Regulation mechanisms of the dual ATPase in KaiC

Significance KaiC, a core clock protein in the cyanobacterial circadian clock system, hydrolyzes adenosine triphosphate (ATP) at two distinct sites in a slow but ordered manner to measure the circadian timescale. We used biochemical and structural biology techniques to characterize the properties and interplay of dual-adenosine triphosphatase (ATPase) active sites. Our results show that the N-terminal and C-terminal ATPases communicate with each other through an interface between the N-terminal and C-terminal domains in KaiC. The dual-ATPase sites are regulated rhythmically in a concerted or opposing manner dependent on the phase of the circadian clock system, controlling the affinities of KaiC for other clock proteins, KaiA and KaiB.

of KaiC ATPase, the mechanisms of its activation and inactivation remain unknown. In this study, we measured the contributions of C1-ATPase and C2-ATPase separately by introducing amino acid substitutions in KaiC. Then, we attempted to estimate and parameterize the degree to which C1-ATPase is activated and inactivated by the C2 domain. Furthermore, we performed a crystal structure analysis of the activated and inactivated forms of KaiC. Our results suggest that the components (C) Measured rates of ADP production. Gray, white, and hatched bars represent the ATPase activities of full-length KaiCs (contributions from C1 and C2), full-length KaiCs carrying the E318Q substitution (contribution from C1), and truncated KaiCs (KaiC1) consisting solely of the C1 domain (C1-ATPase basal ; C1 basal activity without the C2 domains). ATPase activities were assayed by measuring ADP production for 10 to 16 h. In the case of KaiC-ST (0.20 mg/mL) + KaiA (0.12 mg/mL), data are given as apparent activities estimated by the ADP production for 10 h. The ATPase activities were analyzed using one-way ANOVA (F 4,28 = 2.714, P = 2.30 × 10 À17 ) and the Bonferroni post hoc t test. *Insignificant (P > 0.05/10); **significant (P < 0.005/10); ***significant (P < 0.0005/10). (D) Calculated rates of ADP production in the C1 (C1-ATPase full ; red bars) and C2 domains (C2-ATPase full ; blue bars) of the full-length KaiCs. C1-ATPase full indicates ATPase activity of fulllength KaiCs carrying the E318Q substitution (white bars in C). C2-ATPase full indicates ATPase activity of full-length KaiCs (gray bars in C) minus C1-ATPase full (white bars in C). *Insignificant (P > 0.05): t test of C2-ATPase full . (E) The b values defined as the ratio of C1-ATPase full (red bars in D) to C1-ATPase basal (hatched bars in C) (details are in Eq. 1 and Materials and Methods). The b values were analyzed using one-way ANOVA (F 3,26 = 2.975, P = 3.95 × 10 À17 ) and the Bonferroni post hoc t test. *Insignificant (P > 0.05/6); **significant (P < 0.005/6); ***significant (P < 0.0005/6). (F) Potential correlation between b value and KaiB-KaiC affinity. The fraction of KaiB forming KaiB-KaiC complexes was determined by native PAGE analysis (SI Appendix, Fig. S3A). C1/C2-ATPase and b values for a series of mutants (black circles) are compiled in SI Appendix, Table S3. of the dual ATPase communicate with each other through C1-C2 interaction to control the assembly and disassembly cycle of KaiA and KaiB.

Results
Contributions of C1-and C2-ATPases. The steady-state C1/C2-ATPase activity of fully dephosphorylated KaiC (KaiC-ST) was 13.6 ± 1.4 d À1 at 30°C (gray bars in Fig. 1C). To estimate the contribution of C1-ATPase in full-length KaiC (C1-AT Pase full ), we inactivated the kinase and C2-ATPase by replacing the catalytic glutamate 318 with glutamine (13)(14)(15)(16)22). The resultant KaiC E318Q -ST exhibited a measured activity of 15.8 ± 0.6 d À1 (white bars in Fig. 1C), which was comparable with the activity of KaiC-ST. Given that this measured activity of KaiC E318Q -ST reflects the C1-ATPase full activity of KaiC-ST (red bars in Fig. 1D), the contribution of C2-ATPase full can be estimated as the difference in the measured activities between KaiC-ST and KaiC E318Q -ST, which was as small as À2.2 ± 1.6 d À1 (blue bars in Fig. 1D). On the other hand, the ATPase activity of a truncated KaiC (KaiC1) consisting solely of the C1 domain (11), which reflects the basal activity of the C1-ATPase (C1-ATPase basal ) without the influence of the C2 domain, was 10.4 ± 0.5 d À1 (hatched bars in Fig. 1C).
The regulatory effect of the C2 domain on C1-ATPase full was evaluated using a parameter (b value) defined as the ratio of C1-ATPase full to C1-ATPase basal by the following equation: where C1-ATPase full and C1-ATPase basal correspond to the ATPase activities of full-length KaiC with the E318Q substitution and truncated KaiC consisting solely of the C1 domain, respectively. The b value was 1.52 ± 0.10 for KaiC-ST (Fig.  1E), reflecting the up-regulation of its C1-ATPase by the C2 domain. These results suggest that the C1-ATPase full activity in KaiC-ST is ∼50% up-regulated by the C2 domain (Fig. 1E), while the contribution of the C2-ATPase full in KaiC-ST is negligibly small (Fig. 1D). It must be noted that we did not rely on an alternative strategy of inactivating C1-ATPase by corresponding E77Q/E78Q mutations (13)(14)(15)(16) to estimate the contribution of C2-ATPase, as KaiC E77Q,E78Q -ST and even KaiC1 E77Q,E78Q exhibited residual C1-ATPase activity as high as 3.4 ± 1.4 and 1.9 ± 0.6 d À1 , respectively ( Fig. 1C and SI Appendix, Supplementary Text).
We found that KaiC-AA is rather similar to a KaiAstimulated state of KaiC-ST. KaiA was previously shown to activate the ATPase activity of KaiC (12). Consistent with that study, the addition of KaiA to KaiC-ST resulted in the activation of the dual ATPase. The C1-ATPase full activity of KaiAstimulated KaiC-ST was 18.2 ± 1.7 d À1 (Fig. 1D), and it was ∼80% up-regulated relative to KaiC-ST alone (t test: **significant, P < 0.005/10 in Fig. 1C and b = 1.75 ± 0.18 in Fig.  1E). The contribution of C2-ATPase full in KaiC-ST became very obvious in the presence of KaiA, with enhanced activity of 15.2 ± 1.7 d À1 for the initial 10 h (Fig. 1D). These observations suggest that the KaiA stimulation of C1/C2-ATPase of KaiC-ST is mimicked in KaiC-AA even without KaiA.  Table S2). Dark-colored circles correspond to the mean W1 positions from independent C1-C1 interfaces (pale-colored circles).
Structural Basis for Up-and Down-Regulation of C1-ATPase full .
ATP hydrolysis includes a reaction step in which a lytic water molecule (W1) attacks the phosphorus atom (P γ ) of the terminal γ-phosphate of ATP. Thus, the relative positioning of W1 and P γ is one of the crucial factors determining the reaction efficiency, as reported previously (11). To investigate the W1 position, we sought to crystallize KaiC-AA (SI Appendix, Table  S1) and to compare the results with those for KaiC-ST and KaiC-pSpT, which we previously reported (23). We could identify a reasonable electron density for W1 in all cases ( Fig. 2 A-C and SI Appendix, Table S2), except for KaiC-pSpT. Fortunately, however, another 2.2-Å crystal structure of thermophilic KaiC from Thermosynechococcus elongatus (TeKaiC) was determined in the TeKaiC-pSpT state (SI Appendix, Table S1), with a clear electron density for W1.
In TeKaiC-pSpT ( Fig. 2A), W1 was hydrogen bonded to the carbonyl oxygen atom of F200 and R227 N η (F199 and R226 in KaiC) and sequestered at the position most unfavorable for S N 2-type ATP hydrolysis, with a W1-P γ distance of 5.1 Å and a W1-P γ -O 3β angle of 141° (Fig. 2D). By contrast, W1 was located at a less unfavorable position in KaiC-ST (Fig. 2B), with a shorter W1-P γ distance (4.0 Å) and a larger W1-P γ -O 3β angle (147°) (Fig. 2D). W1 was found in positions more suitable for ATP hydrolysis in KaiC-AA ( Fig. 2 C and D). The descending and ascending orders of the W1-P γ distance and the W1-P γ -O 3β angle (Fig. 2D), respectively, matched the increasing order of the C1-ATPase full activity (KaiC-EE[pSpT] < KaiC-ST < KaiC-AA) ( Fig. 1 C and D). These results confirm that the relative positioning of W1 and P γ is one of the factors impacting up-and down-regulation of C1-ATPase full .
Structural Basis for Up-and Down-Regulation of C2-ATPase full .
The electron densities for W1s involved in C2-ATPase could not be identified in the crystal structures of KaiC-pSpT, TeKaiC-pSpT, KaiC-ST, or KaiC-AA, possibly due to their dynamic nature. On the other hand, we found unique variation patterns in a tunnel-shaped void in the C2-C2 interface (Fig.  3), through which bulk water molecules migrate to the C2-ATPase active site.
In KaiC-ST, the distal side of the γ-phosphate of C2-ATP is stereochemically crowded by several residues (E318, S431, and T432) and consequently, does not have enough space to stably accommodate any water molecules ( Fig. 3 A, Inset). Although a tunnel-shaped void was confirmed near the distal side, it was undulated ( Fig. 3A) and too narrow (Fig. 3D) to freely take up water molecules (radius of ∼1.4 Å) from the inner-radius side of the hexamer. The corresponding water tunnels were not uniform within the KaiC-pSpT hexamer (SI Appendix, Fig. S1), but the shortest one suggests more effective uptake by KaiC-pSpT than by KaiC-ST ( Fig. 3 B and D). By contrast, the distal side of KaiC-AA was more relaxed. A wider straight channel  Fig. S2) are shown by green, blue, magenta, and gray lines, respectively. Note that the diversity of tunnel shapes at each protomer interface is more pronounced in KaiC-pSpT (SI Appendix, Fig. S1). Open circles correspond to the point where the tunnel radius first falls below the radius of a water molecule (1.4 Å; dashed line in D). The traces of KaiC-AA and the A431S/A432T model of KaiC-AA are terminated at the path length of ∼10 Å because their tunnels are shorter by ∼5 Å than those in other KaiCs. In KaiC-ST, the first half of the tunnel is undulated (thick black line in A, Inset) and then narrowed by bottleneck residues down to a radius of ∼0.8 Å, far smaller than the radius of the water molecule. Thus, the tunnel of KaiC-ST is not wide enough to freely take up water molecules from the inner-radius side. By contrast, the tunnel without a bottleneck that exhibits straight extension in KaiC-AA is ready to transfer water molecules from the inner-radius side to the active site of C2-ATPase. The modeling of A431S/A432T using the KaiC-AA template results in a narrowing of the tunnel radius at the path length of around 3 Å, but neither the total length of the tunnel nor the radius near the origin are affected at all.
( Fig. 3C) connected the space in the distal side to the exterior of the hexamer and appeared to allow effective migration of water molecules into the active site of C2-ATPase (Fig. 3D). Furthermore, the side chain of catalytic E318 was positioned at one end of the water tunnel and could immediately activate the migrated water molecules (Fig. 3 C, Inset). The descending and ascending orders of the path length and width of the tunnel-shaped voids, respectively, approximately matched the increasing order of the C2-ATPase full activity (KaiC-ST < KaiC-EE[pSpT] < KaiC-AA) ( Fig. 1 C and D). These observations provide a structural explanation for why C2-ATPase is down-regulated in KaiC-ST but up-regulated in KaiC-EE and KaiC-AA.
To evaluate local effects of the S431A/T432A substitutions that intrinsically reduce the volume of the side chains, we constructed an A431S/A432T model using the main chain structure of KaiC-AA as a template (SI Appendix, Fig. S2). While a partial decrease in the tunnel radius at the path length of around 3 Å was observed (gray line in Fig. 3D), neither the total length of the tunnel nor the radius at the origin were affected at all, and the position where the tunnel radius first became below the radius of the water molecule was sufficiently closer to the origin than that of KaiC-ST and KaiC-pSpT (open circles in Fig. 3D). The efficient uptake of the water molecules into C2-ATP in KaiC-AA can be attributed to the local reduction of the side-chain volume by the dual alanine substitutions and to other nonlocal structural changes that shorten the tunnel length and enlarge the radius around the origin. Quaternary Structural Changes. A region upstream of the dual-phosphorylation sites in the C2 domain called phosphor switch (PSw) (23) adopts coiled and helical conformations in KaiC-pSpT (EE) and KaiC-ST, respectively (Fig. 4A). Our previous study (23) suggested that this fold switch of PSw influences the quaternary structure of the C1 ring through the C1-C2 interface. When superimposed using the C1 domains of KaiC-pSpT and KaiC-ST as references (Fig. 4C), one of the two adjacent C1 domains (right subunit in Fig. 4C) of KaiC-pSpT shifted by ∼1 Å away from the C2 domain, but conversely, the other C1 domain (left subunit in Fig. 4C) shifted toward the C2 domain. These observations indicate that during the helix to coil transition of PSw from KaiC-ST to KaiC-pSpT, every C1 domain gently tilts and then leans over a neighboring C1 domain (Fig. 4C). This tilting and sliding movement causes W1, which is sequestered by F199 and R226 (F200 and R227 in TeKaiC), to move one position further toward the ATP molecule bound to the C1 domain (Figs. 2D and 4E).
PSw of KaiC-AA was found to adopt a loop conformation (Fig. 4A), providing the tunnel-shaped void in the C2-C2 interface to allow uptake of bulk water molecules to the C2-ATPase active site (Fig. 3 C and D). Compared with KaiC-ST, the coiled PSw of KaiC-AA was shifted away from the nearest C2-ATP, similar to what was observed in KaiC-pSpT (Fig. 4A). However, the effects of these PSw shifts on two adjacent α-helices (α 8 and α 7 ) were slightly but notably different between KaiC-AA and KaiC-pSpT. In KaiC-AA, the short helix (α 9 ) located downstream of PSw was shifted to the outerradius side of the hexamer, and the resultant steric hindrance between I433 (α 9 ) and I397 (α 8 ) pushed the N terminus of α 8 toward the C1 direction by ∼1 Å (Fig. 4B). Concomitantly, α 7 placed in parallel to α 8 was pushed in the same direction. The side chain of E357 (α 7 ) was hydrogen bonded to P237 and R218 in the C1 domain, and it was inserted into the C1 side as α 7 changed its orientation. These positional shifts of PSw, α 9 , α 8 , and α 7 in KaiC-AA assist the movement of every C1 domain to the outer-radius side by ∼1 Å (Fig. 4D), finally shifting W1 in every C1-C1 interface into a position more suitable for ATP hydrolysis (Fig. 2D) and thus, further activating C1-ATPase (t test: ***significant, P < 0.0005/6; **significant, P < 0.005/6 in Fig. 1E).
Coiled and shifted PSw also influenced the C-terminal region of KaiC-AA. Amino acids positioned from 488 to 497 form a loop (A loop) (24) in both KaiC-ST and KaiC-pSpT, but the loop is deformed in KaiC-AA to allow its KaiA-binding C terminus (498 to 519) (25) to be more exposed to solvent (Fig. 4A). This observation is consistent with those of previous studies (26,27) that reported a high affinity of KaiA to KaiC-AA, implying that the structure of KaiC-AA reflects the KaiAstimulated or KaiA-postbound state of KaiC-ST. Consistent with the expectation that the A loop is pulled down by KaiA binding to the C terminus of KaiC-ST (24), a key hydrogen bond between G492 and E444 is disrupted in KaiC-AA (Fig. 4A).
Relationship between the Regulatory State of C1-ATPase full and KaiB Affinity. It has been shown that KaiB binds to the C1 domain of KaiC (28)(29)(30), and the affinity and kinetics of the KaiB-KaiC interaction have been investigated in detail (31,32). To evaluate the functional significance of the observed quaternary structural changes of the C1 ring (Fig. 4 C-E), we studied the affinity of KaiC to KaiB with native polyacrylamide gel electrophoresis (PAGE) analyses. A mixture of equimolar amounts of KaiB and KaiC-ST (5 μM on a monomer basis) after incubation at 30°C for 30 h revealed that 50% of KaiB bound to KaiC-ST (>97% dephosphorylation) to form a KaiB-KaiC-ST binary complex (SI Appendix, Fig. S3A). Interestingly, as summarized in Fig. 1F, the KaiB affinity of a series of KaiC mutants revealed a correlation with the b value; the affinity of KaiC for KaiB decreased as the b value increased (SI Appendix, Fig. S3A and Table S3). This correlation suggests that the C1-ring status responsible for KaiB binding switches in the range of b values between ∼1.3 and 1.7. While the b value of KaiC-ST was in the transition region, the affinity of KaiC-AA for KaiB was below the present limit of detection by native PAGE, as reported previously (6,33,34). Astonishingly, as long as the rules for up-and down-regulation are satisfied, KaiC could dramatically switch even from extremely lowaffinity (KaiC-AA) to high-affinity forms (KaiC E357Q -AA). In this context, KaiC-AA is a poor mimic of KaiC-ST in terms of not only structure (Figs. 2 and 3) but also, KaiB binding (Fig.  1F). Our results clearly indicate that the C1-ATPase full of KaiC-ST is not up-regulated enough to completely disrupt the interaction between KaiB and KaiC-ST (Fig. 1F).
The complete disassembly of KaiB from KaiC requires the KaiA-assisted activation of the dual ATPase. Immediately after the addition of KaiA (t = 0 h) to the KaiB-KaiC-ST complex that was preformed for 48 h (black line in Fig. 5A), KaiA was trapped on KaiB interacting with the C1 domain of KaiC-ST and then eluted from a size-exclusion chromatography (SEC) column as the KaiA-KaiB-KaiC-ST ternary complex (t = 0) (Fig. 5A). Within 1.5 h at 30°C, the peak intensity of the ternary complex decreased, whereas that of free KaiB increased (Fig. 5 A, Inset), and the dual-phosphorylation site of KaiC-ST remained unchanged (Fig. 5C). By contrast, more ADP was produced by the KaiA/KaiB/KaiC-ST mixture than by the KaiB/KaiC-ST mixture within 1.5 h, peaking ∼4 h after the KaiA addition (Fig. 5D). A small amount of free KaiA (Fig. 5E and SI Appendix, Fig. S3B) likely binds the C-terminal loop of KaiC-ST and then activates ATPase to disrupt the interaction between KaiB and KaiC-ST (31), as a KaiC mutant (KaiC Δ505 ) lacking the C terminus (506 to 519) (19, 24, 33) was assembled into a KaiA-KaiB-KaiC Δ505 -ST complex that rarely disassembled (Fig. 5B). These results are qualitatively consistent with the earlier observation (35) that KaiB and KaiC-EE are prevented from forming the complex in the presence of an excessive amount of KaiA. Notably, the KaiA-assisted disassembly shown in Fig. 5 has the appearance of an autocatalytic reaction often found in oscillators; a KaiA molecule released from a ternary complex can react with another ternary complex to promote the release of another KaiA molecule (SI Appendix, Fig. S4F).
To examine this hypothesis, we conducted a preliminary mathematical model analysis of the KaiA-assisted disassembly. Our present model provides only a qualitative assessment because it does not take into consideration KaiB rebinding to the KaiC hexamer (SI Appendix, Extended Methods). Nevertheless, important aspects of our experimental observations were reflected by the model when optimized parameter values were used. First, the disassembly of the KaiA-KaiB-KaiC-ST complex preceded the accumulation of phosphorylated KaiC (Fig. 5  A and C and SI Appendix, Fig. S4A). Second, free KaiB accumulated ∼4 h before free KaiA increased (Fig. 5E and SI  Appendix, Fig. S4B). Third, the concentration of the KaiA-KaiC complex peaked at ∼4 h (SI Appendix, Fig. S4A), when the time-dependent increase in KaiC-SpT abundance was maximized (Fig. 5C). Fourth, the present model (SI Appendix, Fig. S4D) successfully predicted the KaiA-dependent acceleration of disassembly and phosphorylation dynamics (SI Appendix, Fig. S4E). Fifth, the KaiA-KaiB-KaiC Δ505 -ST complex, which was rarely disassembled and phosphorylated (Fig.  5B), could be reproduced when the binding rates of KaiA to the C2 domain of KaiC Δ505 -ST were 30-to 50-fold lower than those to the C2 domain of KaiC-ST (SI Appendix, Fig. S4C). These findings qualitatively support the KaiA-assisted and autocatalytic disassembly of the KaiA-KaiB-KaiC-ST complex through the activation of C1/C2-ATPase.
Although our results may emphasize a unidirectional causality from the C2 domain to the C1 domain, we also obtained several clues for an allosteric reversal from the C1 domain to the C2 domain. As listed in SI Appendix, Table S3, the R217A substitution in KaiC1 little affected the C1-ATPase basal activity (9.0 ± 0.6 d À1 with R217A and 10.4 ± 0.5 d À1 without R217A). However, in the full-length KaiC, the effect on the C2-ATPase full activity became pronounced (8.5 ± 1.9 d À1 with R217A and À2.2 ± 1.6 d À1 without R217A). The tendency of the allosteric reversal is further pronounced in the C2-AT Pase full activity under the KaiC-AA background (195 ± 25.7 d À1 with R217A and 5.0 ± 2.9 d À1 without R217A). It is clear that there exists a bidirectional communication between the C1 and C2 domains.
In this context, it would be important to mention the effect of the E318Q mutation, which was systematically introduced to estimate the contribution of the dual-ATPase activities. Selective suppression of C2-ATPase by the E318Q mutation would result in a longer-lived C2 domain in the ATP-bound state. The analysis to separate the C1/C2 contributions is based on the assumption that such a C2-ATP-bound state affects neither the structure nor activity of the C1 domain. While our experimental data indicate that the E318Q substitution has little effect on the overall C1/C2-ATPase activity (Fig. 1C), the long-lived C2-ATP-bound state could have some effects on the structure of the C1 domain.
The present results showed that the properties of KaiC-AA were more similar to those of KaiC-ST stimulated by KaiA than to those of unstimulated KaiC-ST. Even in the absence of KaiA, C1-ATPase full and C2-ATPase full of KaiC-AA were both activated to a similar level as when KaiA was added to KaiC-ST (Fig. 1D). In contrast to KaiC-ST, PSw of KaiC-AA was coiled (Fig. 4A) to form a tunnel-shaped cavity at the C2-C2 interface for bulk water uptake (Fig. 3C), and at the same time, W1 was relocated to a suitable position for ATP hydrolysis (Fig.  2D) by the quaternary structural change of the C1 ring (Fig.  4E). These results suggest that KaiC-AA retains some of the structural and functional features of KaiC-ST stimulated by KaiA.
Assuming that KaiC-AA can be treated as a functional ( Fig.  1 C and D) and structural (Figs. 2D and 3D) mimic of KaiC-ST stimulated by KaiA, we can infer the results of KaiC-ST activation triggered by KaiA by tracing the conformational change from KaiC-ST to KaiC-AA starting from the KaiA binding site (Fig. 6). The folded A loop hooks the KaiAbinding C terminus (498 to 519) of KaiC-ST, which is in a less exposed configuration (Fig. 6A), by a hydrogen bond formed between the main-chain carbonyl oxygen atom of G492 and the main-chain amide of E444 (Fig. 4A). This sequence of events begins with KaiA binding to the C-terminal tail of KaiC-ST (25) and drawing out the A loop located on the N-terminal side of the tail (24) (Fig. 6B). This induces breaking of the hydrogen bond between G492 and E444, as confirmed in KaiC-AA (Fig. 4A). The destabilization of the A loop causes the helix to coil transition of PSw adjacent to the A loop (Fig. 6B). Eventually, the tunnel-shaped void at the C2-C2 interface is expanded, and water molecules are taken up through it to the C2-ATPase active site where E318 and C2-ATP are located (Fig. 3). The effect of the structural change in PSw is not confined to the C2 ring but extends to the C1 ring through the C1-C2 interface. The short α 9 -helix downstream of PSw moves along its helical axis to the outer-radius side of the hexamer, pushing the α 8 -and α 7 -helices up to the C1 side (Fig. 6C). These perturbations cause a change in the quaternary structure of the C1 domain so that the ring structure expands slightly (Fig. 6D); W1 that reacts with C1-ATP is sequestered at the C1-C1 interface via hydrogen bonds between F199 and R226 (F200 and R227 in TeKaiC) and is relocated to a position much more suitable for ATP hydrolysis (C1-ATPase) by the change in the C1-C1 interface.
By contrast, the mechanism of inactivating C1-ATPase will be inferred by tracing the conformational change from KaiC-ST to KaiC-pSpT or to KaiC-pST (23). The helix to coil transition of PSw from KaiC-ST to KaiC-pSpT is coupled to the rearrangement of polar residues constituting electrostatic interactions in the C1-C2 interface (23), which causes the tilt and slide movement of the C1 domains to facilitate the quaternary structural change of the C1 ring (Fig. 4C). This update of the C1-C1 interface results in W1 sequestration at a position much less suitable for C1-ATP hydrolysis (Fig. 4E).
At the same time, it is necessary to mention the possible side effects of the S431A/T432A substitutions. While the changes in the tertiary and quaternary structures (Figs. 3 and 4), as well as the change in the arrangement of W1 (Fig. 2), are intrinsic observations, we cannot rule out the possibility that the expansion of the local cavity around A431/A432 in KaiC-AA is an artificial volume reduction due to the dual alanine substitutions (Fig. 3D). Although not limited to this study, amino acid variants designed from a limited number of 19 choices do not always show ideal behaviors reflecting only the intention of designers and are sometimes accompanied by unexpected side effects due to amino acid substitutions. The validity of our proposal and the need for its update must ultimately be tested by elucidating the complex structure of KaiC-ST and KaiA.
Our results indicate that the activation of dual-KaiC ATPases contributes to a dawn-phase autocatalytic disassembly of the ternary night complexes (Fig. 6 and SI Appendix, Fig.  S4F) and is crucial for resetting subjective night and then pushing the system forward along the unidirectional cycle. Although the structural details of C2-ATPase are still unclear because we were unable to identify the W1s for C2-ATPase, it is simply amazing that it possesses a dynamic range as wide as 0 to 200 d À1 (Fig. 1D and SI Appendix, Table S3). Given that the activity level of C2-ATPase is suppressed to zero in KaiC-ST, its autoinhibitory mechanism and its physiological significance are the next important research targets, which will hopefully lead to a better understanding of the structural and functional roles of the KaiC dual ATPase in the circadian clock system.
All crystals were obtained by the vapor diffusion method as reported previously (23). The TeKaiC-pSpT crystal in the P2 1 2 1 2 1 space group was obtained in solutions containing 80 mM acetic acid and 1.0 M sodium acetate and frozen with 25% (wt/vol) polyethylene glycol 8000. The KaiC-AA crystal in the R3 space group was obtained in solutions containing 100 mM tris(hydroxymethyl)aminomethane (Tris)ÁHCl (pH 7.0), 1 M KCl, 0.8 M sodium/potassium tartrate, 0.95 M sodium acetate, and 5 mM adenylyl-imidodiphosphate.
Data Collection and Structure Determination. Preliminary X-ray diffraction experiments were conducted using FRX-Synergy (RIGAKU), and the final dataset was collected on beamline BL44XU at SPring-8 (Harima, Japan) at 100 K under a cryostream. Diffraction images were recorded with an MX-300HE (Rayonix) or PILATUS (Eiger) detector and processed using the HKL2000 (37) and XDSGUI (38) software. Initial phases were determined by molecular replacement methods using structures previously deposited as 2GBL (39) or 4O0M (40) in Protein Data Bank (PDB) and MOLREP (41). Refmac5 (42) and COOT (43) were used to refine and model the crystal structures, respectively. Graphic representations were drawn using PyMOL (Schr€ odinger). Tunnel-shaped voids were analyzed with a probe radius of 0.6 Å using CAVER 3.0 (44). Statistics of data collection and refinements are listed in SI Appendix, Table S1.
Biochemical Assays of Kai Proteins. The four phosphorylation states of KaiC were detected by sodium dodecyl sulfate-polyacrylamide gel electrophoresis and then quantified by LOUPE software (45). The number of ATP molecules hydrolyzed into ADP molecules per KaiC monomer per unit time was quantified at 30°C as previously described (18,19). The ATPase activities were analyzed using one-way ANOVA and the Bonferroni post hoc t test.
Determination of b Values as a Measure of Up-and Down-Regulation of C1-ATPase full . In this study, the ATPase activity of a truncated KaiC consisting solely of the C1 domain (11) was defined as the basal activity (C1-ATPase basal ) of C1-ATPase. The ATPase activities of full-length KaiC and its mutants, each of which carries the E318Q substitution that inactivates both kinase and C2-ATPase, were measured to estimate the contribution of C1-ATPase (C1-ATPase full ) (SI Appendix, Table S3). The b value was then calculated as the ratio of C1-ATPase full to C1-ATPase basal using Eq. 1. The b values were analyzed using one-way ANOVA and the Bonferroni post hoc t test.
Data Availability. Atomic coordinates and structure factors have been deposited in PDB (ID codes 7DY1 [TeKaiC] and 7DYE [KaiC-AA]). All other data are included in the manuscript and/or SI Appendix.