Mechanics of the Formation, Interaction, and Evolution of Membrane Tubular Structures

Abstract

Membrane nanotubes, also known as membrane tethers, play important functional roles in many cellular processes, such as trafficking and signaling. Although considerable progresses have been made in understanding the physics regulating the mechanical behaviors of individual membrane nanotubes, relatively little is known about the formation of multiple membrane nanotubes due to the rapid occurring process involving strong cooperative effects and complex configurational transitions. By exerting a pair of external extraction upon two separate membrane regions, here, we combine molecular dynamics simulations and theoretical analysis to investigate how the membrane nanotube formation and pulling behaviors are regulated by the separation between the pulling forces and how the membrane protrusions interact with each other. As the force separation increases, different membrane configurations are observed, including an individual tubular protrusion, a relatively less deformed protrusion with two nanotubes on its top forming a V shape, a Y-shaped configuration through nanotube coalescence via a zipper-like mechanism, and two weakly interacting tubular protrusions. The energy profile as a function of the separation is determined. Moreover, the directional flow of lipid molecules accompanying the membrane shape transition is analyzed. Our results provide new, to our knowledge, insights at a molecular level into the interaction between membrane protrusions and help in understanding the formation and evolution of intra- and intercellular membrane tubular networks involved in numerous cell activities.

Figure 1

Pulling an individual membrane tether from the lipid membrane by exerting a constant force of 200 kJ/mol/nm on a circular lipid patch of r = 6 nm in radius. To see this figure in color, go online.

Figure 2

Effect of the patch radius on the tether formation. (a) Time evolutions of the pulling force on the membrane protrusion at different sizes r of the pulling region are shown. (b) The shortest tube radius as a function of the simulation time depicting the tether development is shown. The force constant was fixed at 1000 kJ/mol/nm², and the pulling velocity was 0.5 nm/ns. To see this figure in color, go online.

Figure 3

Structural evolution of the membrane protrusion at different separation d between two pulling forces f (side view). d = 20 nm (a), 44 nm (b), and 55 nm (c). The radius r of each pulling region was 10 nm, and the pulling velocity was 0.5 nm/ns with a force constant of 1000 kJ/mol/nm². To see this figure in color, go online.

Figure 4

Dynamics of the membrane protrusion at the pulling force separation d = 44 nm. Serving as tracer particles to determine the direction of lipid flow during the membrane protrusion, two groups of lipid molecules were selected: (a) lipids belonging to the membrane region between two pulling patches and (b) lipids close to the two circular patches. (c) Time evolutions of the position of tracer lipids (Z₁) relative to the top of the saddle membrane surface (Z₂). (d and e) Time evolutions of the lengths of three lipid branches formatting the Y junction (d) and the intersecting angles (e) are shown. The inset in (d) represents the membrane height contour at 50 ns. To see this figure in color, go online.

Figure 5

The membrane energy and configurational transition as a function of the separation d at a pulling displacement L/R = 1.5. The insets represent corresponding configurations at the symbols. The configuration in the case of two weakly interacting tubular protrusions (d = 12r) is a schematic plot, whereas the other two are from numerical calculations. The dashed line segments represent the membrane energy of the energetically unstable configurations. Double-headed arrows represent the separation d. Here, the radius of each pulling region is r = 0.15R with R as the radius of the basal membrane, and we assumed that the membrane tension is σ = 50 κ/R². To see this figure in color, go online.