Modeling membrane nanotube morphology: the role of heterogeneity in composition and material properties

Abstract

Membrane nanotubes have been identified as a dynamic way for cells to connect and interact over long distances. These long and thin membranous protrusions have been shown to serve as conduits for the transport of proteins, organelles, viral particles, and mRNA. Nanotubes typically appear as thin and cylindrical tubes, but they can also have a beads-on-a-string architecture. Here, we study the role of membrane mechanics in governing the architecture of these tubes and show that the formation of a bead-like structure along the nanotube can result from a local heterogeneity in the membrane due to protein aggregation or due to membrane composition. We present numerical results that predict how membrane properties, protein density, and tension compete to create a phase space that governs the morphology of a nanotube. We also find that the stability of multiple beads is regulated by an energy barrier that prevents two beads from fusing. These results suggest that the membrane-protein interaction, protein aggregation, and membrane tension closely regulate the tube radius, number of beads, and the bead morphology.

Modeling Membrane Curvature Generation due to Membrane–Protein Interactions

“…Therefore, in most cases, analytical solutions are not possible and the equations are often solved numerically. Over the last few decades, various computational approaches have been developed to solve the set of governing PDEs including the boundary value problem for axisymmetric coordinates [32,66,73,120,121], different finite element methods [122,123,124], Monte Carlo methods [125,126,127], finite difference methods [128,129], and the phase field representation of the surface [130,131,132]. Each of these methods has its own advantages and disadvantages and, depending on the complexity of the problem, one or more of them can be implemented.…”

“…By using the SC model, recent studies have shown for example how a line tension at a lipid phase boundary could drive scission in yeast endocytosis [32,144,145], or how a snap-through transition from open U-shaped buds to closed buds in CME is regulated by the membrane tension [66,73]. Furthermore, the experimentally observed change in the membrane tension (spontaneous tension) in response to protein adsorption [146,147,148], can be explained in the context of the SC model [120,136,140]. The SC model has also been used to elucidate the role of varying membrane tension due to protein-induced spontaneous curvature [120,136,140].…”

“…Furthermore, the experimentally observed change in the membrane tension (spontaneous tension) in response to protein adsorption [146,147,148], can be explained in the context of the SC model [120,136,140]. The SC model has also been used to elucidate the role of varying membrane tension due to protein-induced spontaneous curvature [120,136,140]. While the SC model has been very effective in capturing large-scale deformations of the membrane, it does not take into account the protein density or the curvature induced by individual moieties.…”

“…A major open question in the field is the relationship between protein density, size, and spontaneous curvature. Although current models use a linear proportionality [120,176,188], this choice of functions is critical in determining the energy.…”

Mechanical principles governing the shapes of dendritic spines

“…• We assume that the membrane is locally inextensible, since the stretching modulus of the lipid bilayer is an order of magnitude larger than the membrane bending modulus [91]. We implemented this constraint using a Lagrange multiplier, which can be interpreted as the membrane tension [92][93][94]. We note that this membrane tension, in this study, is better interpreted as the cortical tension including the effective contribution of both the membrane in-plane stresses and membrane-cytoskeleton interactions [95,96].…”