Disclosed are a family of single-chain polypeptide constructs designed to agonize or mimic members of the TGF-.beta. superfamily by binding to a cell surface receptor complementary to the superfamily member. The single-chain constructs of the invention called "morphons" contain in a single biologically active subunit interacting finger and heel regions which together define a tertiary protein structure complimentary to the ligand binding surface of a receptor that binds a TGF-.beta. superfamily member . Also disclosed are truncated versions of the morphon constructs. Methods are disclosed for making and using single-chain morphons that have binding affinity for predetermined receptors of the TGF-.beta. superfamily.