= Solution
The target is \b[<5-Aminohexanoic acid>, $\mathrm{HO_2C(CH_2)_3CH(NH_2)Me}$]. Disconnect its terminal amine/carboxylic-acid relationship through hydrolysis of \b[6-methylpiperidin-2-one]. This six-membered <lactam> follows from a regioselected Beckmann ring expansion of 2-methylcyclopentanone <oxime>.
Start with <cyclopentanone>. Form its <enolate> with <lithium diisopropylamide> in dry THF at low <temperature>, add methyl iodide, then quench to obtain 2-methylcyclopentanone. Control the methyl iodide/base stoichiometry to suppress a second alkylation. React the <ketone> with hydroxylamine to form its <oxime> and select the geometrical <oxime> isomer in which the bond to the methyl-substituted adjacent ring <carbon> is anti to the departing <oxime> <oxygen> group.
Activate the <oxime>, for example under appropriate acid-promoted Beckmann conditions. The anti methyl-bearing C–C bond migrates onto <nitrogen> as the N–O-derived leaving group departs, inserting <nitrogen> \b[between the original <carbonyl> <carbon> and the methyl-substituted ring <carbon>]. Hydration/tautomerization gives 6-methylpiperidin-2-one. The opposite <oxime> geometry would insert <nitrogen> on the other side and ultimately place methyl at a different position in the amino acid; <oxime> geometry is therefore an essential part of this proposal.
Hydrolyse the <lactam> with aqueous acid and <heat>, then adjust the work-up to the desired acid/<ammonium> form. Cleavage of its acyl–<nitrogen> bond opens the ring to $\mathrm{HO_2C(CH_2)_3CH(NH_2)Me}$ after suitable neutralization. All five original <cyclopentanone> carbons are retained, and the one methyl <carbon> comes from methyl iodide. A <racemic mixture> product is appropriate to the stereochemically unspecified target. The reaction sequence is an organic ring-expansion synthesis and requires no biological transformation.
\Image[/past-exam-of-the-chemistry-course-of-the-year-3-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-1-q6-beckmann-route.png]
{title=Original carbon-numbered route through the anti oxime and ring-expanded lactam to the amino acid}
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