Reconstructing the Mitochondrial Proton Motive Force Using Physics-Informed Neural Networks and Surrogate Bioenergetic Signals

The mitochondrial proton motive force (PMF) underlies ATP synthesis, metabolite transport, and energy coupling. Yet, direct measurement of PMF remains technically challenging due to probe invasiveness, calibration drift, and compartmental averaging. Here, we introduce a physics-informed neural network (PINN) framework that reconstructs PMF from surrogate signals including NADH, oxygen, electron flux, proton leak, and reactive oxygen species (ROS). Using a synthetic curriculum dataset derived from biophysical ranges reported in the literature, our model achieved high predictive accuracy (R2 ≈ 0.99, RMSE < 1 mV) under normoxia and hypoxia. SHAP-based interpretability revealed distinct feature contributions: flux and NADH dominated under normoxia, while oxygen and ROS became more influential under hypoxia. Extended analyses demonstrated that PINNs generalize robustly across cross-validation folds, preserve biophysical constraints, and can be adapted to time-series dynamics, capturing PMF decline and recovery during simulated hypoxia-reoxygenation. To our knowledge, this is the first application of PINNs to mitochondrial bioenergetics, bridging machine learning with the chemiosmotic theory. This proof-of-concept establishes a foundation for non-invasive PMF estimation and opens avenues for studying mitochondrial adaptation in physiology and disease.