Power-law decay of force on cell membrane tethers reflects long-ranged relaxation of membrane tension

Membrane tension is an acknowledged regulator of a wide array of cell functions; however, whether it acts locally or globally in different contexts remains debated. Recent experiments that locally perturb tension and measure the response elsewhere on the membrane are not conclusive, and the mechanism of diffusive tension relaxation has been called into doubt. Here, we consider the tension response to a sudden extension of a membrane tether, and report a quantitative signature of dynamic tension relaxation, which up to now is missing. We present a theory based on tension diffusion leading to a prediction of power-law decay in time of the force holding the tether, with a material-independent exponent of 1/3. This prediction is confirmed to within a few percent by re-analyzing eleven sets of tether data from two cell types with distinct membrane cortical architectures. Overall, our scaling results indicate the absence of a relevant characteristic length and therefore generically reflect tension relaxation by long-range membrane lipid flows.