Chapter 4 – Making Light Work Harder in Biology  149

(4.37)

υ

µ

θ

λ

µ

υ λ

θ

D

D

sin

sin

=

∴

=

E

E

E

E

If we consider a molecule as an ideal sphere, and balance the electrophoretic and drag forces,

this indicates that

(4.38)

qE

v

v

E

q

R

=

∴

=

=

γ

µ

πη

E

s

6

where γ is the viscous drag coefficient on the sphere of Stokes radius (Rs) and net surface

charge q in a solution of viscosity η. Thus, the net surface charge on a molecule can be

estimated as

(4.39)

q

R

E

D

s

= ^{6πηυ λ}

θ

sin

The Stokes radius can be estimated using similar autocorrelation analysis to that of DLS earlier.

The net surface charge can be related to other useful electrical parameters of a molecule, such

as the zeta potential. For biological colloidal dispersions such as large biomolecules in water,

the zeta potential is the voltage difference between the water in the bulk of the bulk liquid and

the electrical double layer (EDL) of ions and counterions held by electrostatic forces to the

molecule surface. The EDL is an important parameter in determining the extent of aggrega­

tion between biomolecules in solution.

4.6.4  INTERFEROMETRIC ELASTIC LIGHT SCATTERING FOR MOLECULAR IMAGING

Interferometric light scattering microscopy (a common method used is known as iSCAT)

has sufficiently high contrast to enable imaging of single protein molecules without the

need for any fluorescent labels, for example, demonstrated with the observation of nano­

scale molecular conformational changes of the protein myosin used in the contraction of

muscle tissue. Here, the sample is illuminated using coherent laser light, such that the sample

consists of weakly scattering objects localized on a microscope coverslip at the glass–​water

interface. The detected light intensity (Id) from a fast camera detector is the sum of reflected

light from this interface and that scattered from the proteins on the coverslip surface:

(4.40)

I

E

E

E

R

S

R s

i

d

ref

scat

sin

=

+

=

+

−

(

)

2

2

2

2

2

2

φ

where

Ei, Eref, and Escat are the incident, reflected, and scattered light E-​field amplitudes

R and s are the reflected and scattering amplitudes

ϕ is the phase between the scattered and reflected light

For small scattering objects, the value of |s|² is close to zero. This is because the Rayleigh

scattering cross-​section, and hence the scattering amplitude |s|², scales with V² for a small

scattering particle whose radius is much less than the wavelength of light (see Equation 4.21),

for example, the scattering cross-​section of a 40 nm gold nanoparticle is ~10⁷ that of a typ­

ical globular protein of a few nanometers in effective diameter; a few tens of nanometers is

the practical lower limit for reproducible detection of scattered light from the laser dark-​field