Free serine kinase that uses ADP to phosphorylate L-serine to yield O-phospho-L-serine and AMP. ADP + L-serine = AMP + H(+) + O-phospho-L-serine kcat is 218 sec(-1) with serine as substrate. kcat is 204 sec(-1) with ADP as substrate. Amino-acid biosynthesis; L-cysteine biosynthesis; L-cysteine from L-serine: step 1/2. Disruption of gene does not lead to complete Cys auxotrophy, but mutant displays a growth defect in an amino acid medium depleted of Cys.