Stall, spiculate, or run away: The fate of fibers growing towards fluctuating membranes

We study the dynamics of a growing semiflexible fiber approaching a membrane at an angle. At late times we find three regimes: fiber stalling, when growth stops, runaway, in which the fiber bends away from the membrane, and another regime in which spicules form. We discuss which regions of the resulting phase diagram are explored by (i) single and bundled actin fibers in living cells, (ii) sickle hemoglobin fibers, and (iii) microtubules inside vesicles. We complement our analysis with 3D stochastic simulations.