One peptide that comes to mind is the metabolically important reducing tripeptide glutathione — γ-L-Glutamyl-L-cysteinylglycine:
This is synthesized from cysteine, glutamate and glycine by reactions catalysed by glutamate cysteine ligase and glutathione synthase:
Synthesis of glutathione (GSH) — two subunits of glutamate cysteine ligase (GCL) are shown
Other examples may involve amino acids not specified by the genetic code which have particular roles in metabolism. For example, taurine, which has a sulphonic — rather than a carboxylic — acid group, can be metabolized to the dipeptide γ-Glutamyltaurine which may have a role in the brain.
These two examples relate to L-amino acids, albeit with a peptide bond between the side-chain glutamyl carboxyl group rather than the α-carboxyl group. However a D-amino acid dipeptide, D-alanyl-D-alanine, synthesized in the reaction catalysed by D-alanine-D-alanine ligase, is a precursor of bacterial peptidoglycan synthesis.
All the examples given have in common the fact that the peptides are very short (di- or tri-peptides) and can be synthesized in reactions requiring one or two specialized enzymes. Bacterial antibiotics synthesized by the non-ribosomal peptide complex tend to be appreciably larger, requiring repeated formation of peptide bonds.