We study experimentally a coiling instability of cylindrical multilamellar
stacks of phospholipid membranes, induced by polymers with hydrophobic anch
ors grafted along their hydrophilic backbone. We interpret our experimental
results in terms of a model in which local membrane curvature and polymer
concentration are coupled. The model predicts the occurrence of maximally t
ight coils above a threshold polymer concentration. Indeed, only maximally
tight coils are observed experimentally. Our system is unique in that coils
form in the absence of twist and adhesion.