Decoding the Energetic Logic of Genetic Systems: A Hybrid Neural-Symbolic Framework for Quantum-Informed Bioenergetics

Life is sustained by the dynamic flow of energy through adenosine triphosphate ( ATP ), redox carriers such as NADH , and reactive oxygen species ( ROS ). These molecules not only fuel biochemical reactions but also encode information that regulates gene expression, DNA repair , and replication . Despite decades of biochemical study, the mathematical principles linking cellular energetics to genetic regulation remain unknown. Here we present a hybrid neural-symbolic framework that discovers the governing equations of energy-dependent genetic processes. Using simulated time-series data capturing oscillations in ATP, NADH, and ROS, we trained a neural ordinary differential equation (neural ODE) model to learn the temporal dynamics of gene expression, repair, and replication. The trained model was then analyzed by symbolic regression to extract explicit, interpretable equations describing how energy flow constrains molecular behavior. The resulting system revealed an energetic hierarchy in which transcription dominates during high ATP availability, repair increases under oxidative stress, and replication scales with the NADH/ROS ratio. The symbolic equations recovered exponential and sinusoidal dependencies suggestive of rhythmic, quantum-informed energy coupling. Taken together, these results reveal a mechanistic framework describing how cells distribute energy across competing genetic processes. This work introduces generative bioenergetics , a computational paradigm that unifies machine learning, quantum biology , and mitochondrial systems theory . By translating energy flow into interpretable equations, this approach moves toward a unified model of life as a self-organizing, energy-efficient system where computation and metabolism are fundamentally intertwined.