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A carbon-carbon double bond is a covalent bond of bond order two between carbon atoms, conventionally written $\mathrm{C}=\mathrm{C}$. In a localized orbital description it consists of one sigma bond and one pi bond. The distinction describes the symmetry of the bonding orbitals: the localized pi interaction has a nodal plane containing the internuclear axis, whereas the sigma interaction does not.^[ref]

Ethylene, ${\mathrm{H}}_2\mathrm{C}=\mathrm{C}{\mathrm{H}}_2$, illustrates the counting. Its four carbon–hydrogen connections are sigma bonds, and the carbon–carbon connection contributes another sigma bond plus one pi bond. The localized picture therefore has five sigma bonds and one pi bond, representing six shared electron pairs. Calling the central connection a double bond does not mean that the two bonding interactions are geometrically identical.

Maintaining the pi bond favors an aligned arrangement of the participating orbitals. Rotation that destroys this overlap has an energetic cost, which helps make cis-trans isomerism meaningful when each double-bonded carbon has suitable distinct substituents. Ethylene itself has identical hydrogens at each end, so it does not furnish that geometric distinction.

Chemical reactions can change the connection while retaining the carbon skeleton. Fumarate hydratase adds water across the carbon-carbon double bond of fumarate to produce L-malate; the reverse reaction removes water and restores the double bond.^[ref] Counting atoms and identifying bond order thus reveal different parts of the transformation.

The carbon sequence is oxaloacetate $(4)$ plus an acetyl group $(2)$ to citrate $(6)$, then isocitrate $(6)$, alpha-ketoglutarate $(5)$, succinyl-CoA $(4)$, succinate $(4)$, fumarate $(4)$, malate $(4)$ and back to oxaloacetate $(4)$. The numbers count the cycling carbon skeleton, excluding coenzyme A. Two carbon dioxide releases accompany the changes $6\to 5\to 4$.^[ref]

Per acetyl group: three NADH, one FADH2 equivalent, one GTP or ATP by substrate-level phosphorylation, and two carbon dioxide. Succinate dehydrogenase retains FADH2 and transfers its electrons to ubiquinone, forming ubiquinol. The FADH2 equivalent and ubiquinol count the same electron pair.^[ref]

A useful check adds the stepwise changes. The carbon count is $4+2-1-1=4$; the NADH count is $1+1+1=3$. Each NADH carries two electrons, and the succinate dehydrogenase route supplies another pair, so one turn exports $3\times 2+2=8$ electrons. This arithmetic is an accounting identity, not an ATP yield calculation. Converting it to ATP requires the separate energy coupling and transport assumptions discussed under oxidative phosphorylation.

For a chosen ideal conversion of $5\mu \mathrm{mol}$ of acetyl groups, multiplication gives $15\mu \mathrm{mol}$ of NADH, $5\mu \mathrm{mol}$ of ubiquinol, $5\mu \mathrm{mol}$ of GTP and $10\mu \mathrm{mol}$ of carbon dioxide. The electron output is $40\mu \mathrm{mol}$. If all these electrons subsequently reach oxygen with no competing sinks, four electrons per oxygen molecule require $10\mu \mathrm{mol}$ of oxygen. That is consumption by the connected electron transport chain; it is not an oxygen term in the cycle's own substrate ledger.

No cycle step directly consumes molecular oxygen. In ordinary aerobic mitochondrial operation, however, the mitochondrial respiratory chain must reoxidize NADH and ubiquinol to restore the oxidized electron carriers. Without that outlet, a finite oxidized-carrier pool cannot sustain continued turnover. Other electron acceptors and other forms of metabolism require their own analysis.^[ref]

The pyruvate dehydrogenase complex acts upstream: one three-carbon pyruvate gives one two-carbon acetyl group, one carbon dioxide and one NADH. These are additional to the cycle ledger.^[ref] Consequently, processing one pyruvate through both stages gives three carbon dioxide and four NADH, while the succinate dehydrogenase contribution and the substrate-level phosphorylation contribution each remain one. Counting the upstream step inside the cycle would obscure where the extra carbon dioxide and NADH arise.

Escherichia coli fumarase C is a fumarate hydratase of Escherichia coli, commonly designated FumC. It catalyzes the reversible conversion between fumarate plus water and L-malate in the citric acid cycle. The name identifies a particular enzyme, while the broader activity name can cover related catalysts.^[ref]

The 1995 structure revealed a four-subunit assembly at $2.0\text{A˚}$ resolution, with the active site formed using atoms from three chains.^[ref] Further structures in 1996 used bound inhibitors and poor substrates to distinguish this catalytic A-site from a nearby B-site about $12\text{A˚}$ away. The second site was formed by one subunit rather than three.^[ref]

This gives a concrete interpretation problem for a binding experiment. Detecting a compound somewhere on the protein does not establish that it occupies the catalytic site. Comparing its position with substrate analogues, inhibitory behaviour and the multisubunit geometry supplies additional evidence. Similarly, a change in assembly could affect catalytic activity while retaining the same substrate-contacting amino acid residues. Structure and reaction-rate measurements describe complementary aspects of the working enzyme.

Flavin adenine dinucleotide is a redox coenzyme with a flavin ring system linked to an adenine-containing nucleotide unit. Reduction of the flavin gives FADH2.

In succinate dehydrogenase, an enzyme-bound flavin accepts reducing equivalents during conversion of succinate to fumarate. The flavin is reoxidized through the respiratory electron-transfer machinery, connecting a carbon-metabolism reaction with the mitochondrial respiratory chain.

Fumarase C, often designated FumC, is a classII form of fumarate hydratase. It catalyzes reversible hydration of fumarate to L-malate. The protein designation should be tied to an organism: Escherichia coli fumarase C is a well-studied species-specific example, while the broader enzyme-activity name does not specify one protein sequence.^[ref]

The net substrate inventory makes the chemistry explicit:Four carbon atoms remain four; adding water changes hydrogen and oxygen content without changing the total charge. This hydration is chemically distinct from oxidation of L-malate to oxaloacetate. The enzyme accelerates a reversible reaction rather than making its net direction independent of conditions.^[ref]

The1995 X-ray crystallography study of the E.coli enzyme resolved an assembly of four identical protein subunits at2.0Å. Its proposed active site involved contributions from three of the four protein subunits; a local catalytic environment therefore need not lie inside just one polypeptide chain. A1996 follow-up with bound compounds distinguished the catalytic A-site from a nearby second binding site. These experiments also show why observing ligand binding does not by itself identify a catalytic site.^[ref][ref]

Fumarate is the dianion of fumaric acid, a four-carbon dicarboxylic acid with a trans carbon-carbon double bond. The geometry distinguishes it from its cis isomer.

In the citric acid cycle, oxidation of succinate yields fumarate, and addition of water across the double bond yields malate. This sequence changes the functional groups while preserving the four-carbon framework.^[ref]

Fumarate hydratase, also called fumarase, is the enzyme that reversibly interconverts fumarate plus water with L-malate. The activity is EC4.2.1.2:In the hydration direction, water adds across the carbon-carbon double bond of fumarate. In the reverse direction, water is eliminated. Its lyase classification describes this transformation; the mere presence of water does not make the reaction hydrolysis.^[ref]

For an invented inventory, begin with ten micromoles of fumarate and let six micromoles undergo hydration. Four micromoles of fumarate remain and six micromoles of L-malate form. Each retains a four-carbon skeleton, so the counted carbon inventory remains $4(4+6)=40$ micromoles of carbon atoms. The chosen extent does not determine chemical equilibrium or enzyme kinetics.

A 1995 X-ray crystallography study of Escherichia coli fumarase C found a four-subunit assembly at $2.0\text{A˚}$ resolution. A competitive tungstate derivative helped locate the active site, which included atoms from three of the four protein subunits.^[ref] The example shows why counting subunits and locating a catalytic site are different tasks: several chains can cooperate to build one local reaction environment.

A lyase is an enzyme classified by cleavage through means other than hydrolysis or oxidation. Such reactions commonly eliminate a group to create a double bond or a ring; the reverse direction adds a group across the corresponding structural feature. Lyases form EC class 4, with subclasses organized partly by the bonds affected.^[ref]

The involvement of water alone does not make a reaction hydrolysis. Fumarate hydratase, also called fumarase, interconverts fumarate plus water with the (S) form of malate. In the water-removing direction, it generates the double bond of fumarate. In the reverse direction, water adds across that bond.^[ref] The classification concerns the transformation, not merely whether water appears somewhere in its equation.

An invented bookkeeping example begins with $5\mu \mathrm{mol}$ of (S)-malate. If $3\mu \mathrm{mol}$ undergoes the water-eliminating conversion, $2\mu \mathrm{mol}$ malate remains and $3\mu \mathrm{mol}$ fumarate is formed. No carbon atom is removed from the four-carbon skeleton in this reaction. This is a stipulated extent, not a prediction of the position of chemical equilibrium or the reaction speed.

The distinction can also arise in a multistep reaction. Ribonuclease T1 first produces a cyclic phosphate end by a phosphorus–oxygen lyase step and subsequently hydrolyses that cyclic product. Its classification emphasizes the primary cleavage reaction, even though the overall process also includes hydrolysis.^[ref]

Thus a lyase classification gives useful chemical information but does not uniquely specify a protein's structure, substrate range or physiological role. The actual reaction and its experimentally observed direction remain essential to interpreting the enzyme's name.

Hans Adolf Krebs described the experimental reasoning in his 1953 Nobel lecture. Pigeon breast skeletal muscle retained strong oxidative activity after preparation in a Latapie mincing mill and suspension in aqueous medium. Small fumarate additions increased oxygen uptake by more than complete oxidation of the added fumarate could explain; added four-carbon acids could still be detected afterward. His Table 1 compares the increase in uptake with that calculated from complete consumption of the addition. These comparisons challenge the interpretation that the addition merely supplied extra fuel.^[ref]

The lecture identifies the preparation apparatus but does not describe the gas-measuring instrument behind Table 1. The result supports regeneration, not a unique complete reaction mechanism. Its later discussion combines citrate formation from oxaloacetate with breakdown back toward the four-carbon intermediates to close the cycle. Competitive inhibition supplies another comparison: malonate inhibits succinate dehydrogenase, and succinate accumulates. Such evidence links a blocked step to the surrounding metabolic pathway; damaged tissue and restricted inhibitor access can complicate interpretation.^[ref]

An increase above the added fuel's own oxygen demand is a particularly revealing control on the explanation: it compares the proposed cause with the largest effect that simple consumption could produce. The modern mitochondrial oxygen electrode assay asks a different question about a prepared mitochondrion, testing respiratory control through ADP additions. Neither an oxygen uptake signal nor an accumulating intermediate is by itself a direct measurement of ATP production.

Succinate is the dianion of succinic acid, a four-carbon dicarboxylic acid with structure ${}^{-}\mathrm{OOC}-\mathrm{C}{\mathrm{H}}_2-\mathrm{C}{\mathrm{H}}_2-\mathrm{CO}{\mathrm{O}}^{-}$. It is an intermediate of the citric acid cycle.

Succinate dehydrogenase oxidizes succinate to fumarate, creating a carbon-carbon double bond while passing reducing equivalents into the respiratory machinery. This connects carbon-skeleton chemistry with electron transfer.

Succinate dehydrogenase oxidizes succinate to fumarate and transfers the electrons through bound cofactors to ubiquinone. In mitochondria it is respiratory complex II, linking the citric acid cycle with the respiratory chain.

Unlike complexes I, III, and IV, it does not itself pump protons across the membrane. This distinction explains why electrons entering through succinate contribute differently to the proton-motive output than electrons entering through NADH.