Involved in the biosynthesis of L-aspartate-beta-semialdehyde which is a central intermediate in the biosynthesis of different amino acids (L-lysine, L-methionine, L-threonine). Catalyzes the phosphorylation of the beta-carboxyl group of L-aspartate to yield 4-phospho-L-aspartate. ATP + L-aspartate = 4-phospho-L-aspartate + ADP Allosterically and strongly feedback inhibited by tryptophan. Addition of lysine alone slightly enhances activity. The simultaneous addition of lysine and tryptophan leads to very strong feedback inhibition of the enzyme. The feedback control by tryptophan is reduced in the presence of the compatible solutes hydroxyectoine or ectoine. Amino-acid biosynthesis; L-lysine biosynthesis via DAP pathway; (S)-tetrahydrodipicolinate from L-aspartate: step 1/4. Amino-acid biosynthesis; L-methionine biosynthesis via de novo pathway; L-homoserine from L-aspartate: step 1/3. Amino-acid biosynthesis; L-threonine biosynthesis; L-threonine from L-aspartate: step 1/5. Belongs to the aspartokinase family.