  Filopodia are long, finger-like membrane tubes supported by cytoskeletal
filaments. Their shape is determined by the stiffness of the actin filament
bundles found inside them and by the interplay between the surface tension and
bending rigidity of the membrane. Although one might expect the Euler buckling
instability to limit the length of filopodia, we show through simple energetic
considerations that this is in general not the case. By further analyzing the
statics of filaments inside membrane tubes, and through computer simulations
that capture membrane and filament fluctuations, we show under which conditions
filopodia of arbitrary lengths are stable. We discuss several in vitro
experiments where this kind of stability has already been observed.
Furthermore, we predict that the filaments in long, stable filopodia adopt a
helical shape.
