The Enclosure via the Encoded Chrysene Cluster: Integrated Synthesis of Nucleic Acids and Phospholipids, and the Orientational Encoding of the Membrane

Abstract

The encoding of the corpus operates on a complex of two units: a 6,12-disubstituted chrysene paired with a 3,6,9,12-tetrasubstituted one. The tetrasubstituted unit becomes a nucleobase; the disubstituted unit is the template on which it is shaped, is not consumed, and remains tethered to the base it templated, holding still the two binary orientational data — its alignment to its partner, and its orientation in the cluster's common frame — whose pair indexes base four and constitutes the encoding. A tethered unit is therefore not a label on a sequence but a carrier of it. This paper asks what becomes of those carriers, and of the units of the same family never recruited into a complex. The two questions have one answer: the unrecruited remainder makes a membrane, and the carriers migrate into it, so that an enclosed reaction environment arises from the material of the encoding itself.

Scission is finite and enumerated in full. Four are attachment-admissible; one places its tails in the lamellar range, the selection being by tail length and not by topology. Eliminating rather than reducing the ether at the free substituted position fixes the retained unsaturation at Δ9, and the product is a di-O-(octadec-9-enyl) phosphate, each of whose defining features the enumeration fixed before any comparand was consulted. The minority doubly bridged dimer yields a macrocyclic bolaamphiphile instead. Enclosure is a parity condition: the leaflet map is a Z/2-valued function on the anchor set, and the strand is enclosed exactly when it is constant, crossing the core once at each sign change. The condition is not metric, and since a crossing would carry a charged backbone through an acyl core at a cost of order 10² kBT, the constant case is the one with a route: enclosure reduces to a single bit fixed at closure.

The passage of the encoding into the membrane is posed as a question about a map. The source carries two bits per anchor. One is the pair type, written into the molecule as a tether and a cap by the same event that recorded it, and carried unconditionally. The other is frame-relative, and a closed membrane supplies the frame: its normal is globally defined, so the face a unit presents is one question at every anchor—the condition under which the anchors encode collectively rather than severally. Whether a unit is free to record in that frame is a premise about a nine-atom arm, and it separates two cases: the map injective at two bits per anchor, or the face slaved to the pair type, with fibres of size 2ᵐ and the polarity of every base pair lost. That premise competes with the premise on which the anchoring has a subject at all, both being demands on the same arm. The anchors' ordering is carried by the strand's covalent backbone and costs no premise; a second channel, filtered by helical phase, resolves e bits for e anchors in phase and adds redundancy rather than resolution. Closure requires an unrecruited pool of order 10² vessels per encoded vessel under a stipulated bending tolerance, and the requirement does not grow with the sequence enclosed. Because the strand is anchored rather than free, the operative condition is a curvature and not a volume.