Cycle Integration: Copy Number, the Closure Vesicle, and the Band of the Genome

Abstract

The pore, the lipid supply, the replication schedule, the division rule and the codon-gated loop of the preceding articles are joined here into one cycle and asked a question none of them asked: whether every vessel keeps one strand. Replication runs once per period and division only at dusk, so one strand per vessel holds exactly when every vessel divides at every dusk.

Three statements follow under named hypotheses. One period's lipids close exactly one minimal enclosure of the anchored strand, the closure vesicle, of radius 13.04 nm at 200 units. When every vessel divides at every dusk the mean birth size halves its distance to that vesicle each period, whatever the division rule, so the population comes to consist of closure vesicles dividing symmetrically; large founders persist only as a vanishing share, budding one closure vesicle per period. And the symmetric orbit exists if and only if a single number $g$, the per-period osmolyte gain in units of the closure vesicle's content, does not exceed one. Below one the vessels are flaccid at birth with reduced volume $g$; at one the orbit is taut and marginal; above one the closure vesicle is lost at its first dusk, and so is every other founder tried. Condensation raises the admissible input for an established lineage, but a founder without remnant gains less, and survives only if $g \leq 1/(2 - e^{-\kappa})$.

Computed: for $g$ from 0.6 to 0.99 no founder tried, from 1.5 closure vesicles to the 100-nm founder, loses a cell in fourteen periods; the codon-gated loop at its earlier baseline has $g = 1.87$ at 200 units and meets the condition from about 735; the per-period ledger becomes dominated by membrane, 0.863 of the pool at 200 units; one pore tethered to the strand over-supplies its daughter's nitrogen by a factor of 773,410. The genome's length sets the vessel; its content sets only whether the lineage survives and how flaccid it is. The lower edge of the length band rests on a curvature floor the corpus does not derive. Corrections to the preceding articles are recorded as precedence rulings.