Prochirality and Pro-R/Pro-S

Every NAD(P)H- or FAD-dependent oxidoreductase in metabolism is classified by which face of its cofactor and substrate it uses — the "A-side" and "B-side" hydride transfer classes of dehydrogenases are literally a Re/Si distinction, and this classification is used routinely to group enzyme families, predict isotope-labeling outcomes in metabolic flux studies, and design mechanism-based inhibitors that exploit a specific face's approach trajectory. Terpene and steroid biosynthesis pathways rely on prochiral recognition at essentially every cyclization and hydroxylation step — cytochrome P450 enzymes hydroxylate one specific, prochirally-defined hydrogen among several chemically identical-looking ones, a selectivity now exploited industrially in biocatalytic manufacturing of steroid drugs and complex natural product intermediates. In synthetic asymmetric catalysis, prochiral face selection is the entire mechanistic basis of Sharpless asymmetric epoxidation and dihydroxylation (the chiral tartrate or cinchona-derived ligand differentiates the Re and Si faces of a prochiral alkene), Noyori and Corey–Bakshi–Shibata asymmetric ketone reductions (a chiral catalyst or chiral borane reagent selects one face of a prochiral ketone, directly building on the Re/Si logic developed here), and Jacobsen/Katsuki epoxidation catalysts. Modern biocatalytic desymmetrization — using engineered ketoreductases, lipases, and esterases in industrial routes to chiral drug intermediates (statins, β-blockers, and many antiviral and anticancer agents) — is essentially applied enantiotopic-group discrimination at scale, converting prochiral or meso starting materials into single-enantiomer products with minimal waste. NMR spectroscopists use diastereotopicity constantly and unavoidably: any CH₂ adjacent to (or even several bonds from) a stereocenter routinely shows an ABX pattern rather than a simple triplet, a fact essential for correctly interpreting coupling patterns in natural product structure elucidation. The vocabulary developed here — homotopic, enantiotopic, diastereotopic, Re, Si, pro-R, pro-S — is the precise language in which Stereochemistry of Reactions: Overview discusses how any reagent, chiral or not, chooses among a substrate's available reactive sites.

Ask the tutor: In lactate dehydrogenase, why does hydride delivery to the Si face of pyruvate produce the biologically correct (S)-lactate rather than (R)-lactate — can you walk through the full priority tracing one more time with the viewing geometry made completely explicit?

Start with the simplest possible case: a carbon bearing two hydrogens, one methyl, and one bromine — bromochloro... no, take CH₃–CHBr–CH₃' is wrong too; use the textbook substrate, ethanol's methylene carbon, C1 of CH₃CH₂OH, which carries H, H, OH, CH₃. Two of its four substituents are hydrogens — genuinely identical atoms, same mass, same bonding. The question "are these two hydrogens the same or different" cannot be answered by looking at the atom alone; it must be answered by looking at what happens to the whole molecule if you swap one for something else. The operational test is substitution: mentally replace one of the two identical groups with a test group (conventionally deuterium, or in the CIP formalism a phantom "higher priority" duplicate) and see what kind of molecule results. Do this twice, once for each of the two identical groups, and compare the two outcomes.

• If both substitutions give the same molecule (truly superimposable, not just similar), the two original groups were homotopic. This happens when the two groups are related by a rotational symmetry axis ($C_n$) of the parent molecule. Homotopic groups are utterly indistinguishable by any physical or chemical measurement — same NMR shift under any conditions, same reactivity toward any reagent, chiral or not. Example: the four hydrogens of methane, or the two methyl groups of propan-2-ol's isopropyl carbon are homotopic to each other's methyl-substitution product (replacing one methyl of (CH₃)₂CHOH with an ethyl group and comparing to replacing the other gives enantiomers... actually let's use a cleaner homotopic example) — the three hydrogens of a single freely rotating methyl group are homotopic; the two chlorines of CH₂Cl₂ are homotopic (related by a $C_2$ axis through C and the midpoint of Cl–Cl and H–H).

• If the two substitutions give enantiomers (non-superimposable mirror images) of each other, the two original groups are enantiotopic. This is the ethanol case: replacing one methylene H of CH₃CH₂OH with D gives (R)-CH₃CHDOH; replacing the other gives (S)-CH₃CHDOH. These are enantiomers, so the two original hydrogens are enantiotopic. Enantiotopic groups are chemically identical in an achiral environment (identical NMR shifts in ordinary solvent, identical rate of reaction with an achiral reagent) but become distinguishable the instant a chiral reagent, chiral solvent, or chiral catalyst is introduced — because a chiral reagent reacting with two enantiomeric transition states experiences diastereomeric transition states, which generically have different energies.

• If the two substitutions give diastereomers (stereoisomers that are not mirror images), the two original groups are diastereotopic. This happens whenever the molecule already contains another stereocenter (or another source of chirality/prochirality) elsewhere, so that the new stereocenter created by substitution combines with the old one in two different relative ways. Diastereotopic groups are chemically and spectroscopically distinct even with achiral reagents — this is why the two protons of a CH₂ group adjacent to a stereocenter in an NMR spectrum routinely appear as an AB quartet with different chemical shifts, not as an equivalent doublet.

The same three-way classification applies to faces of a planar trigonal atom, not just to substituent pairs. A ketone carbonyl carbon, an alkene carbon, an enolate carbon, an iminium carbon — anything sp² with three different (or two-same-one-different, as in a symmetric ketone) attached groups — has two faces, "top" and "bottom." Nucleophilic or electrophilic attack can occur from either face, and the two faces are related exactly as the two substituents above: homotopic (formaldehyde H₂C=O, both faces give the same achiral product), enantiotopic (an unsymmetrical ketone like butan-2-one, CH₃COCH₂CH₃: attack on one face gives one enantiomer of the alcohol, attack on the other face gives the other enantiomer), or diastereotopic (a ketone that already bears a stereocenter, e.g. 3-methylpentan-2-one's carbonyl: the two faces give diastereomeric alcohols). To name these two faces unambiguously, chemists use the Re/Si convention, built directly on CIP priority rules. Look at the trigonal atom from one side. Rank its three substituents by CIP priority ($a > b > c$). If tracing $a \to b \to c$ traces a clockwise path as you view it, that face is the Re face (from Latin rectus, right). If the path is counterclockwise, that face is the Si face (sinister, left). Viewed from the opposite side, the priorities trace the opposite sense, so the same three groups look clockwise from one face and counterclockwise from the other — precisely the same logic that makes R and S mirror-related descriptors for a tetrahedral center.

The entire apparatus reduces to two paired statements, each a direct extension of CIP priority logic from real stereocenters to prospective ones.

where: $C_n$ is a proper rotation axis of the whole molecule, $\sigma$ is a mirror plane (or improper axis $S_n$); the classification is a property of the entire molecule, not of the local atom alone — a stereocenter anywhere else in the molecule forces diastereotopicity onto an otherwise-enantiotopic-looking pair.

Reading: ask, for the pair of "identical" substituents, whether the molecule possesses a symmetry element that swaps them while leaving the molecule looking the same. A rotation axis swapping them makes them truly identical (homotopic). Only a mirror plane swapping them means they are non-identical but related as mirror images (enantiotopic). No symmetry relation at all means they were never equivalent to begin with (diastereotopic) — this is the default outcome whenever another stereocenter is present anywhere in the molecule, because a stereocenter destroys all mirror symmetry.

where: $a > b > c$ are the three (real) substituents on the sp² atom ranked by standard CIP hierarchical digraph rules exactly as for a normal stereocenter, applied to the trigonal atom as though it were about to become tetrahedral.

Reading: the Re/Si face label is assigned before any bond forms — it describes the two-dimensional π-face geometry using the same clockwise/counterclockwise logic that R/S uses for a completed tetrahedron, so that "attack on the Re face" and "attack giving the R product" can be connected by a definite, checkable rule once you know what the incoming group's priority will be.

where: $X_a^{\uparrow}$ denotes $X_a$ given an arbitrarily elevated priority — conventionally treated as if it outranks $X_b$ while both retain their real chemical identity — and the resulting R or S descriptor is reported as the "pro-R" or "pro-S" label of the original $X_a$.

Reading: to distinguish two enantiotopic (or diastereotopic) groups by name without actually changing them, you perform the CIP assignment as if one of them had (hypothetically) slightly higher priority than its twin, see what stereodescriptor results, and call that specific physical group "pro-R" or "pro-S" accordingly — this labels real, physically identifiable atoms in the ground-state molecule, not a hypothetical isotopomer.

Example 1 (foundational): classify the two hydrogens of bromochloromethane's higher homolog — CH₂BrCl's prochirality is trivial (no prochirality, it's already got 2 different + 2 H — wait it's Ca₂bc itself). Let's do citrate's central CH₂ groups properly. Citrate is $\text{HOOC–CH}_2\text{–C(OH)(COOH)–CH}_2\text{–COOH}$, symmetric about the central carbon bearing OH and COOH, flanked by two $CH_2COOH$ arms. Citrate synthase famously reacts stereospecifically with only one of the two arms even though the molecule, drawn on paper, looks symmetric (a meso-like, "prochiral" molecule with an internal mirror plane). Step 1: Check for real symmetry. Citrate's central carbon has substituents OH, COOH, CH₂COOH, CH₂COOH — pattern $Ca_2bc$ with $a = CH_2COOH$ (twice), $b=$ OH, $c=$ COOH. The whole molecule has a mirror plane (achiral, meso-type prochiral) but no rotation axis relating the two arms (a $C_2$ rotation would have to simultaneously swap OH and COOH, which are different groups, so no $C_2$ exists) — so the two arms are related only by the mirror, never by a rotation. Step 2: Substitute one arm. Replace a hydrogen on the pro-R arm's CH₂ with, conceptually, a distinguishing label (this is exactly how isotope experiments with ¹⁴C-labeled citrate were designed by Ogston in 1948). Assign CIP priorities at the central carbon with one arm "tagged": OH > COOH > CH₂COOH(tagged) > CH₂COOH(untagged) — wait, for the arms themselves we compare the arm groups to each other: since both arms are $CH_2COOH$, we look one bond further. Tagging one arm's methylene hydrogen doesn't change the arm's identity at C1, so instead the classical test replaces one whole arm's terminal COOH with, hypothetically, CH₂OH or another distinct group to break the tie. Doing this at each arm in turn and comparing gives two products that are enantiomers of each other — so the two arms are enantiotopic, and (since no ordinary chemical reagent is chiral) both arms react identically with any achiral reagent, exactly as observed for non-enzymatic chemistry of citrate. Step 3: Citrate synthase, however, is built entirely from chiral L-amino acids and therefore presents a chiral active site. It binds citrate in one specific orientation (dictated by hydrogen-bonding and steric fit to the OH and both COOH groups) such that only the pro-R arm's $CH_2$ sits adjacent to the catalytic machinery that will process it (in the reverse reaction: aldol cleavage to oxaloacetate + acetyl-CoA). The Ogston "three-point attachment" model explains this: three fixed contacts (OH, central COOH, one specific arm) between substrate and chiral active site force one enantiotopic arm into the reactive position, the other necessarily left non-reactive. Limiting-case check: if citrate's central carbon instead bore two identical extra groups too (i.e., if OH and COOH were also the same group, making the molecule truly $Ca_4$-symmetric, like pentaerythritol's central carbon $C(CH_2OH)_4$), all four arms would become homotopic (related by genuine $C_2$/$S_4$ symmetry) and no enzyme, however chiral, could distinguish them by a three-point-attachment argument alone — this correctly predicts that symmetric tetra-substituted centers show no enantiotopic discrimination, consistent with citrate synthase's selectivity depending entirely on citrate's lower symmetry ($Ca_2bc$, not $Ca_4$).

Example 2 (applied): pro-R/pro-S assignment and mechanism for glycerol-3-phosphate dehydrogenase. Dihydroxyacetone phosphate (DHAP), $\text{HOCH}_2\text{–CO–CH}_2\text{OPO}_3^{2-}$, is reduced by NADH to glycerol-3-phosphate (G3P) by glycerol-3-phosphate dehydrogenase. Step 1: DHAP's carbonyl carbon (C2) is trigonal, substituents $=\!O$, CH₂OH, CH₂OPO₃²⁻. CIP priority: the phosphate ester oxygen chain gives CH₂OPO₃²⁻ a higher-priority first point of difference than CH₂OH (comparing the atoms attached to the CH₂'s oxygen: P vs H, so OPO₃²⁻ beats OH) — actually compare at the branching point: both are CH₂–O–X; X = P (phosphate) vs X = H (hydroxyl); phosphorus (Z=15) outranks hydrogen, so CH₂OPO₃²⁻ > CH₂OH as substituents on the carbonyl carbon. Overall priority: $=\!O$ (a) > CH₂OPO₃²⁻ (b) > CH₂OH (c). Step 2: Determine which face the enzyme's NADH delivers hydride to. This enzyme is known (by isotope-labeling and comparison with structurally characterized homologs) to deliver hydride to the Si face of DHAP's carbonyl carbon. Step 3 — mechanism. NADH's nicotinamide C4–H bond (specifically the pro-R hydrogen of NADH, "the A-side" hydride in this enzyme class) donates a hydride ion in a single concerted step: the C4–H σ bond's electrons flow toward the developing carbocation-like nicotinamide ring (rearomatizing it to NAD⁺, itself now aromatic and highly stabilized — this aromatization is the thermodynamic driving force for the whole hydride transfer), while the hydride lands on DHAP's carbonyl carbon from the Si face. Simultaneously the carbonyl π electrons shift onto oxygen, which is protonated by an active-site acid (often a conserved His or a metal-bound water) to give the neutral alcohol. Step 4 — assign the product's configuration. With H added from the Si face (defined by $=\!O(a) > CH_2OPO_3^{2-}(b) > CH_2OH(c)$ tracing counterclockwise when viewed from that face), the new stereocenter has substituents OH, H, CH₂OPO₃²⁻, CH₂OH. Product priorities: OH(1) > CH₂OPO₃²⁻(2) > CH₂OH(3) > H(4). Tracking through the geometry (H occupies the position viewed from the Si side, so viewed with H pointing away, from the opposite, Re, side, the remaining OH→CH₂OPO₃²⁻→CH₂OH trace clockwise) gives the $(R)$ configuration — matching the biologically produced sn-glycerol-3-phosphate, whose stereocenter is indeed $(R)$. Step 5 — limiting case. If instead a non-enzymatic reducing agent (NaBH₄ in achiral solvent) reduced DHAP, hydride would add to the Re and Si faces with statistically equal probability (both faces enantiotopic, equal energy transition states in an achiral environment), giving racemic glycerol-3-phosphate — precisely the outcome observed, confirming that face-selectivity is a property of the chiral catalyst/enzyme, not of the substrate alone.

Example 3 (exam/competition level): full diastereotopicity analysis and NMR prediction for (2R,3S)-configured 2-bromo-3-methylpentane's C4 methylene. Consider (2R,3S)-2-bromo-3-methylpentane: $\text{CH}_3\text{–}{}^{*}\text{CHBr}\text{–}{}^{*}\text{CH(CH}_3)\text{–CH}_2\text{–CH}_3$, with defined stereocenters at C2 $(R)$ and C3 $(S)$. Classify the two hydrogens on C4 (the CH₂ of the ethyl-like tail) and predict their NMR behavior. Step 1 — is there any symmetry relating the two C4 hydrogens? The molecule already contains two fixed, non-interconverting stereocenters (C2 and C3, both configurationally locked, not subject to any internal mirror or rotation that could relate them to their own mirror images without inverting the whole molecule). Therefore no symmetry operation of this specific molecule can map one C4 hydrogen onto the other while leaving the molecule looking identical — replacing either hydrogen with deuterium creates a new, third stereocenter (C4) superimposed on the pre-existing fixed configuration at C2 and C3. Step 2 — perform the substitution test explicitly. Replacing $H_{pro-R}$ at C4 with D (assign this label by the usual "elevate priority" trick applied to C4: substituents at C4 are H, H, CH₃(C5's methyl via CH₂CH₃... wait C4 is CH₂ flanked by C3 and C5=CH₃, i.e., substituents H, H, CH(CH₃)(CHBrCH₃) [=C3 side], CH₃ [=C5]). Elevating one H gives a new stereocenter; call the descriptor obtained the pro-R hydrogen by convention) gives the diastereomer $(2R,3S,4R)$; replacing the other gives $(2R,3S,4S)$. These two products, $(2R,3S,4R)$ and $(2R,3S,4S)$, share the same configuration at C2 and C3 but differ at C4 — by definition of diastereomers (stereoisomers, not enantiomers, since not all stereocenters are inverted relative to each other), these are diastereomers. Step 3 — conclusion. The two C4 hydrogens are diastereotopic. This is not a subtle or rare situation — it is the generic outcome for any $CH_2$ group anywhere in a molecule that contains a stereocenter elsewhere, however distant (in principle the effect attenuates with distance through bonds but never strictly vanishes for a rigid, non-interconverting framework). Step 4 — spectroscopic consequence. Because the two hydrogens are diastereotopic, they reside in genuinely different chemical environments even in achiral CDCl₃: they show different chemical shifts (typically split by anywhere from a few Hz to over 1 ppm depending on proximity and conformational averaging), and they couple to each other with a geminal coupling constant $^2J_{HH}$ typically $-10$ to $-14$ Hz for an sp³ CH₂, appearing as an ABX (or more complex) multiplet rather than a simple equivalent signal. This is routinely observed and is, in fact, a standard diagnostic: an apparently simple $CH_2$ splitting into two distinct multiplets in a ¹H NMR spectrum is direct experimental proof of a nearby stereocenter. Step 5 — limiting case. If C3's methyl-bearing stereocenter were removed (say, replace CH(CH₃) at C3 with a plain CH₂, giving 2-bromopentane with only one stereocenter at C2), the analogous C4 methylene would then be tested against only C2's stereocenter, and the same diastereotopic argument would still apply for any CH₂ flanked by one fixed remote stereocenter — diastereotopicity from a stereocenter does not require adjacency. Only if all stereocenters were removed from the molecule entirely (fully achiral parent, e.g., plain pentane) would the corresponding methylene hydrogens become homotopic or enantiotopic depending on the remaining symmetry — for pentane's C2 methylene specifically, the two hydrogens are enantiotopic (related by the molecule's mirror plane, no stereocenter present).

The Re/Si and pro-R/pro-S nomenclature was formalized by Kurt Mislow and Morton Raban in the 1960s, building directly on the CIP priority rules that Robert Sidney Cahn, Christopher Ingold, and Vladimir Prelog had established for ordinary stereocenters. Mislow, working at Princeton, was deeply engaged throughout his career with the precise language of stereochemistry — topicity, chirotopicity, and the rigorous classification of symmetry-related atoms were central themes of his research program, motivated in large part by the need to describe NMR-observable and enzymatically-observable distinctions that classical stereochemical vocabulary (built only around fixed, already-formed stereocenters) could not capture. The deeper biochemical insight predates the formal nomenclature by decades. Alexander G. Ogston, in a short but pivotal 1948 Nature paper, resolved a puzzle that had troubled biochemists studying the citric acid cycle: how could citrate synthase (and aconitase) act asymmetrically on citrate, a molecule that appears — if you only count constitution, not three-dimensional shape — to have two "identical" $CH_2COOH$ arms? Ogston's answer, the three-point attachment model, showed that a chiral surface (the enzyme active site) binding a prochiral substrate at three fixed points can, purely geometrically, distinguish two substituents that any achiral test would call equivalent. This was confirmed directly by Frank Westheimer and Birgit Vennesland's isotope-labeling experiments on yeast alcohol dehydrogenase (1953), which showed the enzyme transfers hydride from one specific, stereochemically defined face of ethanol's C1 to one specific, stereochemically defined face of NAD⁺ — the first direct experimental proof that enzymes discriminate enantiotopic atoms.