Mitochondrial glutamate dehydrogenase that converts L-glutamate into alpha-ketoglutarate (PubMed:20670938). Plays a key role in glutamine anaplerosis by producing alpha-ketoglutarate, an important intermediate in the tricarboxylic acid cycle (By similarity). Plays a role in insulin homeostasis (PubMed:16959573). May be involved in learning and memory reactions by increasing the turnover of the excitatory neurotransmitter glutamate (By similarity). H2O + L-glutamate + NAD(+) = 2-oxoglutarate + H(+) + NADH + NH4(+) H2O + L-glutamate + NADP(+) = 2-oxoglutarate + H(+) + NADPH + NH4(+) Subject to allosteric regulation. Activated by ADP. Inhibited by GTP and ATP. ADP can occupy the NADH binding site and activate the enzyme. Inhibited by SIRT4 (By similarity). Inhibited by HADH (PubMed:20670938). Homohexamer (By similarity). Interacts with HADH; this interaction inhibits the activation of GLUD1 (PubMed:20670938). Mostly translocates into the mitochondria, only a small amount of the protein localizes to the endoplasmic reticulum. Acetylation of Lys-84 is observed in liver mitochondria from fasted mice but not from fed mice. ADP-ribosylated by SIRT4, leading to inactivate glutamate dehydrogenase activity (PubMed:16959573). Stoichiometry shows that ADP-ribosylation occurs in one subunit per catalytically active homohexamer (By similarity). Belongs to the Glu/Leu/Phe/Val dehydrogenases family.