Division Without a Device: The Dusk Shape, the Tethered Domains, and the Window of the Gain

Abstract

The preceding article asked what force divides a vessel at the closure scale and found the line tension of the anchored domain short of the bending cost of fission. That cost was mispriced. It charged the vessel the difference between one sphere and two, but the vessel at dusk is not a sphere: the cycle brings it to reduced volume 0.7071, which is exactly the limit shape of two touching spheres, of the same bending energy as the pair. The deformation has been paid for by growing flaccid. What remains is the single new closed surface, $4\pi\kappa_G$, which is negative: −101 to −251 $k_B T$ over the moduli considered. At the dusk shape fission lowers the energy, and no curvature device is needed to make it possible.

The same geometry does not, however, bound the cycle from below. A vessel can form at most $v^{-2}$ equal spheres, but availability is not preference: each further sphere costs 4.00 to 4.80 $\pi\kappa$ more, so three are never preferred to two, and two flaccid daughters are available at every reduced volume. The lower bound on the gain that counting seems to offer does not follow, and what selects binary fission is structural: a vessel carrying two strands carries two tethered footprints, and if those demix they are the two centres about which the daughters form. What the geometry does give is $g \leq 1$, the condition that the vessel is not too taut, and the observation that $g = 1$ is the point the cycle is built around.

The reduced volume does not fall of its own accord: on the orbit area and volume double together and $v$ is constant. Division is approached only by incorporation biased toward the membrane, which moves the set point to $g_{\mathrm{eff}} = g_0(1 + F/\lambda)^{-3/2}$. A genome of 200 units, which the preceding article placed outside the viable band, is returned to the window by an environmental flux of 0.53 to 0.75 $\lambda$ per period. The tethers that insert as a strand is nucleated cover one to five per cent of the bilayer each: they fix the fission axis, assign one strand to each daughter, and select two as the number, but supply no drive, which under the corrected pricing they need not. Of three candidate devices the photochrome fails as a curvature switch by a factor of four, the strand fails as a constricting ring against its own overstretch force, and the free remnant, if it partitions outward, supplies more area excess than was ever required. Stimulated uptake is bounded below, at about a third of a doubling per period at the baseline considered, and above only by the stability of the set point.