Abstract: This disclosure provides a composition containing a conjugate with a modified insulin molecule. The conjugate has an insulin molecule, which can be insulin or an insulin analog, glucagon, GLP-1, GLP-2 or a GLP-1 agonist. The conjugate also contains one or more polymers. Each of the one or more polymers is covalently linked to the insulin molecule. Additionally, each of the one or more polymers is covalently linked to between 0 to 50 copies of a decoy ligand, and to between 0 to 50 copies of a glucose-binding agent, such that the combined total number of glucose-binding agents and decoy ligands covalently linked to each of the one or more polymers is at least 1. The conjugate can reversibly bind to soluble glucose and in which the extent of its glucose-binding controls the extent to which the modified insulin is able to bind to and activate the insulin receptor. Methods of making the conjugate, as well as use of the conjugate in treatment, are also provided.