Chapter 6 – Forces  209

such as viscoelasticity (i.e., a complex combination of viscous and elastic components) over a

range of different length and time scales.

The traditional tool which enables rheology measurements is a rheometer. These benchtop

devices are broadly divided into two types, extensional and shear rheometers, depending up

whether strain or stress deformation is induced. Shear rheometers have a largely consensus

design of an internal often cylindrical metal plate, which can be rotated concentric to an outer

fixed cylindrical plate over a range of speeds enabling the response of the fluid-​like sample

inside, deformed by the shearing force between the plates, to be measured as a function of dis­

tance between from plates typically using optical sensing methods. Extensional rheometers

have more varied designs, for example including piezoelectric and acoustic variants, and are

most useful for high-​viscosity systems in the range 1–​1000 cP in which biological properties

are related to tensile deformation, such as in filamentous biopolymers.

Microrheology methods can be used to measure rheological properties over a scale of

microns down to a few tens of nanometers, much smaller than the capability of traditional

rheometers. Passive microrheology uses intrinsic thermal fluctuations of a tracer probe (e.g.

a micron-​sized bead) diffusing through the sample and tracked using optical localization

microscopy methods either in bright-​field, fluorescence, or laser darkfield (see Chapter 4).

Autocorrelation and Fourier analysis of the tracked position of the probe as a function of

time can reveal the distinct viscous and elastic components of the material, which act 90°

out of phase with each other such that the smaller spatial frequency data are more associated

with viscous components whereas higher spatial frequencies are more sensitive to elastic

components.

The primary limitation is the size of the probe, in that larger probes experience greater

friction drag and so limit the time scale over which measurements can be made and limit

the spatial resolution. In this regard, the most ideal probes currently are gold beads of a few

tens of nanometers in diameter, which can be tracked with sub-​millisecond time resolution

and nanoscale spatial resolution using laser darkfield microscopy over long durations since,

unlike fluorescent probes, they do not photobleach, and experiments can be high throughput

since multiple beads can be tracked simultaneously across relatively large fields of view of up

to a few tens of microns in width. Another bead tracking approach is tethered particle motion

(TPM, see section 6.6.8 for a fuller descrption). Here, typically a biopolymer under investiga­

tion is tethered to a tracker bead while the other end of the molecule is tethered to a coverslip

surface. By tracking the motion of the tethered bead using similar localization microscopy

methods, some of the biomolecular rheological properties can be measured.

Active microrheology uses similar physics concepts but also applies a driving force to

induce deformation over this microscopic length scale, for example using optical or mag­

netic tweezers to controllably deforming single biopolymer molecules (see sections 6.3 and

6.4), which provides high-​precision force and extension measurements but is intrinsically

low throughput. Higher throughput trapping methods involving acoustic trapping of beads,

which are tethered via a biomolecule under investigation to a coverslip surface similar to a

TPM arrangement, are a useful compromise since these allow several beads in a field of view

to be monitored while sacrificing some precision in terms of force and extension (see section

6.6.8).

Aqueous flow can be used to straighten relatively long, filamentous biomolecules in a pro­

cess called molecular combing. For example, by attaching one end of the molecule to a micro­

scope coverslip using specific antibody binding or a specific chemical conjugation group on

the end of the molecule, very gentle fluid flow is sufficient to impart enough viscous drag on

the molecule to extend it parallel to the direction of flow (for a theoretical discussion of the

mechanical responses of biopolymers to external forces, see Chapter 8).

This technique has been applied to filamentous protein molecules such as titin, a large

muscle protein discussed later in this chapter in the context of single-​molecule force trans­

duction techniques, which can then facilitate imaging of the full extent of the molecule, for

example, using fluorescence imaging if fluorophore probes can be bound to specific regions

of the molecule, or using transmission electron microscopy. Binding a micron-​sized bead to

the other end of the molecule increases the viscous drag in the fluid flow and allows higher

forces to be exerted on the molecule, and thus larger molecular extensions. This has been