254 6.6  Electrical Force Tools

discussed previously in this chapter. They reach a state of the art in controlling the 3D deflec­

tion of “smart” microscope nanostages to sub-​nanometer precision (see Chapter 7).

The biophysical application of piezo sensor is best exemplified in the quartz crystal micro­

balance (QCM), especially the QCM with dissipation monitoring (QCM-​D) that uses very

sensitive acoustic detection technology to determine the thickness of an absorbed layer of

biomolecules in a liquid environment. A QCM-​D measures the variation in mass per unit

area from the change in the natural resonance frequency of the quartz crystal. As we have

seen, mechanical stress on a piezoelectric material induces a small voltage change across faces

of the material, but this in turn generates an electrical force that acts to push the material in

the opposite direction, making such a material to naturally oscillate as a crystal resonator.

The resonance frequency of the manufactured quartz crystal resonator being in the range of

a few kHz up to hundreds of MHz depends on the size of the crystal. This is the basis of the

timing signature of cell phones, computers, and digital watches, with the standard normally

set for a wristwatch being 32.768 kHz.

In a QCM-​D, the resonance frequency is changed by the addition or removal of very small

masses on one of the quartz surface faces, with the unbound state resulting in a typical res­

onance frequency of ~10 MHz. For example, a QCM-​D can be used to determine the binding

affinity of biomolecules to chemically functionalized surfaces, with an equivalent monolayer

of bound biomolecules reducing the resonance frequency of the quartz crystal resonator of

the QCM-​D by a few MHz. A typical application here is that of an antibody binding to its

recognition sites that might be expressed controllably on the surface. Similarly, to monitor

the formation of artificial phospholipid bilayers on a surface, since the QCM-​D is sufficiently

sensitive to discriminate between a lipid monolayer and a bilayer bound to the surface.

6.6.8  TETHERED PARTICLE MOTION AND ACOUSTIC TRAPPING

Tethered particle motion (TPM) involves tracking the position of a tracer bead, typically

of a micron diameter or less, which is tethered to one end of a filamentous biopolymer, the

other end of which is immobilized onto a coverslip surface. The forces involved are the ther­

mally driven Langevin force of the surrounding solvent molecules on the bead and the bio­

polymer, which results in random thermal fluctuations in the bead position, and a trapping

force derived from the elasticity of the tether, which, as we will see later in Chapter 8, is pri­

marily entropic in origin. The extent of displacement of the bead, and how this is correlated

in time, is a measure of the mechanical properties of the tether; TPM is often used to quan­

tify the biomolecule’s persistence length by modeling the positional data using typically the

Kratky–​Porod model, which derives from a worm-​like chain approximation to the molecule’s

elasticity (fast forward to section 8.3.3 for details).

As discussed previously for microrheology investigations that use tracer tracking (section

6.2.4), bead frictional drag imposes a limit on the time resolution of TPM, as does drag from

the tethered biomolecule itself. As with tracer tracking in microrheology, laser darkfield using

gold nanobeads is currently the best compromise approach, which maximizes time and space

resolution while also allowing extended duration observations due to the absence of photo­

bleaching effects. Simple stochastic binding to the coverslip is relatively easy to configure,

but for better throughput and consistency, it is also possible to print conjugation chemicals

using a compliant substrate such as polydimethylsiloxane (PDMS) (see section 7.6.2) into

well-​defined grid patterns on a coverslip surface, enabling up to several hundred tethered

beads to be monitored in a single camera detector field of view simultaneously; however, the

bottleneck then becomes the video-​rate speeds of the camera sampling available to such a

wide pixel area (up to ~1 kHz), whereas lower throughput detection methods such as laser

interferometry back focal plane detection (see section 6.3.3) can yield sampling rates two

orders of magnitude faster.

Acoustic trapping or acoustic tweezers can trap microscale particles in the standing wave

nodes created from the interference of ultrasonic waves. It its most useful form it can be seen

as a variant to TPM in that beads tethered to surface-​bound single biopolymer molecules

can be stably trapped and so by then varying the height of the coverslip by manipulating the

KEY BIOLOGICAL

APPLICATIONS:

ELECTRICAL

FORCE TOOLS

Molecular separation and iden­

tification; Quantifying biological

torque; Measuring ionic currents.