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

## Abstract

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.

## Introduction

Homeostatic activities of biological systems are regulated through dynamically concerted assembly and disassembly of biomolecules1,2,3,4,5. This is best exemplified by the circadian clock in cyanobacteria (Kai-clock), which is constituted of three proteins, KaiA, KaiB, and KaiC. These proteins undergo an association–dissociation cycle coupled with phosphorylation–dephosphorylation oscillation of KaiC in the presence of adenosine triphosphate (ATP)6,7. During the circadian cycle, the Kai-clock system generates three forms of complex, two binary KaiAC and KaiBC complexes and one ternary KaiABC complex, at specific clock phases8,9.

KaiA consists of N-terminal domain (residues 1–161, referred to as NA), canonical linker (residues 162–181), and C-terminal domain (residues 182–284, referred to as CA) and forms a homodimer (A2) through cA10,11. KaiB assumes a single thioredoxin domain and forms a homotetramer (B4)12,13. KaiC consists of two domains (CI and CII) and forms a homohexamer (C6) with a double doughnut-like shape14,15,16. The KaiC hexamer can interact with one A2 dimer through the C-terminal tails of CII domains, giving rise to the A2C6 complex17,18,19. The KaiC hexamer can also bind six KaiB molecules, which are arranged in a hexameric ring on the top of the CI domains of C6, forming the B6C6 complex8,20,21. Regarding the ternary KaiA-KaiB-KaiC complex (ABC complex), not only supramolecular architecture but also stoichiometry in the complex have been controversial for a long time22,23,24. Recently, a cryo-EM study revealed the structure of ABC complex (more precisely, A12B6C6 complex) in which six A2 dimers were captured onto the KaiB ring in the B6C6 subcomplex25,26. In that structure, each A2 interacts with one KaiB protomer through one of two dimerized CA domains. Hereafter, CA domains will be termed C1A and C2A depending if it is bound or unbound to KaiB, respectively. In total, 6 C1A and 6 C2A domains were visualized as a ring structure like an Elizabethan collar on the top of B6C6 subcomplex. In contrast, the NA domains were missing in the cryo-EM structure, suggesting that the NA domains could dynamically fluctuate in the A12B6C6 complex. Accordingly, the overall structure of A12B6C6 complex still remained to be completely solved.

The ABC complex is critical in switching from positive to negative feedback in both KaiC phosphorylation and complex formation cycles20,27,28. In addition, previously reported mutational studies indicated that the NA domain is essential for generation of circadian rhythm29,30. Therefore, it is crucially important to solve the overall structure of A12B6C6 complex, including the locations of NA domains.

Small-angle X-ray and neutron scattering (SAXS and SANS) provide overall structural information of supramolecular complex in solution31,32,33 and can potentially be used for investigating a dynamic structure by combination with computational analysis34,35,36. However, there are three issues to be addressed in elucidating the structure of A12B6C6 complex with small-angle scattering. The first is how to eliminate contributions to scattering from undesirable components. The A12B6C6 complex stably exists only in a solution mixture with over-saturation of A2, B4, and B6C6 complex. This means that the sample solution of A12B6C6 complex inevitably includes non-integrated A2, B4, and/or B6C6 complex and their aggregates as undesirable components, which interfere with SAXS measurements. To observe SAXS only from the A12B6C6 complex in the multi-component solution, we utilized SAXS coupled with size-exclusion chromatograph (SEC-SAXS)37,38,39.

The second issue is how to selectively observe the scattering originating from the components of interest in a complex. In the previous works, the structures and dynamics of multi-domain proteins and protein complexes were investigated with SAXS and coarse-grained molecular dynamics (CG-MD) simulations40,41,42. However, a single SAXS profile is not enough to analyze the structure of the large A12B6C6 complex with the fluctuating NA domains and then it is required to edit scattering data focusing on the KaiA protomers in question. For this purpose, we applied inverse contrast-matching SANS (iCM-SANS), which enables selective observation of hydrogenated component(s) within a biomacromolecular complex consisting of hydrogenated and deuterated components by taking advantage of the isotope effect of hydrogen in neutron scattering4,21,33,43,44,45,46. When we measured SANS of the A12B6C6 complex consisting of hydrogenated KaiA (hA), 75%-deuterated forms of KaiB and KaiC (dB and dC) in 100% D2O buffer, we selectively observe the hA protomers in hA12dB6dC6 complex. However, our sample solution also included hA2, dB4, dB6dC6, and their aggregates. To overcome such problems, we recently developed a method based on the combined use of SEC-SANS47,48 with iCM-SANS (SEC-iCM-SANS)49.

The third issue is how to build a three-dimensional structural model and characterize conformational dynamics of the large complex. To address this issue, we developed a method combining computational and experimental approaches. A vast array of computational models of the A12B6C6 complex were generated based on the cryo-EM and X-ray crystallographic structures and subjected to screening based on the SEC-SAXS and SEC-iCM-SANS data. Eventually, selected models were verified through molecular dynamics simulations.

By overcoming these challenges with the state-of-the-art solution scattering techniques, SEC-SAXS and SEC-iCM-SANS, in conjunction with the computational approach, the present study successfully provided information on the overall structure of A12B6C6 complex, highlighting spatial arrangements of the NA domains.

## Results

### Oligomeric state of the ABC complex

On the dephosphorylation process, KaiC hexamer interacts with six KaiBs and six KaiA dimers, thus forms the A12B6C6 complex (Supplementary Fig. 1a)25,26. We established a preparation method of the A12B6C6 complex under over-saturation conditions of A2, B4, and B6C6, thereby overcoming the instability of the ternary complex (see Materials and methods, Supplementary Figs. 1b, 2a). The sample was subsequently subjected to analytical ultracentrifugation (AUC), which confirmed that the major component (p4) was the A12B6C6 complex (Supplementary Fig. 2b and Supplementary Tables 1 and 2). The AUC profile also indicated, however, the presence of minor components, corresponding to the peaks, p1, p2, p3, and p5, in the sample solution. Because these minor components deteriorated the scattering data50, as indicated in the last column (contribution ratio in the forward scattering intensity, t) of Supplementary Table 2, it was essential to exclude them from the solution.

### SEC-SAXS of A12B6C6 complex

SEC-SAXS enables the determination of the SAXS profile of the target molecular species in a multi-component mixture, by immediate measurement after its isolation by the SEC. Using this technique, we could separate the A12B6C6 complex from the minor components (Supplementary Fig. 2c). Figure 1a, b shows the SAXS profile corresponding to the A12B6C6 complex and its Guinier plot. The radius of gyration, $${R}_{{{{{{\rm{g}}}}}}}$$, was calculated to be 69.5 ± 0.2 Å. We also calculated the SAXS profile of the A12B6C6 complex structure solved by cryo-EM25, which is depicted as a green line in Fig. 1a, b and indicates a $${R}_{{{{{{\rm{g}}}}}}}$$ of 55.5 Å. The deviation of the SAXS profile (χ2 = 1195, defined as eq. (S1) in Supplementary note 1) from our experimental profile and the smaller $${R}_{{{{{{\rm{g}}}}}}}$$ were ascribed to the lack of NA domains in the cryo-EM structure. An overall structural model of the A12B6C6 complex, by superimposing the full-length KaiA dimers onto the cryo-EM structure (see the procedure in Supplementary note 2) yielded the cyan line in Fig. 1a, b. The scattering profile became closer to the experimental one but still deviated largely (χ2 = 366). The calculated $${R}_{{{{{{\rm{g}}}}}}}$$ was 62.2 Å, still smaller than that derived from the SEC-SAXS experimental value. This discrepancy is presumably due to dislocation of the NA domains in the A12B6C6 complex in solution.

### SEC-iCM-SANS of A12B6C6 complex

The iCM-SANS technique enables selective observation of hydrogenated components in a complex consisting of hydrogenated and 75%-deuterated components in 100% D2O solution (Supplementary Fig. 3a). We prepared the A12B6C6 complex with hydrogenated KaiA (hA), 75%-deuterated forms of KaiB and KaiC (dB and dC) (designated as hA12dB6dC6 complex), utilizing our established method (Supplementary Fig. 3b and see Supplementary note 3). The sample solution inevitably includes undesirable components, hA2, dB4, dB6dC6-complex and their aggregates. Consequently, we conducted SEC-iCM-SANS, which provided the scattering profile of hA protomers in the hA12dB6dC6 complex in the multi-component solution (Supplementary Fig. 3b).

Figure 1c, d shows a SANS profile of hA12hB6hC6 complex in D2O solution and its Guinier plot after SEC operation (Supplementary Fig. 2d). The SEC-iCM-SANS profile of fully hydrogenated hA12hB6hC6 complex and its $${R}_{{{{{{\rm{g}}}}}}}$$ of 69.9 ± 0.4 Å well agreed with those obtained by the SEC-SAXS measurement of A12B6C6 complex (dotted lines in Fig. 1c, d) as expected. In contrast, the SEC-iCM-SANS profile of hA12dB6dC6 complex in D2O solution (Fig. 1e and Supplementary Fig. 2e) and its Guinier plot (Fig. 1f) were drastically different from those of hA12hB6hC6 complex (Fig. 1c, d). The scattering profile decreased with Q−2, indicating that a scatterer was a disk-like shape based on the classical interruption for a SAS profile31. This observation suggested that the six KaiA dimers were arranged in a doughnut-like shape on top of the B6C6 subcomplex as reported in the cryo-EM study. In addition, its larger $${R}_{{{{{{\rm{g}}}}}}}$$ of 78.1 ± 1.0 Å supported this doughnut-like arrangement.

### A12B6C6 complex modeling

We computationally built three-dimensional models of the overall structure of A12B6C6 complex, which reproduced the SAXS and iCM-SANS profiles. The models obtained were further examined and screened through MD simulations from a viewpoint of stability. Our modeling procedure is described below (Fig. 2).

#### Step 1: Preparation of the initial model

Since the cryo-EM structure (PDB:5n8y) lacks the side-chain information, we built an initial model with crystal structures providing them. There are currently three crystal structures available that can be used to build the structure model of A12B6C6 complex: a KaiC hexamer (C6, PDB code: 3dvl)16, a ternary complex (CA2-B-CIC, PDB code: 5jwr)26 consisting of two C-terminal domains of KaiA dimer (CA2), a KaiB monomer (B) and a CI domain of KaiC (CIC), and a full-length structure of KaiA dimer (A2, PDB code: 1r8j)11. Here, we outline the initial modeling procedure of A12B6C6 (for details, see Supplementary note 2). First, we placed six CA2-B-cIC to C6 by superposing the CIC domain (green) (Supplementary Fig. 4a), thereby modeling the A12B6C6 complex, referred to as Complex 1. Note that Complex 1 does not have any NA domains. Complex 1 well agreed with the previously reported cryo-EM structure (RMSD = 3.9 Å between them). Next, we placed six full-length A2 to Complex 1 by superposing the C1A and C2A domains (Supplementary Fig. 4b). Note that the N1A (blue) and N2A (red) domains are derived from one A2 dimer and connected to the C1A (cyan) and C2A(magenta) domains, respectively (inset of Supplementary Fig. 4b). Finally, we obtained an overall structure model of A12B6C6 complex, referred to as Complex 2. In this structure, each N2A domain (red) structurally overlapped with KaiB (yellow) (Supplementary Fig. 4c), indicating that the A2 dimer undergoes a conformational change in terms of the spatial arrangements of NA domains upon formation of the A12B6C6 complex.

#### Step 2: Generation of the structural candidates

To remove the KaiA-KaiB structural overlap in Complex 2, we systematically altered the positions and orientations of individual N1A and N2A domains belonging to one A2 dimer and gave the same conformation for the remaining five A2 dimer (applying the C6 symmetry around the first axis defined by B6C6). At this stage, we ignored the linkers connecting NA and CA domains to reduce the computational cost. As a result, we obtained ~20 million models of A12B6C6 complex as initial structural candidates (Supplementary Fig. 4d and see Supplementary note 4).

#### Step 3: Selection of models without linkers based on the SAXS and SANS data

We calculated the scattering curve for each of the models for screening based on the criterion of $${\chi }_{{{{{{\rm{SAXS}}}}}}}^{2} \, < \,10.0$$ to the experimental SAXS data. We obtained about 400,000 models from the candidates generated in Step 2. The selected models were classified into three types, i.e., Types 1, 2, and 3, based on the location of the NA domains (Supplementary Fig. 5a). Type 1 holds both N1A (blue) and N2A (red) domains below the reference plane defined by the top plane of KaiB hexameric ring in the B6C6 subcomplex. Type 2 has one of NA domains below the reference plane while the other upper. In Type 3, both N1A and N2A domains are located upper the reference plane. The numbers of models were 331,000, 3000, and 62,000 for Types 1, 2, and 3, respectively.

Next, we evaluated the SAXS-selected models based on the iCM-SANS data as source information on the KaiA protomer conformations in the A12B6C6 complex. We found that only Type 1 gave the small χ2 values ($${\chi }_{{{{{{\rm{SA}}}}}}{{{{{\rm{N}}}}}}{{{{{\rm{S}}}}}}}^{2} \, < \,3.0$$) among the three types (Supplementary Fig. 5b), therefore leaving the Type 1 models as candidates. Thus, the combining of multiple experimental data can compensate their low resolution, underscoring the importance of multilateral evaluation in structural modeling of a huge complex.

Through step 3, we selected 29,809 models with small χ2 values ($${\chi }_{{{{{{\rm{SAXS}}}}}}}^{2} \, < \,6.0$$ and $${\chi }_{{{{{{\rm{SANS}}}}}}}^{2} \, < \,1.5$$) (structures within a white dotted box in Supplementary Fig. 5c) from the set of Type 1. Using the Rosetta program suite51,52, we attempted to complement these models with an NA–CA linker, which was ignored in the previous steps. Consequently, linker modeling was successful for about a quarter of the models (8608). For each of these models, about 100 multiple linker conformations were tested and the best model containing the linkers with the smallest χ2 value for the SAXS data was selected.

#### Step 5: Second selection of models with linkers by SAXS and SANS

We noticed that the linker addition affected their χ2 values for the SAXS and SANS (Supplementary Fig. 5d, e). We then re-evaluated and selected 1550 models for the overall A12B6C6 complex, which met the experimental SAXS and iCM-SANS profiles with $${\chi }_{{{{{{\rm{SAXS}}}}}}}^{2} \, < \,5.0$$ and $${\chi }_{{{{{{\rm{SANS}}}}}}}^{2} \, < \,1.5$$ (models within a white dotted square in Supplementary Fig. 5f).

Here we summarize the structural features of the selected models: although the NA domains occupy variable positions, we attempt to identify common features on positioning with respect to the B6C6 subcomplex. For this purpose, we defined the coordinate as shown in Fig. 3a and examined the positions of the NA domains. The space is divided into cells considering the symmetry of the cryo-EM structure, Complex 1 (for details of the space division and grouping procedure, see Supplementary note 5). The positions of NA domains were classified into two distinct groups: one distributed on the upper (U) rings surrounding Complex 1, and the other one, on the lower (L) ring (Fig. 3a, b). We also found significantly preferred positions for NA domains. In one A2 dimer, when one NA domain was located at the U ring, the other one was always at the lower L ring (Supplementary Fig. 6a). In each ring, two sets of possible positions were available for the NA domain, i.e. U1, U2, L1, and L2. In the U ring, the six NA domains distribute into mutually exclusive locations, U1 (blue spheres) and U2 (green spheres), each of which follows a six-fold symmetry (Supplementary Fig. 6a, b). In the L ring, the six NA domains also distribute into mutually exclusive locations with six-fold symmetry, L1 (red spheres) and L2 (orange spheres) (Supplementary Fig. 6c). In addition, we considered the linker connections between NA and CA domains in one A2 dimer, i.e., N1A–C1A and N2A–C2A (Fig. 3c, d). Taken together, the structural models were classified into eight groups as shown in Fig. 3e–l. In Groups I, II, and III, the N1A and N2A domains in one A2 dimer are located at U1 and L1, respectively. In Group III’, the positions of N1A and N2A domains are swapped from those in Group III, i.e., N1A and N2A are at L1 and U1, respectively. In Groups IV and V, the N1A and N2A domains in one A2 dimer are at U1 and L2, respectively. In Group V’, N1A, and N2A domains are reversely arranged as compared with those in Group V. In Group VI, N1A, and N2A domains are located at U2 and L2, respectively. The A2 dimer exhibits distinct conformations among the different groups as clarified in Fig. 3e–l (surrounded by red line).

In summary, in the L ring, the NA domains tend to be located at L1 or L2 (θ ~ 200 or 220 in Fig. 3 and Supplementary Fig. 6c) with six-fold symmetry. Their positions are between C1A and C2A domains belonging to two adjacent A2, respectively. At the U ring, the NA domains radially sit at the staggered positions with respect to its counterpart NA domains in the L ring. This exclusive rule is true for all the groups except Group VI. The structural features of the eight groups are summarized in Supplementary Table 3.

#### Step 6: Verification by MD simulation

In the screening procedure of Steps 1–5, the protein domains were treated as rigid bodies and only the exclusive volume of the molecules was considered. Thus, we further checked structural stability of the obtained models using MD simulation. As the first quick test for stability, we randomly selected the 384 models with$$\,{\chi }_{{{{{{\rm{SAXS}}}}}}}^{2} < 5.0$$, $${\chi }_{{{{{{\rm{SANS}}}}}}}^{2} < 1.25$$ from the eight groups and performed 10-ns MD simulations. Figure 4a, b shows the relative locations of NA domains with $${\chi }_{{{{{{\rm{SAXS}}}}}}}^{2}$$ after 10 ns. The values of $${\chi }_{{{{{{\rm{SAXS}}}}}}}^{2}$$ are expressed in colors, as green, yellow, and red dots correspond to the structures with$$\,{\chi }_{{{{{{\rm{SAXS}}}}}}}^{2} < 5.0$$,$$\,5.0\le {\chi }_{{{{{{\rm{SAXS}}}}}}}^{2} < 10.0$$ and $$10.0\le {\chi }_{{{{{{\rm{SAXS}}}}}}}^{2}$$, respectively, and no model exceeds 1.5 of $${\chi }_{{{{{{\rm{SANS}}}}}}}^{2}$$ after 10 ns MD simulation. The results clearly indicate that the models belonging to Groups II, III, and III’ maintained$$\,{\chi }_{{{{{{\rm{SAXS}}}}}}}^{2} < 5.0$$ but the model in the other groups yielded larger $${\chi }_{{{{{{\rm{SAXS}}}}}}}^{2}$$. This suggests that the L1 position is more suitable for NA domains than L2. Moreover, Group I did not have any stable model, possibly because the stretching of the linker between C1A and N1A would make the structure unstable (Fig. 3e).

Considering the results above, we extended the simulation for 100 ns on 22 randomly selected models from Groups II, III’, and III that maintained stability during the 10 ns MD simulations. The number of selected models is 13, 4, and 5 for Groups II, III, and III’, respectively. For each model, we recorded trajectories every 20 ps and calculated the SAXS and SANS profiles of the 5000 snapshot structures. The averaged$$\,{\chi }^{2}$$ and $${R}_{{{\rm{g}}}}$$ fits to the SAXS and SANS profiles are shown in Fig. 4c, e are summarized in Table 1. To find the structural models reproducing SAXS and SANS over the simulation time, we marked values with asterisks in Table 1, where two asterisks, one asterisk and no asterisk for$$\,{\chi }^{2}$$ denote $${\chi }^{2} > {\chi }_{0}^{2}\times 1.2$$, $${\chi }_{0}^{2}\times 1.2\ge {\chi }^{2} > {\chi }_{0}^{2}$$, and $${\chi }^{2}\le {\chi }_{0}^{2}$$ ($${\chi }_{0}^{2}$$ = 5.0 for SAXS and $${\chi }_{0}^{2}$$ = 1.5 for SANS), respectively, and they for $${R}_{{{\rm{g}}}}$$ also denote $$|\triangle {R}_{{{{{{\rm{g}}}}}}}| \, > \, 2\times {{{{{\rm{Error}}}}}}$$, $$2\times {{{{{\rm{Error}}}}}}\ge |\triangle {R}_{{{{{{\rm{g}}}}}}}| \, > \, {{{{{\rm{Error}}}}}}$$, and $$|\triangle {R}_{{{{{{\rm{g}}}}}}}|\le {{{{{\rm{Error}}}}}}$$ ($$\triangle {R}_{{{\rm{g}}}}={R}_{{{{{\rm{g}}}}},{{{{{\rm{MD}}}}}}}-{R}_{{{{{\rm{g}}}}},{{\mathrm exp}}}$$), respectively. The structures that best reproduce the averaged scattering profiles are Model II-12 in Group II and Model III-2 in Group III. We further examined the time evolutions of $${\chi }_{{{{{{\rm{SAXS}}}}}}}^{2}$$ and $${\chi }_{{{{{{\rm{SANS}}}}}}}^{2}$$ as shown in Fig. 4d, f. Model II-12 shows that $${\chi }_{{{{{{\rm{SAXS}}}}}}}^{2}$$ and $${\chi }_{{{{{{\rm{SANS}}}}}}}^{2}$$ were initially small but gradually increased (after 50 ns). On the contrary, both $${\chi }_{{{{{{\rm{SAXS}}}}}}}^{2}$$ and $${\chi }_{{{{{{\rm{SANS}}}}}}}^{2}$$ of Model III-2 remained stable for all the 100 ns. In addition, trajectories and root mean square fluctuations (RMSFs) of center of mass (COM) of CA domains of Models II-12 and III-2 are calculated in the 100 ns MD simulations (Supplementary Fig. 7). In Model II-12, four C2A domains (C2-1, C2-3, C2-5, and C2-6) gives RMSFs of over 4.0 Å and the averaged value was also 4.0 Å. On the contrary, Model III-2 has only one C2A domain, which yielded a large fluctuation and then the averaged RMSF for the C2A domains was less than 4.0 Å (3.16 Å). This means if the fluctuation as seen in Model III-12 occurs, the structures of C2A domains would not be determined with a method like cryo-EM analysis. However, the cryo-EM study clearly observed the C2A domains in the A12B6C6 complex. Accordingly, we excluded Model II-12 from the structural candidate.

In conclusion, Model III-2 is considered as the best compromised model, reproducing satisfyingly both the SAXS (Fig. 5a) and SANS (Fig. 5b) data and remaining stable in 100 ns MD simulation. Figure 5c–h and Supplementary Movies 1 and 2 show its structure and dynamic fluctuations.

## Discussion

By integrating the experimental and computational approaches, the structure of the overall A12B6C6 complex was fully described. Although each NA domain could not be stabilized at a fixed position, we found their preferential positions in proposed models. Consequently, we successfully obtained a structural model, Model III-2, which does not only reproduce SEC-SAXS and SEC-iCM-SANS data but also remains structurally stable during the 100 ns-long MD simulation.

Figure 6a shows the spatial fluctuations of KaiA domains of Model III-2 during the 100 ns simulation. Even though the COMs of NA domains are fluctuating, they remain around their initial positions. Furthermore, RMSF of COM of NA and CA domains (Fig. 6b) and overlayed respective images of C6 domain, B6 domain, CA domains and NA domains (Fig. 6c–f) clearly indicate that the NA domains are more mobile than the rest of the A12B6C6 complex. Also, the correlative motions between the NA domains of Model III-2 were examined during the 100 ns MD simulation. In the dynamical cross-correlation maps53 (Supplementary Fig. 8a, b), no clear correlation was observed among the six NA domains at the U ring, indicating that the motions of these domains are not synchronized. Concerning the NA domains at the L ring, only one pair (chains H and F) exhibit moderate correlation, basically indicating the non-synchronous motion of NA domains. All the results indicate the NA domains are randomly fluctuating, explaining why NA domains are invisible in the cryo-EM structure25.

It should be noted that the relative domain arrangement of the A2 in each of our A12B6C6 complex models (including Model III-2) is totally different from that in the crystal structure of A2 alone (PDB code: 1r8j) (Supplementary Fig. 8d, e) because they resolve structural overlap (pointed in Supplementary Fig. 4c). This suggests the possibility that the KaiA dimer structure in solution could undergo large conformational changes compared to that determined by the X-ray crystal analysis. To address this, we performed 500 ns MD simulations of the KaiA dimer in solution starting from the conformations in our A12B6C6 complex models (Mode lII-2) to examine the conformational stability of A2 (see Supplementary note 6). We computed SAXS profiles during the simulations to compare with the experimental one (described in AUC-SAXS of Materials and methods). Surprisingly, the $${\chi }^{2}$$ values were kept relatively small and converged to ~3 after a few hundred nano-second, which were comparable to that for the crystal structure ($${\chi }^{2}$$=1.6) (Supplementary Fig. 8f, g). This suggests that the isolated KaiA dimer exhibits conformational variability in solution, including its crystallographic snapshots and simulated conformers in the A12B6C6 complex. These data suggest the A2 dimer potentially has multiple stable conformations and one of them could make induced fit when binding to the B6C6 complex.

Next, we considered the role of NA domains related with their positions. During the circadian cycle, the KaiC phosphorylation switches the interaction modes with KaiA. Namely, the dephosphorylated C6 does not bind KaiB but interacts with A2 through its C-terminal tails, thereby forming the A2C6 complex (Process 1 in Supplementary Fig. 1)16,54,55. In contrast, the phosphorylated KaiC hexamer can form the B6C6 complex (Process 2 in Supplementary Fig. 1)22,56,57, which subsequently promotes direct binding of the KaiA dimer to the KaiB hexameric ring8,26, giving rise to the A12B6C6 complex (Process 3 in Supplementary Fig. 1)25, which has been characterized in this study. The KaiC dephosphorylation is accelerated in the ABC complex (Process 4 in Supplementary Fig. 1)20,27,28. In the A2C6 complex, a hydrophobic surface close to the dimeric interface of CA domains (a black dot circle in Fig. 7a) accommodates the C-terminal tail of KaiC (a black string in Fig. 7b). This binding surface appears to be exposed to solvent in the cryo-EM structure of A12B6C6 complex, which does not have electron densities of the NA domains (Fig. 7c). Intriguingly, this binding surface is masked by the N1A domain on the U ring in our structural model of the A12B6C6 complex (Model III-2), presumably hindering potential interaction via the KaiC C-terminal tail to form a larger complex (Fig. 7d). This is consistent with the AUC data indicating that the ABC complex did not form any complex larger than A12B6C6 complex (Supplementary Fig. 2b). Our findings provide a structural basis for the mechanism behind the precise circadian rhythm, that the formation of ABC complexes prevents the N1A domains on the U ring from additional interactions with any of the KaiC hexamers in the system, which would lead to infinite elongation of the complex.

During the 10 ns MD simulation, the N2A domains on the L ring traveled around the center between two adjacent CA domains (C1A and C2A domains, Fig. 7e). As each C1A domain bind one KaiB protomer in the B6C6 subcomplex, there exist six vacant spaces between adjacent CA domains (Fig. 3a). That is why the positioning of KaiA protomer in the complex appears unstable. However, the N2A domains of our models can be accommodated in these vacant spaces, which could stabilize the positioning of KaiA protomers.

In summary, we firstly succeeded in delineating the overall structure of A12B6C6 complex by the integration of experimental techniques such as SEC-SAXS, SEC-iCM-SANS, and AUC and computational modeling and simulations. The main issue to be resolved was to locate the NA domains missing in the cryo-EM structure. For this purpose, we used two different sets of scattering data, from SEC-SAXS reflecting the overall shape and from SEC-iCM-SANS extracting the conformational information of KaiA domains for screening the structures generated by the computational modeling. We emphasize that the SEC-iCM-SANS could reject the models, Types 2 and 3, which could not be excluded on the basis of the SAXS data only (Supplementary Fig. 5a). In addition, we demonstrated that MD simulation can be used for further model selection. In fact, the SAXS profiles of Model II-7 gave a small averaged $${\chi }_{{{{{{\rm{SAXS}}}}}}}^{2}$$ value and they were stable during the 100 ns MD simulation (Fig. 4c, d). However, the SANS profiles clearly showed the difference among the models with small $${\chi }_{{{{{{\rm{SANS}}}}}}}^{2}$$ (Fig. 4e, f). For example, the KaiA domains of Model II-7 was conformationally transformed from a six-fold symmetry to a pseudo-3-fold symmetry within a short time (20 ns). This latter conformation could well meet the experimental SAXS profiles but not the iCM-SANS profiles. Thus, this study demonstrates that the integrated approach of modern solution scattering methods, the SAXS and iCM-SANS techniques, and computational modeling and molecular dynamics simulation provide a powerful and generally applicable tool for resolving structures of supramolecular complexes harboring dynamically fluctuating domains/subunits like the KaiABC complex.

## Materials and methods

### Expression and purification of hydrogenated and deuterated Kai proteins

KaiA, KaiB, and KaiC from Synechococcus sp. PCC 7942 were expressed in Escherichia coli. KaiA was cloned into pET-28b according to the literature60. KaiA was expressed as hexahistidine (his)-tagged recombinant protein and purified after the cleavage of the his-tag as described previously45. KaiB was expressed as a glutathione S-transferase (GST)-tagged recombinant protein and purified after the cleavage of the GST-tag as described previously61. KaiC was expressed and purified as a Strep-tagged recombinant protein as described previously9,21. Here, we used the phosphorylation mimic KaiC in which one phosphorylation sites (S431) was substituted with an aspartate residue, because of its high affinity for KaiB.

For preparation of the deuterated proteins, the bacterial cells were grown in M9 minimal media containing glucose as a mixture with varying ratios of isotopically natural and fully deuterated glucose (1,2,3,4,5,6,6-D7, 98%, Cambridge Isotope Laboratories, Inc.), along with varying ratios of H2O and D2O as previously described62.

### Preparation for solution of A12B6C6 complex

We established a two-steps procedure to prepare a fully assembled ABC complex, which was expected to be A12B6C6 complex. In the first step, we produced B6C6 complex by mixing of KaiB and KaiC with the ration of 9:6 in the buffer, 20 mM Tris–HCl buffer (pH 8.0) containing 150 mM NaCl, 5 mM MgCl2, 0.5 mM EDTA, 1 mM DTT, and 1 mM ATP at 10 °C. Then, the BC complex was isolated from the mixture with SEC (Supplementary Fig. 2a). In the second step, oversaturating KaiA was added to the purified solution of B6C6 complex for preparing the A12B6C6 complex: The final mixing molar ratio was [KaiA]:[KaiB]:[KaiC] of 24:12:6 (Supplementary Fig. 2a). The formation of A12B6C6 complex was confirmed with AUC (Supplementary Fig. 2b). We used all hydrogenated Kai proteins in H2O buffer for the SAXS and AUC measurements. On the other hands, for preparing the samples of the SANS experiments, we used the proper combinations of hydrogenated and 75%-deuterated Kai proteins in D2O buffer: For example, to observe the conformations of KaiA domains in A12B6C6 complex, we used the combination of hydrogenated KaiA and 75%-deuterated forms of KaiB and KaiC.

### AUC

Sedimentation velocity-AUC (SV-AUC) measurements were conducted with a ProteomeLab XL-I (Beckman Coulter Inc., Brea, CA, USA). The optical path and the volume of the used cell were 12 mm and 400 μL, respectively. All measurements were performed using Rayleigh interference optics at 60,000 rpm at 30 °C. With this setting, we measured five samples (listed Supplementary Table 1), simple solutions of KaiA, KaiB, and KaiC, binary mixture solution of KaiB and KaiC, and ternary mixture solution of KaiA, KaiB, and KaiC. The first four sample were references and the last one was the sample solution including A12B6C6 complex as expected. The concentrations of the sample solutions of KaiA alone, KaiB alone, KaiC alone, KaiB-KaiC mixture, and KaiA-KaiB-KaiC mixture were 0.5, 0.5, 0.5, 0.6, and 1.0 mg/mL, respectively.

The AUC profile, the weight concentration distribution of particles in a solution c(s20,w), was obtained as a function of sedimentation coefficient by fitting the time evolution sedimentation data with Lamm formula using SEDFIT software (http://www.analyticalultracentrifugation.com/sedfit.htm)63. The sedimentation coefficient was normalized to be the value at 20 °C in pure water, s20,w. In addition, the molecular weight for each component was calculated using the corresponding peak value s20,w and the friction ratio f/f0, which was also provided in the data reduction with SEDFIT (summarized in Supplementary Table 1).

For each component included in the ternary mixture sample, the weight fraction r was calculated from the corresponding peak-area in c(s20,w) and then the contribution ratio t in the forward scattering intensity of SAXS was also estimated from the molecular weight50. The results are listed in Supplementary Table 2.

### SEC-SAXS

SEC-SAXS experiment for the A12B6C6 complex was performed with Photon Factory BL-10C (Tsukuba, Japan) using UPLC ACQUITY (Waters Corp., Milford, MA, USA) integrated with a SAXS setup47. The wavelength of the injected X-ray and the detector were 1.50 Å and PILATUS3 2 M detector, respectively. The sample-to-detector distance were set to 3034.9 mm and then the covered Q-range was from 0.005 to 0.18 Å−1.

In the measurement, the sample solution of 250 μL of 11.7 mg/mL was loaded onto a Superose 6 increase 10/300GL (GE Healthcare, Chicago, IL, USA) pre-equilibrated with the buffer at a flow rate of 0.5 mL/min. During the elution of proteins, the flow rate was reduced to 0.05 mL/min. The SAXS and UV spectra at 280 nm were recoded every 20 and 10 s, respectively. The observed SAXS intensity was corrected for background, empty cell and buffer scatterings, and transmission factors and subsequently converted to the absolute scale using SAngler47. The unit of scattering intensity was converted to the absolute scale by referring to a standard scattering intensity of water at 293 K (1.632 × 10−2 cm−1)64.

There appeared a clear peak corresponding to A12B6C6 complex in the elusion chart (Supplementary Fig. 2c). We selected appropriate time ranges (indicated with the pink zones in Supplementary Fig. 2c) and made the average of the scattering intensities over the time range, where the averaged concentration was 1.02 mg/mL. We obtained the timing-coincident integrated scattering intensities in the Q-range from 0.008 to 0.015 Å−1. (Supplementary Fig. 2c).

### AUC-SAXS

AUC-SAXS experiment for A2 in solution was performed with ProteomeLab XL-I (Beckman Coulter Inc., Brea, CA, USA) and NANOPIX (RIGAKU Co., Ltd., Tokyo, Japan). SV-AUC measurement was carried out using Rayleigh interference optics at 60,000 rpm. The optical path and the volume of the AUC cell were 1.5 mm and 50 μL, respectively. SAXS measurement was conducted with the point-focused generator of a Cu-Kα source (wavelength = 1.54 Å) and HyPix-6000 detector. The sample-to-detector distance were set to 1280 mm and then the covered Q-range was from 0.01 to 0.2 Å−1. We subjected 1.0 mg/mL of KaiA solution to these measurements at 25 °C. AUC-SAXS treatment was conducted to eliminate the effect of aggregates and make the scattering data precise according to the previous report50.

### SEC-iCM-SANS

SEC-iCM-SANS experiments for hA12dB6dC6 and hA12hB6hC6 (as reference) were performed with the SEC system at D22 of the Institut Laue-Langevin (ILL), Grenoble, France. The neutron wavelength and the sample-to-detector distance were set to 6.0 Å and 5600 mm, respectively, and the covered Q-range was from 0.008 to 0.15 Å−1.

In the measurement, the sample solutions of 235 μL with 23.4 mg/mL (ternary mixture of hAdBdC) and 275 μL with 18.9 mg/mL (ternary mixture of hAhBhC) were loaded onto a Superose 6 Increase 10/300GL column (GE Healthcare, Chicago, IL, USA) with the D2O buffer at a flow rate of 0.5 mL/min. During the elution of proteins, the flow rate was reduced to 0.07 mL/min. The SANS data were collected for every 30 s and UV absorbance at 260 nm were recorded every 1 s. The observed SANS intensity was corrected for background, empty cell and buffer scatterings, and transmission factors and subsequently converted to the absolute scale using GRASP software using incident beam flux65. There appeared clear peaks corresponding to A12B6C6 complex in the elusion charts (Supplementary Fig. 2d, e). We selected the time range of FWHM of the peak and made the average of the scattering intensities over the selected time range (indicated with the pink zones in Supplementary Fig. 2d, e), where the averaged concentrations were 1.34 mg/mL and 1.27 mg/mL for the hA12hB6hC6 complex and hA12dB6dC6 complexes, respectively. We obtained the timing-coincident integrated scattering intensities in the Q-range from 0.008 to 0.015 Å−1. (Supplementary Fig. 2d, e).

### MD simulations for model verification

We performed MD simulations with the models that well reproduced the experimental SAXS and SANS profiles to examine whether they existed stably in solution. We performed conventional MD simulations (NVT) at a temperature of 300 K with no restraint using GROMACS66,67,68,69,70,71,72 with the Amber 14SB force field73 and the TIP3P water model74. The temperature was controlled using the V-rescale method75. The Na+ and Cl ions were added to neutralize the system and maintain the salt concentration at 150 mM. The salt concentration was set at the same value as the scattering experiment (see Supplementary Table 4 for other details).

SAXS and iCM-SANS profiles of MD snapshot structures were calculated with CRYSOL76 and CRYSON77. The smearing effect of instrumental resolution on iCM-SANS profile was considered with the resolution provided by GRASP65.

### Dynamical cross-correlation map

The dynamical cross-correlation53 is calculated for the C$${{{{{\rm{\alpha }}}}}}$$ atom pairs in the NA domains during the 100 ns-long MD simulation. The correlation coefficient between ith and jth C$${{{{{\rm{\alpha }}}}}}$$ atoms, whose positions are $${{{{{{\bf{r}}}}}}}_{{{{{{\rm{i}}}}}}}\,$$and $${{{{{{\bf{r}}}}}}}_{j}$$ respectively, is defined as $${c}_{{ij}}/({c}_{{ii}}^{1/2}{c}_{{jj}}^{1/2})$$, where $${c}_{{ij}}=\langle ({{{{{{\bf{r}}}}}}}_{i}-\langle {{{{{{\bf{r}}}}}}}_{i}\rangle )\cdot ({{{{{{\bf{r}}}}}}}_{j}-\langle {{{{{{\bf{r}}}}}}}_{j}\rangle )\rangle$$ and $$\langle \rangle$$ denotes the average during the simulation. Before the calculation, the atoms in each KaiA dimer are structurally aligned by the RMS-fitting so that all the CA2 domains during the simulation overlap each other. In this way, the comparison of the motions of the six KaiA dimers is straightforward. The correlations between upper NA domains and those between lower NA domains are computed (Supplementary Fig. 8a, b).

### Statistics and reproducibility

The fittings for Guinier formula to derive I(0) and Rg were performed with the linear least-square method. The errors were defined as the standard deviation.

### Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.

## Data availablity

The datasets generated and analyzed during the current study are available from the corresponding authors on reasonable request. The SEC-SAXS and SEC-iCM-SANS data are deposited in SASBDB under SASDNJ2 and SASDNK2, respectively58. The 100 ns MD trajectory of the representative model of the A12B6C6 complex (III-2) are deposited in to the Biological Structure Model Archive (BSM-Arc) under BSM-ID BSM0003059.

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## Acknowledgements

SEC-SAXS experiments at Photon Factory were performed under Proposal No. 2017G100 and 2018G680. SEC-iCM-SANS, and iCM-SANS at Institut Laue Langevin were performed under Proposals No. 8-03-854, 8-03-884, 8-03-924, and 8-03-938. Analytical ultracentrifuge and SAXS experiment at Institute for Integrated Radiation and Nuclear Science, Kyoto University (KURNS) were performed under Proposal Numbers, 31006, R2024, and R3063 to H.Y. and R3003 to M.Y.-U. This work was supported by the JSPS Research Fellowship for Young Scientists (to Y.Y. and R.Y.) and the Grants-in-Aid for Scientific Research (Grant Numbers, JP18J21063 to Y.Y., JP18K06101 to A.Mat., JP19K16088 and JP21K15051 to K.M., JP17K07816 to N.S., JP20K06579 and JP19KK0071 to R.I., JP20K22629 to M.Sh., JP18H05229 and JP18H03681 to M.Su., and JP18H05534 to M.Su. and H.K.) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. The study was partially supported by the Platform Project for Supporting Drug Discovery and Life Science Research (Basis for Supporting Innovative Drug Discovery and Life Science Research (BINDS)) from AMED (JP21am0101106, support number 2121) to A.Mat. and H.K. This study was also supported by Joint Research of the Exploratory Research Center on Life and Living Systems (ExCELLS) (ExCELLS program No. 21-408 to K.M., No. 20-326 and 21-315 to M.Su., and No. 20-308 and 21-308 to H.Y.), by Joint Research by Institute for Molecular Science (IMS program No. 19-205, 20-207 and 21-217 to M.Su.), by Research Fund for Young Scientists in Kyoto University (to K.M.) and by Fund for Project Research in KURNS (to Y.Y., K.M., M.Sh., and A.O.). This work was also partially supported by the project for Construction of the basis for the advanced materials science and analytical study by the innovative use of quantum beam and nuclear sciences in KURNS. Computations were carried out at National Institutes for Quantum Science and Technology, at Japan Atomic Energy Agency, and at Tokyo Institute of Technology Global Scientific Information and Computing Center.

## Author information

Authors

### Contributions

This research was designed by H.K., H.Y., K.K., and M.Su. Sample preparation was performed by Y.Y., A.O., R.U., K.T., and H.Y. SEC-SAXS experiment was performed by R.I., M.Y.-U., M.Sh., and M.Su. SEC-iCM-SANS experiments were performed by A.Mar., L.P., N.S., R.Y., T.T., and M.Su. AUC experiment was performed by Y.Y. and K.M. Computational modeling and molecular dynamics simulation were performed by A.Mat. and H.K. Integrative analysis was performed by Y.Y., A.Mat., H.K., H.Y., K.K., and M.Su. All the authors wrote the paper.

### Corresponding authors

Correspondence to Hidetoshi Kono, Hirokazu Yagi, Koichi Kato or Masaaki Sugiyama.

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### Competing interests

The authors declare no competing interests.

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Yunoki, Y., Matsumoto, A., Morishima, K. et al. Overall structure of fully assembled cyanobacterial KaiABC circadian clock complex by an integrated experimental-computational approach. Commun Biol 5, 184 (2022). https://doi.org/10.1038/s42003-022-03143-z

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• DOI: https://doi.org/10.1038/s42003-022-03143-z

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