Sleep is critical for hippocampus-dependent memory consolidation. However, the underlying mechanisms of synaptic plasticity are poorly understood. The central controversy is on whether long-term potentiation (LTP) takes a role during sleep and which would be its specific effect on memory. To address this question, we used immunohistochemistry to measure phosphorylation of Ca 2+ /calmodulin-dependent protein kinase II (pCaMKIIα) in the rat hippocampus immediately after specific sleep-wake states were interrupted. Control animals not exposed to novel objects during waking (WK) showed stable pCaMKIIα levels across the sleep-wake cycle, but animals exposed to novel objects showed a decrease during subsequent slow-wave sleep (SWS) followed by a rebound during rapid-eye-movement sleep (REM). The levels of pCaMKIIα during REM were proportional to cortical spindles near SWS/REM transitions. Based on these results, we modeled sleep-dependent LTP on a network of fully connected excitatory neurons fed with spikes recorded from the rat hippocampus across WK, SWS and REM. Sleep without LTP orderly rescaled synaptic weights to a narrow range of intermediate values. In contrast, LTP triggered near the SWS/REM transition led to marked swaps in synaptic weight ranking. To better understand the interaction between rescaling and restructuring during sleep, we implemented synaptic homeostasis and embossing in a detailed hippocampal-cortical model with both excitatory and inhibitory neurons. Synaptic homeostasis was implemented by weakening potentiation and strengthening depression, while synaptic embossing was simulated by evoking LTP on selected synapses. We observed that synaptic homeostasis facilitates controlled synaptic restructuring. The results imply a mechanism for a cognitive synergy between SWS and REM, and suggest that LTP at the SWS/REM transition critically influences the effect of sleep: Its lack determines synaptic homeostasis, its presence causes synaptic restructuring.

Sleep is important for long lasting memories. There exists, however, a controversy regarding the mechanisms by which sleep modifies synapses to consolidate enduring memories. One theory posits that sleep weakens synapses, leading to the forgetting of all but the strongest memories. The alternative theory proposes that sleep promotes both weakening and strengthening of different connections, the latter through a process known as long-term potentiation (LTP). Here we measured the levels of a phosphorylated protein related to LTP during the sleep cycle of rats and used the data to build models of sleep-dependent synaptic plasticity. By feeding one model with spikes recorded from the rat hippocampus, we observed that LTP during sleep not merely strengthens certain connections, but actually reorganizes how these connections are ranked in strength, leading to substantial changes of the overall pattern. A more detailed model of hippocampus and cortex showed that the interaction of the mechanisms predicted by the competing theories promotes a more efficient control of which memories are stored. Our results provide a step forward in the understanding of the cognitive role of sleep by indicating that the current competing theories are not mutually exclusive. Instead, each constitutes an important stage of memory consolidation.

Funding: Support obtained from Financiadora de Estudos e Projetos ( http://www.finep.gov.br/ ) Grant # 01.06.1092.00 to SR; Conselho Nacional de Desenvolvimento Científico e Tecnológico ( http://www.cnpq.br/ ): Grants 481506/2007-1, 481351/2011-6 and 306604/2012-4 to SR, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior ( http://www.capes.gov.br/ ) and Ciencias sem Fronteiras ( http://www.cienciasemfronteiras.gov.br/web/csf/home ) to AT and CRC; Fundação de Amparo à Pesquisa do Rio Grande do Norte ( http://www.fapern.rn.gov.br/ ): Grant Pronem 003/2011 to SR; Fundação de Amparo à Pesquisa do Estado de São Paulo ( http://www.fapesp.br/ ): Grant #2013/ 07699-0 - Center for Neuromathematics to SR; CMP and VRC supported by post-doctoral fellowships from Fundação de Amparo à Pesquisa do Rio Grande do Norte /CNPq. Additional support obtained from the Federal University of Rio Grande do Norte ( www.ufrn.br ); Ministry of Science, Technology and Innovation ( http://www.mcti.gov.br/ ); Associação Alberto Santos Dumont de Apoio à Pesquisa ( http://natalneuro.com/associacao/index.asp ); Pew Latin American Fellows Program ( http://www.pewtrusts.org/en/projects/pew-latin-american-fellows/ ) to SR; Informatics Department of the Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Norte ( http://portal.ifrn.edu.br/ ) to WB. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Copyright: © 2015 Blanco et al. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Since both SHY and the synaptic embossing theory have empirical support, computational work may be particularly insightful. SHY has been modeled at the single neuron and network levels, but without real neurophysiological inputs [ 4 , 10 ]. A recent SHY model found deleterious effects for memory when instantaneous potentiation was switched on during sleep [ 10 ], but the synaptic embossing hypothesis is yet to be simulated with realistic LTP onset and dynamics. To that end, we computationally investigated the network consequences of LTP triggered during sleep, by feeding simulated neurons with action potentials recorded from the rat hippocampus across the sleep-wake cycle. LTP was applied at REM onset as constrained by the empirical results. Synchronization-based LTP was calculated from coincident spiking during SWS only or SWS+REM, while an alternative model captured the notion that short-term changes in pCaMKIIα levels determine long-term increases in synaptic weights. Finally, we investigated the interaction of synaptic homeostasis and embossing mechanisms by simulating the dynamics of memory formation during a sleep cycle in a canonical hippocampo-cortical model.

To address this debate, we first assessed phosphorylated Ca 2+ /calmodulin-dependent protein kinase II (pCaMKIIα) in the hippocampus of rats exposed (or not) to novel objects, and killed immediately after subsequent WK, SWS or REM ( S1 Fig ). CaMKIIα phosphorylation is one of the earliest mechanisms with a critical role in LTP, memory and learning [ 34 , 35 ]. CaMKIIα undergoes conformational changes towards the active form within seconds after the beginning of synaptic stimulation [ 36 ], triggering later events that include the up-regulation of immediate-early genes required for long-term synaptic remodeling, such as Zif-268 [ 37 ]. Given the very fast kinetics of CaMKIIα phosphorylation [ 36 ] in comparison with Zif-268 [ 38 ], pCaMKIIα levels were hypothesized to show experience-dependent changes immediately after SWS and/or REM, while Zif-268 protein levels were expected to be invariant immediately after any given state. The protein levels of total CaMKIIα and Actin were also assessed as negative controls expected to show invariant levels across groups, given their much slower transcriptional and translational regulation. To gain insight in the state dependency of pCaMKIIα regulation, we also investigated the relationship between pCaMKIIα levels and electrophysiological markers of SWS (delta oscillations), REM (theta oscillations) or the SWS/REM transition (neocortical spindles) [ 39 ].

The theories also differ on the roles of the different sleep states in memory consolidation. SHY only considers SWS and does not propose any role for REM [ 4 , 26 ], while the embossing theory encompasses both states [ 6 , 12 , 13 ]. The substantial differences in the firing and correlation regimes of SWS and REM suggest that the two states should be separately and sequentially modeled [ 6 , 12 , 27 ]. One study has suggested that SWS leads to general memory reinforcement while REM leads to forgetting of all but the strongest memories traces [ 28 ]. LTP during SWS has been proposed to amplify the synaptic changes acquired during WK [ 29 ], with further processing of the resulting synaptic weights during REM [ 30 , 31 ]. In fact, plasticity factors such as protein kinases and transcription factors encoded by immediate-early genes are up-regulated during REM [ 14 – 16 , 20 , 32 , 33 ]. Therefore, it is possible that a complete sleep cycle traversing SWS and REM leads to important perturbations in the pattern of synaptic weights [ 6 , 12 , 27 ], rather than to the simple weight convergence observed during SWS alone [ 4 ].

Two theories are in dispute. The synaptic homeostasis hypothesis (SHY) proposes that SWS causes generalized synaptic weakening [ 7 – 9 ], leading to the down-selection of weak synapses [ 10 ]. The notion that synaptic depression is determinant for off-line memory processing departs from the conventional Hebbian learning rule, by which connections among simultaneously firing neurons are reinforced [ 11 ]. On the other hand, the synaptic embossing hypothesis postulates the combination of non-Hebbian rescaling and Hebbian potentiation of synaptic weights in complementary circuits during REM [ 6 , 12 , 13 ]. The core of the dispute is the controversy on whether long-term potentiation (LTP) occurs during sleep. Empirical studies diverge considerably, with molecular, electrophysiological and morphological evidence for [ 14 – 22 ] and against [ 4 , 7 , 23 – 25 ] it.

In the hippocampus, slow-wave sleep (SWS) is characterized by large amplitude, low-frequency oscillations of the local field potential (LFP), concomitant with a phasic regime of neuronal firing, with relatively low mean firing rates and intermittent synchronization [ 1 – 4 ]. In contrast, rapid-eye-movement sleep (REM) displays small amplitude, high-frequency oscillations that underlie a tonic firing regime, with relatively high mean firing rates and decreased synchrony [ 1 – 4 ]. Both sleep states play a role in the consolidation of hippocampus-dependent memories [ 5 , 6 ], but the mechanisms remain poorly understood.

The significance of T S and T H was assessed using a normal fit to the distribution of 200 surrogate values obtained from shuffling of the memory selectivity pattern in the network after sleep.

The memory selectivity of neuron i was considered to switch during sleep when Sel i [t sleep ]⋅Sel i [∞] = −1 and was considered stable when Sel i [t sleep ]⋅Sel i [∞] = 1. The proportion of switches in the memory selectivity,T S , was measured as: (13)

The memory selectivity of a given neuron i at time t, Sel i [t], was set as 1 for memory A, -1 for memory B and 0 if there is no memory selectivity: (12)

LTP was triggered during sleep by setting = 405 s. LTP was used to influence memory selectivity of each neuron. The intended selectivity pattern in the network was a permutation of the original pattern prior to sleep. Specifically, the gain factor, , depends on the normalized synaptic weight between input j and a randomly picked neuron k ≠ i before t sleep : (11) where H(⋅) is a Heaviside function.

The sum of all plastic events, , updated the weight values, W ij [t + 1]. To ensure weight stability, the sum of all weights was kept stable with a mean value of ω = 0.25 nS:

LTP, , was implemented as a Gaussian function with peak at , standard deviation of = 45 s. is modulated by a gain factor specific for each synapse, , and a magnitude parameter κ sleep : (7) Where A is such that the integral of equals 0.05 nS.

Input-neuron synapse conductance, W ij [t], between input unit j and neuron i was subject to modification according to spike-timing dependent plasticity (STDP) and LTP effects. STDP was based on the relation, , between the time of the last presynaptic spike, where , and the time of the last postsynaptic spike, where . Potentiation, , occurred when δt ij > 0 and depression, , when δt ij < 0, and are described by: (5) (6) Where τ STDP = 20 ms, C p = 3.2 nS, C d = 0.03 and v is a stochastic factor with zero mean and σ = 0.015.

We built a network of 45 leaky integrate-and-fire neurons with network feedback inhibition [ 50 – 52 ] ( S6 Text ). Each neuron received synaptic connections from 200 input units and was not directly connected to other neuron. Half of the input units were assigned to memory A (M A = [1 … 100]) and the other half to memory B (M B = [101 … 200]). Input unit i emitted actions potentials (S[t] = 1 if there is a spike at time t, S[t] = 0, otherwise) following a Poisson distribution with mean frequency f active = 20 Hz when in an active state and f inactive = 10 Hz when in an inactive state. Input pattern was determined in 125 ms windows by randomly selecting one memory to be in an active state. Each cell gets selective to a specific memory through the synaptic weight dynamics driven by the plasticity mechanisms described below.

The network was considered to reach the convergence point when the absolute variation over time (slope) of every synaptic connection value reached a negligible value, i.e. when |dw ij /dt|< = ε, ε = 0.00025 for ∀i and ∀j.

Net synaptic weight changes (M ∆w ) was calculated as the mean of the differences (element by element) between the synaptic weight values at time t 1 and t 2 (t 2 >t 1 ): . Since w ii = 0, N(N-1) is the number of connections among neurons. Global synaptic downscale is defined as M ∆w <0; global synaptic upscale occurs when M ∆w >0.

In order to model LTP during sleep, we added a Gaussian curve to Eq 1 [ 48 , 49 ], which is a function of time with the following parameters: t T , the moment the Gaussian is triggered (30s after the beginning of the selected REM sleep) ( S8 Fig ); μ, the peak time (30 min); and σ the variance. The synaptic potentiation is thus defined as: (4) where Cieg ij models the effect of immediate-early genes by modulating the amplitude of the Gaussian gain. Cieg ij was calculated in 2 ways: based on spike synchronization (LTP1) and on the trajectory of synaptic weights (LTP2). In LTP1, Cieg ij is the ratio of presynaptic spikes that occurred synchronously with postsynaptic spikes during specific sleep stages ( S10A Fig ). Three variations of LTP1 were implemented depending on which epoch Cieg ij was computed for: using the entire SWS prior to the REM stage (LTP1 full SWS); the last 30s of SWS prior to REM (LTP1 30s SWS end); and the last 30s of SWS and the first 30s of REM (LTP1 60s SWS/REM). In LTP2, synaptic connections were selected based on the angle β ij formed by w ij (t) at the SWS/REM transition; β ij was obtained from the linear fit of w ij (t) values 30s before and after the transition ( S10B and S10C Fig ). Two variations of LTP2 were implemented: selecting for potentiation in all w ij (t) trajectories with a positive REM slope, with β ij smaller than 3π/2 (LTP2 permissive 60s SWS/REM) ( S10B Fig , left panel, dark blue dots, cases 1, 2 and 3); and selecting only trajectories with β ij smaller than π (LTP2 restrictive 60s SWS/REM) ( S10B Fig , left panel, light blue dots, cases 1 and 2).

Instantaneous plasticity was adapted from the stable Hebb's rule for synchronous firing [ 45 ]. Discrete synaptic potentiation (when the pre- and post- synaptic neurons fire synchronously) is described as: (1) (2) where ∆t = 0.004s and C p = 6.25s -1 ; notice that J makes the potentiation larger for weak than strong synapses [ 46 – 48 ]. The synaptic weakening (when the pre-synaptic neuron fires and the post-synaptic neuron does not fire) is described as: (3) where θ = 1 and C d = 0.021s -1 .

The network was exposed to 2 types external inputs (e i (t)): Real spike data and Poisson spike trains with same mean firing rates as those observed during WK, SWS and REM ( S4A Fig ). When Poisson spike trains were used as inputs, the network was composed of 150 neurons. When real spike data were used, the network was composed by the same number of neurons as recorded in each animal (Rat1 = 45, Rat2 = 39, Rat3 = 39, Rat4 = 34, Rat5 = 22 and Rat6 = 13). Despite the lack of inhibitory neurons, this simplified network replicates the synaptic rescaling dynamics (see below) of a more complex network with both excitatory and inhibitory processing units [ 4 ].

The network was implemented as a modified Boltzmann machine [ 44 ]. The total synaptic current for each neuron i is defined as where N is the number of neurons, e i (t) is an external input and v j (t) is the state of pre-synaptic neuron j; w ie and w ij are the corresponding synaptic weights. The neuron state is binary (0 or 1) and stochastically updated by the adjusted sigmoid function , where K t = 6 and K s = 11 are constants; with these values the mean firing rate of the spontaneous network activity (when w ie = 0) is around 0.5 and 1Hz ( S9 Fig ). During all simulations, we used w ie = 0.5 and pre-synaptic weights w ij were randomly initiated following a uniform distribution between 0 and 1, except when i = j, in which case the synaptic weight is set to 0 throughout the simulation.

Customized Matlab routines were used to quantify spectral power in the delta (0.5 to 4.5 Hz) and theta (4.5 to 12 Hz) bands, and to detect and quantify spindles, 7–14 Hz oscillations that last from 0.5 to 4 seconds [ 42 ]. As expected [ 39 ], spindles were detected during SWS and during the intermediate sleep (IS) state that separates SWS from REM [ 43 ]. See S5 Text .

Labeling specificity of the immunohistochemistry for pCaMKIIα, total CaMKIIα, Actin and Zif-268 ( S2A Fig ) was confirmed by Western blots ( S2B Fig ). Quantification of the immunohistochemistry comprised 2 sections per animal, with all sections processed as a single batch (n = 5 for groups exposed to objects, n = 4 for control groups). See S3 and S4 Text.

After 3h the animals were randomly assigned to the WK, SWS or REM groups ( S1 Fig ). SWS animals were killed immediately after 10 min of uninterrupted SWS; REM animals were killed immediately after 2 min of uninterrupted REM; WK animals were kept awake for additional 10 min before killing. Group assignment was identically performed for unexposed controls.

Precise determination of sleep-wake states was obtained by real time spectral analysis of LFP. Customized Matlab routine was used to build a 2D spectral map that sorts WK, SWS and REM in real time [ 20 , 39 ]. On experiment day, 6 groups were defined by prior experience (with or without exploration of novel objects) and state displayed immediately before killing (WK, SWS or REM). See S1 Fig and S2 Text . Following object exploration, rats were kept awake by gently tapping the recording box every time they approached SWS on the online spectral map. This mild sleep deprivation was used to temporally disambiguate the changes induced by novel object exploration from the subsequent sleep-dependent changes in pCaMKIIα levels. By keeping all the animals awake for 3h, overall behavioral experience was equalized across groups and therefore the specific sleep-wake state achieved immediately before killing became the key variable to consider. We have successfully employed this procedure in the past for the assessment of other plasticity factors during post-learning sleep [ 14 , 20 , 32 , 41 ].

Animals were transferred to the recording box at 07:00 pm. After cycling freely across sleep-wake states for 2h, 4 different novel objects were placed in the box corners for 10 min [ 31 ] ( S1A Fig ). Controls were not exposed to novel objects ( S1B Fig ).

For the LFP recordings, rats were implanted with monopolar LFP electrodes for cortical and reference leads, and microwires in the dentate gyrus. LFPs were recorded with a 32-channel multichannel acquisition processor, synchronized with video recordings and animal tracking (Plexon, USA). See S1 Text . Real spike data, used as inputs to the fully connected excitatory network, were previously obtained by chronic extracellular multi-electrode recordings from hippocampal CA1 field (n = 6 rats; same data as in [ 20 , 40 ]).

For quantification of pCaMKIIα and Zif-268 levels, adult male Wistar rats (n = 27, 300–350 g) were housed, surgically implanted and recorded according to National Institutes of Health (NIH) guidelines and Edmond and Lily Safra International Institute of Neuroscience of Natal (ELS-IINN) Committee for Ethics in Animal Experimentation (permit # 05/2007). Implanted animals were housed in individual home cages with food and water ad libitum, and were kept on a 12h light/dark schedule with lights on at 06:00. At the end of the experiment, rats were anesthetized with isoflurane 5%, and decapitated.

Results

Modeling Sleep-Dependent LTP in a Computational Network Fed with Hippocampal Spikes The results above support the notion that LTP is triggered at the SWS/REM transition. To model the consequences of this phenomenon, we first investigated how state-dependent variations in firing regimes affect the synaptic weights of a fully-connected network comprising an excitatory population of stochastic binary units (see Materials and Methods). The synaptic weights were initialized with a random uniform distribution, and therefore with maximum entropy. A stable Hebbian learning rule based on pairwise synchrony was used to update synaptic weights over time [45]. Synchrony was evaluated in 4-ms bins, well within the interval of maximum STDP [47], and lack of synchrony led to a fixed amount of synaptic weight weakening. The simulations were generated by feeding the network with 2 kinds of external inputs (S1 Table; representative example): Poisson spike trains at various rates; and actual spike trains recorded from the rat hippocampal field CA1 during WK, SWS and REM [20]. The data statistics conformed to the expected state-dependent changes across the sleep-wake cycle [1–3]: SWS featured low mean firing rates (Fig 3A; representative example) and decreased firing synchronization (Fig 3B; representative example) compared with WK. REM was characterized by mean firing rates in between those of WK and SWS (Fig 3A), with very low firing synchronization (Fig 3B). For data from 5 other rats see S4 Fig. Fig 3C depicts the durations of intervals separating consecutive SWS/REM transitions (left panel; n = 6), and a cumulative plot showing that 91,6% of these intervals are shorter than 30 min (right panel). PPT PowerPoint slide

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larger image TIFF original image Download: Fig 3. Statistics of real spikes from the hippocampal CA1 field during WK, SWS or REM. (A) Probability distributions of spike rates across states, with mean population values represented by dashed lines (left panel). Mean and variance of spike rates recorded during each state (right panel). (B) Square matrix of Pearson's linear correlation coefficient for spiking of 45 neurons during WK, SWS or REM (left panel), and the corresponding mean and variance (left panel). Significant differences of the Pearson's coefficient distribution were found between WK and SWS (Kolmogorov-Smirnov (KS) p = 6.9607e-023), WK and REM (KS, p = 1.0890e-023), and SWS and REM (p = 4.0259e-017). (C) Distribution of durations for intervals separating consecutive REM episodes (left panel, n = 6 rats; 28.8 hours of recordings). Cumulative plot of the REM-to-REM interval durations (right panel). Note that 91.6% of the intervals are shorter than 30 min (dashed line). More examples in S4 Fig; see also S1 Table. https://doi.org/10.1371/journal.pcbi.1004241.g003 Two major scenarios were implemented, with and without LTP during sleep. For statistical robustness, all simulations were independently repeated 25 times. The dynamics of the synaptic weight patterns were quantified using 2 metrics: the Similarity Index measured the sum of absolute differences between a given synaptic weight pattern and a reference pattern, while the Spearman´s correlation quantified ranking changes among synaptic weights compared to the reference pattern. Altogether, these metrics allowed us to estimate the rescaling and restructuring of the synaptic weight patterns over time. Rescaling was indicated by a reduction in the Similarity Index without major changes in Spearman´s correlation. Restructuring was indicated by a reduction in the Similarity Index accompanied by a reduction of Spearman´s correlation.

Feeding the Network with Poisson Data We began by characterizing the rate-dependency of synaptic weight dynamics during a regime of non-correlated external inputs. The network was fed Poisson surrogated spike trains with mean rates between 5 and 10 Hz, which represent the real data range (Figs 3A and S4A). The distribution of synaptic weights was rescaled over time to a narrow range of values (S5A and S6A Figs), exactly as observed previously for a single cell model [45], as well as a network model with both excitatory and inhibitory units [4]. The mean synaptic weight at the convergence time point (S5A Fig, dashed black lines) depended on the mean firing rate of the inputs (S6B Fig, blue curve). By the same token, the time required for the synaptic pattern to converge was inversely proportional to the input rate (S6B Fig, red curve). For simulations with low rate inputs typical of SWS (Figs 3 and S4A), mean synaptic weights at the time of convergence were smaller than 0.5, resulting in net weakening (M w <0, see Material and Methods) of the synaptic weights (S5A and S6A Figs, distributions for 3, 5 and 7Hz). However, synaptic weights that were initially below the mean at the time of convergence became strengthened (S5A Fig, bottom panels). Therefore, net weakening of synaptic weights does not imply that all synaptic weights decay over time, since weak synaptic connections are potentiated. Conversely, for simulations in which inputs had higher rates typical of REM or WK (>7Hz), synaptic weights at the time of convergence were larger than 0.5, resulting in net potentiation of synaptic weights (S5A Fig, for 10Hz and its corresponding gray distribution in S5C and S6A Figs, distributions for 12, 20 and 40Hz). Yet, synaptic weight values initially above the convergence range were reduced over time (S5A Fig, bottom panels). In summary, when the network was fed with non-correlated Poisson inputs, the wide range of synaptic weights used to initialize the network converged to a narrow and stable distribution, producing net weakening or net potentiation of the synapses for low and high firing rates, respectively.

Feeding the Network with Real Spike Trains To further characterize the state-dependency of synaptic weights, we fed the network with spike data from concatenated WK, SWS or REM episodes (S5B Fig). The simulations confirmed that the mean firing rates of the external inputs determine the mean value reached over time by the distribution of synaptic weights P(w), as shown for Poisson data in previous work [45] and in the preceding section. Periods of increased spike rate and synchronization, such as WK, resulted in a smaller standard deviation of the synaptic weights when the network reached steady state, in comparison with periods of reduced spike rate and correlation, such as SWS or REM (S1 Table and S5B and S5C Figs green distributions). Note that the standard deviations at steady state were even smaller for non-correlated Poisson data of identical mean rates, and also obeyed the relationship WK<REM<SWS (S1 Table and S5C Fig, gray distributions). Next we investigated how external inputs with the real dynamics of state alternation affected the distribution of synaptic weights. Fig 4 shows results when the network inputs were real spike data recorded over 5 hours from one rat (Rat1) cycling freely through the sleep-wake cycle, i.e. containing the natural alternation of WK, SWS and REM (Fig 4A, hypnogram). As expected, population firing rates were markedly state-dependent throughout the recording (Fig 4A, Pop. rate). The model displayed net potentiation during WK and net weakening during sleep (Fig 4B). We also observed that most synaptic connections did not reach extreme values (close to 0 or to 1) but converged to the middle range of possible values (Fig 4B). PPT PowerPoint slide

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larger image TIFF original image Download: Fig 4. LTP during sleep leads to marked changes in synaptic weight trajectories. (A) Hypnogram of representative recording (top panel) and corresponding population spike rate activity over time (bottom panel). Three different simulations were run using real spike data: (B) without LTP; (C) with LTP 1 full SWS model, modulated by the amount of synchronized spikes observed during the SWS episode that preceded the 4th REM period (duration of SWS episode = 658s), and (D) with LTP 2 permissive model, related to the changes in synaptic weight trajectories at the SWS/REM transition. Black arrow indicates the time point at the SWS/REM transition when the LTP Gaussian was triggered (~10,500s; 30s were elapsed for LTP evaluation before bonuses was applied). To focus on the sleep period, the (C) and (D) simulations are plotted from 8,000s to 16,200s. The initial synaptic weight values were uniformly distributed in the range [0..1]; consequently, colors (from dark blue to dark red) are also homogeneously distributed for w ij values in [0..1]. Initial color maintained for each synaptic weight trajectory during entire simulation. In (B), bottom panel indicates the period during which the Gaussian curve affected the synaptic values to simulate LTP (blue curve). See also S7 and S8 Figs. https://doi.org/10.1371/journal.pcbi.1004241.g004

Modeling LTP during Sleep Two alternative LTP models triggered near the SWS/REM transition were investigated. Since LTP is tightly associated with firing synchrony [11, 47, 54], one model attempted to capture the notion that SWS causes LTP through firing synchronization [55–57] and enhanced calcium influx [19, 30, 58], leading to calcium accumulation during SWS that would then lead to increased pCaMKIIα levels at REM onset. To simulate this scenario, LTP1 full SWS model applied a long-term bonus to each synapse starting at the SWS/REM transition, but according to the amount of pairwise synchrony observed throughout an entire SWS episode (87.06 ± 47.47, mean ±SEM in seconds, n = 6 rats). The second model (LTP2) simulated short-term changes in pCaMKIIα levels as short-term increases in synaptic weights at the SWS/REM transition, and then used these short-term increases to determine long-term increases in synaptic weights. This model is compatible with the empirical data (Figs 1 and 2), and with the evidence of REM-dependent upregulation of plasticity factors [14–16, 20]. For each synaptic weight, LTP2 model coupled short-term changes at the SWS/REM transition to a gradual long-term bonus. The rationale for this coupling was the fact that the balance between high and low calcium influx in the millisecond scale is reflected in the balance between kinase and phosphatase activation in the seconds range, in particular CamKIIα, and determines the subsequent activation for over 30 min of Rho GTPases such as cdc42, and consequently to changes in gene regulation and protein synthesis in the hours scale [59–63]. To simulate this scenario, short-term changes in synaptic weights assessed for 60s at the transition from SWS (30s) to REM (30s) determined long-term bonuses applied for 30 min to the synaptic weights (see Material and Methods). Specifically, the angle formed by the synaptic weight trajectory at the transition from SWS to REM determined a long-term bonus. To comply with the notion that LTP requires positive calcium transients, LTP was applied exclusively to synaptic weights whose trajectory showed a positive slope during REM (LTP2 permissive 60s SWS/REM). The long-term bonus applied in both models consisted of a Gaussian curve with onset at a reference SWS/REM boundary and peak value at 30 min, to match the duration of the spine-specific signaling cascade Ca2+–CaMKIIα–Cdc42 [64].