Catalyzes the fifth step in the leucine degradation pathway, the reversible hydration of 3-methylglutaconyl-CoA (3-MG-CoA) to 3- hydroxy-3-methylglutaryl-CoA (HMG-CoA) (PubMed:11738050, PubMed:12434311, PubMed:12655555, PubMed:16640564). Can catalyze the reverse reaction but at a much lower rate in vitro (PubMed:16640564). HMG-CoA is then quickly degraded by another enzyme (such as HMG-CoA lyase) to give acetyl-CoA and acetoacetate (PubMed:16640564). Uses other substrates such as (2E)-glutaconyl-CoA efficiently in vitro, and to a lesser extent 3-methylcrotonyl-CoA (3-methyl-(2E)-butenoyl-CoA), crotonyl-CoA ((2E)-butenoyl-CoA) and 3-hydroxybutanoyl-CoA (the missing carboxylate reduces affinity to the active site) (PubMed:16640564). Originally it was identified as an RNA-binding protein as it binds to AU-rich elements (AREs) in vitro (PubMed:7892223). AREs direct rapid RNA degradation and mRNA deadenylation (PubMed:7892223). Might have itaconyl-CoA hydratase activity, converting itaconyl-CoA into citramalyl-CoA in the C5-dicarboxylate catabolism pathway (PubMed:29056341). The C5-dicarboxylate catabolism pathway is required to detoxify itaconate, an antimicrobial metabolite and immunomodulator produced by macrophages during certain infections, that can act as a vitamin B12-poisoning metabolite (PubMed:29056341). {ECO:0000269|PubMed:11738050, ECO:0000269|PubMed:12434311, ECO:0000269|PubMed:12655555, ECO:0000269|PubMed:16640564, ECO:0000269|PubMed:7892223, ECO:0000303|PubMed:16640564, ECO:0000303|PubMed:29056341}. This is the function of Ensembl gene identifier ENSG00000148090 (AUH, AU RNA binding methylglutaconyl-CoA hydratase).