Boundary conditions for synaptic homeodynamics during the sleep-wake cycle

21 Understanding synaptic dynamics during the sleep -wake cycle is crucial yet controversial. While 22 some studies report synaptic depression during non-rapid eye movement (NREM) sleep , others 23 observe synaptic potentiation. To find boundary conditions between these contradictory 24 observations, w e focused on learning rule s and firing pattern s that contribute to the synaptic 25 dynamics. Using computational models, we found that under Hebbian and spike-timing dependent 26 plasticity (STDP), wake-like firing patterns decrease synaptic weights, while sleep -like patterns 27 strengthen synaptic weights. Conversely, under Anti-Hebbian and Anti-STDP , synaptic depression 28 during NREM sleep was observed, aligning with the conventional synaptic homeostasis hypothesis. 29 Moreover, synaptic changes depend ed on firing rate differences between NREM sleep and 30 wakefulness. We provide a unified framework that could explain synaptic homeodynamics under 31 the sleep-wake cycle. 32 33 34 35 36 37 38 39 40 .CC-BY-NC-ND 4.0 International licensemade available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity.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 The copyright holder for this preprintthis version posted August 19, 2024. ; https://doi.org/10.1101/2024.08.14.607872doi: bioRxiv preprint 3 Main Text 41

42 During wakefulness, organisms perceive external worlds through the five senses to learn and take 43 appropriate actions. During sleep, organisms disconnect from the environment to reorganize 44 memory and recover from fatigue. Recent studies have revealed that cortical neurons are 45 responsible for these brain functions underlying learning and memory formation (1) and that the 46 dynamics of the cortical synaptic weights are associated with the sleep -wake cycle (2, 3). A 47 hypothesis known as the synaptic homeostasis hypothesis (SHY) proposed that wakefulness 48 potentiates synapses through learning with the costs of higher energy demand while the sleep 49 state depresses less important synapses to restore synaptic homeostasis (2). However, the 50 dynamics of synaptic weights in the sleep-wake cycle, especially during sleep, remain controversial. 51 Several studies have demonstrated that NREM sleep potentiate s synapses, contributing to 52 memory consolidation (4, 5). Furthermore, SHY suggests that synapses strengthened during 53 wakefulness are less susceptible to synaptic depression during NREM sleep (2). In contrast, other 54 studies propose the normalization of neuronal activities, where fast-firing neurons and slow-firing 55 neurons during wakefulness are weakened and strengthened, respectively, during NREM sleep 56 (6). We sought to find the boundary conditions tha t reconcile these discrepancies and to 57 comprehensively understand the sleep-wake synaptic dynamics. 58 The heterogeneity of brain states can confound in vivo studies because the slow-wave 59 oscillation (SWO), that is a characteristic firing pattern of NREM sleep, also occurs in wakefulness 60 and sleep states include REM sleep, which has wake -like firing patterns (7, 8). To address this 61 issue, we developed computational models to investigate the direct relationships between synaptic 62 weights and neuronal firing patterns characteristic of each brain state. To account for the diversity 63 of neurons, we prepared various sleep- and wake-like firing patterns based on in vivo experiments. 64 Additionally, we devised a unified function that recapitulates typical synaptic learning rules in the 65 .CC-BY-NC-ND 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted August 19, 2024. ; https://doi.org/10.1101/2024.08.14.607872doi: bioRxiv preprint 4 cortex for updating the synaptic weights (9). These settings allowed us to simulate the dynamics 66 of synaptic weights under specific types of spike trains, such as burst firing , based on synaptic 67 learning rules (10). The synaptic learning rules we studied include the Hebbian rule, STDP, and 68 their r everse types (Anti -Hebbian and Anti -STDP). According to the Hebbian rule, a synaptic 69 connection between two neurons strengthens when pre - and post -synaptic neurons fire 70 simultaneously (11). A temporally asymmetric form of Hebbian rule is STDP . The classical STDP 71 describes that synaptic potentiation occurs when pre-synaptic spikes precede post-synaptic spikes 72 within a certain temporal window, while synaptic depression occurs in post-synaptic spikes precede 73 pre-synaptic spikes (12). Reverse types of them (Anti-Hebbian and Anti-STDP) are also observed 74 in the mammalian cortex (13) and play important roles in information processing (14). 75 Our simulations revealed that synaptic weights become higher in sleep-like synchronized 76 states than in wake-like desynchronized states under Hebbian and classical STDP, assuming the 77 same mean firing rates for both sleep- and wake-like firing patterns. We refer to these dynamics 78 as Wake Inhibition and Sleep Excitation (WISE). In contrast, synaptic depressions during sleep -79 like firing patterns, which represents SHY , were observed under Anti -Hebbian and Anti -STDP. 80 Moreover, our results suggested that the synaptic dynamics also depend on mean firing rates, 81 providing a unified framework for the synaptic homeodynamics of neural networks during the sleep-82 wake cycle. 83 84

85 WISE under Hebbian and STDP , SHY under Anti-Hebbian and Anti-STDP 86 To investigate synaptic dynamics in NREM sleep and wakefulness with synaptic learning rules, we 87 used a Ca2+-based plasticity model. Graupner et al. proposed that the Ca2+-based plasticity model 88 with two thresholds for post-synaptic Ca2+ can describe the various types of synaptic learning rules 89 .CC-BY-NC-ND 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted August 19, 2024. ; https://doi.org/10.1101/2024.08.14.607872doi: bioRxiv preprint 5 (15). Based on Graupner’s model, we developed a modified Ca 2+-based plasticity model to 90 represent four different types of learning rules (Hebbian, STDP , Anti-Hebbian, and Anti-STDP) by 91 setting eight p arameters ( 𝜃𝑝 : potentiation threshold, 𝜃𝑑 : depression threshold, 𝛾𝑝 : potentiation 92 amplitude, 𝛾𝑑 : depression amplitude, 𝜏𝑝𝑟𝑒 : time constant for Ca 2+ from NMDAR (N-methyl-D-93 aspartate receptor), 𝜏𝑝𝑜𝑠𝑡 : time constant for Ca 2+ from VGCC (Voltage -gated Ca 2+ channel), σ: 94 amplitude for noise, and 𝜏𝑠: time constant for synaptic change) (Fig. 1A and supplementary text 95 I A). We confirmed that our model could predict the experimentally observed changes of post-96 synaptic Ca2+ and synaptic strength under stimulations with different time lags (Fig. 1, B and C). 97 We randomly generated more than 1 million parameter sets and selected 1,000 parameter sets 98 that well represent either one of four learning rules (Fig. 1, D and E, and supplementary text I B). 99 Each learning rule has a clear cluster in the distribution of thresholds and amplitudes (Fig. 1F). 100 The distributions of other parameters and those in other fitting conditions are shown in fig. S1. To 101 evaluate the change of synaptic weights during sleep-like and wake -like firing patterns, we 102 assumed one post-neuron connected with ten pre-neuronal synapses and the same mean firing 103 rates both in sleep-like and wake -like patterns ( Fig. 1G and supplementary text I D ). Firing 104 patterns were derived from previous in vivo recordings (6, 16) (fig. S18 and supplementary text I 105 E) and s ynaptic weights were defined as being linearly related to synaptic efficacy ( 𝜌) (Eq. 1 in 106 supplementary text I A) (15). With the setting, the mean synaptic efficacy became higher in sleep-107 like states than in wake-like states under Hebbian and STDP, representing WISE (Fig. 1H). The 108 opposite results were observed in Anti -Hebbian and Anti-STDP, representing SHY. Thus, WISE 109 and SHY are observed under the specific types of learning rules, with both states exhibiting equal 110 mean firing rates. 111 112 Robustness of WISE and SHY 113 .CC-BY-NC-ND 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted August 19, 2024. ; https://doi.org/10.1101/2024.08.14.607872doi: bioRxiv preprint 6 Next, we investigated the robustness of the WISE and SHY in different settings. We first simply 114 extended the previous model with o ne post-neuron connected by ten pre-neuronal synapses to 115 have 96 pre-neuronal synapses. This extended model still exhibited WISE under Hebbian and 116 STDP , while it showed SHY under Anti-Hebbian and Anti -STDP (Fig. 2A ). Next, we tested a 117 randomly connected model and modified parameters of time constants and amplitudes of learning 118 rules to see if WISE and SHY depend on the properties of learning rules. Even in those settings, 119 we found that these trends still held (Fig. 2, B and C, and fig. S3). In Fig. 2, D and E, we generated 120 various s leep-like firing patterns by changing parameters such as the log10( mean inter -spike 121 interval) (ISIM), log10( mean Up -state duration ) (UPM), and log10( mean Down -state duration ) 122 (DOWNM). We tested ranges of parameters for each targeted mean firing rate by changing either 123 DOWNM (Fig. 2D) or ISIM (Fig. 2E). We found that the mean synaptic efficacy was higher in sleep-124 like states with most of the parameters in the tested range. Notably, this trend was more apparent 125 at lower firing rates. T hese results validated that WISE and SHY were robust under various 126 biologically feasible conditions. 127 128 WISE and SHY in Hodgkin-Huxley-based network models 129 We then tested whether WISE and SHY hold in a more realistic setting where the synaptic efficacy 130 can change the firing pattern. To recapitulate the variable firing pattern, we introduced the 131 Hodgikin-Huxley model to network models based o n our previous study (17), with a ratio of 132 excitatory and inhibitory neurons of 4:1 (Fig. 3A and supplementary text II). In this study, we 133 considered molecules responsible for generating SWO in three subcellular compartments (post-134 synaptic, intracellular (cell body), and pre -synaptic compartments) (17, 18). We assumed that 135 NMDAR and VGCC function in post-synapses and cell bodies, respectively, for generating SWO 136 (17). In addition, because pre-synaptic transmission is crucial for generating SWO in the cortex 137 .CC-BY-NC-ND 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted August 19, 2024. ; https://doi.org/10.1101/2024.08.14.607872doi: bioRxiv preprint 7 (18), we modeled AMPAR, NMDAR, and GABAR to receive the neural transmission. Parameter 138 searches for SWO and bifurcation analysis for a single neuron were based on previous articles 139 (17). First, we randomly generated parameter sets from a large parameter space within the 140 biophysically feasible range and searched for parameter sets that yield firing patterns of SWO. 141 Then, we searched for parameter sets that bifurcate from wake -like to sleep -like patterns as a 142 network (Fig. 3B and supplementary text II B ). Clear desynchronization and synchronization , 143 evaluated by a sleep score (supplementary text IV), were observed with parameter sets for each 144 subcellular component (Fig. 3, C and D , and fig. S4). We then selected the parameter sets that 145 showed almost the same mean firing rates in sleep -like and wake -like states and evaluated 146 synaptic efficacy in the sleep-like and wake-like states (fig. S6 and S7). WISE was observed under 147 STDP (Fig. 3E), while SHY was observed under Anti-STDP (Fig. 3F). Similar trends were observed 148 under Hebbian and Anti-Hebbian and in network models with different connections (fig. S9 and 149 S10). These results validated WISE and SHY in a realistic network model. 150 151 WISE under Hebbian and STDP and SHY under Anti-Hebbian and Anti-STDP is compatible 152 with models including sleep-wake dynamics 153 Next, w e incorporated the spontaneous sleep -wake cycle into our network models. P revious 154 phosphoproteomic studies suggested that phosphorylation of several synaptic proteins is 155 associated with sleep need s (19, 20). The sleep needs increase during wakefulness and 156 decreases with the onset of sleep . This homeostatic oscillation of sleep needs is referred to as 157 Process S (21). In the present model, we assumed that c alcium/calmodulin-dependent protein 158 kinase II (CaMKII) is responsible for the homeostatic oscillation (22). To evaluate the synaptic 159 efficacy across a series of sleep-wake cycles, we assumed that CaMKII changes its states i n a 160 use-dependent manner during wakefulness and induce s SWO by interacting with channels or 161 .CC-BY-NC-ND 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted August 19, 2024. ; https://doi.org/10.1101/2024.08.14.607872doi: bioRxiv preprint 8 receptors that regulate neuronal membrane potentials or enzymes that regulate neurotransmitters 162 (8, 22). This assumption aligns with observations that CaMKII has multiple phosphorylation states 163 and changes its function accordingly (23). We integrated the use-dependent change of CaMKII’s 164 function for activating channels such as NMDAR into the sleep-wake dynamics model (Eq. 57-62 165 in supplementary text III ). The initial state of CaMKII, such as pT286/287 CaMKI I, has self -166 activating ability and Ca2+-dependent activation (24). This initial state activates the second state of 167 CaMKII, such as pT305/306 CaMKII, or phosphatases, such as calcineurin, which can be regulated 168 during sleep (25). We assumed that the second state directly interacts with molecules that induce 169 SWO from the result of optimizing correlation to Process S for network models (fig. S11A). 170 In the simulation of a representative model, we observed that pT286/287 CaMKII, represented as 171 r in Fig. 4A, gradually increased due to Ca2+ influx and autoactivation during wakefulness, which 172 was followed by an increase in pT305/306 CaMKII, represented as a in Fig. 4A. The increased a 173 then activated NMDAR and induce d SWO (Fig. 4, C and D). The mean synaptic efficacy was 174 higher during sleep-like periods than during wake-like periods under STDP (Fig. 4, E and G). The 175 opposite results were observed under Anti-STDP (Fig. 4, F and H). Statistical significances were 176 observed in the analysis with multiple parameter sets (fig. S11, B and C). The results of model 177 with other bifurcation mechanisms or systems also showed the same trends ( fig. S12 to S14). 178 These results confirmed that WISE under STDP and SHY under Anti-STDP are compatible with 179 network models that have sleep-wake dynamics. 180 181 Synaptic changes depend on firing rates assuming higher firing rates during wake -like 182 states 183 In the previous sections, we compared synaptic efficacies in sleep-like and wake -like states by 184 assuming the same mean firing rates in both states. While this assumption is feasible in brain 185 .CC-BY-NC-ND 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted August 19, 2024. ; https://doi.org/10.1101/2024.08.14.607872doi: bioRxiv preprint 9 regions such as the visual cortex, where firing rates are almost constant between states (26), 186 regions such as the somatosensory cortex showed higher firing rates during wakefulness (27). To 187 evaluate the synaptic dynamics in the higher firing rates during wake-like states, we assumed that 188 mean firing rates in Up states of sleep -like patterns are equal to those in wake -like patterns and 189 found that WISE was observed at lower mean firing rates while SHY was observed at higher mean 190 firing rates under Hebbian and STDP (Fig. 5A ). Thus, synaptic efficacies change to different 191 directions depending on mean firing rates assuming higher firing rates during wake-like states. 192 193

194 In this study, we investigated how synaptic dynamics interact with firing patterns and learning rules. 195 Under Hebbian and STDP , wake-like firing patterns weaken synapses, while sleep -like firing 196 patterns strengthe synapses. We referred to this tendency as WISE. In contrast, u nder Anti-197 Hebbian and Anti-STDP , wake-like and sleep-like patterns tend to strengthen and weaken synaptic 198 efficacies, respectively, which aligns with SHY . When we set the firing rate of the Up state of sleep-199 like phasic firing patterns equal to the firing rate of wake -like tonic firing patterns, the resulting 200 higher firing rate of wake-like firing pattern tends to strengthen synapses. This indicates that firing 201 rate is the dominant factor in determining the direction of synaptic changes. These findings 202 delineate the boundary conditions of synaptic dynamics during the sleep -wake cycle. We also 203 demonstrated that these boundary conditions are stable under various conditions by using two 204 types of models with numerous parameters derived from biological knowledge. 205 206 Boundary conditions in synaptic homeodynamics 207 From the perspective of homeos tasis, SHY proposes that wakefulness strengthens synapses to 208 learn about the environment, while NREM sleep weakens less important synapses to reduce 209 .CC-BY-NC-ND 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted August 19, 2024. ; https://doi.org/10.1101/2024.08.14.607872doi: bioRxiv preprint 10 energy consumption (2). Although studies, including anatomical and electrophysiological research, 210 support SHY (19, 28, 29), several studies have reported contradictory results (4–6, 30). 211 Our study indicated that the direction of synaptic changes during sleep-like firing patterns 212 depends on synaptic learning rules and firing rates of local networks. Assuming the same mean 213 firing rates in sleep -like and wake -like patterns, SHY is observed under Anti-Hebbian and Anti-214 STDP ( Fig. 1 to 4). Additionally, we observed that higher mean firing rates results in smaller 215 differences in synaptic changes between sleep-like and wake-like states (Fig. 1H and 2, and fig. 216 S9). This finding suggests that neurons with higher firing rates during wakefulness are less 217 susceptible to synaptic depression during sleep, consistent with SHY (2). In contrast, we observed 218 WISE under Hebbian and STDP (Fig. 1 to 4). This observation indicated that the maximum firing 219 rates during sleep, particularly in the Up state of SWO, are higher when the mean firing rates are 220 equal in both sleep and wakefulness. The high maximum firing rates in sleep enhance synaptic 221 learning rules, that is, Hebbian and STDP strengthen synaptic weights while Anti -Hebbian and 222 Anti-STDP weaken synaptic weights. In vivo experiments also reported that the higher firing rates 223 or shorter inter-spike interval (ISI) in the Up state of SWO (6, 7, 16) (fig. S18). Higher maximum 224 firing rates lead to greater Ca 2+ influx and larger changes in synaptic weights during SWO. 225 Additionally, s ynchronization and hyperpolarized Down states that promote Ca 2+ influx in the 226 subsequent Up state (31) likely contribute to elevated post-synaptic Ca2+ during SWO. 227 We propose that synaptic changes depend on the differences in firing rates between 228 NREM sleep and wakefulness. SHY may occur under STDP when mean firing rates during 229 wakefulness are higher than during NREM sleep ( Fig. 5A). A simulation showed that synaptic 230 efficacies of neurons which are stimulated during wake-like states change according to SHY (fig. 231 S15). Similarly, previous studies have demonstrated that exposure to novel stimuli or enforced 232 wakefulness, conditions expected to increase sleep pressure, result in synaptic downscaling 233 during sleep (32, 33). Conversely, quiet conditions, anticipated to yield lower sleep pressure during 234 .CC-BY-NC-ND 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted August 19, 2024. ; https://doi.org/10.1101/2024.08.14.607872doi: bioRxiv preprint 11 wakefulness, have strengthened synapses during sleep (32). These observations align with our 235 proposal because exposure to novel environments or higher activity increases firing rates during 236 wakefulness, leading to SHY . In contrast, the quiet wake causes only limited differences in firing 237 rate between NREM sleep and wakefulness, leading to WISE (Fig. 5A). These different responses 238 to the neuronal activities during wakefulness support the idea that NREM sleep normalizes the 239 neuronal activities that are skewed during the wakefulness, as presented by Watson et al (6). 240 Noteworthy, WISE predicts lower post -synaptic Ca 2+ concentration during wake -like 241 desynchronized firing under Hebbian and STDP . This prediction aligns with the observation that 242 calcineurin, an LTD-related molecule likely to be activated by lower Ca 2+ concentration during 243 wakefulness, plays a role in excitatory post-neuronal synapses for generating SWO in the following 244 NREM sleep (34–36). Another prediction of WISE is synaptic connectivity homeostasis. When 245 synaptic transmission is inhibited, the resulting SWO may strengthen synapses through WISE, 246 compensating for the inhibited transmission. The connectivity homeostasis is also anticipated in 247 the synaptic dynamics during hibernation. Decreases in firing rates and synaptic connections due 248 to low temperatures during hibernation are associated with increases in SWO during NREM sleep 249 and restoration of synaptic connections after hibernation (37, 38), that is contrary to SHY . Since 250 the lower the firing rates, the greater the synaptic potentiation during sleep in our results (Fig. 1H 251 and fig. S9), WISE may explain synaptic dynamics during the hibernation. Likewise, in depressive 252 disorder, which is characterized by reduced waking activity and dysfunction of AMPAR in frontal 253 cortex (42), synaptic increase during NREM sleep may occur. 254 In conclusion, our study provides a unified framework for the synaptic dynamics during 255 the sleep-wake cycle (Fig. 5B). It suggests that SHY , WISE, and the normalization during NREM 256 sleep coexist but occur depending on synaptic learning rules and neuronal activities of networks. 257 Although further studies are needed to investigate relationships between synaptic learning rules, 258 neuronal activities, and synaptic weights, the framework we presented here lays a foundation for 259 .CC-BY-NC-ND 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted August 19, 2024. ; https://doi.org/10.1101/2024.08.14.607872doi: bioRxiv preprint 12 future research. 260 261 Synaptic dynamics and brain functions 262 Our study provides several implications regarding the relationship between synaptic dynamics and 263 brain functions during the sleep -wake cycle. WISE supports the notion that synaptic potentiation 264 in NREM sleep contribute to memory consolidation (4, 30), which can be promoted by STDP (40). 265 On the other hand, we revealed that wake -like desynchronized states can lead to synaptic 266 depression under Hebbian and STDP, especially at lower firing rates (Fig. 1 to 4). One implication 267 of this inhibition during wakefulness is the enhancement of the signal to noise ratio (SNR) (41). 268 Stimulated neurons likely fire at higher rates, and their synaptic efficacies become larger than those 269 of other neurons in the background desynchronized states. 270 We also found that the variability of synaptic efficacy is higher during wakefulness than in 271 NREM sleep under Hebbian and STDP (Fig. 4G and fig. S12 to S14, and S16). Several studies 272 suggest that the variability of synaptic efficacies leads to the variability of network activity and 273 reflects probabilistic inference for external worlds and decision-making (42, 43). In this context, our 274

suggest that awake states, with higher variability of synapses , are advantageous for 275 exploration and behavioral selection. 276 277

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Loudon for helpful discussions. 403 .CC-BY-NC-ND 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted August 19, 2024. ; https://doi.org/10.1101/2024.08.14.607872doi: bioRxiv preprint 17 404 Funding: 405 JST ERATO grant number JPMJER2001 406 the Science and Technology Platform Program for Advanced Biological Medicine 407 (AMED/MEXT to H.R.U.) 408 a Grant-in-aid for scientific research (S) (to H.R.U., grant number JP18H05270) 409 MEXT Quantum Leap Flagship Program (MEXT QLEAP) (to H.R.U., grant number 410 JPMXS0120330644) 411 a Grant-in-Aid from the Human Frontier Science Program (to H.R.U.) 412 RIKEN Junior Research Associate Program. 413 414 Author Contributions: 415 Conceptualization: F.L.K., R.G.Y ., and H.R.U. 416 Methodology: F.L.K., R.G.Y ., K.L.O., and H.R.U. 417 Simulation: F.L.K.; Validation: F.L.K., R.G.Y ., and K.L.O. 418 Writing (original draft): F.L.K. 419 Writing (review and editing): F.L.K., R.G.Y ., K.L.O., and H.R.U 420 421 Competing interests: The authors declare that they have no competing interests. 422 423 424 .CC-BY-NC-ND 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted August 19, 2024. ; https://doi.org/10.1101/2024.08.14.607872doi: bioRxiv preprint 18 Supplementary Materials 425

426 Supplementary Text 427 Figs. S1 to S20 428 Tables S1 to S8 429

430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 .CC-BY-NC-ND 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted August 19, 2024. ; https://doi.org/10.1101/2024.08.14.607872doi: bioRxiv preprint 19 Figures 461 462 .CC-BY-NC-ND 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted August 19, 2024. ; https://doi.org/10.1101/2024.08.14.607872doi: bioRxiv preprint 20 463 .CC-BY-NC-ND 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted August 19, 2024. ; https://doi.org/10.1101/2024.08.14.607872doi: bioRxiv preprint 21 Fig. 1. WISE under Hebbian and STDP, SHY under Anti-Hebbian and Anti-STDP assuming 464 the same firing rates during sleep-like and wake-like firing patterns. 465 (A) Schematic illustration of the Ca2+-based plasticity model for synaptic learning rules. 466 (B) Calcium transients in a post-neuronal synapse when stimulated with short delays under STDP. 467 (C) The dynamics of synaptic efficacy when stimulated with short delays under STDP. 468 (D) The procedure of a parameter search for synaptic learning rules and calculation of synaptic 469 efficacy in the state of sleep and wake. 470 (E) The standardized synaptic change of the 1000 parameter sets for four types of learning rules 471 represented by Gaussian curves. Each row of the upper panels shows synaptic changes simulated 472 with a parameter set whose sum of squared errors (SSE) between analytical results and Gaussian 473 curves was less than 0.25. The line and shadow in the lower panel indicate the mean and standard 474 deviation, respectively. 475 (F) Distributions of 1000 parameter sets for each learning rule in the axes of thresholds and 476 amplitudes. 477 (G) Schematic illustration for connections and firing patterns of neurons used in the calculation of 478 synaptic efficacy. 479 (H) Box plots for mean synaptic efficacy in sleep -like and wake-like firing patterns by different 480 synaptic learning rules and mean firing rates (n=1000 for each firing rate). The whiskers above and 481 below show minimal to maximal values. The box extends from the 25th to the 75th percentile, and 482 the middle line indicates the median. * p < 0.05, ** p < 0.01, *** p < 0.001, **** p < 0.0001, Welch’s 483 t-test was applied. 484 .CC-BY-NC-ND 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted August 19, 2024. ; https://doi.org/10.1101/2024.08.14.607872doi: bioRxiv preprint 22 485 .CC-BY-NC-ND 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted August 19, 2024. ; https://doi.org/10.1101/2024.08.14.607872doi: bioRxiv preprint 23 Fig. 2. Robustness of WISE and SHY. 486 (A) Schematic illustration of network model consisting of one post-neuron connected with 96 pre-487 neuronal synapses and box plots for synaptic efficacy. 488 (B) Schematic illustration of neural network model consisting of randomly connected ten neurons 489 and box plots for synaptic efficacy. 490 (C) The original (black dotted line) and modified (magenta solid line) curves for STDP rule and box 491 plots for mean synaptic efficacy. alr is the amplitude , and τlr is the time constant for Gaussian 492 curves to be fitted by the parameter search. 493 (D) Representative raster plots of the original (black) and modified (magenta) sleep-like firing 494 patterns and the differences in median of mean synaptic efficacies between sleep-like and wake-495 like firing patterns (sleep - wake). The modified mean firing rates of sleep-like firing patterns were 496 generated by changing DOWNM under constant UPM and ISIM (n=1000 for each firing rate). The 497 dotted boxes highlighted the original UPM and ISIM values are 1.5 and 2.7, respectively. 498 (E) Representative raster plots of the original (black) and modified (magenta) sleep -like firing 499 patterns and the differences in median of mean synaptic efficacies between sleep-like and wake-500 like firing patterns (sleep - wake). The modified firing rates of sleep-like patterns were generated 501 by changing ISIM under constant UPM and DOWNM (n=1000 for each firing rate). The dotted 502 boxes highlighted DOWNM =3.0 and UPM = 2.7 , which are the closest to the original values: 503 DOWNM = 3.12 and UPM = 2.7. 504 (A to C) The mean synaptic efficacy was evaluated in sleep-like and wake-like firing patterns with 505 various mean firing rates assuming different synaptic learning rules (n=1000 for each firing rate). 506 The whiskers above and below of box plots show minimal and maximal values, respectively. The 507 box extends from the 25th to the 75th percentile and the middle line indicates the median. * p < 508 0.05, ** p < 0.01, *** p < 0.001, **** p < 0.0001, Welch’s t-test was applied. 509 .CC-BY-NC-ND 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted August 19, 2024. ; https://doi.org/10.1101/2024.08.14.607872doi: bioRxiv preprint 24 (D and E ) ISIM: log10(mean ISI), UPM: log10( mean Up-state duration), DOWNM: log10( mean 510 Down-state duration) 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 .CC-BY-NC-ND 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted August 19, 2024. ; https://doi.org/10.1101/2024.08.14.607872doi: bioRxiv preprint 25 527 .CC-BY-NC-ND 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted August 19, 2024. ; https://doi.org/10.1101/2024.08.14.607872doi: bioRxiv preprint 26 Fig. 3. WISE and SHY in Hodgkin-Huxley-based network models. 528 (A) Schematic illustration of a model with excitatory and inhibitory synapses. A Hodgkin-Huxley-529 based network model was constructed based on the averaged neuron model in a previ ous study 530 (17). 531 (B) Procedures for collecting parameter sets that bifurcate from wake -like to sleep -like firing 532 patterns and comparing synaptic efficacy between the two states in Hodgkin-Huxley-based 533 network models. 534 (C) Representative sleep-like and wake-like firing patterns for three types of bifurcation models. 535 The parameters used in the simulation were obtained by multiplying the original values defined in 536 Table S5 by the presented factors. Simulations were conducted for five seconds and presented for 537 three seconds in each model. 538 (D) Changes in the sleep score, percentage of sleep-like waveforms (sleep (%)), and mean firing 539 rate (FR (Hz)) as the conductance of the channel or receptor, or the coefficients of pre-synaptic 540 activations are gradually increased. The range of the conductance was divided into 80 steps for 541 post-synaptic or intracellular bifurcation, while the range of the coefficient was divided into 75 steps 542 for pre-synaptic bifurcation. Simulations were conducted for ten seconds at each conductance or 543 coefficient step. 544 (E and F) Box plots for mean synaptic efficacy during sleep-like and wake-like firing patterns under 545 STDP (E) and Anti-STDP (F) by three types of network models (n = 191, 52 , and 150 for STDP 546 and n = 121, 36, and 119 for Anti-STDP in post-synaptic, intracellular, and pre-synaptic bifurcation 547 models, respectively). The whiskers above and below of box plots show minimal and maximal 548 values, respectively. The box extends from the 25th to the 75th percentile, and the middle line 549 indicates the median. * p < 0.05, ** p < 0.01, *** p < 0.001, **** p < 0.0001, Student’s t -test was 550 applied. 551 .CC-BY-NC-ND 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted August 19, 2024. ; https://doi.org/10.1101/2024.08.14.607872doi: bioRxiv preprint 27 552 .CC-BY-NC-ND 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted August 19, 2024. ; https://doi.org/10.1101/2024.08.14.607872doi: bioRxiv preprint 28 Fig. 4. WISE under Hebbian and STDP and SHY under Anti-Hebbian and Anti-STDP is 553 compatible with models including sleep-wake dynamics. 554 (A) Schematic illustration of the model for sleep-wake dynamics in excitatory synapses. The initial 555 state of CaMKII such as pT286/287 CaMKII is represented by r. The initial state activates a which 556 corresponds to the second state of CaMKII such as pT305/306 CaMKII or phosphatases such as 557 calcineurin. 𝛼, 𝛽, w, and b corresponds to variables defined in the equations in the supplementary 558 text III. Synaptic efficacies were calculated in Hodgkin-Huxley-based network models bifurcated 559 by the post-synaptic mechanism with sleep -wake dynamics under synaptic learning rules. The 560 conductance of NMDAR was updated by a and the simulations were optimized by Pearson’s 561 correlation coefficients between process S and r. The simulations were conducted for 500 seconds. 562 The parameter set for channel or receptor conduces, learning rule and sleep-wake dynamics and 563 initial values for variables in a representative model are shown in table S5 to S8. 564 (B) Schematic illustration of the network model used in simulations. The network model has 80 565 neurons with the E:1 ratio of 4:1. 566 (C and D) Time changes of post-synaptic membrane potential and Ca 2+ concentration, synaptic 567 efficacy, and the ratio of two phosphorylated states of kinases ( r and a) of a synapse in 568 representative network models under STDP (C) and Anti-STDP (D). The results of 0-300 seconds 569 are shown. 570 (E and F) Raster plots and time changes of mean synaptic efficacy, sleep score, and process S in 571 representative network models under STDP (E) and Anti-STDP (F). The shadow in time changes 572 in mean synaptic efficacy represents SD. The network was considered to be in the state of sleep 573 or wake if the sleep score was above or below the threshold, respectively (the threshold is the 574 value of sleep score where p = 0.01; see supplementary text IV). The results of 0-300 seconds are 575 shown. 576 .CC-BY-NC-ND 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted August 19, 2024. ; https://doi.org/10.1101/2024.08.14.607872doi: bioRxiv preprint 29 (G and H) Mean and coefficient of variance (CV) of synaptic efficacy during the periods of sleep-577 like and wake-like states in representative network models under STDP (E) and Anti-STDP (F). 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 .CC-BY-NC-ND 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted August 19, 2024. ; https://doi.org/10.1101/2024.08.14.607872doi: bioRxiv preprint 30 596 Fig. 5. Synaptic changes depend on firing rates assuming higher firing rates during 597 wakefulness. 598 (A) A Schematic illustration for sleep-like and wake -like spike patterns and b ox plots for mean 599 synaptic efficacy in sleep -like and wake-like firing patterns for different learning rules and mean 600 firing rates (n=1000 for each firing rate). The mean firing rates in wake-like states are equal to the 601 .CC-BY-NC-ND 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted August 19, 2024. ; https://doi.org/10.1101/2024.08.14.607872doi: bioRxiv preprint 31 mean firing rates in Up states of sleep-like states. The sleep-like firing patterns were generated by 602 sampling from the lognormal distributions with log10(mean Up -state duration ) = 2.7 and 603 log10(mean Down-state duration) = 3.0. SD was calculated according to the linear regression 604 analysis based on in vivo data (fig. S18). 605 WISE and SHY dynamics are highlighted under the x-axis according to the change in the direction 606 of synaptic efficacy. The whiskers above and below show minimal to maximal values. The box 607 extends from the 25th to the 75th percentile and the middle line indicates the median. * p < 0.05, 608 ** p < 0.01, *** p < 0.001, **** p < 0.0001, Welch’s t-test was applied. 609 (B) A Graphical abstract of a unified framework for synaptic dynamics during the sleep-wake cycle. 610 SHY: Synaptic homeostasis hypothesis, WISE: Wake Inhibition Sleep Excitation 611 612 .CC-BY-NC-ND 4.0 International licensemade available under a (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 The copyright holder for this preprintthis version posted August 19, 2024. ; https://doi.org/10.1101/2024.08.14.607872doi: bioRxiv preprint