  We consider a one-dimensional elastic membrane, which is pushed by growing
filaments. The filaments tend to grow by creating local protrusions in the
membrane and this process has surface energy and bending energy costs. Although
it is expected that with increasing surface tension and bending rigidity, it
should become more difficult to create a protrusion, we find that for a fixed
bending rigidity, as the surface tension increases, protrusions are more easily
formed. This effect also gives rise to nontrivial dependence of membrane
velocity on the surface tension, characterized by a dip and a peak. We explain
this unusual phenomenon by studying in detail the interplay of the surface and
the bending energy and show that this interplay is responsible for a
qualitative shape change of the membrane, which gives rise to the above effect.
