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Based on a Hamiltonian that incorporates the elastic coupling between atracer and active particles, we derive a generalized Langevin model for thenon-equilibrium mechanical response of active viscoelastic biomatter. Our modelaccounts for the power-law viscoelastic response of the embedding polymericnetwork as well as for the non-equilibrium energy transfer between active andtracer particles. Our analytical expressions for the frequency-dependentresponse function and the positional autocorrelation function agree nicely withexperimental data for red blood cells and actomyosin networks with and withoutATP. The fitted effective active-particle temperature, elastic constants andeffective friction coefficients of our model allow straightforward physicalinterpretation.

Non-Markovian modeling of non-equilibrium fluctuations and dissipation in active viscoelastic biomatter