Kinase that can phosphorylate the inositol polyphosphate Ins(1,3,4)P3 to form InsP4. Also phosphorylates a racemic mixture of Ins(1,4,6)P3 and Ins(3,4,6)P3 to form InsP4. Does not display inositol 3,4,5,6-tetrakisphosphate 1-kinase activity, but possesses inositol 1,4,5,6-tetrakisphosphate and inositol 1,3,4,5-tetrakisphosphate isomerase activity (PubMed:17698066). Ins(1,3,4,6)P4 is an essential molecule in the hexakisphosphate (InsP6) pathway (By similarity). 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 roots, leaf vasculature, cauline leaves, flower buds and siliques. Low inositol hexakisphosphate (phytate) levels in seed tissue. Belongs to the ITPK1 family.