Chapter 6 – Forces  221

6.3.6  CONTROLLING ROTATION USING “OPTICAL SPANNERS”

Cells have, in general, rotational asymmetry and so their angular momentum can be manipulated

in the optical stretcher device. However, the trapped particles used in conventional Gaussian

profile optical tweezers are usually microspheres with a high degree of symmetry and so experi­

ence close to zero net angular momentum, about the optic axis. It is, in general, technically non­

trivial to controllably impart a nonzero mean torque using this approach.

Cells have, in general, rotational asymmetry and so their angular momentum can be

manipulated in an optical stretcher device. However, the trapped particles used in con­

ventional Gaussian profile optical tweezers are usually symmetrical microspheres and so

experience zero net angular momentum about the optic axis. Therefore, it is not possible to

controllably impart a nonzero mean torque.

There are two practical ways that achieve this using optical tweezers; however, both can lay

claims to being in effect optical spanners. The first method requires introducing an asymmetry

into the trapped particle system to generate a lever system. For example, one can controllably fuse

two microspheres such that one of the beads is chemically bound to a biomolecule of interest to

be manipulated with torque, while the other is trapped using standard Gaussian profile optical

tweezers whose position is controllably rotated in a circle centered on the first bead (Figure 6.4b).

This provides a wrench-​like effect, which has been used for studying the F1-​ATPase enzyme

(Pilizota et al., 2007). F1 is one of the rotary molecular motors, which, when coupled to the

other rotary machine enzyme Fo, generates molecules of the universal biological fuel ATP (see

Chapter 2). Fused beads can be generated with reasonable efficiency by increasing the ionic

strength (usually by adding more sodium chloride to the solution) of the aqueous bead media to

reduce to the Debye length for electrostatic screening (see Chapter 8) with the effect of reducing

surface electrostatic repulsion and facilitating hydrophobic forces to stick beads together. This

generates a mixed population of bead multimers that can be separated into bead pairs by centri­

fugation in a viscous solution composed of sucrose such that the bead pairs are manifested as a

distinct band where the hydrodynamic, buoyancy, and centripetal forces balance.

The second method utilizes the angular momentum properties of light itself. Laguerre–​

Gaussian beams are generated from higher-​order laser modes above the normal TEM00

Gaussian profile used in conventional optical tweezers, by either optimizing for higher-​order

lasing oscillation modes from the laser head itself or by applying phase modulation optics in

the beam path, typically via an SLM. Combining such asymmetrical laser profiles (Simpson

et al., 1996) or Bessel beams with the use of helically polarized light on multiple particles on

single birefringent particles that have differential optical polarizations relative to different

spatial axes such as certain crystal structures (e.g., calcite particles, see La Porta and Wang,

2004) generates controllable torque that has been used to study interactions of proteins with

DNA (Forth et al., 2011).

6.3.7  COMBINING OPTICAL TWEEZERS WITH OTHER BIOPHYSICAL TOOLS

Standard Gaussian profile dual-​optical tweezers have been used to generate so-​called nega­

tive supercoiling in single-​molecule tethered DNA samples (King et al, 2019). Here, although

the two optically trapped beads at either end of a single DNA molecule tether are spherical

and ostensibly identical, some level of nonzero torsional control can be enabled through

exploiting the fact that B-​DNA at low tension is intrinsically twisted; if this molecule is

then stretched by moving the two beads apart, then its natural twist will try to unravel. This

imposes a small torque on the biotin–​streptavidin covalent bond links between the beads

and the end of the DNA, which can be sufficient to increase the likelihood for stochastically

breaking these bonds during the time scale of a typical experiment. During this transient bond

breakage before stochastically rebinding, the DNA can then unravel by a few turns, hence

negative supercoiling is inserted into the molecule thereby facilitating a range of experiments

to investigate the effect of negative supercoiling on DNA function and mechanics.

This technique does not use direct angular momentum control on the optically trapped

beads, though small asymmetries in the beads may perhaps result in small nonzero torque

which might work to slow down free rotation of the beads in the optical traps, but relies more