Phosphorylates threonine at 'Thr-1823', 'Thr-1833' and 'Thr-2029' in the C-terminal tail region of myosin II heavy chain (mhcA) (By similarity). This phosphorylation is critical in actin-activated ATPase activity of the myosin and regulating the assembly and disassembly of myosin II filament. In vitro, catalytic domain phosphorylates mhcA, myelin basic protein, myosin regulatory light chain, casein and caldesmon. Drives the disassembly of myosin II filaments for efficient cytokinesis and recycling of myosin II that occurs during late cytokinesis. Can be activated in vitro by autophosphorylation. ATP + L-threonyl-[myosin heavy-chain] = ADP + H(+) + O-phospho-L-threonyl-[myosin heavy-chain] Interacts with myosin II heavy chain (mhcA). Localizes to the cortex of interphase cells, cleavage furrow of mitotic cells (at the late stage of cytokinesis), and posterior side of both migrating cells and daughter cells beginning to separate at the very late stage of cytokinesis. Localization is myosin II-dependent. Occasionally displays transient enrichment in pseudopodial extensions as well. Expressed continuously throughout development. Down-regulated by growth on bacteria. Autophosphorylated in vitro. Null cells exhibit excessive aggregation of myosin II filaments in the cleavage furrows and in the posteriors of the daughter cells once cleavage is complete. The cleavage process is slowed down for cells where the gene is disrupted. Myosin II overassembly increases incrementally in the mutants, with the mhkA, mhkB, mhkC triple mutant showing severe myosin II overassembly and myosin II phosphorylation is highly reduced. Overexpression results in multinucleation of cells. Belongs to the protein kinase superfamily. Alpha-type protein kinase family. ALPK subfamily.