Catalyzes the reversible transfers of an amino group from glutamate to the alpha-ketoacid of the respective amino acid in the final step in the biosynthesis of branchedchain amino acids. The amino acids can be ranked in the following order with respect to their efficiency as amino donor: Leu > Ile > Val. 2-oxoglutarate + L-isoleucine = (S)-3-methyl-2-oxopentanoate + L-glutamate 2-oxoglutarate + L-valine = 3-methyl-2-oxobutanoate + L-glutamate 2-oxoglutarate + L-leucine = 4-methyl-2-oxopentanoate + L-glutamate Inbibited by ammonium sulfate at millimolar concentrations and by O-benzylhydroxylamine (Obe). Amino-acid biosynthesis; L-isoleucine biosynthesis; L-isoleucine from 2-oxobutanoate: step 4/4. Amino-acid biosynthesis; L-leucine biosynthesis; L-leucine from 3-methyl-2-oxobutanoate: step 4/4. Amino-acid biosynthesis; L-valine biosynthesis; L-valine from pyruvate: step 4/4. Homodimer. Belongs to the class-IV pyridoxal-phosphate-dependent aminotransferase family.