Catalyzes the NAD(+)-dependent oxidative deamination of L-alanine to pyruvate, and the reverse reaction, the reductive amination of pyruvate. Its physiological role is not known. Cannot use NADP(+) instead of NAD(+) as a cosubstrate. In the deamination direction, can also efficiently use L-2-aminobutyrate as substrate. In the reductive amination direction, also exhibits high activity with 2-oxobutyrate and oxaloacetate as substrate. In contrast to bacterial homologs, does not exhibit any ornithine cyclodeaminase activity. H2O + L-alanine + NAD(+) = H(+) + NADH + NH4(+) + pyruvate kcat is 6.1 sec(-1) and 9.6 sec(-1) for the oxidative deamination of L-alanine and L-2-aminobutyrate, respectively (at pH 8.5 and 82 degrees Celsius). kcat is 118 sec(-1), 143 sec(-1) and 113 sec(-1) for the reductive amination of pyruvate, 2-oxobutyrate and oxaloacetate, respectively (at pH 8.5 and 82 degrees Celsius). Optimum pH is about 7.0 for both the deamination and amination reactions. Optimum temperature is 82 degrees Celsius for the reductive amination of pyruvate. Retains 30% of its maximum activity at 25 degrees Celsius. Completely loses its activity when incubated at 90 degrees Celsius for 2 hours. The thermostability of the enzyme is increased by more than 10-fold by 1.5 M KCl to a half-life of 55 hours at 90 degrees Celsius. Homodimer. Belongs to the ornithine cyclodeaminase/mu-crystallin family. Archaeal alanine dehydrogenase subfamily.