Quantitative analysis of mitochondrial ATP synthesis

Abstract

We present a computational framework for analyzing and simulating mitochondrial ATP synthesis using basic thermodynamic and kinetic principles. The framework invokes detailed descriptions of the thermodynamic driving forces associated with the processes of the electron transport chain, mitochondrial ATP synthetase, and phosphate and adenine nucleotide transporters. Assembling models of these discrete processes into an integrated model of mitochondrial ATP synthesis, we illustrate how to analyze and simulate in vitro respirometry experiments and how models identified from in vitro experimental data effectively explain cardiac respiratory control in vivo. Computer codes for these analyses are embedded as Python scripts in a Jupyter Book to facilitate easy adoption and modification of the concepts developed here. This accessible framework may also prove useful in supporting educational applications. All source codes are available on at https://beards-lab.github.io/QAMAS_book/.

Keywords: Biochemical thermodynamics; Bioenergetics; Computational modeling; Metabolic pathways; Respiratory.

Figure 1:

Diagram of a mitochondrion with the cytosol, intermembrane space (IMS), and matrix indicated. *Inset from left to right:* Protein channels and complexes associated with oxidative phosphorylation in the cristae of the mitochondrion. Complex I (C1) catalyzes the oxidation of NADH²⁻ to NAD⁻ and reduction of ubiquinone (Q) to QH₂. Complex II (C2) catalyzes the oxidation of FADH₂ to FAD coupled to the reduction of Q. Complex III (C3) catalyzes the oxidation of QH₂ coupled to the reduction of cytochrome c (Cyt c). Complex IV (C4) catalyzes the oxidation of Cyt c coupled to the reduction of oxygen to water. These redox transfers drive pumping of H⁺ ions out of the matrix, establishing the proton motive force across the inner mitochondrial membrane (IMM) that drives ATP synthesis at complex V, or the F₀F₁-ATPase (F₀F₁). The adenine nucleotide translocase (ANT) exchanges matrix ATP for IMS ADP. The inorganic phosphate cotransporter (PiC) brings protons and Pi from the IMS to the matrix. Lastly, there is a passive H⁺ leak across the IMM.

Figure 2:

Steady state solution from Equation (13) for ΔΨ = 175 mV, pH_x = 7.4, and pH_c = 7.2.

Figure 3:

Simulation of concentration versus ΔΨ for Equation (13) for ΔΨ from 100 to 250 mV.

Figure 4:

Steady state solution from Equation (16) for the (a) matrix and (b) cytosol species with ΔΨ= 175 mV, pH_x = 7.4, and pH_c = 7.2.

Figure 5:

Steady state solution from Equation (18) for the (a) matrix and (b) cytosol species with ΔΨ = 175 mV, pH_x = 7.4, and pH_c = 7.2.

Figure 6:

Simulation of concentration versus ΔΨ for Equation (18) for the (a) matrix and (b) cytosol species with ΔΨ from 100 to 250 mV.

Figure 7:

Steady state solution from Equation (30) for the (a) matrix and (b) cytosol species with pH_x = 7.4 and pHc = 2.

Figure 8:

Simulation of respiratory control for (a) the oxygen consumption rate (OCR), (b) matrix NADH concentration ([NADH]_X), and (c) membrane potential (ΔΨ) using the conditions listed in Table 5.

Figure 9:

Comparison of oxygen consumption rate (OCR) simulations to data from [1].

Figure 10:

Simulation of respiratory control in vivo using the system in Equation (33) for (a) the creatine phosphate to ATP ratio ([CrP]_c/[ATP]_c) and (b) cytosolic Pi concentration ([Pi]_c).