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We analyze the non-equilibrium shape fluctuations of giant unilamellarvesicles encapsulating motile bacteria. Owing to bacteria--membrane collisions,we experimentally observe a significant increase in the magnitude of membranefluctuations at low wave numbers, compared to the well-known thermalfluctuation spectrum. We interrogate these results by numerically simulatingmembrane height fluctuations via a modified Langevin equation, which includesbacteria--membrane contact forces. Taking advantage of the length and timescale separation of these contact forces and thermal noise, we furthercorroborate our results with an approximate theoretical solution to thedynamical membrane equations. Our theory and simulations demonstrate excellentagreement with non-equilibrium fluctuations observed in experiments. Moreover,our theory reveals that the fluctuation--dissipation theorem is not broken bythe bacteria; rather, membrane fluctuations can be decomposed into thermal andactive components.

Active Contact Forces Drive Non-Equilibrium Fluctuations in Membrane Vesicles