Many-body quantum percolation sustains ohmic proton flux through the nanoconfined F o motor
Abstract
The F o F 1 -ATP synthase drives cellular bioenergetics by translocating protons across the inner mitochondrial membrane. We recently demonstrated that the lipid cardiolipin acts as a 2D antenna, actively funnelling protons into the nanoconfined F o motor and enforcing severe “dimensional squeezing”. This 1D nanoconfinement forces protons into such close proximity that their hydration shells physically overlap, theoretically generating an infinite classical steric gridlock. Yet, empirical measurements show the F o motor operates at ~90% efficiency and exhibits barrierless, Ohmic conductance, presenting a biophysical paradox. To resolve this contradiction between classical physics and biological reality, we employed a differentiable inverse-physics framework to blindly deduce the proton wire’s geometry based solely on macroscopic physiological constraints: ohmic linearity and a 1.7 Deuterium Kinetic Isotope Effect. By substituting classical diffusion frameworks with a Many-Body Overdamped Quantum Langevin Equation (QLE), the optimiser successfully converged. It deduced that physiological flux dictates a steric boundary of 0.137 nm (aligning with the effective crystal radius of oxygen) and a structural confinement scale of 0.974 nm. We demonstrate that when these discovered biological parameters are evaluated under classical, independent-particle assumptions, the 1/ r 12 steric repulsive forces diverge to infinity, causing a simulation collapse. In contrast, the quantum…
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