The present invention relates to variants of the GAIN domain (G-protein-coupled receptor autoproteolysis-inducing domain) of an adhesion G protein-coupled receptor (ADGRG), such as a GAIN domain variant comprising or consisting of the amino acid sequence of the GAIN domain of ADGRG1 (Adhesion G Protein-Coupled Receptor G1) of SEQ ID NO: 1, wherein (i) one of amino acid positions (3) to (5), preferably amino acid position (4) and one of amino acid positions (47) to (49), preferably amino acid position (48) of SEQ ID NO: 1 are replaced by cysteines, (ii) one of amino acid positions (35) to (37), preferably amino acid position (36) and one of amino acid positions 180 to (182), preferably amino acid position (181) of SEQ ID NO: 1 are replaced by cysteines, (iii) one of amino acid positions (19) to (21), preferably amino acid position 20 and one of amino acid positions (124) to (126), preferably amino acid position (125) of SEQ ID NO: 1 are replaced by cysteines, (iv) one of amino acid positions (56) to (58), preferably amino acid position (57) and one of amino acid positions (65) to (67), preferably amino acid position (66) of SEQ ID NO: 1 are replaced by cysteines, (v) one of amino acid positions (16) to (18), preferably amino acid position (17) and one of amino acid positions (60) to (62), preferably amino acid position (61) of SEQ ID NO: 1 are replaced by cysteines, (vi) the amino acid position at position (40) is replaced by glutamic acid, the amino acid position at position (43) is replaced by leucine and the amino acid position at position (181) is replaced by arginine, (vii) the amino acid position at position (40) is replaced by glutamic acid, the amino acid position at position (43) is replaced by leucine, the amino acid position at position (135) is replaced by arginine and the amino acid position at position (181) is replaced by arginine, (viii) the amino acid position at position (40) is replaced by glutamic acid, the amino acid position at position (43) is replaced by leucine, the amino acid position at position (135) is replaced by arginine, the amino acid position at position (146) is replaced by tyrosine, and the amino acid position at position (181) is replaced by arginine, (ix) the amino acid position at position (33) is replaced by tryptophane, the amino acid position at position (40) is replaced by glutamic acid, the amino acid position at position (43) is replaced by leucine, the amino acid position at position (135) is replaced by arginine, the amino acid position at position (146) is replaced by tyrosine, the amino acid position at position (178) is replaced by tyrosine, the amino acid position at position (181) is replaced by arginine, the amino acid position at position (184) is replaced by glycine, the amino acid position at position (186) is replaced by glutamine, and the amino acid position at position (187) is replaced by glycine, (x) the amino acid position at position (174) is replaced by isoleucine, (xi) the amino acid position at position (218) is replaced by alanine, or (xii) at least two of (i) to (xi) apply; or (B) comprising or consisting of an amino acid sequence sharing at least 80% sequence identity with the variant of (A), provided that the cysteines as defined in (A), item (i), (ii), (iii), (iv) and/or (v), or the amino acid replacement(s) as defined in (A), item (vi), (vii), (viii), (ix), (x) and/or (xi), or the cysteines and/or the amino acid replacement(s) as defined in (A), item (xii) are retained.