The Boolean Breast-Cancer Network (BBCN): durable, controllable apoptosis from faithful feedback and multi-timescale control

We model a breast tumour as a Boolean network of signalling pathways and pose therapy as a control problem: find minimal, druggable interventions that drive the network to a desired cell-fate phenotype as a genuine fixed point of the free dynamics, without permanently forcing any node. A 135-node breast-cancer network, adapted from a published Boolean model and carrying the feedback simplifications usual to such models, driven by a three-tier capped controller, makes the three cell-fate phenotypes controllable to differing degrees on their own (apoptosis 81-86% and proliferation 94-95% of patients across three cohorts, but resistance-off only 4-8%), yet achieving all three in sequence while preserving earlier gains is rare (2-3%), and the baseline network supports no durable apoptotic fixed point at all: the phenotypes share a dominant strongly-connected core (16 of 22 regulatory pathways), and under synchronous updating the network is globally oscillatory. We ask whether this non-durability reflects the biology or the simplified wiring, and show it is the wiring, not the biology. The baseline rules carry a degenerate p53 arm in which MDM2 self-locks and damage never reaches p53, and an AKT-FOXO arm with no closing feedback. Restoring three pieces of textbook regulation, the same biology a reduced bistable switch already uses, a p53-MDM2-ATM damage sensor, an AKT1-FOXO3a loop closed by PHLPP (the 136th node) with an uncoupled-state flag, and a death-engaged commitment latch, changes the picture across three cohorts (TCGA-BRCA, METABRIC, I-SPY2; N=1082/1980/988). Two changes recover durable control and they do different jobs: restoring the three feedback loops to their faithful biological form makes the durable death state exist, while embedding the biological separation of timescales, as a delayed (autoregressive) multirate system with distinct fast-signalling, protein-turnover, and transcription rates, makes that state reachable and stable where a single synchronous clock only oscillates. To our knowledge this direct embedding of timescale separation in the control of a patient-specific Boolean cancer model is novel. Drug resistance becomes a precise molecular state: it equals AKT-FOXO3a uncoupling, a documented resistance mechanism, for 4049 of 4050 patients (99.98%). Survival-axis inhibition durably flips exactly the coupled fraction (33-36%) while genotoxic input is the weak lever (3-4%), reversing the baseline-network reading. A minimal druggable kernel designed on the tractable switch, concentrating on the PI3K/AKT/mTOR axis, is found for 99-100% of resistant patients and commits 92-95% of them to apoptosis on the full network once death is scored by caspase commitment rather than by sustained survival-signal suppression. Under the full staged controller the biology-faithful network supports durable apoptotic fixed points in 15-17% of patients, where the baseline network supported none. We keep two honest readouts of death throughout, a strict one (8-14%) and a commitment one (92-95%), and report both. The model is a structural stratifier and drug-target nominator; it does not predict pathologic complete response, a limitation we trace to endpoint distance rather than signal quality. A minimal switch kernel of about two to three nodes holds this apoptotic state about as durably as a near whole-network controller of about thirty, a roughly 12-fold reduction at equal durability.