  We investigate the shape of a growing interface in the presence of an
impenetrable moving membrane. The two distinct geometrical arrangements of the
interface and membrane, obtained by placing the membrane behind or ahead of the
interface, are not symmetrically related. On the basis of numerical results and
an exact calculation, we argue that these two arrangements represent two
distinct universality classes for interfacial growth: whilst the
well-established Kardar-Parisi-Zhang (KPZ) growth is obtained in the `ahead'
arrangement, we find an arrested KPZ growth with a smaller roughness exponent
in the `behind' arrangement. This suggests that the surface properties of
growing cell membranes and expanding bacterial colonies, for example, are
fundamentally distinct.
