Fission at the Closure Scale: Guest Area, the Curvature Floor, and Line-Tension Drive

Abstract

The preceding article found that a lineage keeping one strand per vessel comes to consist of closure vesicles, the smallest enclosures of the anchored strand, of radius about 13 nm at 200 units. This article asks what the membrane of such a vessel is and whether it can divide.

The chrysene guests of the membrane take 12.4% of its area at 200 units, so the vessel is born a little larger than the closure vesicle, 13.82 nm, and the existence condition of the preceding article relaxes to $g \leq 1.192$. A packing floor of 10–12 nm, rather than the conventional 25, admits genomes from 118–169 units. The contact energy that an earlier article left open is supplied from the stacking energies of the corpus, giving a line tension of 1.03–2.27 $k_B T$ per nanometre.

The central question is whether the line tension of the anchored domain divides such a vessel, and the answer turns on which division criterion is taken. Under the barrier-free threshold the line tension is short in every case considered, by factors of 1.3 to 5.6; under an energy balance it suffices in two cases of six, and with the Gaussian curvature modulus, which fission incurs once, in four, every case with the stronger stacking among them. The drive is comfortable at the 100-nm vessel for which it was proposed and marginal at 14 nm: keeping one strand per vessel brought the vessel to the scale at which the question arises. A shape-minimised calculation at this scale would settle it.

Two aids are examined. Spontaneous curvature would remove a barrier of 12 to 340 $k_B T$ at an outer-leaflet area excess of 0.066 to 0.335; the anchors of the corpus push the other way and its photochrome connectors supply under 0.01, so a curvature-active component is specified rather than found. Lipid taken from the environment enlarges the vessel in three forms, a fixed flux, a diffusion-limited capture, or incorporation proportional to area at less than one doubling per period, the last with set point $\Lambda^* = \lambda/(1-r)$. The guests demix into domains, which a closure vessel can shed only under the laxer criteria. Corrections to earlier articles are recorded as precedence rulings.