Power spectrum of out-of-equilibrium forces in living cells: amplitude and frequency dependence

Abstract

Living cells exhibit an important out-of-equilibrium mechanical activity, mainly due to the forces generated by molecular motors, acting individually or collectively on the cytoskeleton. They contribute to the fact that the fluctuation-dissipation theorem does not apply in living systems. In this work we probe the cytoskeletal out-of-equilibrium dynamics by performing simultaneous active and passive microrheology experiments, using the same micron-sized probe specifically bound to the actin cortex. The free motion of the probe exhibits a constrained, subdiffusive behavior at short time scales (t < 2s), and a directed, superdiffusive behavior at larger time scales, while, in response to a step force, its creep function presents the usual weak power law dependence with time. Combining the results of both experiments, we precisely measure for the first time the power spectrum of the force fluctuations exerted on this probe, which lies more than one order of magnitude above the spectrum expected at equilibrium, and greatly depends on frequency. We retrieve an effective temperature Teff of the system, as an estimate of the departure from thermal equilibrium. This departure is especially pronounced for long time scales, where Teff bears the footprint of the cooperative activity of motors pulling on the actin network. ATP depletion reduces the fluctuating force amplitude and results in a sharp decrease of Teff towards equilibrium.