Infrequent Cerebral Colonization: A Quantum Probabilistic Model of Dormancy and Colonization in Colon Carcinoma Following Basement-Membrane Escape.

Following basement-membrane rupture at the invasive front, colon carcinoma cells undergo sub clonal divergence driven by epithelial-mesenchymal-transition transcription factors (SNAIL, ZEB1, TWIST), giving rise to cells that proceed to active colonization of a secondary site and cells that enter a dormant, quiescent state. Dormant populations are stratified by secondary-site niche, liver, bone, and brain, reflecting the premise that cues governing dormancy induction and reactivation differ substantially by organ. Brain involvement is included as a target cluster despite its rarity: Colorectal-to-brain metastasis occurs in an estimated 1.2 to 3.2 percent of patients over the disease course, in stark contrast to hepatic involvement, paralleling the rationale of an earlier companion analysis of glioblastoma-to-lung dissemination. Fate-assignment probability across the four clusters, colonize, dormant-liver, dormant-bone, and dormant-brain, was modeled with a Variational Quantum Eigensolver probabilistic-clustering approach, with an exclusivity constraint enforcing near-single-fate occupancy, executed on classical simulation and IBM Quantum hardware. The model consistently assigned the lowest fate probability to cerebral colonization across simulated and hardware execution and across a range of transcription-factor inputs, reproducing this clinical rarity. A sweep of the brain-specific reactivation trigger revealed a threshold-like transition in dormant-brain probability, low across most of the range then rising sharply near maximal strength, consistent with dormancy being governed by a discrete molecular switch rather than a continuous process. These results represent relative fate uncertainty, not a mechanistic prediction of cell behavior. Given the neurological and neuropsychiatric consequences of cerebral metastatic disease, this work is of direct relevance to clinical neuropsychiatry as well as oncology.