Mitochondrial glutamate dehydrogenase that catalyzes the conversion of L-glutamate into alpha-ketoglutarate. Plays a key role in glutamine anaplerosis by producing alpha-ketoglutarate, an important intermediate in the tricarboxylic acid cycle (PubMed:11032875, PubMed:11254391, PubMed:16023112, PubMed:16959573). Plays a role in insulin homeostasis (PubMed:11297618, PubMed:9571255). May be involved in learning and memory reactions by increasing the turnover of the excitatory neurotransmitter glutamate (By similarity). {ECO:0000250|UniProtKB:P10860, ECO:0000269|PubMed:11032875, ECO:0000269|PubMed:11254391, ECO:0000269|PubMed:11297618, ECO:0000269|PubMed:16023112, ECO:0000269|PubMed:16959573, ECO:0000269|PubMed:9571255}. This is the function of GLUD1 (glutamate dehydrogenase 1, ENSG00000148672).