Power Spectrum of Out-of-equilibrium Forces in Living Cells : Amplitude and Frequency Dependence

Living cells exhibit an important out-of-equilibrium mechanical activity, mainly due to the forces generated by molecular motors. These motor proteins, acting individually or collectively on the cytoskeleton, contribute to the violation of the fluctuation-dissipation theorem 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 on 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.

💡 Research Summary

In this study the authors combine active and passive microrheology on the same micron‑sized probe that is specifically bound to the actin cortex of living cells, thereby enabling a direct measurement of the non‑equilibrium forces generated by molecular motors. Passive tracking of the probe reveals a two‑regime dynamics: at short times (t < 2 s) the mean‑square displacement follows a sub‑diffusive power law (exponent ≈ 0.7), reflecting the viscoelastic confinement of the cortical meshwork; at longer times the motion becomes super‑diffusive (exponent ≈ 1.3), indicating directed transport driven by collective motor activity. In active experiments a step force is applied with an optical trap and the resulting creep compliance follows a weak power law (exponent ≈ 0.2), characteristic of a broad spectrum of relaxation times in the cytoskeletal network.

By Fourier‑transforming the passive autocorrelation function and the active response function, the authors construct the generalized fluctuation‑dissipation relation for a non‑equilibrium system. The measured force power spectrum S_F(ω) can be expressed as the sum of the equilibrium contribution 2 k_B T Re