148 4.6  Advanced Biophysical Techniques Using Elastic Light Scattering

θ) would be approximated as ~gm using a value of ~1 s for τ. However, in many experiments,

there is often very little observable change in g at values of τ above a few milliseconds, since

this is the typical diffusion time scale of a single molecule across the profile of the laser beam

in the sample.

Q in Equation 4.30 is the θ-​dependent scattering vector as described previously in Equation

4.28. Many conventional DLS machines monitor exclusively at a fixed angle θ =​ 90°; how­

ever, some modern devices allow variable θ measurement. In conventional DLS, the sample

often has to be diluted down to concentration levels equivalent to ~0.l mg mL⁻¹ to minimize

stochastic noise on the autocorrelation function from scattered events through the entire

sample cuvette. “Near” backscatter measurements (e.g., at θ ≈ 170°) have some advantages in

that they allow focusing of the incident laser beam to sample scattered signals just from the

front side of sample cuvette, which reduces the need to dilute the sample, thus increasing the

total scattered intensity signal.

D is the translational diffusion coefficient for the biomolecule. This is related to the drag

coefficient by the Stokes–​Einstein relation (Equation 2.11), which, for a perfect sphere, is

given by

(4.34)

D

k T

R

B

s

= 6πη

where

kB is the Boltzmann constant

T is the absolute temperature

η is the viscosity of the solvent

Thus, by fitting gm to the experimental autocorrelation data, the diffusion coefficient, and

hence the Stokes radius of the molecule, can be determined. A polydisperse system of N

different biomolecule types generates an N-​modal autocorrelation response, which can be

approximated by a more general model of

(4.35)

g

g

D Q

m

m

i

N

i

i

(

,

τ θ

θ

β

τ

, )

exp

=

∞

(

)+

−(

)

=^∑

1

2

2

Thus, in principle, this allows estimation of the Stokes radii of several different components

present in solution, though in practice separating out more than two different components in

this way can be nontrivial unless they have distinctly different sizes.

4.6.3  ELECTROPHORETIC LIGHT SCATTERING

A modification of DLS is electrophoretic light scattering. Here, an oscillating electric E-​field

is applied across the sample during DLS measurements, usually parallel to the incident laser

light. This results in biased electrophoretic velocity of the molecules in solution, v, determined

by the molecules electrophoretic mobility μE, which depends on their net surface charge:

(4.36)

ν

µ

=

E^E

A laser beam is first split between a reference and a sample path, which are subsequently

recombined to generate an interference pattern at the photodetector. The molecular motion

from electrophoresis results in a Doppler shift (νD) on the distribution of fluctuation frequen­

cies observed from the scattered signal, manifested as a phase shift between the sample and

reference beams, which can therefore be measured as a change in the interference pattern at

the photodetector. On simple geometrical considerations