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

Abstract

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.

Keywords: Energy supply-demand matching; F(1)F(o) ATP synthase; Mitochondrial K(+) uptake; Mitochondrial K(+)/H(+) exchanger.

Figure 1.. Current and proposed views of cation flux cycles in mitochondria

Model simulations performed with a minimal model comprising the respiratory chain (from constant levels of NADH, which is a model input), ATP synthase, ANT, Pi carrier and KHE_mito, comparatively tested two possible scenarios: (A) the current view of K⁺ cycling in mitochondria, involving a K_ATP channel unrelated to OxPhos (in orange) which dissipates the potential energy stored in the K⁺ gradient as heat (conventional model); (B) the proposed scheme of K⁺ cycling, in addition to H⁺, through ATP synthase, and KHE_mito mechanism, that harvests the ion motive force to drive ATP synthesis thus avoiding useless energy dissipation (updated minimal model). Extra-mitochondrial values of ions (K⁺ = 137 mM, pH= 7.0) and metabolites correspond to parameters (constant values in a simulation run, with the exception of ADP as detailed below). (C, D) ATP synthesis, respiratory flux obtained with the model in the corresponding column. (E,F) H⁺ and K⁺ uptake, the latter through either an independent K_ATP channel (E, conventional model) or the F₁F_o ATP synthase (F, updated minimal model). Both models were parameterized for K⁺ according to experimental data. The time course in panels C-F show the evolution of variables during the transition from state 4 (1 μM ADP) to state 3 (in the presence of constant ADP 50 μM) from the time indicated with an arrow.

Figure 2.. Simulations performed with the updated minimal model in the absence or presence of inhibition of ATP synthase or ANT

Mitochondrial inner membrane potential (ΔΨ_m panel A), ADP concentration (Panel C), and K⁺ accumulation (Panel B) according to the minimal model during the state 4→3 transition, triggered by addition of 50 μM ADP. Simulations of the minimal model run without (Control, black line) or with ATP synthase (magenta line) or ANT (green line) inhibition, mimicked by decreasing the concentration of ATP synthase units (RhoF1) from 0.5 to 1^.10⁻⁵ or the Vmax of ANT from 3.15 to 0.125, respectively (see also Appendix table A1). Model simulation conditions are detailed in the caption of Figure 1. Note that when ANT was inhibited, mitochondrial ADP levels are negligible and do not change upon ADP addition. Panel D shows the rates of K⁺ uptake via ATP synthase and the KHE_mito that drive the matrix K⁺ accumulation during the transition in the absence of inhibition.

Figure 3.. Scheme of the integrated mitochondrial model accounting for the “core” mechanism of K⁺ and H⁺ driven ATP synthesis

The scheme presented in Figure 1B was integrated into a bi-compartmental mitochondrial model encompassing energetics, redox, ion exchange, ROS production and scavenging (see Model description, for details). TCA, tricarboxylic acid; MCU, mitochondrial Ca²⁺ uniporter; ETC, electron transport chain.

Figure 4.. Simulations performed with the integrated mitochondrial model of K⁺, ΔΨ_m, and volume dynamics in response to increasing K⁺ concentrations

Simulation conditions represent state 4 mitochondria in the presence of 2 mM K⁺ to which pulses of increasing K⁺ concentration, enough to reach final concentrations of: 5, 10, 15 or 20 mM, were added. The key to the line colors of the model results are depicted in Panel C. Panels A, C, E and G show simulation results whereas panels B, D, F and H show the corresponding experimental data of the same variable from reference [21]. The slope of K⁺ accumulation (A) was represented as an inset next to panel E together with the evolution of ΔΨ_m. Panel E and its inset show that K⁺ accumulation precedes ΔΨ_m depolarization. Plotting the maximal value of the rate of K⁺ accumulation (solid square) or its average value across the mid-range (empty square) vs. K⁺ concentration (Panel G), renders a linear relationship similar to the experimental data (H).

Figure 5.. Driving forces and fluxes of ATP synthesis and ions (H⁺ and K⁺) transported by ATP synthase in the presence of 137mM or 2mM K⁺

The initial conditions employed for the simulations of the integrated mitochondrial model correspond to state 4 (1.10⁻³ mM cytoplasmic ADP) to which 0.5 μM ADP (State 3) was added at the time indicated by an arrow. Panel A displays ΔΨ_m following the addition of ADP. Panel B depicts the ATP synthesis calculated in the same simulations shown in A-D. In panel C the proton motive force (PMF) was calculated from ΔΨ_m and the temporal evolution of ΔpH with Eqs. C5 and D24 in Appendices C and D. The right y-axis in panel D corresponds to the K⁺ flux (solid line) and H⁺ flux (dashed line). The numbers next to the color lines in the legend represent the extramitochondrial K⁺ concentration time course during the simulation of state 4 to state 3 transition.

Figure 6.. Effect of the KHE_mito activity on ΔΨ_m, matrix volume, and OxPhos fluxes during the state 4 → 3 transition

Under similar parametric conditions to those utilized in Figure 5 in the presence of 137 mM extra-mitochondrial K⁺, model simulations were run at different values of KHE_mito activity (given as the parameter of KHE_mito protein concentration): 1.95 (black lines, used in the simulations represented in Figure 4 and 5), 1 (red lines) and 0.5 (blue lines). The Respiratory Control Ratio (inset next to panel D) represents the ratio of state 3 over state 4 respiratory flux obtained for each KHE_mito protein concentration as indicated in the x-axis.