An insulin analogue contains one or more modifications at a distinct protein surface comprising one or more of the residues at position B13, B17, A12, A13, and/or A17. Formulations of the above analogues at successive strengths U-100 to U-1000 in soluble solutions a at least pH value in the range 6.8-8.0 either in the presence of zinc ions at a molar ratio of 2.2-10 zinc ions per six insulin analogue monomers or in the presence of fewer than 1 zinc ions per six insulin analogue monomers. Use of the above formulation in an insulin pump functionally integrated with a continuous glucose monitor and computer-based control algorithm as a closed-loop system. A method of treating a patient with diabetes mellitus comprises administering a physiologically effective amount of the insulin analogue to a patient by means of intravenous, intraperitoneal, or subcutaneous injection.
