# Rheology of coss-linked semiflexible polymers

The cytoskeleton is a viscoelastic material with particular, but poorly understood mechanical behavior. From a theoretical point of view, these systems are regarded as networks of reversibly (or permanently) cross-linked semiflexible polymers. Project A16 (Heussinger) developed a theoretical framework based on linear elasticity that allows for calculating elastic and viscous moduli of reversibly cross-linked networks of semiflexible polymers over the whole frequency regime. This approach is highly relevant for standard rheological experiments (Plagge et al., Phys. Rev. E (2016) 93:062502). The rheology of the network is described by representing the linkage as a rough periodic energy landscape distorted by an external force. Project A16 was able to apply this theoretical framework to rheological data obtained from a model system of a minimal actin cortex attached to a membrane (see project A17 (Janshoff, Steinem)). The quantitative analysis of the rheology data allowed for relating the architecture of the membrane attached actin cortex, which is modulated by the number of reversible pinning points at the membrane, to the viscoelastic properties of the composite material (Nöding et al., J. Phys. Chem. B (2018) 122:4537–4545).

**Microrheology on minimal actin cortices.** * A) llustration of the basic model assumptions. (Top) Binding potential experienced by the cross-links plotted along the filament axis. (Bottom) On a mesoscopic scale, the network is represented by a continuum viscoelastic body with modulus g(t). Application of a force F will lead to a network strain γ. On the microscopic scale the individual filaments couple to the same matrix with modulus g at their cross-links. B) Frequency dependent viscoelastic properties of a membrane-attached F-actin network. The frequency dependent experimentally determined storage modulus g' and loss modulus g'' are shown together with the fit according to the theoretical model. C) Schematic of the experimental model system developed, consisting of a lipid bilayer and a thin actin cortex that is rheologically probed by microspheres.*