Inositol phosphate kinase with both monophosphoinositol and diphosphoinositol polyphosphate synthase activities. Able to phosphorylate inositol 1,4,5-trisphosphate (Ins(1,4,5)P3) on both the carbon-3 and carbon-6 positions to synthesize inositol 1,3,4,5-tetrakisphosphate (Ins(1,3,4,5)P4) and inositol 1,4,5,6-tetrakisphosphate (Ins(1,4,5,6)P4), and then to subsequently phosphorylate and convert either isomer of InsP4 to inositol 1,3,4,5,6-pentakisphosphate (Ins(1,3,4,5,6)P5). Also converts (Ins(1,3,4,5,6)P5) to InsP6 (Probable). Has also a role in transcription regulation. The catalytic activity is required for PHO gene repression by phosphate and for NCR gene activation in response to nitrogen availability, indicating a role for inositol pyrophosphates in these controls (PubMed:12828642). Inositol polyphosphates may be involved in the regulation of chromatin remodeling of transcription (By similarity). 1D-myo-inositol 1,4,5-trisphosphate + 2 ATP = 1D-myo-inositol 1,3,4,5,6-pentakisphosphate + 2 ADP + 2 H(+) 1D-myo-inositol 1,4,5-trisphosphate + ATP = 1D-myo-inositol 1,4,5,6-tetrakisphosphate + ADP + H(+) 1D-myo-inositol 1,4,5-trisphosphate + ATP = 1D-myo-inositol 1,3,4,5-tetrakisphosphate + ADP + H(+) 1D-myo-inositol 1,4,5,6-tetrakisphosphate + ATP = 1D-myo-inositol 1,3,4,5,6-pentakisphosphate + ADP + H(+) Belongs to the inositol phosphokinase (IPK) family.