Imaging and Manipulation of Biomolecules - Bionanoelectronics: Bioinquiring and Bioinspired Devices - page 121

that at low frequencies, DNA has a relative electrical permittivity of 80 and a
conductivity of 54 mS/m, while the tobacco mosaic virus, for example, has a relative
electrical permittivity of 55 at 20 MHz. The DNA DEP is reviewed in H olzel ( 2009 ).
A variant of electrophoresis, namely, gel electrophoresis, can be used also in
DNA sequencing if combined with molecule cutting. However, gel electrophoresis
is a technique used mainly to separate and visualize DNA molecules depending
on their size and charge; the gel is a matrix containing holes of various sizes, in
general, a porous cross-linked polymer, so that under an applied electric field, the
distance traveled through the gel by a DNA molecule (or any other molecule) is
inversely proportional to its size (the smaller molecules move further). Generally,
the biological molecules are stained to make their positions visible in the gel after
electrophoresis is complete. Then, various molecules with different sizes and/or
electric charges, spatially separated in the gel, can be easily visualized. For a review
on gel electrophoresis, see ( Chery et al. 2006 ).
Another method to manipulate biological molecules is to use optical tweezers,
which trap them with optical beams. In principle, an optical trap consists of a
laser beam, which is very tightly focused by a lens with a high numerical aperture.
The dielectric particle, which is placed within this beam, is under the influence of
two main forces: (1) the scattering force, oriented toward the beam propagation
direction, and (2) the gradient force, oriented toward the spatial gradient of light
( Neuman and Block 2004 ). The scattering force prevails over the gradient force in
most situations. The gradient force has here a similar meaning as in the case of
dielectrophoresis, i.e., the force is created in the direction of the inhomogeneous
field gradient, which is exerted on a dipole. So the existence of an inhomogeneous
electromagnetic field is crucial as in the case of dielectrophoresis. However, the
techniques to implement these inhomogeneous fields are different. In the case of an
optical trapping laser, fluctuating dipoles, which interact with the inhomogeneous
field, are generated in the dielectric particles, and the particles are trapped in the
laser focus. Thus, to trap dielectric particles, it is necessary that the axial gradient of
the force, which is dragging the particles toward the focal point, is greater than the
scattering force, which drives away the particle from the focal region.
The large gradient necessary for trapping is implemented by focusing a laser
beam to a diffracted-limited spot with a high numerical aperture objective. The
equilibrium between the scattering force and the gradient force maintains the
dielectric particle at a trap position situated a little beyond the focal point, i.e., there
is an offset displacement. If this distance is small (around 150 nm), the restoring
force is proportional to the offset, i.e., the trap is acting analogously to a mechanical
oscillator with F D Kx. An optical trap is displayed in Fig. 3.10 .
If we consider that a sphere with radius R that satisfies the relation R ,
where is the laser wavelength, is treated as a point dipole, the Rayleigh scattering
theory give us the scattering force as

F scat D I 0 n m =c; (3.34)