Histone methyltransferase. Specifically methylates 'Lys-4' of histone H3, inducing di- and tri-methylation, but not monomethylation. Also methylates 'Lys-5' of histone H4. Plays an important role in transcriptional activation as a member of an RNA polymerase complex. Binds DNA containing 5'-CCCTCC-3' or 5'-GAGGGG-3' sequences. L-lysyl(4)-[histone H3] + 3 S-adenosyl-L-methionine = 3 H(+) + N(6),N(6),N(6)-trimethyl-L-lysyl(4)-[histone H3] + 3 S-adenosyl-L-homocysteine Histone methyltransferase activity strongly stimulated by HSPCA. Interacts with HSPCA. Interacts with HELZ. Interacts with POLR2A; the interaction may be indirect and may be mediated by HELZ. Interacts with HSP90AA1; this interaction enhances SMYD3 histone-lysine N-methyltransferase. Mainly cytoplasmic when cells are arrested at G0/G1. Accumulates in the nucleus at S phase and G2/M. Belongs to the class V-like SAM-binding methyltransferase superfamily. Histone-lysine methyltransferase family.