Conformational Coupling by Trans-Phosphorylation in Calcium

Home , Francis Crick Institute

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1 01/04/2019 2 PLOS Comp Biology 3

6 7 Conformational coupling by trans-phosphorylation 8 in 9 calcium calmodulin dependent kinase II 10

12 Alessandro Pandini1,2,5, Howard Schulman3 & Shahid Khan4,5*

14 15 1Department of Computer Science - Synthetic Biology Theme, Brunel University, London, Uxbridge UB8 16 3PH, UK 17 2The Thomas Young Centre for Theory and Simulation of Materials, London, UK 18 3Allosteros Therapeutics Inc., Sunnyvale, CA 94089, USA 19 4Molecular Biology Consortium, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA 20 5Computational Cell and Molecular Biology, the Francis Crick Institute, London NW1 AT, UK 21

23 *Corresponding author

24 E-mail: [email protected]

26 Running title: Autonomous CaMKII activation by trans-phosphorylation

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30 Abstract

32 The calcium calmodulin dependent protein kinase II (CaMKII) is a dodecameric holoenzyme 33 important for encoding memory. Its activation, triggered by binding of calcium calmodulin, persists 34 autonomously after calmodulin dissociation. One (receiver) kinase captures and subsequently phos- 35 phorylates the regulatory domain peptide of a donor kinase forming a chained dimer as a first stage 36 of autonomous activation. Protein dynamics simulations examined the conformational changes trig- 37 gered by dimer formation and phosphorylation, aimed to provide a molecular rationale for human 38 mutations that result in learning disabilities. Ensembles generated from X-ray crystal structures were 39 characterized by network centrality and community analysis. Mutual information related collective 40 motions to local fragment dynamics encoded with a structural alphabet. Implicit solvent tCONCOORD 41 conformational ensembles revealed the dynamic architecture of Inactive kinase domains was co-opted 42 in the activated dimer but the network hub shifted from the nucleotide binding cleft to the captured 43 peptide. Explicit solvent molecular dynamics (MD) showed nucleotide and substrate binding determi- 44 nants formed coupled nodes in long-range signal relays between regulatory peptides in the dimer. 45 Strain in the extended captured peptide was balanced by reduced flexibility of the receiver kinase C- 46 lobe core. The relays were organized around a hydrophobic patch between the captured peptide and 47 a key binding helix. The human mutations aligned along the relays. Thus, these mutations could disrupt 48 the allosteric network alternatively, or in addition, to altered binding affinities. Non-binding protein 49 sectors distant from the binding sites mediated the allosteric signalling; providing possible targets for 50 inhibitor design. Phosphorylation of the peptide modulated the dielectric of its binding pocket to 51 strengthen the patch, non-binding sectors, domain interface and temporal correlations between par- 52 allel relays. These results provide the molecular details underlying the reported positive kinase coop- 53 erativity to enrich discussion on how autonomous activation by phosphorylation leads to long-term 54 behavioural effects. 55

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58 Author Summary 59 Protein kinases play central roles in intracellular signalling. Auto-phosphorylation by bound 60 nucleotide typically precedes phosphate transfer to multiple substrates. Protein conformational 61 changes are central to kinase function, altering binding affinities to change cellular location and shunt 62 from one signal pathway to another. In the brain, the multi-subunit kinase, CaMKII is activated by cal- 63 cium calmodulin upon calcium jumps produced by synaptic stimulation. Auto-transphosphorylation of 64 a regulatory peptide enables the kinase to remain activated and mediate long-term behavioural effects 65 after return to basal calcium levels. A database of mutated residues responsible for these effects is 66 difficult to reconcile solely with impaired nucleotide or substrate binding. Therefore, we have compu- 67 tationally generated interaction networks to map the conformational plasticity of the kinase domains 68 where most mutations localize. The network generated from the atomic structure of a phosphorylated 69 dimer resolves protein sectors based on their collective motions. The sectors link nucleotide and sub- 70 strate binding sites in self-reinforcing relays between regulatory peptides. The self-reinforcement is 71 strengthened by phosphorylation consistent with the reported positive cooperativity of kinase activity 72 with calcium-calmodulin concentration. The network gives a better match with the mutations and, in 73 addition, reveals target sites for drug development. 74 75 76 Keywords 77 protein kinase, allosteric inhibitor, molecular neuroscience, molecular dynamics, net- 78 work analysis, helix melting 79 80 81

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85 Introduction

86 87 The calcium calmodulin dependent protein kinase (CaMKII) is a multifunctional, multi-subunit 88 eukaryotic protein kinase (EPK). It has key roles in calcium regulation of neuronal and cardiovascular 89 physiology (1-3). EPKs mediate reactions whose malfunction promotes disease across a broad physio- 90 logic spectrum. The canonical EPK has a distinctive bi-lobed structure that exploits diverse strategies 91 to achieve allosteric regulation (4). 92 CaMKII has a canonical kinase domain (KD) tethered via a linker to an equally well-conserved 93 association domain (AD) that forms a central hub of the dodecameric holoenzyme with two hexamer 94 rings that stack with mirror symmetry. Linker diversity generates isoforms and splice variants. The ki- 95 nase is activated by rises in cellular calcium that enable calcium-calmodulin (Ca2+/CaM) to bind to and 96 displace an autoinhibitory regulatory domain. The autoinhibitory domain occludes interaction of 97 CaMKII with anchoring proteins, such as NMDA receptor subunit GluN2B (5, 6). More subunits are 98 activated at increasing frequency of calcium pulse trains. The tuning frequency depends on the switch- 99 ing kinetics between the holoenzyme open and closed states (7). 100 In the closed state, the substrate binding surface is occluded by an auto-inhibitory segment 101 composed of a N-terminal segment (R1) and C-terminal -helices (R2, R3) and ATP affinity is low (8). 102 R1 contains the primary auto-phosphorylation site (T286 in  subunit, T287 in others), as well as resi- 103 dues for O-GlcNAC modification (S279) and oxidation (M280, M281 ( isoform)). R2 has a CaM recog- 104 nition motif. Ca2+/CaM binding displaces the regulatory segment to switch CaMKII to the open state, 105 followed by segment capture and T286 autophosphorylation by an adjacent, open (activated) subunit 106 (8, 9) in the holoenzyme. R3 has additional threonine residues (T305, T306) that are primarily phos- 107 phorylated when CaM dissociates from a Ca2+-independent (autonomous) kinase (10, 11) to counter- 108 act T286 phosphorylation (12). X-ray crystal structures show that R1 and its binding determinants in 109 the KD core adopt different conformations. Electron spin resonance (ESR) reports that R1 becomes 110 unstructured upon T286 phosphorylation, while R2 and R3 are disordered in solution (13). 111 Persistent CaMKII activity autonomous of Ca2+/CaM underlies conversion of transient synaptic 112 stimulation to long-term potentiation (LTP); a fundamental problem of neuronal CaMKII biochemistry 113 that underlies certain forms of learning and memory (6, 14-17). Recent studies have identified more 114 than a dozen human mutations in CaMKII that result in various degrees of learning disabilities (18, 19). 115 These mutations when mapped onto structure localize largely with R1 or mutations that alter KD in- 116 teractions with substrates rather than R2. The previously described binding mutations form S (sub- 117 strate binding) and T (Thr286 docking) sites (20, 21)). The substrate binding determinants overlap with 118 the R1 binding groove that can be partitioned into A, B and C sites (8, 22). The T-site is eliminated bioRxiv preprint doi: https://doi.org/10.1101/524660; this version posted January 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 5

119 upon release of the autoinhibitory segment by rotation of helix D whose movement helps form the 120 B site (23). An outstanding issue is whether the human mutations act independently or as part of a 121 collective network to disrupt allosteric communication responsible for frequency tuning (24). The con- 122 ventional form of autonomous activity follows T286 trans auto-phosphorylation, which maintains ac- 123 tivity after dissociation of Ca2+/CaM. Structures of CaMKII complexes with R1 regulatory segments of 124 one subunit (“donor”) captured by the adjacent subunit (“receiver”) upon Ca2+/CaM binding, give im- 125 portant snapshots into trans-phosphorylation (8, 9). A hydrophobic clamp of helix D residues within 126 the receiver KD captures the R1 in an interaction that propagates throughout the crystal lattice. 127 Here, we used tCONCOORD, based on stochastic distance constraints (25), and explicit solvent 128 molecular dynamics (MD) as complementary methods to address the mechanistic basis underlying the 129 medical phenotypes of the human mutations. tCONCOORD ensembles from KD structures described 130 collective motions and conformational coupling between the nucleotide and substrate binding sites. 131 MD examined fine-grained architectural modulations due to primary site phosphorylation on the long- 132 range allosteric network to establish an analytical framework for the coupling within and between 133 subunits. We characterized the long-range allosteric relays in a KD dimer extracted in silico from the 134 crystal lattice as well as KD monomer structures. Two strategies analyzed the network architecture 135 based on mutual information. First, the centrality profile of the complete network of local correlated 136 motions was determined to identify relays of the most strongly coupled fragments. Second, the protein 137 was partitioned into contiguous sectors, with coupled dynamics, that act as semi-rigid bodies – hence- 138 forth defined as “communities” (26). Community size and cross-talk tracked the transition between 139 the auto-inhibited and phosphorylated states. 140 We show that the captured R1 acts as a strained spring, rather than a “grappling hook” (8) to 141 couple nucleotide and substrate binding sites (27, 28). The capture freezes out C-lobe core motions to 142 generate long-distance signal relays between R1 segments of adjacent subunits. The human mutations 143 align along the relays. T286 phosphorylation strengthens the relays to suggest how it might facilitate 144 inter-subunit conformational spread and modulate affinities at distant sites for calmodulin (29) and 145 cytoskeletal actin (30). Notably, we identify a hitherto uncharacterized sector to guide the design of 146 allosteric inhibitors. The simulations should complement experimental ESR (13) and FRET measure- 147 ments (31, 32) on activated CaMKII dimers for dissection of the activation mechanism. bioRxiv preprint doi: https://doi.org/10.1101/524660; this version posted January 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 6

148 Results 149 150 1. The human mutations localize to the KD C-lobe and R1. 151 Figure 1A provides a road-map of the architectural elements investigated in this study. The R1 152 with T286 binds to a groove within the adjacent receiver KD C-lobe that overlaps with the receiver’s S- 153 site and has been sub-divided into three pockets A, B and C (8) in the nematode C.elegans KD dimer 154 (PDB ID:3KK8)). The A-site forms a canonical substrate docking interaction with the ATP binding cleft

155 that contains the DFG motif (D156FG158); the B-site forms a hydrophobic patch with helix D; the C-site 156 has acidic residues for salt-bridges with R1. Residue positions with mutations in the human homolog 157 that result in learning disabilities as well as S-site and T-site mutations are mapped onto the donor KD. 158 The human mutations localized to R1 (I272, H282, R284, T286), or overlapped with, or were adjacent 159 to the S and T-sites (F98S, E109, P138). However, a significant fraction mapped elsewhere. 160 The flexibility profile recorded by the root mean square fluctuations (RMSF) of residue posi- 161 tions computed from the tCONCOORD ensemble of (Figure 1B) is consistent with the b-factor values 162 in the crystal structure. Variable residue positions, identified from the multiple sequence alignment 163 (MSA) of > 500 KD sequences, localized to surface accessible loops when mapped onto 3KK8. The MSA 164 shows strong sequence conservation between species and minimal differences between isoforms 165 within species. The phylogenetic tree indicates that nematode and human sequences are among the 166 most distantly-related (Supporting Information Figure S1). Secondary structure predicted from the 167 MSA for the C. elegans, rat and human sequences matched that observed in the crystal structure. The 168 predictions back ESR evidence for R2 and R3 disorder (13). The human mutations localized to mainly 169 conserved residue positions in both rigid and flexible segments of the KD C-lobe and R1. 170

171 172 bioRxiv preprint doi: https://doi.org/10.1101/524660; this version posted January 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 7

173 Figure 1: CaMKII Functional Mutations. Spheres (cyan) show residue positions where mutations cause 174 learning disabilities in humans. A. CaMKII KD architecture. Structure of the CaMKII kinase domain 175 (3KK8) with N-terminal (pale yellow) and C-terminal lemon) lobes and R1 regulatory segment (yellow). 176 Spheres mark S (orange) and T site (yellow) binding mutations (20), primary auto-phosphorylation site 177 (T286 (red with mesh)). Helix D (double arrow bar). R1 is bound to a groove in an adjacent subunit 178 (white)). The groove has three sites – A, B (and C (8). Asterisk (red) marks magnesium ion location. B. 179 CaMKII KD flexibility and sequence variation. Room mean square fluctuation (RMSF) profile computed 180 from the 3KK8 ensemble. Stick (salmon red) representations identify variable residue positions as iden- 181 tified from the MSA (Figure S1). Vertical bar indicates color scale (1 = high (red); 2 = low (blue)). 182 183 2. The captured R1 forms the central node of the allosteric network. 184 We analyzed local protein dynamics to decipher allosteric signal propagation Three, separate, 185 explicit solvent MD replica runs of the 1.7 angstrom resolution structure of the phosphorylated 3KK8 186 dimer and its non-phosphorylated derivative were performed. The 3KK8 dimer was extracted from the 187 crystal structure electron density with the R1 of the donor KD captured (“bound”) by the adjacent 188 receiver; while the R1 of the receiver KD was unconstrained (“free”), immersed in solvent. Four-residue 189 fragments were encoded by the structural alphabet (SA) (33) in structures within the conformational 190 ensembles and trajectories. In the network, the nodes were the fragments (n = 560), while edges were 191 the correlations (n*(n-1)/2) = 156520). The profile reflected the contribution of individual fragments 192 to the dynamics driving the PC motions and is optimal for detection of network nodes (Figure 2A). The 193 T and S sites emerged as prominent nodes in addition to the captured R1 However, the network archi- 194 tecture is too dense to visualize the spatial extent or interaction strength of the connections formed 195 by individual nodes. 196 Communities (n > 3), each represented as a node, greatly simplify network visualization of the 197 connectivity by encoding concerted domain motions intermediate between global motions and resi- 198 due-level RMSF fluctuations. Community membership and interaction strength were computed based 199 on spectral decomposition (34, 35). Our methodology reproduced the published community map of 200 the PKA catalytic subunit (PDB ID: 1CMK) (26) and showed that the CaMKII KD had similar dynamic 201 architecture to PKA with the ATP binding site forming the community hub (Figure 2B, Supporting In- 202 formation Figure S2). Three major communities (A, B, C) converged at the ATP site. The N-lobe com- 203 munity A included the ATP binding cleft and part of the A-site. The C-lobe was split along its centre 204 into community B with B-site helix D and community C with the C-site acid residue pocket. Donor KD 205 communities B and C coalesced with dimer formation (B’), while one community (A’) accounted for 206 the receiver KD. The top couplings from the global network scored on mutual information (nMI) were 207 superimposed on the community architecture (Figure 2C). The captured R1 replaced the ATP binding 208 site as community hub. The couplings congregated around it to link the donor A site with the receiver 209 B and C sites. 210 bioRxiv preprint doi: https://doi.org/10.1101/524660; this version posted January 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 8

211 212 213 Figure 2: The captured R1 forms the community hub of the chained dimer. A. The global network 214 (donor KD (red), receiver KD (green) and its eigenvector centrality. Spheres mark S (orange) and T site 215 (yellow) mutant residue positions and TPO286 (red). B. Community membership of the CaMKII KD (KK8) 216 monomer (open-form) and dimer (ribbon representations) mapped onto the structures with associated 217 community graphs (node diameter = community size; edge thickness = coupling strength). C. Distinct 218 communities (color-coded C atoms (spheres) and top fragment-fragment couplings (nMI > 0.2 (orange 219 lines)) are superimposed onto the structure. Mesh (circled) marks the captured R1 and contacting res- 220 idues. 221 222 3. The DFG motif and helix D link communities in diverse KD structural states. 223 We compared the 3KK8 KD with other CaMKII KD structural states in the Protein Data Bank 224 (PDB) to first correlate community dynamics with monitors of kinase activity. Activation involves in- 225 ward motion of the DFG side-chains for nucleotide binding and inward tilt of helix D for contact with 226 substrate peptides in many diverse EPKs (36). The states could be grouped into three categories – 227 open, inhibitor-bound and auto-inhibited. tCONCOORD conformational ensembles were generated. 228 The dominant conformations for each ensemble were identified from cluster analysis and aligned (Fig- 229 ure 3A). The two open activated states (3KK8, 2WEL) and the inhibitor-bound form (3KL8) had inwardly 230 oriented DFG motifs and D helices. In contrast, the auto-inhibited states (2BDW, 2VN9, 3SOA) had bioRxiv preprint doi: https://doi.org/10.1101/524660; this version posted January 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 9

231 outwardly rotated helix Ds. While 3SOA has an outwardly oriented DFG motif, the loops for 2BDW 232 and 3SOA had inward orientation albeit at a position distinct from that assumed by activated states.

233 We next catalogued the community membership of the DFG motif (I), fragment L97FEDIVAR104

234 from B-site helix D (II) and fragment P235EWD238 from the C-site acid pocket (III) (Figure 3B-D). The 235 open forms (Figure 3B) differed in their community architecture owing to the bound calmodulin. The 236 calmodulin fragmented community B, with R1 dynamics uncoupled from the C-lobe. In both forms, 237 fragments I and II had multiple membership in communities A and B. The CaMKIINtide inhibitor pep- 238 tide associated with sites A, B and C similarly to the captured R1 (8) (Figure 4C). Accordingly, commu- 239 nity interactions are substantially increased, even though the communities did not coalesce. Commu- 240 nity interactions were weak in the auto-inhibited states (human , human  full-length subunit, and a 241 KD extracted from the nematode coiled-coil dimer) (Figure 4D). Community A extended into the C- 242 lobe when AD contacts limited the relative motions of the N and C-lobes to each other (3SOA). Frag- 243 ment II connected the dominant communities as did fragment I in the auto-inhibited human , as well 244 as the human  KD. 245 In conclusion, the coupled ATP binding DFG motif (Fragment I) and helix D (Fragment II) form 246 a universal hub in activated and inactivated CaMKII KD states based on their multiple community mem- 247 bership. The hub is robust to variations in community interaction strength. Inward movement of helix 248 D is a diagnostic for activation, but that of the DFG motif not necessarily so

249 250 251 Figure 3: A. Analysis of the coupling between ATP and substrate binding sites. Aligned KD C-lobe 252 crystal structures. RMSD’s (angstroms) – 2BDW (reference), 2VN9 (0.30), 2WEL (0.34), 3KK8 (0.23), 253 3KL8 (0.62), 3SOA (0.29). Community dynamics in KD crystal structures. Colors (red (N-lobe), orange 254 (central C-lobe), cyan (basal C-lobe)) denote major communities following the 3KK8 donor KD commu- 255 nity structure (Figure 2B). Top dynamic couplings (orange lines) are mapped on the structures as in 256 Figure 3C. Insets: Community membership of the ATP binding motif D156FG158 (I), helix D L97FEDIVAR104 257 (II) and C site P235EWD238 (III) in B - Open forms. (i). Nematode CaMKII with free R1 (3KK8 donor KD), bioRxiv preprint doi: https://doi.org/10.1101/524660; this version posted January 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 10

258 (ii). human  with bound calmodulin (2WEL). The segment bound to calmodulin forms a distinct com- 259 munity (navy) with community B partitioned into smaller communities. C - Inhibitor-bound form. (i) 260 Nematode CaMKII with bound CaMKIINtide (3KL8). D - Auto-inhibited forms. (i). Human  isoform 261 (2VN9). (ii). Complete (KD with AD) human CaMKII  (3SOA). Contacts between the N-lobe and AD 262 form a distinct community (yellow). (iii). Nematode CaMKII stabilized by R2 helix (coiled-coil dimer) 263 (2BDW). 264 265 4. The captured R1 freezes KD core motions 266 We next characterized collective motions, extracted by principal component analysis (PCA), to 267 better understand the monomer to dimer transition. Principal motions (PCs) primarily delineated rel- 268 ative motions of N and C lobes. The amplitude of the first two PCs accounted for >70% of the combined 269 amplitude. PC1PC2 plots compared the amplitudes of the dimer motions obtained by MD and tCON- 270 COORD (Figure 4A). The 300 ns MD runs reached steady-state configurations between 50 to 150 ns. 271 The PC1PC2 conformational space sampled during each run was typically > 2/3 the space sampled by 272 the tCONCOORD ensemble. The space sampled by the combined MD trajectories was comparable (> 273 90%) to the latter ensemble, with considerable overlap between the two. 274 Motions of the subunit KD cores and R1 segments were compared to evaluate the extent to 275 which captured R1 motions determined dimer flexibility. The mechanical hinge and shear surfaces re- 276 sponsible for the PC motions formed community interfaces, with the ATP binding cleft as hub in the 277 monomer (Supporting Information Movie S1). The captured R1 was revealed to be the central hinge 278 or hub for the dimer PC motions (Supporting Information Movie S2). The PCA shows that the captured 279 R1 acts as an allosteric effector to freeze-out the motions of the kinase core. 280 Simulations on other CaMKII KD structures revealed the principal dimer motions were three- 281 fold greater relative to monomer KD core motions. PC1PC2 spread of the receiver KD core was reduced 282 (> 60%) relative to the spread of donor KD core and, indeed, KD cores from the other structures (Figure 283 4B). The PC1PC2 plots for the R1 segment ensembles formed two distinct groups (Figure 4C). The 284 group with smaller spread represented auto-inhibited structures. The cluster with larger spread (4x) 285 consisted of the captured R1 and free R1 segments. The PC1PC2 spread of the captured R1 was re- 286 duced 50% relative to the free R1 segments. The scenario most simply consistent with these results is 287 of a 3-state transition between autoinhibition and activation. R1 is immobile docked as pseudo-sub- 288 strate (“auto-inhibited” state), mobile when free in solution (“open” state) and constrained upon sub- 289 sequent capture (“activated” state). The mobility of the KD core does not change when R1 is displaced 290 but it is notably reduced upon R1 capture. Therefore, R1 freezes KD core collective motions more 291 effectively when captured than when docked as pseudo-substrate, but with compensatory increase in 292 its own flexibility. 293 bioRxiv preprint doi: https://doi.org/10.1101/524660; this version posted January 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 11

294 295 296 Figure 4: The captured R1 inhibits collective motions of the kinase core. PC1PC2 plots show the rela- 297 tion between the collective motions recorded by the amplitudes of the principal components PC1 and 298 PC2. A. PCiPC2 plot for the 3KK8d dimer. B, C. PC1PC2 plots of the (B) KD core (N-lobe + C-lobe minus 299 R1 and (C) R1 of the donor (3KK8) and receiver (3KK8-H2) KDs of the 3KK8 dimer compared with plots 300 for the KD from 4 crystal structures (auto-inhibited (2BDW) and CaM bound (2WEL) C. elegans; auto- 301 inhibited human  (2VN9) and  (3SOA) isoforms. Structure color code follows 3A. 302 303 5. Energetics of the chained dimer. Allosteric signal transduction has both enthalpic (∆퐻) and 304 entropic terms (∆푆) that contribute to the free energy change (∆퐺). 305 ∆퐺 = ∆퐻 − 푇∆푆

306 Enthalpic changes result from the free energy of solvation and residue pK (log푒 퐾) shifts due 307 to modulation of the dielectric constant upon complex formation or covalent modification.

308 ∆퐺 = 푅푇 log푒 퐾 309 The normalized mutual information (푛푀퐼) provides an information theoretic measure of the 310 coupling. This is consistent to the Shannon entropy 퐻(푋) for pairs of fragments albeit incomplete be- 311 cause of finite sampling (37). For any variable (푋), the entropy ∆푆(푋) is related to the number of

312 microstates and their probability, where 푘퐵 Is the Boltzmann constant. 푛 313 ∆푆(푋) = 푘퐵. ln(푊푋) = 푘퐵. ∑푖=1 푝(푋푖) . ln (p(푋푖))

314 퐻(푋) = ∆푆(푋)/푘퐵. bioRxiv preprint doi: https://doi.org/10.1101/524660; this version posted January 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 12

315 We compared the end-to-end distance distributions of the captured relative to the free R1 to 316 assess strain (Figure 5A, Supporting Movies S3-S4). The captured R1 was constrained to a highly-ex- 317 tended subset of conformations. Secondary structure analysis based on the SA (Figure 5B) revealed

318 the extended configuration resulted from melting of two R1 -helical segments N551RERV and

319 D563VDCL; while the intervening alanine-rich V555ASAI sequence largely retained -helical character.

320 The result was in line with mean residue helical propensity (38) of the fragments (-0.18 (V555ASAI) > -

321 0.29 (N551RERV) and 0.49 (D563VDCL) kcal / mol). 322 We focussed on the C-lobe to evaluate the compensatory decrease in flexibility of the core 323 with greater precision (Figure 5C). Comparison of the RMSF profile of the dimer C-lobes shows that 324 reduced flexibility of the B site helix D and the interfacial surface of the receiver lobe are responsible 325 for the overall decrease reported by PCA (Figure 4B). 326

327 328 Figure 5: Capture strains R1 and freezes the receiver C-lobe. A. End-to-end distance distributions of 329 the free (black) and bound (red) R1 segments. B. SA distribution profile showing loss of -helical char- 330 acter upon transition from (i) free to (ii) bound. The SA letters are color coded (red =  -helical -> blue 331 =  sheet). C. RMSF fluctuations from one MD replica run (TPO form) mapped onto the 3KK8 dimer. R1 332 capture freezes out helix D L97FEDIVAR104 (orange) and interface motions in the C-lobe of the receiver 333 core. D156FG158 motif (red), C-site P235EWD238 (magenta). Vertical bar indicates RMSF value on the same 334 color scale shown in Figure 1B. 335 336 bioRxiv preprint doi: https://doi.org/10.1101/524660; this version posted January 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 13

337 6. Electrostatics of T286 phosphorylation 338 The solvent exposed area and electrostatic properties of the phosphorylation site were calcu- 339 lated for the most populated conformations extracted by cluster analysis. Dimer conformations from 340 each set of MD replicas, as well in the tCONCOORD ensemble with the phosphomimic mutation 341 (T286D) (1) were analysed. Dimer contacts were localized to the C-lobes. Contact between R1 of the 342 donor subunit with the receiver subunit core upon capture accounted for much of the stabilization due 343 to solvation. The total buried surface area due to subunit capture was 2319+42 A2. The contribution 344 to this value due to R1 capture was 1765+81 A2 (~ 75%). The free-energy difference due to the decrease 345 from solvation was twice as great for the phosphorylated (-7.4 kcal/mole) versus the non-phosphory- 346 lated (-4.2 kcal/mole) form. 347 Computed Poisson-Boltzmann electrostatic fields are shown in (Figure 6A). The R1 binding 348 pocket was more acidic and the dimer interface more polar when T286 was phosphorylated (TPO286) 349 or mutated (D286). Polar residues with large (> 0.5) pK shifts between the T286 and TPO286 forms 350 were identified by comparison of the dominant dimer configurations (Figure 6B). These residues local- 351 ized to the C-lobes around the R1 binding pocket and the subunit interface (Figure 6C). Phosphoryla- 352 tion shifted the surface of the R1 binding pocket to acidic values, while its interior became more hy- 353 drophobic. The measured pK shifts accounted for the more rigid interface.

354 355 356 Figure 6: Primary site phosphorylation increases R1 cross-talk. A. Changes in the electrostatic envi- 357 ronment (red = acidic, blue = basic, white = hydrophobic) triggered by T286 modification (-> TPO phos- 358 phorylation or -> D mutation). The binding crevice becomes more acidic while the adjacent subunit 푘 푇 359 interface becomes more basic. Color scale is -1 to + 1 퐵 ⁄푒 mV. B. Phosphorylation dependent residue 360 pK shifts (mean + standard error). C. Map of residue (stick side-chains) pK shifts > 0.5 onto the C-lobes 361 of the 3KK8D.pdb dimer. Colors denote residues shifted towards acidic (red), basic (blue) or more neu- 362 tral (dark grey) values. The computed free energy change is -1.1 kcal / mole. 363 364 bioRxiv preprint doi: https://doi.org/10.1101/524660; this version posted January 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 14

365 7. The allosteric network forms a self-reinforcing R1 relay. 366 Community membership mapped onto structure revealed the captured R1 segment and its 367 binding pocket formed a central community (B’) distinct from A’. B’ had strong interactions with donor 368 KD communities A and B. The adjacent R1 segments were linked by long-range couplings between B’ 369 and B. The nucleotide binding pocket and adjacent fragments of its donor KD also linked to the cap- 370 tured R1 (Figure 7A). Superposition of the network centrality profile onto the structure delineated a 371 signal relay from the donor A-site to the captured R1 via helix D (B-site) in the receiver to its R1 372 (Figure 7B, Supporting Movie S5). 373 R1-R1 communication was increased upon phosphorylation (T -> TPO) due to the creation of 374 strong couplings (nMI > 0.9) between captured R1, the donor A and receiver B and C sites (Figure 7C). 375 The dominant signal relays were remarkably similar to those representing the top couplings from the 376 tCONCOORD D286 ensemble. The map of TPO dimer centrality profile highlighted the relay was more 377 localized to the captured R1, donor A, C and receiver B sites (Figure 7D). 378 Parallel network signal processing in the networks was quantified with community size (resi- 379 due number) and interaction strength represented, as in Figure 2B, by community graphs (Figures 7E, 380 F). Phosphorylation strengthen B -> B’ interactions at the expense of A’ interactions. Two small com- 381 munities mediated A -> B’ and B -> B’ signal relays. These were generated upon R1 capture and 382 strengthened upon phosphorylation. A sector common to both communities comprised a loop be- 383 tween C-lobe -helices 9 and 10 that is well conserved, polar in character and at the opposite face to 384 the R1 binding site (Figure 7G, Supporting Movie S6). The loop is an attractive target for the design of 385 allosteric inhibitors based on these characteristics. 386

387 388 bioRxiv preprint doi: https://doi.org/10.1101/524660; this version posted January 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 15

389 Figure 7: T286 phosphorylation increases R1 cross-talk. A. Community membership and top couplings 390 (yellow lines) of the native dimer. B. Eigen-centrality map of the native dimer. C. Community member- 391 ship and top couplings (orange lines) of the phosphorylated (TPO) dimer. D. Eigen-centrality map of the 392 TPO dimer. G -> R color code (bar) and thin -> fat backbones indicate increasing values. Arrows (black) 393 indicate shortest pathway linking the substrate subunit A site and R1 with the enzyme subunit B site 394 and R1. E, F. Community graphs for the native (E) and TPO (F) dimer show parallel signal processing 395 between the donor R1 (in community B) and the receiver R1 (in community B’). G. Surface protrusion 396 and electrostatics (basic polar) of the receiver KD protein sector (249D-259R, 263D) that forms the 397 intermediate community (teal sidechains) mediating the dominant B -> B’ signal relay in the TPO286 398 dimer. The more distributed signal community mediating the A -> B’ signal relay (blue sidechains) in- 399 creases size by recruiting the same sector from the donor KD upon phosphorylation. Three proline res- 400 idues (P212, P213, P235) (circled) targeted by human mutations (cyan sidechains) cluster between the 401 captured TPO286 (magenta sphere) and the teal community. R1 (yellow). 402 403 8. Temporal correlations within the R1 relay. 404 Transmission of information between subunits encoded by the phosphorylation-dependent 405 couplings was analysed to understand signal relay kinetics. The core network of long-range allosteric 406 couplings (n = 115, nMI > 0.09) linked the bound and free R1 to sites A, B and C (Figure 8A). A patch 407 of three hydrophobic residues that attach R1 to B site helix D (I101, A279”, I280”) formed the central 408 node. This node is less compact in the native (T286) relative to the phosphorylated (TPO286) dimer. 409 Most human mutations causing learning disabilities map within or close to the central and accessory 410 network nodes. In addition to communication between the intermediate relay communities and R1 411 (Figure 7G), the proline (P212, P213, P235) mutations could also regulate interface flexibility. 412 Time series of the local, SA-encoded structural transitions for residue fragments that consti- 413 tute this phosphorylation-dependent network are plotted for one replica run (Figure 8B). The most 414 frequent transitions were short (< 10 ns) and sampled a restricted range of dihedral angles. Dihedral 415 angle jumps scale with the separation between SA letters. Large jumps were rare but persisted for 416 longer times (> 100 ns) when they occurred. Two examples are shown. The large jump for fragment 417 V163 loop to -helix is around the middle (~150 ns) of the time series. There is a smaller jump for 418 fragment E274 between loop (-sheet to -helix) configurations at a similar time. 419 The cross-correlation (CCF) between the nMI time-series for the long-range (> 12 angstrom) 420 couplings in the direct (A279-E-274) and indirect (V163-E74) R1-R1 pathways in the phosphorylated 421 (TPO286) dimer network showed two peaks consistent with the short duration of fragment structural

422 transitions (1-2 ns 1/2 ’s) (Figure 8C). The first peak (t < 1 ns) presumably represents couplings asso- 423 ciated with the direct pathway. The second peak (t ~ 10 ns) represents the lag associated with the 424 first stage of the indirect, two-stage pathway. The CCF for the EED fluctuations of the two R1 segments 425 in the phosphorylated dimer reported a weak correlation (amplitude = 0.35, correlation time  = 15 426 ns). The correlation was not significant for the non-phosphorylated dimer.

427 bioRxiv preprint doi: https://doi.org/10.1101/524660; this version posted January 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 16

428 429 Figure 8. Temporal couplings of the R1-R1 signal network. A. (i) Parallel signal pathways formed by 430 the dominant, long-range couplings in the C-lobe. The hydrophobic patch (circled) formed by helix aD 431 and captured R1 orchestrates the couplings. Two pathways (1 direct (thick red line), 1 indirect (thin red 432 lines) connect the patch and the free R1. The donor C-lobe also links to the patch (dotted red lines). R1 433 segments (yellow) and DFG motifs (purple) are highlighted. Cyan side-chains show residue positions 434 where mutations cause learning disabilities in humans. (ii) atomic (stick) representation of the hydro- 435 phobic patch in the major configurations derived from cluster analysis of the T (cyan) and TPO (yellow) 436 forms. B. Times series from one replica run of structural transitions within the signal pathway frag- 437 ments (name = first residue). Colors denote SA letters as in B. C. CCF couplings between R1 segments 438 in the phosphorylated (TPO) dimer (D ~ 2.5 ns. 1/2 ~ 10 ns) (black line). CCF of information flow to the 439 free R1 from the adjacent C-lobe fragment correlated with the bound R1 fragment that forms part of 440 the hydrophobic cluster. bioRxiv preprint doi: https://doi.org/10.1101/524660; this version posted January 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 17

441 Discussion 442 443 Our findings indicate that the captured R1 freezes collective motions of the receiver subunit 444 C-lobe to orchestrate allosteric coupling based on helix melting. Secondary structure fluctuations re- 445 vealed -helical character of free R1 compatible with ESR evidence (13) and showed that the captured 446 RI transitions to an extended conformation energized by binding site solvation. The strained R1 trig- 447 gered long-range couplings that propagated to the receiver R1. R1 is similar to -helical linkers in the 448 bacterial flagellar basal body that also respond to strain (39). Such “chameleon” helices may play 449 essential roles in propagating conformational states across multiple subunits. While initial R1 capture 450 has an enthalpic contribution, subsequent signal propagation is entropic as found for many systems 451 (40). 452 The allosteric network (1) has a global architecture based upon a generic monomer KD net- 453 work; (2) has retained nucleotide and substrate binding site couplings important for activation; (3) is 454 strengthened by T286 phosphorylation and (4) incorporates mutated residue positions implicated in 455 human disabilities as well as possible therapeutic targets. We discuss these network properties below. 456 457 1. Global architecture. 458 Dynamic couplings consider both population shifts and propagation timescales of conforma- 459 tional ensembles (41). Thus, they provide a more refined readout for mechanistic analysis than the 460 architecture of the protein fold (42). The auto-inhibited CaMKII form is completely inactive since the 461 ATP binding site is not in an optimal conformation and the substrate binding site is occluded by the 462 regulatory segment. The multiple community membership of the DFG and helix D sites drove global 463 adaptations of the network architecture coupling nucleotide and substrate binding. Reduced coupling 464 between the communities, most marked for the coiled-coil dimer (BDW) structure, characterized the 465 inactivated state. R1 capture results in reduced flexibility of the receiver C-lobe core; reported by 466 RMSF, PCA, cluster and community network analysis. 467 The monomer network is co-opted in the chained dimer to generate a network that spans

468 both KDs. A hydrophobic patch between the R1 central residues and helix D orchestrated R1donor->

469 R1receiver signal relays; most dominantly from the patch directly to R1receiver N-and indirectly via the re- 470 ceiver DFG motif. Interfacial interactions linked the donor DFG motif to the patch. The prominent frag- 471 ment couplings lasted a few to a hundred nanoseconds. Most were confined to short (~ 10 ns) transi- 472 tions over a small conformational range. Large conformational transitions were infrequent but per- 473 sisted for longer (>100 ns) times. Transitions between phosphorylated and dephosphorylated confor- bioRxiv preprint doi: https://doi.org/10.1101/524660; this version posted January 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 18

474 mations completed within hundred nanoseconds. The temporal behaviour is consistent with a com- 475 plex free-energy landscape with multiple pathways (43). We suggest the reduced flexibility of the re- 476 ceiver KD C-lobe upon R1 capture will influence the displaced receiver R1 to explore and bind to adja- 477 cent “open” subunits with floppy cores rather than re-associate with its own frozen, occupied core. 478 The outcome is a self-reinforcing network that can be serially transmitted across the ring of KD C-lobes. 479 480 2. Activation dynamics. 481 Our survey of CaMKII KD monomer structures revealed the nucleotide binding DFG motif and 482 the B-site D helix as conserved, coupled network nodes. The DFG motif is OUT when the KD is bound 483 to the AD hub; an interaction analogous to the docking interaction of the PKA catalytic subunit with its 484 regulatory subunit (7). There were two distinct DFG IN orientations, one associated with activated and 485 the other with inactivated states, as in Aurora kinase (AurA) (44). The DFG motif is IN in auto-inhibited 486 KD’s not bound to the hub. Thus, DFG motif orientation may report on compact and extended inactive 487 holoenzyme states that have been visualized by EM cryo-tomography (45). In contrast, helix D is OUT 488 in all auto-inhibited, but IN for activated open and substrate-bound structures. 489 Our results add to data arguing that while the DFG motif is an important determinant of ATP 490 binding its mobilization follows different strategies during activation of EPKs. In AurA, activation by the 491 effector TpX2 involves an equilibrium population shift from the OUT to IN state (46); but activation by 492 phosphorylation triggers a switch between auto-inhibited and activated IN states (44). Multiple strat- 493 egies for kinase auto-inhibition have also been identified, for example, in the ZAP-70 tyrosine kinase 494 (47). 495 Cooperativity in BCR-ABL, a tyrosine kinase identified as hallmark for myeloid leukemia can be 496 either negative (48, 49) or positive (26) depending on the coupling between the nucleotide and sub- 497 strate binding sites. In CaMKII, as reported here, the nucleotide and substrate binding modules are 498 again recruited, but for formation of trans-subunit couplings. Comparative bioinformatics reveal com- 499 mon substrate binding site interactions between CaMKII and phosphorylase kinase (50), but the phos- 500 phorylase holoenzyme is constitutively active and its complexity limits study of nucleotide-substrate 501 coupling. 502 5033. 3. T286 phosphorylation. 504 T286 trans-phosphorylation has short and long-term consequences for LTP. In the short-term, 505 second time scale TPO286 increases CaMKII affinity for calmodulin and decreased affinity for actin, 506 triggering dissociation from the cytoskeleton and sequestration at the PSD in dendritic spines. It facil- bioRxiv preprint doi: https://doi.org/10.1101/524660; this version posted January 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 19

507 itates optimal Ca2+/ CaM binding, increasing its affinity for R2 more than 1000-fold and enables fre- 508 quency-dependent activation (29, 51). It also alters the affinity of some substrates for CaMKII, thus 509 modifying substrate selection (52, 53). In vitro, activation triggers subunit exchange over minutes to 510 propagate the activated state to previously inactive holoenzymes and prolong the lifetime of an acti- 511 vated holoenzyme population (54). Synaptic localization of CaMKII holoenzymes triggered by millisec- 512 ond calcium transients (55) persists over an hour or more (15), implying the activated CaMKII transi- 513 tions to a long-lived state. 514 The MD simulations of T286 and TPO286 modified CaMKII dimers resolved changes triggered 515 by primary site (T286) phosphorylation. T286 phosphorylation strengthened the coupling between 516 chained KDs, with pK shifts of buried residues to more neutral values and surface, interfacial residues 517 to more polar values, accompanied by compaction of the hydrophobic patch. The long-range allosteric 518 network could regulate cytoskeletal interactions, calmodulin trapping and kinase cooperativity; all fac- 519 tors that would in turn modulate frequency tuning – a key parameter determining CaMKII physiology. 520 The dissociated holoenzymes must remain activated during diffusion to the PSD, so as to not 521 rebind to the cytoskeleton. Similarly, during subunit exchange, the activated dimer must last longer 522 than the time for encounter with another holoenzyme. Diffusion and encounter times are on the order 523 of milliseconds based on known spine volumes (~ 1 m3) and spine CaMKII concentrations (> 0.1 M). 524 The increased Ca2+/ CaM binding affinity of the phosphorylated dimer extends the window for R1 cap- 525 ture beyond the transient calcium pulse (< 20 seconds). The greater stability of the phosphorylated 526 versus non-phosphorylated chained dimer predicted here provides additional discrimination to pro- 527 long the activated state after Ca2+/ CaM dissociation. The nanosecond coupling dynamics accommo- 528 date the rapid shifts in calmodulin and actin affinity. We speculate the nanosecond fluctuations would 529 be low-pass filtered in the dodecameric holoenzyme to freeze the activated cores over millisecond 530 times for diffusion to the PSD or subunit exchange. Conformational spread can achieve long-lived (sec- 531 onds) configurations in multi-subunit ring assemblies such as the rotation states of the bacterial fla- 532 gellar motor (56). 533 The self-reinforcing R1 signal relays are likely to facilitate conformational spread. Structural 534 elements that regulate the positive CaMKII kinase cooperativity as with Ca2+/ CaM concentration have 535 been identified. Reported Hill-coefficients (H) for substrate phosphorylation varied from 4.3 to 1.1 with 536 Ca2+/ CaM concentration accompanied by shifts in half-maximal dose. They are downshifted by inhib- 537 itor peptides (H 4.3 -> 1.7), hydrophobic patch residue mutations (3.0 -> 1.5) and native / decoy KD 538 mixtures (1.5 -> 0.9) and correlate inversely with linker length (H =4.3 –> 1.7) in the C. elegans holoen- 539 zyme (8). H is reduced (H 2.1 -> 1.1) by residue mutations in the AD hub interface docking the KD DFG 540 motif in the human holoenzyme (7). The inhibitor peptide and hydrophobic patch modulations of H bioRxiv preprint doi: https://doi.org/10.1101/524660; this version posted January 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 20

541 values agree qualitatively with the main features of the dynamic network we have characterized. The 542 linker length and AD mutations merit study of their role in Ca2+/CaM activation dynamics. Two distinct 543 modes for conformational coupling have been proposed; lateral spread of the activated conformation 544 across the holoenzyme subunits (8) or transverse paired dimers (9, 32). The latter may also mediate 545 activation-triggered subunit exchange, driven by a strained, central AD hub (57) (Supporting Infor- 546 mation Figure S3). 547 548 4. Physiological implications 549 The behavioural, histological and cellular phenotypes of the human mutations have been doc- 550 umented (18, 19), but these phenotypes are too downstream to decipher their molecular basis. This 551 study shows that the mutated residue positions are distributed along the allosteric signal relays gen- 552 erated by R1 capture and strengthened by T286 phosphorylation to provide, for the first time, a mo- 553 lecular rationale. Namely that the mutations principally act to disrupt the allosteric network rather 554 than weaken substrate or nucleotide binding per se. Disruption of the allosteric network could have 555 multiple outcomes as discussed above to produce gain or loss of function with diverse pathophysio- 556 logical consequences. 557 Importantly, this study opens possible avenues for therapeutic treatment. MD simulations 558 have proved useful for determination of the efficacy of peptide inhibitors to ATP-binding pocket resi- 559 due mutations (58). The design of allosteric inhibitors is more challenging as it requires evaluation of 560 the conformational plasticity of the protein assembly but promises greater specificity. We have iden- 561 tified protein sectors based on community analysis that may disrupt conformational coupling without 562 altering calmodulin, nucleotide or substrate binding. Their predicted role as signal relays rather than 563 binding determinants can be tested by mutant screens. An excellent example in the literature of such 564 a mutation is PKA Y204A that disrupts coupling between nucleotide and substrate binding without 565 affecting binding affinities (59). 566 In conclusion, our simulations make the case that the conformational dynamics of chained 567 dimers have advantageous properties for subunit exchange and holoenzyme activation. Network anal- 568 ysis revealed the centrality of the coupled A (DFG motif) and B (helix D) sites in the R1 relay to suggest 569 how substrate affinity is modulated by nucleotide occupancy and how both influence cooperativity. It 570 detailed how T286 phosphorylation strengthened conformational coupling initiated by R1 capture. Fi- 571 nally, community graphs identified targets for rational design of allosteric inhibitors (22). Future work 572 will build on these advances to reconcile the dynamic architecture of the kinase with measurements 573 of its cooperativity. 574 bioRxiv preprint doi: https://doi.org/10.1101/524660; this version posted January 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 21

575 Materials & Methods 576 577 1. Phylogenetics. 578 CaMKII sequences were retrieved from Uniprot (60). MUSCLE was used for multiple sequence 579 alignment (MSA). Secondary structure predictions were made with PsiPred. The MSA was manually 580 curated in Jalview. The phylogenetic tree was constructed with Fast-Tree 2.19 and displayed with Fig- 581 Tree 4.3 (http://tree.bio.ed.ac.uk/software/figtree/). 582 583 2. Structure Preparation. 584 The human  KD structure alone (PDB ID: 2VN9) and with calmodulin (2WEL)(9), complete 585 subunit from the human holoenzyme (3SOA (7)); the C. elegans KD structures alone (2BDW (23), 3KK8 586 (8)) and with CaMKIINtide (3KL8 (8)) and the open form of protein kinase A (1CMK (61)) were down- 587 loaded from Protein Data Bank. Missing atoms were added in Swiss-Pdb viewer 588 (www.expasy.org/spdbv); missing loop segments with Modeller (https:/salilab.org/modeller). Mutant 589 substitutions were made in Pymol (http://pymol.org) then energy minimized in Modeller. 590 591 3. tCONCOORD. 592 Parameters for tCONCOORD runs were as detailed earlier (62). tCONCOORD utilizes a set of distance 593 constraints, based on the statistics of residue interactions in a crystal structure library (25, 63), to gen- 594 erate conformational ensembles from an initial structure without inclusion of solvent. Sets of 164 = 595 65,536 equilibrium conformations with full atom detail were generated for each structure. The overlap 596 between ensemble subsets was > 99% when subset size was < ½ of this value. 597 598 4. Molecular Dynamics. 599 A set of 3 replicas of 300ns were generated for E. coli 3KK8 structure and its 286T equivalent 600 using Gromacs 2016.2 with Amber ff99sb*-ILDNP force-field (64). Each system was first solvated in an 601 octahedral box with TIP3P water molecules with a minimal distance between protein and box bound- 602 aries of 12 Å. The box was then neutralized with Na+ ions. Solvation and ion addition were performed 603 with the GROMACS preparation tools. A multistage equilibration protocol, modified from (65), was 604 applied to all simulations to remove unfavourable contacts and provide a reliable starting point for 605 the production runs including: steepest descent and conjugate gradient energy minimisation with po- 606 sitional restraints (2000 kJ mol-1 nM-2) on protein atoms followed by a series of NVT MD simulations 607 to progressively heat up the system to 300 K and remove the positional restraints with a finally NPT 608 simulation for 250 ps with restraints lowered to 250 kJ mol-1 nM-2. All the restraints were removed for bioRxiv preprint doi: https://doi.org/10.1101/524660; this version posted January 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 22

609 the production runs at 300 K. In the NVT simulations temperature was controlled by the Berendsen 610 thermostat, while in the NPT simulations the V-rescale thermostat (66) was used and pressure was set 611 to 1 bar with the Parrinello-Rahman barostat. A set of 3 replicas with time step 2.0 fs with constraints 612 on all the bonds were used. The particle mesh Ewald method was used to treat the long-range elec- 613 trostatic interactions with the cut-off distances set at 12 Å. The threonine phosphate (TPO286) was 614 changed to threonine (T286) after equilibration to generate the non-phosphorylated form. 615 616 5. Energetics. 617 Contact residues, surfaces and energies were extracted from the PDB files with the sub-rou- 618 tines (ncont, pisa) available in CCP4 version 7 (http://www.ccp4.ac.uk/). Continuum electrostatics were 619 computed with the Poisson Boltzmann solver (http://www.poissonboltzmann.org/)(67). Comparison 620 with experimental B-factors and geometrical analyses were performed with GROMACS version 4.5.7 621 (http://www.gromacs.org/). 622 623 6. Structural alphabet. 624 The mutual information 퐼(푋; 푌) between two variables(푋) and (푌) is 625 퐼(푋; 푌) = 퐻(푋) + 퐻(푌) − 퐻(푋, 푌); 626 where 퐻(푋, 푌) is the joint probability distribution; 627 The normalized mutual information, 푛푀퐼(푋; 푌) = (퐼(푋; 푌) − 휀(푋; 푌))/(퐻(푋, 푌)); 628 where 휀(푋; 푌) is the expected, finite-size error; 629 The 푛푀퐼 couplings are detected as correlated changes in fragment dynamics. In methods 630 based on the dynamics cross-correlation matrix (68), the correlation is calculated from position fluc- 631 tuations of the residue C atoms. In the MutInf method (69), correlations are measured in terms of 632 mutual Information between discretized torsional angles. The residue-based approaches do not di- 633 rectly read-out couplings between structural motifs, e.g. secondary structures. The SA (70), is a set of 634 recurring four residue fragments encoding structural motifs derived from PDB structures. There is no 635 need for discretisation and / or optimisation of parameters as the fragment set is pre-calculated. 636 637 7. Principal Component Analysis. 638 Collective motions were identified by PCA of the conformational ensembles. PCs were 639 generated by diagonalization of the co-variance matrix of Cα positions. For tCONCOORD the 640 motions have no time-scale, but comparison with MD trajectories was consistent with the bioRxiv preprint doi: https://doi.org/10.1101/524660; this version posted January 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 23

641 notion that collective motions represented by the first few PCs are “slow” relative to smaller 642 amplitude motions recorded by the later PCs. 643 644 8. Network Analysis. 645 Statistically significant correlations between columns were identified with GSATools 646 (33) and recorded as a correlation matrix. The correlation matrix was used to generate a net- 647 work model; with the residues as nodes and the correlations as edges. The contribution of a 648 node to the network was estimated by the eigenvector centrality, E, calculated directly from 649 the correlation matrix:

650 퐸. [푀]푐표푟푟= 퐸.λ

651 where [푀]푐표푟푟 is the correlation matrix and λ is the eigenvalue 652 The Girvan–Newman algorithm (34) was used to identify community structure. Then 653 the network was collapsed into a simplified graph with one node per community, where the 654 node size is proportional to the number of residues. Edge weights represent the number of 655 nMI couplings between communities (35). Community analysis of correlation networks iden- 656 tifies relatively independent communities that behave as semi-rigid bodies. Graphs were con- 657 structed with the igraph library (71) in R (https://cran.r-project.org/web/packages/igraph/) 658 and visualized in Cytoscape (http://www.cytoscape.org/). 659 660 9. Quantification and Statistical Analysis. 661 Typical size of a tCONCOORD ensemble was 65,536 conformations (2562). Three MD replicate 662 runs for the two (phosphorylated, dephosphorylated) conformations. Ensemble conformations and 663 MD runs were averaged for computation of the nMI between fragment positions. Significance limits 664 were set in GSATools. Supporting Information Table S1 lists the web databases and software servers 665 used in this study.

666 667 bioRxiv preprint doi: https://doi.org/10.1101/524660; this version posted January 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 24

668

669 Acknowledgments: AP was supported by Brunel BRIEF Award. H.S was supported by 670 National Institutes of Health grant RO1 GM101277. SK had support from the Royal Society collabo- 671 rative exchange grant U1175.70592 and seed funds from the Molecular Biology Consortium. Com- 672 putation for the work described in this paper was supported by the Crick Data Analysis and Man- 673 agement Platform (CAMP), provided by the Francis Crick Institute. 674

675 Author contributions: Conceptualization: AP and S.K. Methodology: AP and SK, Soft- 676 ware: AP, Validation: SK, Writing – First Draft: SK. Writing –Review & Editing: AP, HS and SK, Visual- 677 ization: AP, HS and SK, Supervision / Project Administration: SK. Funding Acquisition: AP, HS and SK.

678

679 Declaration of Interests: The authors declare no competing interests. 680 681 bioRxiv preprint doi: https://doi.org/10.1101/524660; this version posted January 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. 25

682 References

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851 Supporting Information 852 853 Appendix S1: Table & Figures (PDF) 854 Figure S1: CaMKII KD Conservation 855 Figure S2: PKA and CaMKII have Homologous Structure and Dynamics. 856 Figure S3: Conformational coupling in the CaMKII holoenzyme. 857 Table S1: Web Resources. 858 859 Movie S1-S2. PCA of the 3KK8 monomer and dimer (AVI). The three major communities are colour- 860 coded as in Figure 3A. TPO286 (red spheres). The filtered PC, PC1 and PC2 motions are shown. Related 861 to Figure 4A. 862 863 Movie S3-S4: Filtered PC trajectory of the free and captured R1 (AVI). Three replica MD runs of the 864 non-phosphorylated 3KK8 dimer sampled at 600 ps. T286 (yellow sphere). Residues are color-coded 865 according to type (white = hydrophobic, red = acidic, blue = basic). Related to Figure 5A. 866 867 Movie S5: Network architecture of the phosphorylated 3KK8 dimer (AVI). Related to Figure 7C. 868 869 Movie S6: Surface profile and spatial relationship of intermediate relay community residues with 870 the proline cluster targeted by human mutations and TPO286 (AVI). Related to Figure 7G