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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.

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.

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 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.

L-malate is the malate enantiomer with $S$ configuration at its hydroxyl-bearing carbon. In the dianionic form specified here, its formula is ${\mathrm{C}}_4{\mathrm{H}}_4{\mathrm{O}}_5^{2-}$. The stereochemical label and the charge state answer separate questions: one specifies the spatial arrangement around a stereogenic carbon, while the other specifies loss of the two carboxyl protons.^[ref]

The connectivity can be written schematically asbut that flat condensed structural formula does not by itself distinguish the two enantiomers. An opposite configuration has the same elemental formula and charge. Likewise, changing protonation of a carboxyl group is not the same operation as reversing the stereochemical arrangement at the carbon bearing OH.

A metabolic transformation makes this distinction useful. The NAD-dependent oxaloacetate-forming reaction EC1.1.1.37 oxidizes L-malate to oxaloacetate while reducing NAD+ to NADH. Conversion of the hydroxyl-bearing carbon to a carbonyl removes that stereogenic center in the oxaloacetate framework. This is a covalent oxidation, rather than simply another protonation state of malate.^[ref]