Casein kinase 1 dynamics underlie substrate selectivity and the PER2 circadian phosphoswitch

We recently demonstrated that CK1 primes FASP phosphorylation in a slow, rate-limiting step at serine 659 (mouse PER2 numbering, Figure 1A–B), with phosphorylation of the downstream consensus sites following rapidly in a sequential manner (dashed arrows at pSxxS consensus, Figure 1B) (Narasimamurthy et al., 2018). Because tau is a loss of function on the FASP domain, the prevailing model was that this disabled the phosphoswitch to allow for unchecked Degron phosphorylation to degrade PER2 (Gallego et al., 2006). The tau mutation eliminates a positively charged residue in the first of three CK1 family-specific anion-binding sites (Sites 1, 2, and 3) (Figure 1C) (Longenecker et al., 1996). R178 sits at Site 1, located adjacent to the active site, and has been postulated to bind a phosphorylated priming site to position the downstream serine of the consensus motif near the active site (Longenecker et al., 1996; Zeringo and Bellizzi, 2014). Based on this model, we predicted that tau should preferentially disrupt phosphorylation of the downstream consensus sites in the FASP region due to its inability to recruit the primed substrate.

To test this idea, we used a FASP peptide based on the native mouse PER2 sequence (Figure 1B) that was primed synthetically by phosphorylation at S659. We used a constitutively active version of the isolated wild-type (WT) or tau (R178C) kinase lacking its autoinhibitory tail (CK1δ ΔC, with 97% identity between CK1δ and CK1ε in the kinase domain). As expected, tau had significantly lower activity than the WT kinase on this primed substrate (Figure 1D–E). This was also true for a minimal, primed synthetic substrate CK1tide (Figure 1—figure supplement 1). We then asked if tau would influence priming phosphorylation using an unmodified FASP peptide. As we observed before, phosphorylation of the non-consensus priming site occurs with much slower kinetics than the downstream consensus sites (Figure 1F–G) (Narasimamurthy et al., 2018). To our surprise, we found that tau also had significantly diminished activity on an unprimed FASP substrate (Figure 1F–G), indicating that R178 is also important for the non-consensus priming event. The decrease in activity of tau on the priming site was also validated using an ELISA-based kinase assay with an antibody that is specific for phosphorylated S659 (Figure 1—figure supplement 1).

We used an NMR-based kinase assay to confirm that tau influences both priming and downstream events at the FASP region. In contrast to radiolabeled kinase assays, this assay provides site-specific information on the substrate by measuring new peaks that arise for phosphorylated serines over time (Theillet et al., 2013). We established the requirement for priming to initiate phosphorylation of downstream sites in the FASP by CK1 (Narasimamurthy et al., 2018). Therefore, if tau was simply deficient in recruitment of primed substrate, we should observe a similar degree of phosphorylation at the priming site (pS659) compared to WT kinase, but a decreased peak volume for the downstream serine (pS662). By contrast, we observed that the peaks for both pS659 and pS662 were decreased in volume for tau (Figure 1H–I), revealing that the ratio of consensus to priming activity (pS662/pS659) was similar in WT CK1 and tau (Figure 1J).

To see if these findings held in the context of full-length protein, we expressed myc-PER2 and WT or tau myc-CK1ε in HEK293 cells and assessed phosphorylation using an antibody specific for phosphorylation on the priming site at S659. Consistent with our in vitro studies, the activity of tau was much lower on the priming site relative to the WT kinase (Figure 1K). As expected, phosphorylation of the subsequent serine was also decreased with tau (Figure 1—figure supplement 1). To examine the possibility that loss of activity on the FASP region was specifically due to the cysteine mutation (R178C), we also tested an R178A mutant in the cell-based assay and found that it also exhibited much lower activity on the FASP priming site in a cell-based assay (Figure 1—figure supplement 1). Collectively, these data show that loss of R178 at the site one anion-binding pocket in tau leads to a reduction in both the slow priming step as well as the downstream sequential, primed phosphorylation of the FASP region.

Using an antibody specific for phosphorylation of the CK1-dependent β-TrCP recruitment site at S478, we recapitulated the increased activity of tau on the Degron observed previously on myc-PER2 that was transiently expressed with the kinase in HEK293 cells (Figure 1L) (Gallego et al., 2006). Consistent with the phosphoswitch model that FASP phosphorylation antagonizes CK1 activity on the Degron (Figure 1A), we observed an increase in activity of WT kinase on the Degron with the S659A mutant that eliminates all phosphorylation of the FASP region (Figure 1L) (Narasimamurthy et al., 2018). We found that tau also had increased activity on the Degron in the S659A mutant, demonstrating that the tau mutant can still be regulated by the phosphoswitch. Given that kinase activity on the Degron is clearly linked to phosphorylation of the FASP region in cells, we sought to clarify whether tau truly exhibits increased activity at the Degron using a peptide-based kinase assay in vitro (Figure 1M). Here, we found that even on a peptide substrate in vitro, tau had significantly increased activity on the Degron relative to WT kinase (Figure 1N–O). Moreover, both tau and WT kinase maintain their distinct substrate preference in the presence of both FASP and Degron peptides in vitro, with tau showing enhanced activity for the Degron relative to WT kinase (Figure 1—figure supplement 1). These data demonstrate that in addition to any regulation imparted by the phospho-FASP on the Degron in cells, the tau mutation leads to a fundamental change in CK1 activity and substrate specificity.

To explore the molecular basis for tau’s altered substrate specificity, we solved a crystal structure of the CK1δ R178C kinase domain (Figure 2A and Supplementary file 1a). Both WT and tau coordinate an anion at Site three similarly (Figure 2—figure supplement 1). However, the mutation disrupted anion binding at Site 1, although it led to only minor structural changes in this anion-binding pocket (Figure 2B). Unexpectedly, we observed a loss of anion binding at Site two in tau, mediated by an alternate conformation of the activation loop near this pocket that sterically blocks binding of the anion (Figure 2C). This alternate conformation initiates at G175, three residues upstream of the tau mutation (Figure 2C). A rotation of the backbone at G175 to a left-handed configuration dramatically alters the configuration of upstream residues to create a distinct conformation of the activation loop (Figure 2D and ). A backbone flip of a glycine at this conserved position has been observed in other serine/threonine kinases, linking changes in conformation of the activation loop to regulation of kinase activity (Nolen et al., 2004); therefore, the ‘loop up’ conformation observed in tau may lead to different kinase activity than the ‘loop down’ conformation observed in the WT kinase.

The activation loop is a key feature that distinguishes the CK1 family from other serine/threonine kinases. There is little mechanistic insight into CK1 substrate selectivity because it deviates from the highly conserved APE motif in the P+1 region that helps to define substrate specificity in most kinases (Figure 2E) (Goldsmith et al., 2007). The activation loop and surrounding region also contain all of the residues that coordinate the three anions observed in nearly all CK1 structures: the residues that coordinate binding at Sites 1 and 3 are unique to the CK1 family, while R127 and K154, corresponding to Site 2, are broadly conserved in other kinase families. R127 is part of the highly conserved HRD motif that coordinates a phosphorylated residue in the activation loop of many kinases to regulate substrate binding and activity (Figure 2F) (Johnson et al., 1996). CK1 family kinases are generally considered to be constitutively active because they do not require phosphorylation of the activation loop (Goldsmith et al., 2007). However, CK1δ and CK1ε are inhibited by autophosphorylation of their disordered C-terminal tails (Graves and Roach, 1995; Rivers et al., 1998) and potentially by the phosphorylated FASP region (Figure 1L). Therefore, these anion binding sites could represent the basis for a CK1-specific regulatory mechanism by facilitating the binding of phosphorylated C-terminal tails or substrates, and/or anionic signaling molecules (Fustin et al., 2018; Kawakami et al., 2008).

Mutation of the residues corresponding to positions R127 and K154 at Site 2 essentially eliminates the activity of kinases that depend on phosphorylation of the activation loop (Gibbs and Zoller, 1991; Leon et al., 2001; Skamnaki et al., 1999). To test the role of Site 2 anion binding in regulation of CK1 activity, we made charge reversion mutants at positions R127 and K154, as well as at K171 located nearby on the activation loop, and measured enzymatic efficiency (k_cat/K_m) on FASP and Degron peptides in vitro. We observed a modest decrease (~25%) in activity towards the FASP peptide (Figure 2—figure supplement 1 and Supplementary file 1b), suggesting that the ‘loop down’ conformation that is enforced by anion binding at Site 2 may be important for FASP activity. Strikingly, these mutants all increased activity towards the Degron, with a ~ 50% gain in efficiency for R127E (Figure 2—figure supplement 1 and Figure 2G). To further examine the role of K171 in regulation of anion binding, we solved a structure of the K171E mutant crystallized in high sulfate conditions and found a full complement of three anions bound (Figure 2—figure supplement 1), demonstrating that local flexibility in the activation loop allows it to retain sulfate binding at Site 2 to some degree. Overall, these data suggest that anion binding at Site 2 correlates with substrate selectivity on the FASP and Degron peptides. Notably, the change in selectivity with Site 2 mutants in vitro makes them much more tau-like (Figure 2H), consistent with a recent report that both tau and charge reversion mutants at Site 2 lead to decreased PER2 stability in cells (Shinohara et al., 2017).

Two copies of the kinase are found in the asymmetric unit of the tau crystal. We discovered that the mutant kinase can take on either the ‘loop down’ or the ‘loop up’ conformation (Figure 3A). The activation loop is not stabilized by crystal contacts in the alternate ‘loop up’ conformation and was explicitly modeled based on good density in both conformations (Figure 3—figure supplement 1), suggesting that the kinase has an intrinsic ability to take on two discrete conformations in a switch-like manner. Since the first structure of CK1δ published in 1996, nearly all CK1 structures have been determined after crystallization with high concentrations of sulfate or citrate anions (Long et al., 2012; Longenecker et al., 1996; Minzel et al., 2018). Because anion binding at Site two is incompatible with the activation loop in its ‘loop up’ conformation, prior crystallographic conditions have likely disfavored this alternate conformation. The WT structure that we used for our analysis (PDB: 1CKJ) was first crystallized with a low concentration of anions, and then derivatized with tungstate as an analog for phosphate before data collection (Longenecker et al., 1996). Importantly, this structure also displays the same two discrete conformations marked by translocation of residue L173 in the activation loop (Figure 3A), confirming that this switch is an intrinsic property of the CK1δ kinase that has not been explored functionally.

We probed the library of existing CK1δ structures using the positioning of L173 as a quantitative metric for activation loop conformation by measuring interatomic distances of the L173 CD2 atom to either CD2 of L152 (short distance in the ‘loop up’ conformation, long in the ‘loop down’) or the hydroxyl of Y225 (long in the ‘loop up’, short in the ‘loop down’) (Figure 3B). A survey of 68 chains from 26 different crystal structures of CK1δ (in at least 7 space groups) demonstrated that tau and the WT kinase from PDB entry 1CKJ are the only structures of CK1δ to have ever been captured in the ‘loop up’ conformation (Figure 3C). Moreover, the residues that coordinate anion binding are broadly conserved in the CK1 family and anions are also found bound in these sites in other CK1 family kinases (e.g., CK1ε, CK1ɣ3; Supplementary file 1c). To determine if we could independently capture the two states of the activation loop switch in the native kinase, we optimized sulfate-free crystallographic conditions and solved a structure of anion-free CK1δ. Similar to the 1CKJ structure, we observed both conformations of the activation loop in the two molecules of the asymmetric unit (Figure 3—figure supplement 1). Therefore, CK1 has an anion-dependent switch in its activation loop. However, the tau mutation appears to favor the ‘loop up’ conformation because it was observed in crystals that grew in the presence of high sulfate concentrations. Taken together, these data suggest that the tau mutation allosterically regulates anion binding at Site 2 via the activation loop.

To probe the dynamic behavior of CK1 and how this is perturbed by the tau mutation, we performed Gaussian Accelerated Molecular Dynamics (GaMD) simulations (Miao et al., 2015) on four systems: WT and tau CK1 with the activation loop in the crystallographically-defined ‘up’ or ‘down’ conformations (Supplementary file 1d). By monitoring the Root Mean Square Deviation (RMSD) of the activation loop with respect to the ‘down’ or ‘up’ crystallographic conformations, we set out to assess its stability over the course of 500 ns simulations (Figure 4A–D). We found that the activation loop remained stably in position when simulations were started from the ‘loop down’ conformation for both tau and WT. Similar results were seen when the anion was computationally removed from Site 2, suggesting that this conformation of the activation loop is intrinsically stable (Figure 4—figure supplement 1). However, in simulations starting from the ‘loop up’ conformation, the WT activation loop rapidly underwent a conformational change, as shown by increased RMSD^up values. Because we did not see a concomitant decrease in the RMSD_down values, we can conclude that this is not a complete transition from ‘loop up’ to ‘loop down’ on this timescale. Importantly, these transitions occurred more frequently in WT CK1 than in tau (Figure 4C–D). This confirms that the ‘loop up’ conformation is better tolerated in tau, consistent with our observation of this apparently rare conformation in our crystal structure. We also observed that Y225 displayed more conformational freedom in tau compared to the WT kinase (Figure 4—figure supplement 1). Given that Y225 is directly adjacent to K224 in Site one and it also makes contact with L173 in the activation loop in its ‘loop down’ conformation, this suggests that Y225 could be poised to coordinate the conformation of the activation loop with activity at Site 1.

While monitoring the overall dynamics of WT and tau CK1, we detected a major difference in the dynamics of the loop connecting ɑ-helices E and F (loop L-EF, Figure 4—figure supplement 1), part of the anion binding site disrupted by the tau mutation (Figure 4E–H). This is intriguing because temperature-dependent dynamics of loop L-EF were recently shown to be important for the temperature-compensated activity of CK1 on PER2 (Shinohara et al., 2017). In our simulations of the WT kinase, this loop exhibited relatively restricted mobility, regardless of whether the activation loop was in the ‘up’ or ‘down’ conformation (Figure 4E and G). Similar results were observed when the anion was computationally removed from Site 2 (Figure 4—figure supplement 1). However, we observed that the ‘loop down’ conformation of the activation loop was accompanied by a strong disorganization of loop L-EF in tau (Figure 4H), leading to significantly larger conformational freedom compared to the WT kinase (Figure 4G). Surprisingly, the enhanced dynamics of loop L-EF was not observed when tau was in the ‘loop up’ conformation; instead, loop L-EF displayed the same restricted dynamics as the WT kinase (Figure 4E-F. These data suggest that the disruption of Site one by loop L-EF dynamics in the tau mutation may be due to allosteric communication with the activation loop, and by proxy, anion binding at Site 2.

To investigate how the activation loop and dynamics of loop L-EF might influence substrate selectivity, we calculated the volume of the substrate binding cleft and adjacent anion binding sites throughout the 500 ns GaMD simulations (Figure 4 and Figure 4—figure supplement 1). As expected, Site two was completely open only when the activation loop was in the ‘loop down’ conformation for the WT kinase (Figure 4I). Interestingly, this site became partially open in simulations of the WT kinase starting from the ‘loop up’ conformation (Figure 4J), indicating that the intermediate conformational state observed in our simulations might allow the kinase to recover, to some extent, the ability to bind an anion at Site 2. The conformation of the activation loop indirectly affects the volume of the substrate binding cleft with opposing effects in WT and tau. In WT, the substrate binding cleft was open more consistently with the activation loop in its preferred ‘down’ conformation (Figure 4I–J). By contrast, the substrate binding cleft was open more consistently in tau in the ‘loop up’ conformation (Figure 4L) and, due to the dynamic disordering of loop L-EF, often closed when in the ‘loop down’ conformation (Figure 4K). Because the activation loop does not contact the substrate binding cleft, it cannot directly affect the shape of the cleft by steric effects. Instead, closing of the substrate binding cleft in tau occurs due to the conformational disorganization in loop L-EF, which is allosterically induced when the activation loop is in the ‘down’ conformation.

We next used principal component analysis (PCA) to uncover effects of tau on the principal modes of motion displayed by CK1 during the GaMD simulations (Figure 5—figure supplement 1 and Video 1). The 1^st principal component consisted of a clear ‘open-and-close’ movement of the enzyme, achieved mainly by dislocation of the N-terminal lobe (N-lobe) with respect to the top of the helix F (Figure 5A). This mode of motion has been shown to control accessibility to the ATP-binding site and regulate substrate access in other kinases (McClendon et al., 2014). The histograms of the 1^st principal component show that WT CK1 sampled more of the open conformations compared to tau (Figure 5C). The 2^nd principal component consisted of a twisting movement of the N-lobe with respect to the top of helix F and a significant rearrangement of loop L-EF, which can either be extended or collapsed (Figure 5B). When collapsed, loop L-EF had the effect of sterically closing the substrate binding cleft. The histograms of the 2^nd PCA illustrate that loop L-EF adopts more extended conformations in WT CK1 and more collapsed conformations in tau (Figure 5D). The collapsed conformations require loop L-EF to undergo a significant conformational change, which agrees with the high conformational freedom seen in this region when the tau activation loop is in the ‘loop down’ conformation. Altogether, the GaMD simulations suggest that the tau kinase never behaves fully like the WT enzyme; compared to WT, it stabilizes the rare, Degron-preferring conformation of the activation loop that remodels the substrate binding cleft and excludes anion binding at Site 2. By contrast, when tau samples the ‘loop down’ conformation of the activation loop, it leads to a dynamic disordering of loop L-EF that favors conformations of the kinase that likely accounts for its decrease enzymatic efficiency on the FASP region.

To gain further insight into CK1 function, we mapped known mutant alleles that influence circadian rhythms onto the CK1 structure (Figure 6 and Supplemenary File 2). Doubletime (DBT), the CK1δ/ε ortholog in Drosophila, has one allele that causes a short circadian period (dbt^S, P47S) while all others lead to a long period (Kloss et al., 1998; Rothenfluh et al., 2000; Suri et al., 2000). Many long period mutations occur at or near catalytically important residues like the catalytic DFG motif and the regulatory spine that controls kinase activity (Figure 6B) (Taylor and Kornev, 2011; Muskus et al., 2007). Moreover, two loss of function alleles occur in the activation loop: dco¹⁸ (S181F) is located right behind the tau site (R178), linking it to the substrate binding channel and activation loop, while dco² (G175S) occurs at the hinge point for the activation loop switch (Zilian et al., 1999). Although Drosophila and mammalian PER proteins are somewhat functionally divergent, conservation of their Degrons (Chiu et al., 2008; Eide et al., 2005) and FASP-like stabilizing phosphorylation sites (Kivimäe et al., 2008; Top et al., 2018; Xu et al., 2007) suggests that there may be some conservation in their regulation by CK1 (Figure 6C). In line with this, expressing mammalian CK1δ with the tau or dbt^s mutation leads to short period circadian rhythms in flies (Fan et al., 2009). Consistent with this functional conservation, the entire surface-exposed area linking Sites 1 and 2 and the substrate binding cleft are ≥95% identical in 20 species from humans to unicellular green alga where CK1 has been implicated in regulation of circadian clocks (Figure 6—figure supplement 1).

Three short period mutants from humans and Drosophila (T44A, H46R, and P47S) colocalize in the N-lobe right above Site 2 (Figure 6B) (Kloss et al., 1998; Brennan et al., 2013; Xu et al., 2005). Given the changes in N- to C-lobe dynamics that we observed in our simulations of CK1 (Figure 5), we wondered how these mutations would influence substrate selectivity. We first tested the activity of these short period kinase mutants in cell-based transfection assays by monitoring both FASP priming (Figure 7A) and Degron (Figure 7B) phosphorylation. Similar to the Site two mutants we tested earlier (Figure 2—figure supplement 1), the short period mutants T44A, H46R, and P47S each retained substantially more kinase activity on the FASP priming site than tau. A triple mutant of all three short period mutants (3M) did not have additive effects. Likewise, they also appeared to retain kinase activity or even exhibited modest increases in Degron phosphorylation relative to WT (Figure 7B), although not to the same degree as tau. On balance, it appears that mutants near Site two might act differently from tau in that they retain FASP priming activity while increasing activity at the Degron relative to WT.

We also studied another short period mutant located at Site 1, K224D, which was recently reported to have a ~ 20 hr circadian period like tau (Shinohara et al., 2017). Unlike tau, K224D retained FASP priming activity in HEK293 cells (Figure 7C), although it exhibited a sharp increase in Degron phosphorylation similar to tau (Figure 7D). This effect was not dependent on the charge inversion, as we saw the same effect with a K224A mutant (Figure 7—figure supplement 1). Despite retaining priming activity in cells, we noticed that the enzyme efficiency of K224D was decreased on the FASP peptide, which contains multiple serines (Supplementary file 1b). This suggested that while priming of the FASP site S659 might be intact, subsequent phosphorylation of the downstream sites might be compromised in K224D. To test this, we used the NMR-based kinase assay to provide information on the stepwise phosphorylation of the FASP region (Narasimamurthy et al., 2018). Consistent with the cellular data, K224D retained normal priming activity at S659, but phosphorylation of the downstream serines that conform to the pSxxS consensus motif was compromised relative to WT kinase (Figure 7E). Therefore, although tau and K224D both enhance Degron phosphorylation to a similar degree and lead to ~20 hr circadian periods (Lowrey et al., 2000; Shinohara et al., 2017), this is likely achieved through different mechanisms on the kinase—tau reduces both priming and downstream phosphorylation of the FASP region, while K224D (and K224A) likely just disrupts the phosphorylation of the downstream pSxxS consensus motifs.

One commonality of short period mutants is enhanced Degron phosphorylation in cells, as both cellular (Gallego et al., 2006; Vanselow et al., 2006) and in vivo studies of short period mutants demonstrate that PER2 stability is decreased in a CK1-dependent manner (Price et al., 1998; Xu et al., 2007). We measured the effect of CK1 mutants on the half-life of PER2::LUC in real-time after cycloheximide treatment (Figure 7F and ). All of the mutants, apart from L173A, lead to a shorter half-life of PER2::LUC (Figure 7G). We initially mutated L173 because it appears to serve as a latch for the activation loop in both its ‘loop up’ and ‘loop down’ conformations (Figure 2C). We found that the mutant substantially decreased kinase activity at both the FASP priming and Degron sites in the transfection-based assay and in vitro (Figure 7A–B and Supplementary file 1b), and a double mutant with tau decreased its activity on the Degron to a similar degree (Figure 7—figure supplement 1). We hypothesized that the L173A mutant might have a half-life similar to WT because its reduced activity on the stabilizing FASP region was offset to a similar degree on the Degron (Figure 7G and Supplementary file 1b). Indeed, we observed a significant correlation between PER2::LUC half-life and the intrinsic ratio of CK1 kinase activity on these two key sites that establish the phosphoswitch mechanism (Figure 7H). Collectively, these data support a new model for CK1 regulation whereby activation loop dynamics orchestrate substrate specificity and contribute directly to the phosphoswitch regulation of PER2 stability, and therefore, the timing of circadian rhythms (Figure 7I).

HEK293 cells were purchased from American Type Culture Collection (Cat.# CRL-1573, RRID:CVCL_0045↗). Cells were authenticated by STR profiling and routinely tested for mycoplasma using commercial kits.

Cell culture, reagents and transfection myc-mPer2, myc-mPer2 S659A, mPer2::Luc, and myc-CK1ε expression plasmids were described previously (Eide et al., 2005; Eng et al., 2017; Zhou et al., 2015). Mutations of the kinase domain were introduced by Quikchange site-directed mutagenesis (Agilent) and validated by sequencing.

HEK293 were cultured in Dulbecco’s Modified Eagle’s Medium (DMEM, Gibco) supplemented with 10% FBS (Gibco), 50 units/mL penicillin, 50 µg/mL streptomycin (Invitrogen) and maintained at 37°C in a 5% CO₂ environment. Cells were transfected using Lipofectamine 2000 transfection reagent (Life Technologies) following the manufacturer’s instructions. For transfections titrating expression of myc-CK1ε, either 10 or 50 ng of plasmid was used; total plasmid DNA of either 1 or 2 μg was used for each well of a 12 or 6-well-plate respectively.10 µM MG132 was added to cultures 24 hr prior to harvest to prevent proteasomal degradation for experiments shown in Figure 7A and B.

Mouse PER2::LUC expression plasmids (10 ng) were transiently transfected alone or with myc-CK1ε (100 ng) in 35 mm dishes of HEK293 cells in phenol red-free DMEM in the presence of 100 mM D-luciferin (122799, PerkinElmer), 10 mM HEPES and 1.2 g/L sodium bicarbonate. Dishes were sealed with 40 mm cover glasses and vacuum grease, and incubated in the LumiCycle (Actimetrics). The next day, 40 μg/mL cycloheximide (Sigma) was added per 35 mm dish. Luminescence data were used to calculate PER2::LUC half-life in Prism (GraphPad) using one-phase decay algorithm as described previously (Zhou et al., 2015). Briefly, half-lives were calculated using the one-phase decay algorithm in Prism (GraphPad) using the raw luciferase activity, beginning from the point of cycloheximide addition to the plateau at minimum luciferase activity (n = 4).

Whole cell extracts of transfected HEK293 cells lysed on ice with cell lysis buffer (50 mM Tris-HCl pH 8.0, 150 mM NaCl, 1% (vol/vol) Nonidet P-40% and 0.5% deoxycholic acid containing Complete Protease Inhibitors (Roche) and PhosStop Phosphatase Inhibitors (Roche)) were analyzed by denaturing SDS-PAGE gel, which was transferred on PVDF membrane (Immobilon, Millipore). The blot was probed using the indicated primary antibodies: anti-myc (9E10) (sc-40, Santa Cruz Biotechnology; RRID:AB_627268↗) and anti-tubulin (ab52623, Abcam; RRID: AB_869991↗) were purchased from commercial providers, while rabbit polyclonal antibodies were generated against phospho-Ser478, phospho-Ser659 or phospho-Ser662 of mouse PER2 and purified against the phosphopeptides by Abfrontier (Young In Frontier Co.). The phosphopeptides for phospho-Ser478 and phospho-Ser659 have been described elsewhere (Narasimamurthy et al., 2018; Zhou et al., 2015); the phosphopeptide KAESVVpSLTSQ-Cys was used to generate the phospho-Ser662 antibody. HRP-conjugated goat secondary antibodies for anti-rabbit (1706515↗, Bio-Rad) and anti-mouse (1706516↗, Bio-Rad) were with standard ECL reagents (Thermo Fisher Scientific). Densitometric analysis of western blot bands was performed using ImageJ software (National Institutes of Health).

All proteins were expressed from a pET22-based vector in Escherichia coli Rosetta2 (DE3) cells based on the Parallel vector series (Sheffield et al., 1999). The wild-type recombinant FASP peptide (residues 645–687) or Degron peptide (residues 475–505) were cloned from human PER2, and a short wild-type mouse FASP peptide (residues 642–666) all contain an N-terminal WRKKK polybasic motif for in vitro kinase assays and a tryptophan for UV detection during purification. All peptides were expressed downstream of an N-terminal TEV-cleavable His-NusA tag. Human CK1δ catalytic domains (CK1δ ΔC, residues 1–317) were all expressed in Rosetta2 (DE3) cells (Sigma Aldrich) with a TEV-cleavable His-GST tag. Mutations were made using standard site-directed mutagenesis protocols and validated by sequencing. All proteins and peptides expressed from Parallel vectors have an additional N-terminal vector artifact of ‘GAMDPEF’ remaining after TEV cleavage. Cells were grown in LB media (for natural abundance growths) or M9 minimal medium with the appropriate stable isotopes (¹⁵N, ¹³C for NMR, as done before Narasimamurthy et al., 2018) at 37°C until the O.D.₆₀₀ reached ~0.8; expression was induced with 0.5 mM IPTG, and cultures were grown for approximately 16–20 hr more at 18°C.

For CK1δ kinase domain protein preps, cells were lysed in 50 mM Tris pH 7.5, 300 mM NaCl, 1 mM TCEP, and 5% glycerol using a high-pressure extruder (Avestin). HisGST-CK1δ ΔC fusion proteins were purified using Glutathione Sepharose 4B resin (GE Healthcare) using standard approaches and eluted from the resin using Phosphate Buffered Saline with 25 mM reduced glutathione. His₆-TEV protease was added to cleave the His-GST tag from CK1δ ΔC at 4°C overnight. Cleaved CK1δ ΔC was further purified away from His-GST and His-TEV using Ni-NTA resin (Qiagen) and subsequent size exclusion chromatography on a HiLoad 16/600 Superdex 75 prep grade column (GE Healthcare) in 50 mM Tris pH 7.5, 200 mM NaCl, 5 mM BME, 1 mM EDTA, and 0.05% (vol/vol) Tween 20. Purified CK1δ ΔC proteins used for in vitro kinase assays were buffer exchanged into storage buffer (50 mM Tris pH 7.5, 100 mM NaCl, 1 mM TCEP, 1 mM EDTA, and 10% glycerol) using an Amicron Ultra centrifugal filter (Millipore) and frozen as small aliquots in liquid nitrogen for storage at -80°C.

For PER2 peptide preps, cells were lysed in 50 mM Tris pH 7.5, 500 mM NaCl, 2 mM TCEP, 5% glycerol and 25 mM imidazole using a high-pressure extruder (Avestin). His-NusA-FASP or His-NusA -Degron fusion proteins were purified using Ni-NTA resin using standard approaches and eluted from the resin using 50 mM Tris pH 7.5, 500 mM NaCl, 2 mM TCEP, 5% glycerol and 250 mM imidazole. His-TEV protease was added to cleave the His₆-NusA tag from the PER2 peptides at 4°C overnight. The cleavage reaction was subsequently concentrated and desalted into low imidazole lysis buffer using a HiPrep 26/10 Desalting column. Peptides were purified away from His-NusA and His-TEV using Ni-NTA resin with 50 mM Tris pH 7.5, 500 mM NaCl, 2 mM TCEP, 5% glycerol and 25 mM imidazole. Peptides were purified by size exclusion chromatography on a HiLoad 16/600 Superdex 75 prep grade column, using NMR buffer (25 mM MES pH 6.0, 50 mM NaCl, 2 mM TCEP, 1 mM EDTA, 11 mM MgCl₂) or 1x kinase buffer (25 mM Tris pH 7.5, 100 mM NaCl, 10 mM MgCl₂, and 2 mM TCEP) for NMR or ADP-Glo kinase assays, respectively.

Mouse PER2 peptides (primed FASP, RKKKTEVSAHLSSLTLPGKAEpSVVSLTSQ, or unprimed FASP, RKKKTEVSAHLSSLTLPGKAESVVSLTSQ, or the Degron, RKKKPHSGSSGYGSLGSNGSHEHMSQTSSSDSN, from Isojima et al., 2009) and the CK1tide peptide (KRRRALpSVASLPGL, from Isojima et al., 2009; Shinohara et al., 2017) were synthesized and purified to 95% or higher (SABio).

For the radioactive kinase assay, two independent reaction mixtures of 50 μL containing 200 μM of the FASP or Degron peptides in reaction buffer (25 mM Tris pH 7.5, 7.5 mM MgCl₂, 1 mM DTT, 0.1 mg/mL BSA) were preincubated for 5 min with or without 20 nM CK1δ ΔC (for primed FASP substrate) or 200 nM CK1δ ΔC (for unprimed FASP or Degron) and the reaction was started by addition of 750 μM of UltraPure ATP (Promega) containing 1–2 μCi of ɣ-³²p ATP (Perkin Elmer). After incubation of the reaction mix at 30°C, an 8 μL aliquot of the reaction mix was transferred to P81 phosphocellulose paper (Reaction Biology Corp) at the indicated timepoints. The P81 paper was washed three times with 75 mM of orthophosphoric acid and once with acetone. The air-dried P81 paper was counted for P_i incorporation using a scintillation counter (Perkin Elmer) by Cherenkov counting. Results shown are from four independent assays.

For the ELISA kinase assay, unprimed FASP peptide was diluted to 2 μg/mL in Carbonate buffer, pH 9.5 (0.1 M sodium carbonate) and coated onto a 96 well plate (100 μL/well). The next day, wells were washed three times with wash buffer (PBS with 0.05% Tween, PBS-T) and once with kinase buffer (25 mM Tris pH 7.5, 5 mM beta glycerol phosphate, 2 mM DTT and 0.1 mM sodium orthovanadate). Reaction mixture (50 μL) containing 10 ng of CK1δ ΔC purified protein in the kinase buffer including 10 mM MgCl₂ and 200 μM ATP was added onto each well and the plate was incubated at 30°C for 1 hr. Next, the reaction mixture was removed and the wells were washed with three times with wash buffer and incubated with blocking buffer (PBS-T with 5% BSA) for 1 hr at room temperature. Subsequently, wells were incubated with pS659 Ab, anti-rabbit antibody conjugated to Biotin and Streptavidin-HRP for 1 hr at room temperature with a washing step after each incubation as above. For signal detection, TMB (1-Step Ultra TMB-ELISA, Thermo Scientific) was added, incubated for color development at room temperature and stopped with the addition of STOP solution (Thermo Scientific). The plate was read at 450 nm using an xMark Spectrophotometer plate reader (Biorad). Results shown are from four independent assays.

NMR spectra were collected on a Varian INOVA 600 MHz or a Bruker 800 MHz spectrometer equipped with a ¹H, ¹³C, ¹⁵N triple resonance z-axis pulsed-field-gradient cryoprobe. Spectra were processed using NMRPipe (Delaglio et al., 1995) and analyzed using CCPNmr Analysis (Vranken et al., 2005). Backbone assignments were obtained previously for the mouse FASP (BMRB entry: 27306) (Narasimamurthy et al., 2018). NMR kinase reactions were performed at 30°C with 0.2 mM ¹⁵N-mouse FASP and/or Degron, 2.5 mM ATP and 1 µM CK1d ΔC (WT or tau). SOFAST HMQC spectra (total data acquisition = 6 min) were collected at the indicated intervals for 3 hr and relative peak volumes were calculated and normalized as described previously (Narasimamurthy et al., 2018). Data analysis was performed using Prism (GraphPad), with data fit to either a one-phase exponential or linear regression.

Kinase reactions were performed on the indicated recombinant peptides (Degron or FASP) using the ADP-Glo kinase assay kit (Promega) according to manufacturer’s instructions. All reactions were performed in 30 μL volumes using 1x kinase buffer (25 mM Tris pH 7.5, 100 mM NaCl, 10 mM MgCl₂, and 2 mM TCEP) supplemented with ATP and PER2 substrate peptides as indicated. To determine the apparent 2^nd-order rate constants, triplicate reactions containing 10 µM substrate, 100 µM ATP, and 0.2 µM CK1δ ΔC kinase were incubated in 1x kinase buffer at room temperature for 3 hr (and repeated for n = 3 independent assays). Linearity of the reaction rate with respect to time was determined by performing larger reactions (50 µL) with wild-type and tau CK1δ ΔC and either the FASP or Degron substrate; 5 µL aliquots were taken and quenched with ADP-Glo reagent at discrete time points up to 3 hr (data not shown). Luminescence measurements were taken at room temperature with a SYNERGY2 microplate reader in 384-well microplates. Data analysis was performed using Excel (Microsoft) or Prism (GraphPad).

All statistical analyses were done using Prism (GraphPad). p-values were calculated using unpaired two-tailed Students t-tests. In all figures, * indicates p<0.05, **p<0.01, ***p<0.001, ****p<0.0001; ns, not significant.

Crystallization was performed by hanging-drop vapor-diffusion method at 22°C by mixing an equal volume of CK1δ ΔC with reservoir solution. The reservoir solution for CK1δ ΔC tau (R178C) (8.5 mg/mL) was 50 mM sodium acetate pH 6.0, 300 mM ammonium sulfate, and 17.5% (vol/vol) PEG 2000. The reservoir solution for crystallizing CK1δ ΔC wild-type (8 mg/mL) without sulfate was 150 mM succinic acid pH 5.5% and 17% (vol/vol) PEG 3350. The reservoir solution for CK1δ ΔC K171E (7.7 mg/mL) was 50 mM sodium acetate pH 6.0, 350 mM ammonium sulfate, and 17.5% (vol/vol) PEG 3500. The crystals were looped and briefly soaked in a drop of reservoir solution and then flash-cooled in liquid nitrogen for X-ray diffraction data collection. For CK1δ ΔC tau, a cryopreservant of reservoir solution with 20% (vol/vol) glycerol was used. Data sets were collected at the APS beamline 23-ID-D, and the ALS beamline 8.3.1. Data were indexed, integrated and merged using the CCP4 software suite (Winn et al., 2011). Structures were determined by molecular replacement with Phaser MR (McCoy et al., 2007) using the ADP-bound structure of wild-type CK1δ ΔC (PDB: 5 × 17). Model building was performed with Coot (Emsley et al., 2010) and structure refinement was performed with PHENIX (Adams et al., 2011). All structural models and alignments were generated using PyMOL Molecular Graphics System 2.0 (Schrödinger).

Before running the GaMD simulations, we ran 100 ns of conventional MD simulations for each system, using AMBER 16 (Case et al., 2016) These simulations were performed in the NVT regime, with a time step of 2 fs, and all bonds involving hydrogen atoms were restrained with SHAKE (Ryckaert et al., 1977). The PME method (Darden et al., 1993) was used to calculate electrostatic interaction using periodic boundary conditions, and a 12 Å cutoff was used to truncate non-bonded short-range interactions.

The final conformations produced by the cMD simulations were used as starting configurations for the GaMD simulations, which were performed with AMBER 17 (Case et al., 2017). For these simulations, additional acceleration parameters were used to boost the exploration of the conformational space, as described in Miao et al. (2015). All systems had a threshold energy E = V_max and were subjected to a dual boost acceleration of both the dihedral and the total potential energies. To optimize the acceleration parameters we first ran 2 ns of MD simulations with no boost potential, during which the minimum, maximum, average and standard deviation (V_min, V_max, V_av, σ_avg) of the total potential and dihedral energies were estimated and used to derive boost potentials as detailed in Miao et al. (2015). These potentials were used to start 50 ns of Gaussian accelerated MD simulations, during which the boost statistics and boost potentials were updated until the maximum acceleration was achieved. The maximum acceleration was constrained setting the upper limit of the standard deviation of the total boost potential to be 6 kcal/mol.

We ran 5 replicas of production GaMD simulations for each system with fixed acceleration parameters derived from the previous equilibration stage. Each replica started from the same initial conformation, but the atoms were given different initial velocities, consistent with a Maxwell-Boltzmann distribution at 300 K. Each production simulation ran for 500 ns, totalizing 2.5 μs of sampling for each system, and 15 μs in total.