Neurogranin Stimulates Ca2+/calmodulin-dependent Kinase II by Inhibiting Calcineurin at Specific Calcium Spike Frequencies

Calmodulin sits at the centre of molecular mechanisms underlying learning and memory. Its complex, and sometimes opposite influences, via the binding to various proteins, are yet to be fully understood. Calcium/calmodulin-dependent protein kinase II (CaMKII) and calcineurin (CaN) both bind open calmodulin, favouring Long-term potentiation (LTP) or depression (LTD) respectively. Neurogranin binds to the closed conformation of calmodulin and its impact on synaptic plasticity is less clear. We set up a mechanistic computational model based on allosteric principles to simulate calmodulin state transitions and its interaction with calcium ions and the three binding partners mentioned above. We simulated calcium spikes at various frequencies and show that neurogranin regulates synaptic plasticity along three modalities. At low spike frequencies, neurogranin inhibits the onset of LTD by limiting CaN activation. At intermediate frequencies, neurogranin limits LTP by precluding binding of CaMKII with calmodulin. Finally, at high spike frequencies, neurogranin promotes LTP by enhancing CaMKII autophosphorylation. While neurogranin might act as a calmodulin buffer, it does not significantly preclude the calmodulin opening by calcium. On the contrary, neurogranin synchronizes the opening of calmodulin’s two lobes and promotes their activation at specific frequencies, increasing the chance of CaMKII trans-autophosphorylation. Taken together, our study reveals dynamic regulatory roles played by neurogranin on synaptic plasticity, which provide mechanistic explanations to opposing experimental findings. Author Summary How our brains learn and remember things lies in the subtle changes of the strength with which brain cells connect to each other, the so-called synaptic plasticity. At the level of the recipient neuron, some of the information is encoded into patterns of intracellular calcium spikes. Calmodulin, a small bilobed protein which conformation is regulated by the binding of calcium ions, decodes these signals, and modulates the activity of specific binding partners. Two key regulators, calcineurin and calcium/calmodulin-dependent protein kinase II, which respectively weaken or strengthen synaptic connections, bind both lobes of calmodulin in its open form, favoured by calcium. On the contrary, neurogranin binds preferentially to one lobe of calmodulin, in the closed form, unfavoured by calcium. It was thus initially suggested that it would inhibit calmodulin activation and decrease synaptic plasticity. However, past research showed that neurogranin sometimes actually enhances synaptic plasticity, though the mechanism was unclear. Our computational models showed that neurogranin synchronizes the activation of the two lobes of calmodulin, favouring opening at high frequency calcium spikes. By doing so, neurogranin increases the impact of calmodulin on calcium/calmodulin-dependent protein kinase II and reduces its effect on calcineurin, resulting in a strengthening of synaptic connections.


Introduction
did not take the role of Neurogranin into account. A few models attempted to explain 49 how Ng facilitates LTP, putting forward the buffering of calmodulin by Ng in the 50 post-synaptic density (PSD) and the reshaping of free calcium spikes [40,41]. Using 51 mathematical modelling, Romano et al [42] recently showed that Ng facilitates CaMKII 52 activation at a 100 Hz-tetanus stimulation. However they failed to show why, at the 53 same time, Ng hinders LTP induction, observed by the same experimental group [19]. 54 All these models lacked detailed mechanistic descriptions of calmodulin function. 55 In this paper, we present a detailed mechanistic model of calmodulin in the context 56 of synaptic plasticity and its interaction with CaMKII, CaN and Ng, based on the 57 allosteric framework and our previous hemiconcerted calmodulin model [25]. In our 58 model, the four calcium binding sites were explicitly modelled and each lobe of 59 calmodulin undergoes independent state transitions. In addition, we systematically 60 estimated the allosteric parameters concerning the two calmodulin lobes together, as 61 well as the kinetic constants, based on steady states and calcium chelating time course 62 experimental data. We simulated a wide range of calcium spike frequencies in a wild 63 type context and for a neurogranin knock-out situation. We showed the differences of 64 calmodulin lobe responses and how they contribute to, but also are influenced by, the 65 differential activations of calmodulin's binding targets. We show that Ng is not merely a 66 calmodulin buffer protein, but it can adjust the activation of calmodulin at frequencies 67 maximizing CaMKII activation. Ng regulation of LTP induction depends on the local 68 concentration of CaN, and on the amount of CaMKII required for inducing LTP. 69

70
Model Structure 71 We built a mechanistic mathematical model to describe the conformational changes of 72 calmodulin lobes, calcium bindings and calmodulin interaction with binding partners. 73 This model is based on our previous hemiconcerted allosteric model of calmodulin by 74 Lai et al. [25]. The major differences between our model and other published 75 calmodulin models are: 1) We do not assume sequential bindings of calcium ions to the 76 four binding sites. Instead, each calcium binding site on calmodulin is independent, and 77 independent from the binding of protein partners. 2) Calcium saturation does not 78 directly affect calmodulin's affinity for its protein binding partners. Binding CaMKII, 79 CaN or Ng does not necessarily results in increased calcium binding affinities. Instead, 80 modifications of the affinity for all binding partners are solely derived from calmodulin 81 conformational changes. Calcium saturation decreases the free energy of the open state, 82 favouring the association with proteins preferentially binding to that conformation and 83 hindering the association with proteins preferentially binding to the closed state. 84 Symmetrically, protein binding partners shift the conformation equilibrium of 85 calmodulin towards their preferred state. 86 On top of the model developed previously by Lai et al. [25], We explicitly modelled 87 calmodulin's interaction with CaMKII, CaN [43] in the supplementary material and 97 has been deposited in BioModels [44] (accession number: MODEL1903010001). 98 First, we modified the hemiconcerted calmodulin model by Lai et al. 2015 [25], to 99 allow the binding of calcium ions to affect equally, but in opposite directions, both 100 transitions of calmodulin lobes between open and closed conformations. In other words, 101 calcium binding not only speeds up the T to R state transition, but also slows down the 102 R to T state transition. We also removed the assumption that protein partners can bind 103 to all possible conformations of calmodulin. Rather, we defined these bindings based on 104 the described properties of each specific protein. 105 CaMKII monomer binds to calmodulin when both lobes are in open states (namely 106 the "RR" conformation). This binding exposes the kinase domain of CaMKII monomer, 107 allowing it to phosphorylate and to be phosphorylated by its neighbour monomers 108 within the same hexamer ring, if they are also in active conformation [45]. We adapted 109 and improved the approach used by Li et al. 2012 [10] to compute the probability of 110 having an adjacent active monomer, at each time step, based on the proportion of active 111 monomers in the whole system (calmodulin bound and/or phosphorylated). For more 112 details, see the section CaMKII autophosphorylation below. We then used this 113 probability to adjust the global autophosphorylation rate of CaMKII monomers. Once 114 phosphorylated, CaMKII monomers have a higher affinity for calmodulin than their 115 non-phosphorylated counterparts, and remain active even upon calmodulin 116 dissociation [46]. CaMKII monomers are dephosphorylated by Protein Phosphatase 1 117 (PP1). As CaN activates PP1 "linearly" through dephosphorylation of 118 Thr34-phospho-DARPP-32, which then releases PP1 inhibition, we simply modelled a 119 direct dephosphorylation of CaMKII monomers by CaN using Henry-Michaelis-Menten 120 kinetics with total active CaN as the enzyme concentration.

121
CaN is a heterodimer containing a regulatory subunit (CaNB), and a catalytic 122 subunit (CaNA) [47]. In our model, the sequential binding of four calcium ions to CaNB 123 is required before CaNA can bind calmodulin, thereafter becoming active [48,49].

124
CaNA binds to calmodulin when both calmodulin lobes are in the open state ("RR"). 125 As Ng interacts mostly with the C lobe, in this model we considered that it bound 126 to calmodulin only when the C lobe was in the closed state, regardless of the N lobe 127 conformation ("RT" and "TT"). As a consequence, the association of calmodulin with 128 Ng does not prevent the transitions of the N lobe between T and R states. Moreover, 129 due to the lack of relevant experimental data, we assumed that the binding of Ng on the 130 C lobe did not exert any allosteric effect on those transitions.

131
To create a basal level of calcium (0.08 · 10 −6 M), we implemented reactions to 132 create constant influx and removal of ions, by mimicking a passive calcium input 133 channel and a concentration-dependent calcium pump. Calcium input was encoded as a 134 train of calcium spikes at varied frequencies. Each calcium spike was generated by 135 adding a zero-order calcium creation during 8- We estimated the allosteric parameters for both N and C lobes by using 150 experimental data obtained predominantly from full-length CaM, where intrinsic 151 phenylalanine and tyrosine fluorescence were used for monitoring calcium saturation. 152 We used three sets of steady-state experimental data: 1) calmodulin titrating CaMKII 153 peptide with a saturating amount of calcium ions [6], 2) calcium saturation curves of 154 the C lobe in the full length calmodulin either without targets or in the presence of 155 CaMKII peptide or full-length Ng [6,26], 3) calcium saturation curve of the N lobe, in 156 full-length calmodulin, without targets [6]. As the experimental data concerning N lobe 157 calmodulin is relatively scarce, we also used a calcium titration curve of truncated N 158 lobe of calmodulin, that was locked in closed conformation [51].

159
To fully characterise the interactions between calmodulin and calcium, we therefore 160 have to estimate: 1) the binding affinities of calcium to the T state of calmodulin for 161 sites on both lobes. Following Lai et al. [25], we further hypothesized that within each 162 calmodulin lobe, the affinities of the two calcium binding sites were the same and we   Even with the assumptions described above, the amount of parameters to estimate is 176 large and correlations may arise between them. Moreover the experimental conditions 177 used in these estimation procedures are highly diverse. Thus, we proceeded in several 178 stages.

179
Firstly, using calcium titration experiments of truncated N lobe locked in the closed 180 conformation by disulfide crosslinks [51], we estimated the affinity between calcium and 181 the N lobe in the T state to be KN T = 9.38 · 10 −5 M (S1 Fig.a and b).

182
Using experimental measurements where calmodulin titrates CaMKII peptide in the 183 presence of saturating amount of calcium ions [6], we then estimated the affinity 184 between calmodulin and CaMKII peptide (Kd CaMKIIpep RR). Because of the high 185 calcium concentration we assumed that almost all calmodulin molecules were in the R 186 state. This gave a value of Kd CaMKIIpep RR = 5.6 · 10 −9 M (S1 Fig.c and d). This 187 only provides the upper bound for the dissociation constant between CaMKII peptide 188 and RR calmodulin, as not all calmodulin molecules are in the RR state, even with the 189 highest calcium concentration. In fact, this value was reduced to 3.2 · 10 −10 M during  Estimating parameter values requires sampling values within given ranges. We 192 calculated the boundary values of KCT and cC by assuming that the observed calcium 193 saturation levels of the C lobe, in the presence either of CaMKII peptide or of Ng [6,26], 194 reflected the calcium binding affinities when all C lobes were locked in the R or T state 195 respectively, resulting in cC = 0.0011 (cC = KCR/KCT ) and KCT = 1.3 · 10 −5 M 196 (S1 Fig.e-g). This value of cC was used as the upper bound for estimating the real cC, 197 as in reality the CaMKII peptide is not capable of locking all C lobes in the R state. 198 Similarly, KCT was used as the lower bound for KCT , since not all C lobes are locked 199 in the T state by Ng, i.e. the actual affinity of the T state for calcium is lower.

200
Since KCT had the same order of magnitude as our estimated KN T , and calcium 201 affinity for the C lobe should be higher than for N lobe, the range for the real KCT 202 value was narrow. Thus, to further reduce the amount of parameters to be estimated, 203 we simply assumed that, in the closed state, both C and N lobe shared the same 204 calcium binding affinities, that is KCT = KN T = 9.38 · 10 −5 M.  Fig.). We therefore further refined 211 these two parameters while estimating the rate constants.

212
Estimations of kinetic rate constants 213 We estimated the affinity between open calmodulin (conformation "RR") and 214 calcineurin by using the CaN dose-response to calmodulin, in the presence of saturating 215 calcium concentration [52]. We also estimated the association constant between the two 216 proteins using stopped-flow kinetic data, where mutant calmodulin was labelled by 217 Acrylodan (CaM (C75) ACR ) [52]. The estimated affinity was Fig.). 220 We directly used the dissociation constants of CaMKII and phospho-CaMKII from 221 calmodulin taken from the literature (koff CaMKII RR = 1.1 s -1 ; 222 koff CaMKIIp RR = 8.7 · 10 −5 s -1 ) [53], and therefore only had to estimate their 223 association rate constants. Based on previous published works [23,26], we hypothesized 224 that calcium binding to the N lobe was 100 times faster than to the C lobe, 225 (kon N = 100 × kon C), and these did not depend on the conformation of the lobes, 226 therefore reducing the estimation of 8 unknown association rates to only 1, kon CT .

227
Finally, we assumed that the base state-transition rates were the same for the two lobes, 228 k T toRC0 = k T toRN 0. The specific state transition rates, for all liganded populations, 229 depend on the number of calcium bound to the calmodulin lobe, the protein partner 230 bound, and the allosteric parameters estimated for this lobe. We also made use of the 231 relationship between cC and LC described above, and only had to estimate cC. 232 We used stopped-flow fluorometry measurements of quin-2 fluorescence increase, 233 after addition of calcium-saturated calmodulin mix, in the presence of either CaMKII or 234 phospho-CaMKII [31], and measurements of native tyrosine fluorescence decrease in the 235 calmodulin C-terminal in the presence of EGTA, with or without neurogranin [26].  During simulations, we actively adjusted the global autophosphorylation rate of CaMKII 244 monomers based on the total amount of active monomers, that are the phosphorylated 245 and/or calmodulin bound monomers, and the likelihood of them having adjacent active 246 monomers in pseudo hexamer rings, an updated approach from our previous work [10]. 247 Briefly speaking, there are 7 types of hexamers, containing 0 to 6 active monomers. 248 For each type, the possibilities of location for the active monomers are limited and we 249 can easily compute the probability for an active monomer to have a neighbour also 250 active. The main aspect of the procedure is to approximate the fraction of the different 251 types of hexamers when the total number of active monomers is updated from the 252 simulation. We achieved this by running, for every 1 percent increase of active 253 monomers, 1000 independent random distributions of the active monomers to hexamers. 254 For every increase of active monomers, we then computed the average occurrences of 255 each type of hexamers, and transformed them into the probability for a monomer to be 256 distributed in a specific type of hexamer. We then multiplied the distributions of 257 monomers with their corresponding probability of adjacent active neighbours. Finally, 258 the summation of the above were used as the overall probability and the chance of 259 having an active neighbour monomer for each percent increase in total active monomers. 260 We fitted this data with a 5 th order polynomial function and embedded it into the 261 model to adjust the autophosphorylation rate of CaMKII monomer (S9 Fig.).

263
All simulations, including timecourses with calcium spikes were performed with 264 COPASI [54], using the LSODA solver [55]. Parameter estimations were conducted 265 using the SBPIPE package [56], combined with the "Particle swarm" optimization 266 method (2000 iterations with a swam size of 50). Parameters used for simulation of the 267 model are listed in Table 1.

268
The frequency of calcium spikes was directly encoded in the model together with the 269 number of spikes, in order to control the total duration of calcium inputs. We ran the 270 simulations on a computing cluster, using Python's ElementTree package to 271 automatically modify the frequency parameter in CopasiML files.

272
Each simulation started with a 5000 s equilibrium -with output interval size set at 273 1 s, followed by the simulation of 300 calcium spikes at frequencies ranging from 0. 1 Hz 274 to 100 Hz, with output interval size set at 0.0001 s. We recorded the evolution of all 275 protein active forms during 3000 s.

276
In order to evaluate CaMKII and CaN's effects on synaptic plasticity, we measured 277 the "activated area" [10], which was obtained by integrating, over the 3000 s, the 278 product of their relative activations (concentration of active proteins over total 279 concentration) above basal activities (substracting basal levels), by their catalytic 280 constants on AMPA receptor GluR1 subunit. The BCM-like curve [57], useful to 281 characterise bidirectional plasticity, was obtained by subtracting the activated area of 282 CaN from that of CaMKII for each calcium spike frequencies.

284
Neurogranin sequesters closed-state calmodulin 285 We firstly studied how calmodulin (CaM) binding proteins can affect calmodulin's 286 apparent affinity for calcium at steady states. As shown in Fig. 2, and in accord with 287 previous experiments [6,26] and modelling [25], the presence of Ng shifts the   When combined together, the first letter indicates the state of calmodulin's N lobe while the second one indicates the state of the C lobe. Since kon, koff , and Kd are linked (Kd = koff /kon), only two of these three are displayed, depending on which ones were actually estimated. For parameters concerning sequential dissociation of Ca 2+ ions from CaN, the first "Ca" indicates the number of Ca 2+ ions bound to CaN, the second "Ca" shows the one dissociating from CaN.
promote calcium binding to the C lobe, increasing the apparent affinity, through their 293 preferential binding to the open, high-affinity conformation (of both lobes).

294
Calcium saturation curves for full calmodulin show similar trends as for the C lobe 295 (Fig. 2), but they also indicate calmodulin's lobe differences in terms of calcium binding. 296 Based on the allosteric parameters we estimated, the N lobe is more flexible and has 297 greater potential to undergo spontaneous conformational transitions than the C lobe and their presences greatly enhance, not only C lobe but also N lobe's calcium binding. 307 However, N lobe's affinity to calcium is less increased by the conformational change to 308 open state. Although having the highest affinity towards calmodulin, phospho-CaMKII 309 cannot shift N lobe's affinity much compared to non-phospho CaMKII.

310
In line with the findings above, timecourse simulations show that Ng speeds up 311 calcium dissociation from calmodulin's C lobe (Fig. 3), in agreement with stopped-flow 312 fluorometry experimental observations [26]. Taking  about 200 milliseconds, due to calcium pumps and calcium binding proteins [50].

323
Therefore, rather than looking at the responses of calmodulin to calcium steady-states, 324 we must look at its responses to calcium spike frequencies (Fig. 4).  We first simulated the calmodulin model, without protein partners, using a fixed 326 total calcium input applied at varied spike frequencies. The results are in line with the 327 behaviour of our previous fully concerted model [10], and show that both calmodulin concentration is much shorter, which is not shown in the steady state analysis (Fig. 5) lobes was narrowed towards high values (Fig. 5). The duration of the activation was 337 also shortened. Unsurprisingly, no changes were observed for the N lobe (Fig. 5).

338
Overall, the opening patterns of the C lobe in presence of Ng resembles those of the N 339 lobe, restricting the opening to high calcium input frequencies.

340
To better quantify calmodulin's responses to the frequencies of calcium input, we represents the N lobe and the second represents the C lobe. We then plotted them 346 against calcium spike frequencies (Fig. 6).

347
Without Ng, Calmodulin's C lobe is very sensitive to calcium spikes at low 348 frequencies. The conformation TR increases above its basal level (AUC>0, as basal 349 activity has been subtracted.) by calcium stimulation as low as 0.1 Hz (Fig. 6a). The 350 conformation TR increases steeply around 3 Hz, peaks at 20 Hz, then declines while N 351 lobe opens (the increase of RR conformation). There is almost one order of magnitude 352 between the frequencies at which the C and N lobe opens prominently (Fig. 6a).

353
Neurogranin not only suppresses the C lobe opening in response to low frequencies, 354 but also shifts it towards higher frequencies. At about 10 Hz, both TR and RT state 355 start to increase and peak around 25 Hz, indicating the opening of both C and N lobes 356 within different populations of calmodulin molecules (Fig. 6b). In fact, without Ng, the 357 N lobe does not open on its own (Fig. 6a). At these intermediate frequencies, Ng  (Fig. 6b). 362 Therefore, neurogranin does not prevent calmodulin activation by calcium spikes.

363
Instead, neurogranin synchronizes both lobes to respond towards higher calcium spike 364 frequencies, hence narrowing the frequency range at which calmodulin responses.  CaMKII activity, reaching to the same levels ( Fig. 7a). At 30 Hz, the acute elevation of 381 calcium gives rises to sharp and prominent increases of both CaMKII and CaN, and 382 CaMKII overcomes CaN. However, the activation of CaMKII decays very fast to its 383 resting level, potentially due to the slower deactivation and high basal activity of CaN, 384 which prevents the onset of CaMKII autophosphorylation (Fig. 7b) CaMKII monomers remain active for more than 10 minutes, that is far beyond the total 397 duration of calcium stimulation ( Fig. 7d and S10 Fig.). Thus, at high spike frequencies, 398 the presence of Ng promotes the autophosphorylation of CaMKII, which activity lasts 399 beyond calcium spikes and calmodulin association.

400
In most LTP induction protocols, high frequency stimulation is not applied 401 continuously but grouped into discrete bursts. We verified the finding presented above 402 by splitting the 300 calcium spikes at 100 Hz into three 100 Hz, 100-spike bursts, 403 separated by 10-minute intervals [15]. As shown in Fig. 8, we obtained results similar to 404 a setup featuring a continuous 300-spike stimulation (S11 Fig.).  30 Hz, a frequency of stimulation often used to trigger robust LTP. The 419 absence of Ng causes phosphatase activity to be much stronger at low frequencies and 420 less sensitive to frequency increases. The shift towards kinase activity is less sharp, and 421 occurs at lower frequencies, the final plateau representing a much lower kinase activity 422 (Fig. 9a black curve).

423
The difference of responses in the presence and absence of Ng are explained by its 424 combined effects on CaN and CaMKII, different according to the frequency (Fig. 9b).

425
The absence of Ng increases both CaMKII and CaN activation at low spike frequencies, 426 however the effect on CaN is far greater, thus favouring LTD. As the spike frequency stimulations has been observed experimentally [15,19] The frequency response plot (Fig. 9b) shows that the absence of Ng causes a large 453 change of the CaMKII plateau at high frequencies, but a fairly small change of CaN's. 454 It is therefore difficult to see how such a small change of CaN activity could have an 455 important effect on CaMKII autophosphorylation. One thing to bear in mind is that 456 activated-areas, calculated at each frequency, represent the activity above a basal level, 457 as it characterizes the amplitude and duration of the response to the calcium 458 stimulation. However, the inhibition on the CaMKII autophosphorylation is not only 459 due to the dynamics of CaN following calcium signals, but to CaN basal level. The 460 latter is elevated in the Ng-absent situation (Fig. 7a,b). Taking into consideration this 461 increase would cause a vertical shift of about 30 units in its frequency dependence curve 462 (Fig. 9b green crosses) without affecting the CaMKII curve much. Ng presence therefore 463 changes the situation dramatically. CaN activity is higher than CaMKII activity in the 464 absence of Ng, whereas the opposite situation is true when Ng is present.

465
To further assess CaN's role, we removed it from the model and re-simulated the 466 various frequencies of calcium spikes, with or without Ng. As shown in Fig. 10a, . The combined response of CaMKII and CaN to calcium spike frequencies were quantified as described in Fig. 9, with (grey circle) or without neurogranin (black cross). Simulation conditions and concentrations are as described in Fig. 7. Double amount of CaN equals to 16 µM.
We then doubled CaN concentration, to twice its detected level in hippocampus CA1 474 region [59] (Fig. 10b) 482 We tested other CaN concentrations and plotted the differences of CaMKII 483 activation reached at the high calcium spike frequencie (100 Hz), in presence and 484 absence of Ng. Fig. 11 shows a non-linear relationship between the concentration of

496
The concentration of neurogranin impacts LTP induction 497 Previous research showed that Ng undergoes constant shuffling in and out of the PSD. 498 Its function as a regulator of synaptic plasticity may rely on its anchoring in the PSD 499 and the resulting recruitment of more calmodulin [60]. While this is certainly an 500 important aspect of Ng function, modelling Ng and calmodulin translocation in and out 501 the PSD may blur other Ng impacts on plasticity. We have already shown that 502 calmodulin concentration is a limiting factor in the PSD and increasing it has positive 503 effect on LTP induction [10]. Although our current model only incorporates neurogranin 504 binding of calmodulin in an homogeneous compartment, we can already show that 505 increasing Ng concentration, while keeping calmodulin concentration intact, has a 506 positive effect on LTP induction. As shown in Fig. 12, increasing Ng concentration 507 results in a larger activation of CaMKII over CaN, with a steepest transition from CaN 508 to CaMKII as we increase calcium spike frequency, and higher plateaus for CaMKII 509 activity at both low and high frequencies. Despite this relative shift toward CaMKII at 510 all frequencies, the transition between CaN and CaMKII (Θ m ) occurs at higher 511 frequencies when Ng concentration increases.

512
The level of Ng in the brain, especially in the hippocampus, is declining with Computational models with various neurogranin concentration were stimulated by 300 calcium spikes at various frequencies. The activated area of CaMKII and CaN were calculated and their net effects on AMPA receptor phosphorylation were calculated as described in Fig.7, and plotted as a function of calcium spike frequency.

517
Calmodulin's impact on synaptic plasticity are mediated via and regulated by its 518 binding partners [26,31,64]. Contrarily to enzymes which downstream activities are well 519 documented, the role of some of the non-catalytic proteins is less clear. One such 520 protein is neurogranin, a highly expressed brain protein that carries a 521 calmodulin-binding IQ domain [65,66].

530
By setting up a mechanistic model of calmodulin conformational changes of its two 531 lobes, we explored the potential roles neurogranin plays in regulating bidirectional 532 synaptic plasticity mediated by CaMKII and calcineurin. 533 We firstly examined how Ng coordinates calmodulin lobes in response to calcium 534 spikes frequencies. It has been established that calmodulin C lobe, although having 535 higher affinity, has slower binding kinetics for calcium ions than the N 536 lobe [11,20,23,31]. Therefore, it has been proposed that the calcium binding to C lobe 537 is rate limiting for calmodulin opening [26,32,64]. However, our simulation results 538 showed the contrary. When no calmodulin binding partner is presented, calmodulin N 539 lobe is harder to open than C lobe, requiring higher calcium spike frequencies and larger 540 free calcium elevations (Fig. 6a). This is because the fast binding and dissociation 541 kinetics of N lobe make it follows calcium spikes too close to open before releasing 542 calcium. We futher elucidated that the role Ng plays is to reduce these differences 543 between calmodulin lobes and to synchronize their opening at specific calcium spike 544 frequencies. This is achieved by Ng's preferential binding to the C lobe and limiting its 545 opening at low frequencies (Fig. 6b). The advantage of this synchronization is to 546 minimize calmodulin opening when calcium stimulation is weak, therefore reducing 547 basal calcineurin activity and shifting the majority of opened calmodulin to CaMKII 548 when calcium signal is strong (Fig. 7, 9).

549
Our findings are in agreement with some studies that have proposed that Ng and 550 other IQ motif proteins act as calmodulin caches, enhancing the activation of 551 calmodulin binding partners when calcium concentration is high [41,65,68]. Our study 552 went a step further by showing that this increased calcium concentration is the 553 consequence of increased calcium spike frequencies, other than total calcium ion inputs. 554 Furthermore, the mechanisms underlying this dynamic regulation is rooted in the 555 allosteric regulation of calmodulin lobes and the reciprocal influence among calmodulin 556 and its binding partners.

557
Our simplified frequency response curve, that was drawn from the differences of 558 integrated enzymatic efficiencies between CaMKII and CaN (Fig. 9a), matches with the 559 experimental observations by Huang et al. [16]. The absence of neurogranin facilitates 560 LTD but impairs LTP induction, resulting in a down-shift BCM curve. In addition, we 561 observed a slight left shift when Ng was removed, indicating a potential easier onset of 562 LTP at these intermediate frequencies, dependent on the threshold CaMKII required.

563
The major experimental study questioning Ng's positive role on synaptic plasticity is 564 published by Krucker et al. [19]. In their study, the mouse brains that are absent from 565 functional Ng display lowered CaMKII activity, but are enhanced to exhibit LTP under 566 high frequency stimulations [19]. Our research might shed light on this discrepancy, as 567 we showed that the absence of Ng does not abolish CaMKII activation at high intensity 568 calcium stimulation and most importantly, enhances CaMKII activation at intermediate 569 frequencies. With the optimal amount of CaN, CaMKII activity can overturn CaN 570 activity at lower frequency in the absence of Ng than when it is present, therefore 571 potentially facilitating LTP induction. We further elucidated that the LTP induction 572 frequencies are likely to be dynamically regulated by protein expression level, largely 573 due to neurogranin itself (Fig. 12). 574 Perhaps, the most intriguing finding from our research is that CaN facilitates Ng to 575 enhance LTP induction. CaN is one of the highly expressed protein phosphatases in 576 nervous system [69] , and its dysfunction has been associated with many neurological 577 diseases [70][71][72][73]. CaN has been shown to be involved in processes weakening synaptic 578 connections [74][75][76][77][78][79]. And blockage of CaN has shown to encourage learning and 579 memory [80,81].

580
Our finding do not contradict with these views. In fact, we showed that neurogranin 581 positive impact on CaMKII activation and LTP induction is due to its inhibition of 582 CaN, especially at the basal calcium concentrations. When Ng is knocked out, 583 calmodulin is prone to be activated by basal levels of calcium, therefore elevating the 584 resting level of CaN activity, which in turn decreases CaMKII autophosphorylation. The only difference could be that the frequencies we found to be able to induce LTP 618 might be higher than reality, albeit for both scenarios. 619 We have taken a highly simplified concept to build our model upon, in which the 620 PLOS 21/30 effectiveness of the phosphatase and the kinase is directly used as a measure for 621 synaptic plasticity. Although the requirements for these enzymes and their central roles 622 in synaptic plasticity are well established [9,38], there are more modulators and 623 interactions in these processes and at different stages of memory consolidations [9]. The 624 difficulties of incorporating more molecular interactions in the model are estimating 625 their relevant equilibrium and kinetic parameters systematically, and ensuring their 626 identifiabilities, requirements we tried to ensure in this study. Our mathematical model 627 and parameters can be reused and expanded to further our understanding of calmodulin 628 and its binding proteins.

629
In conclusion, our study revealed a complex and dynamic role neurogranin plays in 630 regulating bidirectional synaptic plasticity. It functions via preferential binding to