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J Neurophysiol. 2010 Dec; 104(6): 3476–3493.
Published online 2010 Oct 6. doi:  10.1152/jn.00593.2010
PMCID: PMC3007640

Sleep and Synaptic Renormalization: A Computational Study


Recent evidence indicates that net synaptic strength in cortical and other networks increases during wakefulness and returns to a baseline level during sleep. These homeostatic changes in synaptic strength are accompanied by corresponding changes in sleep slow wave activity (SWA) and in neuronal firing rates and synchrony. Other evidence indicates that sleep is associated with an initial reactivation of learned firing patterns that decreases over time. Finally, sleep can enhance performance of learned tasks, aid memory consolidation, and desaturate the ability to learn. Using a large-scale model of the corticothalamic system equipped with a spike-timing dependent learning rule, in agreement with experimental results, we demonstrate a net increase in synaptic strength in the waking mode associated with an increase in neuronal firing rates and synchrony. In the sleep mode, net synaptic strength decreases accompanied by a decline in SWA. We show that the interplay of activity and plasticity changes implements a control loop yielding an exponential, self-limiting renormalization of synaptic strength. Moreover, when the model “learns” a sequence of activation during waking, the learned sequence is preferentially reactivated during sleep, and reactivation declines over time. Finally, sleep-dependent synaptic renormalization leads to increased signal-to-noise ratios, increased resistance to interference, and desaturation of learning capabilities. Although the specific mechanisms implemented in the model cannot capture the variety and complexity of biological substrates, and will need modifications in line with future evidence, the present simulations provide a unified, parsimonious account for diverse experimental findings coming from molecular, electrophysiological, and behavioral approaches.


Sleep engages one-third of our lives and is common to all animal species, yet its function remains unknown (Cirelli and Tononi 2008). Strong evidence has been collected suggesting that sleep is homeostatically regulated (Borbély 1982; Borbély and Achermann 1999), that it has beneficial effects on cognitive functions (Dinges et al. 1997; Van Dongen et al. 2003), and that it can aid in memory consolidation and desaturate the ability to learn (Maquet 2001; Stickgold 2005; Walker and Stickgold 2004, 2006). Although the basic mechanisms underlying these phenomena remain unclear, a number of recent findings concerning molecular, electrophysiological, and behavioral correlates of sleep suggest that sleep may be especially involved in modulating plastic processes in the CNS (Diekelmann and Born 2010; Maquet 2001; Stickgold 2005; Walker and Stickgold 2006). Molecular studies have shown that markers of synaptic potentiation are higher after periods of wake and lower after sleep in both rodent cortex/hippocampus and fly brains (Cirelli et al. 2004; Gilestro et al. 2009; Vyazovskiy et al. 2008a). Moreover, electrophysiological studies in vivo have shown that the slope of cortical evoked potentials, considered to be a marker for synaptic strength (Rall 1967), increases after a period of wakefulness and decreases after sleep in both rodents and humans (Bellina et al. 2008; Vyazovskiy et al. 2008). Also both the frequency and the amplitude of miniature postsynaptic potentials increase after wake and decrease after sleep in slices obtained from frontal cortex of rats and mice (Liu et al. 2010). Thus wake seems to be associated with a net increase in synaptic strength, which is then renormalized during sleep.

Other evidence ties plastic processes occurring during wake with sleep slow wave activity (SWA; electroencephalographic (EEG) power between 0.5 and 4 Hz), which reflects at the EEG level the synchronous transition of large populations of neurons between depolarized up states and hyperpolarized, silent down states (Burns et al. 1979; Contreras and Steriade 1995; Mukovski et al. 2007; Steriade et al. 1993a, 2001). SWA is a well-characterized marker of sleep need that reflects sleep homeostasis in that it increases with wakefulness and decreases with non rapid eyes movement (NREM) sleep (Achermann and Borbély 2003). A link between plasticity and sleep SWA is shown, for example, by the observation that electrophysiological markers of synaptic strength, such as the amplitude and slope of field potentials evoked during wakefulness, correlate with SWA values during subsequent sleep (Vyazovskiy et al. 2008). Furthermore, rats exposed to an enriched environment during the waking hours, which leads to a diffuse induction of brain-derived neurotrophic factor (BDNF), a marker of synaptic potentiation, show a diffuse increase in SWA during subsequent sleep (Huber et al. 2007). By contrast, the increase in sleep SWA after wake is dampened if neuromodulatory systems such as the noradrenergic system are lesioned (Cirelli et al. 2005). Finally, several studies have demonstrated a link between local plasticity and local SWA regulation. For example, a rotation learning task involving right parietal cortex leads to a local increase in sleep SWA in humans (Huber et al. 2004; see also Kattler et al. 1994; Landsness et al. 2009; Huber et al. 2006). In rats, a reaching task known to be associated with synaptic potentiation in motor cortex also leads to a local increase in sleep SWA (Hanlon et al. 2009). Thus an increase in synaptic strength seems to be associated with an increase in sleep SWA, whereas SWA appears to decrease when synaptic efficacy is reduced (Huber et al. 2006; Vyazovskiy et al. 2008).

A series of recent studies using multi-unit recordings in freely moving rodents have demonstrated that activity patterns associated with waking experiences and learning tasks are “reactivated” during subsequent sleep in both the hippocampal formation and the cerebral cortex (Euston et al. 2007; Ji and Wilson 2007; Lee and Wilson 2002; Louie and Wilson 2001; Wilson and McNaughton 1994). A plausible scenario is that reactivation frequency may reflect the strength of the underlying synaptic traces (Feller 1999; O'Neill et al. 2008; Sutherland and McNaughton 2000), although direct evidence is lacking. Intriguingly, firing sequences “replaying” waking experiences are most frequent at the beginning of sleep and decay within tens of minutes (Ji and Wilson 2007; Kudrimoti et al. 1999). The mechanisms underlying the decay of sequence reactivations are unknown, but it is conceivable that changes in synaptic strength may again be implicated (Feller 1999; O'Neill et al. 2008), although this possibility has not yet been tested either experimentally or in simulations.

Finally, there is growing support for the notion that sleep may enhance performance in many tasks learned during previous waking (Diekelmann and Born 2010; Stickgold 2005; Walker 2009; Walker and Stickgold 2004, 2006). For example, after learning specific sequences of a finger-tapping task, both accuracy and speed increase after sleep but not after equivalent periods of wakefulness (Doyon et al. 2009; Fischer et al. 2002; Walker et al. 2003). Similarly, rotation learning was associated with an enhancement in performance the next day that correlated with a local increase in SWA over right parietal cortex (Huber et al. 2004). Importantly, this enhancement in performance did not occur if during sleep slow waves were partially suppressed using mild acoustic stimuli (Landsness et al. 2009; see also Aeschbach et al. 2008), suggesting that SWA may not merely reflect synaptic plasticity but also influence it (Peigneux et al. 2004; Rasch and Born 2007; Rasch et al. 2007). Complementing the many studies showing a positive effect of sleep on performance, some studies also demonstrate a sleep-dependent memory consolidation effect that renders learned material less susceptible to interference (Korman et al. 2007). Finally, evidence in both animals and humans shows that the ability to learn is reduced after sleep deprivation but is restored after a night of sleep (Stickgold et al. 2000) or even a nap (Mednick et al. 2002, 2003). Again, while the mechanisms underlying these beneficial effects of sleep are not known, it is clear that sleep can affect performance, memory consolidation, and the ability to learn.

Can these seemingly diverse findings be accounted for, in a parsimonious manner, by a relatively simple model of how wake and sleep affect neuronal activity and plasticity? In previous work, we developed large-scale simulations of corticothalamic dynamics during wake and sleep (Esser et al. 2005; Hill and Tononi 2005) and showed that increased synaptic strength in cortical networks can indeed lead to an increase in sleep SWA (Esser et al. 2007). Preliminary work using a similar model also indicated that increased synaptic strength after wake may affect neuronal firing rates and synchrony (Vyazovskiy et al. 2009). In this work, we took advantage of the same model and augmented it by implementing a plasticity mechanism based on spike-timing dependent plasticity (STDP) (Caporale and Dan 2008) modulated by behavioral state. Our aim was to explore whether the interplay of activity patterns and plasticity mechanisms in corticothalamic circuits can provide a link between synaptic changes, changes in neuronal firing, SWA homeostasis, and the effects of sleep on learning, memory, and performance (Tononi and Cirelli 2006). In what follows, we show that 1) in the wake mode, net synaptic strength increases, accompanied by an increase in neuronal firing rates and synchrony; 2) in the sleep mode, net synaptic strength decreases, accompanied by changes in neuronal firing patterns and a decline in SWA; 3) the interplay of activity and plasticity changes implements a control loop that produces an exponential, self-limiting renormalization of synaptic strength; 4) sleep-dependent synaptic renormalization leads to increased signal-to-noise ratios in the representation of the learned sequence, 5) to an increased resistance to interference associated with learning a different sequence, 6) and to a restoration of the ability to learn novel sequences; and 7) when the model is trained with an activation sequence in the wake mode, the learned sequence is preferentially reactivated during sleep, and reactivation declines over time.


Model architecture and connectivity

The present simulations are based on a large-scale model of the corticothalamic system developed in (Hill and Tononi 2005) and further refined in (Esser et al. 2005, 2007, 2009) (Fig. 1A). Previous work showed that the model is able to faithfully reproduce several aspects of neural activity during sleep and waking (Fig. 1, B and C) as well as the response to simple visual stimuli and to transcranial magnetic stimulation (Esser et al. 2005; Hill and Tononi 2005). Extended details about the model can be found in Esser et al. (2009); parameters employed in this model do not differ from those presented there. Here we will only therefore describe the main characteristics of the model and focus on the properties of the plasticity mechanism we implemented.

Fig. 1.
Model architecture. A: general architecture of the large-scale computational model. Three thalamocortical regions are modeled, each made up of several layers and cell types. Each thalamocortical region is subdivided into a cortical (C1, C2, C3) and a ...

The model is composed of three granular cortical regions hierarchically connected (from area 1 to area 3) and three corresponding thalamic and thalamic reticular nuclei (Fig. 1A). Each region consists of three layers (layer 2–3, layer 4, and layer 5–6, in the following identified as L2-3, L4, and L5-6) and has correspondent thalamic and reticular regions. Cortical layers are modeled as 30 × 30 grids, each grid point containing two excitatory neurons and an inhibitory one. Thalamic nuclei (TN) are modeled as 30 × 30 grids with each grid point having an excitatory and an inhibitory neuron; 80% of excitatory units are core cells projecting only to the cortical area associated with the nucleus they belong to, the remaining 20% are matrix cells projecting to all three cortical areas. Thalamic reticular nuclei (TRN) are modeled as 30 × 30 grids of inhibitory neurons. Although our work focused on cortical area 2 only, all three are necessary to reproduce network activity during NREM sleep; in particular inter-area cortico-cortical connections have been shown to play a fundamental role in modulating the synchronization and amplitude of slow oscillatory activity (Hill and Tononi 2005).

Single synaptic connections are established randomly using a Gaussian spatial density profile, which determines the probability of a connection with a postsynaptic neuron at a certain distance from the presynaptic cell. Connectivity has been modeled as in Esser et al. (2009), and details can be found in Supplementary Table S1.1 In brief, in each cortical area, there are both excitatory and inhibitory horizontal intra-layer connections as well as vertical inter-layer excitatory (from L2-3 to L5-6, from L4 to L2-3, and from L5-6 to L2-3 and L4) and inhibitory (from L2-3 to L4 and L5-6) connections. Interarea excitatory cortical connections are established from L2-3 to L4 and from L5-6 to L2-3 and L5-6; the former are feedforward connections, from area 1 to 2 and from area 2 to 3, whereas the latter are feedback ones, from area 3 to 2 and from area 2 to 1. Excitatory cortico-thalamic connections have been modeled between L5/6 and both TN and TRN, while thalamo-cortical connections go from TN to all cortical layers. Finally, the thalamic region is characterized by both horizontal and vertical connections (i.e., between TN and TRN). Last, spontaneous activity is obtained by implementing sparse connections from randomly activating subcortical regions, connected to both cortical (layer L4) and thalamic (area TN) neurons via excitatory connections. For the same goal, we also modeled “minis” (spontaneous miniature synaptic currents) as low threshold postsynaptic potentials (PSPs) (Esser et al. 2009; Timofeev et al. 2000).

Model neurons

Neurons are modeled as single-compartment spiking neurons with Hodgkin-Huxley-style currents (Hodgkin and Huxley 1952). Their subthreshold membrane potential is governed by the following equation


where V is the membrane potential, gNaL and gKL are the sodium and potassium leakage conductances, ENa and EK are the sodium and potassium reversal potentials, Isyn and Iint are the sums of all synaptic and intrinsic currents, and τm is the membrane time constant—accounting for the capacitance term. The resting membrane potential is therefore mainly determined by the sodium and potassium leak conductances. When V reaches or exceeds a threshold θ, a spike is generated, membrane potential is set to 30 mV, and then post spike membrane potential is regulated by intrinsic currents and mostly by a fast potassium current channel, with conductance gspike and time constant τspike.

Following a spike, the threshold θ is set to ENa to model the effect of fast-spiking INa currents, and then it decays according to an exponential law


Neuron parameters are reported in Supplementary Tables S2 and S3.

Synaptic channels

Four types of synaptic channels are present: N-methyl-d-aspartate (NMDA), AMPA, GABAA, and GABAB. The sum of all synaptic currents Isyn is modeled as follows


where i represents the ith channel present on the cell, j stands for the kind of synaptic channel, g(t) is the time-varying conductance, and E the reversal potential of each channel. The time-varying conductance g(t) is modeled as a dual-exponential curve following a each presynaptic spike and represents the time course of PSPs


Here τ1 is the rise time constant, τ2 the decay time constant and τpeak is the time to peak, which can be expressed as a function of τ1 and τ2


It appears clear that peak conductances linearly affect synaptic currents. To implement plastic changes we therefore introduced a method for modulating gpeak values (see next paragraphs for details).

We also modeled the effect of depletion of presynaptic vesicles of neuromodulators by scaling gpeak by the size of the current pool of vesicles (P). The dynamic of each pool is modeled as


where each spike depletes the pool P by a fraction δP, while the peak value of the pool Ppeak is recovered with a time constant τP. All parameters for the different synapses are outlined in Supplementary Table S4.

In the case of NMDA channels, an additional multiplicative term had to be introduced for computing conductance values. Specifically, NMDA channels conductance is modeled as


where m(V) is a factor that, by means of a sum of two exponential functions, models the various fast and slow time constants modulating NMDA conductance, respectively at ~1 and ~20 ms time scales (Vargas-Caballero and Robinson 2003).

GABAB channels show a nonlinear change in conductance following increasing activation levels and need to be modeled differently (Destexhe and Sejnowski 1995)


Here Kd is a constant parameter and [G] is the concentration of activated G protein, the concentration of which changes as a function of the fraction of activated receptor [R] and the strength of each synaptic event [S], according to the following equations


Parameter values are provided in Supplementary Table S4.

Intrinsic channels

Each intrinsic ion channel is modeled following Hodgkin and Huxley equations (Hodgkin and Huxley 1952)


where Iint is the current going through neuronal membrane, gpeak is the peak conductance, m and h are functions that determine the activation and deactivation level of a channel, and N is a factor for modulating the time course of activation with respect to deactivation. Each activation and deactivation function is modeled as


where xss is the steady state activation rate and τx is the time constant of the function.

Four kinds of intrinsic currents have been modeled. Ih is the pacemaker current and is modeled as a noninactivating hyperpolarization-activated cation current (Huguenard and McCormick 1992). IT is the low-threshold fast-activating calcium current (Destexhe et al. 1996; Huguenard and McCormick 1992). INa(p) is the persistent sodium current (Compte et al. 2003; Fleidervish et al. 1996) that activates rapidly after a spike and slowly inactivates across several seconds. IDK is the depolarization activated potassium current; this is modeled as a combination of sodium- and calcium-dependent potassium currents and is regulated by factor that accumulates when the cell is depolarized and decays exponentially. Finally, TRN cells are characterized by the presence of a calcium-activated potassium channel IKCa (Destexhe et al. 1996; Huguenard and McCormick 1992). Supplementary Table S3 summarizes gpeak values for all ionic channels; specific details about the activation and deactivation functions of each intrinsic current can be found in Esser et al. (2009).

Neuromodulatory influences

The effect of neuromodulatory systems is modeled by changing conductance values of both intrinsic and synaptic channels, therefore mimicking the final effects of the activations of neuromodulator receptors on membrane conductances rather than intrinsic neuromodulatory dynamics. Thus by modulating current conductances, it is possible to modulate the vigilance state of the network, switching from the waking to the NREM sleep modality as shown in detail in Hill and Tononi (2005) and Esser et al. (2007). The way parameters were changed for making the model transition from the waking to the sleep mode are detailed in Supplementary Tables S3 and S4. Briefly, when transitioning from waking to sleep, gKL and Ih are increased by the reduced action of acetylcholine; INa(p) and IT are increased by the deactivation of muscarinic acetylcholine receptors; IKS is increased by the reduced influence of both acetylcholine and norepinephrine; finally, glutamate release is decreased when acetylcholine levels decrease (for details, see Supplementary Tables S3 and S4) (also refer to Esser et al. 2007, 2009; Hill and Tononi 2005).

Plasticity mechanisms

For the present purposes, the model was augmented with a mechanism for implementing plastic changes as a function of neuronal activity and behavioral state. Most studies on long term potentiation (LTP) and depression (LTD) have focused on the synaptic responses mediated by AMPA receptors (AMPAR) (Collingridge et al. 2004). Although both NMDA and GABA receptors (NMDAR, GABAR) have been show to undergo plastic modifications, most studies have focused on their role in modulating AMPAR plasticity (Collingridge et al. 2004). In particular, NMDARs are fundamental in triggering AMPAR-mediated LTP and LTD (Brader et al. 2007; Carroll et al. 2001; Castellani et al. 2001; Collingridge et al. 2004; Lu et al. 2001), while GABARs are involved in the modulation of NMDARs activity (Bliss and Collingridge 1993). Finally, several hypotheses exist on whether AMPAR-mediated LTP and LTD are obtained by changing glutamate release probability or the number of postsynaptic AMPAR proteins or their conductance (Benke et al. 1998; Shouval et al. 2002). Computationally, however, the result of any of these modifications can be modeled as a change in synaptic strength and the underlying mechanisms do not need to be considered for the present purposes.

Plastic changes in the model are therefore obtained by affecting synaptic strength w at postsynaptic AMPARs; this parameter is then used to modulate synaptic peak conductances gpeak. Thus all neurons belonging to the same category/layer will have the same gpeak AMPA values, but different w values for each individual synapse. A w value of 1 corresponds to a normal conductance value as per Supplementary Table S4.

The mechanism implemented in the model is based on spike-timing dependent plasticity (STDP), which has been investigated extensively in vivo and in vitro (Abbott and Nelson 2000). We followed the STDP rule as in (Standage et al. 2007) (Fig. S1A) because it does not require imposing an arbitrary maximum weight. The formulation of the weight-changing rule is the following


Where Δw is the change of synaptic weight, the subscripts p and d stand for potentiation and depression, respectively, k is the learning rate, Δt is the difference between the times of post- and pre-synaptic spikes, and m is a weight-dependent factor with the following equation


The values for constants a–d were as in the original paper (Standage et al. 2007), whereas the potentiation and depression learning rates were set to the same arbitrary value, chosen as such that measurable changes in synaptic weights could be detected in a short simulation time (10–20 s). The values we employed were the following: ap = 431, ad = −59, bp = 0.4, bd = 0.1, cp = 0.039, cd = 0.043, kp = 6e-5, kd = −6e-5. Parameters bp and bd, by being smaller than one, assure that small synapses will have – in percent – greater changes than big ones (Fig. S1A). Note that for most the simulations, we chose learning rates such that significant strength changes could be obtained in reasonably short computational times. In a few instances, we confirmed the results using slower learning rates for both potentiation and depression (not shown).

We also modified the standard STDP rule based on evidence that the direction of plastic changes (potentiation or depression) depends on the amount of intracellular calcium entering the postsynaptic terminal via NMDARs (Brader et al. 2007; Castellani et al. 2001). Following Brader et al. (2007) the postsynaptic level of calcium has been modeled according to the following equation


where JCa represents the calcium influx contribution of each postsynaptic spike (the sum is performed over all spikes arriving at time ti) and τCa is the time constant for calcium depletion. We will refer to [Ca] as pseudo-calcium concentration because it does not accurately model the dynamics of calcium currents through NMDARs. Following Brader et al. (2007), we implemented a rule in which for low levels of calcium (and thus of presynaptic activity), no plastic changes occur; at an intermediate level, typical of spontaneous activity, a standard STDP rule applies. At still higher concentration, only potentiation occurs. These thresholds are related to the value of JCa, so that

[Ca]k1JCa[Ca]>k3JCaNo Plasticityk1JCa<[Ca]k2JCaLTP+LTDk2JCa<[Ca]k3JCaLTP

We set all these parameters in such a way that spontaneous activity was on average able to elicit both potentiation and depression, whereas stimulation of cortical patches mostly led to potentiation only (Fig. S1B). This allowed us to train the network in a faster and more effective way (see next paragraph) and, at the same time, evaluate the properties of standard STDP when only spontaneous activity was present. The values for the various parameters are the following: JCa = 20, tCa = 240, k1 = 1.5, k2 = 5, k3 = 15.

Finally, based on the in vivo evidence that sleep appears to be associated with a net decrease in synaptic strength, the simulated decrease in arousal–promoting neuromodulators responsible for the model's entry into the sleep mode (Esser et al. 2007) was also made to reverse the sign of the potentiation learning rate, thus favoring synaptic depression. Although it is currently unclear how plasticity mechanisms are altered as a function of behavioral state, it is well established that the levels of many neuromodulators, such as acetylcholine, norepinephrine, serotonin, histamine, and hypocretin, are much reduced during NREM sleep compared with wake (Jones 2005, 2008; Pace-Schott and Hobson 2002). It is also well established that neuromodulators can powerfully affect plasticity, including STDP polarity. Specifically, changes in cholinergic and noradrenergic modulation can shift the STDP curve to favor depression (Seol et al. 2007). As mentioned in the discussion, other aspects of NREM sleep, such as burst-pause firing (Czarnecki et al. 2007) and high synchrony (Lubenov and Siapas 2008) are also thought to promote synaptic depression. However, while a shift in the sign of plasticity due to neuromodulatory changes could be readily implemented in the current model, burst-pause LTD and decoupling through synchrony were computationally impractical.

Simulation techniques

Simulations were run using Synthesis, an object-oriented neural simulator suitable for large-scale models (www.synthesis-simulator.com). Using a quad-core Mac Pro running Mac OS 10.4 with 9 GB RAM, each second of simulation takes approximately thirty minutes to compute. Numerical integration was performed with the Runge-Kutta fourth order method, using a step size of 0.25 ms. Running the model with a step size of 0.1 ms and lower did not introduce significant differences (Esser et al. 2009).

Data analysis

Firing rates were detected differently depending on the simulated vigilance state. To obtain data comparable—in terms of error band—with related experimental results described in (Vyazovskiy et al. 2009), we did not perform analyses on all neurons but randomly selected a limited number of cortical neurons from each simulation (n = 20). This procedure mimics what happens when an array of microelectrodes is inserted in cortical tissue; however, we verified that results did not change when varying sample size or changing the randomly selected neurons. For waking simulations, firing rates were computed as the total number of spikes in a 20 s window. For sleep, we first had to detect active (on) and silent (off) periods. To detect such periods, at first all time stamps corresponding to individual spikes were concatenated across all selected neurons. Next, the onsets and offsets of the periods characterized by the cessation of unit activity were identified. Such silent periods were referred to as off periods if they lasted ≥50 ms. In all cases (both in early and late sleep), the beginning of the off periods was defined as the time when the last unit of the population stopped firing, whereas the end of the off periods was defined as the time when at least one unit out of the entire population resumed activity. The minimum duration of off periods was chosen in accordance with Vyazovskiy et al. (2009). The on periods were defined as intervals of sustained unit firing lasting between 50 and 4,000 ms, and consisting of ≥10 spike.

Computation of neuronal synchrony at the on-off and off-on transitions was based on on periods longer than 50 ms in which ≥50% of all recorded units generated ≥2 spikes. We defined synchrony as the reciprocal of the latency of the first and last spike of each unit from the onset of population on or off periods, respectively.

Sequences of activation for training and testing

To train the network for a particular sequence of activation, a sequential injection of current was employed. Five patches (A–E) were selected in one cortical region, each patch being a 3 × 3 group of mini-columns (Fig. S1C). The distance between patches was such that direct connections existed only between adjacent patches but not between more distant ones. During training sessions, patches were activated sequentially by injecting depolarizing current directly in neurons. The time course of this stimulation was chosen to be similar to the pattern of activation of place cells in freely moving animals (Lee and Wilson 2002); each patch was activated for 200 ms at a 50 Hz frequency, the delay between the activation of subsequent patches was 50 ms (Fig. S1D). To obtain a precise spiking pattern and exploit the timing characteristics of STDP, each neuron was stimulated with a short and strong current injection (1.0 ms duration, strength of 2,000 base points). Although currents in the model are unit-less (because neurons in the model have no area), we chose a current influx that would always depolarize a unit by ≥100 mV and thus elicit a spike (maximum allowed membrane potential in the model was set at 30 mV). By precisely timing spikes in adjacent patches, it was possible to have presynaptic spikes preceding postsynaptic spikes by ~2 ms and thus elicit the largest changes in synaptic strength allowed by the STDP paradigm (the smaller the delay between pre- and postsynaptic spikes, the larger synaptic strength change, see previous section); the repetitive stimulation at 50 Hz for 200 ms, moreover, was able to increase postsynaptic pseudo-calcium concentration, and thus favor potentiation of the circuits involved in the sequence of activation.

The activation employed for testing the level of learning was the following: all patches, except patch B, were stimulated with a level of depolarizing input current, with an intensity below the threshold for spike generation. Patch B was then given an above threshold current injection, and the forward (patch C) and backward (patch A) responses were measured. Patches A and C–E were therefore continuously stimulated with a depolarizing current with a value of 1 base point, which did not significantly change the spontaneous firing rate of stimulated patches (average membrane potential was not increased above −55 mV). Patch B was stimulated with a 10 ms long stimulation with a value of 500 base points, which was able to elicit activity in all neurons in the patch, although spike times were not the same for all neurons – to mimic spontaneous activation of the patch.

Signal to noise ratio of stored memories

We developed two ways to evaluate the signal-to-noise ratio (SNR) of stored memories. The first method evaluates changes in connectivity across stimulated patches and correspond to the ratio between the average strength of forward connections (A to B, B to C, and so on) and backward connections (B to A, C to B, and so on). We then introduce a SNR index to the characteristics of network response to stimulation of one patch. When all patches but one were stimulated below threshold (see previous paragraph) and one was activated above threshold, an increase in response could be seen in adjacent patches for ~200 ms after stimulation. We defined the SNR index as the ratio between the average firing rates in the patches immediately following and preceding the stimulated patch, in the 200 ms window following stimulation.

Detection of spontaneously repeating sequences

The algorithm for evaluating the repetition rate of the training sequence during spontaneous NREM activity was developed following previous papers (Euston et al. 2007; Ji and Wilson 2007). Analyses were carried out only on signals originating from neurons within the stimulated patches.

The first step was to filter the data. As in Ji and Wilson (2007), frame sequences were obtained by filtering spike counts with a Gaussian window with σ = 25 ms. Within each on period, the maximum value of the filtered signal was detected, its amplitude set to one, and all other values rescaled accordingly. Within each on period, sequences with less than four active neurons were discarded. Then a template frame sequence was created to be compared with the actual sequence from the simulations. This template sequence was generated by setting neurons within a patch as spiking simultaneously, and by setting fixed values for inter-patch delays, i.e., average delays between the peak in spiking activity in two subsequent patches. Several delays must be tried, as in Euston et al. (2007), because the rate at which the training sequence is repeated by the network is not known. The template sequence was then filtered with the same Gaussian window previously employed. This permits, when comparing experimental data with template sequences, to take into account variability in the replicated sequence. The standardized Pearson correlation coefficient was then calculated between the experimental and template sequences (Euston et al. 2007).

A thresholding procedure for calculating significant correlation values was then employed. Surrogate frame sequences were constructed after shuffling spike counts. The corresponding distributions of correlation coefficients were calculated and a value corresponding to the mean value plus three times the SD was chosen as the threshold for the correlation coefficients.


STDP-like rule leading to a net increase in synaptic strength during wake and to a net decrease during sleep produces characteristic changes in neuronal activity and synchrony

Our first goal was to verify that the introduction of an STDP-like, neuromodulation-dependent plasticity mechanism on all AMPA connections in the model led to a net synaptic potentiation during waking and depression during NREM sleep. As expected from the asymmetric properties of experimentally derived STDP rules, which favor potentiation (Standage et al. 2007), spontaneous activity during wake was indeed associated with a net increase in average excitatory connection strength (Fig. 2A). The increase in synaptic strength was not linear but tended toward an upper limit; although clearly visible, such saturating trend could not be discriminated from a linear trend via fitting procedures. As explained in methods, during NREM sleep sessions we enforced a sign reversal of the learning rates to simulate the effects of a changed neuromodulatory milieu (see methods). This led to a progressive decrease in average connection strength (Fig. 2B). The decrease in connection strength was also not linear but followed an exponential decay (r2 = 0.99).

Fig. 2.
Connection strength and neural activity during waking and sleep. A: average connection strength (as a percentage of the initial value) during a waking session with spike-timing dependent plasticity (STDP) and high levels of arousal-promoting neuromodulators ...

We then measured the changes in neural activity associated with changes in net synaptic strength. First, as shown in Fig. 2, C and D, we observed that mean firing rates of excitatory neurons increased progressively during wakefulness and decreased during sleep in line with experimental data (Vyazovskiy et al. 2009). Next, we focused on changes in multiunit activity (MUA) and synchrony between early and late NREM sleep (Fig. 2, F and G). In line with experimental data (Vyazovskiy et al. 2009), depolarized (on) periods became longer, hyperpolarized (off) periods shorter, and overall activity less synchronous during late sleep. Specifically, firing rates during on periods ranged from 12 Hz during early sleep to 6 Hz during late sleep; on periods became longer (from 600 to 700 ms), whereas off periods became shorter (from 200 to 100 ms). Also the synchrony of both on-off and off-on transitions decreased significantly (P < 0.05, independent t-test). Finally, we measured sleep SWA based on the EEG-like signal obtained by averaging the membrane potential of all simulated cortical neurons (Fig. 2E). Consistent with experimental data (Achermann and Borbély 2003; Achermann et al. 1993; Borbély 1982; Borbély and Achermann 1999), SWA values obtained from simulated recordings decreased progressively following a near-exponential time course (Fig. 2E).

Interplay of activity and plasticity changes implements a control loop that produces an exponential, self-limiting renormalization of synaptic strength during NREM sleep

In the simulations, neuronal activity during wake leads, through an STDP-like plasticity mechanism biased toward potentiation, to a progressive increase in synaptic strength. In turn, the increased synaptic strength leads to changes in activity, such as higher firing rates and increased synchrony, which are especially evident when the model enters the sleep mode. During simulated early sleep, the high levels of neuronal activity/synchrony lead, through an STDP-like plasticity mechanism biased toward depression, to a progressive decrease in synaptic strength. In turn, this net decrease in synaptic strength reduces mean firing rates and synchrony, to the point that, during late sleep, the level of activity/synchrony become insufficient to further depress synaptic strength, and the model reaches an equilibrium.

In Fig. 3, the interplay between activity and plasticity during sleep can be understood by considering a simple linear system in which the rate of change of a control variable (synaptic strength s) depends linearly and negatively on measured variables (neuronal activity f, expressed as firing rates and synchrony), whose values are in turn proportional to the control variable. In the linear model of Fig. 3, considering the equilibrium point of s to be zero for simplicity, f depends on s via a multiplicative constant A, which represents activity mechanisms. In turn, plasticity mechanisms P determine the decay rate of s as proportional to f.


Solving these equation yields a time course for the control variable s corresponding to an exponential decay from the starting value to the equilibrium point.


With these equation, we are only trying to model the homeostatic regulation of synaptic strength and neural activity during NREM sleep. Therefore to accomplish stable, self-limiting dynamics, constants A and P must have the same sign. Thus high levels of average connection strength (a consequence of learning activities) will spontaneously self-regulate by inducing synchronous, high firing rate activity during sleep. Because the rate of plastic depression during sleep is proportional to the level of activity itself—or, more precisely, to the imbalance with respect to the equilibrium point, here set to 0 for simplicity—when connection strength reaches its baseline value, no further modification will be induced.

Fig. 3.
A model of homeostatic regulation of connection strength and firing activity. Following the results of our simulations, we developed a model of homeostatic regulation of connection strength and firing activity during non rapid eyes movement (NREM) sleep. ...

In line with this control process, in the model, the decrease in connection strength was accompanied by an exponential decline in neuronal firing rates (Fig. 2D). Moreover, in agreement with experimental data (Borbély 1982; Daan et al. 1984), SWA also followed an exponential decay (Fig. 2E). Finally, as predicted by the control process, the decline in connection strength and related variables was self-limiting in that the model reached a stable state where neuronal firing rates and synchrony were sufficiently low that they would not lead to further decreases in net synaptic strength.

In the wake mode, the network is able to learn a sequence of activation through an STDP-like rule

We then performed tests to validate our stimulation paradigm as a method for storing sequences of activation presented to the network. We measured learning in two ways: as changes in connection strengths between the stimulated patches and as changes in the response of the preceding and subsequent patches after stimulation of one patch. The results for this and the following paragraphs are shown in Figs. 4 and and5.5. Figure 4 deals with training and sleep-related changes in connectivity, while Fig. 5 deals with network responses to stimulation.

Fig. 4.
Changes in connectivity as a consequence of training and sleep. A: ratio between the strengths of 1-step forward connections (from patch A to B, from B to C, and so on) and the corresponding 1-step backward connections (from patch B to A, from C to B ...
Fig. 5.
Changes in network response as a consequence of training and sleep. A: average firing rate in patches C (—) and A (- - -) after stimulation of patch B, for different conditions. Patch B was stimulated above threshold at time 0, patches A and ...

Changes in connection strengths were evaluated using the ratio between one-step forward and one-step backward connection strengths (Fig. 4A). This means computing the average connection strength from patch A to B, B to C, and so on (forward) relative to the corresponding backward strengths—from patch B to A, C to B, etc. This strength ratio was enhanced by ~60% by training with the sequence of activation (Fig. 4A).

Figure 5A shows instead the average firing rates in patches C and A following a stimulation of patch B. To enhance responses in patches A and C, a below-threshold current injection was constantly performed. A similar response is present in both patches A and C at baseline. This response presents a peak at ~100 ms after stimulation. The effect of training is to enhance the response of patch C and, more specifically, to introduce an additional early peak in firing rate at ~60 ms after stimulation.

Sleep-dependent synaptic renormalization increases the SNR of the stored sequence

To establish whether sleep-dependent synaptic renormalization could account for performance enhancements often reported after sleep, we examined changes in the SNR of the stored sequence after training and after sleep. First, we analyzed the change in the ratio between forward and backward connections. As shown in the preceding text, this ratio showed a considerable increase after training during waking. As shown in Fig. 4A, a subsequent period of sleep further increased this ratio (P < 0.05).

We then evaluated the time course of firing rates in patches C and A after the stimulation of patch B. As described in the preceding text, training enhanced the response of patch C by introducing an early peak in the firing rate at ~60 ms after the stimulus. We found that sleep further increased the difference between the responses of patches A and C (Fig. 5A), mainly by reducing the response of patch A.

Finally, we calculated the SNR index, measuring the ratio between the average firing rates in patches C and A in the first 200 ms after stimulation of patch B. As expected, we found that training increased the SNR index by 30% over baseline (Fig. 5B). A further 15% increase over post-training levels followed the sleep session.

To test whether the improvement in SNR we reported was specifically linked to the properties of activity and plasticity during NREM sleep, we performed two additional kinds of simulations. A first condition was a waking session performed after the first training session but without any stimulation. With this simulation, we could test whether synaptic renormalization is a critical component for SNR improvement compared with a period of spontaneous waking activity. Second, we simulated another waking session after the first training session during which we delivered subthreshold stimulation all five cortical patches. As shown in the preceding text, in the model, this additional stimulation is required to produce the reactivation of the stored sequence in the wake mode, whereas no additional stimulation is necessary in the sleep mode. However, in both cases (spontaneous waking activity and additional waking stimulation), we did not observe any significant change in the ratio between forward and backward connections (Fig. 4A). Similarly, no significant change was found in response traces and SNR index (not shown).

The weight-dependent characteristics of the STDP-like learning rule implemented in the model are such that each plastic event has a different consequence on strong and weak synapses. Percentage weight change will be in fact smaller for strong connections than for weak ones. Therefore one should expect that the strongest connections (including those that were potentiated the most during training) should undergo relatively smaller changes than weaker connections with the end result that the difference in strength between strong and weak connections should increase during sleep, despite a net decrease in overall strength. To confirm this prediction, we measured the relative changes of the top 10% and the bottom 10% of all connections following a period of sleep. As expected, these two subsets of connections were the most and the least affected by the sequence of stimulation, respectively. Renormalization didn't modify the top connections, while the average strength of the bottom subset decreased by 7% (Fig. 4B). This happened because initial connection strength and the strength change caused by each plastic event are inversely related. This result suggests that renormalization selectively decreased those connections that were not strengthened during the training process. Therefore while total synaptic strength decreased, the SNR increased because of an increased contrast between trained (strengthened) connections and untrained ones.

Synaptic renormalization consolidates stored sequences by increasing resistance to interference

We also investigated whether synaptic renormalization could contribute to consolidating memories. In a recent study in humans (Korman et al. 2007), subjects were trained to perform a finger-tapping sequence. If a nap was performed between training and an interference session using a second sequence, the original sequence was successfully consolidated, otherwise it was disrupted by the interfering one. In our simulations, following (Korman et al. 2007), the interference condition consisted of a training session during which the sequence was played in the opposite order (i.e., E–A instead of A–E). The SNR index for the original sequence remained unchanged if the model was allowed to sleep before training it for the interfering sequence, but it decreased if the model was kept in the wake mode for an equivalent period of time (Fig. 5, A and C). This effect can be explained by considering that renormalization influences all connections, not only those involved in the training sequence, and that the effect of plasticity is stronger on weak than on strong connections. During a training session, the SNR increases as the sequence is stored through both strong, direct connections between patches, and weaker, indirect pathways. During a subsequent waking period, instead, synaptic strength in most connections increases further due to background activity. So when the network is then trained with an opposite sequence, the latter is stored with a substantial contribution of indirect pathways. Because these indirect pathways contribute in storing both the original sequence and the opposite sequence, the result is interference with the original sequence, the SNR of which is degraded. By contrast, if training with the original sequence is followed by a period of sleep, sleep-dependent processes renormalize preferentially the weaker indirect pathways and reduce their role in storing the interfering sequence. To confirm this hypothesis, we measured the ratio between forward and backward connections between stimulated patches. This ratio decreased by 30% in both the sleep and the waking condition (not shown). However, the ratio between inter- and extra-patch connections increased significantly only when a sleep period was interposed between the training and the interference session (Supplementary Fig. S2A).

Finally, we also performed an additional simulation in which a sleep session occurred after the interference session rather than between the training and the interference session. After this simulation, although the ratio between inter- and extra-patch connections was greater than baseline condition, the SNR index did not increase (not shown). Thus consolidation was due to the joint effect of renormalization and to the timing among training, sleep, and interference, showing that renormalization selectively consolidates previously stored memories.

Synaptic renormalization restores the ability to learn novel sequences

We then examined whether sleep-dependent synaptic renormalization can restore the ability to learn after prolonged wakefulness. Several experimental results have suggested a link between sleep deprivation and an impairment of plasticity (Huber et al. 2000; Stickgold et al. 2000) and possibly with the saturation of connection strength. Moreover, restoring normal learning appears to require sleep (Mednick et al. 2002, 2003; Stickgold et al. 2000). To mimic a near-saturation of synaptic strength after prolonged wake, we increased the strength of all intracortical excitatory connections by 33% over their baseline values. Strikingly, under these conditions, sequence training was not followed by either an increase in the ratio between forward and backward connections or an increase in the SNR of evoked responses (P > 0.05, independent t-test). By contrast, after a period of sleep-dependent renormalization of synaptic strength, learning returned to normal values (not shown).

Reactivation of the stored sequence of activation increases after training and decreases after sleep-dependent renormalization of connection strengths

Finally, we focused on recent experimental work showing that repetitive sequential activation of hippocampal place cells and related cortical areas leads to an increase in the repetition rate of the same spike sequences during subsequent NREM sleep (Euston et al. 2007; Ji and Wilson 2007; Lee and Wilson 2002; Wilson and McNaughton 1994).

To verify whether the model could account for these results, we measured the rate at which the stored sequence of activation was reproduced in the sleep mode before and immediately after training. As explained in methods, we designed a template sequence of activation and measured its rate of reactivation in simulated traces, varying its time scale, i.e., the delay between the activation of two subsequent patches. The training sequence was designed to maximize changes in connection strengths: repetitive stimulation of subsequent patches was separated by 50 ms to allow build-up of intracellular pseudocalcium concentration at the postsynaptic level and corresponding spikes in adjacent patches were separated by ~2 ms. Thus STDP-dependent strength changes were maximized by short delays between post- and pre-synaptic spikes, and higher levels of pseudo-calcium concentration would favor LTP. Spontaneous network dynamics instead determined the pace at which the sequence was reactivated during NREM sleep. The rate of reactivation reached a maximum for all conditions at a time scale corresponding to a delay of ~160 ms between the activation of two subsequent patches. This pace depends on strength and efficacy of connections between patches and on firing rates in patches: high firing rates and strong, specific connections will generally lead to a faster sequential activation of patches. In all simulations trials we performed, testing several degrees of training, the peak of reactivation was lying between 100 and 200 ms. Strikingly, this range is compatible with experimental data on spontaneous replay of sequences of activation (Euston et al. 2007; Ji and Wilson 2007). Moreover, changes in the repetition rate during NREM sleep mirrored changes in connectivity: without sequence training, there was no asymmetric change between forward and backward connections, and there was no change in repetition rates (Fig. 6A).

Fig. 6.
Reactivation of the training sequence as a consequence of training and sleep. A: ratio of repeating sequences during NREM sleep. This is the ratio of sequences of spikes in all 5 patches that correspond to the training sequence, compared with all detected ...

By contrast, after a period of sleep, repetition rates decreased significantly (Fig. 6A); it must be pointed out that the reported values correspond to an average synaptic strength of 75% of the initial level, which required ~20% of the period of time needed by the network to fully renormalize synaptic strength, at ~60% of the initial level (Fig. 2B). This result is consistent with findings in rats because several reports have indicated that repetition rates decay to pretraining values after 20–60 min of sleep (Ji and Wilson 2007; Kudrimoti et al. 1999). Although it is difficult to draw an exact parallel between in computo and in vivo data, qualitatively this result supports the hypothesis of an exponential-like decay of synaptic strength. In fact, although sleep in rats is highly fragmented, they are usually put in a 12 h light/12 h dark cycle and NREM sleep is mostly concentrated in the light period. Therefore the first 20–60 min of NREM sleep represent a small fraction of total daily sleep time. Our simulations show that the reactivation rate is linked to average synaptic strength; if the decay rate in rats did not follow an exponential decay, but for example a linear one, reactivation rate would not be back at baseline levels after only 20–60 min but after a longer period of time.

We also tested whether an increase in the repetition rate could be seen in the wake mode but found no change as a result of training. This was not unexpected because spontaneous repetition of sequences of activation during waking has so far been described only in the hippocampus and in correspondence with high spontaneous levels of activity, such as during sharp wave ripples (see for example Karlsson and Frank 2009; Kudrimoti et al. 1999). Assuming that spontaneous levels of activity in the model wake mode may not be sufficient to elicit the reactivation of newly stored connection patterns, we increased the model excitability by providing sub-threshold activation to all five cortical patches during waking sessions before and after training. This manipulation was sufficient to increase the rate of repetition of the stored sequence after training (Fig. 6B). The time scale corresponding to the maximum rate of reactivation was the same found for sleep sessions.


The present work is based on a large-scale model previously shown to accurately reproduce several aspects of the population and single-unit dynamics of corticothalamic circuits during wakefulness and slow wave sleep (Esser et al. 2005, 2007, 2009; Hill and Tononi 2005). The model was augmented with an STDP-like learning rule to assess the interaction between wake- and sleep-mode activity and plasticity. In the wake-mode, the model reproduced the net increase in synaptic strength observed in experimental work and showed that such changes in synaptic strength can account for the observed increases in neuronal firing rates and synchrony. In the sleep mode, the model reproduced the net decrease in synaptic strength observed experimentally as well as the well-known decline in SWA as a function of sleep. Altogether the model illustrates that the interplay of activity and plasticity changes implements a control loop yielding an exponential, self-limiting renormalization of synaptic strength.

The same model was then used to investigate the consequences of synaptic renormalization on the learning of sequences of activations, which can be seen as an analog of studies on learning of finger-tapping sequences (Korman et al. 2007). First, the simulations showed that synaptic changes induced in the wake mode by learning activation sequences were reactivated in the sleep mode, but the extent of reactivation declined with the progression of sleep. Second, the simulations showed that sleep-dependent synaptic renormalization led to increased SNRs for the learned sequence, increased resistance to interference from other sequences, and desaturated the model's ability to learn novel sequences.

Sleep and the homeostatic regulation of synaptic strength

Recent evidence indicates that net synaptic strength in cortical and other networks increases during waking and returns to a baseline level during sleep. For example, molecular markers of synaptic potentiation were shown to be higher after wake and lower after sleep in both rodents and flies (Cirelli et al. 2004; Gilestro et al. 2009; Vyazovskiy et al. 2008). Electrophysiological markers of synaptic strength, such as the slope and amplitude of evoked responses, also increased after wake and decreases after sleep in humans and rodents (Bellina et al. 2008; Vyazovskiy et al. 2008). Direct evidence also comes from slices obtained from frontal cortex of rats and mice, where both the frequency and the amplitude of miniature postsynaptic potentials increased after wake and decreased after sleep (Liu et al. 2010).

A progressive increase in synaptic strength in the course of wakefulness could be the result of an overall bias in favor of potentiation during learning, consistent with some theoretical considerations (Tononi and Cirelli 2003). Indeed reviews of the experimental literature provide many examples of learning being achieved through synaptic potentiation, at least in physiological models of plasticity in the adult (Feldman et al. 1999; Klintsova and Greenough 1999). It is also possible that even spontaneous activity during wake may lead to a systematic increase in connection strength. For example, several biologically-inspired learning rules, such as pure STDP (Standage et al. 2007) and hybrid rules (Brader et al. 2007) are asymmetric, leading to net potentiation under spontaneous firing.

Our simulations were based on a modified version of STDP, a plasticity mechanism that is well investigated both in the experimental and computational literature (Abbott and Nelson 2000; Dan and Poo 2004). Presumably, similar results would have been obtained using other biologically inspired learning rules (Clopath et al. 2010). In fact the only prerequisites a learning rule should have to be able to replicate our findings are activity and weight dependency. The former is required to implement a self-limiting homeostatic regulation of connection strength, whereas the latter allows to selectively renormalize weak connections at the expense of strengthened (more important) ones.

As expected, the STDP-like rule implemented in the model led to a progressive increase in synaptic strength during spontaneous activity in the wake mode. On balance, sequence learning in the model also led to a net gain in synaptic strength, suggesting that an even greater net increase in strength would have been observed if the model had been engaged in multiple learning tasks as would be the case during normal wakefulness.

Whether or not the details of the plasticity mechanism in the model accurately reflect biological plasticity in the cerebral cortex in vivo, the effects of the net increase in synaptic strength led to changes in the model's activity that closely resembled those reported in vivo. In the model, as in these experiments, neuronal firing rates increased progressively after periods of wakefulness. Furthermore, when the model entered the sleep mode, longer periods of prior wakefulness produced increased activity, synchrony and sleep SWA, in line with experimental results (Vyazovskiy et al. 2009). Thus the model could reproduce both the reported changes in synaptic strength and those in neuronal firing.

The experimental evidence showing that after increasing during wakefulness, net synaptic strength decreases during sleep, raises the question of how plasticity mechanisms are altered in sleep so as to enforce an overall synaptic depression. One possible scenario is that burst firing, which is common in slow wave sleep during transitions between intracellular up and down states (Bazhenov et al. 2002; Steriade et al. 1993), may lead to a long-lasting depression of excitatory postsynaptic potentials (EPSPs) (Czarnecki et al. 2007), mainly via postsynaptic mechanisms. Another possibility is decoupling through synchrony (Lubenov and Siapas 2008). In recurrent networks with conduction delays, synchronous bursts of activity typical of slow wave sleep would lead to net synaptic depression through a straight STDP mechanism. For example, if neurons A and B fire simultaneously and neuron A projects to neuron B, the presynaptic spike will arrive after the postsynaptic one has occurred due to conduction delays. Thus even in a condition that, from a purely Hebbian perspective, should lead to potentiation, one obtains instead depression. A third scenario is motivated by the well-known observation that the levels of many neuromodulators, such as acetylcholine, norepinephrine, serotonin, histamine, and hypocretin, are much reduced during NREM sleep compared with wake (Jones 2005, 2008) and that neuromodulators can powerfully affect plasticity, including STDP polarity. Specifically, changes in cholinergic and noradrenergic modulation can shift the STDP curve to favor depression (Seol et al. 2007).

In the model, simulating a sign inversion of the learning rate as a function of reduced neuromodulation plasticity (Seol et al. 2007) led as expected to a progressive decrease in synaptic strength during the sleep mode. Presumably, similar results would have been obtained using burst-LTD (Czarnecki et al. 2007) and decoupling through synchrony (Lubenov and Siapas 2008). Importantly, all three mechanisms are activity dependent in that higher levels of firing, bursting and synchrony result in relatively greater synaptic depression. Because activity, bursting, and synchrony are all higher in early than in late sleep, all three mechanisms should produce an exponential decrease in synaptic strength as we observed with our particular implementation. A mechanistic interpretation of this phenomena will be presented in the paragraphs in the following text.

Whether or not the details of our implementation accurately reflect the details of plasticity mechanisms in the sleeping cortex, the effects of decreasing synaptic strength on the model's activity closely resembled those reported in in vivo studies. Thus as in the model, unit recording data in vivo show that neuronal firing rates and synchrony decreased progressively during sleep (Vyazovskiy et al. 2009). Moreover, as in the model, on periods become longer, off periods shorter, and there are fewer on-off transitions per minute. Finally, the simulations show that a plasticity mechanism promoting net synaptic potentiation during wake and net synaptic depression during sleep can fully account for the exponential increase in SWA during wake and its decrease as a function of sleep, an experimental finding indicative of sleep homeostasis that has been demonstrated in hundreds of papers in many different species (Achermann and Borbély 2003; Achermann et al. 1993; Borbély 1982; Borbély and Achermann 1999; Borbély and Tobler 1996). Of course other factors beyond changes in synaptic strength, such as progressive changes in the level of arousal-promoting neuromodulators, could contribute to the changes in neuronal activity and in SWA described in vivo. However, such progressive changes in neuromodulators have not yet been documented, and their effects would not account as well for the observed activity changes, according to previous computer simulations (Vyazovskiy et al. 2009).

Activity-plasticity control loop for synaptic homeostasis

Altogether, the present simulations suggest the existence of a control loop to homeostatically regulate synaptic strength during NREM sleep. In this loop (Fig. 3), a net increase in synaptic strength—due to learning activities performed during wakefulness—is “sensed” by the network through its effects on activity: the stronger the synapses, the higher neuronal firing rates and synchrony and, consequently, the higher the levels of SWA when entering the sleep mode. Conversely during NREM sleep, with plasticity mechanisms biased toward depression, network activity acts as an “effector” to regulate synaptic strength: the stronger and the more synchronized the firing of simulated neurons, the more connections are weakened. On the other hand, the weakening of connections reduces firing rates and synchrony, slowing the process of activity-dependent depression. Finally, the network reaches a point where synaptic strength is sufficiently low that firing rates and synchrony are insufficient to further weaken connections, and the system reaches an equilibrium point. The same dynamics could have been obtained with a different plastic paradigm; in fact, the only prerequisite is activity dependency, which assures the stability of the control loop by associating higher levels of activity with faster changes in connectivity toward the equilibrium point. For example, previous studies have shown that high levels of average connection strength introduce a bistability in the network with periods of bursting interposed by periods of low firing (Holcman and Tsodyks 2006). In the model, we were able to obtain bistable network activity during waking by greatly increasing synaptic strength (not shown), although only by changing the neuromodulatory milieu could we trigger a proper transition to the sleep mode. Highly synchronous spiking activity (bursting) triggered by an imbalance in connectivity may lead to synaptic depression via decoupling through synchrony. This mechanism is also activity dependent because high synchrony will lead to a stronger decoupling than low synchrony and when synaptic strength is sufficiently low depression will stop. Moreover, as a secondary effect, reduced average connection strength will help trigger the transition to the waking mode. Unfortunately, the level of synchrony in our model was not sufficiently high to allow decoupling through synchrony, but the switch in the sign of plasticity triggered by neuromodulators yielded equivalent results.

As shown here, this control loop ensures that the decline in synaptic strength during sleep is exponential and self-limiting. Although other kinds of dynamic behavior might be possible, this simple model is in agreement with experimental results. For example, the unfolding of the control loop in the model is reflected in the exponential decrease in SWA during sleep in agreement with experimental data in mammals and birds (Achermann and Borbély 2003; Achermann et al. 1993; Franken et al. 1991; Huber et al. 2000; Jones et al. 2008). The finding that suppressing SWA during the first 3 h of sleep prevents the homeostatic decline of SWA (Dijk et al. 1987) is consistent with the notion of a control loop and suggests that SWA is both a sensor and an effector of a homeostatic process.

Sleep-dependent synaptic renormalization and learning

A burgeoning literature shows that sleep after learning can enhance performance in several kinds of tasks (Diekelmann and Born 2010; Stickgold 2005; Walker 2009; Walker and Stickgold 2004, 2006). For example, accuracy and speed in finger-tapping sequences increase after sleep but not after similar periods of wakefulness (Doyon et al. 2009; Fischer et al. 2002; Walker et al. 2003). It is often assumed that sleep-dependent improvements in performance may be due a further strengthening of synaptic connections during sleep, perhaps mediated by sequence reactivations (Rasch and Born 2007). On the other hand, given the evidence that net synaptic strength appears to decrease during sleep, the question arises of whether and how overall synaptic depression may be compatible with an enhancement in performance. The present simulations support this possibility by showing that synaptic renormalization may actually enhance performance by increasing SNR in neural circuits involved in sequence learning (see also Hill et al. 2008). In the model, the reason SNR improves with renormalization is related to the weight-dependent features of the STDP-like rule, which was implemented according to experimentally derived parameters (Standage et al. 2007). These parameters ensure that stronger synapses undergo relatively smaller changes compared with weaker synapses as illustrated in Fig. 4B. Thus global renormalization further increases the differential between strong and weak connections. To the extent that the strongest connections are those repeatedly potentiated during learning, the result is an increase in SNR. Additional simulations we performed (Supplementary Fig. S2B) suggest another mechanism by which a net depression of synaptic strength can increase SNR even in the presence of a proportional scaling of synaptic strength. In the model, when synapses become weaker than a certain threshold, they cease having an effect on the firing pattern of postsynaptic neurons not even in the presence of high-frequency spiking in presynaptic terminals. This nonlinear threshold effect also contributes to increasing the differential between synapses strengthened by learning and other synapses, thus increasing the SNR. Therefore renormalization may act through two synergistic mechanisms to improve the SNR of store memories: the difference between strong (important) and weak (less relevant) synapses can be enhanced and the efficacy of synapses that were not strengthened during learning activity can be highly reduced by weakening them.

Furthermore, a recently described property of STDP needs to be taken into account (Lubenov and Siapas 2008). Asynchronous activity in simulated and real networks promotes coupling; this, in turn, leads to synchronization of activity, which has the effect, thanks to conduction delays, of causing a generalized decoupling. This process can be seen as a homeostatic loop with an increase in coupling (i.e., potentiation) due to asynchronous activity in waking and a reversed process during sleep, which is characterized by synchronous firing. Training strengthens connections between patches and therefore a spike in patch B will preferentially follow one in patch A even in a situation in which a high level of coupling leads to synchronous activity. Thus a global renormalization process might be counterbalanced by asynchronous activity affecting inter-patch connections with the consequence of preserving these connections from depression and increasing the SNR for the training sequence.

In addition to the beneficial effects of sleep on performance, some studies have also demonstrated that sleep after learning can make the learned material less susceptible to interference from subsequent learning, providing a classic demonstration of memory consolidation (Korman et al. 2007). As shown here, synaptic renormalization during sleep was able to reproduce a similar phenomenon. Specifically, learning a second sequence after a first one reduced the SNR for the first sequence (interference effect). However, interposing a period of sleep before training for the second sequence prevented the reduction in SNR for the first one (memory consolidation effect). As explained in results, this was due to a preferential effect of sleep-dependent renormalization on weaker, indirect pathways connecting the cortical patches. Although the experimental paradigm described in Korman et al. (2007) was designed to test different characteristics of the learning process, our simulations reproduce the finding that sleep between training and an interference session helps in consolidating initially stored memories. Of course, several molecular mechanisms of memory consolidation may also be triggered during sleep in a way that is not mutually exclusive with the specific effects of synaptic renormalization.

Last but not least, the positive effects of sleep on learning and memory are perhaps most evident in terms of restoring normal learning after a period of extended wakefulness. It is well known that sleep deprivation impairs not only performance but also diminishes the capacity to learn new material. As shown in studies in both animals and humans, if subjects are allowed to sleep, their ability to learn is restored to normal levels (Walker and Stickgold 2004). While the electrophysiological and molecular evidence is complex, there is also some indication that sleep deprivation may impair plasticity altogether (Vecsey et al. 2009) may interfere especially with synaptic potentiation (Gilestro et al. 2009; Liu et al. 2010; Vyazovskiy et al. 2008) and may lead to the saturation of certain circuits (Vyazovskiy et al. 2009). In the model, the restoration of the ability to learn is a straightforward consequence of renormalizing overall synaptic strength away from saturation. Again multiple other mechanisms are likely to be involved in vivo, including negative effects of sleep deprivation on aspects of neural function beyond synaptic saturation and beneficial effects of sleep on energy requirements and cellular stress (Attwell and Laughlin 2001).

Circuit reactivation in sleep and wake

Several studies over the past years have shown that spontaneous activity recorded after an animal has been systematically trained on some task bears statistically significant traces of activity patterns induced during the task (Sutherland and McNaughton 2000), usually reflecting task-induced sequences of neuronal activations. Such “reactivations” or “replays” were reported in the hippocampus during NREM sleep (Lee and Wilson 2002; Peyrache et al. 2009; Wilson and McNaughton 1994) and subsequently in other structures, such as the cerebral cortex (Euston et al. 2007; Ji and Wilson 2007). Instances of reactivation have also been described during quiet wakefulness (Davidson et al. 2009; Diba and Buzsáki 2007; Foster and Wilson 2006; Karlsson and Frank 2009) and REM sleep (Louie and Wilson 2001). Finally, it has been reported recently that sequences of activations in NREM sleep may not only replay previous experiences but more generally “play” an animal's cognitive model of its environment (Gupta et al. 2010). A straightforward explanation for the occurrence of reactivations is that the statistical structure of spontaneous neural activity, whether in wake or sleep, is bound to reflect the underlying synaptic connectivity. In other words, if neuron A is much more strongly connected to neuron B than the other way around, for example as a consequence of learning, then spontaneous activity should give rise to more AB than BA sequences. Furthermore, the stronger the level of spontaneous activity, and the more likely reactivation of sequence AB will be.

The present simulations support this scenario: after sequence learning, which selectively strengthens the connections among cortical patches in the direction ABC relative to the direction CBA, one observes a preferential reactivation of neuronal firing sequences ABC compared with CBA when the model is spontaneously active in the sleep mode. A similar result is observed in the wake mode, but only if spontaneous activity is enhanced by subthreshold stimulation. In vivo, reactivation of cortical circuits during quiet waking also occurs in concomitance with other events, such as sharp wave ripples (see for example Karlsson and Frank 2009; Kudrimoti et al. 1999), which may increase overall excitability and promote the reactivation of stored sequences. A possible hypothesis is that spontaneous activity by itself is not sufficient to elicit a distinct reactivation of the training sequence. Further “energy” can be provided by undergoing oscillatory activity, such as slow oscillations during NREM sleep or sharp wave ripples during waking. In the model, we implemented this facilitation of reactivation activity by injecting a low level of depolarizing currents in neurons, therefore reducing the number of endogenous spikes necessary for eliciting reactivation.

Another observation repeatedly reported in the literature is the fact that reactivated sequences are frequent at the beginning of a posttraining episode of NREM sleep and decrease in frequency in the course of the next 20–60 min of NREM sleep (e.g., Ji and Wilson 2007; Kudrimoti et al. 1999). The reason for this progressive decrease in the frequency of reactivation is not clear, but the present results demonstrate that a sleep-dependent, progressive decrease in connection strength, accompanied by an associated decrease in excitability and firing rates, could account for this intriguing finding. A possible explanation for this phenomenon lies in the fact that higher connection strength is associated with higher firing rates and synchrony. Thus activity in one patch will be sufficiently strong to activate—via strengthened connections—neurons in a subsequent patch. When connections are renormalized and firing rates and synchrony decrease accordingly, spontaneous activity will not be strong enough to reactivate the recently reinforced circuit. Moreover, if renormalization follows an exponential course, with most depression occurring at the beginning of NREM sleep, a short period of time will be sufficient for the reactivation rate to go back to baseline levels as has been shown in in vivo studies.

In summary, the present simulations provide a unified, parsimonious account for a considerable number of experimental findings, ranging from molecular and electrophysiological studies indicating net changes in synaptic strength in the course of wake and sleep to electroencephalographic studies demonstrating the homeostatic regulation of slow wave activity to unit recording studies documenting progressive changes in firing rates and synchrony according to behavioral state to unit studies showing a reactivation of firing sequences after learning and their decline during sleep and to behavioral studies documenting a positive effect of sleep in enhancing performance, consolidating memories, and restoring the capacity to learn. Inevitably, the specific mechanisms implemented in the current model cannot capture the full complexity of biological mechanisms and will undoubtedly require further revisions. Furthermore, the results of our simulations suggest new experimental tests to investigate the function of sleep. Recent experiments (Hanlon et al. 2009) have shown that rats learning a reaching task show a specific posttraining increase in SWA only in the cortical region involved in the task (similar data has been reported in humans) (see for example Huber et al. 2004). As we have shown, SWA is a marker of synaptic strength and may play a role in the process of sleep-dependent renormalization. By interfering with the renormalization process, it would be possible to investigate the existence of a causal link between activity during NREM sleep, renormalization, and memory consolidation. One example could be a local disruption of sleep patterns in the cortical region of interest by modifying the levels of arousal-promoting neuromodulators, such as noradrenaline and acetylcholine. An alternative approach would be to reduce the levels of activity in the cortical region of interest to mimic the reduction in SWA or firing rates, which, as we have shown, promote synaptic depression; this could be done by locally injecting reversible cortical silencers such as lidocaine. It will also be interesting to expand the model to test whether a synaptic renormalization framework can account for other important effects of sleep on memory. Memory integration—the ability to connect pieces of information with no explicit links between them—may also be aided by synaptic renormalization by increasing the SNR of connections between concepts initially obscured by background noise. It has already been shown that relational memory, i.e., the ability to generalize and bridge different memories, is fostered by sleep-dependent memory consolidation (Ellenbogen et al. 2007). A set of experiments could be developed for testing whether synaptic renormalization plays a role in these processes. Our hypothesis is that, by “smoothing” connectivity profiles, neural circuits showing some overlap could be brought together, thus promoting integration and generalization. Furthermore, the role of synaptic renormalization in consolidating memories could be tested in simple networks of spiking neurons. We argue that learning rules would benefit by the addition of an off-line period characterized by a renormalization of connection strength.


This study was supported by a National Institutes of Health Director's Pioneer Award to G. Tononi and by Defense Advanced Research Projects Agency, Defense Sciences Office (DSO), Program: Systems of Neuromorphic Adaptive Plastic Scalable Electronics (SyNAPSE).


This was not an industry supported study. None of the authors have indicated financial conflicts of interest.

Supplementary Material

Supplemental Figures and Tables:


The authors thank S. Hill for help in developing and validating the computational model and V. Vyazovskiy and U. Faraguna for helpful inputs and conversations.


1The online version of this article contains supplemental data.


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