title: Rheology of the cytoskeleton as a fractal network.
abstract: We model the cytoskeleton as a fractal network by identifying each segment with a simple Kelvin-Voigt element with a well defined equilibrium length. The final structure retains the elastic characteristics of a solid or a gel, which may support stress, without relaxing. By considering a very simple regular self-similar structure of segments in series and in parallel, in one, two, or three dimensions, we are able to express the viscoelasticity of the network as an effective generalized Kelvin-Voigt model with a power law spectrum of retardation times L∼τ(α). We relate the parameter α with the fractal dimension of the gel. In some regimes (0<α<1), we recover the weak power law behaviors of the elastic and viscous moduli with the angular frequencies G'∼G"∼w(α) that occur in a variety of soft materials, including living cells. In other regimes, we find different power laws for G' and G".
authors.affiliation: ISEL-Instituto Superior de Engenharia de Lisboa, Instituto Politécnico de Lisboa, 1959-007 Lisboa, Portugal.|CEDOC, Faculdade de Ciências Médicas, Universidade Nova de Lisboa, 1169-056 Lisboa, Portugal.
authors.forename: P
authors.initials: P
authors.lastname: Patrício
authors.affiliation: ISEL-Instituto Superior de Engenharia de Lisboa, Instituto Politécnico de Lisboa, 1959-007 Lisboa, Portugal.|Centro de Investigação em Agronomia, Alimentos, Ambiente e Paisagem, LEAF, Instituto Superior de Agronomia, Universidade de Lisboa, 1349-017 Lisboa, Portugal.
authors.forename: C R
authors.initials: CR
authors.lastname: Leal
authors.affiliation: ISEL-Instituto Superior de Engenharia de Lisboa, Instituto Politécnico de Lisboa, 1959-007 Lisboa, Portugal.|Center for Mathematical Analysis, Geometry and Dynamical Systems, Mathematics Department, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal.
authors.forename: J
authors.initials: J
authors.lastname: Duarte
authors.affiliation: ISEL-Instituto Superior de Engenharia de Lisboa, Instituto Politécnico de Lisboa, 1959-007 Lisboa, Portugal.
authors.forename: C
authors.initials: C
authors.lastname: Januário
mesh_terms: D003599:Cytoskeleton; D017709:Fractals; D012212:Rheology