensity

t 1 t 1 + τ t 2 t 2 + τ

Fig. 9.10 Sampling of a
time-varying signal at two
different time intervals

9.3 Fluorescence Correlation Spectroscopy 271