Chapter 4 – Making Light Work Harder in Biology  145

deeper into tissue, for example, by directing an optical fiber through natural channels in an

animal whose diameter is larger than that of a cladded optical fiber. A multimodal cladded

fiber has a diameter of a few hundred microns, which is small enough to be directed through

the gut, large blood vessels, and lymphatic vessels. This at least allows the light source/​

detector to be brought close enough to the internal surface of many organs in the body within

significant disruption to the native physiology.

4.6  ADVANCED BIOPHYSICAL TECHNIQUES USING ELASTIC LIGHT

SCATTERING

Scattering of light, as with all electromagnetic or matter waves, through biological matter

is primarily due to linear optical processes of two types, either elastic or inelastic. Rayleigh

and Mie/​Tyndall scattering (see Chapter 3) are elastic processes in which an emergent

scattered photon has the same wavelength as the incident photon. In the previous chapter,

we encountered Mie/​Tyndall scattering used in simple optical density measurements in a

visible light spectrophotometer to determine the concentration of scattering particles such

as cells in a sample. More advanced applications of elastic light scattering, which can reveal

molecular level details, include specific techniques called “static light scattering” (SLS) and

“dynamic light scattering” (DLS).

Rayleigh scattering occurs when the scattering particle has a length scale at least an order

of magnitude less than the incident light (a semiarbitrary condition often used is that the

length scale is less than ~1/​20 of the light wavelength), such that the entire surface of the par­

ticle will in effect scatter roughly with the same phase. This is the length scale regime of many

small biomolecules and molecular complexes. If molecules are randomly positioned, the

arrival of a photon at any molecular surface will be random, resulting in incoherent scattered

light whose intensity is just the sum of squares of the amplitudes from all particles. Using a

simple harmonic dipole oscillator model for electromagnetic radiation scattering leads to the

Rayleigh equation (or scattering formula):

(4.23)

I

I

C

d

n

n

r

s

s

)=

cos

)

(

(

θ

π

λ

θ

0

1

2

2

1

1

1

2

4

2

2

6

2

( )



^



^

^



^

−

+



^



^

+

where IS is the Rayleigh scattered light of wavelength λ when measured at a distance d and

angle θ from the incident light direction from a sample composed of C scattering particles

per unit volume of refractive index n and effective radius r. Thus, the scattered intensity is

proportional to the reciprocal of the fourth power of the light wavelength and the sixth power

of its radius.

4.6.1  STATIC LIGHT SCATTERING

SLS can be used to obtain estimates for the molecular weight Mw of an in vitro biological

sample in the Rayleigh scattering regime, and for larger molecules in the Mie scattering regime

can estimate Mw as well as generate a measure of the length scale of such macromolecules

given by their root-​mean-​squared radius, denoted as the radius of gyration, RG.

Typically, the scattered intensity from a visible laser light beam incident on an in vitro

solution of a particular type of biomolecule at high concentration (equivalent to ~1 mg mL⁻¹),

or a mixture of molecule types, is measured as a function of the scatter angle θ (Figure 4.4b),

either by rotating the same detector or by using multiple fixed detectors located at different

angles (multiangle light scattering), often using 10 different values of θ spanning a typical

range ~30°–​120°. A time-​averaged scattered signal intensity is obtained at each angle; hence,

there is no time-​resolved information and so the technique is described as “static.”

One analytical approach to understand these data is to apply continuum modeling (i.e.,

to derive an analytical formulation) to Rayleigh scattering (which is clearly from discrete