Catalyzes the carbon skeleton rearrangement of L-glutamate to L-threo-3-methylaspartate ((2S,3S)-3-methylaspartate). (2S,3S)-3-methyl-L-aspartate = L-glutamate kcat is 20.6 sec(-1) for mutase activity with L-glutamate. Amino-acid degradation; L-glutamate degradation via mesaconate pathway; acetate and pyruvate from L-glutamate: step 1/4. Heterotetramer composed of 2 epsilon subunits (GlmE) and 2 sigma subunits (GlmS). GlmE exists as a homodimer and GlmS as a monomer (Probable). Belongs to the methylaspartate mutase GlmE subunit family.