  Motivated by experimental and numerical studies revealing that discoidal
high-density lipoprotein (HDL) particles may adopt flat elliptical and
nonplanar saddle-like configurations, it is hypothesized that these might
represent stabilized configurations of initially unstable flat circular
particles. A variational description is developed to explore the stability of a
flat circular discoidal HDL particle. While the lipid bilayer is modeled as
two-dimensional fluid film endowed with surface tension and bending elasticity,
the apoA-I belt is modeled as one-dimensional inextensible twist-free chain
endowed with bending elasticity. Stability is investigated using the second
variation of the underlying energy functional. Various planar and nonplanar
instability modes are predicted and corresponding nondimensional critical
values of salient dimensionless parameters are obtained. The results predict
that the first planar and nonplanar unstable modes occur due to in-plane
elliptical and transverse saddle-like perturbations. Based on available data,
detailed stability diagrams indicate the range of input parameters for which a
flat circular discoidal HDL particle is linearly stable or unstable.
