Chapter 6 – Forces  253

square microns. This arrangement is called an anti-​Brownian electrophoretic/​electrokinetic

(ABEL) trap . It can operate on any object that can be imaged optically, which can acquire an

electric charge in water, and was first demonstrated on fluorescently labeled microspheres

using a device whose effective trap stiffness was four orders of magnitude smaller than that

of a typical single-​beam gradient force optical trap (Cohen and Moerner, 2005). Further

refinements include real-​time positional feedback parallel to the z-​axis (e.g., automated

refocusing by fast feedback of the bead’s detected position to a nanostage) to ensure that the

particle lies in the same lateral plane as the four microelectrodes.

The application of ABEL traps permits longer continuous observation of, for example,

molecular machines in solution that otherwise may diffuse away from their point of action

relatively quickly over a time scale of milliseconds away from the detector field of view.

Earlier, similar approaches for confining a single biomolecule’s Brownian motion directly

(i.e., without using a relatively large adapter particle such as a micron-​sized bead) used sur­

face binding either via surface tethering of molecules or surface binding of lipid vesicles

containing a small number of molecules for use in smFRET investigations (see Chapter 4);

however, the advantage of the ABEL trap is that there are no unpredictable surface forces

present that could interfere with molecular properties.

ABEL trapping has been applied at the single-​molecule level to provide ~1 nm precise

trapping. This level of spatial resolution opens the possibility for measuring molecular

conformational transitions in single biomolecules in solution in real time. For example,

this approach has been used to monitor differences in electrokinetic mobility of single

fluorescently labeled DNA molecules in the presence or absence of a DNA-​binding protein

called “RecA” (which is involved in repairing damaged DNA in the living cell) over periods of

several seconds (Fields and Cohen, 2011).

6.6.7  PIEZOELECTRIC TECHNOLOGIES

The piezoelectric effect is a consequence of electrical charge redistribution in certain solid

materials dependent on mechanical stress, typically a ~0.1% change in mechanical strain

resulting in a measurable piezoelectric current. Such piezoelectric materials have revers­

ibility in that they also exhibit a converse piezoelectric effect, such that the application of an

electrical field creates mechanical deformation in the solid. Piezoelectric materials include

various crystals (quartz being the most common) and synthetic ceramics and semiconductors

but also include natural biological material including bone, certain proteins and nucleic acids,

and even some viruses (see Chapter 9), with a role being potentially one of a natural force

sensor.

The piezoelectric effect involves a linear electromechanical interaction between the

mechanical and the electrical state in crystalline materials, which possess no inversion sym­

metry. Crystals that have inversion symmetry contain a structure comprising a repeating

unit cell (there is a point in each known as the inversion center that is indistinguishable from

that point in any other unit cell), whereas piezoelectric material has no equivalent inver­

sion center. The piezoelectric effect results from a change of bulk electric polarization of

the material with mechanical stress caused either by a redistribution of electric dipoles in

the sample or their reorientation. The change in electrical polarization results in a variation

of electrical charge density on the surface of the material. The strength of the piezoelec­

tric effect is characterized by its dielectric constant, which for the most common piezo­

electric synthetic ceramic of lead zirconate titanate (also known as “PZT”) is in the range

~300–​3850 depending on specific doping levels in the crystal, with an equivalent dielectric

strength (the ratio of measured voltage change across faces of the crystal to the change in

separation of the faces) of ~8–​25 MV m⁻¹ (equivalent to ~1 mV for a single atomic diameter

separation change).

Primary uses of piezoelectric material in biophysical techniques are either as sensitive

force actuators or force sensors. Actuators utilize the converse piezoelectric effect and can

involve relatively simple devices such as mechanical valves in microfluidics devices and for

the fine control of the steering of optical components as well for scanning probe microscopes