Catalyzes the phosphorylation of D-erythrulose to D-erythrulose-4P. Involved in the degradation pathways of erythritol and D-threitol, that allow M.smegmatis to grow on these compounds as the sole carbon source. ATP + D-erythrulose = ADP + D-erythrulose 4-phosphate + H(+) kcat is 2.88 sec(-1) with D-erythrulose as substrate. kcat is 0.091 sec(-1) with L-erythrulose as substrate. kcat is 0.063 sec(-1) with dihydroxyacetone as substrate. Carbohydrate metabolism; erythritol degradation. Carbohydrate metabolism; D-threitol degradation. Up-regulated during growth on erythritol, D-threitol or L-threitol relative to growth on glycerol. Cells lacking this gene are defective for growth with D-threitol and are totally unable to grow on erythritol.