Stability of discoidal high-density lipoprotein particles

Abstract

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.

Continuum Theory for the Edge of an Open Lipid Bilayer

“…It can then be shown that f n ¼ 0 and f n ¼ s. These results are consistent with previous findings of, e.g., Maleki & Fried (2013b). The force and bending moment that S exerts on C are À ( f n n þ f n n) and À (m e e þ m n n), respectively.…”

Small-Angle X-Ray Scattering of the Cholesterol Incorporation into Human ApoA1-POPC Discoidal Particles

“…Although the effect of this additional symmetry break of the model could most likely also have been obtained by other means, e.g., through introduction of saddle-splay deformations, the appearance of a lense shape introduces only one more fit parameter and is furthermore in good accordance with an expected pinching effect at the rim of the disks due to interactions between the lipid bilayer and the ApoA1-protein (34). We refer to the literature for more elaborate discussions on out-of-plane geometry of lipid bilayers (34,35). The histidine tags of truncated ApoA1 protein as well as the N-terminal domain of ApoA1 were modeled as Gaussian random chains in agreement with previous findings (3).…”

Stability of lipid membranes

“…Substituting equation ( 22) into equation (20) yieldṡ…”

“…A classic example is the loss of stability in membrane tubules, known as the pearling instability [18,19]. The stability of flat discs has been recently studied in the context of high density lipoproteins [20] and disc-to-vesicle shape transition [21]. While these studies have given fundamental insights into the stability of homogeneous membranes with quadratic energy, there is a need to extend the framework to study systems with heterogeneous properties and higher-order bending energies.…”