Dr Claude Touzet
email: claude.touzet@univ-amu.fr

Morvan's syndrome and the sustained absence of all sleep rhythms for months or years: an hypothesis

Despite the predation costs, sleep is ubiquitous in the animal realm. Humans spend a third of their life sleeping, and the quality of sleep has been related to co-morbidity, Alzheimer disease, etc. Excessive wakefulness induces rapid changes in cognitive performances, and it is claimed that one could die of sleep deprivation as quickly as by absence of water. In this context, the fact that a few people are able to go without sleep for months, even years, without displaying any cognitive troubles requires explanations. Theories ascribing sleep to memory consolidation are unable to explain such observations. It is not the case of the theory of sleep as the hebbian reinforcement of the inhibitory synapses (ToS-HRIS). Hebbian learning (Long Term Depression) guarantees that an efficient inhibitory synapse will lose its efficiency just because it is efficient at avoiding the activation of the post-synaptic neuron. This erosion of the inhibition is replenished by hebbian learning (Long Term Potentiation -LTD) when pre and post-synaptic neurons are active togetherwhich is exactly what happens with the travelling depolarization waves of the slow-wave sleep (SWS). The best documented cases of months-long insomnia are reports of patients with Morvan's syndrome. This syndrome has an autoimmune cause that impedes -among many things -the potassium channels of the post-synaptic neurons, increasing LTP and decreasing LTD. We hypothesize that the absence of inhibitory efficiency erosion during wakefulness (thanks to a decrease of inhibitory LTD) is the cause for an absence of Slow-Wave Sleep (SWS), which results in the absence of REM sleep.

Predation during sleep

. An evolutionary increase in sleep exposure is associated with an evolutionary decrease in SWS time. In other words, when phylogeny is controlled, birds that sleep in riskier locations have low SWS times, while birds in safer sleeping locations have greater amounts of SWS. The conclusion is that sleep (in both birds and mammals) is related to the risk of predation associated with sleeping sites.

Ubiquity of sleep in the animal kingdom

).

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Unihemispheric slow-wave sleep is extremely interesting in the context of a theory of sleep. It demonstrates that evolution can alter sleep (one hemisphere at a time), but its presence sustains the notion that it must be essential [START_REF] Cirelli | Is sleep essential?[END_REF].

A further evidence is provided by the northern fur seal (Callorhinus ursinus), which can alternate between bilateral and unilateral SWS depending on its location while sleeping. While on land, 69% of SWS occurs bilaterally; however, when sleep takes place in water, 68% of all SWS is found with interhemispheric EEG asymmetry, indicating unihemispheric SWS (reported in [START_REF] Rattenborg | Behavioral, neurophysiological and evolutionary perspectives on unihemispheric sleep[END_REF]).

Human sleep durations

The average sleep duration in adulthood is between 7 and 8 hours per day. Sleep duration varies through life: babies sleep more than children, who sleep more than teenagers, who sleep more than adults, who sleep more than older adults (> 65 years old). There is also a large variation of sleep duration among the population: some people are satisfied with only 4 hours of sleep, when others require 10 hours [START_REF] Hirshkowitz | National Sleep Foundation's sleep time duration recommendations: methodology and results summary[END_REF].

Sleep quality

The quality of sleep appears to be more and more essential for health, as demonstrated by the implication of SWS in the pathogenesis of Alzheimer's disease [START_REF] Kang | Amyloid-beta dynamics are regulated by orexin and the sleep-wake cycle[END_REF], long sleep with mortality [START_REF] Youngstedt | Long sleep and mortality: rationale for sleep restriction[END_REF], and sleep disturbances with suicide [START_REF] Bernert | Sleep disturbances and suicide risk: A review of the literature[END_REF].

Sleep restriction

A number of conditions are impacted by sleep deprivation, starting with increases of blood pressure and stress hormone levels. Sleep deprivation makes it difficult for the body to process blood sugar and reduces levels of leptin, an appetite-depressing hormone. These two changes could lead to diabetes and weight gain [START_REF] Taheri | Short Sleep Duration Is Associated with Reduced Leptin, Elevated Ghrelin, and Increased Body Mass Index[END_REF]. Lack of sleep also increases inflammation, thought to be a key element in the development of heart disease.

Experiments on sleep restriction demonstrate that excessive wakefulness quickly impacts cognitive performances -such as those measured by the classical PVT [START_REF] Van Dongen | The cumulative cost of additional wakefulness: dose-response effects on neurobehavioral functions and sleep physiology from chronic sleep restriction and total sleep deprivation[END_REF]. The fact that a debt of sleep must be slept away is also a good indication that sleep is necessary [START_REF] Van Dongen | Sleep debt: theoretical and empirical issues[END_REF]. A further proof is offered by the fact that a total lack of sleep kills initially healthy rats in less than a month [START_REF] Everson | Sleep deprivation in the rat: III. Total sleep deprivation[END_REF].

Total insomnia

Total insomnia without impact on the cognitive function exists. The first one that received all the modern medical scrutiny has been reported by Jouvet [START_REF] Fischer-Perroudon | Sur un cas d'agrypnie (4 mois sans sommeil) au cours d'une maladie de Morvan[END_REF], the famous French sleep specialist.

At the age of 27, the patient started to have acute insomnia, which was confirmed 6 months later by polysomnography at the hospital. There, his total insomnia duration was 4 months (after what the patient died) -but during this time period, he did not show any sign of cognitive impairment. The evaluation of his cognitive functions was considered normal (attention, short-term memory, learning, etc.). His lack of sleep was continuously monitored and controlled by the medical staff. He was diagnosed with Morvan's syndrome. Severe insomnia, including total insomnia, is the most reported symptom in Morvan's syndrome.

Total insomnia and sleep theories

All theories of sleep that advocate a crucial role of sleep in memorization [START_REF] Diekelmann | The memory function of sleep[END_REF][START_REF] Walker | Overnight alchemy: sleep-dependent memory evolution[END_REF][START_REF] Rasch | Maintaining memories by reactivation[END_REF][START_REF] Huber | Local sleep and learning[END_REF][START_REF] Sejnowski | Why do we sleep?[END_REF] are unable to explain the lack of impact of severe (even total) insomnia on cognitive performances. In fact, these patients are "living" proof that sleep-dependent memory consolidation theories are wrong.

The case of the synaptic homeostasis hypothesis [START_REF] Tononi | Sleep function and synaptic homeostasis[END_REF] is different since sleep (SWS) is supposed to downscale (excitatory) synaptic strength to a baseline level that is energetically sustainable. Cognitive performance could be maintained if downscaling was provided in a different way -or made unnecessary.

The theory of sleep as the hebbian reinforcement of the inhibitory synapses [START_REF] Touzet | Sleep: the hebbian reinforcement of the local inhibitory synapses[END_REF] offers a hypothesis compatible with total insomnia.

Theory of sleep as the hebbian reinforcement of the inhibitory synapses (ToS-HRIS)

This theory is based on several observations. Firstly, as long as the brain stays awake, hebbian learning guarantees that efficient inhibitory synapses lose their efficiency [START_REF] Maffei | The many forms and functions of long term plasticity at GABAergic synapses[END_REF] -just because they are efficient at avoiding the activation of the targeted neurons. Secondly, since hebbian learning is the only known mechanism of synapse modification [START_REF] Lamsa | Hebbian LTP in feed-forward inhibitory interneurons and the temporal fidelity of input discrimination[END_REF] that operates within the required time frame (hours) [START_REF] Turrigiano | Too many cooks? Intrinsic and synaptic homeostatic mechanisms in cortical circuit refinement[END_REF], it is necessary that in order to replenish the inhibitory synapses efficiency [START_REF] Scelfo | Learning-related long-term potentiation of inhibitory synapses in the cerebellar cortex[END_REF][START_REF] Kullmann | Plasticity of Inhibition[END_REF], source and targeted neurons must be activated together [START_REF] Woodin | Coincident pre-and postsynaptic activity modifies GABAergic synapses by postsynaptic changes in Cl-transporter activity[END_REF]. Thirdly, a travelling wave of depolarization [START_REF] Massimini | The Sleep Slow Oscillation as a Traveling Wave[END_REF] is exactly what is needed to ensure the strengthening of local inhibitory synapses.

ToS-HRIS states that it is exactly the purpose of the "slow-wave sleep" (SWS). It also states that the purpose of the REM sleep (Random Eye Movements sleep, also named paradoxical sleep), which follows each session of SWS, is to counteract the eroding effect of SWS on the excitatory long distance connections coding the events of the previous day. Indeed REM activity resembles that of the awake state, except that it is played much faster and not in the same order [START_REF] Euston | Fast-Forward Playback of Recent Memory Sequences in Prefrontal Cortex During Sleep[END_REF]. ToS-HRIS explains the synergy between NREM (non REM: Light Sleep + SWS) and REM sleep, acting together to guarantee that when the subject awakes, his inhibitory synaptic efficiency is restored and his (excitatory) long distance associations are still there.

A number of findings should be made clear, in the context of the ToS-HRIS: 1-REM is only required because of SWS. If there is no SWS, then no REM is required. 2-SWS is only required because of the LTD of the inhibitory synapses (I-LTD) during wakefulness. 3-If inhibitory synapses' LTD (I-LTD) is reduced or impeded, then SWS is not required anymore (our hypothesis).

Total insomnia: hypothesis

Could it be that I-LTD is reduced or impeded in such a way that SWS is not required anymore (i.e., total insomnia)? The observation that Morvan's syndrome may induce severe (even total) insomnia without any negative impacts on cognitive functions is intriguing.

Morvan's syndrome

The insomnia of Morvan's syndrome is similar to that described in delirium tremens and fatal familial insomnia. It is characterized by reduced or absent sleep spindles and K complexes. It is also characterized by REM sleep without atonia and absent or severely reduced SWS [START_REF] Abou-Zeid | Morvan syndrome: a case report and review of the literature[END_REF]. As opposed to fatal familial insomnia in which degeneration of the thalamus is progressive, the dysfunction in Morvan's syndrome is thought to be reversible. Hallucinations and delusions are commonly associated positive symptoms related to the encephalopathy. Seizures are uncommon in Morvan's syndrome. They can appear during the acute phase of the disease, or a few months earlier.

Less than 30 cases of Morvan's syndrome were documented in the literature between 1986 and 2009 [START_REF] Abou-Zeid | Morvan syndrome: a case report and review of the literature[END_REF]. Current evidence supports the concept of Morvan's syndrome as an autoimmune synaptic disorder. Voltage-gated potassium channel (VGKC) antibodies have been found in several patients with this syndrome [START_REF] Liguori | Morvan's syndrome: Peripheral and central nervous system and cardiac involvement with antibodies to voltage-gated potassium channels[END_REF][START_REF] Cornelius | Sleep Manifestations of Voltage-Gated Potassium Channel Complex Autoimmunity[END_REF] and symptoms may improve with immuno-modulating therapy (e.g., steroids, azathioprine, plasmapheresis). The natural history of Morvan's syndrome is highly variable, including spontaneous remission, and has a fatal issue in 10% of cases [START_REF] Cottrell | Sub-acute presentation of Morvan's syndrome after thymectomy[END_REF].

Typical presentation of Morvan's syndrome includes muscle twitching (thus the name "shaker"), hyperhidrosis, insomnia, fluctuating cognition, and limb paresthesia. The precise pathophysiology of Morvan's syndrome has not yet been established [START_REF] Josephs | Neurophysiologic studies in Morvan syndrome[END_REF], and is highly variable [START_REF] Abou-Zeid | Morvan syndrome: a case report and review of the literature[END_REF].

Voltage-gated potassium channels and Morvan's syndrome K+ channels play a crucial role in returning the depolarized neuron to its resting state. If missing, then the return to the resting state takes much longer, which affects synaptic plasticity. There is a high degree of diversity in the neuronal K+ channel population, probably serving specific physiological requirements of different locations. VGKC are the most ubiquitous and diverse group of voltage-dependent ion channels found in the body. VGKC are expressed widely in the central nervous system, but the cerebellum and hippocampus have received the most attention due to the genetic disorders associated with the dysfunction of VGKC (especially epilepsy and episodic ataxia) [START_REF] Kleopa | Autoimmune Channelopathies of the Nervous System[END_REF].

VGKC play a major role in regulating the excitability of hippocampal pyramidal neurons by modulating neurotransmitter release, post-synaptic responses to excitatory inputs, neuronal spike properties, and firing frequency. How auto-antibodies impair VGKC function remains unclear. They appear to be heterogeneous and may bind to multiple Kv subunits [START_REF] Kleopa | Autoimmune Channelopathies of the Nervous System[END_REF]. Kv1.1-1.6 are highly expressed in different combinations in the cerebellar molecular and granule cell layers as well as at the basket cell terminal, and in specific layers of the hippocampus containing excitatory axon terminals, most prominently in the molecular layer of the dentate gyrus, in the CA3 mossy fiber zone and in the stratum radiatum of CA1-3.

Antibodies to Shaker-type (KvI) K+ channels are known to be associated to neuromyotonia, limbic encephalitis and Morvan's syndrome. In the central nervous system, each disease correlates positively with at least one Kv1.1, Kv1.2 or Kv1.6 antibodies. However, compared to the two others, Morvan's syndrome is the most variable and less prominent [START_REF] Kleopa | Neuromyotonia and limbic encephalitis sera target mature Shaker-type K+ channels: subunit specificity correlates with clinical manifestations[END_REF].

K+ channels and LTD/ LTP

Active conductances located and operating on neuronal dendrites are expected to regulate synaptic integration and plasticity. Studies support the notion that Kv4.2 subunits are required to form A-type K1 channels in dendrites of CA1 pyramidal neurons [START_REF] Chen | Deletion of Kv4.2 Gene Eliminates Dendritic A-Type K+ Current and Enhances Induction of Long-Term Potentiation in Hippocampal CA1 Pyramidal Neurons[END_REF]. Pharmacological block and genetic elimination of the Kv4.2-mediated IA currents facilitates the induction of long-term potentiation of excitatory inputs [START_REF] Chen | Deletion of Kv4.2 Gene Eliminates Dendritic A-Type K+ Current and Enhances Induction of Long-Term Potentiation in Hippocampal CA1 Pyramidal Neurons[END_REF][START_REF] Ramakers | A postsynaptic transient K+ current modulated by arachidonic acid regulates synaptic integration and threshold for LTP induction in hippocampal pyramidal cells[END_REF].

Using Kv4.22/2 mice, Zhao et al. investigate how Kv4.2-mediated A-type K1 channels (and Ca21-activated K1 channels) are involved in the induction process of Hebbian type plasticity that requires correlated pre-and post-synaptic activities [START_REF] Zhao | Dendritic mechanisms controlling the threshold and timing requirement of synaptic plasticity[END_REF]. They demonstrate using CA1 pyramidal neurons that elimination of dendritic A-type K1 currents resulted in an expanded time window, making LTP less dependent on the temporal relation of pre-and post-synaptic activity. For LTD, the threshold was significantly increased. This shift in the depression threshold was restored to normal when the appropriate amount of internal free calcium was chelated during induction.

In summary, actions on the K+ channels of the post-synaptic neuron (of glutamate excitatory synapse) modify the LTP and LTD. If the action removes the K+ currents (with an antagonist of the Kv) then LTP is facilitated (expanded time window) and LTD is made more difficult (a shift of threshold allows an easier potentiation).

The previous research focused on excitatory synapses, but inhibitory (GABA) synapses target the same post-synaptic neurons and exhibit similar LTP/LTD variations [START_REF] Luscher | GABAA Receptor Trafficking-Mediated Plasticity of Inhibitory Synapses[END_REF][START_REF] Castillo | Long-term plasticity at inhibitory synapses[END_REF].

Conclusion

When VGKC action is impeded (by a disease such as Morvan's syndrome), then LTP and LTD are modified in such a way as to render inhibitory synapse LTD (I-LTD) very difficult. Since ToS-HRIS asks for SWS as long as I-LTD occurs (SWS is supposed to replenish the inhibitory synapse efficiency through I-LTP), if there is no I-LTD, then there is no requirement for SWS (i.e., for sleep -since REM is only required because of SWS's negative impact on the excitatory long distance connections). This agrees with the "local" aspect of sleep: the local duration of sleep depends on the use of a given cortical region in the wakefulness state [START_REF] Huber | Local sleep and learning[END_REF].

ToS-HRIS is the only sleep theory able to account for prolonged wakefulness without negative impact on cognitive performances.

Total insomnia without any adverse effect?

In addition to severe (even total) insomnia, Morvan's syndrome patients may be affected by many problems such as daytime drowsiness, intermingled with confusional oneiric status, and the emergence of atypical REM sleep from wakefulness. The symptoms picture is highly variable, certainly associated with the fact that the distribution of the various (about 50) Kv channels is highly variable between individuals. Could it be that there exist individuals who show no other symptoms than total insomnia? For example, Al Herpin (1862-1947) was an American known as the "Man Who Never Slept". In 1904, journalists reported that he had not slept during the last 10 years (which starts his total insomnia at the age of 32). His claim was investigated by medical professionals who could not demonstrate the opposite. He was in good health, and lived until his 85 th year without sleeping. He had a constant level of high awareness.

Another case is reported (2006) in Vietnam: Hai Ngoc (1942-) says that he could not sleep at night after getting a fever in 1973 (which starts his total insomnia at the age of 31). He has already spent three decades without sleep, and is considered healthy by local medical doctors.

Interestingly, in both cases the total insomnia started after 30 years old, in one case after a "fever". Following our hypothesis, there is a high probability that these people were affected by an autoimmune disease inducing the "just right" combination of K+ channels inactivation to end up with only one symptom: total insomnia.

Future directions

Why did evolution not find and retain this solution, if not for humans, then for another species? Maybe the necessary conditions to reunite are extremely rare. Humans amount to several billions and only two cases were reported in the twentieth century.

Should humans consider developing a total insomnia without side effect technology in order to increase their life time (within the same lifespan), then a logical direction of research would be to seek a better understanding of the various K+ channelopathies.


Sleep is ubiquitous among the animal realm, and represents about 30% of our lives. Despite numerous efforts, the reason behind our need for sleep is still unknown. The Theory of neuronal Cognition (TnC) proposes that sleep is the period of time during which the local inhibitory synapses (in particular the cortical ones) are replenished. Indeed, as long as the active brain stays awake, hebbian learning guarantees that efficient inhibitory synapses lose their efficiency -just because they are efficient at avoiding the activation of the targeted neurons. Since hebbian learning is the only known mechanism of synapse modification, it follows that to replenish the inhibitory synapses' efficiency, source and targeted neurons must be activated together. This is achieved by a local depolarisation that may travel (wave). The period of time during which such slow waves are experienced has been named the "slow-wave sleep" (SWS). It is cut into several pieces by shorter periods of paradoxical sleep (REM) which activity resembles that of the awake state. Indeed, SWS -because it only allows local neural activation -decreases the excitatory long distance connections strength. To avoid losing the associations built during the awake state, these long distance activations are played again during the REM sleep. REM and SWS sleeps act together to guarantee that when the subject awakes again, his inhibitory synaptic efficiency is restored and his (excitatory) long distance associations are still there.

Introduction

All creatures with a brain are able to learn -and must sleep. Indeed, sleep evidence has been found in most species studied, including cubomedusan jellyfish [START_REF] Seymour | Do Box Jellyfish Sleep at Night?[END_REF], tree frogs [START_REF] Hobson | Electrographic Correlates of Behaviour in Tree Frogs[END_REF], lizards [START_REF] Ayala-Guerrero | Sleep patterns in the lizard Ctenosaura pectinata[END_REF], drosophilas [START_REF] Nitz | Electrophysiological Correlates of Rest and Activity in Drosophila melanogaster[END_REF][START_REF] Gilestro | Widespread Changes in Synaptic Markers as a Function of Sleep and Wakefulness in Drosophila[END_REF], zebrafish [START_REF] Yokogawa | Characterization of Sleep in Zebrafish and Insomnia in Hypocretin Receptor Mutants[END_REF], birds [START_REF] Amlaner | Principles and Practice of Sleep Medicine[END_REF], and all mammals [START_REF] Siegel | Do all animals sleep?[END_REF] (starting with the platypus [START_REF] Siegel | Sleep in the platypus[END_REF]). Sleep may take curious forms such as for the dolphin [START_REF] Mukhametov | Interhemispheric asymmetry of the electroencephalographic sleep patterns in dolphins[END_REF] whose sleep implies only one hemisphere at a time. This happens because breathing is a voluntary act, and requires an awake state. Therefore the dolphin exhibits a two hours sleep in one hemisphere, one hour of awake state for both hemispheres followed by two hours of sleep in the other hemisphere, all over the twelve hours of night. During their migration, several species of birds fly for several days, and sleep while flying a few seconds at a time [START_REF] Rattenborg | Do birds sleep in flight?[END_REF], or one hemisphere at a time.

Sleep seems ubiquitous in the animal realm, and occurs as soon as the species exhibits learning abilities. Only a few (primitive) species seem to be deprived of sleep [START_REF] Siegel | Do all animals sleep?[END_REF]. Since sleep puts the subject in a dangerous situation with greatly reduced sensory responsiveness (and therefore increased possibility to be eaten by predators), one could conclude that if the process of natural selection has not banished sleep from the behaviour repertoire [START_REF] Cirelli | Is sleep essential?[END_REF], then it must be mandatory. It looks like sleep is a necessary component of learning -even an integral part of it. It is the opinion of most sleep researchers [START_REF] Diekelmann | The memory function of sleep[END_REF][START_REF] Walker | Overnight alchemy: sleep-dependent memory evolution[END_REF][START_REF] Tononi | Sleep function and synaptic homeostasis[END_REF][START_REF] Rasch | Maintaining memories by reactivation[END_REF][START_REF] Huber | Local sleep and learning[END_REF][START_REF] Sejnowski | Why do we sleep?[END_REF].

The duration of sleep varies between species, and also among members of a same species. Humans sleep an average of 8 hours per day, but a few of us are satisfied with only three hours of sleep, while others demand ten hours [START_REF] Siegel | Do all animals sleep?[END_REF]. Also, sleep requirements varies with the age. Toddlers sleep more than children, who sleep much longer than elderly people [START_REF] Siegel | Do all animals sleep?[END_REF]. It is acknowledged that young subjects learn more during the day than elderly ones [START_REF] Ramscar | The Myth of Cognitive Decline: Non-Linear Dynamics of Lifelong Learning[END_REF], which emphasizes again the relation between learning and sleeping. Since both actions are intrinsically connected, the explanation of sleep must lay in the learning process.

Learning in the brain

At a neuronal level, learning obeys the hebbian rule, the only known rule of synapse efficiency modification. It was formulated in 1942 by Donald Hebb [START_REF] Hebb | The Organization of Behavior: A Neuropsychological Theory[END_REF], confirmed by electrophysiology several decades later [START_REF] Frégnac | A reexamination of Hebbian-covariance rules and spike timing-dependent plasticity in cat visual cortex in vivo[END_REF], and since that time, no other proposal has shown up in order to explain learning at a neuronal level. Hebb's rule states that "neurons who fire together get reinforced", and neurons which do not (fire together) see their connection efficiency diminish.

As stated by the Theory of neuronal Cognition (TnC), the brain does not process information -but represents it [START_REF] Touzet | Consciousness, Intelligence, Free-will: the answers from the Theory of neuronal Cognition -tome 1[END_REF]. Therefore, it is most important that world regularities are associated to identifiable sets of neurons. The neural localisation of a world event is an identification per se, and allows to act consequently. Neural localization is obtained thanks to inhibitory connections which limit the number of excited neurons at any given time. The proportion of inhibitory connections in the human brain is about 40% of all connections [START_REF] Braitenberg | On the Texture of Brains[END_REF].

In the case of the human species, 22% of the neurons belong to the cortex [START_REF] Herculano-Houzel | The human brain in numbers: a linearly scaled-up primate brain[END_REF]. The (human) cortex is composed of about 160,000 cortical columns [START_REF] Mountcastle | The columnar organization of the neocortex[END_REF] (a column is a set of about 100,000 neurons), each column belonging to one of the estimated 160 cortical maps that form the cortex. The columnar architecture of the cortex is genetically determined (FIG. 1), but the fine-tuning of its functioning relies on neuroplasticity [START_REF] Verhag | Synaptic Assembly of the Brain in the Absence of Neurotransmitter Secretion[END_REF].

Inhibitory synapse efficiency

Wakefulness functioning requires inhibition to induce localization of the information at the cost of suppressing neighbour activities (in order to end up with only one locally activated column). The inhibitory connections are plastic and obey hebbian learning [START_REF] Scelfo | Learning-related long-term potentiation of inhibitory synapses in the cerebellar cortex[END_REF][START_REF] Kullmann | Plasticity of Inhibition[END_REF][START_REF] Maffei | The Many Forms and Functions of Long Term Plasticity at GABAergic Synapses[END_REF][START_REF] Gillespie | Inhibitory synapses in the developing auditory system are glutamatergic[END_REF][START_REF] Liu | Local structural balance and functional interaction of excitatory and inhibitory synapses in hippocampal dendrites[END_REF][START_REF] Woodin | Coincident Pre-and Postsynaptic Activity Modifies GABAergic Synapses by Postsynaptic Changes in Cl# Transporter Activity[END_REF][START_REF] Roberts | System of Mormyrid Electric Fish Modeling Inhibitory Plasticity in the Electrosensory[END_REF]. Since local inhibitory connections are efficient at suppressing the targeted neurons' activity, these inhibitory connections are never reinforced, and their strength diminishes as the day progresses.

On the contrary, excitatory long distance connections linking two or more columns belonging to separated cortical maps are reinforced as soon as they are activated in the same time frame (Hebb rule again) and are constitutive of the learned experience. As advocated by the TnC, such long distance excitatory connections are representative of « high level » information extraction, and may even account for our flashes of « intelligence » [START_REF] Touzet | The Illusion of Joy[END_REF].

There is no secret that as the day progresses, we are less and less cognitively efficient. In case of sleep deprivation, the subjects thinking process becomes fuzzy, prone to hallucinations, etc. [START_REF] Van Dongen | The cumulative cost of additional wakefulness: dose-response effects on neurobehavioral functions and sleep physiology from chronic sleep restriction and total sleep deprivation[END_REF]. Van Dongen et al. [START_REF] Van Dongen | The cumulative cost of additional wakefulness: dose-response effects on neurobehavioral functions and sleep physiology from chronic sleep restriction and total sleep deprivation[END_REF] provide evidences that the build-up of neurobehavioral deficits is not caused by reduction of sleep time per se, but rather by excessive wakefulness beyond a maximum period during which stable neurobehavioral functioning could be maintained. "Excess wakefulness" is all waking time beyond a hypothetical critical period. They provide results showing a near-linear relationship linking each consecutive hour of wake extension (i.e., excess wakefulness) to an increase in lapses of behavioural alertness (FIG. 2).

Our hypothesis is that the reduced alertness is the result of Hebb learning onto the inhibitory intercolumn connections. Less inhibitory efficiency means that instead of a unique activated column in a given location, there may be two, or more, which induces a less precise representation of the event. If this event is a world situation perceived by the body senses, it may require more time to be recognized (lapse of behavioural alertness). In some cases, it may even be wrongly recognized (confusion, hallucination).

Sleep organization

After a good (night of) sleep, our brain is again as sharp as usual. Sleep is organized in several stages (II and III) characterized by the fact that the EEG frequency diminishes (from over 20 Hz to less than 3.5 Hz), while the amplitude of the EEG signal becomes several times larger, and paradoxical sleep (also named Random Eye Movements sleep -REM) that resembles the awake state (FIG. 3). It follows that non-REM sleep (NREM) matches sleep stages II and III. More specifically, stage III is also named Slow-Wave Sleep (SWS). It is important to note that surface EEG has been related to underlying neural activity [START_REF] Whittingstall | Frequency-Band Coupling in Surface EEG Reflects Spiking Activity in Monkey Visual Cortex[END_REF] and that the slow waves travel [START_REF] Massimini | The Sleep Slow Oscillation as a Traveling Wave[END_REF].

Hebbian learning balancing

EEG amplitudes during sleep stages II and III demonstrate that there are several times more neurons acting synchronously than during the wake period. Those neurons are all localized in the same region (beneath the EEG electrode), which means that they belong to neighbouring cortical columns. In particular, the neurons responsible for inter columns inhibitory connections are activated, as are also the neurons targeted by these connections. Following the hebbian learning rule, these inhibitory connections are reinforced. Our hypothesis states that this reinforcement nullifies the previous wakefulness erosions of efficiency.

Our hypothesis also provides an explanation for the succession of various sleeps. The REM sleep is defined by the fact that the EEG is very similar to recordings obtained during the wakefulness period, and also because it follows sleep stages III. It seems that -inserted between periods of inhibitory strength reinforcement -there are periods of long distance excitatory reinforcement (cf. FIG. 4). The explanation may be that during the sleep periods (II and III), the long distance connections are themselves subject to hebbian efficiency erosion (it is the exact inverse situation as in the awake state). Since these connections are important to preserve, they are periodically reinforced during the night.

To resume, limitations of the Hebb's rule impose a balancing between reinforcement of excitatory connections and its concomitant decrease of inhibitory connections (a characteristic of the wake state), and replenishment of inhibitory connection efficiency without impacting the excitatory long distance connections (which is characterizing the sleep).

Sleep as a localised process

Recent results show that the quantity of sleep, its repartition among the various stages, as also its local repartition between various zones of the cortex are influenced by the nature and quantity of information acquisition during the day [START_REF] Huber | Local sleep and learning[END_REF]. For example, if today you have done more music exercises than usual, your cortical zones devoted to music will require deeper and longer sleep periods. This is in accord with our hypothesis: it is the inhibitory connection efficiency that regulates the amount and repartition of sleep. Sleep will be displayed by a given cortical zone until the local inhibitory efficiency is restored.

The paradoxical sleep activity has been analysed by Euston et al. [START_REF] Euston | Fast-Forward Playback of Recent Memory Sequences in Prefrontal Cortex During Sleep[END_REF] as a replay of the day's activations, but not in the same order, and about 6 to 7 times faster. In which case, 90-120 minutes of a night's paradoxical sleep are equivalent to 9-12 hours of wake state. TABLE 1 shows that over the 24 hours day, the NREM sleep exactly compensates for the erosion of the inhibitory efficiency due to wakefulness and REM sleep. It is important to remark that the situation is symmetrical: there is an exact identical compensation of the negative impact of NREM sleep on the excitatory synapse efficiencies. Therefore, in the context of our hypothesis, there is no discrepancy between the duration of both REM and wakefulness compared to NREM sleeps. Replay as also been found during the awake state [START_REF] Carr | M Hippocampal replay in the awake state: a potential substrate for memory consolidation and retrieval[END_REF].

The function of sleep

Nature, with a unique solution available to manipulate the synapse efficiency (Hebb's rule), had to find a trick (using Hebb's rule) in order to replenish the inhibitory efficiency. Since the necessary brain local depolarisations have absolutely no functional relations with the perceived world events, the best solution is to forbid any body movement, any action -which would be necessarily maladapted, even potentially life-threatening. In the context of our hypothesis, sleep is necessarily a period of time during which the body must stay still, whatever the animal species.

Discussion

Many facts point towards a sleep-dependent memory consolidation. Diekelmann and Born [START_REF] Diekelmann | The memory function of sleep[END_REF] suggest that during slow-wave sleep (SWS), memory representations are transferred from a temporary to a long-term "store" and thereby undergo reorganization in a process of system consolidation. Walker and Stickgold [START_REF] Walker | Overnight alchemy: sleep-dependent memory evolution[END_REF] propose to link such processes of reorganization to the REM sleep. Our hypothesis states that the contribution of SWS comes from a better local inhibition, where REM sleep's replay strengthened the long-distance excitatory synapses -both effects allow for a faster and more precise selection of representations.

The synaptic homeostasis hypothesis of Tononi and Cirelli [START_REF] Tononi | Sleep function and synaptic homeostasis[END_REF] is another proposal for the function of sleep. It hypothesises that plastic processes occurring during wakefulness result in a net increase in synaptic strength in many brain circuits. The role of SWS is then to downscale synaptic strength to a baseline level that is energetically sustainable. The goal of sleep is the homeostatic regulation of the total synaptic weight impinging on neurons. Their hypothesis accounts for a large number of experimental facts, and has implications for both sleep and mood disorders. The synaptic homeostasis hypothesis does not explain the role of REM sleep, otherwise our hypothesis agrees that sleep acts as a homeostatic regulator of the connection strength. Tononi and Cirelli's proposal only focuses on the excitatory connections. Our hypothesis in considering both inhibitory and excitatory synapses could be envisaged as a generalisation of the synaptic homeostasis hypothesis, and explains the role of REM sleep.

Rasch and Born [START_REF] Rasch | Maintaining memories by reactivation[END_REF] propose that some memory formations require sleep because these formations need to be done "off-line" (due to transient destabilization of memory traces). We do not agree to such proposal which claims that there is a difference in form or nature between the event to record and the long-term memory. In our opinion, the event to record only requires durable synaptic strength modifications, and not a transfer to another location. Therefore, there is no requisite for a transient destabilization in order to memorise (since memorisation will only "fix" already experienced pattern of brain activity).

Sejnowski and Destexhe [START_REF] Sejnowski | Why do we sleep?[END_REF] propose that alternating fast (NREM) and slow waves sleep (SWS) consolidate information acquired previously during wakefulness. They propose a plausible biophysical mechanism targeting pyramidal neurons. Our hypothesis differs in the sense that the primary targets of sleep are the inhibitory neurons.

Dreaming

Dreams fascinate because they do occur without our conscious will, and we do not tolerate to be a puppet in the hands of our neurons. This is the reason why many are searching for dream meaning in the form of premonitory information, or a window into subconscious [START_REF] Hobson | REM sleep and dreaming: towards a theory of protoconsciousness[END_REF]. In the context of our hypothesis, dreams are less "romantic", they are the results of brain activity reaching language maps, but in a non-coherent manner.

Dreams which occur during NREM sleep (slow wave sleep) are the less numerous [START_REF] Chellappa | Cortical activation patterns herald successful dream recall after NREM and REM sleep[END_REF]. They are the result of the depolarisation waves. These neuronal activities have no link to recent (awake) events. However, there may be recurrent dreams: the same depolarisation waves generating the same cortical columns pattern of activity night after night.

Dreams which occur during the paradoxical sleep (REM) reflect the repeated and disorganised activation of the connections that were once activated during the awake state. It is therefore quite normal to find elements of the previous days, in disorder since there is no order in the replay.

Feelings of flying, weightlessness and impossibility to move seem to be related to the reduction by the reticular active system of the afferent activity (sensors and motor activities) reaching the cortex [START_REF] Evans | Sleep, consciousness and the spontaneous and evoked electrical activity of the brain. Is there a cortical integrating mechanism?[END_REF]. We know that we should experience gravity, or that we are sending order to our muscles, but the absence of effect is "logically" interpreted by our brain as an absence of cause: we are floating in the air, we have been tied, etc.

A last word about "premonitory" dreams which occur in particular when the subject is falling asleep, or when he wakes up. They are better built than the other dreams because the brain functioning is less altered at these times. In the light of the TnC, light sleep (LS) affects long distance connections, including those implicated in the verification of the validity of current brain processing representations with our entire life stored events (which requires functional access to the hippocampus, and has a lot in common with hypnosis [START_REF] Touzet | Sleep, Placebo: the answers from the Theory of neuronal Cognitiontome 2[END_REF]). These dreams are the result of normal local processing, without supervision (i.e., no comparison to previous experiences). They may provide us with a new (and maybe true) information, an information that (in the awake state) would never have existed because of its lack of coherence with our previous knowledge (a hypothesis similar to Charlton's proposal [START_REF] Charlton | The Sleep Elaboration-Awake Pruning (SEAP) theory of memory: Long term memories grow in complexity during sleep and undergo selection while awake. Clinical, psychopharmacological and creative implications[END_REF]). Therefore, premonitory dreams exist, but it is our brain that makes the prediction.

Concluding remarks

Inhibitory neurons amount for a large part of the brain neurons (40%). They are plastic, a major component of cortical organization, and difficult to study since inhibition effectiveness is ascertained by an absence (suppressed) of activity. More than seventy years after Hebb's insight, we ask and answer the question about how inhibitory synapses could regain their efficiency: "sleep".

Siegel [START_REF] Siegel | Do all animals sleep?[END_REF] stresses the fact that some animals never exhibit a state that meets the behavioural definition of sleep ("a rapidly reversible state of immobility and greatly reduced sensory responsiveness"). He was not the first one to alert on the limits of this definition. Following the hypothesis we have explored in this paper, a new definition of sleep is necessary. We propose the following: "sleep is when the reinforcement of inhibitory connections -that were lessened by awake functioning -occurs". Sleep may happen in such a way as to impede the quality of the behavioural response. In order to avoid the expression of these maladaptive responses, various mechanisms may enter into action such as immobility, reduced sensory responsiveness, etc. Following this new definition, immobility is no longer a prerequisite for sleep, and sleep may occur without immobility. In the same manner, reduced responsiveness may or may not be a side effect of sleep. The question of who sleeps, or doesn't, is not an issue anymore. The right question is "how does a given species succeed to replenish the efficiency of its cortical inhibitory connections?"

Our definition of sleep -the reinforcement of the inhibitory connections -is not readily identified in clinical practice. In order to help promote this new definition, we need to emphasize how it could be implemented, and how it would be applied in the practice of sleep medicine. Today, we know of no tool able to directly measure the strength of the cortical inhibitory connections. But an indirect measure is possible using an (ecologically plausible) test of attention before and after sleeping (TnC states that attention performance is related to the quality of the local cortical inhibition). Also, hebbian learning states that the amount of synaptic strengthening is directly proportional to the number of neuronal co-activations, a number that can be estimated from the amount of delta waves, minus the amount of REM activations. Using the numbers given on table 1 (% recruitment), it is possible to compute the amount of reinforcements of both excitatory and inhibitory synapses, and therefore estimate the overall quality of sleep, and its components (NREM/REM sleep). Another important factor is the alternation between NREM/REM sleep. A way to evaluate the quality of the alternation is to measure the episodic memory before and after sleep (using interview or selfreport). A degraded performance would be an indicator of a sub-performing REM sleep.

Fig. 1 a) Following the proposal of T. Kohonen [START_REF] Kohonen | Self-Organizing Maps, 3rd edn[END_REF], the TnC models the cortex as an homogeneous organization of cortical columns. Each column is a set of about 1,000 minicolumns, each minicolumn containing about 110 neurons (in the human cortex [START_REF] Mountcastle | The columnar organization of the neocortex[END_REF][START_REF] Buxhoeveden | The minicolumn hypothesis in neuroscience[END_REF]). b) The columns belong to one of the estimated 160 cortical maps, each map is specific to a certain kind of information. The maps belonging to the primary and secondary cortex represent dimensions of the sensory events. Maps of higher level of abstraction combine and fuse information from lower level maps [START_REF] Silver | Topographic maps in human frontal and parietal cortex[END_REF]. This fact prohibits an easy interpretation of the information they represent (see Tanaka [START_REF] Tanaka | Mechanisms of visual object recognition studied in monkeys[END_REF] for examples of high level information representations). The cortical map columns prevent their neighbour activations through lateral inhibition [START_REF] Favorov | Minicolumnar organization within somatosensory cortical segregates. I. Development of afferent connections[END_REF][START_REF] Favorov | Minicolumnar organization within somatosensory cortical segregates. II. Emergent functional properties[END_REF] -but are potentially excitatorily connected to any other columns of the cortex [START_REF] Braitenberg | On the Texture of Brains[END_REF] (adapted from [START_REF] Touzet | Consciousness, Intelligence, Free-will: the answers from the Theory of neuronal Cognition -tome 1[END_REF]).

Fig. 2 The panels show behavioral alertness, as measured by psychomotor vigilance task (PVT) performance lapses (relative to baseline), plotted as a function of cumulative excess wakefulness (panel A) and as a function of cumulative sleep debt (panel B). Cumulative wake extension (i.e., excess wakefulness -A), rather than cumulative loss of sleep (i.e., sleep debt -B), is the primary cause of progressively reduced behavioural alertness both across days of chronic sleep restriction and across days of total sleep deprivation. Subjects in all four experimental conditions (sleep restriction: 8 h (diamond), 6 h (light square), 4 h (circle) and 0 h (black square) appeared to experience the same cumulative "cost" (i.e., increase in lapses of behavioural alertness) for each consecutive hour they extended their wake periods (near-linear relationship, fig. A), but if considered from the perspective of sleep debt (fig. B), the response to total sleep deprivation (black square) is fundamentally different from the chronic sleep restriction (adapted from [START_REF] Van Dongen | The cumulative cost of additional wakefulness: dose-response effects on neurobehavioral functions and sleep physiology from chronic sleep restriction and total sleep deprivation[END_REF]). Fig. 3 Hypnogram: NREM and REM sleeps alternate in a cyclic fashion. Recordings during the various sleep stages show that wake and REM sleeps EEG are similar, and that NREM sleep involves slower and larger waves (from light sleep to slow wave sleep). A wave is a depolarisation that moves along the cortical tissue. In stage 1 (S1), theta waves appear (frequency between 4-7 Hz and an amplitude between 30 to 50 microvolts). In stage 2 (S2), EEG recordings tend to show characteristic "sleep spindles", which are short bursts of high frequency brain activity (around 13 Hz), and "K-complexes" which are delta wave lasting only one second (amplitude between 50 to 100 microvolts). Stage 3 consists of 20% or more slow waves (delta) with a frequency of less than 1 Hz, and an amplitude around 200 microvolts. Total REM sleep duration is between 90 to 120 minutes, and total sleep is around 8 hours (adapted from [START_REF] Genzel | Light sleep versus slow wave sleep in memory consolidation: a question of global versus local processes?[END_REF]). Fig. 4 During wakefulness (16 hours), the inhibitory connections lose their efficiency. During SWS (dotted line), these connections get reinforced until there are fully replenished at the end of the sleep period (exact same efficiency). During the day, new events are recorded by setting up new long distance excitatory connections (reinforcement of efficiency, we assume a linear progression of the number of new events). During the sleep, the SWS impacts negatively these new connections, but cyclic REM periods (bold line) allow to replay and therefore reinforce these same connections. At the end of the sleep, no excitatory efficiency has been lost. A new day starts with a refreshed inhibition and no excitatory loss (i.e., no memory loss of the previous day's new events).

Fig. 1

 1 Fig.1

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Fig. 3

 3 Fig.3

Fig. 4

 4 Fig.4

Table 1 . Duration and percentage of neurons recruited over a 24 hours day

 1

	Effect on synapses	Reinforcement of excitatory and decrease	Reinforcement of inhibitory and decrease
		of inhibitory connections	of excitatory connections
	Period of the day	Wakefulness	REM	LS (Light Sleep)	SWS
	Repartition / day	16 hours	1 h 30	3 h 30	3 h
	% recruitment	15% (6 times less	100%	50%	100% (maximal
		than REM)			as in REM)
	Hours equivalent	2h24	1h30	1h45	3h
	100% recruiting	4h54		4h45

Acknowledgement

Part of this research was funded by the French Research Agency ANR 2010-CORD-013 "Cognilego -From pixels to semantics: a cognitive approach". We greatly thank Martin Meneval for proofreading the manuscript.

Conflict of interest statement

The author declares no conflict of interest associated with this publication.