Chapter 4 – Making Light Work Harder in Biology  133

generates a pulse of fluorescence emission prior to diffusing out of the confocal volume. The

time correlation in detected emission pulses is a measure of fluorophore concentration and

rate of diffusion (Magde et al., 1972). FCS is used mainly in vitro but has been recently also

applied to generate fluorescence correlation maps of single cells.

4.4.1  DETERMINING THE AUTOCORRELATION OF FLUORESCENCE DATA

FCS is a hybrid technique between ensemble averaging and single-​molecule detection. In

principle, the method is an ensemble average tool since the analysis requires a distribution

of dwell times to be measured from the diffusion of many molecules through the confocal

volume. However, each individual pulse of fluorescence intensity is in general due to a single

molecule. Therefore, FCS is also a single-​molecule technique.

The optical setup is essentially identical to that for confocal microscopy. However, there is

an additional fast real-​time acquisition card attached to the fluorescence detector output that

can sample intensity fluctuation data at tens of MHz to calculate an autocorrelation function,

IAuto. This is a measure of the correlation in time t of the pulses with intensity I:

(4.10)

I

t

I t

I t

I t

t

I t

t

I t

Auto

′

′

′

( ) =

( ) −〈( )〉

(

)

+

(

) −〈

+

(

)〉

(

)

〈( )〉²

where

the parameter t′ is an equivalent time interval value

〈( )〉

I t

is the time-​averaged intensity signal over some time T of experimental observation

(4.11)

〈( )〉=

( )

∫

I t

T ^{I t}

t

T

1

0

d

If the intensity fluctuations all arise solely from local concentration fluctuations δC that are

within the volume V of the confocal laser excitation volume, then

(4.12)

δ

δ

I

I P r

C r

V

V

=

( )

( )

∫1



d

where

r is the displacement of a given fluorophore from the center of the confocal volume

P is the PSF

I1 is the effective intensity due to just a single fluorophore

For normal confocal illumination FCS, the PSF can be modeled as a 3D Gaussian volume (see

Chapter 3):

(4.13)

P x y z

x

y

w

z

w

xy

z

, ,

(

) =

−

+

(

) +





























exp

1

2

2

2

2

where wxy and wz are the standard deviation widths in the xy plane and parallel to the optical

axis (z), respectively. The normalized autocorrelation function can be written then as

(4.14)

I

t

I t

I t

t

I t

Auto

′

′

( ) = ^〈

( )

+

(

)〉

〈

( )〉

δ

δ

δ

2