Despite their overwhelming complexity, living cells display a high degree of internal mechanical and functional organization which can largely be attributed to the intracellular biopolymer scaffold, the cytoskeleton. Being a very complex system far from thermodynamic equilibrium, the cytoskeleton's ability to organize is at the same time challenging and fascinating. The extensive amounts of frequently interacting cellular building blocks and their inherent multifunctionality permits highly adaptive behavior and obstructs a purely reductionist approach. Nevertheless (and despite the field's relative novelty), the physics approach has already proved to be extremely successful in revealing very fundamental concepts of cytoskeleton organization and behavior. This review aims at introducing the physics of the cytoskeleton ranging from single biopolymer filaments to multicellular organisms. Throughout this wide range of phenomena, the focus is set on the intertwined nature of the different physical scales (levels of complexity) that give rise to numerous emergent properties by means of self-organization or self-assembly.

The mechanics of complex soft matter often cannot be understood in the classical physical frame of flexible polymers or rigid rods. The underlying constituents are semiflexible polymers, whose finite bending stiffness ($\kappa$) leads to nontrivial mechanical responses. A natural model for such polymers is the protein actin. Experimental studies of actin networks, however, are limited since the persistence length ($l_p\propto \kappa$) cannot be tuned. Here, we experimentally characterize this parameter for the first time in entangled networks formed by synthetically produced, structurally tunable DNA nanotubes. This material enabled the validation of characteristics inherent to semiflexible polymers and networks thereof, i.e., persistence length, inextensibility, reptation, and mesh size scaling. While the scaling of the elastic plateau modulus with concentration $G_0\propto c^{7/5}$ is consistent with previous measurements and established theories, the emerging persistence length scaling $G_0\propto l_p$ opposes predominant theoretical predictions.

Bundles and networks of semiflexible biopolymers are key elements in cells, lending them mechanical integrity while also enabling dynamic functions. Networks have been the subject of many studies, revealing a variety of fundamental characteristics often determined via bulk measurements. Although bundles are equally important in biological systems, they have garnered much less scientific attention since they have to be probed on the mesoscopic scale. Here, we review theoretical as well as experimental approaches, which mainly employ the naturally occurring biopolymer actin, to highlight the principles behind these structures on the single bundle level.

Actin networks are adaptive materials enabling dynamic and static functions of living cells. A central element for tuning their underlying structural and mechanical properties is the ability to reversibly connect, i.e., transiently crosslink, filaments within the networks. Natural crosslinkers, however, vary across many parameters. Therefore, systematically studying the impact of their fundamental properties like size and binding strength is unfeasible since their structural parameters cannot be independently tuned. Herein, this problem is circumvented by employing a modular strategy to construct purely synthetic actin crosslinkers from DNA and peptides. These crosslinkers mimic both intuitive and noncanonical mechanical properties of their natural counterparts. By isolating binding affinity as the primary control parameter, effects on structural and dynamic behaviors of actin networks are characterized. A concentration‐dependent triphasic behavior arises from both strong and weak crosslinkers due to emergent structural polymorphism. Beyond a certain threshold, strong binding leads to a nonmonotonic elastic pulse, which is a consequence of self‐destruction of the mechanical structure of the underlying network. The modular design also facilitates an orthogonal regulatory mechanism based on enzymatic cleaving. This approach can be used to guide the rational design of further biomimetic components for programmable modulation of the properties of biomaterials and cells.

Composite networks of actin and vimentin filaments can be described by a superposition via an inelastic glassy wormlike chain model.