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