Nanoscale spatial confinement of proton flux by cardiolipin drives high-speed lateral proton transport in mitochondria

Cellular respiration depends on the rapid, lateral flow of protons along the inner mitochondrial membrane to drive ATP synthesis. The precise nanoscale thermodynamic forces confining protons to this local circuit remain highly debated. Previous attempts to model macroscopic interfacial proton diffusion have been hindered by parameter equifinality and geometric artifacts, preventing the deconvolution of structural water networks from lipid electrostatics. Here, we resolve this ambiguity using a constrained, high-resolution two-dimensional continuum model. By incorporating experimentally validated buffer proton consumption rates as strict biological priors, we break mathematical degeneracy and isolate the specific thermodynamic components of planar lipid bilayers. Calibrating our model against time-resolved DOPG fluorescence kinetics, we decouple a universal structural water barrier (5.7 kBT) from the specific -1e electrostatic trap (4.3 kBT). Extrapolating these first principles, we predict the confinement architecture of cardiolipin, the signature -2e dimeric lipid of mitochondria. Our simulations reveal a deep kBT thermodynamic well. Crucially, this massive barrier confines protons within 1 to 2 nanometres of the membrane surface, virtually abolishing vertical leakage into the bulk aqueous phase of the inter-membrane space. We demonstrate that this spatial confinement triggers dimensional squeezing, preserving a robust lateral concentration gradient that actively accelerates radial proton wave propagation. Biologically, these findings reveal that cardiolipin does not merely prevent proton dissipation, it functions as a highly efficient, quasi-two-dimensional nanoscale antenna that captures and rapidly channels protons directly to ATP synthase, ensuring the kinetic viability of eukaryotic energy production.