IChO 2006 · Theory problem 11

Enzyme Reaction

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Shikimic acid biosynthesis is an important pathway for amino acids, alkaloids and heterocyclic natural product production. Nature converts shikimic acid to chorismic acid through a cascade of enzymatic reactions. Then chorismate mutase catalyzes the conversion of chorismic acid to prephenic acid at the branch point for the biosynthesis of aromatic amino acids such as tyrosine and phenylalanine.

Figure 1

11.1 During the transformation of shikimic acid to chorismic acid, dehydration is occurring. Choose the hydroxyl group in shikimic acid that is lost through above dehydration among all possible reactions.

11.2 Chorismate mutase rearranges chorismic acid into prephenic acid without changing the molecular formula. Chorismic acid becomes prephenic acid through the Claisen rearrangement, a concerted pericyclic process like the Cope rearrangement as shown below:

Figure 2

Based on the following spectral data, propose the structure of prephenic acid.

\(\ce{^{1}H}\)-NMR (\(\ce{D2O}\), 250 MHz): \(\delta\) 6.01 (2H, d, J = 10.4 Hz), 5.92 (2H, dd J = 10.4, 3.1 Hz), 4.50 (1H, t, J = 3.1 Hz), 3.12 (2H, s). Note that there are three protons, which have been exchanged by \(\ce{D2O}\) very fast, and two protons at \(\delta\) 3.12, which are exchanged slowly in prephenic acid. \(\ce{^{13}C}\)-NMR (\(\ce{D2O}\), 75 MHz): \(\delta\) 203, 178, 173, 132 (for two identical carbons), 127 (for two identical carbons), 65, 49, 48.

\(\delta\), chemical shift; H, integrals; d, doublet; dd, doublet of doublet; J, coupling constant; t, triplet; s, singlet

Figure 3

Chorismate mutase is believed to stabilize the transition state of Claisen rearrangement. Thus it is an interesting target for inhibitor design. Inhibitors, called transition state analog (TSA)s that resemble the transition state (TS, e.g., the species in brackets “[ ]” above) of the reaction are designed to occupy the active site. Several inhibitors were designed and synthesized, and among them eight turned out to be potent inhibitors of the enzyme. The lower is the \(\mathrm{IC}_{50}\) (inhibitor concentration of 50 % of the enzymatic activity) value, the better is the inhibitor.

Figure 4

11.3 Choose all correct statements based on the structures and \(\mathrm{IC}_{50}\) values of above inhibitors. Increase of factor 5 is considered to be important.

(a) Configuration of the hydroxyl group plays an important role in the TS and inhibitor design.

(b) The presence of both carboxylic groups is important in the TS and inhibitor design.

(c) Transition state of the reaction contains two six-membered rings with one chair and one twist-boat conformation.

(d) 7 and 8 can be distinguished on the basis of the \(\ce{^{1}H}\)-NMR of \(\mathrm{H}_a\).

11.4 Draw the transition state of the transformation of chorismic acid to prephenic acid based on the TSA structures and their \(\mathrm{IC}_{50}\) values.

11.5 Compared with the uncatalyzed thermal conversion, chorismate mutase accelerates conversion of chorismic acid to prephenic acid \(1.0\times10^6\) fold at 25 °C by lowering the activation energy of the reaction. Calculate the decrease in activation energy of chorismate mutase at 25 °C.

\(\Delta H_{\mathrm{uncat}}^{\ne}\) is 86,900 J mol\(^{-1}\) for the thermal conversion of chorismic acid to prephenic acid. At what temperature will the rate of the uncatalyzed thermal conversion be the same as that of the enzyme-catalyzed conversion at 25 °C, assuming that \(E_a=\Delta H^{\ne}\).

Official English text of the problem.

Answers

  • 11.1: Hydroxyl group 3.
  • 11.2: Prephenic acid, O=C(O)[C@]1(CC(=O)C(=O)O)C=C[C@H](O)C=C1. Its ring hydroxyl and ring-bound carboxyl group are cis.
  • 11.3: (a), (c), and (d).
  • 11.4: A concerted \([3,3]\)-Claisen transition state resembling inhibitor 8, with a chair-like pericyclic ring and a twist-boat carbocyclic ring. The ring–oxygen bond breaks while a bond forms between the carboxyl-bearing ring carbon and the terminal methylene carbon of the side chain.
  • 11.5: Activation-energy decrease: \(34.2\ \mathrm{kJ\,mol^{-1}}\). Matching uncatalyzed temperature: \(492\ \mathrm{K}\), approximately \(219\,^\circ\mathrm{C}\).

Solution

11.1 — Identifying the hydroxyl group lost

The structures in the overall transformation are:

Name SMILES
Shikimic acid O=C(O)C1=C[C@@H](O)[C@@H](O)[C@H](O)C1
Pyruvic acid CC(=O)C(=O)O
Chorismic acid O=C(O)C1=C[C@@H](OC(=C)C(=O)O)[C@H](O)C=C1
Water O

The balanced overall equation represented by the supplied scheme is

\[ \ce{C7H10O5 + C3H4O3 -> C10H10O6 + 2H2O}. \]

The decisive information is the relative stereochemistry, rather than the positions occupied by groups on the page:

  • In shikimic acid, hydroxyl groups 1 and 2 are trans, whereas 2 and 3 are cis.
  • In chorismic acid, the remaining ring hydroxyl and the oxygen bearing the enolpyruvyl side chain are trans.

Thus hydroxyl 2 remains the alcohol, and the oxygen of hydroxyl 1 becomes the ether oxygen. Hydroxyl 3 is lost.

To track the carbon skeleton explicitly, number the original shikimate ring clockwise from its carboxyl-bearing carbon as \(S_1,\ldots,S_6\). Hydroxyls 3, 2, and 1 then occupy \(S_3,S_4,S_5\), respectively. The final double bonds are \(S_2=S_3\) and \(S_6=S_1\), and the side chain is attached through the oxygen at \(S_5\). Reading this product ring in the opposite direction gives the orientation used in the supplied chorismic-acid drawing. No inversion of either retained oxygen-bearing stereocentre is required.

11.2 — Identifying prephenic acid

Chorismic acid has formula \(\ce{C10H10O6}\), which is retained during rearrangement. Its degree of unsaturation is

\[ \mathrm{DBE}=\frac{2(10)+2-10}{2}=6. \]

The carbon spectrum accounts for these six units as one ring, two carbon–carbon double bonds, and three carbonyl groups:

\(\delta_{\mathrm C}\), ppm Assignment
203 Ketone carbonyl
178, 173 Two carboxyl carbonyls
132, 127, each representing two carbons Four alkene carbons in two equivalent pairs
65 Alcohol-bearing methine carbon
49, 48 Quaternary ring carbon and side-chain methylene carbon

These features require a symmetric cyclohexa-2,5-diene ring carrying both a carboxyl group and a \(\ce{-CH2-C(=O)-CO2H}\) side chain at C1, with an alcohol at C4.

The proton spectrum supports this connectivity:

Signal Assignment and explanation
\(\delta 6.01\), 2H, d, \(J=10.4\ \mathrm{Hz}\) H2 and H6; each couples principally to the other proton on its double bond. C1 has no hydrogen.
\(\delta 5.92\), 2H, dd, \(J=10.4,3.1\ \mathrm{Hz}\) H3 and H5; each couples to its alkene neighbour and to H4.
\(\delta 4.50\), 1H, t, \(J=3.1\ \mathrm{Hz}\) H4 on the alcohol-bearing carbon, coupled equally to H3 and H5.
\(\delta 3.12\), 2H, s The side-chain methylene, between a quaternary carbon and a ketone carbonyl; neither adjacent carbon bears a hydrogen.

The three rapidly exchanged hydrogens belong to two carboxyl groups and one alcohol. The methylene hydrogens exchange more slowly with heavy water, [2H]O[2H], through enolization next to the ketone.

The product is therefore prephenic acid:

O=C(O)[C@]1(CC(=O)C(=O)O)C=C[C@H](O)C=C1

Its ring hydroxyl is cis to the ring-bound carboxyl group and trans to the carbon side chain. The NMR establishes the connectivity and symmetry; this relative configuration follows from the supplied reactant stereochemistry and the concerted rearrangement.

The balanced isomerization is

\[ \underbrace{\ce{C10H10O6}}_{\text{chorismic acid}} \xrightarrow{\text{chorismate mutase}} \underbrace{\ce{C10H10O6}}_{\text{prephenic acid}}. \]

11.3 — Evaluating the statements

For explicit structural identification, the numbered inhibitors used in the comparisons can be represented as follows. Their chair and twist-boat conformations must be described separately from their SMILES.

Name in the problem SMILES
Carbocyclic inhibitor 3 O=C(O)[C@]12C[C@H]([C@H](O)CC1)C[C@@H](C(=O)O)C2
Monocarboxylic inhibitor 4 [C@H]12C[C@H]([C@H](O)CC1)C[C@@H](C(=O)O)C2
Hydroxyl epimer 5 O=C(O)[C@]12C[C@H]([C@@H](O)CC1)C[C@@H](C(=O)O)C2
Oxabicyclic inhibitor 7 O=C(O)[C@]12C[C@H]([C@H](O)C=C1)O[C@@H](C(=O)O)C2
Oxabicyclic inhibitor 8 O=C(O)[C@]12C[C@H]([C@H](O)C=C1)O[C@H](C(=O)O)C2

(a) Correct. Compare hydroxyl epimers 3 and 5:

\[ \frac{\mathrm{IC}_{50}(5)}{\mathrm{IC}_{50}(3)} =\frac{5.3}{0.78}=6.8. \]

Changing the hydroxyl configuration decreases potency by more than the stipulated factor of five.

(b) Incorrect. Compare dicarboxylic inhibitor 3 with monocarboxylic inhibitor 4:

\[ \frac{\mathrm{IC}_{50}(4)}{\mathrm{IC}_{50}(3)} =\frac{1.1}{0.78}=1.4. \]

Removing this carboxyl group changes potency by less than fivefold. Thus the data do not support the claim that the presence of both carboxyl groups is important under the stated criterion.

(c) Correct. The transition-state assembly contains two distinct six-membered rings. The six-atom ring involved in the Claisen electron redistribution is chair-like, while the original carbocyclic ring adopts a twist-boat conformation. The geometry represented by the potent bicyclic analogue 8 accommodates both. Describing only the chair-like rearranging ring would omit the second ring.

(d) Correct. Compounds 7 and 8 are diastereomers at the carbon bearing \(H_a\). In the depicted chair framework, \(H_a\) is approximately axial in 7 and equatorial in 8. Consequently, their vicinal coupling patterns differ: the axial proton can have a large approximately antiperiplanar coupling to an adjacent axial methylene hydrogen, whereas the equatorial proton has smaller corresponding couplings. Their \(H_a\) resonances can therefore distinguish them.

The correct selection is (a), (c), and (d).

11.4 — Describing the transition-state drawing

Number the chorismic-acid ring clockwise from its carboxyl-bearing carbon:

  • C1 bears the ring carboxyl group.
  • The initial ring double bonds are C1=C2 and C5=C6.
  • C3 bears the ether oxygen \(O_{\mathrm e}\).
  • C4 bears the alcohol.
  • In the side chain, call the substituted alkene carbon \(C_\alpha\) and the terminal methylene carbon \(C_\beta\). Thus the side chain is \(O_{\mathrm e}-C_\alpha(=C_\beta)-\ce{CO2H}\).

The six-atom pericyclic circuit is

\[ C_1-C_2-C_3-O_{\mathrm e}-C_\alpha-C_\beta-C_1. \]

Draw this circuit in a chair-like conformation, with the original carbocyclic ring in a twist-boat conformation, following inhibitor 8. Its potency relative to 7 is

\[ \frac{\mathrm{IC}_{50}(7)}{\mathrm{IC}_{50}(8)} =\frac{0.0059}{0.00015}\approx39, \]

supporting the substituent orientation represented by 8.

The drawing should show these simultaneous bond changes:

Bond Change during rearrangement
C3–\(O_{\mathrm e}\) Breaking
\(C_\beta\)–C1 Forming
C1=C2 Double to single
C2–C3 Single to double
\(O_{\mathrm e}\)–\(C_\alpha\) Single to carbonyl double bond
\(C_\alpha=C_\beta\) Double to single

The three concerted electron-pair movements are:

  1. The C1=C2 \(\pi\) electrons form the C2=C3 \(\pi\) bond.
  2. The C3–\(O_{\mathrm e}\) \(\sigma\) electrons form the \(O_{\mathrm e}=C_\alpha\) carbonyl \(\pi\) bond.
  3. The \(C_\alpha=C_\beta\) \(\pi\) electrons form the new \(C_\beta\)–C1 \(\sigma\) bond.

Show the forming and breaking bonds as dashed partial bonds, indicate partial \(\pi\)-bond redistribution along the other four edges, and enclose the assembly in brackets with a superscript \(\ddagger\).

The side chain approaches the ring on the same face as the departing C3–oxygen linkage. The C4 hydroxyl lies on the opposite face. Place the side-chain carboxyl group in the orientation modeled by 8. This produces the cis relationship between the ring hydroxyl and ring-bound carboxyl group in prephenic acid.

Ordinary SMILES cannot encode fractional transition-state bonds or these conformations; the endpoint SMILES and the specified bond changes define the requested drawing.

11.5 — Activation-energy decrease and equivalent temperature

Use the Arrhenius model

\[ k=Ae^{-E_a/(RT)}, \]

with the unchanged-prefactor assumption implicit in attributing the acceleration to a decrease in activation energy.

At \(T_0=298.15\ \mathrm K\),

\[ \frac{k_{\mathrm{cat}}}{k_{\mathrm{uncat}}} = \exp\!\left( \frac{E_{a,\mathrm{uncat}}-E_{a,\mathrm{cat}}}{RT_0} \right) =10^6. \]

Therefore,

\[ \begin{aligned} \Delta E_a &=RT_0\ln(10^6)\\ &=(8.314\ \mathrm{J\,mol^{-1}K^{-1}}) (298.15\ \mathrm K)(13.8155)\\ &=3.4246\times10^4\ \mathrm{J\,mol^{-1}}. \end{aligned} \]

Thus the activation-energy decrease is

\[ \boxed{\Delta E_a=34.2\ \mathrm{kJ\,mol^{-1}}}. \]

With \(E_{a,\mathrm{uncat}}=86.900\ \mathrm{kJ\,mol^{-1}}\), the corresponding catalyzed barrier in this model is approximately \(52.7\ \mathrm{kJ\,mol^{-1}}\).

For the uncatalyzed reaction to reach the catalyzed rate at \(298.15\ \mathrm K\), its rate must increase by \(10^6\):

\[ \ln(10^6) = \frac{E_{a,\mathrm{uncat}}}{R} \left(\frac{1}{T_0}-\frac{1}{T}\right). \]

Hence

\[ \begin{aligned} T &= \left[ \frac{1}{298.15\ \mathrm K} - \frac{8.314\ \mathrm{J\,mol^{-1}K^{-1}}} {86\,900\ \mathrm{J\,mol^{-1}}} \ln(10^6) \right]^{-1}\\ &=492.07\ \mathrm K. \end{aligned} \]

Therefore,

\[ \boxed{T\approx492\ \mathrm K\approx219\,^\circ\mathrm C}. \]

The solution was checked against the official solution.