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Ca2þ-Dependent Hyperpolarization Pathways in Sleep
Homeostasis and Mental Disorders
Shoi Shi and Hiroki R. Ueda*
awake to sleep. In this sense, Process S is anegative feedback system for maintaining a
constant total wake duration (or quality)(Figure 1B), whereas Process C is a feedforward system for synchronizing the internal
states of the brain (and body) with the external
environment. A major focus of modern sleep
studies is to identify the molecular mechanisms involved in Process S.
According to basic control theory, robust
control can be achieved by an integrated
negative feedback loop, in which the integralof the time difference between the current
state (e.g., the current wake duration) and aset point (e.g., a target wake duration) is
negatively fed back into the system[2](Figure 1C). Therefore, Process S might be
represented as an integrated negative feedback system that includes an accumulation
process, although it is still unclear what is
actually accumulated (or recorded) during
wakefulness and how and where thisaccumulation occurs. One of the simplest
realizations of Process S is an integrated system within cells during
the awake state (Figure 1D). In this case, activity-dependentchanges in intracellular processes, including ion concentration,
gene expression, post-translational modiﬁcation, or the degradation of ion channels or pumps are possible candidates for Process
S. Alternatively, Process S might consist of intercellular mechanisms involving different brain regions,[3,4] in which neurotransmitters or other extracellular substances might accumulate
outside cells during an awake state (Figure 1E). In this case, one
possible realization of Process S is the accumulation of
extracellular substances such as sleep-promoting substances(SPSs), whose concentration increases during prolonged wakefulness and decreases during the subsequent recovery sleep.

Although we are beginning to understand the neuronal and biochemical
nature of sleep regulation, questions remain about how sleep is homeostatically regulated. Beyond its importance in basic physiology, understanding
sleep may also shed light on psychiatric and neurodevelopmental disorders.
Recent genetic studies in mammals revealed several non-secretory proteinsthat determine sleep duration. Interestingly, genes identified in these studies
are closely related to psychiatric and neurodevelopmental disorders, suggesting that the sleep-wake cycle shares some common mechanisms with these
disorders. Here we review recent sleep studies, including reverse and forward
genetic studies, from the perspectives of sleep duration and homeostasis. We
then introduce a recent hypothesis for mammalian sleep in which the fastand slow Ca2þ-dependent hyperpolarization pathways are pivotal in generating the SWS firing pattern and regulating sleep homeostasis, respectively.
Finally, we propose that these intracellular pathways are potential therapeutictargets for achieving depolarization/hyperpolarization (D/H) balance in
psychiatric and neurodevelopmental disorders.

1. How Do Animals Implement a Sleep-Wake
Cycle?
To describe the mechanisms of sleep, Alexander Borbely postulated
the two-process model,[1] in which sleep is regulated by “Process C”
and “Process S” (Figure 1A). Process C is determined by circadianclocks, and regulates the daily pattern of sleep (e.g., rodents usually
sleep during the day whereas humans sleep at night), and Process S
regulates the sleep duration per day. This homeostatic Process S
represents the sleep pressure, which increases and decreases during
wakefulness and sleep, respectively, and promotes the transition fromDr. S. Shi, Prof. H. R. Ueda
Department of Systems Pharmacology
Graduate School of Medicine
University of Tokyo
7-3-1 Hongo
Bunkyo-ku, Tokyo 113-0033, Japan
E-mail: uedah-tky@umin.ac.jp

1.1. Is Sleep Homeostasis Regulated by Sleep-Promoting
Substances?

Prof. H. R. Ueda
Laboratory for Synthetic Biology
RIKEN Quantitative Biology Center
1-3 Yamadaoka
Suita, Osaka 565-5241, Japan© 2017 The Authors, BioEssays Published by Wiley Periodical, Inc.
This is an open access article under the terms of the Creative Commons
Attribution License, which permits use, distribution and reproduction inany medium, provided the original work is properly cited.

DOI: 10.1002/bies.201700105

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SPSs were ﬁrst discovered over 100 years ago in the
cerebrospinal ﬂuid (CSF) of sleep-deprived dogs.[5] Thisﬁnding was conﬁrmed by Pappenheimer and colleagues in
1967, who observed that the CSF from a sleep-deprived goat
induced sleep when injected intraventricularly into cats andrats. These experiments suggested that endogenous humoral
substances accumulate during prolonged wakefulness and areimportant drivers of homeostatic sleep pressure.[6] In later
studies, several SPSs were identiﬁed, including cytokines,© 2017 The Authors, BioEssays Published by Wiley Periodical, Incwww.advancedsciencenews.com

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Figure 1. Models for the regulation of sleep-wake cycles. A) The two-process model. The sleep-wake cycle is regulated by Process C and Process S.
Process C regulates the daily pattern of sleep, and Process S regulates the amount of basal sleep/awake duration per day. A prolonged awake state results
in prolonged sleep, called rebound sleep. B) Negative feedback system in the sleep-wake cycle. The sleep-wake cycle can be achieved by a negative
feedback system, in which the awake and sleep states are mutually inhibited by each other. Sleep pressure increases during the awake state, which
promotes sleep. C) Integrated feedback system in the sleep-wake cycle. The sleep-wake cycle can be achieved by an integrated feedback system, in which
the time integration of the awake state negatively feeds back on itself by increasing the sleep pressure. D) The simplest realization of the sleep-wake cycle.
A neuron can hold each state, awake and sleep. The sleep pressure is represented as intracellular properties, which trigger the transition between the twostates. E) Another proposed realization of the sleep-wake cycle. Awake and sleep states are maintained by different populations of neurons. Sleeppressure occurs by the increased concentration of extracellular substances.

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prostaglandin D2 (PGD2), and adenosine.[7,8] Cytokines
regulate the immune system. In addition, several cytokines,
such as interleukin-1 (IL-1) and tumor necrosis factor-alpha(TNFα), whose receptors are present in the brain, can promote
sleep. The administration of each of these cytokines increases
the duration of non-rapid eye movement (NREM) sleep in
mice, and the levels of these cytokines in the brain increase
with prolonged wakefulness, fulﬁlling criteria for Process S.[9]However, knockout (KO) mice of the receptors of thesecytokines show signiﬁcantly but only slightly decreased sleep
duration,[10] suggesting that the sleep-promoting role ofcytokines is not essential for daily sleep-wake cycles.
The injection of either PGD2 or adenosine into the brain induces
sleep,[8,11] and prolonged wakefulness induces elevated concentrations of both molecules in CSF.[12] The adenosine level also increases
in response to glutamatergic stimulation of the basal forebrain(BF).[13] Consistent with this ﬁnding, a lesion of cholinergic neurons
in the BF attenuates the sleep deprivation-induced increase inadenosine, suggesting that adenosine’s main source is localized to theBF.[14] However, adenosine A2A receptor KO mice do not exhibit
signiﬁcant changes in basal sleep duration, but do show a decrease inrebound sleep,[15] indicating that the regulation of sleep duration
involves mechanisms other than the adenosine pathway.

1.2. Genetics in Sleep Research
Recent forward and reverse genetic experiments in ﬂy andmouse identiﬁed various molecules involved in the regulation of
sleep duration, which may shed light on Process S. Forward andreverse genetics are complementary approaches; the former
starts with a phenotype (e.g., a speciﬁc sleep phenotype) andseeks to identify the genotype that causes the phenotype, and thelatter starts with a genotype (e.g., the KO of a speciﬁc gene) andexamines the phenotype caused by the genotype. A successful
example of forward genetics in animal sleep behavior was theisolation of clock mutants: Konopka and Benzer used ethyl
methanesulfonate (EMS) to induce point mutations in the
Drosophila melanogaster genome, and isolated three clock
mutants (independent mutations of per) that showed abnormal
rhythms in eclosion.[16]Forward genetic experiments using EMS in ﬂies also revealed
the ﬁrst sleep mutant with strikingly short sleep duration,
minisleep.[17] The responsible mutation is a loss-of-function
mutation in the voltage-dependent potassium channel alphasubunit (Shaker), which mediates a voltage-activated fastinactivation IA current. The mammalian homologs of Shaker
based on sequence similarity are the alpha subunits of the Kv1,
Kv2, Kv3, and Kv4 potassium channels. Although Kv1.2 KO miceshow a short sleep phenotype, which is not as severe as the
Shaker phenotype in Drosophila melanogaster,[18] Kv3.1 and Kv3.3
double KO mice exhibit a signiﬁcant short-sleep phenotype, andno signiﬁcant rebound response to 6 h of sleep deprivation.[19]These observations suggested that potassium channels might
have an important role in regulating sleep duration and Process
S. This possibility is supported by another striking short-sleep
mutant in the ﬂy, sleepless.[20] The responsible mutation forsleepless is in a glycosylphosphatidylinositol-anchored protein,which has a similar expression pattern to Shaker. In the absence

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of Sleepless, Shaker shows an altered localization, and adecreased current density and kinetics, suggesting that Sleeplessregulates Shaker.[21] Although the detailed molecular mechanism underlying the interaction between shaker and sleepless isstill unknown, recent studies showed that neural excitability is
increased in both mutants and that a neuron-glia interaction via
GABA transaminase is involved in the sleepless phenotype.[21,22]
Thus, these genes may be important for regulating the sleep
duration and Process S.
Reverse genetic experiments have also contributed to sleep
research, especially for validating proposed hypotheses. In theascending reticular activation system (ARAS), a central mechanism of arousal maintenance, reverse genetic studies showedthat the noradrenergic and histaminergic systems are importantfor maintaining arousal; Hdc KO (histamine-deﬁcient) or Dbh
KO (noradrenaline/adrenaline-deﬁcient) mice have an increased
sleep phenotype.[23] Moreover, adenosine receptor (A2AR) KO
mice are insensitive to the wake-promoting effects of caffeine.[24]This result is consistent with a study showing that a genetic
variant in A2AR contributes to individual sensitivity to the wakepromoting effects of caffeine.[25] These studies illustrate thatreverse genetics is a powerful tool for validating the roles ofmolecules, especially when used to test a hypothesis. In thisrespect, reverse genetic experiments can be profoundly powerfulwhen combined with computational biology, which can provide
testable hypotheses for complex systems such as the sleep-wakecycle.

1.3. What Have Computational Studies Brought to Sleep
Research? – Recent Findings via the Averaged-Neuron
Model
1.3.1. Recapitulating Oscillatory Patterns During Sleep
Computational biology is playing an increasing role in biology
studies. For example, a computational model can be used toreveal the mechanism for a complex biological phenomenon bypresenting it as a system with a simple set of components. Oneof the most elegant examples is Hodgkin and Huxley’s model forthe action potential in neurons: a model combining simple
nonlinear differential equations for the membrane potential andion currents successfully described how action potentials inneurons are initiated and propagated.[26]Computational models have also contributed to sleep
studies. During sleep, EEG scans exhibit typical oscillatory
patterns (spindle oscillation, delta oscillation, and slow-wave
oscillation), which result from the integration of various
dynamic neuronal membrane potentials in the cortex(Figure 2A and B). Intracellular and local ﬁeld potential
recordings in vivo and in vitro together with computationalmodels have begun to elucidate the molecular and cellularmechanisms underlying these oscillations. A spindle oscillation of the EEG consists of 7–14 Hz waves that recur
periodically with a rhythm slower than 0.1–0.2 Hz, and are
typically observed during the early stage of NREM sleep.
Intracellular and local ﬁeld potential recordings in vivo and invitro indicated that the minimal unit for generating a spindle© 2017 The Authors, BioEssays Published by Wiley Periodical, Incwww.advancedsciencenews.com

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Figure 2. Typical neuronal activities during the sleep-wake cycle. A) Typical EEG patterns during the NREM sleep and the awake state in mice. The NREM
sleep state is characterized by high-amplitude and low-frequency fluctuations on EEG scans (left). The awake state is characterized by low-amplitude andhigh-frequency fluctuations on EEG scans (right). B) Typical intracellular firing patterns in a cortical neuron during slow wave oscillation (left) and delta
oscillation (middle). A typical intracellular firing pattern in a reticular thalamic neuron during spindle oscillation (right).

oscillation is the reticular thalamic (RT) neuron itself [27] and/or
the interactions between RT neurons and thalamocortical (TC)neurons in the thalamus.[28] In particular, the latter hypothesis
has been computationally modeled,[29] and this model showsthat a burst ﬁring of RT neurons decreases the membranepotential of TC neurons via GABAA and GABAB, which
activates a low-threshold T-type calcium current, resulting in
the burst ﬁring of TC neurons, and ﬁnally, TC neurons induce
the burst ﬁring of RT neurons via AMPA.
Another well-known EEG feature during sleep is the delta
oscillation. Delta oscillations (1–4 Hz) are recorded in humanand animal models during sleep, and have a thalamic origin.[30]A thalamic delta oscillation appears to be generated by a cellintrinsic oscillator in TC neurons involving a low-threshold Ttype calcium current (It) and a hyperpolarization-activated cation
current (Ih).[31] According to a computational model proposed fora thalamic delta oscillation,[32] the after-hyperpolarization of It
induces Ih, which depolarizes the membrane potential and inturn re-activates It to generate a periodic membrane potential.
Compared to the spindle and thalamic delta oscillations, lessis known about the molecular and cellular mechanisms
underlying a slow-wave oscillation in the EEG (<1 Hz), a
dominant oscillation seen during slow-wave sleep but not during

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REM sleep and awake state. During slow-wave oscillations,cortical neurons exhibit a typical membrane-potential pattern(slow-wave-sleep ﬁring pattern, SWS ﬁring pattern) characterized by alternating depolarized bursting and hyperpolarizedsilent phases.[33,34] Several computational models have been
constructed to elucidate the molecular or cellular mechanism
underlying the SWS ﬁring pattern.[35–38] These neural-networkmodels are based on the TC neural network, and successfullyreconstruct the SWS ﬁring pattern and recapitulate themembrane-potential changes of cortical and thalamic neurons
during slow-wave oscillations. In short, these studies indicatethat the transition from bursting phase to silent phase isfacilitated by 1) the enhancement of Ca2þ- and Naþ-dependentKþ channels in pyramidal neurons[36–38], or 2) inhibition of theexcitatory synaptic current between pyramidal neurons,[37] or 3)
the enhancement of feedback inhibition among pyramidal
neurons and interneurons.[38] However, these simulated neuralnetwork models usually involve a huge parameter space, so thenumber and type of parameter sets that can generate slow-wave
oscillation or the SWS ﬁring pattern cannot be identiﬁedcomprehensively. Therefore, a simple computational model isrequired to elucidate the mechanisms underlying the SWS ﬁring
pattern.

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1.3.2. The Averaged-Neuron Model
To simplify these neural-network models, Ueda and colleagues
performed mean-ﬁeld approximations of a homogeneous
population of neurons to construct an “averaged-neuron”(AN) model.[39] The ion ﬂuxes regulating the averaged neuron
are as follows: Naþ currents are mediated by AMPA receptors(IAMPA), and Ca2þ currents are mediated by NMDA receptors(INMDA). The neuron also contains Cl currents mediated by
GABAA receptors, IGABA as extrinsic currents. Depolarizing
Naþ currents are mediated by voltage-gated (INa) or persistent(INaP) Naþ channels, Ca2þ currents and/or ﬂux are mediated byvoltage-gated Ca2þ channels (ICa) and Ca2þ pumps/exchangers
with a time constant (τCa), and Kþ currents are mediated byseveral types of Kþ channels, including voltage-gated (IK), leak(IL), fast A-type (IA), inwardly rectifying (IAR), slowly inactivating (IKS), and Ca2þ-dependent (IKCa) Kþ channels as intrinsic
currents. By searching nearly 20,000,000 randomly generated
parameter sets, they identiﬁed 1113 parameter sets thatgenerate SWS ﬁring patterns with alternating bursting andsilent phases, suggesting that SWS ﬁring patterns can begenerated by a homogeneous population of neurons. Using
these parameter sets, they also conducted the bifurcation
analysis (i.e., asking whether a gradual change in eachparameter value induces a sleep to wakefulness transition) of
the conductance of each intrinsic and extrinsic current and of
the Ca2þ efﬂux rate, based on the idea that prolonged sleepchanges the quality or quantity of these channels or pumps,
leading to the transition from sleep to wakefulness. This
analysis revealed that decreasing the conductance through the
NMDAR (gNMDA), Cav channels (gCa), KCa channels (gKCa), and/or reducing the time constant (τCa) of Ca2þ efﬂux mediated by
PMCA caused the transition from SWS to awake ﬁring
patterns. In addition, parameter searches under the KO ofindividual or multiple channels (by assuming the conductanceequals 0) revealed that the Ca2þ inﬂux is redundantly mediatedby Cav channels and that the NMDAR activates KCa channels to
induce the SWS ﬁring patterns.
According to Tatsuki et al., the putative mechanism ofgenerating the SWS ﬁring pattern is as follows (Figure 3A): 1)
The bursting phase of the SWS ﬁring pattern is initiated by Ca2þentry mainly through the NMDA receptor (NMDAR) andvoltage-gated Ca2þ channels (Cav channels). 2) The intracellularCa2þ concentration is determined by the ratio of the Ca2þ inﬂux
and efﬂux through the NMDAR and Cav channels or the plasmamembrane Ca2þ ATPases (PMCA), respectively. 3) The transition to the silent phase occurs when the Ca2þ-dependent Kþchannels (KCa channels) is activated, which requires a certain
level of intracellular Ca2þ concentration. 4) The activation of KCachannels induces a Kþ efﬂux-mediated depolarization of themembrane potential and generates the silent state. Because themajor difference between the cortical ﬁring patterns during
NREM sleep and other states,[34] awake and REM sleep, iswhether the silent phase exists or not, this Ca2þ-dependent Kþ
efﬂux-mediated depolarization might underlie the mechanismof generating the SWS ﬁring pattern. Building upon this putative
mechanism, the hypothesis that Ca2þ-dependent hyperpolarization pathway plays a role in generating the SWS ﬁring pattern
was proposed.

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Recent studies showed that extracellular environment (e.g.,
extracellular ion concertation or astroglial networks) might
contribute to the regulation of the sleep-wake cycle.[40,41]
According to Ding et al., the extracellular ion concentrations
alter in response to sleep or awake state change in vivo and theextracellular Kþ concentration is relatively low during sleep
and high during awake state. Interestingly, this extracellularKþ bias between sleep and awake state might be consistent
with the hypothesis that the Ca2þ-dependent hyperpolarization pathway plays a role in generating the SWS ﬁring pattern.
Because the ratio between the extracellular and intracellularKþ concentrations affects the relative tendency of Kþ ﬂux, therelatively low extracellular Kþ concentration during sleep
could support Kþ efﬂux through KCa channels, and hence
generate the silent phase. Consistently, the extracellular Ca2þconcentration is relatively high during sleep,[41] which could
support Ca2þ inﬂux through Cav channel and NMDAR andhence generate the silent phase via activating KCa channels
during sleep. However, there is no obvious evidence tovalidate that the intracellular Ca2þ concentration during the
SWS ﬁring pattern is higher than the awake one. Further Ca2þimaging studies with high time resolution, which is enough tocapture the dynamics of the SWS ﬁring pattern, will clarify the
relationship between the intracellular Ca2þ concentration and
the SWS ﬁring pattern.

2. Role of Fast and Slow Ca2þ-Dependent
Hyperpolarization Pathways in the Regulationof Sleep Duration
The AN model and its comprehensive bifurcation analyses
predicted that a fast Ca2þ-dependent hyperpolarization pathway
consisting of ion channels (NMDAR, Cav, and KCa channels) andpumps (PMCA) that directly generate relatively fast dynamics
like the SWS ﬁring pattern, plays a central role in the regulationof sleep duration (probably NREM sleep duration), where 1)
impairment of ion channels involved in the Ca2þ-dependent
hyperpolarization pathway will increase the awake duration and2) impairment of Ca2þ-pumps/exchangers will increase thesleep duration (probably NREM sleep duration).[39] On the other
hand, the AN model also predicted that higher hyperpolarization
activity (i.e., sleep state) can be triggered via Ca2þ inﬂux by slowly
activating a slow Ca2þ-dependent pathway, which consists ofmolecules, such as calcium/calmodulin-dependent kinase II(CaMKII) family members, that might be able to modulate thecomponents in the fast pathway and hence indirectly modulate
the ﬁring patterns.

2.1. Fast Ca2þ- Dependent Hyperpolarization Pathway in
the Regulation of Sleep Duration
To test their predictions about the fast Ca2þ-dependent
hyperpolarization pathway, Ueda and colleagues conducted acomprehensive in vivo KO study in which they produced andanalyzed the phenotypes of 26 KO mice of KCa channels, Cav
channels, NMDARs, and PMCAs. Their results revealed that the© 2017 The Authors, BioEssays Published by Wiley Periodical, Incwww.advancedsciencenews.com

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Figure 3. The role of Ca2þ-dependent hyperpolarization pathway in fast and slow dynamics. A) Schematic diagram of the role of Ca2þ-dependent
hyperpolarization pathway in generating the SWS firing pattern. Predominant Ca2þ influx via NMDARs and Cav channels generates the bursting state of
the SWS firing pattern (top). Kþ efflux via activated KCa channels generates the down state of the SWS firing pattern (middle). Predominant Ca2þ efflux
generates the awake firing patterns (bottom). B) Hypothetical mechanism for the possible interactions between the slow and fast Ca2þ-dependent
hyperpolarization pathways in sleep homeostasis. During awake state, Ca2þ influx activates CaMKIIα/β (a component of the slow Ca2þ-dependent
hyperpolarization pathway) quantitatively and/or qualitatively via increasing phosphorylated CaMKIIα/β (left). These phosphorylated CaMKIIα/β modify
molecules involved in the fast Ca2þ-dependent hyperpolarization pathway via phosphorylation (middle), which alters the properties (e.g., conductance)of the molecules and elicit the transition from awake state to sleep state (right).

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KO mice of Ca2þ-dependent Kþ channels [SK2 (Kcnn2) and SK3(Kcnn3)], voltage-gated Ca2þ channels [Cav3.1 (Cacna1g) andCav3.2 (Cacna1h)], or NMDAR subunit (Nr3a) exhibit asigniﬁcantly decreased sleep duration, whereas the KO mouseof PMCA (Atp2b3) exhibits a signiﬁcantly increased sleep
duration.[39,42] Furthermore, the acute or chronic pharmacological inhibition of NMDARs (possibly Nr1/Nr2b) in glutaminergic
and GABAergic neurons in WT mice results in a short-sleep
phenotype, conﬁrming the contribution of Nr1 or Nr2b, the KOof which is embryonically lethal, in sleep-duration regulation.[39]In addition, a whole-brain imaging study of neural activity atsingle-cell resolution followed by an in-situ hybridization
analysis of brain slices revealed that inhibiting NMDARs(possibly Nr1/Nr2b) in glutaminergic and GABAergic neurons
directly induces neural excitability in the cortex.[39] These results
supported a model in which the sleep duration in mammals isregulated by a Ca2þ-dependent hyperpolarization pathway, inwhich Ca2þ inﬂux through voltage-dependent Ca2þ channels
and NMDARs activates Ca2þ-dependent potassium channels to
induce the SWS ﬁring pattern.
2.2. Slow Ca2þ- Dependent Hyperpolarization Pathway in
the Regulation of Sleep Duration
The bifurcation analysis of the AN model predicted that thefast Ca2þ-dependent hyperpolarization pathway can betargeted by the homeostatic Process S. The molecularmechanism of Process S also presumably senses the awake
and/or slow-wave-sleep states (e.g., through the concentrationor temporal patterns of Ca2þ) to allow reversible transitions
between the SWS and awake ﬁring patterns. For this Ca2þsensing pathway, Ueda and colleagues focused on the major
protein kinase in the brain, calcium/calmodulin-dependent
protein kinase type II (CaMKII),[39] which can sense Ca2þ. To
test their prediction about the slow Ca2þ-dependent hyperpolarization pathway, Ueda and colleagues conducted an in vivo
KO study of the CaMKII family. The production andphenotype analysis of four KO mice of the CaMKII family
revealed that CaMKIIα (Camk2a) and CaMKIIβ (Camk2b) KOmice exhibit a signiﬁcantly decreased sleep duration.[39] These
results indicated that higher hyperpolarization activity, suchas the NREM sleep state, can be induced by Ca2þ inﬂux byactivating a Ca2þ-dependent pathway mediated by CaMKIIα/β. On the other hand, it is reported that the acutepharmacological inhibition of CaMKII in the pedunculopontine tegmental nucleus (PPT) or the dorsal raphe nucleus(DRN), which consists of wake-promoting neurons,[4] decrease awake. Thus, the brain-region-speciﬁc (e.g., cortexspeciﬁc) down/up-regulation of CaMKII as well as the slow
Ca2þ-dependent hyperpolarization pathway will be required tovalidate their role in sleep. The fast Ca2þ-dependent
hyperpolarization pathway is initiated by Ca2þ inﬂux via
Cav channels and/or NMDARs, followed by the activation of
KCa channels and Ca2þ efﬂux through PMCAs. The slow Ca2þdependent hyperpolarization pathway is initiated by theactivation of CaMKII, which enhances the fast Ca2þdependent hyperpolarization pathway to induce cell hyperpolarization. Thus, the fast and slow Ca2þ-dependent

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hyperpolarization pathways, the separate pathways that bothuse Ca2þ, could underlie the mechanism of generating the
SWS ﬁring pattern and sleep homeostasis, respectively.
However, detailed molecular interactions between the fastand slow Ca2þ-dependent hyperpolarization pathways remain
to be elucidated.

3. Role of Fast and Slow Ca2þ- Dependent
Hyperpolarization Pathways in Sleep
Homeostasis
Although the above results suggested that fast and slow Ca2þdependent hyperpolarization pathways are involved in theregulation of sleep duration, it remains unclear how the fastCa2þ-dependent hyperpolarization pathway, including KCa
channels [SK2 (Kcnn2) and SK3 (Kcnn3)], Cav channels[Cav3.1 (Cacna1g) and Cav3.2 (Cacna1h)], MK-801-targeted
NMDAR subunits (Nr1 and Nr2b), and Ca2þ pumps (Atp2b3),
or the slow Ca2þ-dependent hyperpolarization pathway initiatedby CaMKII [CaMKIIα (Camk2a) and CaMKIIβ (Camk2b)], affects
sleep homeostasis. One possibility is that Process S can be
represented directly as the quality or quantity of molecules
involved in the fast and slow Ca2þ-dependent hyperpolarization
pathways. In this case, Process S is identiﬁed as an activitydependent effect (e.g., phosphorylation) and/or a mechanism
affecting the quantity (e.g., translation) of target molecules(Figure 3B). Given the increasing evidence for the posttranslational modiﬁcation of KCa channels,[43] Cav channels,[44]and NMDARs,[45] one of the plausible execution mechanisms ofProcess S is activity-dependent protein modiﬁcations (e.g.,
phosphorylation or dephosphorylation) of components of thefast and slow Ca2þ-dependent hyperpolarization pathways. The
ﬁnding that the impairment of CaMKIIα (Camk2a) and
CaMKIIβ (Camk2b), which are well-known to bind and modify
Cav channels and NMDARs, decreases sleep duration may
support this mechanism. Interestingly, a recent forward genetic
study identiﬁed a gain-of-function mutation in the Sik3 protein
kinase gene that causes a profound increase in sleep duration[46];this ﬁnding also supports the idea that Process S is driven by
activity-dependent protein modiﬁcations. Building on this idea,
the intracellular model of sleep-wake-cycle regulation(Figure 1D) can be realized by interactions between fast andslow Ca2þ-dependent hyperpolarization pathways.
The two-process model assumes that the mechanisms forregulating the basal amount of sleep and response to sleep
deprivation are tightly coupled and difﬁcult to separate.
However, in more general homeostatic systems, a mechanism
determining a basal set point can be independent from a
responsive mechanism to perturbation from the set point. For
example, a mutant with altered set point (i.e., a short/longsleeper mutant) could exhibit a normal response to theperturbation (i.e., a normal response to sleep deprivation)
whereas a mutant with normal set point (i.e., a mutant withnormal daily sleep duration) could exhibit an abnormal responseto the perturbation (i.e., an abnormal response to sleep
deprivation). In other words, the complementary Process S,
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daily sleep duration. In fact, a recent neural circuit screen in
Drosophila revealed that a subset of neurons generates sleep
pressure; the neurons respond to prolonged wakefulness, andtheir inhibition eliminates the rebound sleep after sleep
deprivation, while the basal sleep duration is unaffected.[47]Therefore, one possible mechanism for the complementary
Process S is that the amount of SPSs or the neural activity of
speciﬁc neurons integrates prolonged wakefulness with thebasal wake duration (or insufﬁcient sleep amount with the basal
sleep duration) and then promotes sleep (Figure 1E). An
important remaining challenge is to discover how such
extracellular signaling mechanisms can affect fast and slow
Ca2þ-dependent hyperpolarization pathways to transiently
regulate sleep duration.

4. Role of Fast and Slow Ca2þ- Dependent
Hyperpolarization Pathways in Sleep-Wake
Cycle
One interesting and remaining question is how the transition
between sleep and awake state is regulated. As discussed, thetransition from awake state to sleep might be driven by theregulation of fast Ca2þ-dependent hyperpolarization pathway via
the slow pathway; the increase in quality or quantity of thephosphorylated CaMKII activates the fast Ca2þ-dependent
hyperpolarization pathway, which drives the transition fromawake ﬁring pattern to the SWS ﬁring pattern, and hence awake
state to sleep. In this context, it might be reasonable to assume
that the transition from sleep to awake state is regulated bydown-regulating the fast Ca2þ-dependent hyperpolarization
pathway. In other words, the increased quality or quantity ofthe phosphorylated CaMKII and the activity of the fast Ca2þdependent hyperpolarization pathway should be decreased
during sleep via translational or post-translational mechanisms(e.g., dephosphorylation by phosphatase or natural turn-over ofphosphorylated proteins). Since the sleep-related phosphatase
has not been discovered in mammals, further studies will beneeded to understand phosphorylation-mediated sleep-wakecycle regulation.
To summarize the above discussion, the simplest mechanismof the sleep-wake cycle may be as follows: During the awake
state, the quality or quantity of phosphorylated CaMKII will
increase in neurons (probably cortical neurons). CaMKII
activates the components of the fast Ca2þ-dependent hyperpolarization pathway via modifying the conductance of components by translational or post-translational mechanisms. This
activation of the fast Ca2þ-dependent hyperpolarization pathway
induces the SWS ﬁring pattern in cortical neurons, the slowwave oscillation in the cortex, and hence sleep. On the other
hand, during the sleep state, the quality or quantity of thephosphorylated CaMKII and the activity of the fast Ca2þdependent hyperpolarization pathway will decrease via translational or post-translational mechanisms (e.g., dephosphorylationby phosphatase or natural turn-over of phosphorylated proteins),
which prevents neurons to continue the SWS ﬁring pattern aswell as the cortex to continue the slow-wave oscillation andinduces the transition from sleep to awake state. In this sense,
the slow pathway (i.e., the change of quality or quantity of the

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phosphorylated CaMKII) regulates the fast pathway to achieve
sleep homeostasis.

5. Role of Ca2þ- Dependent Hyperpolarization
Pathways in Mental Disorders
Sleep disorders are major complications of psychiatric disorders
such as schizophrenia,[48] bipolar disorder,[49] and major
depressive disorders.[50] It also accompanies neurodevelopmental disorders such as autism spectrum disorders (ASD).[51]Indeed, patients with schizophrenia are reported to exhibit
longer sleep latency and increased sleep duration during thedaytime.[52] Patients with bipolar disorder are also reported to
exhibit longer sleep latency.[53] It is unclear whether there is acausal relationship between sleep disorders and psychiatric orneurodevelopmental disorders. However, it is reasonable toassume that there is a common molecular mechanism among
sleep disorders and psychiatric and neurodevelopmental
disorders because of a high complication rate among these
disorders. In fact, Ca2þ-dependent hyperpolarization pathways
appear to play important roles in psychiatric and neurodevelopmental disorders. For example, a genome-wide association study (GWAS) revealed a correlation between some key
molecules in the Ca2þ-dependent hyperpolarization pathways
and psychiatric disorders, such as schizophrenia, bipolar
disorder, and major depressive disorders, and neurodevelopmental disorders such as ASD.[54–58] Thus, evidence suggeststhat Ca2þ-dependent hyperpolarization pathways are involved in
psychiatric and neurodevelopmental disorders, and therefore,
Ca2þ-dependent hyperpolarization pathways are potential drug
targets for psychiatric and neurodevelopmental disorders(Figure 4A).
5.1. Ca2þ Influx via Voltage-Gated Calcium Channels in
Mental Disorders
Cav channels are important conveyors of Ca2þ inﬂux in neurons.
A correlation between single nucleotide polymorphisms (SNPs)
in calcium-channel genes and psychiatric disorders has beenreported.[56] In particular, Cav1.2 (CACNA1C) has been
repeatedly reported to be associated with various psychiatricdisorders, including schizophrenia,[57,59,60] bipolar disorders,[54,55,61] and major depressive disorders.[60] In addition, a
study comparing the whole genome sequences of healthy versus
schizophrenic individuals revealed that rare (less than 1 in
10,000) alleles in several calcium channels [e.g., Cav2.2(CACNA1B), Cav1.2 (CACNA1C), and Cav3.2 (CACNA1H)]
were enriched in the schizophrenia group[62] [e.g., two point
mutations in Cav1.2 (CACNA1C) and one deletion in Cav3.2(CACNA1H)]. In particular, one mutation in Cav1.2 (CACNA1C)
converts a glutamine residue to a stop codon, indicating that it isa loss-of-function mutation. Interestingly, infants who have the
CACNA1C variant rs4765913, rs4765914, or rs2239063 that isreported to have signiﬁcant association with bipolar disorder or
schizophrenia,[55,56] exhibited longer sleep latency.[63] Indeed,patients with schizophrenia or bipolar disorder both exhibited
longer sleep latency, suggesting that CACNA1C might be© 2017 The Authors, BioEssays Published by Wiley Periodical, Incwww.advancedsciencenews.com

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Figure 4. Slow and fast Ca2þ-dependent hyperpolarization pathways in mental disorders. A) Schematic diagram of the role of Ca2þ-dependent
hyperpolarization pathways in psychiatric and neurodevelopmental disorders. Lines of different colors represent reported correlations between eachmolecule and each psychiatric and neurodevelopmental disorders. B) Schematic diagram of the intracellular depolarization/hyperpolarization (D/H)
balance model. A single neuron holds each state, depolarization and hyperpolarization, whose balance is maintained appropriately in normal conditions,but impaired in psychiatric and neurodevelopmental disorders. C) Schematic diagram of the circuit-level excitatory/inhibitory (E/I) balance model.
Excitatory and inhibitory neurons comprise neural circuits, whose balance is maintained appropriately in normal conditions, but impaired in psychiatricand neurodevelopmental disorders.

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associated with both sleep and psychiatric disorders.[52,53] These
results suggest that an impairment of voltage-gated calcium
channels and hence an impairment of Ca2þ-dependent
hyperpolarization pathways may contribute to schizophrenia.
Several calcium channels are also associated with ASD [e.g.,
Cav1.2 (CACNA1C), Cav1.3 (CACNA1D), Cav3.1 (CACNA1G),
Cav3.2 (CACNA1H), and Cav3.3 (CACNA1I)].[64] Interestingly, awhole-genome sequencing (WGS) study in families with ASD
detected a rare mutation in Cav1.2 (CACNA1C) (R1522Q).[65]Another ASD-associated point mutation in Cav1.2 (CACNA1C)
is G406R, which has also been identiﬁed as the causal mutationof Timothy syndrome,[66] a disorder characterized by multiorgan
dysfunction, including lethal arrhythmias, the webbing ofﬁngers and toes, congenital heart disease, immune deﬁciency,
intermittent hypoglycemia, cognitive abnormalities, and ASD.
This mutation results in a prolonged inward Ca2þ current
through Cav1.2 (CACNA1C), suggesting that the molecularproperties of Cav1.2 (CACNA1C) play a role in in ASD.[66]Consistent with this possibility, a heterozygous knock-in (KI) of
this human mutation into mice results in ASD-like behavior.[67]These ﬁndings suggest that a dysfunction of voltage-gatedcalcium channels and hence Ca2þ-dependent hyperpolarization
pathways may play a role in ASD.
5.2. Ca2þ Influx via NMDARs in Mental Disorders
NMDARs also contribute to Ca2þ inﬂux in neurons and areassociated with psychiatric disorders. Ketamine and phencyclidine (PCP), noncompetitive antagonists for NMDARs,[68] can
induce psychotogenic effects.[69] PCP at plasma concentrations
that block the NMDAR can induce positive, negative, andcognitive symptoms associated with schizophrenia.[70] Similarly,
ketamine can induce positive, negative, and cognitive schizophrenia symptoms when administered to healthy volunteers.[71]Interestingly, these effects of PCP and ketamine could not be
observed in the neonatal rat.[72] Furthermore, patients withencephalitis associated with antibodies against NMDARs exhibit
positive, negative, and cognitive schizophrenia symptoms.[73]Interestingly, a GWAS also revealed that the NMDAR subunits
Nr3a and Nr3b, whose KO mice exhibit a short-sleep phenotype,are associated with schizophrenia.[74] On the other hand, theinhibitor of glycine transporter, which results in NMDAR
activation, exhibits signiﬁcant therapeutic effects on schizophrenia symptoms.[75] Consistent with these results in humans, PCP
and MK-801, a more speciﬁc inhibitor of NMDARs, can induce
positive-, negative-, and cognitive-symptom-like phenotypes inanimals.[76] In addition, mice with reduced expression of the
NMDAR subunit (Nr1) display the positive-, negative-, andcognitive-symptom-like phenotypes related to schizophrenia.[77]These results indicate that NMDAR dysfunction and hence theimpairment of Ca2þ-dependent hyperpolarization pathways may
play a role in schizophrenia.
In addition to their relationship with schizophrenia,
NMDARs have been implicated as a potential drug target for
major depressive disorders. For example, ketamine, an
NMDAR antagonist, can rapidly improve the symptoms ofmajor depressive disorders.[78] Consistent with these clinicalresults, ketamine and MK-801 can rapidly trigger anti-

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depressant effects in animals.[79] These ﬁndings suggest thatan enhancement of Ca2þ-dependent hyperpolarization pathways, which can be treated by blocking NMDARs, may be
associated with some major depressive disorders.
In addition to their involvement in psychiatric disorders,
NMDARs are also associated with ASD. Genome sequencing of
NMDARs in patients with ASD revealed de novo mutations in
the NR2B gene.[80] SNP analysis for NMDARs also revealed asigniﬁcant association between ASD and haplotypes in the
NR2B gene.[81] Importantly, clinical studies suggested that thepharmacological enhancement of NDMA receptors can improve
ASD symptoms; for example, D-cycloserin, an agonist for
NMDARs, signiﬁcantly improves symptoms, such as social
withdrawal and repetitive behaviors in ASD patients,[82]suggesting that NMDARs are impaired in some types of ASD.
In addition, an enhancement of NMDARs may be associatedwith other types of ASD, given that memantine, an antagonist
for NMDARs, and its analog amantadine can improve ASD
symptoms in some cases.[83]Consistent with the results of clinical studies, a role of
NMDARs in ASD-related symptoms has also been demonstrated
in animals. For example, KO mice for Neuregilin-1 exhibit
decreased NMDAR function,[84,85] because Neuregilin-1 directlyinteracts with NMDARs and promotes their localization tosynapses. Interestingly, Neuregilin-1 homozygous mutants
exhibit increased self-grooming behavior, which represents
ASD-related symptoms in mice. Notably, this symptom isquickly normalized in about 30 min by injecting D-cycloserin.[84]In addition, some ASD patients have a mutation in the Shank2
gene, in which exons 6 and 7 are missing.[86] Shank2
homozygous mutant mice exhibit decreased NMDAR function
and social deﬁcits, which are quickly abolished by the systemic
administration of D-cycloserin.[87]In contrast to Neuregilin-1 or Shank2 mutant mice, IPSp53
homozygous KO mice exhibit increased NMDAR function andimpaired social interaction.[88] Memantine, an antagonist of
NMDARs, normalizes the NMDAR function and social
interaction in these mice. Collectively, these results suggestthat the dysfunction (both the enhancement and the
impairment) of NMDARs[89] and hence the dysfunction of
Ca2þ-dependent hyperpolarization pathways may be associated with ASD.

5.3. KCa Channels in Mental Disorders
In Ca2þ-dependent hyperpolarization pathways, Ca2þ inﬂux
via Cav channels and/or NMDARs activates KCa channels,
which are also associated with mental disorders. SK3 (Kcnn3),
a Ca2þ-dependent Kþ channel, contains a CAG repeat regionin its ﬁrst exon that is highly conserved among species.
Several studies have shown that an increased length of thisregion is associated with psychiatric disorders (e.g., anorexia
nervosa, migraine, ataxia, epilepsy, and schizophrenia).[90,91]
The longer CAG repeat decreases SK3 (Kcnn3) channel
conductance.[92] With respect to Ca2þ-dependent hyperpolarization pathways, this decreased channel conductance of SK3(Kcnn3) could increase neuronal excitability, as observed inmice treated with an NMDAR inhibitor.[39] Although the© 2017 The Authors, BioEssays Published by Wiley Periodical, Incwww.advancedsciencenews.com

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correlation between CAG-repeat length and the developmentof schizophrenia is still controversial,[90,92,93] it will beinteresting to determine whether the impairment of Ca2þdependent hyperpolarization pathways caused by a decreased
channel conductance of SK3 (Kcnn3) due to longer CAG
repeats can be associated with the development and/or
symptom variations of mental disorders such as
schizophrenia.
5.4. Ca2þ/ Calmodulin-Dependent Protein Kinase II in
Mental Disorders
In the Ca2þ-dependent hyperpolarization pathways, the Ca2þinﬂux via Cav channels and/or NMDARs also activatesdownstream Ca2þ-dependent intracellular signaling pathways,
such as those involving CaMKII protein kinases. Interestingly,
the potential involvement of CAMK2 in psychiatric disorders
has been shown in human clinical studies, in which changes in
CAMK2 gene expression were found in bipolar disorders,[94]schizophrenia,[95,96] and major depressive disorders.[95,97] In
addition, the potential involvement of CAMK2 in neurodevelopmental disorders was indicated by the identiﬁcation of ade novo CAMK2A missense mutation in an ASD proband in
the Simons Simplex Collection.[98] In animal studies, roles of
CaMKII in major depressive disorders and schizophrenia havebeen well documented.[99] In a rat model for major depressive
disorders, CaMKIIβ is signiﬁcantly increased in the habenula,[100] and this increase is abolished by imipramine, anantidepressant drug. CaMKIIβ overexpression in the habenula
results in depression-like behaviors in rats and mice,[100]whereas Camk2b KO mice have an antidepressant phenotype,suggesting that CaMKIIβ is involved in major depressive
disorders and that CaMKIIβ might serve as a potential drug
target for major depressive disorders. Interestingly, CaMKIIαalso plays a role in major depressive disorders in a different
brain region. The antidepressant effects of ﬂuoxetine in mice
are abolished by overexpressing CaMKII in the nucleus
accumbens (NAc), whereas the inhibition of NAc CaMKII
activity mimics the ﬂuoxetine-treatment phenotype.[99] Basedon the short-sleep phenotype of Camk2a and Camk2b KO mice,
CaMKII might be involved in decreasing neuronal excitability.
With respect to the Ca2þ-dependent hyperpolarization pathways, CaMKII inhibition might enhance neural excitability,
which could provide resistance to major depressive disorders.
In animal studies of schizophrenia, Camk2a heterozygous KO
mice exhibited behavioral phenotypes, such as working
memory deﬁcits, social withdrawal, and hyperactivity, which
are observed in schizophrenia patients.[101] In addition, Camk2a
heterozygous KO mice have an immature dentate gyrus (DG),
which is also reported in schizophrenia patients.[102] Interestingly, forebrain-speciﬁc KO mice of Ppp3r1, a regulatory
subunit of the Ca2þ-dependent phosphatase Calcineurin,
exhibit hyperactivity and have an immature dentate gyrus.[103]With respect to the Ca2þ-dependent hyperpolarization pathways, impairments of CaMKII and other molecules, such as
Calcineurin, might inhibit the Ca2þ-dependent hyperpolarization via phosphorylated/dephosphorylated regulations and leadto enhanced neural excitability, which could explain the

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hyperactivity and other clinical phenotypes observed inschizophrenia patients.
Animal studies for neurodevelopmental disorders haveindirectly suggested the roles for CaMKII.[99] For example,
fragile X syndrome, which is caused by a lack of the fragile X
mental retardation protein (FMRP),[104] leads to an autistic
phenotype with a severe cognitive disability. FMRP is an mRNAbinding protein[105] that is important for translational control in
dendritic spines.[106] In dendritic spines, the translation of
CaMKIIα mRNA is controlled by neural activities,[107] and FMRP
targets many mRNAs, including the CaMKIIα mRNA, andsuppresses their translation.[108] Therefore, the synapses of
FMRP KO mice exhibit upregulated CaMKIIα protein [108].
Another example is spinocerebellar ataxia type 2, caused by amutation of the ataxin-2 gene,[109] which codes for anothermRNA-binding protein.[110] Interestingly, a ﬂy study demonstrated that Ataxin-2 can also bind to CaMKIIα mRNA, andnegatively regulates its translation together with FMRP.[111]Therefore, FMRP KO ﬂies exhibited upregulated CaMKII
translational reporter activity.[111] On the other hand, a reduced
CaMKIIα level and/or activity is also associated with neurodevelopmental disorders.[99] For example, Rett syndrome ispartly caused by a mutation of methyl-CpG binding protein 2(MeCP2),[112] which is important for the epigenetic control ofgenes. A mutation of MeCP2 results in a decrease in CaMKIIαprotein.[113] Another example is Angelman syndrome, which is
caused by a mutation of the ubiquitin ligase E3A gene
(Ube3a).[114] Ube3a KO mice exhibit increased phosphorylationof T305/T306 of CaMKIIα, which results in decreased CaMKII
activity.[115] Crossing Ube3a KO mice with T305V/T306A
CaMKIIα heterozygous mutant mice rescues the Angelmansyndrome-like phenotypes of Ube3a KO mice.[116] Collectively,
these results suggest that a dysfunction (either increase or
decrease) of CaMKIIα may be associated with the clinicalphenotypes observed in patients with neurodevelopmental
disorders.

6. Conclusions and Perspectives: Ca2þDependent Hyperpolarization Pathways as
Potential Therapeutic Targets to Achieve
Depolarization/Hyperpolarization Balance(D/H Balance) in Mental Disorders
In the previous sections, we discussed the Ca2þ-dependent
hyperpolarization pathways as a plausible core mechanism forsleep homeostasis, and described the close association of theseCa2þ-dependent hyperpolarization pathways with psychiatricand neurodevelopmental disorders. In this section, we will
discuss the potential of these hyperpolarization pathways as drug
targets for psychiatric and neurodevelopmental disorders. As
discussed in the previous sections, the Ca2þ-dependent
hyperpolarization pathways appear to be impaired in some
psychiatric disorders, such as schizophrenia, bipolar disorders,and some neurodevelopmental disorders, indicating that theappropriate balance between depolarization and hyperpolarization of neurons (termed here as “D/H balance”) is impaired inthese disorders. In this context, the goal of the pharmacologicalregulation of Ca2þ-dependent hyperpolarization pathways is to© 2017 The Authors, BioEssays Published by Wiley Periodical, Incwww.advancedsciencenews.com

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restore the imbalanced D/H balance to treat psychiatric andneurodevelopmental disorders (Figure 4B).
A similar but different concept, an excitation/inhibition
balance (E/I balance) of circuits, is a well-known hypothesis inneuroscience that emphasizes the balance of neural circuits
composed of excitatory and inhibitory neurons[117] (Figure 4C).
According to the E/I balance hypothesis, psychiatric disorders,such as schizophrenia, and neurodevelopmental disorders,such as ASDs, are caused by an E/I imbalance of neuralcircuits.[118] On the other hand, the D/H balance hypothesis is acell-autonomous concept that originated in sleep studies,[39,42]
and emphasizes the balance in neural excitability achieved by
the control of Ca2þ-dependent hyperpolarization pathways.
According to this hypothesis, psychiatric disorders, such as
schizophrenia, bipolar and major depressive disorders, andneurodevelopmental disorders, such as ASDs, are caused by a
D/H imbalance of neural excitability. Interestingly, the animalmodel of schizophrenia generated by NMDAR inhibitor
administration exhibits the enhanced excitability of both
excitatory and inhibitory neurons,[39] suggesting that the D/
H imbalance (i.e., increased depolarization) in both neurons
might respectively underlie the very heterogeneous phenotypeof this animal model and hence schizophrenia. Therefore, tocomprehensively elucidate the pathology of psychiatric andneurodevelopmental disorders, both circuit-level abnormalities, such as E/I imbalance, and cell-autonomous abnormalities, such as D/H imbalance, should be investigated. Thesestudies will lead to better strategies for treating and preventing
these diseases in the future.

Abbreviations
ASD, autism spectrum disorders; AN model, averaged-neuron model;
CSF, cerebrospinal fluid; KCa channel; Ca2þ-dependent Kþ channel;
NMDAR, N-methyl-D-aspartic acid receptor; PMCA, plasma membrane
Ca2þ ATPase; RT, reticular thalamic; SPSs sleep-promoting substances;
SWS, slow-wave-sleep; TC, thalamocortical; D/H balance, depolarization/
hyperpolarization balance; E/I balance, excitatory/inhibitory balance; Cavchannel voltage-gated Ca2þ channel.

Acknowledgements
We are very grateful to Dr. Koji Ode and Dr. Arthur Millius for their very
helpful and extensive comments on this manuscript.

Conflict of Interest
The authors declare no conflict of interest.

Keywords
Ca2þ-dependent hyperpolarization pathways, depolarization/
hyperpolarization (D/H) balance, neurodevelopmental disorders,
psychiatric disorders, sleep
Received: June 13, 2017
Revised: October 19, 2017
Published online: December 4, 2017

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