The present invention is based, in part, on our discovery that EGF can be engineered to generate mutants that bind to the EGF receptor (EGFR) of a cell and that have a desirable effect on the activity of the cell. For example, the mutants can agonize the receptor (i.e., increase a biological activity of the receptor), or antagonize the receptor (i.e., decrease or inhibit a biological activity of the receptor). In turn, the rate at which the cell proliferates, for example, can be changed. Moreover, some of these mutants bind EGFR with a higher affinity than wild-type EGF exhibits. The affinity may increase by about, for example, 2-, 5-, 10-, 15-, 20-, 25-, 30-, 50-, or 100-fold relative to wild-type EGF.