Catalyzes the reversible oxidative deamination of L-glutamate to 2-oxoglutarate and ammonia, thereby playing a key role at the intersection of the carbon and nitrogen metabolic pathways. Is strictly specific for NAD(+)/NADH as the acceptor/donor, since it cannot use NADP(+)/NADPH. May function in vivo in the catabolic direction. Also catalyzes at low rates the oxidative deamination of L-norvaline, L-2-aminobutyrate, L-valine and L-isoleucine, and the reductive amination of 2-oxovalerate and 2-oxobutyrate. H2O + L-glutamate + NAD(+) = 2-oxoglutarate + H(+) + NADH + NH4(+) Is not regulated allosterically. kcat is 17 sec(-1) for oxidative deamination of L-glutamate, and 65 sec(-1) for reductive amination of 2-oxoglutarate (at 50 degrees Celsius). Optimum pH is 10.5 for oxidative deamination, and 9.5 for reductive amination. Retains more than 80% of its activity after incubation for 30 minutes at pH 4.0-10.5. Optimum temperature is 80 degrees Celsius for oxidative deamination. Retains full activity after incubation for 10 minutes at temperatures up to 105 degrees Celsius. Homohexamer. Is constitutively expressed. Belongs to the Glu/Leu/Phe/Val dehydrogenases family.