Mechanical and Civil Engineering Seminar
The packaging and transport of cholesterol in the bloodstream are mediated by nanoparticles called lipoproteins. In a process known as ``reverse cholesterol transport," high-density lipoprotein (HDL) particles scavenge cholesterol from tissues and other lipoproteins and thereafter deliver it to the liver for excretion or other use. During this process, which is consistent with the observed inverse relationship between levels of HDL and the risk of atherosclerosis, HDL particles undergo various shape transitions. The functional properties of these particles are believed to be closely tied to shape. Discoidal and spheroidal shapes are observed. For discoidal HDL, experimental evidence and molecular dynamics simulations have led to the proposition of an analog model involving an elastic loop spanned by a soap film, corresponding respectively to the major protein component of the HDL and the lipid molecules. On the basis of a variational formulation, we obtain a boundary-value problem for a vector field that parametrizes both the bounding loop and the spanning surface. Working with the first and second variations of the relevant free-energy functional, we conduct detailed bifurcation and stability analyses. We also discuss the extension of the theory to account for curvature elasticity and other salient effects.