Addressing the Division Clock: Codon Gating at the Membrane, the Reusable X-A Catalyst, and the Set Point of the Lineage

Abstract

The three preceding articles concluded that at a fixed line of their loop the lineage divides once per forcing period whatever the condensation rate. With the division reset applied, no dividing vessel is born on that line: division in one cycle requires no net growth, and a lineage held there reaches the dilution floor in 39.5 generations at α = 0.10. While the osmolyte input is proportional to the particle count, no membrane-limited condensation law linear or saturating in the remnant sets a size.

The input is therefore changed. Lipids arrive as a per-cycle flux tied to genome length, one lipid to a pair of units. Genome hexamers AAA and TTT template the tethered adenosine–chrysene triplet X-A X-A X-A in the bilayer, as in the patent record. Codons expressed on lipid-tethering events excise its middle unit; the flanking units reform and serve again, and condensation runs at the same units.

Under named hypotheses the catalyst density is the root of a quadratic; the bud is born with osmolyte per lipid equal to the mother's free remnant per lipid at division, Rbud = R0 wdiv/u0; the period is the time to regrow one bud's lipids, equal to the forcing period exactly when one cycle's lipids close one bud; and without condensation every mother line converges for bud fractions below one half. The mother line's bud is the largest of a distribution: at the baseline three births in four fall below the floor, a fraction fixed by lineage structure, and a population with every birth viable needs about twice the mother line's input. A gate mixing tethering events with standing membrane keeps the set point locally, in a basin that the basal share bounds and condensation widens. Under one codon per event the viability conditions become conditions on the sequence, which a random 200-unit genome meets at most one time in five. The sequence content sets the scale of the size distribution; the genome length sets the period. Corrections to the preceding articles are recorded as precedence rulings.