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A protein repressing GLI's transcription factor activity when SMO signalling is inactive. Upon ligand binding to the upstream receptor PTC (Patched) GLI dissociates from SUFU and activates transcription of hedgehog-target genes. In mammals it consists of SUFU and one of the GLI family proteins.
An example of this is SUFU in human (Q9UMX1) in PMID:24311597 (inferred from direct assay).