gravity, then the force needed to pick up a medium-sized 100-gm apple is
0.98 N. On a smaller scale, a force of F = 3.4× 103 pN is needed to pick up
a veryfine grain of sand that has a mass m = 3.5× 10 −^10 kg. (b) Forces at
the molecular scale are on the order of piconewtons (pN), which is 10−^12 N.
Table11.1gives some examples of forces related to breaking molecular
bonds. For example, 1600 pN are needed to break a covalent bond such as
C–C and 4 pN are required to break a hydrogen bond.Among the numerous applications of optical trapping techniques are cell
nanosurgery, manipulation and assembly of carbon nanotubes and nanoparticles,
and studies of protein-protein binding processes, DNA-protein interactions, DNA
mechanical properties, mechanical-chemical processes in the cell, elastic properties
of cells, cell-cell interactions, and cell transport, positioning, sorting, assembling,
and patterning [ 8 – 11 ].
A simple geometric ray optics picture can be used for an elementary description
of the operational principle of optical tweezers and optical trapping. This operation
is based on the exertion of extremely small forces on nanometer and
micrometer-sized dielectric particles by means of a highly focused laser beam. First
consider a spherical, transparent dielectric particle located in a lightfield that has an
inhomogeneous intensity distribution in a plane transverse to the optical axis, as is
shown in Fig.11.1. Here two light rays (shown in red) with different intensities are
incident symmetrically on a sphere. The two rays will be refracted as they enter and
exit the sphere, and thus will travel in different directions from those of the original
paths. Becauselight has a momentum associated with it, the changes in direction
mean that the momentum has changed for the photons contained in each ray. Thus,
according to Newton’s third law, there is an equal and opposite momentum change
on the particle. Because the force on a dielectric object is given by the change in
momentum of light induced by the refraction of the light by the object, the incident
rays 1 and 2 will produce corresponding forces F 1 and F 2 , respectively. As a result
of ray 1 being less intense than ray 2, the force F 1 is smaller than F 2. Consequently,
a transverse intensity gradient will result in a netgradient forceFgrad, which points
towards the region that has the highest intensity.
Table 11.1 Forces involved at the biological level
Type of force Bond strength (pN)
Covalent bond such as C-C 1600
Noncovalent bond between biotin and streptavidin 160
Bond between two actin monomers 100
Force required to extract a tether out of an erythrocyte 50
Weak bond such as hydrogen 4
50 % stretching of double-stranded DNA 0.111.1 Optical Manipulation 325