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A glutamic acid residue supplies a carboxyl group whose protonation state can change with the active site environment. The following five schematic contributions are possible in a hypothetical enzyme; they are alternatives and overlapping physical effects, rather than five independently established reactions of this enzyme. In the diagrams $E$ is the protein tether, and $C6$ is the reacting purine carbon.

general acid catalysis: $\mathrm{E}-\mathrm{C}{\mathrm{O}}_2\mathrm{H}\cdots N1\to \mathrm{E}-\mathrm{C}{\mathrm{O}}_2^{-}+\mathrm{H}-\mathrm{N}{1}^{+}$. Donation of the carboxyl proton activates the amidine-like C6 center for water attack. The same acid could instead assist the amino leaving group: $\mathrm{E}-\mathrm{C}{\mathrm{O}}_2\mathrm{H}+-\mathrm{N}{\mathrm{H}}_2\to \mathrm{E}-\mathrm{C}{\mathrm{O}}_2^{-}+-\mathrm{N}{\mathrm{H}}_3^{+}$. These are two locations for general acid catalysis, rather than two different categories.

general base catalysis: $\mathrm{E}-\mathrm{C}{\mathrm{O}}_2^{-}\cdots \mathrm{H}-\mathrm{OH}\to \mathrm{E}-\mathrm{C}{\mathrm{O}}_2\mathrm{H}+\mathrm{O}{\mathrm{H}}^{-}$, coupled to oxygen attack on C6. Accepting a proton makes water a more effective nucleophile. This does not require an appreciable pool of free hydroxide in bulk solution.

covalent catalysis: a glutamate oxygen can in principle attack activated C6 to form $C6-\mathrm{O}-\mathrm{C}(\mathrm{O})-\mathrm{E}$. After addition/elimination replaces the amino group, water must hydrolyze that transient enzyme–substrate bond to release product and regenerate $\mathrm{E}-\mathrm{C}{\mathrm{O}}_{2}H/C{\mathrm{O}}_2^{-}$. Such a pathway is a chemically distinct possibility, not established by the given structure.

electrostatic catalysis: the carboxylate can stabilize a developing positive charge, for example in a protonated purine or amino leaving group; a protonated carboxyl can also donate a hydrogen bond to an oxygen developing negative charge. This contributes only if the reacting configuration is stabilized relative to the bound starting state. A carboxylate placed next to an oxyanion without compensating geometry would instead be unfavorable.

proximity and orientation catalysis: donor and acceptor hydrogen bonds can hold the purine and attacking water in a productive arrangement, schematically $\mathrm{E}-\mathrm{C}{\mathrm{O}}_2\mathrm{H}\cdots N1-C6\cdots \mathrm{O}{\mathrm{H}}_2$. Binding reduces unproductive orientations and can distort the substrate toward a reactive geometry. This last contribution is sometimes described through substrate binding or strain; a binding interaction is not automatically catalytic unless it improves access to the transition state.

An ionizable Asp296 carboxyl group is not essential to the measured catalytic pathway at pH 7. Asparagine retains a similar side-chain size and an amide donor/acceptor pair, while losing the carboxyl group's ordinary acid/base chemistry and negative charge. Preserved kinetics are therefore consistent with a binding or positioning hydrogen bond that survives the conservative substitution, or with a dispensable/redundant contact.

This does not prove that Asp296 makes no interaction in the native enzyme, nor that every substitution at that position would be harmless. The displayed Asp296 contact is also distinct from Asp295, which coordinates zinc; their neighboring residue numbers must not be conflated. Other pH values could expose a contribution hidden by the assay condition.

The functional group interaction profile compares donor strength $\alpha$ and acceptor strength $\beta$. In water, strong–strong contacts compensate for desolvation, giving the upper-right black region. Strong–weak contacts lose favourable solvent interactions without adequate replacement, giving the two grey regions. Weak–weak association gives the lower-left black region through the hydrophobic effect.

Ethanol's ethyl groups preferentially solvate weakly polar sites, removing this incentive for their association: the lower-left region becomes approximately neutral. Its hydroxyl group retains competition for hydrogen bonds elsewhere in the profile.^[ref]

For a carbonyl oxygen of residue $i$ accepting from the NH of a later residue, the possibilities are:

The alpha helix provides a favourable combination of allowed backbone torsions, reasonably linear hydrogen bonds, and side-chain packing. Its successive side chains advance by about $100^{\circ }$, rather than lining up in the three columns of the narrower 3-10 helix. Smaller repeating rings impose more severe backbone constraints; the wider pi helix gives a different, generally less favourable packing arrangement. Short 3-10 and pi-helical segments can still occur in proteins, so this is a preference for a common extended secondary structure, not a prohibition of the alternatives. Proline and sequence-specific interactions can disrupt the idealized backbone donor pattern.

At pH 7, a glutamate residue is normally carboxylate. Its most natural role is general-base activation of the attacking water. Draw the carboxylate oxygen lone pair toward a water H, the water O–H pair toward its oxygen, and that oxygen's lone pair toward C3 while the conjugated pi system moves toward the carbonyl oxygen:This can be concerted, avoiding a freely diffusing hydroxide intermediate. The protonated glutamate subsequently returns its proton to the enolate system, directly or through solvent, regenerating carboxylate. A favorable arrangement is needed; ordinary carboxylate does not quantitatively deprotonate bulk water in a prior equilibrium.

The side-chain amide of glutamine is neutral. Its N–H can donate a hydrogen bond to the carbonyl oxygen and stabilize developing enolate charge, while its amide oxygen can accept a hydrogen bond to orient attacking water. Draw $\mathrm{Gln}-\mathrm{CON}{\mathrm{H}}_2\cdots \mathrm{O}=C1-C2=C3$, with the dotted interaction from amide N–H to substrate oxygen. This assists polarization and transition state stabilization; the amide nitrogen is not an ordinary amine base because its lone pair is delocalized into its own carbonyl.

The guanidinium group of arginine is positively charged. It can stabilize developing negative charge by hydrogen bonding and electrostatic attraction, drawn $\mathrm{Arg}-\mathrm{guanidiniu}{\mathrm{m}}^{+}\cdots {\mathrm{O}}^{\delta -}-C1$. Its delocalized cation is not the preferred neutral general base at pH 7. Productive catalysis requires stronger stabilization of the reacting arrangement than of the unreactive ground-state complex.

Phenylalanine and leucine have hydrocarbon side chains and provide no conventional acid/base or hydrogen-bond donor/acceptor group here. They can position the enone, exclude unproductive solvent and select the attacked face through hydrophobic effect and steric hindrance. Those binding effects can assist catalysis but should not be drawn as an imaginary side-chain proton relay. The original schematic depicts the Glu water relay and the Gln/Arg oxyanion-stabilizing contacts.

The beta-carbon bond-forming transition state retains the same basic connectivity across this pH range, but the predominant proton-transfer route and enzyme protonation change. Near the acidic end, protonated glutamate can act as a general acid, donating a proton or a strong hydrogen bond to carbonyl oxygen and making C3 more electrophilic; it is less available as the carboxylate general base that activates water. Above its local $p{K}_a$, carboxylate-mediated water activation is favored. Acid catalysis therefore shifts positive-charge stabilization toward a protonated carbonyl, whereas base-assisted attack reduces positive-charge buildup on incoming water. Neither a unique transition-state geometry nor a numerical pH optimum follows from pH alone.

Using a free-solution glutamate side-chain $p{K}_a\simeq 4.2$ only as an illustration, the deprotonated fraction is $[1+10^{p{K}_a-\mathrm{pH}}{]}^{-1}$: about 0.059 at pH 3 and 0.998 at pH 7. An enzyme environment can shift that $p{K}_a$ substantially. The glutamine amide and the hydrocarbon side chains remain in their ordinary forms from pH 3 to 10; arginine guanidinium, with a typical free side-chain $p{K}_a$ around 12.5, remains predominantly positive even at pH 10. Thus the major side-chain switch among those listed is glutamate. At the alkaline end, bulk hydroxide can also contribute to nonenzymatic conjugate addition. A measured pH-rate profile must control substrate stability and enzyme folding before assigning every loss of activity to an active-site titration.

Hydride is delivered to steroid C5 and a proton to C4; the C3 ketone is retained. Use the conjugated fragment $\mathrm{O}=C3-C4=C5$. Carbonyl hydrogen bonds from Tyr91–OH and protonated Glu57 lower the barrier to conjugate reduction. Draw a curved arrow from the nicotinamide C4–H bond of NADPH to steroid C5, shift the C4=C5 pi pair toward C3–C4, and shift C3=O pi electrons onto oxygen. The nicotinamide ring rearomatizes to NADP+; the steroid becomes a bound enolate, or its protonated enol equivalent. electron shifts across the nicotinamide ring must accompany C–H bond cleavage rather than leaving an unexplained neutral carbon radical.

Next, reform C3=O and protonate steroid C4 from an appropriately positioned acid, directly or through an enol/proton-relay route. This regenerates the catalytic acid after solvent reprotonation. The enzyme fixes the hydride-accepting face so that the new C5–H has the 5α configuration, giving dihydrotestosterone; delivery to the opposite face would give a different ring-junction configuration. This is not simple 1,2 reduction of the C3 carbonyl to an alcohol. The net local bookkeeping is one hydride plus one proton across C4=C5, with two electrons supplied by NADPH. The original reactive-fragment diagram shows the enolate-forming arrows and the separate protonation step.

Saponification cleaves the acetate ester side groups while the intended carbon backbone remains intact:The ideal target C is therefore a vinyl chloride-vinyl alcohol copolymer, containing $-\mathrm{C}{\mathrm{H}}_2-\mathrm{CH}(\mathrm{Cl})-$ and $-\mathrm{C}{\mathrm{H}}_2-\mathrm{CH}(\mathrm{OH})-$ units in the original sequence positions. The carbon–oxygen bond to the backbone remains; hydrolysis removes the acetyl group from oxygen. Incomplete hydrolysis would leave a three-component population of chloride, acetate and alcohol units. New hydroxyl groups can strengthen adhesion and coating interactions through hydrogen bonds.

Product 6 is a remotely oxidized ketone of the undecylammonium chain, retaining the ammonium group and its counterion. Number from the ammonium-bearing carbon as C1. Crown-mediated recognition positions the remote C8–C9 region near the Mn–oxo center. A representative major-site product is the C8 ketone,Its adjacent possible regioisomer is the C9 ketone $[{\mathrm{H}}_3{\mathrm{N}}^{+}-(\mathrm{C}{\mathrm{H}}_2{)}_8-\mathrm{C}(\mathrm{O})-\mathrm{C}{\mathrm{H}}_2-\mathrm{C}{\mathrm{H}}_3]\mathrm{B}{\mathrm{F}}_4^{-}$. The precise single-site assignment is a limitation discussed below.

The crown ether binds the primary ammonium end through several N–H···O hydrogen bonds. This host–guest complex holds a folded portion of the chain close to the manganese oxidant, so the effective local concentration of a remote secondary C–H bond can overcome the intrinsic advantage of a free tertiary C–H bond. Such recognition-driven reversal of substrate preference is experimentally established.^[ref]

The key intermediates are the crown-bound ammonium–Mn=O assembly, a remote carbon radical after H abstraction, and the rebound secondary alcohol. A second oxidation removes the remaining hydrogen on the carbinol carbon to give the ketone. The overall oxygen-equivalent count isThus one ketone requires two equivalents of peroxide, explaining a maximum near 50% ketone yield with one equivalent and near-complete conversion with two.

The primary remote-oxidation study reports preference for C8 and C9, not a universally unique carbon. The schematic catalyst drawing and the oxygen budget alone cannot distinguish those positions quantitatively. The “single product” wording is therefore treated as an idealized remote-site assignment; a uniquely verified C8:C9 ratio is not invented.^[ref]

The end groups associate reversibly through a complementary hydrogen-bond array. At low concentration, bringing the two ends of the same molecule together avoids the concentration-dependent cost of finding another molecule, so an intramolecular ring is favored.

For A, increasing concentration permits end-to-end intermolecular association to compete successfully with ring closure. It produces long, reversible supramolecular chains. Increasing chain length and entanglement account for the highly viscous solution without requiring covalent polymerization.

B has more favorably positioned attachment points on its rigid aromatic core. Its arms can close a less strained ring, so intramolecular association remains strongly competitive over the stated range. Predominantly discrete rings do not form the same extended chain network, explaining the retained fluidity. Both compounds can make the same local hydrogen bonds; their different balance of ring strain, preorganization and intermolecular association explains the macroscopic difference.

The terminal ureidopyrimidinone groups supply the association sites. Their urea/pyrimidinone NH donors and carbonyl/ring-nitrogen acceptors can form a self-complementary array of four hydrogen bonds between two UPy units. Joining the two terminal units of one molecule by this noncovalent association closes the ring.

The ether-containing arms provide flexibility and spacing; they are not covalently joined together during ring formation. The ring is therefore a supramolecular conformation of the existing molecule, rather than a new covalent ether macrocycle.

The molecule combines three chemically different binding regions.

These assignments identify the preferred local sites, rather than guaranteeing three independent binding constants: occupancy can alter conformation, electrostatics and the affinity of neighboring sites.

The important change is preorganization of the chloride-binding amide groups. In the hydroxylated host, intramolecular hydrogen bonds from the phenolic OH groups to the amide carbonyl oxygens restrict rotation and favor a geometry in which the amide NH donors converge on the anion-binding cavity. chloride can therefore accept two favorable hydrogen bonds with a smaller conformational penalty than in the unsubstituted host. The hydroxyl groups need not be counted as two additional freely available chloride donors: their role includes organizing the existing donors.

The association constant increases by $5230/195=26.8$. At $298\mathrm{K}$, the corresponding difference in standard Gibbs free energy isThis is a modest molecular free-energy advantage amplified into a substantial change in the equilibrium constant. solvent competition and changes in solvation also contribute to measured binding; the structures chiefly suggest the preorganization explanation.

Two neutral carboxylic acids can form a carboxylic acid dimer with two reciprocal O–H···O=C hydrogen bonds. In water, each acid group already makes favourable solvent contacts. Association must displace some of those contacts and loses translational freedom, so the extra stabilization of the dimer may be small. Any ionized carboxylate population also cannot form the same neutral two-donor carboxylic acid dimer.

A nonpolar, weakly hydrogen-bond-accepting solvent such as dry toluene or a compatible hydrocarbon generally favours this dimerization relative to water, provided the acid dissolves. The solvent competes less strongly for the donor and acceptor sites. Dilution still disfavors the dimer because $K=[(\mathrm{HA}{)}_2]/[\mathrm{HA}{]}^2$: the dimer fraction depends on concentration even in a favourable solvent. Thus trace dimer in the aqueous sample is not evidence that the acid lacks hydrogen-bonding ability.

A protein is synthesized as a polypeptide whose sequence constrains its possible interactions. Protein folding is the acquisition of a functional three-dimensional structure: local hydrogen bonds organize secondary structure, while packing, electrostatic interactions and burial of nonpolar groups through the hydrophobic effect stabilize the overall fold. Some proteins also form protein disulfide bonds. Folding reduces the chain's conformational entropy, but the relevant balance includes the entropy of the surrounding water; it is the total Gibbs free energy that is minimized at fixed pressure and temperature.

A folding funnel describes a biased but rugged energy landscape: increasingly native-like conformations become favorable, while barriers can trap intermediates. The chain therefore does not have to test every possible conformation in a uniform random search. Molecular chaperones can prevent protein aggregation and help escape kinetic traps; some proteins remain disordered or require partners, so a unique isolated compact fold is not universal.

The ribonuclease A refolding experiment connects this thermodynamic account to a measurement. Unfolding the enzyme with urea while reducing its disulfide bonds removes activity; suitable removal of the denaturant and restoration of disulfide bonds recover activity. Oxidizing while the chain remains unfolded instead produces incorrectly paired disulfides and little activity. Thus sequence, solvent conditions and the route past kinetic traps all matter; restoration of enzyme activity provides a functional test of folding.

Creating a liquid surface changes the molecular environment and costs interfacial free energy. In the dispersion-only cleavage model, the attractive Van der Waals force per area has magnitude $A/(6\pi h^3)$. Separating two contacting halves from a molecular cutoff $h_0$ to infinity takes work per areaHere $A_H$ denotes the Hamaker constant, to distinguish it from an area. Cleavage creates two free surfaces, giving the Hamaker estimate of liquid surface tensionThe continuum attraction diverges at zero separation and neglects molecular impenetrability and short-range repulsion. The cutoff is therefore an effective contact separation of molecular size, commonly of order $0.1$–$0.3\mathrm{nm}$, not a limit that can be taken to zero.

An experimental limitation is the strong temperature dependence of surface tension. For water in equilibrium with its vapour, the recommended experimental values decrease from $71.98\mathrm{mN}{\mathrm{m}}^{-1}$ at $25{}^{\circ }\mathrm{C}$ to $58.92\mathrm{mN}{\mathrm{m}}^{-1}$ at $100{}^{\circ }\mathrm{C}$, and the fitted tension vanishes at the critical point. A fixed pairwise cleavage energy misses interfacial entropy, changing density and many-body correlations.^[ref] The dispersion-only model is unsuitable when cohesion is dominated by hydrogen bonds, ionic interactions or metallic bonding; liquid metals are a clear example of the latter failure.

The central dogma of molecular biology concerns sequence information: DNA can be copied by DNA replication; transcription makes RNA from DNA; and translation makes a protein from messenger RNA. The familiar $\mathrm{DNA}\to \mathrm{RNA}\to \mathrm{protein}$ diagram is not an assertion that all information transfer is one-way: reverse transcription and RNA replication are compatible with the dogma. Its key exclusion is transfer of a protein's amino-acid sequence back into nucleic-acid sequence by a general templating mechanism.

DNA is a polymer of deoxyribonucleotides with a sugar–phosphate backbone joined by phosphodiester bonds. Its usual DNA double helix contains antiparallel strands with complementary bases, adenine paired with thymine and guanine with cytosine. The base sequence stores inherited information; complementary pairing supports accurate copying and repair. A strand has distinct $5^{\prime }$ and $3^{\prime }$ ends, and ordinary chain synthesis extends the $3^{\prime }$ end. Packaging into chromosomes compacts and regulates access to the genetic material.

RNA uses ribose, with a $2^{\prime }$ hydroxyl group, and uracil in place of thymine. It is usually single-stranded but forms extensive paired secondary and tertiary structures. Messenger RNA conveys coding information, transfer RNA couples codons to amino acids, and ribosomal RNA provides both structural organization and catalysis within the ribosome. Other RNA molecules regulate expression or catalyse reactions. Thus RNA is not merely a passive intermediate.

Proteins are polypeptides of amino acids linked by peptide bonds, read from an amino terminus to a carboxyl terminus. Their primary sequence guides protein folding; backbone hydrogen bonds organize helices and sheets, while hydrophobic, electrostatic and other interactions produce tertiary and sometimes quaternary protein structure. Their functions include catalysis, transport, signalling, mechanical support and molecular movement. Sequence alone does not guarantee function: folding, modifications, partners and cellular conditions matter. During translation, a ribosome reads successive triplet codons in messenger RNA, with charged transfer RNA molecules supplying the corresponding amino acids; initiation and termination define the reading frame.

Protein primary structure is the ordered amino acid sequence of a polypeptide, linked by covalent peptide bonds. The approximately planar peptide bond restricts local geometry, while backbone torsion angles give conformational freedom subject to steric exclusion. Protein secondary structure comprises local backbone arrangements, especially the alpha helix, with backbone hydrogen bonds between residues $i$ and $i+4$, and the beta sheet, whose strands are joined by backbone hydrogen bonds. Turns and loops connect these elements. Protein tertiary structure is the full three-dimensional organization of a single chain, often including several protein domains. Protein quaternary structure is the arrangement of multiple chains in a protein complex.

Protein folding is governed by the Gibbs free energy of the chain together with its solvent, not by the chain's energy alone. Folding reduces the chain's conformational entropy, but can gain solvent entropy through the hydrophobic effect, burying nonpolar side chains away from water. Favorable hydrogen bonds, Van der Waals forces, electrostatic interactions and sometimes covalent disulfide bonds stabilize particular structures. Steric repulsion prevents atomic overlap. At fixed temperature and pressure, the native ensemble is favored when its total $\Delta G=\Delta H-T\Delta S$ is lower than competing ensembles. The balance depends on the solvent, pH, salt and ligands. Molecular chaperones help avoid aggregation or kinetic traps; a stable fold is not a perfectly rigid conformation, and some proteins have disordered regions.

For a soluble globular protein, a typical pattern is a nonpolar core and a polar, hydrated surface. A transmembrane protein instead presents nonpolar side chains to the hydrocarbon interior of the lipid bilayer. Membrane-spanning alpha helices satisfy their polar backbone groups through internal hydrogen bonds; a roughly membrane-thickness helix commonly contains about twenty residues, depending on tilt and bilayer thickness. Multiple helices can enclose polar channels or binding sites. Membrane-spanning beta barrels likewise expose mainly nonpolar groups outward towards lipid while arranging backbone hydrogen bonds between strands and often lining an aqueous pore with polar groups. Exposed loops and domains contacting water can resemble soluble proteins. Not every membrane-associated protein spans the membrane: peripheral attachment and lipid anchoring are distinct possibilities.

The organizing distinction is the environment of each surface: water favors accessible polar groups, while the membrane core favors outward-facing nonpolar groups. Buried polar groups can still be essential to a transport pathway or catalytic site.

The protein primary structure is the ordered protein sequence along a polypeptide, from its N-terminus to its C-terminus. In cells, information in a DNA coding sequence is copied into messenger RNA by transcription. During translation, the ribosome reads successive three-base codons; transfer RNA molecules match these by their anticodons and supply the corresponding amino acids. The genetic code is degenerate: different codons can encode the same amino acid. A start establishes the reading frame and a stop terminates translation. Peptide bonds link the amino acids into the backbone, leaving chemically different side chains. Thus the sequence specifies the order of side-chain interactions, rather than a literal coordinate list for the folded molecule.

Protein secondary structure describes local backbone arrangements. An alpha helix is stabilized by a regular pattern of backbone hydrogen bonds, typically between the carbonyl of residue $i$ and the amide of residue $i+4$. Beta sheets assemble extended strands through inter-strand hydrogen bonding, with parallel or antiparallel strand orientations. Turns and loops connect these elements; not every region belongs to a helix or sheet. The peptide bond is approximately planar, while backbone torsion angles provide conformational freedom subject to steric restrictions.

Protein tertiary structure is the complete three-dimensional organization of one chain, often arranged into protein domains. Protein quaternary structure describes the organization of multiple chains in an assembly. Soluble globular proteins often bury nonpolar side chains and expose polar ones; membrane proteins can instead expose hydrophobic surfaces to the surrounding lipid. Other stabilizing interactions include hydrogen bonds, electrostatic interactions, Van der Waals forces and sometimes covalent disulfide bonds. These competing contributions define active sites, binding pockets and mechanically useful structures; folded proteins are dynamic ensembles, not perfectly rigid objects.

The connection from sequence to structure is thermodynamic and kinetic. Folding usually decreases the chain's conformational entropy, but favorable interactions and changes in solvent entropy, including the hydrophobic effect, can lower the total Gibbs free energy. Under suitable conditions the native ensemble is favored over unfolded alternatives. A change in sequence can therefore change the balance of accessible conformations and alter folding or function. Reversible refolding of a denatured protein in an appropriate environment demonstrates that the sequence can contain the information needed for its native structure.^[ref]

The environment is part of the specification: temperature, pH, ionic conditions, ligands and post-translational modifications matter. Molecular chaperones can prevent aggregation and help chains escape kinetic traps without providing a residue-by-residue structural template. Some sequences are intrinsically disordered proteins or disordered regions, and some require partners for a stable fold. Thus primary structure strongly constrains structure, but does not guarantee one unique rigid shape independent of conditions.

The chemical mismatch types are A–C and G–T, with either strand acting as template. In the fixed ring alignment shown, A–C has no correct hydrogen bonds while G–T retains one. Relative probabilities must specify the template: template A loses two bonds versus A–T, giving $e^{-10}$; template G loses two versus G–C, giving $e^{-10}$; template C loses three versus C–G, giving $e^{-15}$; template T loses one versus T–A, giving $e^{-5}$. Equal incoming activities and $5k_{B}T$ per bond give approximate relative weights $4.5\times 10^{-5},4.5\times 10^{-5},3.1\times 10^{-7},6.7\times 10^{-3}$ respectively.

For roughly equal template frequencies the mean error probability is order $1.7\times 10^{-3}$, or several million errors across $3\times 10^9$ copied base pairs. Restricting the estimate to purine templates instead gives order $10^5$ errors; neither is an accurate replication model. Both greatly exceed the source's order-one surviving mutation input. Polymerase kinetic discrimination, proofreading and mismatch repair suppress errors, and a transient mismatch need not become an inherited mutation. Ring relaxation, stacking, solvent and rare tautomers are missing from this simple hydrogen-bond calculation. Real G–T wobble geometry can form additional bonds. The source's mutation rate is illustrative, not a universal measured human rate.^[ref]