Quantum Constrained Bioenergetic Instability as a Physical Limit on Early Cancer Signal Detection

Overview

Early cancer detection is commonly framed as a classification problem, yet such approaches rarely address whether early disease states are physically detectable in molecular data at all. Here, I present a physics first framework that reframes early cancer as a state of bioenergetic instability, rather than metabolic failure, and asks when such instability becomes theoretically resolvable. Using Marcus electron transfer theory, I model mitochondrial electron transport and define a Bioenergetic Instability Index (BII) that quantifies the sensitivity of electron transport flux to stochastic perturbations in quantum parameters. I apply this framework to N = 178 bulk RNA-seq transcriptomes from the TCGA pancreatic ductal adenocarcinoma (PAAD) cohort, demonstrating that tumor associated samples occupy a distinct high instability regime despite overlapping mitochondrial transcriptional capacity with normal tissue. Importantly, BII values are strongly coupled to compensatory mitochondrial stress responses, including nuclear encoded mitochondrial genes and redox stress pathways, indicating that bioenergetic instability is transcriptionally encoded prior to energetic collapse. Finally, by explicitly modeling molecular sampling noise, I derive a conservative detectability floor, showing that instability signals become resolvable only above tumor fractions on the order of 10^-3 to 10^-4, depending on effective sequencing depth, independent of algorithmic complexity. Together, these results establish a principled framework for understanding the physical limits of ultra early cancer signal detection and shift the focus from prediction accuracy to detectability feasibility under fundamental constraints.