Power laws in cell microrheology : creep function, viscoelastic modulus and modelization
Résumé
We compare and synthesize the results of two microrheological experiments performed on the actin cytoskeleton of single cells. In the first one, the creep function J(t) of an entire cell stretched between two glass plates is measured after applying a constant force step [1]. In the second one, a micrometric bead specifically bound to transmembrane receptors is driven by an optical trap oscillating at frequency f, and the viscoelastic coefficient Ge(O is retrieved [2]. Both J(t) and Ge(O exhibit power law behaviors: J(t) =At ~ and IGe(f)l = GOf~, with the same exponent a:~0.20. This power law behavior is very robust, since a does not appreciably depend on the cell type, on the nature of the complex transmitting the mechanical stress, nor on the kind of experiment. Oppositely, the prefactors A and Go appear sensitive to these parameters. Within a same cell type, the exponents a are normally distributed over a cell population, while the prefactors A and Go follow a log-normal repartition. We interpret these results in the frame of a semi-phenomenological model, based on scaling arguments: in the cell, the number of mechanical units of size / is assumed to follow a power law, which implies a broad power law distribution P0(T) c~ T~-2 of relaxation times T. The natural dispersity from one cell to the other is simulated by randomly selecting a set of relaxation times Ti from the ideal distribution P0. This model accurately predicts the behaviors of J(t) and Ge(O and the statistical distribution of the parameters a, A and Go, in agreement with experiments. It leads to an estimate of the largest response time TM :-~-~1000s of the cytoskeletal network.