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6.1.4.2 Analysis of oscillatory data
In oscillatory measurements, the applied force is modulated in time, typically in a
sinusoidal or triangle waveform, and the resulting bead displacement measured as
a function of time ( Fig. 6.9 B). This modulation can occur around a stress-free state
using a ring magnet geometry, or around an offset force (prestress) using a cube mag-
net geometry. From these data, we can extract important physical characteristics of
the MT network. To measure stiffness, we calculate the ratio of peak force to peak
displacement ( Lin & Valentine, 2012b ). Peak positions and amplitudes are deter-
mined through a parabolic fit to those force or position data with amplitudes within
30% of the peak value. This can be repeated for a range of driving frequencies or
forces to directly measure the time- and force-dependent response. The force range is
determined by the magnet shape, size, the presence of iron focusing tips, etc., as de-
scribed earlier. The frequency range is typically limited by the speed range of the
motor that drives the magnet position above the sample plane. The ratio of elastic
and viscous contributions to gel rheological response can be determined quantita-
tively by observing the time lag between the peaks in the force and displacement.
This time lag is commonly recast in terms of the phase angle d , defined as the ratio
of time lag to oscillation period and normalized such that for elastic gels when F ( t )
and
0 , whereas for viscous solutions when F ( t ) and
D
z ( t ) are in phase,
D
z ( t ) are
90 .
out of phase,
SUMMARY
Reconstituted MT networks together with other cytoskeletal networks exhibit a rich
set of mechanical properties and provide both a testing ground for fundamental poly-
mer physics and a minimal model of cell mechanics. Microscope-mounted NdFeB-
based magnetic tweezers devices enable the study of the relationships between local
viscoelastic properties and microstructures. It is possible to vary the magnitude and
frequency of applied force, and to simultaneously measure the network structure to
determine the molecular origins of MT network strength. We have successfully ap-
plied these devices to show that entangled networks are enthalpic viscoelastic solids
dominated by filament bending and compression rather than thermal undulations,
and that the mechanics of cross-linked networks is dictated primarily by the
force-induced failure of chemical bonds ( Yang et al., 2012 ). Future applications will
focus on extending these tools to study heterogeneous and enzymatically active cy-
toskeletal networks of increased chemical complexity to further our understanding of
cytoskeleton mechanics and remodeling.
Acknowledgments
Authors thank Jun Lin (UCSB) who with MTV designed and constructed the magnetic twee-
zers devices outlined herein, Leslie Wilson and Omar Saleh (UCSB) for helpful discussions
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