Computational modeling of mitochondrial K⁺- and H⁺-driven ATP synthesis

ATP synthase (F₁F_o) is a rotary molecular engine that harnesses energy from electrochemical-gradients across the inner mitochondrial membrane for ATP synthesis. Despite the accepted tenet that F₁F_o transports exclusively H⁺, our laboratory has demonstrated that, in addition to H⁺, F₁F_o ATP synthase transports a significant fraction of ΔΨ_m-driven charge as K⁺ to synthesize ATP. Herein, we utilize a computational modeling approach as a proof of principle of the feasibility of the core mechanism underlying the enhanced ATP synthesis, and to explore its bioenergetic consequences. A minimal model comprising the 'core' mechanism constituted by ATP synthase, driven by both proton (PMF) and potassium motive force (KMF), respiratory chain, adenine nucleotide translocator, Pi carrier, and K⁺/H⁺ exchanger (KHEmito) was able to simulate enhanced ATP synthesis and respiratory fluxes determined experimentally with isolated heart mitochondria. This capacity of F₁F_o ATP synthase confers mitochondria with a significant energetic advantage compared to K⁺ transport through a channel not linked to oxidative phosphorylation (OxPhos). The K⁺-cycling mechanism requires a KHE_mito that exchanges matrix K⁺ for intermembrane space H⁺, leaving PMF as the overall driving energy of OxPhos, in full agreement with the standard chemiosmotic mechanism. Experimental data of state 4➔3 energetic transitions, mimicking low to high energy demand, could be reproduced by an integrated computational model of mitochondrial function that incorporates the 'core' mechanism. Model simulations display similar behavior compared to the experimentally observed changes in ΔΨ_m, mitochondrial K⁺ uptake, matrix volume, respiration, and ATP synthesis during the energetic transitions at physiological pH and K⁺ concentration. The model also explores the role played by KHE_mito in modulating the energetic performance of mitochondria. The results obtained support the available experimental evidence on ATP synthesis driven by K⁺ and H⁺ transport through the F₁F_o ATP synthase.