A Simple Hydraulic Analog Model of Oxidative Phosphorylation

Abstract

Mitochondrial oxidative phosphorylation is the primary source of cellular energy transduction in mammals. This energy conversion involves dozens of enzymatic reactions, energetic intermediates, and the dynamic interactions among them. With the goal of providing greater insight into the complex thermodynamics and kinetics ("thermokinetics") of mitochondrial energy transduction, a simple hydraulic analog model of oxidative phosphorylation is presented. In the hydraulic model, water tanks represent the forward and back "pressures" exerted by thermodynamic driving forces: the matrix redox potential (ΔGredox), the electrochemical potential for protons across the mitochondrial inner membrane (ΔGH), and the free energy of adenosine 5'-triphosphate (ATP) (ΔGATP). Net water flow proceeds from tanks with higher water pressure to tanks with lower pressure through "enzyme pipes" whose diameters represent the conductances (effective activities) of the proteins that catalyze the energy transfer. These enzyme pipes include the reactions of dehydrogenase enzymes, the electron transport chain (ETC), and the combined action of ATP synthase plus the ATP-adenosine 5'-diphosphate exchanger that spans the inner membrane. In addition, reactive oxygen species production is included in the model as a leak that is driven out of the ETC pipe by high pressure (high ΔGredox) and a proton leak dependent on the ΔGH for both its driving force and the conductance of the leak pathway. Model water pressures and flows are shown to simulate thermodynamic forces and metabolic fluxes that have been experimentally observed in mammalian skeletal muscle in response to acute exercise, chronic endurance training, and reduced substrate availability, as well as account for the thermokinetic behavior of mitochondria from fast- and slow-twitch skeletal muscle and the metabolic capacitance of the creatine kinase reaction.

Figure 1:. Simple Models of Oxidative Phosphorylation.

Modular (A) and hydraulic analog (B) models of oxidative phosphorylation showing the transduction of energy from oxidative fuels which are transported into the mitochondria and converted into matrix redox potential (ΔG_redox) by dehydrogenase enzymes (DH). ΔG_redox is then converted into a protonmotive force (Δp or ΔG_H+) by the electron transport chain (ETC). Δp is converted to ATP by Complex V (C V ) and transported out of the mitochondria by adenine nucleotide translocase (ANT) where it contributes to the free energy of ATP hydrolysis (ΔG_ATP) available to be used by cytosolic ATPases. Electron leak (O₂^.−) from the ETC and proton leak back across the inner mitochondrial membrane are also depicted. In the hydraulic model, the water level in each tank represents the availability of the respective free energy forms and the diameter of the pipes is proportional to the activity of the enzymes along that portion of the pathway. The height of the water in each tank exerts a pressure on both the upstream and downstream adjacent pipes. Water flow (or flux, J) between two tanks is thus proportional to the difference in water levels between each tank (ΔG₁ – ΔG₂) as well as the size of the pipe (conductance, L) between them.

Figure 2:. Mitochondrial Proton Leak Kinetics.

Non-phosphorylating proton flux back across the mitochondrial inner membrane in rat liver mitochondria increases exponentially with the proton motive force (ΔG_H+).

Figure 3:. Effects of Exercise and Training.

A) Mild exercise in the hydraulic model. A mild increase in cellular contractile activity slightly opens the ATPase valve and water flow through the ATPase pipe (ATP utilization) causes the ΔG_ATP tank water level to fall. In turn, water flow (fuel oxidation and ATP synthesis) from upstream tanks increases to match the demand (steady state ATP turnover). B) Simulating moderate exercise by a larger opening of the ATPase valve (more contractile activity) results in even greater water flow (ATP sythesis) and a further fall in the level of the water tanks (free energies). Note that with the lower levels of the water tanks, the leak reactions are reduced. C) Endurance training resulting in increased mitochondrial content in skeletal muscle is depicted as an increase in pipe diameters. Repeating the “moderate exercise” bout by opening the ATPase valve (same contractile activity) to the same level as in B now results in better maintenance of the water levels in the tanks (free energies). D) Experimental support for the hydraulic model predictions in C. Doubling mitochondrial content results in a greater free energy level (ΔG_ATP) at a given rate of oxygen consumption (J_O2) in isolated rat hindlimb skeletal muscle mitochondria.

Figure 4:. Effect of Reduced Fuel Availability.

Substrate depletion simulated by reducing the water level in the fuel tank results in lower water levels (free energies) in the downstream tanks and drives less water flow (lower ATP production). Compare with Figure 3C.

Figure 5:. Differences between Fast and Slow Twitch Muscle Mitochondria.

A) Mitochondria isolated from rabbit gracilis (Type II, glycolytic) muscle maintain a higher free energy level (ΔG_ATP) at a given oxygen consumption rate (J_O2) than soleus (Type I, oxidative) muscle mitochondria. Greater free energy availability (higher water levels) in the hydraulic model predicts increases in the leak reactions. Mitochondria isolated from rat white, glycolytic hindlimb muscle produce more superoxide (C) than mitochondria isolated from red, oxidative hindlimb muscle (B) under conditions simulating rest (oligomycin) and mild (−14.0) and moderate (−13.5) exercise. P+M: pyruvate (1 mM) and malate (1 mM), G3P: glycerol 3-phosphate (10 mM), G+M+A: glutamate (10 mM), malate (1 mM), and arsenite (10 mM).

Figure 6:. Capacitance of the Creatine Pool.

A) Addition of a high capacitance water tank with adjacent large diameter pipes to the hydraulic model representing the high concentrations of phosphocreatine (PCr) and creatine kinase (CK) and equilibrium with ΔG_ATP in skeletal muscle. B) Upon opening the ATPase valve, the transition to steady state is slowed due to the large amount of water in the PCr tank. C) The large PCr capacitance does not affect steady state height of the other water tanks. D) The Creatine Kinase Energy Clamp. In isolated mitochondria with no added ATPase, ΔG_ATP can be set and maintained at steady state by adding saturating CK, 5 mM ATP, and known ratios of PCr and creatine (Cr). In the presence of a constant fuel source, the resulting water flow (metabolic flux) is thus completely controlled by the diameters of the pipes (effective mitochondrial enzyme activities).