Extracting the dynamic correlation length of actin networks from microrheology experiments

Abstract

The mechanical properties of polymer gels based on cytoskeleton proteins (e.g. actin) have been studied extensively due to their significant role in biological cell motility and in maintaining the cell's structural integrity. Microrheology is the natural method of choice for such studies due to its economy in sample volume, its wide frequency range, and its spatial sensitivity. In microrheology, the thermal motion of tracer particles embedded in a complex fluid is used to extract the fluid's viscoelastic properties. Comparing the motion of a single particle to the correlated motion of particle pairs, it is possible to extract viscoelastic properties at different length scales. In a recent study, a crossover between intermediate and bulk response of complex fluids was discovered in microrheology measurements of reconstituted actin networks. This crossover length was related to structural and mechanical properties of the networks, such as their mesh size and dynamic correlation length. Here we capitalize on this result giving a detailed description of our analysis scheme, and demonstrating how this relation can be used to extract the dynamic correlation length of a polymer network. We further study the relation between the dynamic correlation length and the structure of the network, by introducing a new length scale, the average filament length, without altering the network's mesh size. Contrary to the prevailing assumption, that the dynamic correlation length is equivalent to the mesh size of the network, we find that the dynamic correlation length increases once the filament length is reduced below the crossover distance.

Response of a polymer network to the motion of a rigid sphere

“…If we assume the limits of large λ/a and η b /η (both satisfied in most practical circumstances), we are left with functions of ξ/a ≡ x alone. Such single-variable scaling functions are useful for comparison between experiment and theory [12] and for reliable extraction of material parameters, such as the correlation length ξ [13]. We concentrate on the properties γ, v (1) , and r (v) c , in the limit a ≪ ℓ c , as these are the most relevant experimentally.…”

“…(18), depending on the fluid viscosity η and characteristic pore size ξ. Hence, ξ is identified with the network's mesh size [10], up to a proportionality factor close to unity [12,13]. It also characterizes the spatial decay of transverse (shear) stresses due to the friction between the two components and, therefore, decreases with increasing Γ .…”

“…This function can be measured from the longitudinal displacement correlations of particle pairs in the extended twopoint technique [12,13]. We define the scaling functioñ v…”

“…A recent study, applying two-point microrheology to entangled F-actin networks [12,13], revealed a wide range of distances, intermediate between the microscopic scale (the network's mesh size ξ) and the macroscopic (asymptotically large) one, in which the dynamic pair correlations were qualitatively different from those at larger distances. This intermediate behavior ended at a distinct dynamic length, ℓ c , much larger than ξ, which marked the crossover to the macroscopic response.…”

“…As we shall see below, the intermediate region corresponds to the relative motion of the material's two components (network and solvent), whereas in the asymptotic region the material moves collectively, as a whole. The application of these ideas to a combination of one-and two-point measurements gives rise to an extension of microrheology, allowing for better characterization of complex fluids (e.g., extracting their correlation length) [12,13].…”