  We study the effect of membrane proteins on the shape, composition and
thermodynamic stability of the surrounding membrane. When the coupling between
membrane composition and curvature is strong enough the nearby composition and
shape both undergo a transition from over-damped to under-damped spatial
variation, well before the membrane becomes unstable in the bulk. This
transition is associated with a change in the sign of the thermodynamic energy
and hence has the unusual features that it can favour the early stages of coat
assembly necessary for vesiculation (budding), while suppressing the activity
of mechanosensitive membrane channels and transporters. Our results also
suggest an approach to obtain physical parameters that are otherwise difficult
to measure.
