On the role of membrane anisotropy in the beading transition of undulated tubular membrane structures

The Helfrich expression for the isotropic membrane bending energy was generalized for the case of anisotropic membranes by taking into account two intrinsic (spontaneous) curvatures, i.e., the intrinsic mean curvature Hm and the intrinsic curvature deviator Dm. Using this generalized expression for the membrane bending energy the shape equation for closed axisymmetric anisotropic membranes is solved numerically for the case of undulated tubular shapes. It is shown that the variation of one of the two intrinsic curvatures, Hm or Dm, may induce the first-order-like shape transitions between the undulated tubular membrane structures. The predicted discontinuous shape transitions were applied to explain the beading transitions without stretching, which were recently observed in nerve fibres