Polyglutamylase which modifies tubulin, generating polyglutamate side chains on the gamma-carboxyl group of specific glutamate residues within the C-terminal tail of tubulin. Preferentially mediates ATP-dependent initiation step of the polyglutamylation reaction over the elongation step. Preferentially modifies the alpha-tubulin tail over a beta-tail (By similarity). Required for CCSAP localization to both polyglutamylated spindle and cilia microtubules. Increases the effects of transcriptional coactivator NCOA2/TIF2 in glucocorticoid receptor-mediated repression and induction and in androgen receptor-mediated induction (By similarity). ATP + L-glutamate + L-glutamyl-[protein] = ADP + gamma-L-glutamyl-L-glutamyl-[protein] + H(+) + phosphate (L-glutamyl)(n)-gamma-L-glutamyl-L-glutamyl-[protein] + ATP + L-glutamate = (L-glutamyl)(n+1)-gamma-L-glutamyl-L-glutamyl-[protein] + ADP + H(+) + phosphate Interacts with the transcriptional coactivators NCOA1/SRC-1 and NCOA2/TIF2. Localized to the base of the connecting cilium between the basal body and the adjacent daughter centriole of the cilium. In osteosarcoma cells, found in both cytoplasm and nucleus in the absence of steroid but located exclusively in the nucleus in the presence of steroid. The flexible c-MTBD (cationic microtubule binding domain) region mediates binding to microtubules. It is positively charged and becomes ordered when bound to microtubules: it interacts with a negatively charged patch on tubulin. The presence of positive charges in the c-MTBD region is essential for proper binding. Arg-186 is the main determinant for regioselectivity, which segregates between initiases and elongases in all tubulin--tyrosine ligase family. A glutamine residue at this position is found in elongases TTLL6, TTLL9, TTLL11, TTLL13, TTLL10 and favors glutamate-chain elongation, whereas an arginine residue is found in initiases TTLL2, TTLL4, TTLL5, TTLL3, TTLL8 and favors initiation. Belongs to the tubulin--tyrosine ligase family.