Oxidative phosphorylation: regulation and role in cellular and tissue metabolism

Abstract

Oxidative phosphorylation provides most of the ATP that higher animals and plants use to support life and is responsible for setting and maintaining metabolic homeostasis. The pathway incorporates three consecutive near equilibrium steps for moving reducing equivalents between the intramitochondrial [NAD⁺]/[NADH] pool to molecular oxygen, with irreversible reduction of oxygen to bound peroxide at cytochrome c oxidase determining the net flux. Net flux (oxygen consumption rate) is determined by demand for ATP, with feedback by the energy state ([ATP]/[ADP][P_i]) regulating the pathway. This feedback affects the reversible steps equally and independently, resulting in the rate being coupled to ([ATP]/[ADP][P_i])³. With increasing energy state, oxygen consumption decreases rapidly until a threshold is reached, above which there is little further decrease. In most cells, [ATP] and [P_i] are much higher than [ADP] and change in [ADP] is primarily responsible for the change in energy state. As a result, the rate of ATP synthesis, plotted against [ADP], remains low until [ADP] reaches about 30 μm and then increases rapidly with further increase in [ADP]. The dependencies on energy state and [ADP] near the threshold can be fitted by the Hill equation with a Hill coefficients of about −2.6 and 4.2, respectively. The homeostatic set point for metabolism is determined by the threshold, which can be modulated by the $P_{{\mathrm{O}}_2}$ and intramitochondrial [NAD⁺]/[NADH]. The ability of oxidative phosphorylation to precisely set and maintain metabolic homeostasis is consistent with it being permissive of, and essential to, development of higher plants and animals.

Abbreviations

ArP

arginine phosphate

CAC

citric acid cycle

Cr

creatine

CrP

creatine phosphate

GK

glucokinase

HK

hexokinase

PFK

phosphofructokinase

PK

pyruvate kinase

TN

turnover number

Introduction

Life requires continuous input of energy from the environment. This energy is needed to carry out the chemical synthesis that maintains metabolism and physical structure of the cells as well as to transport the molecules and ions that establish and maintain the intracellular environment. All of these diverse processes have to be precisely regulated and yet operate at a sustainable energy cost. The energy that can be derived from the environment is limited and there is competition among organisms for that energy supply. Other factors being equal, being able to more rapidly and efficiently extract that energy and/or more efficiently use the extracted energy provides a competitive, and therefore evolutionary, advantage. The requirements for regulation and energy efficiency in metabolism often conflict: the rates of reactions far displaced from equilibrium (irreversible) can be precisely controlled but result in loss of large amounts of energy as heat whereas reactions near equilibrium are energy efficient but the rates cannot be used to directly regulate metabolic flux. Modulation of the rate of irreversible reactions is an effective way to regulate metabolism because any alteration in their rate changes flux through the pathway. Elimination of the back reaction has a price, however: the release of a large amount of energy (typically greater than −17 kJ mol⁻¹) as heat. Reactions near equilibrium, in contrast, have minimal energy loss and are therefore very efficient but the net flux is small relative to the forward reaction rate. This limits their regulatory role to the effect of their reactant concentrations on the irreversible reactions. Evolution has selected for: (1) irreversible reactions positioned at the beginning of each pathway in order optimize regulation of the metabolic flux; (2) irreversible reactions following branch points in the pathway in order to optimize distribution of the flux through the branches; (3) near equilibrium reactions within the pathway to minimize energy loss and where the presence of irreversible reactions would destabilize the regulatory system. Figure 1 shows this pattern very schematically using glycolysis as a model. In glycolysis, there are three irreversible steps, hexokinase (HK) or glucokinase (GK), responsible for committing glucose to further metabolism, phosphofructokinase (PFK), which regulates flux from fructose‐6‐phosphate to pyruvate, and pyruvate kinase (PK), which is the valve that determines whether phosphoenolpyruvate is used to make glucose or pyruvate. At each irreversible step there is a substantial energy loss, but the rest of the reactions are near equilibrium. The three irreversible steps determine the direction and rate of the flux while the near equilibrium reactions allow this to be achieved with a minimal energy cost. The result is an overall energy efficiency of about 50% as glucose is converted to lactate. The advantage to this design is greatest for metabolic pathways where there is a large flux, such as glycolysis and oxidative phosphorylation. In high flux pathways, inefficiency imposes a high energy ‘cost’ for the organism and poor regulation has a major negative impact on cellular metabolism and function.

Figure 1. A skeleton representation of glycolysis.

Each reaction in the pathway from glucose (Glu) to lactate is represented with an arrow indicating whether it is fully reversible and near equilibrium (↔) or irreversible (→). There are three irreversible steps responsible for regulating the pathway, hexokinase (HK) or glucokinase (GK), phosphofructokinase (PFK), and pyruvate kinase (PK). All of the other reactions are freely reversible (free energy change near zero) and operate either in the forward (glycolysis) or reverse (gluconeogenesis) direction as needed. Each of the irreversible reactions is accompanied by an energy loss (−free energy change) of more than 12.5 kJ mol¹ as heat. The irreversible steps determine the net forward flux through that part of the pathway and act as valves controlling the direction of the flux, i.e. PFK determines whether carbon from glucose is stored as glycogen or metabolized to pyruvate for oxidation by the citric acid cycle (CAC) or exported as lactate.

Understanding research on metabolism and the role of computational modelling

Metabolic pathways typically involve many different reactions and metabolites. As emphasized by Imre Lakatos (1970, 1978), in biology the collection and interpretation of experimental data involves large numbers of assumptions/hypotheses, many of which are not stated or are presented as facts. Core hypotheses, those which are considered most important, strongly influence the interpretation given to sets of experimental data. Perceived inconsistencies between data and the core hypothesis result in addition of auxiliary assumptions/hypotheses designed to remove the inconsistency and protect the core hypothesis. These auxiliary assumptions/hypotheses constitute the protective belt of a Lakatosian Research Programme. Challenges to the research programme are mostly directed toward the auxiliary assumptions/hypotheses in the protective belt, and the research programme fails when the protective belt becomes seriously eroded.

Relevance of the Lakatosian Research Programme to the study of metabolism is readily observed in the literature. Metabolic pathways involve a large number of variables and investigators are limited by not being able to measure all of the variables, limited accuracy of the measured values, variations among cell types and other sources of uncertainty, each of which requires additional hypotheses/assumptions. Many of these limitations can be overcome by building a computational model. Properly designed computational models involve: (1) listing all of the metabolites and metabolic transitions considered to be responsible for the regulating flux and; (2) writing equations that explicitly quantify the contributions of each to the whole. This process makes clear the hypotheses and assumptions made. In addition, it forces proposed interpretations of the data to recognize and account for all of the relevant parameters, including those not measured due to limitations in technology and/or experimental design. Computational models should be developed using Occam's razor because each variable more than the required minimum increases both the uncertainty for any given solution and the number of possible solutions when fitting the model to a data set. Occam's razor requires: (1) determining the minimum number of chemically and mechanistically sound equations required to quantify the behaviour; (2) identification of the minimum number of variables with important regulatory roles; and (3) confirmation that the resulting computational model predicts behaviour consistent with experimental observation. Once a minimal ‘core’ model has been developed and the values for the essential parameters determined, additional complexities can be ‘grafted’ onto the minimal model. Because the parameters of the minimal model have already been determined, only the ‘add on’ complexity needs to be quantified and evaluated and this can be readily done. Successful models are ones that predict relationships among the metabolites that are chemically reasonable, quantitative, and consistent with existing data. This consistency provides empirical support for the hypotheses/assumptions made in developing the model. It also provides justification for using the model to conduct virtual experiments prior to doing the actual experiments. Such virtual experiments predict outcomes, an invaluable resource for optimizing experimental design and interpreting the resulting data.

Oxidative phosphorylation: essential role in higher animals and plants

Mitochondria are believed to be the result of incorporation of a prokaryote with oxidative phosphorylation into another cell (a eukaryote?), during the Precambrian period (Margulis & Sagan, 1986; Gray, 2012; Keeling & Koonin, 2014; Poole & Gribaldo, 2014). Oxidative phosphorylation was present and integrated into cellular metabolism by the time of the ‘Cambrian explosion’ approximately 540 million years ago. Only organisms with oxidative phosphorylation went on to develop into ‘higher’ animals and plants: i.e. animals and plants having morphologically and metabolically distinct parts with specialized functions that are essential to the life of the organism. In higher animals, oxidative phosphorylation is the primary source of ATP for metabolic and mechanical work, providing most of the energy used in for biosynthesis, maintaining proper ion balance, and mechanical work. In higher plants, it provides energy when photosynthesis is not available, as during periods of darkness, as well as in tissues without photosynthesis (roots etc.). The presence of oxidative phosphorylation in all higher plants and animals implies that it is of great importance to their existence. Thus, understanding the role of oxidative phosphorylation in metabolism is necessary for understanding their metabolism. It further implies that oxidative phosphorylation was a prerequisite for evolutionary development of higher plants and animals on earth. Understanding the role of oxidative phosphorylation in metabolism will provide significant insight into the environmental and evolutionary conditions that give rise to higher life forms.

In order to assess the role of a metabolic pathway, such as oxidative phosphorylation, it is desirable to study tissues for which the flux changes over the widest possible range. As a result, although experimental data are available for multiple different tissues of animals (liver, heart, skeletal muscle, etc.) and plants, discussion of the regulation in vivo relies heavily on in vivo data from oxidative skeletal muscle during exercise. The transitions between resting and work in skeletal muscle gives rise to the widest range of rates of ATP utilization of any tissue, over 100‐fold (Wilson et al. 1981; Wilson & Vinogradov, 2014; Wilson, 2015a,b, 2016). In addition, skeletal muscle of vertebrates includes creatine kinase, an enzyme which catalyses a reaction in which ATP reacts with creatine (Cr) to form ADP and creatine phosphate (CrP): i.e. CrP + ADP = Cr + ATP. This reaction is near equilibrium (Lawson & Veech, 1978) and ³¹P NMR can be used to measure the concentrations of some of the important metabolites in energy metabolism (ATP, CrP and P_i) non‐invasively and in real time (Hogan et al. 1983, 1992; Kawano et al. 1988; McCully et al. 1989; McAllister & Terjung, 1991; Marsh et al. 1993; McCann et al. 1995; McCreary et al. 1996; Haseler et al. 1999; Chacko et al. 2000; Rossiter et al. 2002). There is also widespread interest in muscle physiology and biochemistry during exercise, particularly in humans. As a result there are many studies of energy metabolism in muscle, providing a rich data base on which to evaluate computational models (see also Holloszy, 1967; Hassinen & Hiltunen, 1975; Nishiki et al. 1978; Nuutinen et al. 1982; Constable et al. 1987; Poole et al. 2007; Rumsey & Wilson, 2011; Golub & Pittman, 2012; Wilson, 2013). There a number of published exercise protocols with measurements over large (20‐ to 60‐fold) rates of ATP utilization and with little or no evidence of fatigue or other complicating features. These are well suited for evaluation of the performance of computational models. Although consistency with the data from exercising skeletal muscle is essential to any proposed hypothesis about the regulation of oxidative phosphorylation, the properties of oxidative phosphorylation are general and such hypotheses should also apply to all other cells and tissues with fully functional oxidative phosphorylation (see Erecinska et al. 1978, 1979; Erecinska & Wilson, 1982; Wilson et al. 1981; Wilson, 2015, 2017).

Overview of oxidative phosphorylation and a computational model

A schematic diagram of oxidative phosphorylation is presented in Fig. 2. It is a nearly linear pathway with flow of reducing equivalents from the intramitochondrial NAD pool with an oxidation–reduction potential near −0.35 V to molecular oxygen with a potential near 0.815 V. There is some in/out flux at the level of the b cytochromes, but this is usually small relative to total flux through the pathway. The reducing equivalents from the NAD pool are transferred to oxygen in 4 steps. The first step is from the NAD pool to the cytochrome b–ubiquinone pool, the second from there to the cytochrome c–cytochrome a pool, and the third from there to the bound peroxide intermediate in cytochrome c oxidase. These 3 steps are coupled to ATP synthesis, with the reactions and coupling being fully reversible and near equilibrium. The fourth ‘step’ is the transfer of two of the 4 reducing equivalents to oxygen at cytochrome c oxidase to form the bound peroxide (Wilson et al. 1973, 1979, 1981, 2014; Wilson & Vinogradov, 2014, 2015; Wilson, 2017). This step is strongly exergonic and irreversible. The 3 steps that are coupled to ATP synthesis do so through a common intermediate, and this constrains all three steps to having the same voltage difference. When the energy state is less than that for equilibrium with this voltage difference, reducing equivalents can flow to oxygen, coupled to ATP synthesis, but if the energy state is raised above that required for equilibrium, the available reducing equivalents can flow from the oxidase to the NAD pool, coupled to ATP hydrolysis. Note that because the reactions are near equilibrium, the behaviour is determined by thermodynamics and is consistent with all coupling mechanisms as long as the reactions involved are near equilibrium. In addition, the observation of near equilibrium means that all of the partial reactions within the whole are near equilibrium, i.e. none of the internal reactions (ATP/ADP exchange, P_i transport, energy coupling reactions, etc.) is significantly displaced from equilibrium.

Figure 2. A schematic diagram of oxidative phosphorylation.

Most of the reducing equivalents used in oxidative phosphorylation come from intramitochondrial NADH, which is produced by the citric acid cycle, fatty acid oxidation, and amino acid metabolism. The intramitochondrial [NAD⁺]/[NADH] ratio is regulated and is typically maintained at a redox potential near −0.35 ± 0.03. All of the reactions within oxidative phosphorylation are near equilibrium except the reduction of molecular oxygen to the bound peroxide in cytochrome c oxidase. The redox components of the respiratory chain are organized in groups with half‐reduction potentials near −0.3 V, −0.00 V, 0.25 V, and 0.6 V, the most positive being the bound peroxide intermediate of the oxidase. Within each group of redox components the exchange rates sufficiently exceed the net flux through oxidative phosphorylation that they form an isopotential ‘pool’ of reducing equivalents. Feedback by the energy state is applied equally and independently to each step, resulting in 3 stage amplification of the signal.

In cells under physiological conditions, where the cytochrome c turnover is 5–10 s⁻¹, the energy state is near 4 × 10⁴ m ⁻¹ (a free energy of hydrolysis of ATP near −14.6 kcal mol⁻¹ or −61.1 kJ mol⁻¹). For resting conditions, the potential difference across each of the three steps of oxidative phosphorylation is near 0.32 V. As a result, approximately 0.96 V of the available 1.165 V is used to synthesize ATP. This is a high, about 80%, overall coupling efficiency. The about 20% loss is as heat released when oxygen is reduced to the bound peroxide intermediate of cytochrome c oxidase (step 4). This loss results in the reaction being irreversible and therefore responsible for regulation of the metabolic flux. Because there are three sequential steps in the respiratory chain and they are all near equilibrium, feedback of the energy state is applied equally and independently to all three steps. A decrease in energy state that would cause a 3‐fold increase in the flux through one step results in an increase of 3³ or 27 applied to all 3 steps. This amplification of the feedback response greatly decreases the amount that the energy state needs to decrease in order to evoke particular increase in ATP synthesis.

In the present review, our published model of oxidative phosphorylation (Wilson et al. 1979, 1981, 2012, 2014; Wilson & Vinogradov, 2014, 2015; Pannala et al. 2015; Wilson, 2017; Appendices A and B) will be used to illustrate the most distinctive features of the regulation of oxidative phosphorylation. This model, including the steady state rate equations and MatLab (www.mathworks.com) program can also be accessed at URL: http://www.med.upenn.edu/biocbiop/faculty/wilson/index.html. The predictions of the model have been shown to be consistent with the available experimental data for intact tissues (Erecinska et al. 1978, 1979; Wilson et al. 1979, 1981, 2006; Erecinska & Wilson, 1982; Wilson, 2013, 2015a,b, 2016, 2017; Wilson & Vinogradov, 2015), most notably the extensive data on exercising muscle (Wilson, 2015, 2016, 2017). The current review, therefore, focuses on understanding how the unique metabolic and regulatory properties of oxidative phosphorylation, as exemplified in the model, had a central role in the evolutionary development of higher animals and plants.

In vivo, the rate of oxidative phosphorylation (the rate of ATP synthesis) is determined by the rate of ATP utilization (demand). That means the rate of ATP synthesis is tightly coupled to the rate of utilization and provides a steady state in which there is little variation in [ATP]. In that context, the role of the independent variables is to determine the energy state at which [ATP] is maintained. The independent regulatory variables are $P_{{\mathrm{O}}_2}$, energy state ([ATP]/[ADP][P_i]), intramitochondrial [NAD⁺]/[NADH], cytochrome concentration, and pH. This review addresses only conditions for which pH is nearly constant.

Our model for oxidative phosphorylation (see Appendix A) is constrained as follows.

• (1)It is based on the mechanism of oxygen reduction by cytochrome c oxidase (Wilson et al. 1973, Wilson & Vinogradov, 2014, 2015). The steady state expression for the rate of reaction has been derived and the internal parameter values obtained by fit to data obtained from measurements of the cytochrome c oxidase activity of isolated mitochondria.
• (2)It contains the minimum number of parameters required for consistency with experimental measurements for oxygen reduction by cytochrome c oxidase. Importantly, the number of parameters in the model for which there are no model independent experimental measurements has also been minimized, i.e. Occam's razor has been applied throughout.
• (3)It does not contain any ad hoc parameters that can be varied in order to ‘fit’ the model to different sets of data. The parameter values obtained from isolated mitochondria are used for all different cell and tissue types with the exception of the metabolite and cytochrome concentrations, which are cell and tissue specific. The internal parameters in the model were obtained by fit to experimental data for oxidative phosphorylation as a whole, but with the values constrained to be consistent with available model independent measurements.
• (4)It is the model for cytochrome c oxidase extended to include the reactions from cytochrome c to the intramitochondrial NAD pool by taking advantage of the reactions being near equilibrium (Hassinen & Hiltunen, 1975; Erecinska et al. 1978, 1979; Nishiki et al. 1978; Wilson et al. 1979, 1981; Erecinska & Wilson, 1982; Forman & Wilson, 1982; Greenbaum & Wilson, 1991; Wilson, 2013, 2015a,b, 2016, 2017) and using known equilibrium constants (no additional fitting required).
• (5)It has been shown to predict behaviour of oxidative phosphorylation that is consistent with the measured energy state and respiratory rates in many tissues as well as with changes that occur during the work‐to‐rest (Wilson, 2016) and rest‐to‐work (Wilson, 2015a) transitions in oxidative skeletal muscle.

The model is for oxidative phosphorylation in intact cells and tissues rather than preparations of isolated mitochondria. Mitochondria are extensively damaged during isolation and this damage, combined with the use of non‐physiological assay conditions, yields data that can be very misleading if interpreted out of context. An example is the widespread focus on the rate of oxygen consumption under two conditions: the maximal rate of oxygen consumption (excess P_i, ADP, and oxidizable substrate), called State 3, and that after most of the ADP is converted to ATP (State 4) during which oxygen is being consumed but there is no net synthesis of ATP (see Chance & Williams, 1955). Neither ‘State 3’ nor ‘State 4’ are representative of behaviour of oxidative phosphorylation in vivo. The respiration not coupled to ATP synthesis, State 4, that is induced during isolation is most problematic. It has given rise to many specious hypotheses including that oxidative phosphorylation in vivo is inherently ‘leaky’ as well as severely limiting the range of respiratory rates experimentally studied (see, however, Wilson et al. 1973). Despite the damage during isolation, isolated mitochondria are very useful for studying of the partial reactions of oxidative phosphorylation and these are important to understanding how the pathway functions both in vivo and in vitro. The model used in this review was developed in large part through study of isolated mitochondria and is consistent with the behaviour of isolated mitochondria, but only when the damage during isolation is appropriately taken into account. Importantly, the behaviour predicted by the model is consistent with that observed for oxidative phosphorylation in vivo for both animals and plants.

Integration of oxidative phosphorylation into the rest of metabolism

When considering how oxidative phosphorylation and the rest of metabolism work together, it is necessary to keep in mind that all of the cells and tissues of higher plants and animals share many of the mechanisms used to regulate energy metabolism in general. This includes real time regulation of metabolic pathways, such as glycolysis, the citric acid cycle, and purine synthesis, as well as regulation of the genes that code for many enzymes. Metabolic charts typically show hundreds of reactions for which the energy state, as expressed through the concentrations of ATP, ADP, P_i or AMP, is an important modulator. These common mechanisms have similar dependences on [ADP] and [AMP] in all cells that have oxidative phosphorylation and in many cells without oxidative phosphorylation. As a result, metabolism in different cell types is constrained to maintain similar levels of [ADP] and [AMP] even when there are large differences in their rates of ATP synthesis/utilization. The concentration of ATP in cells is a few millimolar and this is quite constant as long as the conditions are physiologically viable, meaning conditions that are within the ‘normal’ range and not pathological. For many cells, [ATP] and [P_i] are much higher than [ADP] so most of the change in energy state is through change in [ADP]. Other things being equal, this would mean that large differences in the rates of ATP utilization among cell types (such as oxidative muscle vs. liver) would also mean large differences in [ADP]. Maintaining similar [AMP], however, is even more restrictive because most cells have high adenylate kinase activity and the reaction: ATP + AMP = 2 ADP is near equilibrium. As a result, [AMP] changes as [ADP]² and cells with different ranges of ATP utilization would be expected to have very different ranges in [AMP]. Without metabolic compensation, the large differences in [ADP] and [AMP] would make it impossible for cells to share extensive regulatory mechanisms having similar dependencies on [ADP] and [AMP]. The cells do share these mechanisms, however, so during evolution mechanism(s) have developed for minimizing the differences in [ADP] and [AMP].

When the intramitochondrial [NAD⁺]/[NADH], [ATP], and [P_i] are constant at 0.1, 6 mm, and 3 mm, respectively, the turnover number (TN) of cytochrome c (rate of ATP synthesis) increases with increase in [ADP] as shown in Fig. 3 A. The turnover number remains very low until a threshold near 30 μm is reached, above which the rate increases rapidly with increase in [ADP]. For turnover numbers below about 10 s⁻¹, as would be observed in hepatocytes, the curve is sigmoidal and can be readily fitted to the Hill equation (Fig. 3 B). This results in an apparent Hill number (n) of 4, larger than that for O₂ binding to haemoglobin. This behaviour results in a metabolic ‘set point’ just above the elbow in the curve. Cells typically operate with ‘time average’ cytochrome c turnover numbers of about 5 s⁻¹. This is just above the elbow and the [ADP] is 30–40 μm and the energy state near 3–4 × 10⁴ m ⁻¹. When cells are faced with a metabolic challenge that increases ATP consumption, this results in an increase in [ADP]. This increase in [ADP], and decrease in energy state, is much smaller than would be expected for most regulatory schema because the rate of ATP synthesis increases as [ADP]⁴.

Figure 3. The dependence of the net flux through oxidative phosphorylation on [ADP] when [NAD⁺]/[NADH] and [O₂] are constant, as predicted by the model.

A, as [ADP] increases the net flux, expressed as the turnover number (TN) of cytochrome c, remains very low until the [ADP] is 30–40 μm and then the rate begins to increase very rapidly with further increase in [ADP]. This pattern is typical of functions (y‐axis) which have an exponential dependence on a parameter (x‐axis). In biology this is most commonly discussed in the binding of oxygen to haemoglobin (Hill equation) and other cooperative reactions while in electronics it often discussed in relation to control circuits (Zener diodes, for example). B, the threshold region of the curve and its fit to the Hill equation. There is clearly an excellent fit of the date (χ² = 0.006) when the fitting parameters are V _m = 16.5, k = 79, and the Hill coefficient (n) = 4. This indicates for these conditions the net flux increases as the fourth power of the ADP concentration ([ADP]⁴). It must be noted that although for these conditions the behaviour gives a good fit to the Hill equation, and the flux is changing as [ADP]⁴, the underlying mechanism is different from cooperative binding as observed in oxygen binding to haemoglobin.

The intramitochondrial NAD couple ([NAD⁺]/[NADH]) and modulation of energy metabolism

Intramitochondrial [NAD⁺]/[NADH] is the source of most of the reducing equivalents used for oxidative phosphorylation and sets the source redox potential. The half‐reduction potential used for the NAD couple is −0.320 V at pH 7.0, but the intramitochondrial pH is believed to be approximately 7.4 (Forman & Wilson, 1982; Greenbaum & Wilson, 1991). The in vivo measurements of the intramitochondrial [NAD⁺]/[NADH] are based on tissue metabolite assays. Assuming an intramitochondrial pH of 7.4, and equilibrium of the glutamate dehydrogenase (Graham & Saltin, 1989), these indicate a potential near −0.35 V in both skeletal and cardiac muscle while assuming equilibrium of β‐hydroxybutyrate dehydrogenase in liver gives a value nearer −0.31 V. The model does not directly include this difference in pH, and an [NAD⁺]/[NADH] of 0.1 is equivalent to a potential of −0.35 V. Figure 4 A shows the predicted effect of changing [NAD⁺]/[NADH] on the relationship between the turnover number of cytochrome c and when [O₂] is 60 μm O₂. The relationship is presented for three different values of the intramitochondrial [NAD⁺]/[NADH], 0.3, 0.1 and 0.03, equivalent to redox potentials of −0.334, −0.350 and −0.364 V, respectively. The effect of increasing reduction of the intramitochondrial NAD pool is to shift the energy state to higher values and the [ADP] (Fig. 4 B) to lower values for each value of cytochrome c turnover. A 10‐fold decrease in [NAD⁺]/[NADH] increases the energy state and decreases [ADP] by a factor of 10^1/3 (a factor of 2.1). Thus, modulating the intramitochondrial [NAD⁺]/[NADH] is an effective method for ‘fine tuning’ the metabolic energy state and the homeostatic set point since this can be done through change in the metabolite being oxidized (fat vs. sugar), intracellular [Ca²⁺], dehydrogenase content, etc.

Figure 4. The dependence of the net flux on energy state (A) and [ADP] (B) at constant [O₂] but different [NAD⁺]/[NADH] levels.

A, the net flux, expressed as the turnover number (TN) for cytochrome c, is plotted against the energy state. The [ATP] and [ADP] are constant at 6 mm and 3 mm, respectively, while the predicted behaviour is was calculated for [NAD⁺]/[NADH] values of 0.3, 0.1, and 0.03. At each [NAD⁺]/[NADH] value, as the energy state increases the rate of ATP synthesis (net flux) initially falls rapidly but then slows progressively and asymptotically approaches zero at high energy states. Decrease in the [NAD⁺]/[NADH] (increased reduction of the NAD couple and more negative redox potential) shifts the curves to higher energy states by a factor of 2.1 for each 10‐fold decrease in the [NAD⁺]/[NADH]. B, the cytochrome c turnover (net flux) is plotted against [ADP] for cells that do not have significant content of creatine phosphate or arginine phosphate. In these cells the [ATP] and [P_i] are a few millimolar whereas the [ADP] is tens of micromolar , and most of the change in energy state is through change in [ADP]. As seen also in Fig. 3 A and B, the turnover number for cytochrome c remains very low until a threshold value near 30 μm is reached, after which the flux increases very rapidly with further increase in [ADP]. Decrease in [NAD⁺]/[NADH] (reduction of the NAD pool) lowers the threshold [ADP] and increases the steepness of the rise in cytochrome c turnover number with increase in [ADP] above threshold.

The role of arginine kinase and creatine kinase in enhancing the performance of oxidative phosphorylation

Evolution operates, in large part, through competition of species for available resources, with ‘fitness’ determining which survive and which go extinct. Whether predator or prey, there is a significant advantage to being able to move faster and to sustain that speed for a longer period of time. As a result, evolution selected for cells, particularly muscle cells, that allowed the organism to attain higher work rates (use more ATP per second) and to sustain these rates for longer periods of time. As noted above, however, this increase in ATP utilization and production by oxidative phosphorylation had to occur with minimal change in [ADP] and [AMP]. Appropriately enhanced performance was achieved in two stages, the first of which was to include arginine kinase: ArP (arginine phosphate) + ADP = arginine + ATP. This reaction is present in most invertebrates, insects and crustaceans (Scholl & Eppenberger, 1972; Newsholme et al. 1978; Buth et al. 1985; Ratto et al. 1989). The equilibrium constant is 33 (Teague & Dobson, 1999) and [ArP] can be present at concentrations of many millimolar. The arginine kinase reaction provides significant buffering of the [ATP]/[ADP] and, more importantly, as the energy state decreases the hydrolysis of ArP releases a stoichiometric amount of P_i. As shown in Fig. 5, the increase in [P_i] contributes to the change in energy state, and decreases the amount that [ADP] and [AMP] need to increase for a given decrease in energy state (increase in the rate of ATP utilization and synthesis). As noted above, however, for oxidative phosphorylation in resting muscle the energy state is near 5 x 10⁴ m ⁻¹ where the [ATP]/[ADP] near 150. As a result, significantly better performance was achieved by replacing arginine kinase with creatine kinase. The creatine kinase reaction has an equilibrium constant near 150 (Lawson & Veech, 1978), and when [CrP]/[Cr] is 1.0 the [ATP]/[ADP] is 150. Figure 4 compares the dependence of rate of oxidative phosphorylation on [ADP] without arginine or creatine kinase (no Crt or Art), with arginine kinase and 40 mm for total arginine (Art = 40), and with creatine kinase and 40 mm total creatine (Crt = 40). A dramatic increase in the rate of ATP synthesis is observed for each [ADP] when either arginine or creatine kinases is added. This increase is significantly greater for creatine kinase than for arginine kinase. This difference is large enough that it is probably the evolutionary basis for vertebrates (reptiles, amphibians, fish and mammals (Scholl & Eppenberger, 1972; Buth et al. 1985), having creatine kinase instead of arginine kinase. Higher plants, unlike higher animals, do not have large ranges in their rates of ATP consumption and therefore have little need to buffer their [ATP]/[ADP] or to suppress the changes in [ADP] and [AMP] by increasing [P_i].

Figure 5. The effect of inclusion of arginine kinase or creatine kinase on the regulation of oxidative phosphorylation when [O₂] and [NAD⁺]/[NADH] are held constant.

The cytochrome c turnover number (TN) is plotted against [ADP] for cells without either arginine or creatine kinase (no Art or Crt), with arginine kinase and 40 mm total arginine concentration (Art = 40 mm) or with creatine kinase and 40 mm total creatine (Crt = 40 mm). In all cases the [O₂] was held constant at 60 μm and the [NAD⁺]/[NADH] constant at 0.1. Both the arginine and creatine systems result in a dramatic increase in the flux attained for each [ADP] but have little effect on the threshold. The latter is because the [P_i] near the threshold (resting conditions) is very similar for most cells. The contributions of ArP or CrP hydrolysis to [P_i] provides a more effective response (higher rates at similar [ADP]) to metabolic challenges such as increased work rate. Note that if the cytochrome c turnover were plotted against energy state there would be no effect of adding these enzymes since their contribution is entirely due to the change in [P_i] that accompanies the hydrolysis of ArP or CrP.

Arginine and creatine kinases are also present in white muscle where the contribution of oxidative phosphorylation to energy metabolism is small. At first glance this would seem to be inconsistent, with the primary role in oxidative cells being to provide P_i and enhance oxidative phosphorylation. This is not the case, however, because white muscle is also subject to large changes in the rate of ATP utilization, although for shorter periods of time, and is also constrained to meet these challenges without large changes in [ADP] and [AMP]. In this case, [P_i] is a potent activator of glycogen phosphorylase (Chasiotis et al. 1982). Here, as in oxidative muscle, an important role of creatine or arginine phosphate is to provide increased [P_i] in response to increased ATP consumption. The increase in [P_i] activates ATP production, making possible large changes in the rate of ATP synthesis with minimal changes in [ADP] and [AMP].

Regulation of vertebrate physiology and metabolism by oxidative phosphorylation

Oxidative phosphorylation requires large amounts of oxidizable substrate and molecular oxygen. As the size and complexity of vertebrate animals increased, the system for delivery of nutrients, particularly molecular oxygen, to the tissues became more sophisticated. Lungs, heart and blood vessels were developed that worked together to form a highly coordinated and responsive nutrient delivery (and waste removal) system. This delivery system is able to supply oxygen and remove waste products (notably CO₂) at rates accurately matched to the metabolic requirements of individual tissues. To function properly, this cardio‐pulmonary‐vascular (CPV) system needs sufficient capacity to meet maximal demand. At maximal rate, however, the energy cost is high and this high rate is not needed most of the time. Sensors in each tissue provide signals that are used to regulate the CPV system, adjusting breathing, heart rate, etc. so that energy consumption is limited to that required to meet demand. The need for reliability and tissue specificity has led to substantial regulatory redundancy, with many different sensors and signalling pathways contributing to overall regulation. Oxidative phosphorylation, however, is both essential to survival and has the greatest metabolite delivery requirement, and is necessarily of central importance to regulation of the CPV system. It is not surprising that there are many signalling systems linked to oxidative phosphorylation. Metabolically important independent variables involved in regulating oxidative phosphorylation include [O₂], intramitochondrial [NAD⁺]/[NADH], and the rate of ATP utilization, with the energy state as the dependent variable. If two of the independent variables are held constant, the energy state becomes a specific sensor for the third. If, for example, intramitochondrial [NAD⁺]/[NADH] and ATP utilization are constant, the energy state is a sensitive function of [O₂] (Fig. 6). When [NAD⁺]/[NADH] and cytochrome c turnover are held constant at 0.1 and 6 s⁻¹, respectively, as [O₂] decreases [ADP] and [AMP], increase. The increases, particularly in [AMP], are large enough to provide an accurate measure of tissue oxygenation throughout the physiological range of oxygen concentrations. The most widely recognized messaging system that responds to the energy state is the AMP dependent protein kinase (AMPK). AMPK has been called the master regulator of energy metabolism (Wyatt et al. 2007; Evans et al. 2012; Hardie et al. 2012; Mihaylova & Shaw, 2012) and when tissues are exposed to conditions for which [ADP] and [AMP] are chronically increased, and AMPK induces increased content of mitochondria as well as increased or decreased content of other enzymes (Towler & Hardie, 2007; Hardie et al. 2012). AMPK is a general energy metabolism regulator, and similar, although smaller, changes have been observed in muscles exposed to chronic mild ischaemia (for review, see Rumsey & Wilson, 2011). There are many other functional responses coupled to oxidative phosphorylation. Perfusate flow in isolated perfused rat hearts has, for example, been shown to be closely correlated with tissue energy state (Nuutinen et al. 1982) although the mechanism by which the energy state modulates vascular resistance remains uncertain.

Figure 6. The dependence of oxidative phosphorylation on [O₂] in the microenvironment.

The predicted behaviour of the energy state has been calculated for a constant reduction of the NAD couple ([NAD⁺]/[NADH] = 0.1) and constant cytochrome c turnover number (TN; 6 s⁻¹) while [O₂] was decreased from 80 μm to zero. The resulting changes in energy state, [ADP] and [AMP] are plotted as a function of [O₂]. All three parameters increase continuously as the [O₂] decreases, with the largest increase occurring in [AMP]. Under physiological conditions the mean intracellular oxygen concentrations are typically 50–60 μm (13, 60) and if this decreases to 10 μm, the tissue is seriously hypoxic.

One of the sensory functions definitively linked to oxidative phosphorylation is regulation of the afferent neural activity of the carotid body (Wilson et al. 1994). The carotid body is located at the bifurcation of the carotid artery and its blood supply is drawn directly from the carotid artery. As such it is ideally positioned for detecting the oxygen content of the arterial blood that supplies the brain. When the blood is well oxygenated, afferent activity on the carotid sinus nerve, a branch of the glossopharyngeal nerve, is low but the activity increases continuously with decrease in oxygenation of the arterial blood. This afferent nerve activity travels to both the brain and the diaphragm, helping to regulate breathing and cardiac output in order to maintain the $P_{{\mathrm{O}}_2}$ in the carotid artery. Strong inferential evidence for the role of oxidative phosphorylation includes the observation that inhibitors of cytochrome c oxidase (hydrogen sulfide, carbon monoxide, cyanide, and azide) and uncouplers of oxidative phosphorylation can induce increase afferent activity (see Ortega‐Saenz et al. 2003; Li et al. 2010; Peers et al. 2010). Definitive evidence that oxidative phosphorylation, more precisely the activity of cytochrome a₃, is the $P_{{\mathrm{O}}_2}$ sensor responsible for the oxygen dependent modulation of the afferent neural activity was obtained using isolated perfused/superfused carotid bodies. The activity in the afferent nerve has a response to decrease in $P_{{\mathrm{O}}_2}$ very similar to that in vivo, with the advantage that oxygen delivery is no longer dependent on the blood, which contains haemoglobin. As measured by the afferent neural activity, carbon monoxide added to the perfusion/superfusion medium is competitive with oxygen, i.e. increasing P _CO increases the afferent activity as if the $P_{{\mathrm{O}}_2}$ had decreased, and increasing $P_{{\mathrm{O}}_2}$ reverses the effect of adding a particular P _CO. Adding a P _CO of 560 Torr to perfusate equilibrated with a $P_{{\mathrm{O}}_2}$ of 130 Torr leads to an afferent neural activity equivalent to a $P_{{\mathrm{O}}_2}$ of approximately 3 Torr (Warburg & Negelein, 1928; Wilson et al. 1994; Wilson, 2004). The effect of added P _CO can be fully and reversibly removed by strong white light. This distinctive feature of the effect of CO is characteristic of a class of haem oxygenases in which the haem forms an inhibitory reduced haem–CO complex. If the reduced haem–CO complex absorbs a photon of visible light, the energy from the photon can be transferred to, and break, the bond to CO. The fraction of the haem oxygenase that remains inhibited at a particular P _CO and $P_{{\mathrm{O}}_2}$, and therefore the activity of the oxygenase, depends on the brightness and the wavelength of the light. The wavelength dependence of the light induced change, measured at the same quantum flux for each different wavelength, is called the photochemical action spectrum and is a direct measure of the absorption spectrum of the haem–CO complex. The action spectrum for the carotid body, measured by the afferent neural activity, is the same as the absorption spectrum of the reduced cytochrome a₃–CO complex (Warburg & Negelein, 1928; Wilson et al. 1994; Castor & Chance, 1955; Wilson, 2004). This identifies cytochrome a₃ as the oxygen sensor responsible for the oxygen concentration dependence of the afferent neural activity of the carotid body.

In summary, oxidative phosphorylation not only provides most of the ATP used by higher animals and plants to support life but is also responsible for setting and maintaining metabolic homeostasis. In vivo, the rate of ATP synthesis is matched to the rate of ATP utilization through feedback regulation by the energy state. Feedback from the energy state effects the three coupling sites equally and independently, resulting in three stage amplification of the signal. As a result of this amplification the rate of ATP synthesis increases little with decrease in energy state until a threshold is reached, below which the rate increases rapidly with further decrease in energy state. In most cells, the [ATP] and [P_i] are much higher than [ADP] and changes in energy state are due to the change in [ADP]. When the rate of ATP synthesis is plotted against [ADP], the rate remains low as [ADP] increases until a threshold is reached at about 30 μm and then increases rapidly with further increase in [ADP]. The dependencies on energy state and [ADP] can be fitted by the Hill equation with Hill coefficients (n values) of about −2.6 and 4.2, respectively. The homeostatic set point for metabolism is just above the threshold, which is approximately 4 × 10⁴ m ⁻¹, a value which can be ‘fine tuned’ by increasing or decreasing intramitochondrial [NAD⁺]/[NADH]. Enhanced performance of oxidative phosphorylation was obtained by incorporating arginine kinase or creatine kinase and their substrates. These reactions increase the contribution of [P_i] to the energy state through hydrolysis of ArP or CrP. The increase in [P_i] both decreases the amount that [ADP] and [AMP] increase for a given increase in the rate of ATP synthesis and increases the maximal rate of ATP synthesis that can be achieved. Oxidative phosphorylation, through its highly efficient production of ATP and unique regulatory design, is able to set and maintain metabolic homeostasis over wide ranges ATP utilization. This is consistent with oxidative phosphorylation being permissive of, and essential to, development of higher plants and animals.

Additional information

Competing interests

None declared.

Biography

David F. Wilson received a BS in Chemistry from Colorado State University, a PhD in Biochemistry from Oregon State University, and is currently Professor of Biochemistry and Biophysics at the University of Pennsylvania. His research interests are in metabolism and metabolic regulation, particularly oxidative phosphorylation and energy metabolism in general. Life requires continuous input of energy so the efficiency and rate at which energy is produced and used to support life processes has strongly affected the course of evolution. Understanding metabolism and how metabolic pathways are regulated, integrated, and homeostasis established is a fascinating quest.

Appendix A.

Steady state rate expression for oxygen reduction by cytochrome c oxidase in vivo

Assumptions

1. Only the reaction for reduction of the bound oxygen to bound peroxide (either III and IV) is irreversible.

2. The overall reaction is in a steady state, i.e. the concentrations of the intermediates are not changing.

   $$\begin{array}{ccc}\hfill -\frac{\mathrm{d}I}{\mathrm{d}t}& =& k1\times \mathrm{cr}\times \mathrm{I}-k1r\times \mathrm{co}\times \mathrm{II}+k4\mathrm{a}\times \mathrm{cr}\times \mathrm{III}\hfill \\ & & -k4\mathrm{b}\times \mathrm{cr}\times \mathrm{IV}\hfill \end{array}$$ (1)

   $$\begin{array}{ccc}\hfill -\frac{\mathrm{d}II}{\mathrm{d}t}& =& k2\times \mathrm{O}\times \mathrm{II}-k2r\times \mathrm{III}-k1\times \mathrm{cr}\times \mathrm{I}\hfill \\ & & +k1r\times \mathrm{co}\times \mathrm{II}\hfill \end{array}$$ (2)

   $$\begin{array}{ccc}\hfill -\frac{\mathrm{d}III}{\mathrm{d}t}& =& k2r\times \mathrm{III}-k2\times \mathrm{O}\times \mathrm{II}-(k4a\times \mathrm{cr}\times \mathrm{III}\hfill \\ & & +k4b\times \mathrm{cr}\times \mathrm{IV})\hfill \end{array}$$ (3)

   $$\begin{array}{ccc}\hfill -\mathrm{d}V/\mathrm{d}t& =& k1\times \mathrm{cr}\times \mathrm{I}-k1\mathrm{r}\times \mathrm{co}\times \mathrm{II}\hfill \\ & & -k4\mathrm{a}\times \mathrm{cr}\times \mathrm{III}-k4\mathrm{b}\times \mathrm{cr}\times \mathrm{IV}\hfill \end{array}$$ (4)

   $$K3=\frac{\mathrm{IV}}{\mathrm{III}\times \mathrm{H}}$$ (5)

   $$\mathrm{IV}=K3\times \mathrm{H}\times \mathrm{III}$$ (6)

   $$K5=\left\{\frac{\mathrm{I}\times Q}{V\times {\mathrm{H}}^2}\right\}\times {\left(\frac{\mathrm{co}}{\mathrm{cr}}\right)}^2$$ (7)

Figure A1. A schematic diagram of the kinetically important reactions involved in the reduction of oxygen by cytochrome c oxidase.

The individual reaction intermediates are designated by the Roman Numbers I through V and these numerals are used for setting up the differential equations describing the rates of formation and removal of these intermediates. The steady state rate expression is then derived assuming the rates are equal and there is no change in the concentrations of the intermediates. Only the reactions of oxidative phosphorylation from cytochrome c to oxygen are presented. All of the electron transfer reactions are assumed to occur across the same difference in redox potential (energy coupled) for which ΔG = −46.183 kcal V⁻¹ (193.23 kJ V⁻¹).

From eqn (2):

$$\begin{array}{ccc}\hfill k2\times \mathrm{O}\times \mathrm{II}& =& k2\mathrm{r}\times \mathrm{III}+k4\mathrm{a}\times \mathrm{cr}\times \mathrm{III}\hfill \\ & & +k4\mathrm{b}\times \mathrm{cr}\times \mathrm{IV}\hfill \end{array}$$ (8)

$$\begin{array}{ccc}\hfill \mathrm{II}& =& \{(k2\mathrm{r}+k4\mathrm{a}\times \mathrm{cr}+k4\mathrm{b}\times \mathrm{cr}\times K3\times \mathrm{H})/\hfill \\ & & k2\times \mathrm{O}\}\times \mathrm{III}\mathrm{II}=\mathrm{A}\times \mathrm{III}\hfill \end{array}$$ (9)

From eqn (1):

$$\begin{array}{ccc}\hfill k1\times \mathrm{cr}\times \mathrm{I}& =& k2\times \mathrm{O}\times \mathrm{A}\times \mathrm{III}-k2\mathrm{r}\times \mathrm{III}\hfill \\ & & +k1\mathrm{r}\times \mathrm{co}\times \mathrm{A}\times \mathrm{III}\hfill \end{array}$$ (10)

$$\begin{array}{ccc}\hfill \mathrm{I}& =& \{(k2\times \mathrm{O}\times \mathrm{A}-k2\mathrm{r}+k1\mathrm{r}\times \mathrm{co}\times \mathrm{A})/\hfill \\ & & k1\times \mathrm{cr}\}\times \mathrm{III}\mathrm{I}=\mathrm{B}\times \mathrm{III}\hfill \end{array}$$ (11)

$$\mathrm{V}=\left\{\frac{Q}{{\mathrm{H}}^2}\right\}\times {\left(\frac{\mathrm{co}}{\mathrm{cr}}\right)}^2\times \mathrm{B}\times \mathrm{III}\mathrm{V}=\mathrm{C}\times \mathrm{III}$$ (12)

$$\mathrm{V}=\left\{\frac{\mathrm{B}\times Q}{K5\times {\mathrm{H}}^2}\right\}\times {\left(\frac{\mathrm{co}}{\mathrm{cr}}\right)}^2\times \mathrm{II}$$ (13)

The total cytochrome a₃ is the sum of the individual intermediates, i.e.:

$$\mathrm{a}3\mathrm{t}=\mathrm{I}+\mathrm{II}+\mathrm{III}+\mathrm{IV}+\mathrm{V}$$ (14)

or

$$\mathrm{a}3\mathrm{t}=\left(1+A+\mathrm{B}+\mathrm{C}+K3\times \mathrm{H}\right)\times \mathrm{III}$$ (15)

The rate of oxygen consumption is determined by the irreversible step (reduction of III and IV)

$$\begin{array}{c}\hfill v=(k4a\times \mathrm{cr}+k4b\times \mathrm{cr}\times K3\times \mathrm{H})\times \frac{4}{\mathrm{ct}}\\ \hfill (\mathrm{cytochrome}\mathrm{c}\mathrm{turnover}\mathrm{number})\end{array}$$ (16)

Since the oxidative phosphorylation is a particulate enzyme system, all simulations are carried out for a single cytochrome concentration (cytochrome a, 1 μm; cytochrome c, 2 μm). For other cytochrome concentrations the obtained rates are linearly extrapolated to the new cytochrome concentrations (mitochondrial content). The energy coupling is mathematically expressed as the equivalent redox voltage difference Q. This acts as an effective resistance to electron transfer and the forward rate constant decreases and the back rate constant increases with increasing energy state by Q/0.0595 (1 electron transfer) or Q/0.0296 (2 electron transfer). The rate constants put into the model are those for no energy coupling, so energy coupling is included for k1, k1r, and for the equilibrium constant K5. It is not applied to k4a and k4b. These reactions are irreversible and there is no significant back reaction under any relevant conditions.

Abbreviations

cr, concentrations of reduced cytochrome c; H, hydrogen ion; O, oxygen; co, oxidized cytochrome c; a3t, total cytochrome a3; k1, k2, k3, k4a, k4b, forward reaction rate constants; k1r, k2r, reverse rate constants; K3 and K5, equilibrium constants; Q, energy state in volts, can be converted to energy units by multiplying by 46.18 for kcal V⁻¹ or 103.23 for kJ V⁻¹.

Published in Wilson & Vinogradov (2014) as modified by Wilson & Vinogradov (2015).

Addition of the first two sites of oxidative phosphorylation

Addition of the first two sites of oxidative phosphorylation to the cytochrome c oxidase in order to obtain a steady state rate expression for all of oxidative phosphorylation (NADH to oxygen);

The first two sites are near equilibrium so they can be approximated by the expression for the reaction:

$$\begin{array}{ccc}\hfill \mathrm{NADH}& & +2{\mathrm{c}}^{3+}+2\mathrm{ADP}+2{\mathrm{P}}_i\leftarrow \text{-}\text{-}\text{-}\text{-}\text{-}\to \mathrm{NA}{\mathrm{D}}^{+}\hfill \\ & & +2{\mathrm{c}}^{3+}+2\mathrm{ATP}\hfill \end{array}$$

for use in the model the energy state is replaced by the thermodynamically equivalent redox potential difference:

$$\mathit{Ke}=[\mathrm{NA}{\mathrm{D}}^{+}]{[{\mathrm{c}}^{2+}]}^2[{\mathrm{H}}^{+}]/[\mathrm{NADH}]{[{\mathrm{c}}^{3+}]}^2$$

The equilibrium constant calculated from the half‐reduction potentials for the NAD and cytochrome c couples (−0.32 V and 0.235 V, respectively) at pH 7.0 is 6.4 × 10¹¹  m. This equilibrium expression is used to approximate the concentrations (near equilibrium) of the reduced and oxidized forms of cytochrome c for any value of intramitochondrial [NAD⁺]/[NADH] and Q. The intramitochondrial pH is higher than that in the cytosol by 0.3 to 0.5 pH units but it is the potential which is used in the calculations and this does not affect the calculations. It does affect the [NAD⁺]/[NADH] calculated from the potential. A redox potential of −0.35V, for example, would be an [NAD⁺]/[NADH] of 0.1 at pH 7.0 and about 0.3 at pH 7.5.

Published in Wilson (2015a).

Appendix B.

Oxidative phosphorylation in vivo: all constants are given for no energy coupling so when the reducing equivalents are transferred across a difference in potential the appropriate energy term has to be included.