ARTICLE
DOI: 10.1038/s41467-018-05438-4

OPEN

Revealing circadian mechanisms of integration
and resilience by visualizing clock proteinsworking in real time1234567890():,;

Tetsuya Mori 1, Shogo Sugiyama2, Mark Byrne3, Carl Hirschie Johnson1,4,
Takayuki Uchihashi5 & Toshio Ando 6

The circadian clock proteins KaiA, KaiB, and KaiC reconstitute a remarkable circa-24 hoscillation of KaiC phosphorylation that persists for many days in vitro. Here we use highspeed atomic force microscopy (HS-AFM) to visualize in real time and quantify the dynamic
interactions of KaiA with KaiC on sub-second timescales. KaiA transiently interacts with
KaiC, thereby stimulating KaiC autokinase activity. As KaiC becomes progressively more
phosphorylated, KaiA’s afﬁnity for KaiC weakens, revealing a feedback of KaiC phosphostatus
back onto the KaiA-binding events. These non-equilibrium interactions integrate highfrequency binding and unbinding events, thereby reﬁning the period of the longer term
oscillations. Moreover, this differential afﬁnity phenomenon broadens the range of Kai protein
stoichiometries that allow rhythmicity, explaining how the oscillation is resilient in an in vivo
milieu that includes noise. Therefore, robustness of rhythmicity on a 24-h scale is explainableby molecular events occurring on a scale of sub-seconds.

1 Department of Biological Sciences, Vanderbilt University, Nashville, TN 37235, USA. 2 Department of Physics, College of Science and Engineering, Kanazawa
University, Kanazawa 920-1192, Japan. 3 Department of Chemistry, Physics, and Engineering, Spring Hill College, 4000 Dauphin St., Mobile, AL 36608, USA.
4 Department of Molecular Physiology and Biophysics, Vanderbilt University School of Medicine, Nashville, TN 37232, USA. 5 Department of Physics andStructural Biology Research Center, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan. 6 Nano Life Science Institute (WPI-NanoLSI), Kanazawa
University, Kanazawa 920-1192, Japan. These authors contributed equally: Tetsuya Mori, Shogo Sugiyama. Correspondence and requests for materials
should be addressed to C.H.J. (email: carl.h.johnson@vanderbilt.edu) or to T.U. (email: uchihast@d.phys.nagoya-u.ac.jp)
or to T.A. (email: tando@staff.kanazawa-u.ac.jp)

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NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-05438-4

ircadian rhythms are circa-24 h oscillations in biologicalprocesses that are controlled by an endogenous biochemical pacemaker. The processes coordinated by theseclocks range from gene expression, metabolism, and cell division
to development and behavior1. A key diagnostic property of thesebiological clocks is the robust persistence of the oscillations inconstant conditions (usually DD or LL at constant temperature).
They must be noise resistant to combat the ﬂuctuations ofmolecular components that can affect intracellular oscillators2–4.
Synthetic cellular oscillators often produce distinctly irregularperiodicities under different metabolic conditions5,6 and yet incontrast, circadian clocks are extremely precise2,7. The precisionand resilience of these oscillators (± only a few min per day) is
difﬁcult to explain from biophysical and biochemical perspectives
given their long 24-h timing circuit.
The quintessential example of biochemistry underlying circadian rhythms is the in vitro oscillator composed of the circadianproteins KaiA, KaiB, and KaiC from the model cyanobacterial
system, Synechococcus elongatus8–12. These three proteins plus
ATP reconstitute a circa-24 h rhythm of KaiC phosphorylationthat robustly oscillates in vitro for at least 10 days without
damping13. In addition to using ATP for its autokinase activity,
KaiC hydrolyzes ATP and this reaction is an intrinsicallyconstant-rate timer that drives KaiC phosphorylation and determines the period of the oscillation14,15. The status of KaiC
phosphorylation feeds back to switch the KaiABC nanocomplex
between its autokinase and autophosphatase states11,16,17. The
KaiABC reaction uniquely remains the only circadian oscillator
that has been reconstituted in vitro.
KaiC phosphorylation also oscillates in vivo18,19 with resilience
under different conditions of environment, cell division status,and metabolism4. This remarkable characteristic is crucial for
accurate timekeeping, but difﬁcult to explain because KaiC
phosphorylation in vitro oscillates within an allowed range of Kai
protein stoichiometry9 and the concentrations of Kai proteins arelikely to change under different metabolic/environmental conditions3. The transcription feedback loop is partly responsible formaintaining Kai proteins in appropriate concentrations andstoichiometry4, but a surprisingly broad range of permissive
stoichiometry is also clear from analyses of the in vitro
reaction9,20,21. What is not obvious, however, is the molecularmechanism(s) by which variations in Kai protein stoichiometry/
concentration (that must occur in vivo) are tolerated so thatconsistent rhythmic amplitude and period is produced.
The process of testing a model for the intermolecular synchronization of KaiC phosphostatus in the in vitro KaiABC
reaction22 led us to serendipitously discover dynamic highfrequency interactions between KaiA and KaiC that explain how abroader range of KaiA:KaiC stoichiometry is permissive. This
result is unexpected because KaiA interacts with KaiC hexamers
during the phosphorylation half-cycle phase of the in vitro
oscillator repeatedly on and off on the timescale of fractions ofseconds; this is a timescale that has been ignored in previous
analyses of the KaiABC oscillator because interactions of thisfrequency are not intuitively expected to help explain a biochemical oscillation of circa-24 hours. These single-molecule
methods reveal KaiC-phosphoform dependent differential afﬁnity(PDDA) of KaiA for KaiC. PDDA enables the integration of highfrequency events into oscillations on the circadian timescale.
Moreover, PDDA has broad consequences that were not anticipated by previous modeling and demonstrates an exquisite
interplay of mechanisms that enable oscillatory resilience tochanges in clock protein concentrations that are likely to occur
in vivo3,20. We computationally and experimentally test PDDAconferred resilience by in silico simulations and by biochemical
manipulation of the in vitro KaiABC oscillation. These results2

indicate how a model biochemical oscillator is able to integrate
high-frequency molecular events into a circadian timekeeper inenvironments of ﬂuctuating clock protein levels resulting frommolecular noise.
Results
Differential KaiA–KaiC afﬁnity could stabilize oscillations. A
hypothesis of allosteric control and differential afﬁnity between
KaiA and KaiC was proposed by van Zon and coworkers22 on thebasis of a modeling approach with no speciﬁc experimental
support to explain how KaiC hexamers maintain synchrony inthe population of hexamers over the in vitro oscillation13. Brieﬂy,
they posited a differential afﬁnity of KaiA for individual KaiC
hexamers based on the state of KaiC’s phosphostatus that prevents the hexamers from drifting out of phase with each otherduring the half-cycle when KaiC is phosphorylating (Supplementary Fig. 1a–c)22. We will refer to this phenomenon as KaiC
Phosphoform-Dependent Differential Afﬁnity for KaiA (PDDA).
To ascertain if PDDA can potentially explain synchronization in
the phosphorylation half-cycle, we more fully explored theparameter space of the simpliﬁed van Zon model22, and conﬁrmed that PDDA could stabilize oscillations (Supplementary
Fig. 1d). Additionally, our in silico analyses of the van Zon et al.
model predict only a limited range of variation in PDDA values
that support oscillations; stronger PDDA values can result in
KaiC population dephosphorylation due to insufﬁcient KaiA
association (large α) and PDDA values that are too weak do not
sufﬁciently synchronize the population (small α, Supplementary
Fig. 1d).
KaiA is a critical regulator of the remarkable switch of KaiC
hexamers between autokinase and autophosphatase states12,23–25.
At physiological temperatures, the autophosphatase activity of
KaiC predominates when KaiA is absent. On the other hand,when KaiA is present, the KaiA homo-dimers enhance KaiC’s
autokinase activity by transiently binding to the C-terminal
peptide tentacles of KaiC during the phosphorylation phase18,26,
triggering autophosphorylation of T432 and S431 residues within
the KaiCII ring27,28 (or alternatively, by inhibiting dephosphorylation29). T432 is phosphorylated ﬁrst in the cycle, followed byphosphorylation at S431 (S/T → S/pT → pS/pT)16,30. KaiB binds tohyperphosphorylated KaiC30 and the KaiB•C complex sequesters
KaiA into a stable KaiA•B•C complex where both KaiA and KaiB
are bound to the CI ring of KaiC so that KaiA is no longer
available for stimulation of KaiC autophosphorylation16,25,31.
Sequestration into the stable KaiA•B•C complex thwarts KaiA’s
activity, enabling KaiC’s autophosphatase to take over anddephosphorylation of T432 and S431 proceeds via a phosphotransferase reaction that results in the regeneration of ATP fromthe phosphates at T432/S431 and the ADP bound at the Ploop32,33. The dephosphorylation reaction proceeds (pS/pT → pS/
T → S/T) such that the overall process from the hypo- to thehyper- and back to the hypo-phosphorylated state of KaiC
involves the following stages: S/T → S/pT → pS/pT → pS/T → S/
T16,30. The dephosphoryation half-cycle is characterized as wellby exchange of monomers among the hexamers in the populationof KaiC molecules9,13,34. KaiA sequestration and KaiC monomer
exchange aid inter-hexamer synchrony during the half-cycle inwhich KaiC is dephosphorylating (Supplementary Fig. 1a)4,9,13,16,34–36.
Visualizing KaiC hexamers by single-molecule HS-AFM. To
test the PDDA model of hexamer synchronization during thehalf-cycle when KaiC is phosphorylating22, we set out to measure
the phase-dependent dynamics of interaction of individual
KaiA–KaiC molecules, which occur on the timescale of seconds

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a

–KaiA
0s

+KaiA
4s

8s

12 s

CI
6
nm

CII

4
2

Bare mica

0

b

0s

4s

CII

8s

12 s
nm

10
CI

5

AP-mica
0

c

CI

0s

4s

8s

12 s

10
nm

CII
Bare mica

5
0

d

0s

4s

CII

8s

12 s

10
nm

CI

5

AP-mica0Fig. 1 Orientation-speciﬁc immobilization of KaiCWT and interaction with KaiA. a KaiCWT on bare mica without (middle) and with (right) the addition of
KaiA. b KaiCWT on AP-mica without (middle) and with (right) the addition of KaiA. c KaiC with deletion of C-terminal tentacles (KaiC-ΔC) on bare mica
without (middle) and with (right) the addition of KaiA. d KaiC with deletion of C-terminal tentacles (KaiC-ΔC) on AP-mica without (middle) and with(right) the addition of KaiA. All images shown in the middle and the right columns were acquired at a frame rate of 1 fps and 1.25 fps, respectively. The
images on the right columns are shown every 4 s. Scale bar = 15 nm. Also see Supplementary Movies 1–4

or less9,21,31,37. Among biophysical techniques to study
protein–protein interactions at the single molecule level, highspeed atomic force microscopy (HS-AFM) is unique in its ability
to directly observe individual proteins at submolecular spatial
resolution and sub-100 ms time resolution in physiological solutions38–40 and is therefore ideal for this test. Figure 1 shows thatorientation-speciﬁc immobilization of native wild-type KaiC
hexamers (KaiCWT) was achieved on surfaces of either bare mica
or 3-aminopropyl-trietoxy silane-treated mica (AP-mica). KaiC
bound to AP-mica was available to interact with KaiA (Fig. 1b),but KaiC in the opposite orientation as bound to bare mica did

not interact with KaiA (Fig. 1a), nor was KaiC with deletion of the
C-terminal tentacles able to interact with KaiA (Fig. 1c, d). The
orientation of KaiC binding to bare mica versus AP-mica isprobably due to the major differences in the electrostatic charges
on the opposite poles of KaiC hexamers; in particular, the CI pole
has mostly negative charge, while the CII pole has mostly positive
charge41.
Images of the KaiC hexamers attached to a bare mica surface
showed hexagonal ring-like structures with a pore in the center(Figs. 1a and 2a, c). Based on the crystal structure of KaiC28,41, asimulated AFM image of the N-terminal side of the hexamer

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b

c

0s

3.0 s

3.5 s

6.5 s

7.0 s

10.0 s

0s

3.0 s

3.5 s

6.5 s

7.0 s

10.0 sBare micade

AP-micagfh

AP-micaFig. 2 HS-AFM images of KaiCWT hexamers. a HS-AFM images of native KaiCWT hexamers immobilized on bare mica. Scale bar = 15 nm. b Simulated AFM
image of KaiC (bottom) viewed from the N-terminal side. This construction was made using a hypothetical probe with a radius of 0.5 nm and a cone angleof 10°, as illustrated (top). Scale bar = 5 nm. c Time lapse images of KaiCWT hexamers attached to bare mica, which visualizes the N-terminal side of KaiC
hexamers in the presence of 2 mM Mg2+-ATP. Images were acquired at a frame rate of 2 fps and images taken every 0.5 s are shown. Scale bar = 5 nm.
d HS-AFM image of native KaiCWT hexamers immobilized on AP-mica. Scale bar = 15 nm. e Simulated AFM image of KaiC (bottom) viewed from the Cterminal side. This construction was made using a hypothetical probe with a radius of 0.5 nm and a cone angle of 10°, as illustrated (top). Scale bar = 5 nm.
f Time lapse images of KaiC hexamers attached to AP-mica. The images show the C-terminal side of KaiCWT hexamers in the presence of 2 mM
Mg2+-ATP. Imaging was carried out at a frame rate of 2 fps and images every 0.5 s are shown. Scale bar = 5 nm. g HS-AFM images of KaiC-ΔC hexamers(in which the C-terminal tentacles are truncated), immobilized on bare mica. Scale bar = 15 nm. The insert is an enlarged image (scale bar within insert = 5nm). h Simulated AFM image of KaiC-ΔC (bottom) viewed from the C-terminal side without the tentacles. This construction was made using ahypothetical probe with a radius of 0.5 nm and a cone angle of 10°, as illustrated (top). Also see Supplementary Movies 5–12

(KaiCI) has a pore in the center (Fig. 2b) and matched theobserved AFM image of the KaiC sample attached to bare mica
(Fig. 2a, c). On the other hand, KaiC attached to AP-mica
surfaces had no obvious pore in the center (Figs. 1b, 2d, f). The
simulated AFM image of the C-terminal side of the hexamer(KaiCII) lacked a pore due to the presence of C-terminal tentacles
that obscure the pore (Fig. 2e)28,41 and closely resembles theobserved AFM image of KaiC hexamers attached to an AP-mica
surface (Fig. 2d, f). Moreover, when the C-terminal tentacles aretruncated (KaiC-ΔC), the pore in AP-mica-immobilized KaiC
4

becomes apparent again (Fig. 2g, h). Figures 1 and 2 indicate that
HS-AFM accurately detects the various orientations of KaiC, andthat the N-terminal side of KaiC hexamer selectively attaches to
AP-mica surfaces, thereby exposing the C-terminal tentacles of
the KaiC hexamer (KaiCII) with which KaiA interacts andinﬂuences the conformation of the internal A-loop of
KaiC27,31,42.
Since KaiC forms a hexamer43,44 and exhibits ATPase
activity14,29, changes of conformation and subunit assembly
within KaiC hexamers might be predicted to occur as a result of

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aKaiC-pS/pT(KaiC-DE)

P

P

KaiC
phosphorylation

P

P

KaiC-S/T(KaiC-AA)
S431

KaiC-S/T(KaiC-AA)

T432

KaiC-pS/T(KaiC-DA)

KaiC-S/pT(KaiC-AE)

b
1s

2s

3s

4s

5s

6s

0s

1s

2s

3s

4s

5s

6s

DA

DE

0s

1s

2s

3s

4s

5s

6s

5

AE

0s

nm

10

0
1s

2s

3s

4s

5s

6s

AA
AA

0s

c
DE

100

bound = 0.26 ± 0.05 s(n = 211)
CountsCounts

80
60
40

80

DA

60

bound = 0.43 ± 0.14 s(n = 236)

40

20

20

0

0
0

2

4

6

8

10

0

Dwell time of bound state (s)bound = 1.0 ± 0.15 s(n = 64)

4

6

8

10

AA

bound = ND
(n = 96)

8Counts

8Counts

10

AE

10

2

Dwell time of bound state (s)

6
4

6
4
2

2
0

0
0

2
4
6
8
Dwell time of bound state (s)

10

0

2
4
6
8
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ATP hydrolysis and nucleotide exchange as previously observedby HS-AFM investigations of F1-ATPase45. Indeed, modest
conformational changes due to phosphorylation and ATPhydrolyses have also been reported for the KaiC hexamer15,46.
We monitored hyper- and hypo-phosphorylated KaiC hexamersin the imaging buffer containing Mg2+-ATP continuously ineither the CI end-up (Fig. 2c) or CII end-up (Fig. 2f) orientations.
However, we did not observe distortions of KaiC structure,
conformational changes, or rotational subunit rearrangements
within our observation time windows (Fig. 2c, f). Further highresolution images of KaiC from the CI side conﬁrmed the absenceof rotational changes in conformation (Supplementary Fig. 2).
Perhaps the fact that KaiC has remarkably low rates of (i) ATP
hydrolysis (~90 ATP molecules hydrolyzed per day per KaiC
and(ii)
autokinase/autophosphatasehexamer)14,15
activities18,23,29 means that rotational conformational changes of
KaiC are either too slow or too small to be detected by HS-AFM
within our observation intervals.
KaiA interaction depends upon KaiC phosphostatus. To
explore the dynamics of the interaction of KaiA with KaiC, we
immobilized native KaiC on an AP-mica surface and conﬁrmed
by HS-AFM the CII-up orientation of the hexamers. Then, native
KaiA was added to the imaging solution, after which time an
object (approximately 3.5-nm high) was transiently attracted to
the C-terminal end of KaiC (‘+KaiA’ in Fig. 1b). Several lines ofevidence conﬁrm that this object was KaiA, which is known tointeract with the C-terminal tentacles of KaiC27. As mentioned
above, the bright object did not interact with KaiCWT attached toa bare-mica surface in the CI-up orientation in which the Cterminal tentacles are unavailable for KaiA binding (Fig. 1a), nor
did it interact with a mutated KaiC in which the KaiA-interacting
tentacles are removed (aka KaiC-ΔC, Fig. 1c, d)31,42. Moreover,
non-KaiA proteins such as bovine serum albumin (BSA) or green
ﬂuorescent protein (GFP) did not interact with the KaiCWT
hexamer (Supplementary Fig. 3). Therefore, the interaction is
speciﬁc to KaiA and the tentacles of KaiCIIWT, conﬁrming thatthe bright 3.5-nm high object was KaiA.
Mimics of the various phospho-states of KaiC are a valuable
tool for characterizing the phosphorylation-dependent propertiesof KaiC19,21,24,30,31. HS-AFM measurements show dynamic
KaiA–KaiC interactions at a single-molecule level that vary
among the KaiC phospho-mimics (Fig. 3). The KaiA•KaiC
complex formed frequently and dissociated within seconds formost of the KaiC phospho-mimics (Fig. 3b). (The data of Fig. 3b
also support the conclusion that the phosphorylation state of the
KaiCWT hexamers did not alter the characteristics of KaiCWT
attachment to mica-based surfaces.) To determine the frequencyof the binding reaction between KaiA and KaiC, the dwell timesof the bound state of KaiC (on-event duration) were measured
and are plotted in Fig. 3c. Consistent with the PDDA hypothesis,

mimics of hypo-phosphorylated KaiC (KaiC-AE and KaiC-AA)
bind KaiA for a signiﬁcantly longer time (AE: τbound = 1.00 ±0.15 s, AA: too slow to determine accurately) than mimics ofhyperphosphorylated KaiC (DE: τbound = 0.26 ± 0.05 s, DA:τbound = 0.43 ± 0.14 s, Fig. 3c). When 1 mM ATP was includedin the observation buffer, the τbound values were essentially
identical: τbound for AE = 0.95 ± 0.04 s, DE = 0.31 ± 0.01 s, DA =0.43 ± 0.01 s, and again τbound for AA was too slow to determine
accurately (Supplementary Fig. 4).
Cyclic KaiA–KaiC afﬁnity during the in vitro oscillation. Theτbound values of the KaiC phosphomimics correlate with the circadian phase-dependent changes of KaiCWT phosphostatus(Fig. 3a). Therefore, if the KaiC phosphomimics accurately reﬂect
the various KaiC phospho-states, the data of Fig. 3 predict that
KaiA–KaiCWT afﬁnity should oscillate over the circadian timescale in the in vitro KaiABC reaction due to the oscillation of
KaiC phosphorylation status. In this in vitro oscillator, the three
Kai proteins interact to form phase-dependent complexes9 suchthat during the phosphorylation phase, KaiA•KaiC complexes
and unbound free KaiC hexamers predominate34. To determine
experimentally whether the KaiA-binding afﬁnity to native
KaiCWT changes over the in vitro oscillation, we observed theinteraction of KaiA with KaiCWT samples that had been removed
at different phases from the in vitro reaction and applied to APmica (Fig. 4a). Free KaiA was added to the lawn of immobilized
KaiCWT hexamers to quantify the duration of the transient
KaiA–KaiC interactions. As shown in Fig. 4a (and see also Supplementary Figs. 5-7), the afﬁnity between KaiC and KaiA
reproducibly oscillated in antiphase concert with the KaiC
phosphorylation cycle. KaiCWT from the peak phase of thephosphorylation cycle exhibited a lower average afﬁnity to KaiA(τbound = 0.46 ± 0.02 s at the 24-h timepoint) while KaiCWT fromthe trough phosphorylation phase exhibited a higher average
afﬁnity (τbound = 0.77 ± 0.05 s at 15 h)(Fig. 4a, c, d and Supplementary Fig. 5). These afﬁnity values are averages due to thevarying proportions of KaiCWT phosphostates that are present at
each phase of the in vitro oscillation. There is a strong correlation
between the KaiC phosphorylation state and the mean lifetime of
the KaiA•KaiC complex (Fig. 4b), namely that KaiA dwells for alonger time on unphosphorylated KaiC than on phosphorylated
KaiC, as predicted from the PDDA hypothesis.
KaiC phospho-status affects both koff and kon rates. To reﬁnethe salient characteristics of the hyperphosphorylated versus
hypo-phosphorylated states of KaiC, we compared a KaiCWT
preparation that was 81% phosphorylated with a KaiC preparation that was 27% phosphorylated (Fig. 5). KaiA remains bounddramatically longer to hypo-phosphorylated KaiCWT than to
hyperphosphorylated KaiCWT; the bound-state dwell times(exponential time constant τbound) for hypo-phosphorylated

Fig. 3 KaiC phospho-status modulates the binding afﬁnity of KaiA for KaiC. a Circadian cycling of the phosphorylation state of KaiC. KaiC harbors two
phosphorylation sites: S431 and T432 that undergo the sequential phosphorylation order shown over the circadian cycle16,30, where ‘p’ means the site is
phosphorylated (e.g., ‘S/pT’ means that T432 is phosphorylated, but S431 is not). The phosphomimics for each stage in the phosphorylation cycle areshown in parentheses (e.g., ‘KaiC-AE’ is the phosphomimic for the ‘S/pT’ phosphoform of KaiC). b Various phospho-mimics of KaiC were attached to APmica in the CII-end up (C-terminal-up) orientation. KaiA was added to the observation solution and then the dynamic interaction between KaiA and the
KaiC phospho-mimics was monitored by HS-AFM in the absence of ATP. The following phospho-mimics were used: DE, KaiC-DE (mimic of pS/pT); DA,
KaiC-DA (mimic of pS/T); AE, KaiC-AE (mimic of S/pT), and KaiC-AA (mimic of S/T). Concentration of KaiA, 1 μM. Frame rate, 1 fps. Scale bars = 20 nm.
Also see Supplementary Movies 13–16. c Dwell time analysis for KaiA-bound state of phospho-mimics of KaiC observed by HS-AFM. The AFM images
used in this analysis were captured at 10 fps. Each black solid line overlaid on the corresponding histogram of dwell time was obtained by ﬁtting thehistogram to a ﬁrst order reaction model with a time constant (τbound) shown, except for the case of AA, where the value of τbound could not be determined(ND)
6

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1.0

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

b
Binding lifetime, bound (s)1.0KaiC phosphorylation ratio

Binding lifetime, bound (s)

a

0

12

24

36

r 2 = 0.79

0.8
0.7
0.6
0.5
0.4
0.3
0.2

0.0

0.0

0.9

0.3

48

c

0.5

0.6

0.7

0.8

d
50

15 h

70

24 h

40

bound = 0.77 ± 0.05 s(n = 233)

60

bound = 0.46 ± 0.02 s(n = 212)50

30CountsCounts0.4

KaiC phosphorylation ratio

Time (h)

20

40
30
20

10

10
0

0
0

2
4
6
8
10
Dwell time of bound state (s)

12

0

2
4
6
8
10
Dwell time of bound state (s)12Fig. 4 KaiA’s afﬁnity to KaiC oscillates with the KaiC phosphorylation rhythm in vitro. a KaiA’s bound state lifetime (τbound) depends on KaiCWT
phosphostatus over a 51-h time course of the in vitro cycle of phosphorylation. Puriﬁed KaiA (to a ﬁnal concentration of 1.9 μM) was added to KaiC
immobilized onto AP-mica and dynamics were observed by HS-AFM. See Supplementary Fig. 5 for dwell time data at each phase. Parallel samples werecollected and immunoblotted to conﬁrm KaiC phospho-status (blue) at each timepoint (Supplementary Fig. 6). KaiA–KaiC binding lifetime τbound was
calculated from the bound-state dwell time analysis (red). b Correlation between the extent of KaiC phosphorylation and KaiA’s bound state lifetime(τbound). c, d Dwell time analysis of KaiA’s bound state lifetime c at the peak phase of phosphorylation cycle (24-h timepoint in a) or d at the troughphosphorylation phase (15-h timepoint in a). Dwell time analysis at each time point is shown in Supplementary Fig. 5, and a replicate experiment is shownin Supplementary Fig. 7

versus hyperphosphorylated KaiCWT were 1.12 ± 0.03 s and 0.44
± 0.01 s, respectively (Fig. 5b). We also estimated the unboundstate dwell times (τunbound) from the interval of time in which
KaiC hexamers remain unassociated between consecutive KaiAbinding events (Fig. 5b). Calculated unbound-state dwell times(τunbound) for hypo- and hyperphosphorylated KaiCWT were 5.47
± 0.12 s and 7.90 ± 0.19 s, respectively. Equivalent results wereobtained when the observation buffer contained ATP (Supplementary Fig. 8).
KaiA interactions with hypo- and hyperphosphorylated
KaiCWT (Figs. 4, 5) and hypo-phospho- and hyper-phosphomimic KaiC derivatives (Fig. 3), conclusively demonstrate that
initiation of KaiA–KaiC binding differs as a function of thephosphorylation state of KaiC hexamer (τunbound) and once KaiA
and KaiC are associated, enhanced KaiC phosphorylation
destabilizes the association (τbound). Therefore, the KaiC hexamer
has differential afﬁnity to KaiA depending on its phosphorylation
state. Because KaiA binding to the C-terminal tentacles stimulates
KaiC autokinase activity27,42, these differential KaiA–KaiC
afﬁnities (PDDA) undoubtedly contribute to KaiA-dependent
differences in the rate of KaiC autophosphorylation as a functionof KaiC phospho-status21.
PDDA enhances oscillatory resilience. The consequences ofthese insights into KaiA–KaiC interactions were simulated with aconstrained Monte Carlo model of population hexamer dynamics
that was updated to include phosphoform transitions in each
KaiC protomer (See Supplementary Methods for model details
and parameters). The stochastic simulations simultaneously
include several hundred distinct hexamer states in simple

mathematical matrix form (including bound and unbound statesof KaiC) and these simulations include intrinsic variability in thetransition rates from Monte Carlo reaction probabilities. In
contrast, a continuum ordinary differential equation (ODE)
population model would need to include all the unique KaiC
states of the system explicitly encoded in several hundred coupled
ODEs (including multi-protein complexes) unless additional
assumptions were made to lower the dimensionality of the system. In stochastic simulations PDDA was simulated by directly
varying the relative binding probability of KaiA to KaiC as afunction of KaiC hexamer phosphoform composition, while in
non-PDDA simulations the relative binding probability of KaiA
for KaiC was locked to a ﬁxed value independent of hexamer
composition. The simulations used a pseudo-steady-state calculation of the fraction of KaiA•KaiC complexes that form from a
simple 1:1 binding model, A2+C6↔(A2C6). +PDDA was
implemented by varying the dissociation of KaiA from KaiA•KaiC as a weighted function of the phospho-states based on theτunbound and τbound values (i.e., association rate kon and dissociation rate koff) that were experimentally measured by HSAFM (using the data from the phosphomimics for each phosphostate). Simulations of the KaiA–KaiC interactions indicate that
+PDDA increases the fraction of pS/T states that form as compared with −PDDA, as expected from reduced KaiA binding tohyperphosphorylated states (Supplementary Figs. 9b, 10a).
Intuitively, because KaiA becomes less effective in stimulating
KaiC phosphorylation as the hexamers more closely approach thehyperphosphorylated pS/pT state, the dephosphorylation of
hyperphosphorylated pS/pT to the pS/T phosphoform isfacilitated.

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a
0s

1s

2s

3s

4s

81%-phospho

8

nm

6
4
2
0
0s

1.6 s

3.2 s

4.8 s

6.4 s

27%-phospho

8

nm

6
4
2
0

b

15

45

81%-phospho, unbound stateunbound = 7.90 ± 0.19 s(n = 99)
Counts

5

15

0

0
0
40

10
20
30
40
Dwell time of unbound state (s)

0

50
45

27%-phospho, unbound stateunbound = 5.47 ± 0.12 s(n = 217)2468Dwell time of bound state (s)1027%-phospho, bound statebound = 1.12 ± 0.03 s(n = 285)

30Counts30
Countsbound = 0.44 ± 0.01 s(n = 139)

30

Counts1081%-phospho, bound state

20

15
10

0

0
0

10
20
30
40
Dwell time of unbound state (s)

50

0

2

4
6
8
Dwell time of bound state (s)10Fig. 5 The values of τbound and τunbound depend upon KaiC’s phospho-status. a HS-AFM images of KaiC and KaiA interaction. Native KaiC hexamers(KaiCWT) that were approximately 81% phosphorylated (upper panels) or approximately 27% phosphorylated (lower panels) were immobilized on APmica surfaces and KaiA was added (ﬁnal concentration of 0.4 µM) to the observation buffer. Images were acquired at a frame rate of 1 fps (upper) and 1.25
fps (lower). Brighter spots show KaiA bound to surface-immobilized KaiC. Scale bars = 30 nm. Also see Supplementary Movies 17, 18. b Dwell time
analysis for KaiA-bound and KaiA-unbound states of hyperphosphorylated (81%; top) and hypo-phosphorylated (27%; bottom) KaiC. Each black line
overlaid on the corresponding histogram of dwell time was obtained by ﬁtting the histogram to a ﬁrst order reaction model with a time constant (τbound orτunbound) shown. ‘n’ shown in each graph indicates the number of detected events used for the analysis

Our simulations were ﬁrst directed toward testing thesynchronization effect predicted by van Zon and coworkers22.
Unexpectedly, the magnitude of PDDA that our experiments
veriﬁed did not support the original predictions upon which weoriginally undertook this project. Our HS-AFM measurements
indicated an approximate 10 × change in KaiA kon and koff rates
between hyper- and hypo-phosphorylated KaiC, but the8synchronization effect predicted by van Zon and coworkers intheir modeling study22 suggested that ~100 × −1000 × changes in
PDDA are needed for sustained oscillations (see Supplementary Table 2 of van Zon et al., 2007 and Supplementary Fig. 1d).
Therefore, with our experimentally veriﬁed values, there was onlya slight improvement in hexamer synchrony in the population
when PDDA is included in simulations of either partial reactions

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a

b
2.5
2.0
1.5
0.5
0.0

0

24

48

72

96 120 144 168 192

3.0
2.5
2.0
1.5

c

1.0

–PDDA

1.0
0.8
0.6
0.4
0.2
0.0

[A2]/[C6]

0
1.0
0.8
0.6
0.4
0.2
0.0

24

48

72

3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.1

96
+PDDA

0

24

48
Time (h)

72

96

50

0.5
0.0

0

24

48

72

3.0
2.5
2.0
1.5

–PDDA

40

96 120 144 168 192
Period (h)KaiC phosphorylation (–PDDA & +PDDA)
Ratio of [KaiA2] to [KaiC6]

1.0

KaiC phosphorylation

3.0

+PDDA
30
20

1.0
10

0.5
0.0

0

24

48

72

96 120 144 168 192
Time (h)0012[KaiA2] / [KaiC6]

3

4

Fig. 6 PDDA enhances resilience to variations in Kai protein stoichiometry. a Simulated effect of PDDA on oscillatory consistency. Three examples ofsimulated randomly changing variation of KaiA concentration (green) on KaiC phosphorylation patterns +PDDA (red) versus −PDDA (black).
Concentrations of KaiC and KaiB were held constant as [KaiA] was varied. b Representative KaiC phosphorylation as the ratio of concentrations of KaiA
dimer to KaiC hexamer was varied from the beginning of the time course without subsequent changes in KaiA, KaiB, or KaiC concentrations. Simulations
were performed in the absence of PDDA (−PDDA, top) and with PDDA activated (+PDDA, bottom). The scale of [KaiA]: [KaiC] is shown to the right([A2]/[C6]). In the case of −PDDA, the top two simulations ([A2]/[C6] = 3.0 and 3.5) coincide. c Range of allowed oscillatory regime (dashed verticallines) and estimated oscillatory period as KaiA dimer to KaiC hexamer ratio ([KaiA2]/[KaiC6]) was varied with (+PDDA, red) or without PDDA (−PDDA,
black). Simulations performed as shown in b. Absence of oscillations is indicated as period = 0. Error bars are ±S.D.

or the complete oscillator (Supplementary Figs. 9–11). In thecourse of our simulations; however, we discovered another effectof PDDA that is even more signiﬁcant in terms of the resilience ofthe oscillation under in vivo conditions. In particular, we found
an improvement in allowable [KaiA dimer]:[KaiC hexamer]
stoichiometry. As the concentration of KaiA is changed relative tothat of KaiC (either via random ﬂuctuations or changes in thesteady-state concentration), PDDA allows rhythmicity over abroader range of [KaiA dimer]:[KaiC hexamer] ratios (Fig. 6a).
This happens because PDDA facilitates the transition of KaiC to
the state that binds KaiB, thereby potentiating the formation of
the stable KaiA•B•C complex that inactivates KaiA. Therefore,
excess KaiA is sequestered and inactivated better in the presenceof PDDA. Additionally, within a range of [KaiA dimer]:[KaiC
hexamer] ratios that support rhythmicity for both +PDDA and−PDDA (approximately 0.3–2.6),+PDDA maintains an accurate
period because the transition of KaiC to the KaiB-binding state isfacilitated, so the period remains closer to the typical value of thein vitro reaction (~22 h) than in the case of -PDDA (Fig. 6b, c andSupplementary Fig. 12). A limitation of the current model is a
general tendency for increasing oscillatory periods near the nonoscillatory regime for excess [KaiA dimer]:[KaiC hexamer] ratios.
While phosphorylation proceeds more rapidly with excess KaiA,
additional time is required for sequestration with higher KaiA
concentrations. The model indicates that +PDDA can partiallymitigate this effect by initiating the dephosphorylation phaseearlier.
We explored these predictions of PDDA-enhanced resilienceby further numerical simulations and by in vitro experiments. In
simulations in which [KaiA dimer]:[KaiC hexamer] was alteredby the addition of KaiA to various ﬁnal concentrations, +PDDA
was able to tolerate a larger range of [KaiA dimer]-to-[KaiC

hexamer] ratio in terms of amplitude, waveform, and period.
When [KaiA] was suddenly increased in simulations by theaddition of KaiA to the reaction, the in vitro oscillation continued
in the +PDDA system, but rapidly damped with constantKaiA–KaiC afﬁnity (i.e., see ‘−PDDA’ in Fig. 7b). To conﬁrm thatthe +PDDA simulations can qualitatively predict non-trivial
experimental dynamics under KaiA concentration changes, we
performed an in vitro experiment where stepwise KaiA
concentrations were added to the oscillating system during thedephosphorylation phase as in the simulations (Fig. 7a). Remarkably, we observed that the oscillation indeed continued as
predicted from the +PDDA simulation (compare Fig. 7a with
Fig. 7b). In particular, while the +PDDA step simulations predict
many of the resultant waveform features observed in theexperimental data, the non-PDDA simulations predict both
waveform and period changes that scale with the magnitude of
the KaiA step that were not observed in the experimental data. To
be speciﬁc, non-PDDA predicts (i) a large period lengthening forthe step change of [KaiA2]/[KaiC6] = 1.33 → 2.4, and (ii) a loss ofrhythmicity for the 1.33 → 3.0 step. On the other hand, +PDDA
accurately predicts the minor period and amplitude effects in thesubsequent rhythmicity that were observed experimentally(Fig. 7a, b).
Discussion
Single-molecule assessments of molecular activity in real-timeallow unparalleled insights into the dynamics of proteins in
populations. Coupling HS-AFM with stochastic modeling, thisinvestigation revealed insights into the interactions of circadianclock proteins that promote oscillatory resilience. We report herethat the binding of KaiA to the KaiCII tentacles as well as the

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NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-05438-4ab[A2]/[C6]

KaiC phosphorylation

1.33 →4.1
1.33 →3.0

1.33 → 2.4

1.0

0.5

1.0

1.33 →1.9

0.5

1.33 →1.33

0.0

0.0
0

0

12 24 36 48 60 72 84 96 108 120
Time (h)12 24 36 48 60 72 84 96 108 120
Time (h)cHigh frequency
KaiA-KaiC binding(~10,000 day–1)

On

On

Off

Off

On

Off
S/pT

S/T

KaiA affinity to
KaiC

On

On

Off
pS/pT

Off
pS/T

S/T

KaiC
phosphorylation

Dwell time

KaiB affinity to
KaiC

PDDA decreases
KaiA affinity as KaiC
phosphorylates

PDDA promotes
KaiB binding(less dependent on [KaiA])

KaiA sequestration

Fig. 7 In silico and in vitro tests of PDDA enhancement of resilience. a Experimental conﬁrmation of the simulation’s prediction of the effects of an acute
KaiA concentration increase during the in vitro oscillation. KaiA concentrations were augmented at hour 32 by the addition of a concentrated KaiA solution
to a KaiABC cycling reaction. The traces are vertically offset for clarity. The ordinal scale for each trace is the same as for the control reaction (bottom
trace, black/red). b Simulation of predictions for the experimental test in a, where the ratio of KaiA dimer to KaiC hexamer ([A2]:[C6]) was increased from1.33 to 1.9, 2.4, 3.0 or 4.1 at hour 27. Depicted are KaiC phosphorylation patterns resulting from KaiA steps during the dephosphorylation phase with PDDA(+PDDA, colored traces) as compared to the absence of PDDA (−PDDA, black traces). The [A2]/[C6] values at the far right apply to the experimental
data (a) and the simulations (b). The traces are vertically offset for clarity as in a. c Model of PDDA’s action. During the phosphorylation phase of KaiC (S/T→S/pT→pS/pT), PDDA causes KaiA afﬁnity for KaiC to decrease progressively, resulting in a shorter dwell time. Therefore, KaiC phosphostatus feeds
back upon KaiA/KaiC interaction, changing the pattern of high-frequency KaiA/KaiC binding events and slowing its own rate of phosphoryation. Thisaffects the kD of KaiA-stimulated KaiC phosphorylation, thereby inﬂuencing the period of the oscillation during the phosphorylation half-cycle. Moreover,
PDDA facilitates the pS/pT→pS/T transition (by reducing the pS/T→pS/pT back reaction), enhancing KaiB association and the entry into thedephosphorylation half-cycle. This makes the overall oscillating reaction less sensitive to KaiA:KaiC stoichiometry and thus more resilient to ﬂuctuations of
the concentrations of the Kai proteins. KaiC, green; KaiA, gold; KaiB, purple

duration of the bound state is a function of KaiC phosphostatus.
As shown in Fig. 7c, PDDA progressively decreases the afﬁnity of
the rapid on/off binding of KaiA for the KaiC tentacles as KaiC
hexamers become progressively more phosphorylated. The simple
and intuitive assumption that longer KaiA-binding durations lead10

to an enhanced probability of KaiC phosphorylation thereby
explains why the rate of KaiA-stimulated KaiC autokinase activity
is greater for less highly phosphorylated KaiC hexamers than for
more highly phosphorylated hexamers21. Therefore, PDDA is afeedback mechanism whereby KaiC’s phosphostatus progressively

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modulates the kinetics of KaiA binding, allowing the integrationof high-frequency interactions into longer term timekeeping.
Moreover, PDDA assists this biochemical KaiABC oscillator tokeep accurate timing in environments of ﬂuctuating clock protein
levels resulting from molecular noise.
Our measurements of PDDA and modeling vindicates theprediction of van Zon and coworkers that PDDA of KaiA for
KaiC exists, but we ﬁnd that the mechanistic signiﬁcance of
PDDA is more far-reaching than that suggested by the modelonly approach of van Zon and co-authors22. Their model predicted that synchronization can be achieved in the phosphorylation half-cycle of the KaiABC oscillator by differential KaiA
afﬁnity (PDDA), and this phenomenon allows sustained oscillations (Supplementary Fig. 1). However, the speciﬁc values for
PDDA that are necessary for the magnitude of effects they report
appear to require that the average KaiA–KaiC afﬁnity parameterschange by ~1000 × as a function of KaiC phospho-status (seeSupplementary Table 2 of van Zon et al., 2007 which indicates avariation in the KaiA off-rate of 36 = 729). Our empirical measurements of PDDA by HS-AFM range over approximately 50 ×at best for KaiCWT (Figs. 4, 5). Within the ~50 × range, the effectsof PDDA on inter-hexameric synchronization predicted by van
Zon and coworkers in their allosteric ODE model appear to beminor, based on simulations that include site-dependent phospho-transitions and KaiA sequestration.
However, using a stochastic model incorporating KaiC
phosphosite-dependent KaiA sequestration (see Supplementary
Methods), we ﬁnd that PDDA values based on our experimental
results make the remarkable KaiABC in vitro oscillator resistant
to intrinsic noise that can arise in vivo from transcriptional noise,ﬂuctuating metabolites, cell division, etc.2,3. PDDA allows abroader range of [KaiA2]-to-[KaiC6] stoichiometries as permissive conditions for robust rhythmicities (Fig. 6 and Supplementary Fig. 12). As mentioned above in Results, this phenomenon
happens because PDDA facilitates the transition of free KaiC to
the stable KaiA•B•C complex that sequesters and inactivates
excess KaiA. Therefore, as KaiA or KaiC concentrations in the cell
ﬂuctuate due to intrinsic noise from transcriptional/translational/
degradation or to environmental effects on metabolism/redox,
PDDA enhances resilience by making the system less sensitive toexcess KaiA. Moreover, introducing PDDA into the model brings
the period of the KaiABC oscillator into a shorter, more realistic
period range than that obtained without PDDA (Fig. 6c). Notethat our model incorporates switching of KaiC to the KaiBbinding state in both the pS/T and pS/pT forms (Fig. 7c) because
we are persuaded by phosphomimic data that both the pS/T andpS/pT forms can bind KaiB (i.e., KaiB binds to KaiC-EE and
KaiC-DE)30,31, so we used this parameter set because we believe it
to be more reﬂective of physiological conditions in the cells. On
the other hand, if the more commonly modeled pS/T-only switch
is implemented in our model, then +PDDA can be required forsustained oscillations and more generally enables oscillations ofan appropriate period over a broader range of effective KaiB onrates compared to simulations without PDDA (Supplementary
Fig. 13c, d). This phenomenon is potentially important because
the recent demonstration of slow fold-switching of KaiB introduces a much slower effective rate for the formation of KaiB•KaiC
complexes10. PDDA can potentially compensate for the effective
slow rate of KaiB•KaiC formation correlated with the slow
timescale of KaiB fold-switching by promoting the transition to
the dephosphorylation phase (see Supplementary Methods).
Regarding extrinsic and intrinsic noise in vivo2,3, PDDA provides a satisfying explanation for the excellent resilience of circadian rhythms in cyanobacterial cells undergoing ﬂuctuations in
KaiA:KaiC stoichiometry. For example, we reported robust
rhythms of KaiC phosphorylation from cells in the face ofdramatic variations in KaiC abundance elicited by exposure todiffering light/dark conditions (constant light, light/dark cycles of
12 h light/12 h dark, and light/dark cycles of 2 h light/2 h dark)4.
Moreover, experimental induction of KaiA speciﬁcally uncovereda range of KaiA:KaiC wherein the circadian KaiC phosphoryation
oscillation (and the rhythm of gene expression it controls) tolerated signiﬁcant increases of KaiA abundance4. These observations are the in vivo correlate of the simulations and experimental
manipulations described here (Figs. 6, 7). Generally, PDDA aids
nonlinearity in the KaiA-sequestration oscillatory system bypushing the system during the beginning of the phosphorylation
half-cycle and releasing (inactivating KaiA by sequestration) at
the end of the half-cycle when the phosphorylation peak isreached. This effect is analogous to the variation in the speed of apendulum as it transitions from maximum speed at the nadir of
the path to zero speed at the turning point (maximum excursion).
How do transient, rapid interactions (~1 s) between KaiA and
KaiC confer resilience to a 24-h oscillation? The phosphorylation
status of the central KaiC clock protein is the key for the KaiABC
system, but note that phosphorylation is a general property ofclock proteins in all organisms and resilience is crucial for all
circadian oscillators. KaiA promotes the autophosphorylation of
KaiC, but on average many KaiA-binding/unbinding events are
required before a phosphorylation reaction on a T432 or S431
residue occurs. Each KaiA-binding/unbinding event enhances theprobability that a phosphorylation reaction occurs, and the basisof our analysis is that the duration of the KaiA binding inﬂuences
this probability; a longer duration of KaiA binding is more likely
to stimulate a phosphorylation event. Our empirical discovery of
the PDDA phenomenon adds a critical insight; every phosphorylation event on a KaiC protomer decreases the afﬁnity of KaiA
for KaiC (i.e., decreases the duration of KaiA binding to the KaiC
tentacles) for subsequent interactions, thereby reducing theprobability of KaiA-enhanced phosphorylation (Fig. 7c). Consequently, while each KaiA binding to a KaiC tentacle is a subsecond event, this interaction is ratcheted over the duration of the
12-h phosphorylation half-cycle by KaiC phospho-status.
Therefore, each phosphorylation event during the phosphorylation half-cycle calibrates the duration of subsequent KaiA-toKaiC interactions.
What is the mechanism by which PDDA is accomplished? In a
study of KaiA–KaiC interactions, Kim and coworkers concluded
that each KaiA-interacting C-terminal tentacle is directly linked
by a β-strand segment to the phosphorylatable S431/T432
region42. Kim et al. hypothesized that binding of KaiA to a KaiC
tentacle pulls on the β-strand linker, causing conformationalchanges in the S431/T432 region. There are two phospho-sites ineach protomer, and therefore 12 sites within the KaiC hexamer; as
KaiC is phosphorylated, extra H-bonds are added in this key
region of the KaiCII domain that reduce free energy and stabilize
KaiCII conformation47. This stabilization of the S431/T432
region may radiate back to the linker segment and C-terminal
tentacles, thereby modifying the kinetics of KaiA binding. Consequently, KaiC phospho-status is both a marker of circadianphase and a regulator of KaiC’s myriad activities (e.g., ATPase,
autokinase, autophosphatase, phosphotransferase, and nanocomplex formation12), including modulating the afﬁnity of KaiA
interaction.
Phosphorylation is a general property of circadian clock proteins and resilience is crucial for all circadian oscillators48,49.
Therefore, the properties of modulation of phosphorylation rates
at different phases of the rhythm and integration of highfrequency events that we report here are likely to be found in all
circadian oscillators, including the insight that molecular noisein vivo might be buffered by fast kinetic binding events amongclock proteins. The KaiABC system provides the best biophysical

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insights to date on the mechanisms by which the phospho-statusof clock proteins can biophysically achieve molecular resilience inthe face of intrinsic and extrinsic noise that lead to ﬂuctuating
concentrations and/or properties of core clock proteins.
Methods
Protein puriﬁcation. Native (unmutated) and mutant Kai proteins from S. elongatus were expressed as N-terminal GST fusions in Escherichia coli and puriﬁed as
described previously19,31,34. E. coli BL21 (Novagen, EMD Millipore) or DH5α(Thermo Fisher Scientiﬁc) cells harboring pGEX-based expression
construct8,19,24,31,34 were grown in 1 liter of Lysogeny broth (LB) medium containing 100 mg ampicillin or carbenicillin, and recombinant protein was expressedby induction with 100 μM IPTG at room temperature (22–24 °C) for 24 h. The cells
were harvested by centrifugation and resuspended in 35 mL of extraction buffer
containing 50 mM Tris-HCl, pH 8.0, 150 mM NaCl, 1 mM DTT. For the nativeand mutated KaiC proteins, 5 mM MgCl2 and 1 mM ATP were always present in
the buffers throughout the puriﬁcation process. The cells were homogenized bypassing through a French pressure cell (5.5 MPa) four times. The cell homogenate
was centrifuged at 20,000×g for 90 min, and the resulting supernatant was applied
to a glutathione-agarose (Pierce, Thermo Fisher Scientiﬁc) afﬁnity chromatography
column (~1 mL bed volume packed in a PD-10 column, GE Healthcare Life Sciences). After washing the column with 40–60 mL of the extraction buffer, GSHagarose beads were resuspended in 2 mL of the extraction buffer, and the GSTfusion protein was digested in the column with GST-human rhinovirus 3C(HRV3C) protease at 4 °C overnight. Tag-free protein was eluted from the column
with 8 mL of the extraction buffer. The eluted protein was diluted with 20 mM
Tris-HCl, pH 8.0, 1 mM DTT (plus 5 mM MgCl2 and 1 mM ATP for KaiCs) to
reduce NaCl concentration to 90 mM and applied to an anion exchange column (1mL Q Sepharose Fast Flow, GE Healthcare Life Sciences). For KaiA and KaiC
samples, protein was eluted from the column by a stepwise gradient of NaCl (10mM increments, from 100 to 450 mM) in buffer containing 20 mM Tris-HCl, pH
8.0, 1 mM DTT (5 mM MgCl2 and 1 mM ATP for KaiC) using gravity ﬂow of 1.0
or 1.5 mL per step. Since KaiB protein does not bind to Q Sepharose, ﬂow-throughfrom the anion exchange column was collected, concentrated, applied to a gel
ﬁltration column (Sephacryl S-100 HR, GE Healthcare Life Sciences, 1.5 cm ×45 cm) and eluted with 20 mM Tris-HCl, pH 8.0, 300 mM NaCl, 0.5 mM EDTA,
1 mM DTT at a ﬂow rate of ~0.25 mL per min. Elution peaks from the ionexchange or gel ﬁltration column were determined by protein assay and SDSPAGE. Peak fractions were combined, concentrated (1–3 g L−1) and buffer
exchanged into 20 mM Tris-HCl, pH 8.0, 150 mM NaCl, 1 mM DTT (plus 5 mM
MgCl2 and 1 mM ATP for KaiC) by using an Amicon Ultra centrifugal ﬁlter unit
(MWCO 30 K or 100 K, EMD Millipore). The proteins were >98% pure as
determined by SDS-PAGE analysis using Blue silver colloidal Coomassie detection50. Protein concentration was determined by the Bradford protein assay using
BSA as standard. The puriﬁed proteins were snap-frozen in liquid nitrogen andstored at −80 °C until use.

HS-AFM imaging. HS-AFM experiments were carried out using a laboratory-built
High-Speed-Atomic Force Microscope38,39. For tapping-mode HS-AFM imaging, asmall cantilever with a resonant frequency of ~0.8 MHz, quality factor of ~2 andspring constant of ~0.1 N m-1 was oscillated at near the resonant frequency andchanges in the oscillation amplitude caused by probe–surface interaction was
detected by an optical deﬂection method. The cantilever’s free oscillation amplitude
was set at 1–2 nm and the set-point amplitude for feedback control was approximately 90% of the free oscillation amplitude to avoid an undesirable disturbance ofinteractions between Kai proteins. KaiC hexamers were immobilized to either baremica or chemically functionalized mica with 3-aminopropyltriethoxy silane (APmica). The observation buffer used was 20 mM Tris-HCl (pH 8.0) and 5 mM
MgCl2. In some experiments, 1 or 2 mM ATP and/or 150 mM NaCl were present
in the buffer, which is indicated in the ﬁgure legends. All AFM experiments werecarried out at constant temperature (25–28 °C). The KaiC hexamers attached to themica surfaces as follows: (i) on bare mica, the C-terminal side of the KaiC hexamer
attached to the mica (CI end-up orientation), and (ii) on AP-mica, the N-terminalside attached to the AP-mica (CII end-up orientation, Figs. 1, 2).
AP-mica was prepared by placing a droplet (3 μL) of 0.1% 3aminopropyltriethoxy silane on freshly cleaved mica. After 5 min incubation, thesurface was thoroughly washed with 50 μL of pure water. A sample droplet
including KaiC hexamers (in the buffer containing Mg-ATP as described above)
was placed on the surface and incubated for 5 min. Then residual proteins were
washed off with the observation buffer. After conﬁrming by HS-AFM imaging that
the KaiC hexamers were homogeneously immobilized on the substrate, a KaiA
solution was added into the observation buffer to the ﬁnal KaiA concentration
indicated in the ﬁgure legends. After this addition, the buffer solution was well
mixed by several cycles of pipetting to provide a uniform concentration of KaiA.
With the exception of Figs. 2c, f and Supplementary Figs. 4 and 8 (that include
ATP in the observation buffer), all of the data of Figs. 1–5 were obtained in theabsence of ATP to prevent KaiC phosphorylation during the brief assay interval,
but the presence vs. absence of 1 mM ATP in the incubation buffer did not alter the
12

dynamic interactions between KaiA and KaiC (compare Fig. 3 with Supplementary
Fig 4, and Fig. 5 with Supplementary Fig. 8).
HS-AFM image analyses. To estimate the binding lifetime (τbound) of KaiA•KaiC
complexes, the bound-state dwell lifetime was measured from successive HS-AFM
images. In addition, the dwell-time between two consecutive events of binding of
KaiA dimers to an identical KaiC hexamer was measured to estimate the lifetime of
the KaiA-unbound-state (τunbound). The binding and unbinding of KaiA wasjudged by eye inspection as bright spot appearance or disappearance on a KaiC
hexamer. All analyses were carried out for HS-AFM images recorded more than
5 min after KaiA addition to ensure the observation of dynamic interaction eventsin a well-mixed steady state.
Construction of simulated HS-AFM images. For the construction of simulated
AFM images of KaiC, we used the crystal structure of KaiC (PDB code; 2GBL)28
and applied a simple hard sphere model to the individual atoms in the atomic
structure. The image construction was accomplished by calculating the contact
points between surface atoms of KaiC and a cone-shaped AFM probe with a radiusof 0.5 nm and a cone angle of 10°. The simulated AFM image of KaiC-ΔC wasconstructed using the crystal structure of KaiC from which the C-terminal tentacles
were removed.
Rhythmic in vitro reactions. As described previously8,34, In vitro reactions contain 50 mg L-1 (1.52 μM) KaiA, 50 mg L-1 (4.27 μM) KaiB and 200 mg L-1 (3.43 μM)
KaiC unless otherwise speciﬁed in reaction buffer containing 20 mM Tris-HCl, pH
8.0, 150 mM NaCl, 5 mM MgCl2, 1 mM ATP, 0.5 mM EDTA and incubated at 30 °C in a water bath or a thermal block. At each time point, a portion of the reaction
was taken for HS-AFM and SDS-PAGE analysis. SDS-PAGE was used to quantify
the phosphorylation states of KaiC. The reaction was stopped by mixing with equalvolume of 2× SDS-PAGE sample buffer and stored at −20 °C. Different KaiC
phosphorylation forms were separated by SDS-PAGE (10% acrylamide gels, 37.5:1
acrylamide:bis-acrylamide). Gels were stained with SYPRO Ruby (Thermo Fisher
Scientiﬁc) and scanned with Typhoon (GE Healthcare Life Sciences). Digital
images were analyzed by NIH ImageJ.
Statistical analysis. The time constants of the binding lifetime (τbound) andunbound-state (τunbound) of KaiA to KaC were estimated by ﬁtting the histogramswith a single exponential curve. The ﬁtting was performed by using the standard
regression analysis function of IgorPro. All error bars and data quantiﬁcations are
expressed as mean ± standard error of the mean (SEM) unless stated otherwise.
Data availability. Data supporting the ﬁndings of this paper are available from thecorresponding authors upon reasonable request.

Received: 9 January 2018 Accepted: 9 July 2018

References1.

Dunlap, J. C., DeCoursey, P. J. & Loros, J. J. Chronobiology: Biological
Timekeeping. (Sinauer Associates, Sunderland, MA, 2003).
2. Mihalcescu, I., Hsing, W. & Leibler, S. Resilient circadian oscillator revealed inindividual cyanobacteria. Nature 430, 81–85 (2004).
3. Chabot, J. R., Pedraza, J. M., Luitel, P. & van Oudenaarden, A. Stochastic gene
expression out-of-steady-state in the cyanobacterial circadian clock. Nature
450, 1249–1252 (2007).
4. Qin, X., Byrne, M., Xu, Y., Mori, T. & Johnson, C. H. Coupling of a core posttranslational pacemaker to a slave transcription/translation feedback loop in acircadian system. PLoS Biol. 8, e1000394 (2010).
5. Elowitz, M. B. & Leibler, S. A synthetic oscillatory network of transcriptional
regulators. Nature 403, 335–338 (2000).
6. Tigges, M., Marquez-Lago, T. T., Stelling, J. & Fussenegger, M. A tunable
synthetic mammalian oscillator. Nature 457, 309–312 (2009).
7. Njus, D., Gooch, V. D. & Hastings, J. W. Precision of the Gonyaulax circadianclock. Cell Biophys. 3, 223–231 (1981).
8. Nakajima, M. et al. Reconstitution of circadian oscillation of cyanobacterial
KaiC phosphorylation in vitro. Science 308, 414–415 (2005).
9. Kageyama, H. et al. Cyanobacterial circadian pacemaker: Kai protein complex
dynamics in the KaiC phosphorylation cycle in vitro. Mol. Cell 23, 161–171(2006).
10. Chang, Y.-G. et al. Circadian rhythms. A protein fold switch joins thecircadian oscillator to clock output in cyanobacteria. Science 349, 324–328(2015).
11. Egli, M. & Johnson, C. H. A circadian clock nanomachine that runs withouttranscription or translation. Curr. Opin. Neurobiol. 23, 732–740 (2013).

NATURE COMMUNICATIONS | (2018)9:3245 | DOI: 10.1038/s41467-018-05438-4 | www.nature.com/naturecommunications

ARTICLE

NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-05438-4

12. Johnson, C. H., Zhao, C., Xu, Y. & Mori, T. Timing the day: what makes
bacterial clocks tick? Nat. Rev. Microbiol. 15, 232–242 (2017).
13. Ito, H. et al. Autonomous synchronization of the circadian KaiC
phosphorylation rhythm. Nat. Struct. Mol. Biol. 14, 1084–1088 (2007).
14. Terauchi, K. et al. ATPase activity of KaiC determines the basic timing forcircadian clock of cyanobacteria. Proc. Natl Acad. Sci. 104, 16377–16381(2007).
15. Abe, J. et al. Circadian rhythms. Atomic-scale origins of slowness in the
cyanobacterial circadian clock. Science 349, 312–316 (2015).
16. Rust, M. J., Markson, J. S., Lane, W. S., Fisher, D. S. & O’Shea, E. K. Orderedphosphorylation governs oscillation of a three-protein circadian clock. Science
318, 809–812 (2007).
17. Tseng, R. et al. Structural basis of the day-night transition in a bacterial
circadian clock. Science 355, 1174–1180 (2017).
18. Iwasaki, H. KaiA-stimulated KaiC phosphorylation in circadian timing loops
in cyanobacteria. Proc. Natl Acad. Sci. 99, 15788–15793 (2002).
19. Nishiwaki, T. et al. Role of KaiC phosphorylation in the circadian clock system
of Synechococcus elongatus PCC 7942. Proc. Natl Acad. Sci. USA 101,
13927–13932 (2004).
20. Nakajima, M., Ito, H. & Kondo, T. In vitro regulation of circadianphosphorylation rhythm of cyanobacterial clock protein KaiC by KaiA andKaiB. FEBS Lett. 584, 898–902 (2010).
21. Lin, J., Chew, J., Chockanathan, U. & Rust, M. J. Mixtures of opposing
phosphorylations within hexamers precisely time feedback in the cyanobacterial
circadian clock. Proc. Natl Acad. Sci. USA 111, E3937–E3945 (2014).
22. van Zon, J. S., Lubensky, D. K., Altena, P. R. H. & ten Wolde, P. R. An
allosteric model of circadian KaiC phosphorylation. Proc. Natl Acad. Sci. USA
104, 7420–7425 (2007).
23. Xu, Y., Mori, T. & Johnson, C. H. Cyanobacterial circadian clockwork: roles of
KaiA, KaiB and the kaiBC promoter in regulating KaiC. EMBO J. 22,
2117–2126 (2003).
24. Kitayama, Y., Nishiwaki-Ohkawa, T., Sugisawa, Y. & Kondo, T. KaiC
intersubunit communication facilitates robustness of circadian rhythms incyanobacteria. Nat. Commun. 4, 2897 (2013).
25. Tseng, R. et al. Structural basis of the day-night transition in a bacterial
circadian clock. Science 355, 1174–1180 (2017).
26. Williams, S. B., Vakonakis, I., Golden, S. S. & LiWang, A. C. Structure andfunction from the circadian clock protein KaiA of Synechococcus elongatus: apotential clock input mechanism. Proc. Natl Acad. Sci. 99, 15357–15362 (2002).
27. Vakonakis, I. & LiWang, A. C. Structure of the C-terminal domain of theclock protein KaiA in complex with a KaiC-derived peptide: implications for
KaiC regulation. Proc. Natl Acad. Sci. USA 101, 10925–10930 (2004).
28. Pattanayek, R. et al. Analysis of KaiA–KaiC protein interactions in the cyanobacterial circadian clock using hybrid structural methods. EMBO J. 25,
2017–2028 (2006).
29. Nishiwaki-Ohkawa, T., Kitayama, Y., Ochiai, E. & Kondo, T. Exchange of
ADP with ATP in the CII ATPase domain promotes autophosphorylation of
cyanobacterial clock protein KaiC. Proc. Natl Acad. Sci. USA 111, 4455–4460(2014).
30. Nishiwaki, T. et al. A sequential program of dual phosphorylation of KaiC as abasis for circadian rhythm in cyanobacteria. EMBO J. 26, 4029–4037 (2007).
31. Qin, X. et al. Intermolecular associations determine the dynamics of thecircadian KaiABC oscillator. Proc. Natl Acad. Sci. USA 107, 14805–14810 (2010).
32. Nishiwaki, T. & Kondo, T. Circadian autodephosphorylation of cyanobacterial
clock protein KaiC occurs via formation of ATP as intermediate. J. Biol. Chem.
287, 18030–18035 (2012).
33. Egli, M. et al. Dephosphorylation of the core clock protein KaiC in the
cyanobacterial KaiABC circadian oscillator proceeds via an ATP synthasemechanism. Biochemistry 51, 1547–1558 (2012).
34. Mori, T. et al. Elucidating the ticking of an in vitro circadian clockwork. PLoS
Biol. 5, e93 (2007).
35. Clodong, S. et al. Functioning and robustness of a bacterial circadian clock.
Mol. Syst. Biol. 3, 90 (2007).
36. Brettschneider, C. et al. A sequestration feedback determines dynamics andtemperature entrainment of the KaiABC circadian clock. Mol. Syst. Biol. 6, 389(2010).
37. Murakami, R., Mutoh, R., Ishii, K. & Ishiura, M. Circadian oscillations of
KaiA–KaiC and KaiB-KaiC complex formations in an in vitro reconstituted
KaiABC clock oscillator. Genes Cells21, 890–900 (2016).
38. Ando, T. et al. A high-speed atomic force microscope for studying biologicalmacromolecules. Proc. Natl Acad. Sci. USA 98, 12468–12472 (2001).
39. Uchihashi, T., Kodera, N. & Ando, T. Guide to video recording of structure
dynamics and dynamic processes of proteins by high-speed atomic force
microscopy. Nat. Protoc. 7, 1193–1206 (2012).

40. Ando, T., Uchihashi, T. & Kodera, N. High-speed AFM and applications tobiomolecular systems. Annu. Rev. Biophys. 42, 393–414 (2013).
41. Pattanayek, R. et al. Visualizing a circadian clock protein: crystal structure of
KaiC and functional insights. Mol. Cell 15, 375–388 (2004).
42. Kim, Y.-I., Dong, G., Carruthers, C. W., Golden, S. S. & LiWang, A. The day/night switch in KaiC, a central oscillator component of the circadian clock of
cyanobacteria. Proc. Natl Acad. Sci. 105, 12825–12830 (2008).
43. Mori, T. et al. Circadian clock protein KaiC forms ATP-dependent
hexameric rings and binds DNA. Proc. Natl Acad. Sci. 99, 17203–17208(2002).
44. Hayashi, F. et al. ATP-induced hexameric ring structure of the
cyanobacterial circadian clock protein KaiC. Genes Cells 8, 287–296(2003).
45. Uchihashi, T., Iino, R., Ando, T. & Noji, H. High-speed atomic force
microscopy reveals rotary catalysis of rotorless F1-ATPase. Science 333,
755–758 (2011).
46. Murayama, Y. et al. Tracking and visualizing the circadian ticking of the
cyanobacterial clock protein KaiC in solution. EMBO J. 30, 68–78 (2011).
47. Johnson, C. H., Egli, M. & Stewart, P. L. Structural insights into a circadianoscillator. Science 322, 697–701 (2008).
48. Edery, I., Rutila, J. E. & Rosbash, M. Phase shifting of the circadian clock by
induction of the Drosophila period protein. Science 263, 237–240 (1994).
49. Lee, C., Etchegaray, J. P., Cagampang, F. R., Loudon, A. S. & Reppert, S. M.
Posttranslational mechanisms regulate the mammalian circadian clock. Cell
107, 855–867 (2001).
50. Candiano, G. et al. Blue silver: a very sensitive colloidal Coomassie G-250
staining for proteome analysis. Electrophoresis 25, 1327–1333 (2004).

Acknowledgements
This work was supported by grants from the USA National Institutes of Health (R37
GM067152 to C.HJ.), Japanese Society for the Promotion of Science (JP15H03540,
JP16H00830, and JP16H00758 to T.U. and JP24227005, JP26119003, and 17H06121 toT.A.), and Japan Science & Technology Agency/CREST (JPMJCR13M1 to T.A.).

Author contributions
T.U. and S.S. performed HS-AFM experiments and statistical analyses of the data, while
T.M. prepared the protein samples. T.U. and T.A. set up the HS-AFM imaging system
including both hardware and software. M.B. designed the model and M.B. and T.M.
implemented mathematical modeling and simulations. T.M., T.U., and C.H.J. designed
experiments. T.M., M.B., and C.H.J. wrote the ﬁrst draft of the manuscript, T.U., T.M.,
S.S., and M.B. prepared ﬁgures. All authors (T.M., S.S., M.B., C.H.J, T.U. and T.A.) edited
the manuscript.

Additional information
Supplementary Information accompanies this paper at https://doi.org/10.1038/s41467018-05438-4.
Competing interests: The authors declare no competing interests.
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