ProtoNetStack for DNA-Encoded Source Routing and Majority Aggregation in Protocell Molecular Nanonetworks

Abstract

Protocell communities can support programmable molecular nanonetworks, yet most demonstrations use broadcast diffusion or fixed sender-receiver circuits. We introduce PO_SCPLOWROTOC_SCPLOWNO_SCPLOWETC_SCPLOWSO_SCPLOWTACKC_SCPLOW, a network-layer abstraction in which a logical DNA-encoded packet carries a payload, a processing-address list, and an optional forwarding budget. The list determines where localized molecular services transform the packet, not its bidirectional diffusive trajectory. We formulate a finite-state reaction-transport model whose concentration dynamics and single-copy continuous-time Markov chain use the same generator. Under ideal specificity, positive rates, connected transport, no degradation, and sufficient budget, packet stages advance only in the encoded order and delivery occurs almost surely. All injected concentration is delivered asymptotically. Uniform first-order degradation makes delivery probability the Laplace transform of the lossless delivery-time distribution. A union-bound result separates endpoint delivery from route-faithful delivery under off-target processing. As an application, we develop cancellation-based strict-majority aggregation on rooted protocell trees. Conservation of token imbalance proves asymptotic correctness and yields a finite-time certificate. With one initial token per node, outside-root mass below one guarantees the correct root sign. Direct matrix-exponential calculations show sequential processing, branching addressability, route-length attenuation, and bounded forwarding work. A 16-condition finite-copy benchmark with 20,000 trajectories per condition shows that off-target reactions can increase endpoint arrival while decreasing route-faithful delivery. Adaptive ordinary differential equation simulations on trees up to 511 compartments show decision time increasing approximately with maximum tree depth and quantify bias from asymmetric loss. PO_SCPLOWROTOC_SCPLOWNO_SCPLOWETC_SCPLOWSO_SCPLOWTACKC_SCPLOW is therefore a formally analyzable molecular networking architecture and an experimentally testable blueprint. Sequence-resolved gates and chassis calibration remain future work.