132 4.4  Fluorescence Correlation Spectroscopy

b

Using the same assumptions as for part (a), then, from the donor intensity values,

the FRET efficiency before adding ATP is

1 6270

−

counts/6450counts=0.03

Similarly, using the acceptor intensity values,

(5560

5380

−

counts)/(5380counts)=0.03

This is significantly less than 0.5 and therefore “low FRET.” Upon adding ATP,

there is a molecular conformational change, and FRET efficiency can be similarly

calculated using either the donor or acceptor intensity values to be ~0.20, which

is “high” FRET.

  A “loose” linkage implies isotropic excitation absorption and emission of the

dye molecules; thus, the size of the displacement during the conformational

change of the FRET pair dye molecules is given by

( .

( / .

.

/

/

5 6

1 0 03

2

1 6

1 6

nm)

1)

(1/0.20

1)

9 nm

×

−

−

−

(

) =

This conformational change is accomplished in 5 ms; therefore, the average

speed is given by

( .2 9

10

5 10 5

10

58

9

3

1

1

×

×

(

) =

×

=

−

−

−

−

−

m)/

5.8

ms

ms

7

µ

c

A “tight” linkage prevents free rotation of the dye molecules; therefore, the

brightness in the absence of FRET (no ATP added) of the molecule is a function

of the projection of the polarization excitation vector onto the respective

dye dipole axis. The fact that the dye brightness values are similar to part

(b) is consistent with a random orientation of the construct on the coverslip

surface, since the dyes themselves cannot undergo free rotation relative to the

molecular complex. Since there is no translational movement, the change in

FRET efficiency must be due to relative rotational movement of the dipole axes

of two dye molecules due to relative rotation between the whole lever arm

and the rest of the molecular complex. If θ is the relative angle between the

acceptor and donor dipole axes, then the E-​field from the donor projected onto

the acceptor scales as cos θ; the FRET efficiency scales as the local intensity of

the donor E-​field, which scales as the square of the amplitude of the f-​field and

thus as cos² θ. Thus,

cos

0.03/(1 5800/6450)

0.30

2θ =

−

=

indicating θ ≈ 57°.

Thus, the molecular conformational change upon ATP hydrolysis is comprised of both

a translation component and a rotation component of the lever arm, suggesting a

combination of both a “pincer” and a “twister” model.

4.4  FLUORESCENCE CORRELATION SPECTROSCOPY

Fluorescence correlation spectroscopy (FCS) is a technique in which fluorescently labeled

molecules are detected as they diffuse through a confocal laser excitation volume, which