Rheology of the cytoskeleton as a fractal network

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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 similar to tau(alpha). We relate the parameter alpha with the fractal dimension of the gel. In some regimes ( 0 < alpha < 1), we recover the weak power law behaviors of the elastic and viscous moduli with the angular frequencies G' similar to G{''} similar to w(alpha) that occur in a variety of soft materials, including living cells. In other regimes, we find different power laws for G' and G{''}.}}
Original languageEnglish
Article number040702
JournalPhysical Review E
Issue number4
Publication statusPublished - 29 Oct 2015


  • Physics


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