molecular mass and the concentration of macromolecule. For globular structures such as proteins with
molecular weight 500kDa or less, light scattering is uniform in all directions. Therefore, the amount of light
scattered by a solution is measured at some angle relative to the incident laser beam. However for nucleic
acids or other rod-like macromolecules, the scattering varies significantly with angle. Hence multiangle
laser light scattering must be employed where light scattering is measured at a number of different angles.
This allows the absolute molecular weight as well as the geometric size to be determined.
The fluctuation in polarisabilityobserved in light scattering is caused by Brownian motion and is there-
fore related to the viscosity () of the solution and the diffusion coefficient (D) of the macromolecule. The
diffusion coefficient is directly related to the hydrodynamic radius (Stokes radius) (Rh) as shown in
Equation (11.6).
(11.6)where kBis the Boltzmann constant and Tthe temperature.
In solutions of large DNA molecules, one can observe the translational diffusion coefficients and also
the rotational coefficients of the species. Also, because large DNA molecules exhibit a certain degree of
flexibility, it is possible to determine the motions of small internal segments of these molecules.
Dynamic light scatteringis a technique in which the time dependence of the light scattering from a
small focussed region of the solution is measured over a timescale ranging from tenths of a millisecond to
milliseconds. The time-dependent fluctuations in the intensity of scattered light are related to diffusion of
molecules in and out of the region under study, which occur by Brownian motion. The data can be analysed
to determine diffusion coefficients, or a distribution of diffusion coefficients if multiple species are present.
In most cases, data is presented not in terms of the diffusion coefficient but rather in terms of particle size. The
Stokes radius derived from this analysis gives the size of a spherical particle that would have a diffusion
coefficient equal to the one observed for the protein or nucleic acid. Of course, most biological molecules,
especially nucleic acids, are not spherical and their apparent hydrodynamic sizes are dependent on their
shape, i.e.conformation, and molecular mass. Their diffusion is also affected by the hydration state. Hence
the hydrodynamic size determined from dynamic light scattering could be significantly different from the
true physical size observed in NMR or X-ray crystal structures.
11.4.3 Gel Electrophoresis
In free solution, the movement of DNA in an electric field is independent of shape and molecular mass and
dependent only on charge. However when the DNA is exposed to an electric field in a gel matrix, the
movement is dependent on size and shape as well as charge. Gels commonly used for nucleic acid elec-
trophoresis are made of agarose and polyacrylamide. Both types of material consist of 3D networks of
cross-linked polymer strands, which contain pores whose size varies according to the concentration of
polymer used. The mobility of DNA in such gels is dependent mainly on size and shape, since the charge
per unit length of DNA is effectively constant.
For linear DNA, there is an inverse relationship between size and rate of migration, such that mobility is
approximately inversely proportional to log 10 of the molecular mass. Horizontal agarose gel electrophoresis
is useful for the separation of linear DNA molecules up to 2000 kbp. Staining with ethidium bromide can
reveal the position of DNA in the gel or sometimes the DNA is labelled with^32 P, in which case the DNA is
detected by use of a phosphor imager or by autoradiography. Polyacrylamide gel electrophoresis(PAGE)
is used for smaller DNA fragments. It can be used preparatively for species up to 1 kbp, and it forms the
basis of rapid nucleic acid sequencing methods, when 8M urea is added to denature the oligonucleotide.
One proposed explanation for the theoretical basis of size selection in gel electrophoresis is that the
mobility is proportional to the volume fraction of the pores that can be entered. This theory predicts that
mobility would decrease with increasing gel concentration and also with increasing molecular mass. This is
consistent with the observation that very small nucleic acid fragments move independently of molecular mass.
R
kT
h D
B
6 442 Chapter 11