Catalyzes the phosphorylation of 1D-myo-inositol 1,4,5-trisphosphate (InsP3) into 1D-myo-inositol 1,3,4,5-tetrakisphosphate and participates to the regulation of calcium homeostasis. 1D-myo-inositol 1,4,5-trisphosphate + ATP = 1D-myo-inositol 1,3,4,5-tetrakisphosphate + ADP + H(+) Activated by calcium/calmodulin. Expressed in brain. Belongs to the inositol phosphokinase (IPK) family.