Subdiffusion and Anomalous Local Viscoelasticity in Actin Networks

Abstract

We use magnetic tweezers to study local viscoelastic response in filamentous actin networks. The choice of magnetic, colloidal particles of varying size allows us to explore properties on the relevant micron and submicron scales. At these scales the mechanical response is determined by the bending properties of individual filaments and described by an anomalous power-law behavior. In the absence of external forces the particles exhibit a subdiffusive motion. [S0031-9007(96)01627-4] Complex molecular systems, such as polymer solutions, polymer melts, gels, (micro)emulsions, and foams, often display a combination of the elastic properties of solids and the viscous properties of fluids. Using classical rheological methods [1], the viscoelastic properties of such materials have been described at scales much larger than the molecular dimensions, and the systems under study have mostly been treated as homogeneous media. In many situations, however, local mechanical properties are of critical importance. For instance, the shape and motility of living cells, as well as cytoplasmic transport, are strongly influenced by the mechanical properties of cytoskeleton networks [2] at submicron and micron scales.Actin filaments ( f-actin), formed upon polymerization of globular actin proteins, are major components of the cytoskeleton and are involved in both transport and motility [3]. Easily purified and polymerized in vitro, actin is a model system for the study of the mechanics and assembly of biopolymers [4,5]. In this paper we show, using the example of actin filaments, how micromechanical measurements can provide information about local viscoelastic properties of the medium.f-actin is a rigid polymer with a persistence length L p of the order of 15 mm [6]. At high enough concentrations, in the so-called semidilute regime, the polymers form a three-dimensional network with a mesh size L. L is typically of the order of a micron and thus much smaller than L p . Viscoelastic properties of this inhomogeneous medium can be locally studied by inserting colloidal magnetic beads and perturbing them with external magnetic forces. In fact, such simple methods have been used for many years to explore the cytoplasm [7]. For beads with diameter, d, much larger than L, the mechanical perturbation is macroscopic. On the other hand, if d is much smaller than the mesh size, the bead is expected to probe only the solvent viscosity and geometrical constraints introduced by polymers. Therefore, the regime that is relevant for exploring the local network mechanics is one for which d is comparable to L. In this case, the bead is moving inside a "cage" of typical linear size L. To move further, it has to perturb the polymers of the cage, either through the influence of an external force or via thermal fluctuations. In both cases, one can study the viscoelastic properties on micron scales by observing the motion of individual beads. We show below that this approach can be made quantitative, and that local mechanical properties of the network can be...

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