Overall structure of fully assembled cyanobacterial KaiABC circadian clock complex by an integrated experimental-computational approach

In the cyanobacterial circadian clock system, KaiA, KaiB and KaiC periodically assemble into a large complex. Here we determined the overall structure of their fully assembled complex by integrating experimental and computational approaches. Small-angle X-ray and inverse contrast matching small-angle neutron scatterings coupled with size-exclusion chromatography provided constraints to highlight the spatial arrangements of the N-terminal domains of KaiA, which were not resolved in the previous structural analyses. Computationally built 20 million structural models of the complex were screened out utilizing the constrains and then subjected to molecular dynamics simulations to examine their stabilities. The final model suggests that, despite large fluctuation of the KaiA N-terminal domains, their preferential positionings mask the hydrophobic surface of the KaiA C-terminal domains, hindering additional KaiA-KaiC interactions. Thus, our integrative approach provides a useful tool to resolve large complex structures harboring dynamically fluctuating domains.

KaiC, binary mixture (KaiB and KaiC), and ternary mixture (KaiA, KaiB and KaiC) solutions, respectively. The distinct peaks at 2.9 S, 3.6 S, 11.4 S, and 12.4 S on the former four solutions, indicated with broken lines, were assigned to KaiA dimer (A 2 ), KaiB tetramer (B 4 ), KaiC hexamer (C 6 ) and BC complex with 6:6 (B 6 C 6 ), respectively (Supplementary Table 1). In the ternary mixture solution, the distinct and sharp peak at 17.5 S was clearly assigned to A 12 B 6 C 6 complex form its molecular weight as described in Supplementary Table 2. In addition, the other peaks in the profile of the ternary mixture solution indicated that the solution was not mono-dispersed: Peaks around s 20,w =3.5, 14.5, and 19.7 S correspond to the mixture of A 2 and B 4 , the other minor complex with a molecular mass of c.a. 610 kDa, and aggregated object, respectively (See Supplementary Table 2). (c-e) Coincidence display between elution from SEC system, observed scattering intensities, and R g of (c) SAXS of hA 12 hB 6 hC 6 and iCM-SANS of (d) hA 12 hB 6

for SAXS and SANS profiles
To select appropriate atomic models that well reproduced the experimentally obtained scattering profiles, we used  2 value defined as 1 , S1 where was the number of experimental points ; , and were the experimental profile and that computed from an atomic model, respectively; was the experimental error; was a scale factor given by / ; S2 and " " was the offset that accounts for possible systematic errors due to mismatched buffers in the experimental data. The profiles were computed using CRYSOL for SAXS profiles supplementary 1 and CRYSON for SANS profiles supplementary 2 . Smaller values indicated a better fit to the experimental profile but the value less than 1.0 means the over fitting.

Supplementary note 2. Initial modeling of A 12 B 6 C 6 complex
We initially constructed the A12B6C6 complex according to the procedure shown in Supplementary Fig. 4a. In the figure, CI and CII domains (CIC and CIIC) in one of KaiC protomers are highlighted with green and light green, respectively, and the others with grey. The ternary complex CA2-B-CIC (PDB code: 5jwr) is also shown in Supplementary Fig. 4a: C1A (cyan) and C2A (magenta) domains are Cterminal domains of one A2 dimer bound and unbound to KaiB, respectively, and KaiB is colored yellow, and CIC green. We first added the six of cA2-B-cIC to C6 (PDB code: 3dvl) by superposing the CIC domain (green) and then obtained A12B6C6 complex (Complex 1).
The root-mean-square-deviation (RMSD) of heavy atoms between the two CIC domains from 3dvl and 5jwr is about 2.5 Å.
Next, as shown in Supplementary Fig. 4b, we placed six full-length A2 dimers onto Complex 1 by superposing the C1A and C2A domains: N1A (blue) and N2A (red) domains are N-terminal domains of A2 linking to c1A (cyan) and c2A (magenta) domains, respectively. We named this overall structure model of A12B6C6 complex as Complex 2. The RMSD between two sets of superimposed CA portions from the two crystal structures (PDB codes: 5jwr and 1r8j) was about 2.4 Å, suggesting that the quaternary structure of dimeric CA domains is maintained upon binding to KaiB.
There was a problem in Complex 2 that N2A domain (red) heavily overlapped with KaiB (yellow) as shown in Supplementary Fig. 4c, indicating that Complex 2 is not a real structure. The SAXS profile and its Guinier plot of Complex 2 are shown in Fig.1a,b with cyan color, which also indicate discrepancy with the experimental curve.

Supplementary note 3. Inverse Contrast Matching Small-Angle Neutron Scattering (iCM-SANS)
Neutron scattering intensity is proportion to the square of the difference in scattering length density between solute and solvent. Therefore, 75%-deuterated protein is invisible but hydrogenated one is visible in 100% D2O solvent ( Supplementary Fig. 2). In the case of the complex consisting of hydrogenated domain/subunit and 75%-deuterated ones in 100% D2O, SANS allows us to only observes the hydrogenated domain/subunit, this is named as inverse contrast matching SANS (iCM-SANS) supplementary 3-7 .

Supplementary note 4. Modeling of A 12 B 6 C 6 complex without any atomic overlap
In this step, we assumed that the six A2 dimers in A12B6C6 complex adopted the same conformations. This assumption saved computational cost and only two NA domains in one A2 were moved independently. This assumption was liberated in the final step, in which the structural stability was tested by MD simulation. Each N-terminal domain was systematically moved at the interval of 3 Å along the (x, y, z)-axes starting from the position in Complex 2 ( Supplementary Fig. 4d) and was given 72 different orientations (the minimum angular difference between two orientations was about 60 degree: Supplementary Fig. 4d). In this treatment, we regarded the regions from V1 to Q161 in KaiA proteins as N-terminal domains (NA domains) and those from E162 to N181 as linker regions which were not included in this step of the modeling. Instead, the Cα distance between Q161 (the end of NA domain) and L182 (the beginning of C-terminal domain, CA domain) in KaiA was limited less than 60 Å, which is a distance that can be connected with a linker. The linkers were modeled later at step 4. Finally, we obtained 20 million of the models of A12B6C6 complex which did not have any atomic clash.

Supplementary note 5. Grouping of structural models of A 12 B 6 C 6 complex
We examined the 1,550 model structures within the white dotted box in Supplementary Fig. 5f. The spatial coordinates are set for describing C6 sub-complex: an origin and z axis are a center of mass (COM) and a six-fold symmetry axis of C6 sub-complex, respectively, and x and y-axes are set as shown in Fig. 3a and Supplementary Fig. 6c.
Firstly, we investigated the locational distribution of the COMs of NA domains. As shown in Fig. 3b, the COMs clearly distributed on two rings, named as the upper (U) and the lower (L) rings: the averages of radius r and height z of the U ring were (r1, z1) = (91, 72) and those of the L ring were (r2, z2) = (72, 38) in unit of Å. Fig. 3a also shows the relative positions of the two rings for Complex1, of which components are expressed with color spheres.
As mentioned above, two NA domains in one A2 protomer are located on the U and the L rings in a mutually exclusive manner.
Supplementary Fig. 6a also shows the correlated distributions of NA domains between the U and the L rings. There were three pair distributions, U1-L1 (red squares), U1-L2 (orange squares) and U2-L2 (a green square), but no U2-L1 pair. Furthermore, considering the linker connections from N1A to C1A and from N2A to C2A, we classified all structural models of KaiABC complex into eight groups. Fig.   3c,d shows the correlation distribution map of N1A and N2A domains which are connected to C1A (θ=225⁰) and C2A (θ=250⁰), respectively, indicating the locational correlations of the eight groups. The models were classified into eight groups, i.e. Groups I-VI plus Groups III' and V'. In Groups I-VI, the N1A and N2A domains are located on the U and L rings, respectively (Fig. 3c). In contrast, in Groups III' and V', the N1A and N2A domains are located on L and U rings, respectively (Fig. 3d). Fig. 3e-l show the structural features of the eight groups in detail. As shown in Fig. 3e-h, Groups I-III and III' have N1A and N2A domains falling in U1-L1 combination sets. The difference between them is the linker connection between NA and CA domains, as highlighted by blue line surrounding one A2 protomer: For example, the N1A and N2A domains in Group I were located at <U180> and <L260> cells, respectively (for other Groups, see Supplementary Table 3). Again, the locational correlations of N1A and N2A domains between Groups III and III' are opposite. As shown in Fig. 3i-k, Groups IV, V and V' have N1A and N2A domains falling in U1-L2 combination set. Their difference between is also the linker connection between NA and CA domains, as highlighted by blue line surrounding one A2 protomer. Again, the locational correlations of N1A and N2A domains between Groups V and V' are opposite. As shown in Fig. 3l, Group VI has N1A and N2A domains falling in U2-L2 combination sets. The structural features of the eight groups are summarized in Supplementary Table 3.

Supplementary note 6. Comparison of KaiA dimer conformations in crystal, complex and solution
We compared the A2 structure in Model III-2 with the crystal structure of A2 alone (PDB code: 1r8j) and found their considerable difference ( Supplementary Fig. 7d,e). The crystal structure of A2 well reproduced its SAXS profile in solution ( 1.6), indicating that structure of A2 in solution could be quite similar to the crystal structure. This raised a question whether A2 in solution undergoes a conformational change upon complex formation. To address this question, we performed MD simulation of A2 starting from the A2 conformation in Model III-2. Supplementary Fig. 7f shows the time evolution of . Unexpectedly, was dropped to around 2.5 in a short time (~100 ns). Supplementary Fig. 7g compares the experimental SAXS profile with the theoretical profiles computed from the MD-derived model and the crystal structure. These results suggest that the A2 potentially has multiple stable conformations and one of them could make induced fit when binding to the B6C6 complex.