  We study a membrane tube with unidirectional ion pumps driving an osmotic
pressure difference. A pressure driven peristaltic instability is identified,
qualitatively distinct from similar tension-driven Rayleigh type instabilities
on membrane tubes. We discuss how this instability could be related to the
function and biogenesis of membrane bound organelles, in particular the
contractile vacuole complex. The unusually long natural wavelength of this
instability is in agreement with that observed in cells.
