*2.4.2 Recipe for preparing crosslinker complexes that are concentrated by a factor X in a volume* VFC

Further, these measurements probe the macroscopic mechanical properties of the networks but are unable to probe mechanics at the molecular and cellular scales (μm). Finally, these methods are ill-equipped to measure spatial heterogeneities in

Microrheology offers a complementary approach to characterizing the microscale mechanical and viscoelastic properties of cytoskeleton networks. While passive microrheology tracks freely diffusing microspheres embedded in networks to extract viscoelastic moduli, active microrheology uses optical tweezers to actively force embedded microspheres through networks and measure the force exerted to resist this strain. Active microrheology enables one to probe both molecular and mesoscopic scales and perturb networks far from equilibrium to access the nonlinear regime. Specifically, optical tweezers can be used to drag microspheres over distances that are large (5–30 μm) relative to the mesh size of the network (<μm) at speeds much faster than the molecular relaxation rates. The force exerted

network response, and can irreversibly disrupt or damage the network.

*Microscale Mechanics of Plug-and-Play In Vitro Cytoskeleton Networks*

*DOI: http://dx.doi.org/10.5772/intechopen.84401*

on the bead to resist the strain, as well as the subsequent relaxation of force

cytoskeleton networks described in Section 2 [18, 19, 26–28].

Reference [25] provides a thorough overview of the underlying principles and execution of optical tweezers microrheology to characterize the mechanics of biopolymer networks. Here, the focus is on the key results obtained using the in vitro

Active microrheology experiments have been carried out on entangled actin networks (Section 2.1) to characterize the dependence of the viscoelastic response and stress relaxation on the rate of the applied microbead strain *γ*\_ and actin concentration *c* (1 mg/mL = 23.2 μM) [26, 27]. The results are largely described within the framework of the tube model for entangled polymers, pioneered by de Gennes and Doi and Edwards [29, 30]. Comparisons to new theories and extensions of the

Entangled actin networks (*c* = 0.5 mg/mL; mesh size *ξ* = 0.42 μm) subject to strain rates of *γ*\_ = 1.4–9.4 s<sup>1</sup> (corresponding to speeds of *v* = 1.5–10 m/s) display a unique crossover to appreciable nonlinearity at a strain rate *γ*\_<sup>c</sup> comparable to the

networks exhibit stress-stiffening, which, importantly, is not apparent at the macroscopic scale. This stiffening behavior occurs over very short time scales, comparable to the predicted timescale over which mesh size deformations relax *τξ*, and has been shown to arise from suppressed filament bending. At times longer than *τξ*, deformed entanglement segments are able to bend to release stress, and stress softening ensues until the network ultimately yields to an effectively viscous regime, over a timescale comparable to *τent*. This terminal viscous regime exhibits

notably less pronounced than the thinning exhibited by flexible entangled polymers

for increasing strain rates; and for rates greater than *γ*\_c, the relaxation displays a complex power-law dependence on time, as opposed to the expected exponential decay. This power-law relaxation is indicative of dynamic strain-induced entanglement tube dilation and healing, which corroborates recent theoretical predictions

). Surprisingly, the force relaxation following strain proceeds more quickly

. Above *γ*\_c,

0.34, which is

theoretical rate of relaxation of individual entanglement segments *τ*ent*<sup>1</sup>*

shear thinning due to release of entanglements, with scaling *η γ*\_

following strain, is measured.

**3.1 Entangled actin networks**

*3.1.1 Strain rate dependence*

(*η γ*\_ *1*

**201**

for rigid rods [31, 34].

tube model are also highlighted [31–33].

Prepared complexes are viable for 24 h on ice. Biotinylated protein [*B-P*] used depends on the type of crosslinking as follows:

**Actin**: [B-P] = [B-A]

**Microtubule**: [B-P] = [B-T]

**Co-linked**: [B-P] = [B-A] + [B-T]; [B-A] = [B-T] = ½[B-P]

**Both**: Prepare Actin and Microtubule solutions. Add equal parts of each to final sample chamber.


Sonicate complex solution for 90 min at 4°C. Add volume *VCL* to solution below.
