We have studied the pearling instability induced on hollow tubular lipid ve
sicles by hydrophilic polymers with hydrophobic side groups along the backb
one. The results show that the polymer concentration is coupled to local me
mbrane curvature. The relaxation of a pearled tube is characterized by two
different well-separated time scales, indicating two physical mechanisms. W
e present a model, which explains the observed phenomena and predicts polym
er segregation according to local membrane curvature at late stages.