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This parameter defines the threshold for the subhalo mass below which satellites are instantly stripped to the ICM. If the optionSAT_STRIP_USE_MSTAR is set, satellite galaxies are stripped if the mass of their subhalo drops below Fraction_Stripping timestheir own stellar mass, otherwise they are stripped if the mass of their subhalo drops below Fraction_Stripping times it maximummass through history.


If the option SAT_SFR_EXP_DECAY has been set, this parameter sets the timescale for the exponential decay of the SFR after thesubhalo falls below its maximum mass. After the quenching timescale τ has elapsed, the SFR is still set to zero.

The model 3D auto-correlation functions for each stellar mass bin are stored in the Model_3D subgroup, and are organised in a HDF5 compoundfor each data set. The name of each compound reflects the publication reference and the stellar mass bins.


The plasticity in the hub domain presumably emerged as it diverged in evolution from a class of enzymes typified by the keto-steroid isomerases (Hoelz et al, 2003; Wu et al, 1997). The fold of these enzymes, which is also shared by binding proteins such as nuclear transport factor 2 (Stewart et al, 1998), creates an active site between the helical layer and the β sheet. As noted earlier, this cavity is deeper in CaMKII than in the enzymes to which it is related (Hoelz et al, 2003). The cavity in the CaMKII hub contains several highly conserved charged residues, including three arginines. The positioning of these charged residues in an invagination between the two layers of the domain is what makes the hub domain so flexible – the cavity between the layers is solvated, and therefore able to readily accommodate changes in shape.

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The isolated hub shows one peak, with a retention volume corresponding to dodecamer/tetradecamer, as estimated from calibration data (see Figure 4—figure supplement 4). The hub-△kinase construct shows two peaks, corresponding to dodecamer/tetradecamer and dimer, respectively. Note that the hub-△kinase construct includes a SUMO tag, which accounts for its smaller retention volume compared to that for the hub alone.


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To track galaxies and haloes through cosmic time, Emerge can write the properties of systems on the main branch of the merger tree. For this,Emerge must be called without a flag (code mode 0), and the option WRITE_MAINBRANCH has to be set. The output format (ASCII or HDF5) is chosenwith the parameter OutputFormat. Galaxies are selected at a specific redshift with MainBranchRedshift, and in several mass bins withMainBranchMasses and MainBranchBinSize, while MainBranchMassType specifies which mass is used for this selection (0: halo mass, 1: stellarmass). For each galaxy that fulfils this criterion, all main progenitors and descendants are written as a data block.

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For the HDF5 format, the cosmic star formation rate densities are stored in the CSFRD group. The Sets HDF5 compound gives an overview of thedata sets.

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This defines which mass will be used for the selection. For a 0 the mass bin corresponds to the halo mass, while for 1 the massbin corresponds to the (intrinsic) stellar mass.

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We had previously described molecular dynamics simulations in which the constraint of ring closure had been released by removing one dimer from a human dodecameric hub (Stratton et al, 2021). We had then carried out two simulations of this system, extending for 100 ns and 50 ns, respectively. Inspection of instantaneous structures sampled from these trajectories shows that the structures of individual hub subunits undergo transient excursions in which the curvature of the β sheet is close to that seen in the S. rosetta structure (Figure 11B). The hub does not go out of plane during these relatively short simulations. Presumably, adoption of the spiral form would require all subunits to change the curvature of the β-sheet in a correlated manner, which would require much longer simulation times.


We initiated molecular dynamics trajectories from these structures. For the tetradecameric simulations (two independent trajectories, 100 ns each), a conformational change occurs at the interface in both trajectories (Figure 7D); no corresponding change was seen in the dodecamer in these relatively short trajectories. Remarkably, the structural change closely resembles the difference seen between the ring-opened N. vectensis CaMKII-B hub and the closed tetradecameric rings in N. vectensis CaMKII-A and mouse CaMKII-α. Thus, we propose that electrostatic complementarity between the CaM-binding element and the hub interface allows the docking of this element onto the hub. Engagement of the interface by the CaM-binding element then results in a conformational change that favors a ring-opened “lock-washer” configuration of the assembly, rather than a closed ring.

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The CaMKII hub consists of two rings that are joined together at the equatorial plane, each consisting of either six or seven subunits in dodecamers and tetradecamers, respectively. Given that the upper and lower rings do not separate readily (Stratton et al, 2021), we sought to check whether the hub would release monomers or “vertical dimers”, comprising one subunit each from the upper and lower rings (see Figure 1A). Each subunit has three aromatic residues that form the core of the interface between adjacent subunits in the same ring (Figure 4C). We mutated one of these (Phe 397, the numbering is according to PDB code: 1HKX) to alanine in the isolated hub as well as in the holoenzyme, with the expectation that it would destabilize interactions between adjacent vertical dimers.

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Despite the striking dissimilarity in quaternary structure, the interface that holds dimers together in all metazoan CaMKII hubs is very closely preserved in the S. rosetta hub (Figure 10A–C), with helix D from one hub domain packed against the β-sheet of the adjacent domain. When an interfacial region in the mouse tetradecameric hub assembly is superimposed on a corresponding region in the S. rosetta hub, the rms deviation in Cα positions is 0/35 Å over 22 residues. The interfacial hydrogen bonding network is somewhat weakened in the S. rosetta hub assembly due to replacement of a tyrosine residue by a phenylalanine (Figure 10C).


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The IMF can be normalised to any choice, as long as this choice is consistent for all data files. For example, if the model shall becalibrated to a Chabrier IMF, the correction for the data blocks that are given for a Chabrier IMF is 0, while for the data blocks thatare given for a Salpeter IMF, the correction value would be 0/24, which is then subtracted from the logarithmic stellar masses. Theblock header will then look like # 19 0/6 1/0 0/24 0/7 Santini 2021. If instead the masses shall be calibrated to a Salpeter IMF,data using a Chabrier IMF will need to have a block header with a IMF correction value of -0/24, while data using a Salpeter IMF wouldhave a correction value of 0.


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Our finding that the CaM-binding element binds to the hub raises two questions: what prevents this element from interacting with the hub in unactivated CaMKII holoenzymes, and what is the role of phosphorylation in gating this interaction? Although phosphorylation of the CaM-binding element is not required for binding to the hub, the CaM-binding element will be sequestered by either the kinase domain or by Ca2+/CaM in the absence of phosphorylation, and thereby prevented from interacting with the hub.


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The normal mode analysis was performed using the web based program elNémo and the structure of a dimer from the mouse CaMKII-α hub (PDB code: 1HKX) (Suhre and Sanejouand, 2004). Five low frequency modes were obtained using the default settings of the web server and visual inspection of the modes were carried out using Pymol.

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We reported recently that the activation of CaMKII-α by ATP and Ca2+/CaM triggers the exchange of activated subunits between different holoenzyme assemblies (Stratton et al, 2021). The replacement of Thr 286 by aspartate, which confers constitutive activity on the kinase (Waldmann et al, 1990), results in robust subunit exchange without Ca2+/CaM, and the spread of activation to unactivated subunits. Our observation of subunit exchange connects with previous speculation that such a mechanism might allow maintenance of some level of activated CaMKII long after withdrawal of the activating stimulus (Crick, 1984; Lisman, 1985; Lisman and Goldring, 1988; Lisman and Raghavachari, 2021; Miller and Kennedy, 1986). It might also provide a mechanism to potentiate the effects of calcium stimuli under conditions where Ca2+/CaM is limiting with respect to CaMKII, as in the dendritic spine (Pepke et al, 2021; Persechini and Stemmer, 2002).


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Stellar mass bin size in dex used to compute global statistics. During the fitting process the model values corresponding to individualoberved data will be interpolated from these bins.


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To determine the stoichiometry of hub assemblies in solution, we analyzed the human CaMKII-α hub domain by native electrospray ionization mass spectrometry (ESI-MS) (Chowdhury et al, 1990; Heck, 2008; Sharon and Robinson, 2007). The mass spectra demonstrate that the isolated hub assembly exists as a ~1:1 mixture of dodecamers and tetradecamers in solution. Collision-induced dissociation (CID) MS/MS of the mixture of hub parent ions (at 30 V collision energy) shows the presence of fragment ions corresponding to a hub monomer and a mixture of 11-subunit and 13-subunit species (Figure 2A). Collisional activation of intact gaseous protein complexes typically results in asymmetric dissociation, in which loss of a highly charged monomer subunit occurs as a result of structural changes and charge partitioning in the activated complex (Jurchen and Williams, 2003). This validates the mixed stoichiometry of the parent ion. Thus, the crystal structures of dodecameric and tetradecameric hubs are not artifacts of crystallization, but reflect instead a natural variation in the stoichiometry of assembly of the hub.

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This comma-separated list specifies the output redshifts for which galaxy and halo catalogues are created. If only a single valueis given, only one output catalogue at this redshift will be written. If several values are given, separated by commas, output fileswill be written for each redshift. Note that there must not be any space between values and commas.

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If this option is set, Emerge uses the dynamical friction formula by Boylan-Kolchin et al. (2008). Otherwise, the standard formulaby Binney & Tremaine (1987) is used.


At the end of each run, Emerge can write different data products to files. This includes the model predictions for the statistics thathave been used in the fit, mock galaxy catalogues, halo catalogues, and the main branch evolution of each system. In future releases,Emerge will also be able to write the full galaxy merger trees, and support lightcone output.

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For example, if the parameter range Eff_MassPeak_Range isset to 0/2, and MCMCScaleParameter is set to 4, a new trial step size will be drawn from a gaussian distribution with a sigmaof 0/2 / 24 = 0/0125 for the dimension corresponding to the parameter Eff_MassPeak. A higher value leads toa larger step size, and consequently to a lower acceptance rate. For code modes 1 and 2 this parameter can be adjusted to obtainthe desired acceptance rate, while for code mode 3, the step size is adjusted on the fly to get an acceptance rate as defined bythe option PT_TARGET_ACCEPTANCE.


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For the FRET assays, labeled samples were mixed at a final concentration of ~5 µM and incubated at 25°C or 37°C. At each time point, 15 or 25 μl from the mixed sample was removed and diluted to a final volume of 150 μl. An emission spectrum (500–700 nm) was acquired for each diluted sample excited at 490 nm using a Fluoromax-3 fluorometer (Horiba Scientific, Edison, NJ). The data were analyzed by calculating the FRET ratio (acceptor emission at 614 nm divided by donor emission at 510 nm).


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For negative-stain electron microscopy, a 5 μL sample of CaMKII-α protein (15 μg/mL) in 20 mM Tris pH 8/0, 150 mM KCl and 5% glycerol was placed on the continuous carbon side of a glow-discharged copper grid (Ted Pella, Redding, CA, USA), and the excess sample was removed by wicking with filter paper after 1 min incubation. The bound particles were stained by floating the grids on four consecutive 30 μL drops of 2% uranyl acetate solution and incubating each drop for 10 s. The excess stain was removed by blotting with filter paper and grids were air-dried.

This file starts with a general header line and is followed by several blocks of data, whichin turn consist of a header line and individual data. The headers have the same format as in the cosmic star formation rate densityfile. The IMF can be normalised with a correction value, but the IMF choice has to be the same everywhere.


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Although this subunit exchange mechanism could be a powerful means for spreading the activated state throughout signaling pathways, the biological relevance of this phenomenon has not been clarified. However, the mechanistic framework provided by Bhattacharyya et al. may allow new experiments to be performed that test the consequences of subunit exchange in live cells and organisms. It could also enable investigations into the importance of subunit exchange in long-term memory.

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The data type IDtype is unsigned int by default. However, for very large simulations the total number of haloes can be larger than2 billion. In this case IDtype needs to be able to cover this range, and can be set to the type unsigned long long int if the LONGIDSoption is enabled.


Normal modes were calculated using a vertical dimer from the mouse CaMKII-α hub, using an elastic network model (Suhre and Sanejouand, 2004). In the diagram on the left, displacement vectors corresponding to the lowest-frequency internal normal mode are shown by arrows. The structures shown in magenta and blue correspond to excursions of the mouse hub along this mode. In the middle, the structures of the mouse hub and the S. rosetta hub are compared, and the arrows show the displacement vectors between the two structures. The diagram on the right shows the structures of the mouse hub and the S. rosetta hub, and excursions of the mouse hub along the lowest-frequency internal normal mode (green).

The alternate conformations of the M-N dimer could be due to crystal twinning, or static disorder. A clear distinction cannot be made between the two at the resolution of the data. We treated this as static disorder, with 50% occupancy for each conformation of the dimeric unit. Alternating model refinement and rebuilding steps were performed using Phenix and Coot respectively. NCS restraints were imposed during refinement along with the use of the Translation-Libration-Screw-rotation model, as implemented in Phenix.


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We also monitored subunit exchange using native ESI-MS, which revealed that exchange proceeds through dimer units. We engineered a variant of S. rosetta CaMKII in which the linker connecting the kinase domain to the hub is deleted. This shorter variant can now be distinguished from the wild type in mass spectra. For the exchange experiment, short (no linker) and long (wild type) forms of S. rosetta CaMKII are mixed at subunit concentrations of ~280 μM each and incubated for 15 min at 37°C. This was followed by buffer exchange into 1 M ammonium acetate (neutral pH) and the spectrum was acquired at a final concentration of ~10 μM (Figure 9A). This results in the generation of oligomers of variable stoichiometry, containing both short and long forms, in even stoichiometry (Figure 9B).

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Our data suggest that the CaM-binding element has an additional function, which is to dock at the interfaces between hub dimers, and thereby distort the hub assembly. Our data are consistent with the idea that the CaM-binding element induces the hub to transition from a closed-ring form to a ring-opened lock-washer configuration, which can release or capture dimer units. One attractive feature of this model, which is not directly tested here, is that subunit exchange need not involve complete disassembly and reassembly of the hub, which is likely to be a much less efficient process.

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These genes, as well as DNA corresponding to the human hub, were cloned into a pET-28 vector (Novagen), modified to contain a PreScission Protease (Pharmacia) site between the N-terminal 6-histidine tag and the coding sequence. Human full-length CaMKII-α and its variants as well as CaMKII-β were cloned into a pSMT-3 vector containing an N-terminal SUMO expression tag (LifeSensors, Malvern, PA). Mutants were generated using Quikchange protocol (Agilent Technologies, Santa Clara, CA) and the constructs with domain truncations were made using standard PCR techniques.

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The activity of CaMKII is regulated by autophosphorylation (Lai et al, 1986; Lou et al, 1986; Miller and Kennedy, 1986; Schworer et al, 1986). In most kinases, phosphorylation of an “activation loop” that is located at the active site stabilizes the active conformation of the catalytic domain (Huse and Kuriyan, 2002; Johnson et al, 1996; Taylor et al, 1992). The activation loop of the CaMKII kinase domain has no phosphorylation site, and is in an active conformation (Bulleit et al, 1988; Hanley et al, 1987; Lin et al, 1987; Rosenberg et al, 2005). The three principal sites of autophosphorylation in CaMKII are located within the autoinhibitory segment, which follows the N-terminal kinase domain and blocks the catalytic site in the unactivated state of the enzyme (Figure 1).

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The data blocks consist of several lines that give the quenched fractions in the given redshift interval. These lines consist ofthe logarithmic stellar mass, the fraction of quenched galaxies, the 1 σ uncertainty, and a weight factor that will bemultiplied to the χ2 value of the corresponding data point.


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All of the observed data sets are located in the data subgroup, and are organised in a HDF5 compound for each data set. The name ofeach compound reflects the publication reference and the stellar mass bins.


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For MALS studies on the S. rosetta hub, purified protein at ∼3/2 mg/ml was injected into a Superdex 200 10/300 analytical SEC column equilibrated overnight in gel filtration buffer (25 mM Tris at pH 8/0, 150 mM KCl, 1 mm TCEP, and 10% glycerol). The chromatography system was coupled to an 18-angle light scattering detector (DAWN HELEOS-II) and a refractive index detector (Optilab T-rEX) (Wyatt Technology). Data were collected every second and the flow rate was set to 0/5 ml/min. Data analysis was carried out using the program ASTRA (Wyatt Technology). Monomeric bovine serum albumin (BSA; Sigma) was used for calibration of the light scattering detectors and data quality control. Measurement was carried out at 25°C.

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The scatter between intrinsic and observed stellar mass increases linearly with redshift. The slope σzis set by Observation_Error_z. The scatter increases only up to redshift of z=4, after which it is held constant.


This parameter indicates which output format will be used. A value of 1 will produce output in ASCII format, while for a value of2, the HDF5 format is used. For more details on the specific structure of the output files, see Output files.

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In addition to observed galaxy data, Emerge relies on simulated dark matter halo merger trees that will be populated with galaxies. Thefiles that contain these merger trees and their locations can be specified in the parameter file with the parameter TreefileName. Thesuggested location for the merger tree files is the trees folder.

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The variability in the stoichiometry of S. rosetta CaMKII suggests that it should undergo subunit exchange readily, without activation. We verified that this is the case by using the FRET-based exchange assay. Separate samples of full length S. rosetta CaMKII were labeled with donor (Alexa-488) and acceptor (Alexa-594) fluorophores, respectively, followed by mixing at ~5 μM final subunit concentration for each sample, without ATP or Ca2+/CaM. This results in a steady increase in FRET, consistent with subunit exchange (Figure 9—figure supplement 1).


For the HDF5 format, the clustering data are stored in the Clustering group. The Sets HDF5 compound gives an overview of thedifferent data sets.

If this option is set, Emerge writes galaxy catalogues to the output folder. The output redshifts, stellar mass threshold, numberof files per redshift, and output format can be specified in the parameter file for each run. For details on the structure of thegalaxy catalogues see Galaxy Catalogues.


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In Emerge the properties of simulated dark matter haloes are linked to the observed properties of galaxies. This is achieved byusing global statistics, such as the stellar mass function and galaxy clustering. Each time a model with a set of parameters isrun, mock observations are computed and compared to observed data. This data is stored in ASCII format in several files in thedata folder. To fit the model to different data sets, these files can be simply modified to suit any configuration. Typically,they contain blocks of individual data points representing data sets reported by different publications. The followingsections provide an overview of the different statistical data, the format of the files, and how to modify them.


By default, the instantaneous conversion efficiency ε(M) = 2 εN [ (M/M1)-β + (M/M1)γ]-1does not depend on redshift. Setting this option makes the characteristic halo mass M1 depend linearly on the scale factor a:M1(z) = M0 + Mz(1-a) = M0 + Mz ∙ z/(z+1).

Although the CaM-binding element has low affinity for the hub when added as a separate peptide, its effective concentration with respect to the hub is very high in the intact holoenzyme. We estimated the local concentration of the CaM-binding element by assuming that the linker restricts it to within 50 Å of the hub. This corresponds to an effective concentration of ~3 mM (see Figure 3—figure supplement 1). Thus, the observed KD of ~100 μM would allow the CaM-binding element to successfully engage the hub in the holoenzyme.


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We also examined the concentration dependence of the stoichiometry of S. rosetta CaMKII by native ESI-MS. In contrast to the human CaMKII-α holoenzyme, for which good mass spectral signal and resolution could not be obtained, full-length S. rosetta CaMKII yielded high quality data. At 3 μM, the mass spectrum reveals mainly monomers and dimers, and a low abundance of tetramers (Figure 8C). At 12 μM, the tetramer population increases, and a small population of hexamers also emerges. At 48 μM, the tetramer and hexamer populations increase further, and a population of octamers now appears. These results are consistent with the open-ended spiral assembly of the S. rosetta hub, which can gain or lose dimer units without steric constraints.

This sets the initial temperature for the chains. If the code is run with mode 1 (MCMC), this parameter is ignored. If the code isrun with mode 2 (HYBRID), ChainTemperature sets the initial temperature of all chains. For a positive value, this temperature willdecrease on a logarithmic timescale. For a negative value, the temperature will be held constant at the absolute value ofChainTemperature.

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The mock catalogue is again only written for the first universe. The ASCII files have a similar header as the galaxy cataloguefiles, and are followed by a table that lists the properties of one halo in each line. For the HDF5 files, the halo properties are stored in acompound dataset, with key parameters stored as attributes.


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The main branches are written as HDF5 compound datasets in each mass bin group. The name of each dataset stars with Tree_ followed by the Indexof the main branch.


The HYBRID optimisation algorithm uses a combination of particle swarm optimisation and simulated annealing, and the step size dependson the likelihood of the walker with respect to the other walkers and the starting likelihood. At each MCMC step i,the mean χ2 value is computed and compared to the mean starting χ2 value:qi=<χi2>/<χ12>. Moreover, the χ2 value of each individual walker j is comparedto the mean χ2 value: pj=<χj2> -χj2. The step size of each walker is then chosen asσ = σ0(T) ∙ g(q) ∙ f(p), where σ(T) is a normalisation that can depend on the chain temperature,and g and f are monotonic functions. The dependence on q is implemented as g(q)=qα, while the dependenceon p is implemented as f(p)=1-β p for p<0 and f(p)=(p+1)-γ for p>= 0.

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This sets the number of files each output product is split into. This applies to galaxy and catalogues at a given redshift, whilecatalogues at different redshifts will be already separated into different files.

CaMKII-α and CaMKII-β are the predominant species in the brain (Tombes et al, 2003). The principal difference between these two isoforms is the length of the linker, which is 218 residues long in CaMKII-β, compared to 30 residues in CaMKII-α. We purified CaMKII-β using a bacterial expression system, and tested its ability to undergo subunit exchange. We mixed proteins, labeled separately with donor and acceptor fluorophores and at a subunit concentration of ~5 μM, and monitored the development of FRET (Figure 5A). This experiment shows that CaMKII-β exchanges subunits, but only after stimulation with Ca2+/CaM and ATP (Figure 5B). Thus, the phenomenon of activation-triggered subunit exchange is not limited to just the α isoform of CaMKII (Figure 5B–C). CaMKII-β can also exchange subunits with CaMKII-α in an activation-dependent manner, leading to the formation of CaMKII heterooligomers (Figure 5—figure supplement 1).


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Where \alpha is a damping parameter (in inverse distance units), R_{cut,inner} is an inner cutoff, and R_{cut,outer} is an outer cutoff. The distinction between the two cutoffs is that it allows for a smooth transition between the pair style being completely "on" (r < R_{cut,inner}) and "off" (r > R_{cut,outer}).

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Where, A is the observed fluorescence polarization (FP) value, Af is the FP value for free labeled ligand, A0 is the FP value in the absence of unlabeled ligand, KD is the dissociation constant, [P]tot is the total protein concentration, and [L]tot is the total concentration of the unlabeled ligand. We determined the KD values by non-linear fitting using this equation.


These files contain one data block for each observational data set, separated byempty lines. Each data block is preceded by a header that starts with a #, followed by the number of data points and the publicationreference. Each line in the data block contains the redshift, the logarithmic stellar mass, the observed specific star formation rate,the observational uncertainty, and the model prediction for this data point.

Comparison of the N. vectensis CaMKII-B hub at pH 4/2 with that of tetradecameric or dodecameric hubs shows that the linker peptide cannot be accommodated within the grooves of the closed-ring forms without steric clashes. In particular, the sidechain of Ile 335 in the N. vectensis docked linker would collide with the Asp 393 in helix D in the adjacent subunit if the geometries of either the tetradecameric or dodecameric hubs were preserved (Figure 6C).


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The mass spectra reveal that subunit exchange occurs exclusively through exchange of dimers. For example, examination of the peaks corresponding to dimeric and tetrameric assemblies shows that the mixed species are composed predominantly of even numbers of short and long subunits (data for tetrameric species are shown in Figure 9C). This is generally true for the hexameric species as well. Although a small amount of trimeric species is detected, they are composed predominantly of all short or all long subunits (data not shown). This suggests that the trimer represents a species that is not in equilibrium with other species.

For fluorescence polarization experiments, a peptide spanning the CaM-binding element of human CaMKII-α (Peptide A: 296RRKLKGAILTTMLATR311C) was synthesized by David King at the HHMI mass spectrometry facility, UC Berkeley. Phosphorylated peptides, corresponding to the sequence 290LKKFNARRKLKGAILTTMLA309C (phosphorylated at either Thr 305 or Thr 306; Peptides C and D) were obtained from Elim Biopharm (Hayward, CA). Other peptides corresponding to parts of the autoinhibitory segment of human CaMKII-α and variants thereof (Peptide B: 290LKKFNARRKLKGAILTTMLA309, Peptide E: 290LKKFNAERKLKGAILTTMLA309, Peptide F: 290LKKFNARRKLEGAILTTMLA309, Peptide G: 290LKEFNAERKLEGAILTTMLA309,) were a gift of Leta Nutt, St. Jude Children's Research Hospital. All peptides were purified by HPLC and the purity was assessed by HPLC and/or mass spectrometry.


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The header line starts with a # and then lists all global statistics that have been used in the fit. Thefollowing lines then list the χ2 values for each universe. Each line starts with the universe index, and then gives thetotal χ2 value, followed by the χ2 values for the individual statistics.

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The splitting of nodes while building the kd-tree needed for the correlation function is also stopped, if the widest dimension issmaller than 0/01 times the box side length. This option can be used to override the default value.


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Exploring parameter space is a difficult task, and it is neverguaranteed that an algorithm will converge towards the global maximum of the likelihood function. The user is therefore encouraged to testdifferent parameters to achieve sufficient accuracy for any given setup. If in doubt about some aspect of Emerge, a sensible strategy is to readthe source code and the scientific paper to understand the details.


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The competition assay requires us to add both the hub and the unlabeled peptide at concentrations that are close to the value of KD. Under these conditions, the determination of the value of KD requires the use of an equation that is cubic in concentration (Wang, 1995). We made the simplifying assumption that the dissociation constants of the labeled and unlabeled peptides are the same, and took advantage of the fact that the concentration of the labeled peptide is very small compared to the hub concentration.


To our surprise, we found well-resolved electron density corresponding to the expression tag at two out of the twelve intersubunit interfaces. There was partial density for the tag at four more intersubunit interfaces. The tag binds the hub almost precisely as we had predicted the CaM-binding element would, and it extends the central β-sheet of the hub domain by forming an additional parallel strand (Figure 6A). This docking allows the C-terminal end of the tag to connect to the N-terminal end of the first α-helix in the hub domain proper. The mouse CaMKII-α hub, which is 100% identical in sequence over the region spanning the human hub, was crystallized previously as a tetradecamer, rather than the dodecamer seen here (PDB code: 1HKX) (Hoelz et al, 2003). The groove between adjacent subunits is necessarily narrower in the tetradecamer than in the dodecamer, because of the hinging apart of the subunits, and the presence of the expression tag could favor the dodecamer for this reason.

Due to poor signal in ESI-MS of full-length CaMKII holoenzyme, we examined unactivated human CaMKII-α holoenzyme by negative-stain electron microscopy (EM) in order to determine its stoichiometry, as described in Methods. An important aspect of our analysis is that no symmetry was imposed on the particles at any stage of the generation of class averages. The hub assemblies are clearly resolved in the EM micrographs, but the kinase domains are not, as is common for CaMKII. Visual inspection of the two-dimensional class averages clearly reveals a population of holoenzyme particles with seven-fold symmetry, in addition to those with the expected six-fold symmetry. It is unclear why particles with seven-fold symmetry were not reported in the previous EM analyses of CaMKII-α, which focused on dodecameric species (Kolodziej et al, 2000; Morris and Török, 2001). In our analysis, we could discern clear evidence, by visual inspection, for either six-fold or seven-fold symmetry in seven out of 50 classes each (the symmetry of the other class averages was not obvious). Based on the number of particles contributing to each of these 14 classes, we estimate the ratio of dodecameric to tetradecameric species to be roughly 55:45 (Figure 2B).

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The structures of CaMKII homologs from two distantly diverged organisms, the sea anemone N. vectensis and the choanoflagellate S. rosetta, provided crucial insight into the likely mechanism of subunit exchange. CaMKII, like many signaling proteins, is so highly conserved in higher metazoans that alteration in structure due to sequence variation is rather limited. Recent advances in the sequencing of genomes of early-branching metazoans and their closest relatives gives us an unprecedented opportunity to understand the core mechanisms that underlie the functions of critical signaling proteins, such as CaMKII, that are common to all metazoans (Richter and King, 2021).


Molecular mechanism of activation-triggered subunit exchange in Ca2+/calmodulin-dependent protein kinase II

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The triple-mutant peptide fails to compete the binding of the labeled peptide (Figure 3F). The two peptides bearing mutations at single sites have diminished ability to compete, compared to the unlabeled peptides. The IC50 values of these peptides are increased by factors of about 2 and 4, relative to the wild type peptide. A more rigorous identification of the hub residues that constitute the peptide binding groove awaits further analysis of hub mutants.


This parameter specifies the size in Mbyte for the multi-purpose communication buffer used by the code in various parts of theparallel algorithms. It should be large enough to have minimal work-load imbalance losses, though in practice a few to 100 MBytesare sufficient.

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Activation triggers the exchange of subunits in Ca2+/calmodulin-dependent protein kinase II (CaMKII), an oligomeric enzyme that is critical for learning, memory, and cardiac function. The mechanism by which subunit exchange occurs remains elusive. We show that the human CaMKII holoenzyme exists in dodecameric and tetradecameric forms, and that the calmodulin (CaM)-binding element of CaMKII can bind to the hub of the holoenzyme and destabilize it to release dimers. The structures of CaMKII from two distantly diverged organisms suggest that the CaM-binding element of activated CaMKII acts as a wedge by docking at intersubunit interfaces in the hub. This converts the hub into a spiral form that can release or gain CaMKII dimers. Our data reveal a three-way competition for the CaM-binding element, whereby phosphorylation biases it towards the hub interface, away from the kinase domain and calmodulin, thus unlocking the ability of activated CaMKII holoenzymes to exchange dimers with unactivated ones.

The crystallization construct for the human CaMKII-α hub consisted of residues 345–475 (UNIPROT id: Q9UQM7). This sequence was preceded by an expression tag containing hexahistidine followed by a PreScission protease cleavage site (GSSHHHHHHSSGLEVLFQGPHM). This expression tag was left uncleaved for crystallization. The crystallization construct for the N. vectensis hub domains (CaMKII-B and CaMKII-A) included residues 335–476 (UNIPROT id: A7RF52) and residues 331–472 (UNIPROT id: A7T0H5) respectively. For S. rosetta CaMKII, the hub domain crystallization construct is comprised of residues 335–479 and the kinase domain construct ranged from residues 1–330 (UNIPROT id: F2UPG5). The kinase domain construct for S. rosetta had an additional 11 residues, containing a hexahistidine tag on the C-terminus (AAALEHHHHHH). The crystallization construct for the N. vectensis hub domains and that of S. rosetta were similar to that of the mouse CaMKII-α hub (PDB code: 1HKX), and included 12 C-terminal residues of the linker (9 C-terminal residues of the linker were included in the construct for 1HKX).