Science Wiki

Bioenergetics is the field of biochemistry and biophysics that studies how living cells and organisms capture, convert, store, and use energy, using the principles of thermodynamics. Living systems maintain highly ordered, low-entropy macromolecular states far from thermodynamic equilibrium. They can do so only by drawing on a continuous supply of Gibbs free energy, which drives endergonic processes such as anabolic biosynthesis, active transmembrane transport, and mechanical work.

At the molecular level, the main energy currency that couples energy-releasing (catabolic) reactions to energy-consuming ones is adenosine triphosphate (ATP). ATP does not simply release energy when it is hydrolyzed in solution. Instead, it drives unfavorable reactions mainly by transferring a phosphoryl, pyrophosphoryl, or adenylyl group to a substrate. This forms reactive intermediates that lower activation barriers and shift equilibria. Other currencies include transmembrane ion gradients, reduced NADPH, thioesters, and phosphocreatine.

At the scale of the biosphere, energy flow is governed by two complementary and evolutionarily coupled metabolic networks. Photosynthesis captures sunlight and stores it in the chemical bonds of reduced organic carbon compounds. Cellular respiration oxidizes organic compounds back to carbon dioxide and water, regenerating ATP. Together they form a largely closed biogeochemical cycle of matter that is driven by an open, one-way flow of energy from the Sun to heat radiated into space.

Free energy and non-equilibrium systems

According to the second law of thermodynamics, the total entropy of the universe increases in any spontaneous process (ΔS_univ = ΔS_sys + ΔS_surr > 0). A living cell is an open, approximately isothermal and isobaric dissipative system. It maintains structural and informational order (ΔS_sys < 0) by taking up free energy from its surroundings and releasing heat and high-entropy waste products such as CO₂ and H₂O, so that the entropy of the surroundings rises by more than the entropy of the cell falls (ΔS_surr > |_ΔS__sys|).

At constant temperature T (in kelvin) and pressure, the driving force of a reaction is its change in Gibbs free energy:

where ΔH is the change in enthalpy, which reflects bond energies and non-covalent interactions, and ΔS is the change in entropy of the system. In biochemistry, standard free energy changes are usually reported for the biochemical standard state, written _ΔG_°′. This state is defined at 25 °C, a pressure of 1 bar, pH 7.0 (that is, [H⁺] = 10⁻⁷ M), unit activity of water, and 1 M for the other reactants. Tabulated values for phosphorylated compounds also assume a stated ionic strength and free Mg²⁺ concentration (often 1 mM).

The actual free energy change inside a cell depends on both _ΔG_°′ and the reaction quotient Q, which is calculated from the actual intracellular concentrations:

Here R is the gas constant (8.3145 J mol⁻¹ K⁻¹), and _K_′_eq = exp(−_ΔG_°′ / RT) is the apparent biochemical equilibrium constant. A reaction is exergonic if ΔG < 0 and endergonic if ΔG > 0. Catabolic pathways are net exergonic and conserve part of the free energy released as ATP and reduced coenzymes. Anabolic pathways are net endergonic and use that conserved energy to build macromolecules.

Coupled reactions

Free energy changes of sequential or coupled reactions are additive. An endergonic reaction can proceed if it shares an intermediate with a sufficiently exergonic reaction, so that the sum of the two free energy changes is negative. In enzymatic catalysis the coupling is usually physical and not merely an arithmetic one: the enzyme transfers a group from the donor to the acceptor, or holds a high-energy intermediate in its active site. Coupling cannot change the equilibrium of a single reaction, but it allows cells to hold many metabolite ratios far from equilibrium.

ATP and phosphoryl group transfer potential

The hydrolysis of the terminal phosphoanhydride bond of ATP (ATP + H₂O ⇌ ADP + P_i) has _ΔG_°′ = −30.5 kJ/mol. Active metabolism keeps ATP far above its equilibrium ratio to adenosine diphosphate (ADP) and inorganic phosphate (P_i). Typical cytosolic values are [ATP] of about 2 to 8 mM, free [ADP] of about 0.05 to 0.2 mM, and [P_i] of about 1 to 5 mM. The actual free energy of ATP hydrolysis, called the phosphorylation potential, is therefore considerably more negative:

For example, with [ATP] = 5 mM, [ADP] = 0.1 mM, and [P_i] = 5 mM, the logarithmic term gives ΔG_p ≈ −53 kJ/mol. This corresponds to a mass-action ratio roughly nine to ten orders of magnitude displaced from equilibrium.

Phosphorylated metabolites can be ranked by their phosphoryl group transfer potential, which is defined as −_ΔG_°′ of hydrolysis. Compounds with a higher potential than ATP can phosphorylate ADP directly in substrate-level phosphorylation. These include phosphoenolpyruvate (PEP, −61.9 kJ/mol), 1,3-bisphosphoglycerate (about −49 kJ/mol), and phosphocreatine (−43.0 kJ/mol). ATP in turn can phosphorylate acceptors with lower potential, such as glucose, to give glucose 6-phosphate (hydrolysis _ΔG_°′ = −13.8 kJ/mol) or glycerol 3-phosphate (−9.2 kJ/mol). The overall hexokinase reaction (glucose + ATP → glucose 6-phosphate + ADP) therefore has _ΔG_°′ ≈ −16.7 kJ/mol, which is the sum of −30.5 and +13.8.

An adult human contains only about 50 grams of ATP at any moment, yet turns over an amount equivalent to roughly the body's mass each day, so each ATP molecule is recycled on the order of a thousand times daily.

Adenylate energy charge

Energy charge, a concept introduced by Daniel Atkinson, expresses the fraction of the adenylate pool that carries high-energy phosphoanhydride bonds:

The value ranges from 0 (all adenosine monophosphate, AMP) to 1 (all ATP). Healthy, metabolizing cells keep it at about 0.80 to 0.95. Adenylate kinase (2 ADP ⇌ ATP + AMP) buffers the adenylate pool. Falls in energy charge are sensed by regulatory enzymes, notably AMP-activated protein kinase (AMPK), which switches on catabolic pathways and switches off anabolic ones when AMP and ADP rise.

Redox potentials

Photosynthetic and respiratory electron transport harvest free energy by passing electrons from carriers with lower reduction potentials to carriers with higher ones. At pH 7.0 the tendency of a half-reaction (oxidant + n e⁻ ⇌ reductant) to accept electrons is expressed by its standard biochemical reduction potential _E_°′, measured in volts against the standard hydrogen electrode. For comparison, the H⁺/H₂ couple has _E_°′ = −0.414 V at pH 7. For a reaction in which n electrons pass from a donor to an acceptor, the potential difference _ΔE_′ = _E_′_acceptor − _E_′_donor depends on concentrations according to the Nernst equation:

where F is the Faraday constant (96,485 C/mol). Free energy and potential are related by:

When electrons flow from NADH/NAD⁺ (_E_°′ = −0.320 V) to O₂/H₂O (_E_°′ = +0.816 V), _ΔE_°′ = 1.136 V, so for two electrons _ΔG_°′ ≈ −219 kJ/mol.

Chemiosmosis and the proton-motive force

In the chemiosmotic theory proposed by Peter D. Mitchell in 1961, membrane-bound electron transport chains convert redox free energy into an electrochemical gradient of protons across a lipid bilayer: the bacterial plasma membrane, the inner mitochondrial membrane, or the thylakoid membrane. The gradient is expressed in volts as the proton-motive force (Δp):

Here Δψ = ψ_P − ψ_N is the electrical potential difference between the positive, proton-accumulating side (the P side) and the negative side (the N side). The term _Δ_pH = pH_P − pH_N is negative when the P side is more acidic, and 2.303 RT / F is about 59.2 mV at 25 °C and 61.5 mV at 37 °C. The return of protons down this gradient through rotary ATP synthase drives ATP synthesis. Mitchell received the 1978 Nobel Prize in Chemistry for this work.

Photosynthesis is the process by which phototrophs (plants, algae, cyanobacteria, and several groups of anoxygenic photosynthetic bacteria) capture light energy and store it in organic compounds. In oxygenic photosynthesis, water is the electron donor and CO₂ is the carbon source:

In eukaryotes, photosynthesis takes place in chloroplasts, which arose by endosymbiosis of a cyanobacterium. In land plants and green algae the chloroplast is bounded by two membranes, whereas the plastids of some other algal groups have three or four. Light-dependent reactions occur in the internal thylakoid membrane network, and carbon assimilation occurs in the surrounding aqueous stroma.

Light-dependent reactions

The light-dependent reactions occur in the thylakoid membranes, which are organized into stacked regions (grana, enriched in photosystem II) and unstacked regions (stroma lamellae, enriched in photosystem I and ATP synthase).

Light harvesting and the Z-scheme

Light is absorbed by antenna complexes such as the trimeric light-harvesting complex II (LHCII), which bind dense arrays of chlorophyll a, chlorophyll b, and carotenoids. Carotenoids broaden the absorption spectrum within the 400 to 700 nm range of photosynthetically active radiation and also quench chlorophyll triplet states and singlet oxygen. When a pigment absorbs a photon, an electron is promoted to an excited singlet state. The excitation energy, in the form of an exciton, is passed between pigments by Förster resonance energy transfer on picosecond timescales until it reaches a reaction center. Two photosystems operate in series along the "Z-scheme" of electron flow:

1. Photosystem II (PSII) and charge separation. Excitation reaches the P680 chlorophyll a pair in the D1 and D2 reaction-center proteins. The excited state P680* is a very strong reductant (about −0.6 V or lower) and passes an electron within picoseconds to pheophytin, then to the bound plastoquinone Q_A, and finally to the mobile plastoquinone Q_B.
2. Water oxidation. The oxidized pair P680^•+ (_E_°′ about +1.25 V) is among the strongest biological oxidants. It is reduced by a tyrosine residue (Tyr_Z, Tyr161 of D1), which in turn takes electrons from the oxygen-evolving complex (OEC), a Mn₄CaO₅ cluster. One photon moves one electron, but oxidizing two water molecules to O₂ requires removing four electrons. The cluster therefore accumulates oxidizing equivalents stepwise through the S-states of the Kok cycle (S₀ → S₁ → S₂ → S₃ → [S₄] → S₀) and releases O₂ and four protons into the lumen at the transient S₄ step. Overall: 2 H₂O + 2 PQ + 4 H⁺_stroma + 4 photons → O₂ + 2 PQH₂ + 4 H⁺_lumen.
3. Cytochrome b₆f and the Q cycle. Plastoquinol (PQH₂) diffuses within the membrane to the Q_o site of cytochrome b₆f. In a bifurcated Q cycle, one electron passes through the Rieske iron-sulfur protein and cytochrome f to the lumenal copper protein plastocyanin, and the second passes through the _b_-type hemes to reduce a plastoquinone at the Q_i site. The net result is the release of about two protons into the lumen for every electron delivered to plastocyanin, which is eight protons for four electrons.
4. Photosystem I (PSI) and NADP⁺ reduction. Plastocyanin donates electrons to oxidized P700^•+ in PSI. Absorption of a second photon raises P700 (_E_°′ about +0.45 V) to P700* (about −1.2 V). Electrons then pass through chlorophyll A₀, phylloquinone A₁ (vitamin K1), and the iron-sulfur clusters F_X, F_A, and F_B to soluble ferredoxin. Ferredoxin-NADP⁺ reductase uses reduced ferredoxin to convert NADP⁺ to NADPH. Four photons at each photosystem (eight in total) yield one O₂ and two NADPH.

Photoprotection and non-photochemical quenching

Absorbing more light than the Calvin cycle can use leads to over-reduction of the electron carriers and the formation of triplet chlorophyll and singlet oxygen, which damage the photosynthetic apparatus. Plants dissipate excess excitation as heat by non-photochemical quenching (NPQ). The fastest and most important component, called energy-dependent quenching (qE), is triggered by acidification of the lumen. Protonation of the PsbS protein and the conversion of violaxanthin to zeaxanthin in the xanthophyll cycle shift antenna complexes into a dissipative state on a timescale of seconds to minutes. Damage that is not avoided is repaired. For example, the D1 protein of PSII turns over rapidly in high light and is replaced by a dedicated repair cycle, and photoinhibition occurs when the rate of damage exceeds the rate of repair.

Thylakoid proton-motive force and cyclic electron flow

Water oxidation (4 H⁺) and the Q cycle (8 H⁺) together deposit about 12 protons in the lumen per four electrons, that is, per O₂ evolved and per two NADPH formed. Compared with mitochondria, the thylakoid membrane is permeable to counter-ions such as K⁺, Cl⁻, and Mg²⁺, which move through channels and transporters and dissipate most of the electrical component. In the steady state in light, the proton-motive force is therefore stored mostly as a pH gradient. In vivo, _Δ_pH values of roughly 1.5 to 2.5 units are common, with a stromal pH of about 7.8 to 8.0 and a lumenal pH of about 5.5 to 6.5.

Protons return to the stroma through the CF_OCF₁ ATP synthase. In spinach chloroplasts its rotor ring contains 14 c subunits, so one full rotation uses 14 H⁺ to make three ATP, which is about 4.67 H⁺ per ATP. Linear electron flow (12 H⁺ per 2 NADPH) therefore yields about 2.57 ATP per 2 NADPH, an ATP:NADPH ratio of about 1.29. The Calvin cycle needs 3 ATP per 2 NADPH (a ratio of 1.5), and photorespiration raises the ATP demand further. The shortfall is made up by cyclic electron flow around PSI, in which electrons from ferredoxin return to the plastoquinone pool by pathways involving the PGR5/PGRL1 proteins or the chloroplast NDH complex. This pumps additional protons without producing NADPH or O₂. Other mechanisms, including the water-water cycle and export of reducing equivalents through the malate valve, also adjust the ATP:NADPH balance.

Calvin–Benson–Bassham cycle

The Calvin cycle in the stroma uses ATP and NADPH from the thylakoids to reduce CO₂ to triose phosphates. The term "dark reactions" is misleading because several of its enzymes are regulated by light. Light-driven changes in stromal pH, Mg²⁺ concentration, and, through the ferredoxin-thioredoxin system, the redox state of regulatory disulfide bonds activate enzymes such as fructose-1,6-bisphosphatase, sedoheptulose-1,7-bisphosphatase, and phosphoribulokinase, and influence RuBisCO activase. The cycle is usually described for three CO₂ molecules, which yield one net triose phosphate, and has three stages:

1. Carboxylation. RuBisCO (ribulose-1,5-bisphosphate carboxylase/oxygenase, a hexadecamer of eight large and eight small subunits that can make up as much as half of soluble leaf protein) must first be activated by carbamylation of an active-site lysine (Lys201 in spinach) by a non-substrate CO₂ molecule, which then binds an Mg²⁺ ion. The enzyme binds ribulose 1,5-bisphosphate (RuBP) and promotes the formation of a 2,3-enediolate, which attacks CO₂. The resulting six-carbon intermediate is hydrated and cleaved into two molecules of 3-phosphoglycerate (3-PGA): 3 RuBP + 3 CO₂ + 3 H₂O → 6 3-PGA.
2. Reduction. Phosphoglycerate kinase uses 6 ATP to convert the six 3-PGA into 1,3-bisphosphoglycerate. NADPH-dependent glyceraldehyde 3-phosphate dehydrogenase then uses 6 NADPH to reduce these to six glyceraldehyde 3-phosphate (G3P), which equilibrates with dihydroxyacetone phosphate. One net G3P leaves the cycle. It is exported to the cytosol by the triose-phosphate/phosphate translocator to make sucrose, or it is retained in the chloroplast to make starch.
3. Regeneration. The remaining five triose phosphates (15 carbons) are rearranged by aldolase, fructose-1,6-bisphosphatase, transketolase, and sedoheptulose-1,7-bisphosphatase into three pentose phosphates. Phosphoribulokinase uses 3 ATP to convert these into three RuBP, which closes the cycle.

The overall stoichiometry is 3 CO₂ + 9 ATP + 6 NADPH + 6 H⁺ + 5 H₂O → G3P + 9 ADP + 8 P_i + 6 NADP⁺. Synthesis of one hexose requires 6 CO₂, 18 ATP, and 12 NADPH.

Photorespiration

The enediolate intermediate of RuBP can react with O₂ as well as CO₂, so RuBisCO also acts as an oxygenase. Its specificity for CO₂ over O₂ (about 80 to 100 in land plants) favors carboxylation, but air contains about 21 percent O₂ and only about 0.04 percent CO₂, and the dissolved concentrations at 25 °C are roughly 250 μM O₂ and 10 to 12 μM CO₂. Oxygenation becomes more frequent as temperature rises, because the specificity factor falls and CO₂ solubility declines faster than O₂ solubility. It is also favored when closed stomata limit CO₂ entry while photosynthesis raises internal O₂.

Oxygenation of RuBP yields one 3-PGA and one 2-carbon 2-phosphoglycolate, which inhibits several enzymes, including triosephosphate isomerase. Photorespiration recovers about 75 percent of its carbon through a pathway spanning the chloroplast, peroxisome, and mitochondrion. Glycolate is oxidized in the peroxisome to glyoxylate (producing H₂O₂) and transaminated to glycine. In the mitochondrion, the glycine cleavage system and serine hydroxymethyltransferase convert two glycines into one serine, releasing CO₂ and NH₃. Serine is converted to glycerate in the peroxisome, and glycerate kinase in the chloroplast uses ATP to regenerate 3-PGA. The glutamine synthetase and GOGAT cycle re-assimilates the released ammonia at the cost of ATP and reduced ferredoxin. In C₃ plants, photorespiration reduces net carbon gain by roughly 25 percent under moderate conditions, and more at high temperature.

Carbon-concentrating mechanisms

Several lineages have evolved mechanisms that raise the CO₂ concentration around RuBisCO. In C₄ and CAM plants the first step is catalyzed by phosphoenolpyruvate carboxylase (PEPC), which does not react with O₂. It fixes bicarbonate (made from CO₂ by carbonic anhydrase) onto PEP to form the four-carbon acid oxaloacetate.

C₄ photosynthesis

C₄ photosynthesis has evolved independently more than 60 times, in groups that include many tropical grasses (maize, sugarcane, sorghum) and some eudicots. In the classical form, which depends on "Kranz" leaf anatomy, PEPC in mesophyll cells produces oxaloacetate, which is converted to malate or aspartate. These diffuse through plasmodesmata into bundle-sheath cells, where decarboxylases (for example NADP-malic enzyme) release CO₂ around RuBisCO. The resulting three-carbon product returns to the mesophyll, where pyruvate, phosphate dikinase regenerates PEP at a cost of two ATP equivalents per CO₂. The pump raises the CO₂ concentration around RuBisCO roughly ten-fold or more, which greatly reduces photorespiration. A few species achieve a C₄ cycle within single cells, without Kranz anatomy.

CAM photosynthesis

Crassulacean acid metabolism (CAM) separates carbon capture and fixation in time. It occurs in many arid-zone succulents, epiphytes, and some aquatic plants. At night, stomata open and PEPC fixes CO₂, and malic acid accumulates in the vacuole, which is driven by proton pumping. During the day, stomata stay largely closed to save water, malate is released and decarboxylated, and the CO₂ is refixed by RuBisCO using the products of the light reactions.

Carbon-concentrating mechanisms in cyanobacteria and algae

Cyanobacteria and many algae concentrate inorganic carbon actively. Cyanobacteria use bicarbonate transporters and CO₂-uptake systems to raise the intracellular bicarbonate concentration, and they enclose RuBisCO together with carbonic anhydrase in protein-shelled microcompartments called carboxysomes. Many eukaryotic algae, such as Chlamydomonas, cluster RuBisCO in a pyrenoid, a condensate held together by linker proteins, and supply it with CO₂ from a bicarbonate pool. These mechanisms are a major reason why aquatic phototrophs are productive at low dissolved CO₂.

Energetic efficiency of photosynthesis

At least eight photons are needed to evolve one O₂ and fix one CO₂ (four photons at each photosystem), and measured values for C₃ plants under favorable conditions are about 9 to 10. Reduction of one mole of CO₂ to the level of carbohydrate stores about 478 kJ (one sixth of 2,870 kJ). Eight moles of 680 nm photons carry about 1,400 kJ, so the maximum conversion of absorbed red light into stored chemical energy is about one third. Losses at other wavelengths, in photoprotection, in photorespiration, and in the metabolic cost of building and maintaining the plant reduce the conversion of incident sunlight into biomass much further. Theoretical maxima are about 4.6 percent for C₃ and about 6 percent for C₄ photosynthesis, and the average over a growing season in crops is typically about 1 percent or less.

Cellular respiration oxidizes reduced fuels (carbohydrates, fatty acids, and amino acids) and transfers the electrons to a terminal acceptor, conserving a fraction of the free energy as ATP. In aerobic respiration the terminal acceptor is O₂. For glucose:

In eukaryotes the process has four stages: glycolysis in the cytosol, pyruvate oxidation, the citric acid cycle, and oxidative phosphorylation in the mitochondria.

Glycolysis

Glycolysis is a ten-step pathway that converts one six-carbon glucose into two three-carbon pyruvates in the cytosol. It does not require oxygen.

• Energy-investment phase (steps 1 to 5). Two ATP are consumed per glucose. Hexokinase (or glucokinase in liver) phosphorylates glucose to glucose 6-phosphate (_ΔG_°′ ≈ −16.7 kJ/mol), which is charged and is trapped inside the cell. After isomerization to fructose 6-phosphate, phosphofructokinase-1 (PFK-1) uses a second ATP to form fructose 1,6-bisphosphate (_ΔG_°′ ≈ −14.2 kJ/mol). PFK-1 is the committed step of glycolysis. It is inhibited by ATP and citrate and activated by AMP, ADP, and fructose 2,6-bisphosphate. Aldolase then cleaves the six-carbon sugar into two triose phosphates, which interconvert through triosephosphate isomerase.
• Energy-conserving phase (steps 6 to 10). Each glyceraldehyde 3-phosphate is oxidized by glyceraldehyde 3-phosphate dehydrogenase, which uses an active-site cysteine, reduces NAD⁺ to NADH, and incorporates P_i to form 1,3-bisphosphoglycerate. Phosphoglycerate kinase transfers its high-energy phosphoryl group to ADP, producing 3-phosphoglycerate (substrate-level phosphorylation). After phosphoglycerate mutase, enolase makes phosphoenolpyruvate. Pyruvate kinase then transfers its phosphoryl group to ADP (_ΔG_°′ ≈ −31.4 kJ/mol), driven by the spontaneous conversion of enol-pyruvate to keto-pyruvate.

The net reaction is glucose + 2 NAD⁺ + 2 ADP + 2 P_i → 2 pyruvate + 2 NADH + 2 H⁺ + 2 ATP + 2 H₂O.

Fermentation

Without a terminal electron acceptor, NAD⁺ must be regenerated from NADH or glycolysis stops. In fermentation, pyruvate or a derivative is reduced instead. Muscle and red blood cells use lactate dehydrogenase to produce lactate. Yeast decarboxylates pyruvate to acetaldehyde, which is reduced to ethanol. Fermentation yields only the 2 ATP made in glycolysis per glucose, a small fraction of the yield of aerobic respiration.

Pyruvate oxidation and the citric acid cycle

Pyruvate enters the mitochondrion through the outer membrane protein VDAC and is imported across the inner membrane by the heterodimeric mitochondrial pyruvate carrier (MPC1/MPC2), a proton symporter that is driven by the pH gradient.

Pyruvate dehydrogenase complex

In the matrix, the pyruvate dehydrogenase complex (PDC, a multienzyme assembly of several megadaltons) catalyzes the irreversible oxidative decarboxylation of pyruvate. It contains E₁ (pyruvate dehydrogenase), E₂ (dihydrolipoyl transacetylase), and E₃ (dihydrolipoyl dehydrogenase) and uses five cofactors: thiamine pyrophosphate, lipoamide, coenzyme A, FAD, and NAD⁺. The reaction is pyruvate + CoA + NAD⁺ → acetyl-CoA + CO₂ + NADH (_ΔG_°′ ≈ −33 kJ/mol).

The citric acid cycle

Acetyl-CoA enters the citric acid cycle (also called the tricarboxylic acid or Krebs cycle) in the mitochondrial matrix. All of its enzymes are in the matrix except succinate dehydrogenase, which is in the inner membrane.

1. Citrate synthase condenses acetyl-CoA with oxaloacetate to form citryl-CoA, whose thioester hydrolysis (about −32 kJ/mol) releases citrate.
2. Aconitase has an Fe₄S₄ cluster and isomerizes citrate to isocitrate through _cis_-aconitate.
3. Isocitrate dehydrogenase catalyzes the first oxidative decarboxylation (_ΔG_°′ ≈ −21 kJ/mol), producing CO₂, NADH, and α-ketoglutarate.
4. The α-ketoglutarate dehydrogenase complex, which is homologous to the PDC and uses the same five cofactors, catalyzes the second oxidative decarboxylation (about −33 kJ/mol) and yields CO₂, NADH, and succinyl-CoA.
5. Succinyl-CoA synthetase couples cleavage of the thioester to substrate-level phosphorylation of GDP or ADP (depending on the tissue-specific isoform) through a phosphohistidine intermediate, which gives succinate.
6. Succinate dehydrogenase (respiratory Complex II) oxidizes succinate to fumarate. The reaction has _E_°′ near +0.03 V, too high to reduce NAD⁺, so the enzyme uses covalently bound FAD and passes electrons to ubiquinone.
7. Fumarase adds water to fumarate to form L-malate.
8. Malate dehydrogenase oxidizes malate to oxaloacetate and produces NADH. The reaction is endergonic under standard conditions (+29.7 kJ/mol) but is pulled forward in vivo because citrate synthase keeps the concentration of oxaloacetate very low.

Each turn of the cycle, per acetyl-CoA, releases 2 CO₂ and generates 3 NADH, 1 FADH₂, and 1 GTP or ATP. For the two acetyl-CoA derived from one glucose, the totals are 4 CO₂, 6 NADH, 2 FADH₂, and 2 GTP or ATP.

The cycle is amphibolic, serving both catabolism and anabolism. Intermediates are withdrawn for biosynthesis: citrate for fatty acids and sterols, α-ketoglutarate and oxaloacetate for glutamate and aspartate, and succinyl-CoA for heme. Anaplerotic reactions replenish the pool, mainly through the biotin-dependent carboxylation of pyruvate to oxaloacetate by pyruvate carboxylase, which is activated by acetyl-CoA.

Fatty acid oxidation

Beta oxidation in the mitochondrial matrix degrades fatty acyl-CoA two carbons at a time. Each cycle produces one FADH₂, one NADH, and one acetyl-CoA. Complete oxidation of palmitate (16 carbons) requires seven cycles and yields 7 FADH₂, 7 NADH, and 8 acetyl-CoA. After counting two ATP equivalents for activation, the net yield is about 106 ATP with the conventional P/O values of 1.5 and 2.5.

Oxidative phosphorylation

Oxidative phosphorylation takes place at the inner mitochondrial membrane, which is folded into cristae. Per glucose, it oxidizes 10 NADH (2 from glycolysis, 2 from the PDC, and 6 from the citric acid cycle) and 2 FADH₂.

The respiratory complexes

Electrons flow from NADH and FADH₂ to O₂ through four membrane protein complexes, linked by two mobile carriers. Ubiquinone diffuses in the lipid bilayer, and cytochrome c diffuses in the intermembrane space. The complexes often associate into supercomplexes (respirasomes, for example I₁III₂IV₁), which are stabilized by cardiolipin.

Reducing O₂ to two H₂O requires four electrons. The heme a₃-Cu_B center, assisted by a cross-linked tyrosine, holds the partially reduced intermediates (the peroxy and ferryl states) until all four electrons have arrived, which prevents release of reactive oxygen species:

Oxidation of one NADH via Complexes I, III, and IV therefore translocates 4 + 4 + 2 = 10 protons. Oxidation of one FADH₂ through Complexes III and IV (bypassing Complex I) translocates 4 + 2 = 6 protons.

ATP synthase

The proton-motive force across the inner mitochondrial membrane is about 150 to 200 mV. In contrast to chloroplasts, it is mainly electrical (Δψ about 150 to 180 mV, matrix negative), with a small pH component (_Δ_pH about 0.5 to 0.8 units, matrix pH about 7.8 and intermembrane space pH about 7.2).

This force drives the F₁F_O ATP synthase (Complex V), a reversible rotary enzyme consisting of two coupled motors:

• The membrane-embedded F_O motor contains a stationary a subunit with two offset half-channels and a ring of c subunits. In mammalian mitochondria the ring has 8 c subunits, in yeast mitochondria 10, and in bacteria 10 to 15. Each c subunit has a conserved carboxylate (Glu58 in the bovine enzyme). Protonation from the P-side half-channel neutralizes the carboxylate and allows the subunit to rotate into the lipid. After almost a full turn, the carboxylate meets the N-side half-channel, releases its proton into the matrix, and is positioned by a conserved arginine of the a subunit.
• The F₁ head has the composition α₃β₃γδε and is held in place by the peripheral stalk. The central γ subunit is attached to the c ring and rotates inside the α₃β₃ hexamer in discrete steps (about 120° per ATP, with 80° and 40° substeps in some enzymes). In the Boyer binding-change mechanism (for which Boyer and John Walker shared the 1997 Nobel Prize in Chemistry), the three catalytic β subunits cycle through open (O), loose (L), and tight (T) conformations. ADP and P_i bind in the open and loose states and are condensed to ATP in the tight state. The energy of the proton-motive force is used mainly to release the tightly bound ATP, and not to form the phosphoanhydride bond itself.

P/O ratios

Because the mammalian c ring has eight subunits, a full rotation consumes 8 H⁺ to make 3 ATP, or 8/3 ≈ 2.67 H⁺ per ATP. ATP must also be exported from the matrix in exchange for ADP by the electrogenic adenine nucleotide translocator (ANT), and P_i is imported by the phosphate carrier with a proton. Together, this transport is usually counted as about one additional proton per ATP, which gives about 3.67 H⁺ per ATP delivered to the cytosol. The estimated yields are therefore about 10/3.67 ≈ 2.7 ATP per NADH and 6/3.67 ≈ 1.6 ATP per FADH₂. The commonly used consensus values of 2.5 and 1.5 allow for some proton leak and slippage. The P/O ratio is defined as the number of ATP made per pair of electrons passed to oxygen, and measured values depend on conditions and on the tissue.

Cytosolic NADH shuttles and ATP yield

The inner membrane is impermeable to NADH, so electrons from cytosolic NADH enter through one of two shuttles:

• The malate–aspartate shuttle (liver, kidney, heart) transfers reducing equivalents to matrix NADH, which yields about 2.5 ATP each. Total yield per glucose is 2 (glycolysis) + 2 (citric acid cycle) + 10 × 2.5 + 2 × 1.5 = 32 ATP. Its aspartate-glutamate carrier is electrogenic and consumes some proton-motive force, so the actual yield is somewhat lower.
• The glycerol phosphate shuttle (brown adipose tissue and some skeletal muscle) uses a flavin-dependent mitochondrial glycerol-3-phosphate dehydrogenase that passes electrons to ubiquinone, bypassing Complex I. Each cytosolic NADH then yields about 1.5 ATP, and the total is about 30 ATP per glucose.

Textbook totals of 30 to 32 ATP are theoretical maxima, and measured values are probably somewhat lower. Under standard conditions, 30 ATP at −30.5 kJ/mol conserve about one third of the 2,870 kJ released, but at the physiological ΔG_p of about −55 to −60 kJ/mol the conserved fraction is more than half.

Proton leak, uncoupling, and reactive oxygen species

Some protons return across the inner membrane without passing through ATP synthase. This basal proton leak, which depends on the adenine nucleotide translocator and other carriers, is estimated to account for roughly a fifth of basal metabolic rate in some tissues. In brown adipose tissue, uncoupling protein 1 (UCP1, thermogenin) is activated by fatty acids and short-circuits the proton-motive force to produce heat. A small fraction of electrons (well below 2 percent of O₂ consumption) leaks to O₂ at Complexes I and III to form superoxide, which is converted to H₂O₂ by superoxide dismutase and removed by peroxidases and catalase.

Diversity of respiratory metabolism

Respiration is not limited to oxygen. Many prokaryotes use other terminal electron acceptors in anaerobic respiration, including nitrate (_E_°′ of NO₃⁻/NO₂⁻ about +0.43 V), fumarate (+0.03 V), sulfate (SO₄²⁻/H₂S about −0.22 V), and CO₂ in methanogenesis (CO₂/CH₄ about −0.24 V). The energy available falls as the potential of the acceptor becomes more negative, and so does the ATP yield per electron. Chemolithotrophs use inorganic donors such as H₂, Fe²⁺, or reduced sulfur compounds. Bacterial respiratory chains often have simpler or alternative complexes and different proton stoichiometries from those of mitochondria. Plants, fungi, and some protists also have an alternative oxidase that transfers electrons from ubiquinol to O₂ without proton pumping at Complexes III and IV, which dissipates energy as heat. In thermogenic flowers such as the skunk cabbage, this raises the temperature of the inflorescence.

Quantitative Stoichiometry and Chemiosmotic Parameters

Why is the proton-motive force dominated by ΔpH in chloroplasts but by Δψ in mitochondria?

Mitochondria and chloroplasts partition the proton-motive force (Δp) differently because of the ion permeability of their energy-transducing membranes and the pH sensitivity of their enzymes. The inner mitochondrial membrane has low intrinsic permeability to counter-ions, so pumping protons out of the matrix rapidly builds a large transmembrane voltage (Δψ ≈ 150 to 180 mV) with a small _Δ_pH (~0.5 to 0.8 units), protecting matrix enzymes from extreme alkalinity. Conversely, thylakoid membranes open Cl⁻, K⁺, and Mg²⁺ channels that collapse Δψ and store Δp as a steep _Δ_pH (~2.0 units), which allosterically triggers photoprotective non-photochemical quenching (qE) in the acidic lumen.

How does the number of c-ring subunits in ATP synthase alter the bioenergetic cost of an ATP molecule?

Rotary F₁F_O ATP synthase synthesizes exactly 3 ATP molecules in its catalytic α₃β₃ head during each 360° rotation of the central γ-stalk, regardless of species. However, the number of proton-binding c subunits in the membrane F_O rotor ring varies from 8 in vertebrate mitochondria to 10 in yeast mitochondria and 14 in plant chloroplasts. Consequently, vertebrate mitochondria require only 8/3 ≈ 2.67 H⁺ per matrix ATP (high thermodynamic gearing), whereas spinach chloroplasts require 14/3 ≈ 4.67 H⁺ per ATP.

Why do C₄ and CAM plants outperform C₃ plants at high temperatures and low atmospheric CO₂?

High temperatures penalize C₃ photosynthesis through two coupled physicochemical effects: the intrinsic specificity of RuBisCO for CO₂ relative to O₂ decreases as thermal motion increases, and the aqueous solubility of CO₂ declines more steeply with temperature than that of O₂. Both factors accelerate RuBisCO oxygenation and wasteful photorespiration. C₄ and CAM plants overcome this by using phosphoenolpyruvate carboxylase (PEPC)—which binds HCO₃⁻ and has zero affinity for O₂—to concentrate CO₂ ten-fold around RuBisCO.