Regulator of the tubulin polyglutamylase complex (TPGC) that controls cytoskeletal organization, nuclear shape, and cilium disassembly by balancing microtubule and actin assembly (PubMed:34782749). Regulates the assembly and stability of the TPGC and thereby modulates polyglutamylation of the microtubule, which antagonizes MAP4 binding (PubMed:34782749). Interacts with PCM1 (PubMed:34782749). Interacts with TTLL1, TPGS1, TPGS2 and LRRC49; the interactions link CSTPP1 to the complex TPGC (PubMed:34782749). Binds to alpha-tubulin (PubMed:34782749). Associated with microtubules. Belongs to the CSTPP1 family.