The equilibrium fluctuations of a semiflexible filament cross linked into a network

TL;DR

This paper investigates how cross linking in semiflexible filament networks affects their equilibrium fluctuation spectrum, revealing three dominant fluctuation regimes and proposing a method for noninvasive network tension measurement.

Contribution

It introduces a theoretical framework analyzing the nonlinear effects of network compliance on filament fluctuations and proposes a novel tension microrheology technique.

Findings

Identification of three principal fluctuation regimes: tension, bending stiffness, and compliance.

Demonstration that filament fluctuations can serve as a probe for network tension.

Development of a response function for quantitative tension analysis.

Abstract

We examine the equilibrium fluctuation spectrum of a constituent semiflexible filament segment in a network. The effect of this cross linking is to modify the mechanical boundary conditions at the end of the filament. We consider the effect of both tensile stress in the network, and its elastic compliance. Most significantly, the network's compliance introduces a nonlinear term into the filament Hamiltonian even in the small-bending approximation. We analyze the effect of this nonlinearity upon the filament's fluctuation profile. We also find that there are three principal fluctuation regimes dominated by one of the following: (i) network tension, (ii) filament bending stiffness, or (iii) network compliance. We propose that one can use observed filament fluctuations as a noninvasive probe of network tension, and we provide the necessary response function to quantitatively analyze this sort of "tension microrheology" in cross linked semiflexible filament networks.