(a) Proteins are dynamic molecules rather than static structures. Explain this phenomenon using hemoglobin as an example. (10…

(a) Proteins as dynamic molecules: haemoglobin (10 marks)

A crystal structure gives one time-averaged picture, but a protein in solution is an ensemble of interconverting conformations. Motions span femtoseconds (bond vibrations) to milliseconds and longer (loop and domain movements, subunit rearrangement), and the energy differences between conformers are only a few kJ/mol, so ligands, pH and temperature can shift the populations. Function often depends on this flexibility: binding sites open and close, and a ligand at one site can change the shape and affinity of a distant one (allostery).

Haemoglobin (Hb, α₂β₂, four haems) shows this at three levels.

Quaternary switch. Deoxy-Hb exists in the tense (T) state, with low O₂ affinity and stabilised by salt bridges between the subunits (for example the C-terminal His146 of each β chain with Asp94, and the C-terminal Arg141 of each α chain with the opposite subunit). Oxy-Hb is in the relaxed (R) state, with high affinity. Binding of O₂ moves Fe²⁺ from about 0.6 Å out of the porphyrin plane into it; this pulls the proximal His F8 and the F helix, breaks the salt bridges, and rotates one αβ dimer by about 15° relative to the other, narrowing the central cavity.

Cooperativity. Because each bound O₂ favours the T → R change, the next O₂ binds more easily. The result is a sigmoidal saturation curve (Hill coefficient about 2.8, P₅₀ about 26 torr) against the hyperbolic curve of monomeric myoglobin (P₅₀ about 3 torr). This allows nearly full loading in the lungs and efficient unloading in tissues. It is described by the concerted (MWC) model, in which T and R pre-exist in equilibrium and O₂ shifts the balance towards R, and by the sequential (KNF) model, in which subunits change one at a time.

Allosteric effectors. H⁺ and CO₂ (the Bohr effect) and Cl⁻ stabilise T, reducing affinity where tissues are acidic. 2,3-Bisphosphoglycerate binds in the central cavity of T Hb, between the β chains (with His2, Lys82 and His143), and shifts the curve right. Fetal Hb (γ chains, where His143 is replaced by Ser) binds it less and so has a higher O₂ affinity.

Local breathing motions. In myoglobin and Hb the haem pocket is buried, and the static structure shows no open path for O₂. Ligand entry and exit require transient opening of channels and movement of the distal His E7 gate, on picosecond to nanosecond time scales (seen in flash photolysis and molecular dynamics). Together these show that the function of Hb is a property of a moving structure, not a rigid one.

(b) Stereochemistry and mechanism: m-CPBA and NBS/NaOH (10 marks)

The substrate is a cyclopentene carrying a methyl group on the allylic carbon (C3) and a tert-butyl group on C4, both on the same face (cis, drawn as wedges). Call this the top face; the bottom face is free. Both reagents deliver oxygen to the double bond, but by different routes.

Route (a), m-CPBA. The peracid transfers its terminal oxygen in a single concerted "butterfly" transition state, syn to the double bond, and it approaches the less hindered face. The face opposite the allylic methyl (the bottom) is preferred. The product is the epoxide anti (trans) to both the methyl and the tert-butyl group: 3-tert-butyl-2-methyl-6-oxabicyclo[3.1.0]hexane with the epoxide oxygen on the face opposite the substituents. The by-product is m-chlorobenzoic acid.

Route (b), NBS then NaOH. In water-containing solvent NBS supplies Br⁺, which forms a bromonium ion on the less hindered bottom face. Water opens it by anti (backside) attack from the top face, at the carbon that is less hindered (the alkene carbon away from the methyl), giving the trans-bromohydrin: Br down, OH up. Then NaOH removes the O-H proton, and the alkoxide attacks the adjacent C-Br carbon from the back in an intramolecular SN2 (a Williamson closure) which needs the trans, anti-periplanar arrangement. This displaces Br⁻ from below and puts the ring oxygen on the top face. The product is the epoxide cis (syn) to the methyl and tert-butyl groups. The regiochemistry of water attack does not matter for the final epoxide, because either trans-bromohydrin closes to the same top-face epoxide.

Net result: the two epoxides are diastereomers. m-CPBA gives the epoxide on the face opposite to the substituents; NBS/NaOH gives it on the same face, because two inversions (anti-addition of Br⁺/H₂O, then SN2 closure) reverse the facial selectivity of the first step.

(c) 2-Methylbenzophenone: photoenolisation (10 marks)

Why the reaction is rapid. On absorbing light the ketone reaches the n,π* singlet, and intersystem crossing to the triplet is almost complete within picoseconds, as in benzophenone. In this triplet the carbonyl oxygen is electron-deficient and behaves like an alkoxy radical. In the conformation with the o-methyl group syn to the C=O, one hydrogen of the methyl group lies about 2.5 Å from the oxygen, in a six-membered (1,5) arrangement. Intramolecular γ-hydrogen abstraction is therefore very fast (about 10⁸ s⁻¹ or more) and gives a 1,4-triplet biradical, a ketyl radical and a benzylic radical, which is stabilised because the two centres are joined through the ring as an o-quinodimethane. Intersystem crossing of the biradical gives the closed-shell photoenol.

Why it is reversible. The photoenol is a high-energy o-quinodimethane that has lost the aromaticity of one ring, and it also reverts by reverse proton transfer. It returns to the ketone by a thermally allowed suprafacial [1,5]-hydrogen shift (or by acid/base-catalysed proton transfer). Since nothing net is formed, 2-methylbenzophenone is photostable, a property used in photoprotective UV absorbers and photo-removable protecting groups.

Stereoisomerism of the photoenol. The photoenol has a new enol double bond, C(OH)Ph=C(ring), which can be of two geometries, Z and E. In the Z-enol (kinetic, formed directly), the OH group lies close to the exocyclic CH₂, so the H can be handed back at once by the [1,5] shift: lifetime about tens of nanoseconds to a microsecond, and it is not observed by ordinary product analysis. The E-enol, formed by the other rotamer, has its OH pointing away from the CH₂ and cannot return by that intramolecular route; it reverts only by slow, intermolecular (solvent, trace acid or base) proton transfer and lives for milliseconds to seconds. This long-lived E-enol is the one trapped by dienophiles (Diels-Alder, as an o-quinodimethane) or seen by flash photolysis. Its lifetime falls sharply in protic or basic solvents.

(d)(i) Distinguishing pairs by IR (5 marks)

(a) Ethyl benzoate and phenyl propanoate are isomeric esters, told apart by ν(C=O).

• Ethyl benzoate, an alkyl benzoate: the C=O is conjugated with the ring, which lowers its frequency to about 1720 cm⁻¹ (an aliphatic ester absorbs near 1740).
• Phenyl propanoate, an aryl alkanoate: the C=O is not conjugated with the ring, and the oxygen lone pair is drawn into the phenyl ring, so it donates less to the C=O, which stays strong and at higher frequency, about 1760 cm⁻¹.

(b) 4-Bromo-N-methylbenzamide and 4′-bromoacetanilide are both secondary amides, told apart by amide I (C=O) and N-H.

• 4-Bromo-N-methylbenzamide: the C=O is conjugated with the ring, and the N lone pair donates fully into C=O, giving about 1640 cm⁻¹; N-H stretch about 3300 cm⁻¹ (H-bonded solid, about 3450 in dilute solution).
• 4′-Bromoacetanilide: the N lone pair is shared with the aryl ring, so it donates less to C=O, and the amide I band appears higher, about 1665 cm⁻¹; N-H stretch is about 3300-3320 cm⁻¹ (slightly higher and sharper than in the benzamide).

(d)(ii) Woodward-Fieser calculation (5 marks)

Structure A (triene): C(Me)=C-C=C-C=C, a linear conjugated triene in which two of the double bonds lie in one ring (homoannular diene).

• Base value, homoannular diene: 253 nm
• One extra conjugated C=C: +30
• Exocyclic C=C, two: +10
• Alkyl substituents and ring residues on the chromophore, six: +30 (the methyl and five ring CH₂/CH residues)
• λmax = 253 + 30 + 10 + 30 = 323 nm

Structure B (cross-ring dienone), O=C-Cα=Cβ-Cγ=Cδ in a six-membered ring ketone:

• Base value, six-ring enone: 215 nm
• One extra conjugated C=C: +30
• Exocyclic C=C, two: +10
• α ring residue: +10
• β ring residue: +12
• γ ring residue: +18
• δ substituents, methyl and ring residue: +18 + 18 = +36
• λmax = 215 + 30 + 10 + 10 + 12 + 18 + 36 = 331 nm

(e)(i) ¹H NMR of ethene and ethyne (5 marks)

Ethene absorbs at δ about 5.3 and ethyne at δ about 1.8-1.9 (for comparison, ethane is at 0.9). Judging by hybridisation alone, the sp C-H of ethyne (50% s-character, more electronegative carbon) should be more deshielded than the sp² C-H of ethene, so the observed order is the reverse of the prediction.

The reversal is explained by magnetic anisotropy. In the field B₀ the π electrons circulate, and the induced field is what matters at the proton. In ethene, with the molecular plane perpendicular to B₀, the π electrons circulate above and below the plane and the induced field lines close round the in-plane hydrogens in the same direction as B₀, so these hydrogens are deshielded. Ethyne tends to align along B₀, and the π electrons circulate around the molecular axis; the induced field along the axis opposes B₀ where the hydrogens lie (the shielding cone), so they are shielded, and this outweighs the hybridisation effect. The same effect deshields aromatic protons (δ about 7.3) and shields the terminal alkyne proton.

(e)(ii) Benzyl cation to tropylium cation (5 marks)

The benzyl cation (m/z 91) arises when an alkylbenzene molecular ion loses the alkyl radical by benzylic cleavage. It then ring-expands to the seven-membered tropylium ion, C₇H₇⁺, also m/z 91.

Mechanism:

• (1) The exocyclic CH₂⁺ is attacked by a ring C-C σ bond (the ipso-ortho bond), so that a ring carbon migrates to the CH₂ carbon, giving a bicyclic cyclopropyl-type cation (the norcaradienyl-type cation, bicyclo[4.1.0]heptadienyl) in which the CH₂ carbon is now part of a three-membered ring.
• (2) The cyclopropane bond common to the two rings breaks (electrocyclic opening), expanding the ring to seven carbons and delocalising the charge to give the tropylium ion, C₇H₇⁺.

Driving force: tropylium is a planar, cyclic, fully conjugated system with 6 π electrons in a ring of seven p orbitals, obeying Hückel's 4n + 2 rule (n = 1), so all seven CH groups are equivalent and the ion is much more stable than benzyl and forms the base peak of many toluene and alkylbenzene spectra.

Evidence: ¹³C and deuterium labelling of toluene shows that the CH₂ carbon and the ring carbons become equivalent in the m/z 91 ion, and the ion goes on to lose C₂H₂ to give m/z 65 (C₅H₅⁺) in the same way whether it comes from toluene or from cycloheptatriene.