Scale-Dependent Nonaffine Elasticity of Semiflexible Polymer Networks

Abstract

The cytoskeleton of eukaryotic cells provides mechanical support and governs intracellular transport. These functions rely on the complex mechanical properties of networks of semiflexible protein filaments. Recent theoretical interest has focused on mesoscopic properties of such networks and especially on the effect of local, non-affine bending deformations on mechanics. Here, we study the impact of local network deformations on the scale-dependent mobility of probe particles in entangled networks of semiflexible actin filaments by high-bandwidth microrheology. We find that micronsized particles in these networks experience two opposing non-continuum elastic effects: entropic depletion reduces the effective network rigidity, while local non-affine deformations of the network substantially enhance the rigidity at low frequencies. We show that a simple model of lateral bending of filaments embedded in a viscoelastic background leads to a scaling regime for the apparent elastic modulus G '(! )~! 9 16 ,

The Mechanical Properties of Early Drosophila Embryos Measured by High-Speed Video Microrheology

“…The elastic modulus G'(f) shows a power-law slope between 1 and 3/4 in the relatively noisy low-frequency range and appears to approach an elastic plateau at high frequencies between 100 and 1000 Hz. This behavior distinctly differs from what is seen in differentiated cells (42) or in strongly entangled or cross-linked in-vitro F-actin networks (22,34) and is more comparable with the response of dilute weakly entangled polymer solutions such as filamentous virus (43) where internal filament dynamics become visible at short times, below a characteristic disentanglement time. We therefore conclude that the parts of the embryo we could access with our 1 mm probe beads contain at most loosely entangled cytoskeletal networks.…”

“…The compressional modulus is assumed to be negligible because of the incompressibility of water, as usual (16). 1PMR can both underand overestimate shear moduli in the presence of semiflexible filaments because of depletion and local nonaffinity effects (34). 2PMR avoids such problems (21,22,35,36), but because it involves extensive ensemble-and time averaging, the approach is not feasible in the rather inhomogenous interior of the rapidly developing embryos.…”

Bulk rheometry at high frequencies: a review of experimental approaches

“…For instance, cells are active soft materials, and the protein filaments that compose the cytoskeleton display fast dynamics unique to semiflexible polymers (Koenderink et al 2006;Kollmannsberger and Fabry 2011). Atakhorrami et al (2014) studied the Fig. 12 High-frequency rheology of living fibroblasts, measured by AFM (Reprinted by permission from the Licensor: Springer Nature, Rigato et al (2017), Copyright (2017)).…”

Entanglement Density Tunes Microscale Nonlinear Response of Entangled Actin

“…Several macro-and microrheology studies have reported agreement with the c 7/5 scaling, 23,34,44 and recent microrheology measurements of the microscale creep compliance of entangled actin reported that viscosity scales as η ∼ c 7/5 . 20 On the other hand, other recent microrheology measurements 8,44,45 reported scaling of G ∼ c while still others [46][47][48][49] showed G ∼ c 11/5 and G ∼ c 9/16 . Further, the majority of experimental and theoretical studies have reported stress softening of entangled actin rather than stiffening in the nonlinear regime, understood to be due to the available non-affine bending modes not present in crosslinked or rigid rod networks.…”