An insulin analogue comprises a B-chain polypeptide containing the acidic two-residue extension GluB31-GluB32, and optionally an A-chain polypeptide containing acidic substitution GluA8, and additionally optionally a non-standard modification of PheB24. The analogue may also contain additional B-chain substitutions known in the art to enhance the rate of absorption of an insulin analogue formulation following subcutaneous injection or infusion. The analogue may be an analogue of a mammalian insulin, such as human insulin. A nucleic acid encoding such an insulin analogue is also provided. A method of treating a patient comprises administering a physiologically effective amount of the insulin analogue or a physiologically acceptable salt thereof to a patient. The analogue may be administered at a high concentration while maintaining fast-acting properties. A method of semi-synthesis using an unprotected octapeptide by means of modification of an endogenous tryptic site by non-standard amino-acid substitutions.
