In this work, we study in detail the distribution of stochastic forces generated by the molecular motors activity, in the actin cortex of pre-muscular cells. By combining active and passive rheology experiments, performed on the same micro-bead bound to the actin network through membrane adhesive receptors, we measure the auto-correlation function Cff(t) of the average force pulling on the bead. Like for any out-of-equilibrium system, the force distribution differs from the thermodynamical equilibrium one, especially at long time scale t>1sec where the bead motion becomes partially directed. Thus the fluctuation-dissipation theorem does not apply and one can measure the distance from equilibrium through its violation. This work focuses on the influence of various parameters (ligand density, temperature, ATP depletion, molecular motors activity) on the force distribution. In particular, it is shown that the amplitude of active forces increases when the bead is more tighly attached to the cortex: this is interpreted through a model which takes into account the number of bonds between the bead and the cytoskeleton and the viscoelastic properties of the medium. It also increases with temperature, consistently with a description of the cell metabolism in terms of thermally activated reactions. Last, but not least, ATP depletion in the cell, or partial inhibitition of the actomyosin activity, leads to a decrease of the amplitude of the force distribution. Altogether, we propose a consistent and quantitative description for the motion of a micrometric probe interacting with the actin network, and for the amplitude of the stochastic forces generated by molecular motors in the cortex surrounding this probe.
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