Superdiffusive motion with fractional power-law exponents

The spontaneous random motion of microbeads bound to the actomyosin network of living cells is a non-Brownian process [1]. The mean-squared-displacement (MSD) of the bead shows a sub-to-superdiffusive transition, which has recently been traced back to the interplay of noise, dominating at short, and persistent traction forces dominating at long time scales [2]. The MSD increases at long times according to a powerlaw with fractional exponent between 1 and 2, which so far remained unexplained. We propose three different models of cytoskeletal dynamics producing such a fractional exponent. The traction forces are explained by the spontaneous formation and gradual self-assembly of stress fibers, attached to the microbead. While mature fibers constitute an elastic network for the bead, pre-mature fibers produce an increasing level of prestress with long-time powerlaw correlations. Our models focus on different biochemical mechanisms that give rise to such correlations.