Kinase that can phosphorylate various inositol polyphosphate such as Ins(3,4,5,6)P4 or Ins(1,3,4)P3. Phosphorylates Ins(3,4,5,6)P4 at position 1 to form Ins(1,3,4,5,6)P5. This reaction is thought to have regulatory importance, since Ins(3,4,5,6)P4 is an inhibitor of plasma membrane Ca(2+)-activated Cl(-) channels, while Ins(1,3,4,5,6)P5 is not (By similarity). Also phosphorylates Ins(1,3,4)P3 on O-5 and O-6 to form Ins(1,3,4,6)P4, an essential molecule in the hexakisphosphate (InsP6) pathway (PubMed:9126335). 1D-myo-inositol 3,4,5,6-tetrakisphosphate + ATP = 1D-myo-inositol 1,3,4,5,6-pentakisphosphate + ADP + H(+) 1D-myo-inositol 1,3,4-trisphosphate + ATP = 1D-myo-inositol 1,3,4,5-tetrakisphosphate + ADP + H(+) 1D-myo-inositol 1,3,4-trisphosphate + ATP = 1D-myo-inositol 1,3,4,6-tetrakisphosphate + ADP + H(+) Binds 2 magnesium ions per subunit. Monomer. Expressed in siliques. Low inositol hexakisphosphate (phytate) levels in seed tissue. Belongs to the ITPK1 family.