Data collection and structure determination

X-ray diffraction data were collected on beamline BL44XU at SPring-8 (Harima, Japan). Crystals were mounted at 100 K under a cryostream, and diffraction images were recorded with an MX300-HE (Rayonix) or EIGER X 16M (DECTRIS) detector and processed using HKL2000 (40) and XDSGUI (41). Initial phases were obtained using molecular replacement with previously deposited structures [2GBL (42) or 7DYJ] and MOLREP (43). Refinement and modeling were conducted using Refmac5 (44) and COOT (45), respectively. The crystal structure of KaiC-ST was refined using reflections merged from two crystals that had only a 0.7% difference in lattice sizes (a_crystal1 = 94.7 Å and c_crystal1 = 180.5 Å; a_crystal2 = 94.6 Å and c_crystal2 = 181.8 Å) (table S1). The asymmetric unit for the P6₃ crystal contained a dimer of KaiC-ST and was arranged along a crystallographic threefold axis to form a hexamer. The KaiC-SE and KaiC-SV crystals also belonged to the P6₃ space group. KaiC-pSpT crystallized in the space group P2₁2₁2₁ with a hexamer in the asymmetric unit, whereas KaiC-pST crystallized in the space group P2₁ with two hexamers in the asymmetric unit. Graphic representations were generated using PyMOL (Schrödinger). The statistics for data collection and refinement are listed in table S1.