Localised stabilisation of a bistable switch for minimal-kernel phenotype control in a Boolean breast-cancer network

We pose breast-cancer therapy as a control problem on a Boolean network of signalling pathways. The goal is a minimal, druggable intervention that drives the network to apoptosis as a genuine fixed point of the free dynamics, with no node held on by force. On a 141-node network, adapted substantially from Taoma et al. with changes to its feedback wiring, a capped, no-forcing whole-network controller shows that the cell-fate phenotypes are individually controllable but jointly near-exclusive. They share a dominant strongly-connected core, 16 of 22 pathways, so feasibility does not imply joint reachability. We therefore reduce the apoptosis core to a nine-node bistable switch on the AKT1 and TP53 axis. We embed biological timescale separation as a multirate Boolean switch, fast, mid, and slow on a 1:5:25 schedule, with the slow variables sampled and held. We then relax global stabilisation, which is intractable on the full network, to localised stabilisation on the switch. A minimal kernel of about two to three nodes, concentrated on the PI3K/AKT/mTOR axis, drives the switch to its apoptotic attractor. It commits the full 141-node network to a caspase-cascade death fixed point in 15 to 17 percent of patients across three cohorts (TCGA, METABRIC, I-SPY2). It holds that state as durably as a near whole-network controller of about thirty nodes, an order-of-magnitude reduction at equal durability. The model is a structural drug-target nominator, not a response predictor.