68

3.2  Basic UV-VIS-IR Absorption, Emission, and Elastic Light Scattering Methods

Saffman–​Delbrück equations (see Saffman, 1975; Hughes, 1981). Here, the frictional drag γ

of a rotating cylinder is approximated as

(3.15)

ϒ =

+

(

)

( ) =

( )

4

8

1

2

π µ

µ

ε

πη

ε

rC

rC

c

We assume the viscosities of the watery environment just outside the cell membrane and just

inside the cell cytoplasm (μ1 and μ2, respectively) are approximately the same, ηc (typically

~0.001–​0.003 Pa·s). The dimensionless parameter ε is given by

(3.16)

ε

µ

µ

η

η

η

= ⁽

)

+

(

) =

r h

r

h

/

m

c

m

1

2

2

The viscosity of the phospholipid bilayer is given by the parameter ηm (~100–​1000 times

greater than ηc depending on both the specific phospholipids present and the local molecular

architecture of nonlipids in the membrane). The parameter C can be approximated as

(3.17)

C

c

O

ε

ε

ε

ε π

ε

ε

ε

( )

−+

−

(

) +

(

)



^



^



^

^



^

^

−

ln / )

/

ln

/

(2

4

2

2

2

2

1

Here c is Euler–​Mascheroni constant (approximately 0.5772). The effective rotational

diffusion coefficient can then be calculated in the usual way using the Stokes–​Einstein rela­

tion and then the rotational correlation time is estimated.

Typical nanometer length scale fluorophores in the watery cytoplasm of cells have rota­

tional correlation times of a few nanoseconds (ns), compared to a few microseconds (μs) in a

typical phospholipid bilayer. These parameters can be measured directly using time-​resolved

anisotropy, with a suitable fluorescence polarization spectrometer that can typically perform

sub-​nanosecond sampling. The application of fluorescence anisotropy to cellular samples,

typically in a culture medium containing many thousands of cells, offers a powerful method

to probe the dynamics of protein complexes that, importantly, can be related back to the

actual structure of the complexes (see Piston, 2010), which has an advantage over standard

fluorescence microscopy methods.

3.2.5  OPTICAL INTERFEROMETRY

There are two principal bulk in vitro sample optical interferometry techniques: dual polar­

ization interferometry (DPI) and surface plasmon resonance (SPR). In DPI, a reference laser

beam is guided through an optically transparent sample support, while a sensing beam is

directed through the support at an oblique angle to the surface. This steep angle of inci­

dence causes the beam to be totally internally reflected from the surface, with a by-​product

of generating an evanescent field into the sample, generally solvated by water for the case

of biophysical investigations, with a characteristic depth of penetration of ~100 nm. This

is an identical process to the generation of an evanescent field for total internal reflection

fluorescence (TIRF) microscopy, which is discussed later in this chapter. Small quantities of

material from the sample that bind to the surface have subtle but measureable effects upon

polarization in this evanescent field. These can be detected with high sensitivity by meas­

uring the interference pattern of the light that results between sensing and reference beams.

DPI gives information concerning the thickness of the surface-​adsorbed material and its

refractive index.

SPR operates similarly in that an evanescent field is generated, but here a thin layer

of metal, ~10 nm thick, is first deposited on the outside surface (usually embodied is a