Kinase that has a preference for L-erythrulose, producing L-erythrulose-1P. Involved in the degradation pathway of L-threitol, that allows M.smegmatis to grow on this compound as the sole carbon source. Is also able to phosphorylate D-erythrulose and dihydroxyacetone in vitro. ATP + L-erythrulose = ADP + H(+) + L-erythrulose 1-phosphate kcat is 1.79 sec(-1) with L-erythrulose as substrate. kcat is 1.60 sec(-1) with D-erythrulose as substrate. kcat is 2.12 sec(-1) with dihydroxyacetone as substrate. Carbohydrate metabolism; L-threitol degradation. Slightly up-regulated during growth on L-threitol relative to growth on glycerol. Cells lacking this gene are totally unable to grow on L-threitol. The product of the reaction was originally identified as L-erythrulose 4-phosphate (PubMed:26560079). It was then corrected to L-erythrulose 1-phosphate by the same group (PubMed:26978037).