The dynamics of sleep and wake are strongly linked to the circadian clock. Many models have accurately predicted behaviour resulting from dynamic interactions between these two systems without specifying physiological substrates for these interactions. By contrast, recent experimental work has identified much of the relevant physiology for circadian and sleep–wake regulation, but interaction dynamics are difficult to study experimentally. To bridge these approaches, we developed a neuronal population model for the dynamic, bidirectional, neurotransmitter-mediated interactions of the sleep–wake and circadian regulatory systems in nocturnal rats. This model proposes that the central circadian pacemaker, located within the suprachiasmatic nucleus (SCN) of the hypothalamus, promotes sleep through single neurotransmitter-mediated signalling to sleep–wake regulatory populations. Feedback projections from these populations to the SCN alter SCN firing patterns and fine-tune this modulation. Although this model reproduced circadian variation in sleep–wake dynamics in nocturnal rats, it failed to describe the sleep–wake dynamics observed in SCN-lesioned rats. We thus propose two alternative, physiologically based models in which neurotransmitter- and neuropeptide-mediated signalling from the SCN to sleep–wake populations introduces mechanisms to account for the behaviour of both the intact and SCN-lesioned rat. These models generate testable predictions and offer a new framework for modelling sleep–wake and circadian interactions.
The central circadian pacemaker, the suprachiasmatic nucleus (SCN) of the hypothalamus, regulates the 24 h timing of many physiological processes, including sleep and wake behaviour. Recent experimental results demonstrate that circadian modulation of behavioural activity is reliably predicted by the circadian variation of SCN electrical activity . In both nocturnal and diurnal animals, the overall firing rate of SCN neurons varies over 24 h, with a generally higher firing rate during the light period and a generally lower firing rate during the dark period [2–4], though some subpopulations show different firing profiles [5–7]. For the nocturnal rat, this pattern of activity suggests that high SCN firing rates during the light period promote sleep and/or inhibit wake.
Anatomical and physiological evidence constrains the potential mechanisms by which this circadian modulation of sleep–wake behaviour is achieved. Bidirectional projections mediate interactions between the SCN and the neuronal populations involved in sleep–wake regulation. The feed-forward projections from the SCN to the sleep–wake network are both indirect and direct , with indirect projections relaying through the subparaventricular zone (SPZ) and the dorsomedial hypothalamus (DMH) [9–12]. These projections are mediated by gamma-aminobutyric acid (GABA) and glutamate as well as neuropeptides such as vasoactive intestinal peptide (VIP), vasopressin, gastrin-releasing peptide (GRP), somatostatin and neuropeptide Y (NPY) [8,13–15]. Experiments suggest that SCN-associated neurotransmitters and peptides may promote different behavioural states with differential timing of their effects on post-synaptic targets [16–20].
Feedback projections from sleep–wake centres to the SCN allow vigilance state to directly modulate activity of SCN neurons. Higher SCN firing rates are observed during wake and rapid eye movement (REM) sleep states compared with non-REM (NREM) sleep states , and these changes are probably mediated through serotonergic projections from wake-promoting dorsal raphe (DR) and cholinergic projections from laterodorsal tegmental nucleus (LDT) and pedunculopontine tegmental nucleus (PPT) [22,23].
This experimental evidence for bidirectional communication suggests several conceptual models for the interaction of circadian and sleep–wake systems; however, the dynamics of these interactions are not well understood. In this paper, we propose a dynamic, mathematical modelling framework to investigate the neuronal interactions between circadian and sleep–wake regulatory systems in nocturnal rats. Mathematical modelling has provided key insights to both the circadian [24–29] and sleep–wake regulatory systems [30–36]. The classical two-process model has addressed interactions between these systems at a phenomenological level [37–39]. Here, we employ an integrated approach to analyse physiological interactions between these systems. The models we introduce are based on experimentally identified neuronal projection pathways between the SCN and sleep–wake regulatory populations, and they assume a neurotransmitter-mediated circadian signal and standard, entrained 24 h variation in the firing rates of SCN neurons.
The first model we present shows that the SCN signalling that is mediated by the action of a single wake- or sleep-promoting neurotransmitter can accurately produce circadian modulation of sleep–wake patterning consistent with experimental measurements. However, such single transmitter-mediated signalling cannot account for the changes in sleep–wake patterning observed when the SCN is lesioned. Specifically, lesions of the SCN have been shown to eliminate circadian rhythms of sleep and wake states [40–43]. In the rat, this loss of rhythm occurs without significant changes in the average time spent in each state over 24 h [40,42,43], and sleep–wake patterning in SCN-lesioned rats reflects an intermediate level between patterning associated with the dark and light periods of intact rats.
We find that accounting for both circadian modulation of sleep–wake patterning in the intact rat and the loss of circadian variability under SCN lesion conditions, in a physiologically consistent manner, requires that the SCN promotes both sleep and wake at different circadian phases. Therefore, we propose two additional physiologically motivated models that include both transmitter- and peptide-mediated SCN signalling. Both models assume a sleep-promoting effect of the transmitter-mediated signal and a wake-promoting effect of the peptide-mediated signal, but the models differ in the proposed peptide release mechanisms they employ.
In this paper, we describe three different models of interaction between the SCN and the sleep–wake regulatory network: the single-transmitter oscillator (STO) model, the transmitter–peptide dual oscillator (TPDO) model and the collocalized transmitter–peptide (CTP) model (figure 1). First, for the STO model, we present a detailed description of the network connectivity associated with this model, the modelling formalism employed and the representations of homeostatic and circadian drives used in the model. Next, we introduce the TPDO and CTP models with a focus on the features that distinguish them from the STO model and each other. Finally, we describe the protocols for interpreting behaviour from model output and simulating effects of an SCN lesion with each model.
Numerical simulations of each model were computed with a modified Euler (or Heun) integration method with a time step of 0.005 s and were implemented with the software XPPAUT, developed by G. B. Ermentrout and available at ftp://ftp.math.pitt.edu/pub/bardware.
The complete equations and parameter values for each model are given in the electronic supplementary material. The initial choice of parameter values was based on experimental data whenever possible. For example, parameters describing maximal physiological firing rates of each neuronal population were based on relevant experimental reports. When such data were unavailable, we either inferred parameter values from related experiments or chose parameters that were consistent with available experimental characterizations of the system. Examples of these approaches to parameter selection include the choice of neurotransmitter concentration dynamics from voltammetric data for the release and clearance rates of evoked dopamine , and the choice of sufficiently large synaptic signalling weights to ensure distinct activation of different neuronal populations. In all models, we evaluated the parameter sensitivity of network behaviour with respect to free parameters. Additional details regarding parameter sensitivity are provided in §3, and a detailed explanation of the initial choice of parameters in the sleep–wake regulatory network model is available in Diniz Behn & Booth [30,34].
(a) Single-transmitter oscillator model: network connectivity
The sleep–wake regulatory network represented in the model includes wake-promoting populations (locus coeruleus (LC) and DR), sleep-promoting populations (ventrolateral preoptic nucleus (VLPO)) and both REM- and wake- and REM sleep-promoting populations (LDT and the PPT), as well as their associated neurotransmitters (table 1) [9,30,34,45]. Briefly, neurotransmitter-mediated coupling between populations includes inhibition from the monoaminergic wake-promoting populations, LC and DR, to both the sleep-promoting VLPO and the REM-active subpopulation of the LDT/PPT (R), but not the wake/REM-active LDT/PPT subpopulation (WR) . The sleep-promoting VLPO inhibits all wake-promoting and REM-promoting populations. Cholinergic REM- and wake/REM-active populations excite the LC and DR. A reduced schematic of this interaction structure is shown in figure 1d (see electronic supplementary material, figure S1a for the full schematic of the sleep–wake regulatory network); the full equations, provided in the electronic supplementary material, identify the neurotransmitter-mediated coupling among all populations. Although some neurotransmitters and neuropeptides have been shown to exert heterogeneous effects, we will specify a fixed excitatory or inhibitory action for each neurotransmitter on each post-synaptic population. Specific subcomponents of this coupling structure reflect current conceptual models of sleep–wake regulation: specifically, mutual inhibition between the LC and DR, and the VLPO provides the basis for the sleep–wake flip-flop switch , and reciprocal connectivity between LC and DR, and REM-promoting populations (LDT/PPT) reflects the reciprocal interaction hypothesis for NREM–REM cycling [32,48].
Both feed-forward and feedback synaptic pathways mediate neuronal interactions between the circadian pacemaker in the SCN, and brainstem and hypothalamic sleep–wake regulatory centres (see  for a review). In the rat, the majority of the feed-forward projections from the SCN to the sleep–wake network are indirect, proceeding initially to the SPZ and continuing through the DMH, although direct synaptic projections to the VLPO have been identified . To simplify the indirect synaptic pathway in our model network, we model the net synaptic signal determined by the relays along the indirect pathway rather than the direct action of a single neurotransmitter (figure 1d). DMH synaptic pathways target VLPO and the lateral hypothalamic area (LHA) which projects to LC, DR, LDT and PPT [9,45,51]. However, the glutamatergic projection to LHA is excitatory while the GABAergic projection to VLPO is inhibitory . Furthermore, the DMH 24 h activity pattern is reversed with respect to the SCN activity pattern. Thus, the net projection from the SCN to LC, DR, LDT and PPT is inhibitory, and the net projection from the SCN to VLPO is excitatory. These inhibitory and excitatory actions allow both branches of this projection to promote NREM sleep.
The effect of feedback projections from the sleep–wake network to the SCN is apparent in the dependence of SCN firing rate on vigilance state observed in rodents . Specifically, SCN firing rate has been observed to increase during wakefulness and REM sleep states and decrease during NREM sleep states. We model this effect by an excitatory serotonergic projection from the DR and an excitatory cholinergic projection from the LDT/PPT to the SCN population (figure 1d).
(b) Single-transmitter oscillator model: firing-rate model formalism
We use a population and neurotransmitter firing-rate model formalism to model the interaction between neuronal populations [30,34]. In this formalism, the firing rate of a pre-synaptic population, FY(t), induces expression of neurotransmitter concentration, Ci(t), which drives the post-synaptic firing rate FX(t). In the sleep–wake regulatory network, the neurotransmitter concentration Ci(t) for each neurotransmitter (i=N for Y=LC (NE); i=S for Y=DR (5-HT); i=G for Y=VLPO (GABA); i=A(R) for Y=R (ACh); and i=A(WR) for Y=WR (ACh)) and the firing rate FX(t) for each population (in Hz, X=LC, DR, VLPO, R or WR) are modelled by the following equations, where d/dt denotes derivative with respect to time: 2.1and 2.2The functions, and , describe the steady-state neurotransmitter release and firing-rate response profiles to which the variables Ci(t) and FX(t) evolve over time with associated time constants, τi and τX, respectively. The summation term in the argument of contains the concentrations Ci of each neurotransmitter i released to post-synaptic population X weighted by the constant parameters gi,X. The sign of each gi,X distinguishes between an excitatory (gi,X>0) or an inhibitory (gi,X<0) effect of the neurotransmitter. For each post-synaptic population, we assume a fixed excitatory or inhibitory neurotransmitter action.
The Ci variables represent the strength of synaptic signalling averaged over the population, and state-dependent changes in Ci concentration are expected to correlate with state dependence in extrasynaptic neurotransmitter concentrations observed with microdialysis. Because of differences in reported absolute neurotransmitter concentrations between experimental studies, we normalize each neurotransmitter concentration Ci(t) between 0 and 1. The effects of absolute concentration can be included in the gi,X parameter. The steady-state neurotransmitter release function has a saturating profile given by 2.3where the parameter γi controls the sensitivity of release as a function of pre-synaptic firing rate FY(t) (electronic supplementary material, figure S1b). The function σi(t) is a noise factor whose amplitude varies randomly in time. At discrete time points, specified by a Poisson process with a rate of 0.1 Hz, the amplitude is set to a value chosen from a normal distribution with unit mean. This noise factor incorporates variability of neurotransmitter release into the neurotransmitter concentration steady-state function and results in slightly different target neurotransmitter concentrations for fixed pre-synaptic firing rates. This modelling formalism, including this implementation of variable neurotransmitter release, has been described in previous work [30,34].
The steady-state firing-rate response function has a sigmoidal profile, as used in standard firing-rate models , see reviews in [53–55], and is a function of total projected neurotransmitter concentrations c: 2.4The parameters , αX and βX represent the maximum firing rate, sensitivity of response and half-activation threshold, respectively (electronic supplementary material, figure S1c).
The firing rate of the SCN population model, FSCN(t) (electronic supplementary material, figure S1b), is governed by equation (2.2), where the argument of its steady-state response function includes both the circadian, CIRC(t), and synaptic, SYN(t), inputs that drive SCN activity: 2.5The steady-state firing-rate function is given by equation (2.4) with X=SCN. The synaptic inputs, SYN(t), include the feedback projections from the sleep–wake network, namely serotonergic excitation from the DR and cholinergic excitation from the wake and REM sleep-active subpopulations of the LDT/PPT: 2.6The circadian input, CIRC(t), is discussed below.
We model GABA as the primary neurotransmitter released from the SCN projection pathways to the sleep–wake regulatory populations. The concentration of SCN-released GABA, CG(SCN)(t), is governed by equation (2.1) with i=G(SCN) and Y =SCN, and the steady-state transmitter release function is given by equation (2.3) with i=G(SCN). As discussed above, we model the indirect synaptic pathways from the SCN to the LC, DR, VLPO and LDT/PPT as simple direct projections, with the amplitude of the net synaptic signal represented by the SCN-released GABA concentration scaled by a weighting parameter gG(SCN),X. As such, the excitatory projection from the SCN to the VLPO does not represent an excitatory action of GABA but, instead, represents the net effect of the indirect relay pathway that causes a change in the polarity of the signal.
(c) Single-transmitter oscillator model: homeostatic and circadian drives
In the sleep–wake network, we include a homeostatic sleep drive, h(t), that represents the universally recognized propensity for increasing sleep need with time in wakefulness. One mechanism identified in mediating homeostatic sleep drive is adenosine (reviewed in [56,57]) whose levels increase during wakefulness in some parts of the brain, including the basal forebrain [58–61]. The model homeostatic sleep drive, h(t), mimics adenosine dynamics by increasing towards a maximum value, , during wakefulness and decreasing towards 0 during sleep states with time scales τhw and τhs, respectively: 2.7where H[z] is the Heaviside function defined as H[z]=0 if z<0 and H[z]=1 if z≥0. The state dependence of homeostatic activity is gated by the firing rates of the LC and DR. If the combined activities of the LC and DR are greater than the homeostatic threshold value, θw, the network is in a wake state, and the homeostatic sleep drive increases. To incorporate this homeostatic sleep drive into the sleep–wake network model, we model the effects of adenosine on the VLPO [58,62,63] by including an h-dependence in the activation threshold of the VLPO population (compare with equation (2.4)): 2.8where βVLPO(h)=−k h. During wakefulness, as the homeostatic drive increases, the VLPO activation threshold decreases, thereby enabling VLPO activation and a transition to NREM sleep. As the homeostatic drive clears during sleep states, the VLPO activation threshold increases, which causes the VLPO population to inactivate and transitions the network back to the wake state.
The circadian drive, CIRC(t), to the SCN population represents the intracellular mechanisms responsible for the circadian modulation of firing rate in SCN neurons. Briefly, these mechanisms include the interactions of clock genes and their products responsible for a 24 h variation in protein expression levels (reviewed in ). These proteins affect membrane properties of SCN neurons to alter their excitability and cause 24 h variations in their propensity for and patterns of action potential firing [1,5,21]. This intracellularly driven modulation of SCN population firing rate occurs on a time scale of the order of hours, in contrast to synaptically driven modulation of firing rate that can occur on time scales of less than a second. We model the effects of intracellular circadian modulation of neuronal membrane properties that result in the generally sinusoidal 24 h variation in SCN population firing rate with a sinusoidally varying input, CIRC(t), to the steady-state SCN firing-rate function, : This circadian drive leads to overall increases in SCN activity during the light period and decreases in the dark period. In this study, we assume entrained conditions such that the intracellular circadian clock, and hence SCN activity, is phase-locked to a 12 L:12 D cycle (environment alternates between 12 h of lights on and 12 h of lights off).
(d) Transmitter–peptide dual oscillator model
For the TPDO model (figure 1b), we propose distinct expression profiles for transmitter and peptide, with the peak in transmitter levels occurring in the light period and the peak in peptide levels during the dark. Such a contrast in firing profiles may occur as a result of heterogeneity of firing in subpopulations of SCN neurons [6,7,65] or may reflect circadian modulation of VIP release with this phase relationship. We model this difference in expression phases by introducing distinct transmitter-expressing and peptide-expressing populations as separate subpopulations of SCN neurons whose overall firing profiles are modulated by phase-shifted intracellular circadian drives.
Compared with the STO model, the TPDO model contains additional equations for the firing rate of the peptide-expressing subpopulation, FSCN(P)(t), and for peptide concentration, CPEP(t): and The steady-state firing-rate function is given by equation (2.4) with X=SCN(P) and the steady-state transmitter release function is defined by equation (2.3) with i=PEP. The intracellular circadian drive to the peptide-expressing subpopulation, CIRCP(t), is a 24 h sinusoidal function that is phase-shifted relative to the circadian drive to the GABA-releasing SCN subpopulation, CIRC(t): The peptide-expressing SCN subpopulation also receives the feedback synaptic projections from the sleep–wake centres, SYN(t), given by equation (2.6).
Feed-forward synaptic projections from this SCN subpopulation to sleep–wake populations are modelled to parallel those from the GABA-releasing subpopulation. However, we assume that the opposite responses to GABA- and peptide-mediated SCN signalling in the SPZ  are propagated through the remainder of the indirect SCN synaptic pathway and result in opposite net effects to the sleep–wake centres. Specifically, the peptide-mediated projections have excitatory effects on the LC, DR and REM-promoting subpopulation of the LDT/PPT, and inhibitory effects on the VLPO. This difference in GABA and peptide action establishes a dual role for SCN state modulation in which the transmitter is involved in the promotion of NREM sleep while the peptide promotes wake.
(e) Collocalized transmitter–peptide model
As in the TPDO model, the CTP model (figure 1c) assumes that GABA- and peptide-mediated SCN signalling exerts opposite net effects on the sleep–wake centres. However, in the CTP model, the proposed mechanism for transmitter and peptide SCN signalling is based on mechanistic differences in transmitter and peptide release. Peptide release may require higher firing rates or special patterns of firing, such as bursting, compared with collocalized transmitters , and the resulting differential release profiles for collocalized transmitters and peptides have been well documented [67,68].
While our firing-rate model formalism does not account for patterning of individual spikes, the modelled inputs to the SCN population operate on different time scales and can be presumed to evoke different firing patterns. Namely, the intracellular circadian drive to the SCN modulates firing rates on a very slow time scale, of the order of hours. This drive reflects the slow changes in membrane properties of individual neurons that alter their intrinsic propensities for firing as well as their responses to synaptic inputs. By contrast, feedback projections from wake- and REM sleep-promoting populations change firing rates on a much shorter time scale and correspond to excitatory cholinergic and serotonergic synaptic inputs that presumably evoke immediate action potential discharge in individual neurons.
We incorporate such a peptide-release mechanism into the CTP model by assuming that peptide release is induced by the SCN response to the synaptic drive, SYN(t). As such, the concentration of peptide, CPEP(t), depends on the difference of total SCN firing-rate response and the response expected owing solely to the circadian drive: where FSCN is given by equation (2.5). The steady-state firing-rate function is given by equation (2.4) with X=SCN and the steady-state transmitter release function is defined by equation (2.3) with i=PEP. Since the circadian drive, CIRC(t), changes on a longer time scale than the time constant τSCN that governs FSCN activity, the difference reflects the short time-scale changes in FSCN owing to the synaptic drive SYN(t).
As in the TPDO model, peptide signalling in the CTP model occurs on the same synaptic pathways as transmitter signalling, but has an opposite effect: CPEP(t) induces an excitatory effect in the LC, DR and REM-promoting population of the LDT/PPT, and has an inhibitory effect in the VLPO. This translates to a dual role for the SCN in which transmitter signalling has a net effect of promoting NREM sleep while peptide signalling has a net wake-promoting action.
(f) Scoring and evaluating simulated sleep–wake behaviour
For each model, sleep–wake behaviour was scored according to the activity levels of the wake-, NREM- and REM-promoting populations. In general, high FLC and FDR corresponded to wake, and high FR corresponded to REM sleep. NREM sleep was associated with high FVLPO, although FVLPO could be high during REM sleep as well. Owing to the network structure, overlaps between high activity in FVLPO and FLC/FDR were minimal.
We compared the sleep–wake patterning generated by the model with the experimental characterization of sleep–wake behaviour in nocturnal rats in 12 L:12 D phase-locked conditions . Summary statistics of sleep–wake behaviour, including the per cent time in each state, number of bouts and mean duration of bouts, were considered. Since rats often exhibit polyphasic sleep–wake behaviour in which they alternate between states of wake and sleep on a time scale of tens of minutes, these statistics provide a general assessment of sleep architecture.
(g) Simulating behaviour of suprachiasmatic nucleus-lesioned rats
We simulated the effects of an SCN lesion by assuming the absence of activity on all synaptic projections from the SCN to the sleep–wake centres. Namely, we set gG(SCN),X and gPEP,X (X=LC, DR, R and VLPO) to zero in the argument of the steady-state firing-rate functions in equation (2.2) for each population. To our knowledge, summary statistics for mean bout durations and number of bouts for wake, NREM sleep and REM sleep in SCN-lesioned rats have not been reported. However, SCN-lesioned rats preserved normal 24 h averages of time in each state, and hypnograms summarizing sleep–wake behaviour in these animals showed intermediate behaviour that was qualitatively between normal light and dark period behaviour [42,43,70]. Therefore, we compared sleep–wake behaviour in the SCN lesion simulations with averaged values from the 12 h light and dark periods reported in Blanco-Centurion et al. .
(a) Single-transmitter oscillator model
In the STO model, effects of the SCN on the sleep–wake network were mediated by GABAergic signalling, and exerted a solely sleep-promoting effect. This model simulates sleep–wake behaviour and SCN firing rate over 24 h (figure 2). The 24 h variation in SCN firing rate shows higher activity in the light period and lower activity in the dark period, consistent with experimental data [3,4]. In addition, feedback projections onto the SCN promote vigilance-state-dependent changes in SCN firing rate with increases in activity relative to baseline during wake and REM sleep . Since GABA release by the SCN is correlated with SCN activity, the profile of GABA release follows that of SCN firing rate with higher levels of GABA release during the light period than during the dark period.
As described in §2, states of wake, NREM sleep and REM sleep were interpreted based on firing rates of the neuronal populations that promote these states (figure 3). We applied standard summary statistics, including per cent time in each state, mean bout durations and number of bouts over 12 h, to quantify the resulting simulated sleep–wake behaviour. The model accurately described the polyphasic sleep–wake behaviour that is characteristic of nocturnal rats in 12 L:12 D phase-locked conditions , and input from the SCN resulted in appropriate circadian modulation of sleep–wake states (table 2). During the light period, when overall SCN activity was high, there was a higher percentage of NREM sleep and a lower percentage of wake compared with the dark period. These changes reflect a decrease in the duration of wake bouts and an increase in the frequency of NREM and REM sleep (figure 3a). During the dark period, when the SCN firing rate is low, long wake bouts and a decreased frequency of both NREM and REM sleep contributed to a higher percentage of wake, consistent with experimental data (figure 3b).
To understand how SCN projections modulate sleep–wake patterning, we briefly describe their effects on state transitions in the sleep–wake network. During the light period when SCN activity is high, NREM and REM states are promoted by the following effects: (i) SCN-mediated excitation to the VLPO and inhibition to the LC and DR both act to reduce wake bout durations; (ii) SCN-mediated inhibition to the LC and DR also results in longer REM bout durations owing to the reciprocal interaction network structure between the REM-promoting and wake-promoting populations; and (iii) SCN-mediated inhibition to the REM-promoting population acts to delay REM initiation, thus increasing NREM bout durations. In the dark period when SCN activity is low, the reduction in the sleep-promoting signal acts as a permissive gate for increased wakefulness. REM sleep is, in turn, reduced owing to increased activity of the wake-promoting populations. In both the light and dark phases, the SCN-mediated inhibition to both the DR and the LDT/PPT coupled with their excitatory feedback projections to the SCN establishes a negative feedback loop. Ultimately, this feedback loop shortens wake bouts and promotes shifts from wake to NREM sleep, contributing to SCN promotion of sleep.
We simulated lesion of the SCN by removing all SCN inputs to the sleep–wake network. The resulting simulated behaviour, similar to the behaviour associated with low SCN activity in the dark period, was dominated by wake (table 2 and figure 6). This result is inconsistent with experimental observations in which SCN-lesioned rats maintain normal average percentages of wake, NREM sleep and REM sleep over 24 h with a pattern of activity that is characteristic of neither the light nor the dark period [42,43]. Specifically, wake bouts are of intermediate durations and REM sleep occurs with intermediate frequency throughout the circadian cycle . A purely sleep-promoting (or, likewise, purely wake-promoting) SCN action cannot produce both the circadian variation of sleep–wake patterning, consistent with behaviour in intact rats, and the intermediate pattern of activity in the absence of SCN inputs, consistent with behaviour in SCN-lesioned rats. For the presented STO model parameter values, wakefulness in the dark period was maximized, thus the simulated SCN lesion results in constant wakefulness. Different parameter regimes would allow transitions between wake and NREM sleep that are dictated by the homeostatic sleep drive under the simulated SCN lesion; however, the per cent time in waking in the SCN lesion case would represent an upper bound to the levels possible under SCN modulation. Likewise, it was possible to find a parameter regime in which the STO model could generate an intermediate pattern of activity in the absence of SCN inputs, but that version of the STO model could not produce the increase in wakefulness that is characteristic of low SCN activity during the dark period in the presence of circadian modulation (results not shown). Therefore, these simulations reveal a significant limitation of purely wake- or sleep-promoting circadian signalling. In the following sections, we provide the results of two physiologically motivated mechanisms to model both sleep-promoting and wake-promoting SCN effects.
(b) Transmitter–peptide dual oscillator model
In the TPDO model, we extended the STO model to include a subpopulation of peptide-expressing SCN neurons with a phase-shifted circadian drive resulting in phase-shifted profiles of activity and peptide release. As discussed in §§1 and 2, this peptide exerts wake-promoting effects on the sleep–wake network. As in the STO model, the activity of the GABAergic SCN subpopulation (FSCN) results in more GABA release during the light period, and, therefore, a stronger sleep-promoting effect in that phase (figure 4). The activity of the peptide-releasing SCN subpopulation (FSCN(P)) is lower in the light period and higher in the dark period. These opposing effects of GABA and peptide on population activity in the sleep–wake network work together to promote sleep during the light period and promote wake during the dark period. Since the majority of SCN neurons are GABAergic, the average SCN firing-rate profile produced by the TPDO model can be assumed to maintain the characteristic features of high SCN population activity during the light period and low SCN population activity during the dark period.
Simulations of this model reproduce experimental measurements of sleep–wake temporal architecture in both SCN-intact rats and SCN-lesioned rats (table 2 and figure 6) [42,43,69]. As in the STO model, the light period is characterized by shorter wake bouts and an increased frequency of NREM and REM sleep bouts, and the dark period is characterized by long wake bouts and a decreased frequency of NREM and REM sleep bouts (electronic supplementary material, figure S2a,b).
The combination of differential wake- and sleep-promoting signalling by the SCN in the TPDO model results in distinct periods in which NREM sleep or wake dominates the model's behaviour. During the light period, the dominant SCN signal is the GABA-mediated effect that promotes sleep states as in the STO model. During the dark period, the dominant SCN signal is the peptide-mediated effect that promotes wakefulness in the following ways: (i) peptide-mediated excitation to the wake-promoting populations and inhibition to the VLPO lengthen wake bouts and (ii) peptide-mediated excitation to the REM-promoting population promotes its early activation, which truncates NREM bouts. However, higher levels of excitation to the wake-promoting populations that occur in the middle of the dark period can completely suppress REM activation. In addition, the coupling of the net excitatory effect of the peptide-releasing SCN subpopulation on the DR and REM-promoting population with the excitatory feedback projections from these populations to the SCN establishes a positive feedback loop that can promote wake and REM states. However, since the feedback projections drive increased activity in both the GABAergic and peptide-releasing subpopulations, feedback effects vary with the circadian phase.
(c) Collocalized transmitter–peptide model
In the CTP model, we modified the STO model to include peptide release by the SCN population in response to excitatory synaptic inputs from the sleep–wake network. In our model network, the wake-promoting effects of peptide release are driven by state-dependent feedback from wake- and REM-promoting populations in the sleep–wake network. As in the STO model, SCN activity in the CTP model was driven by a single circadian oscillator and produced the characteristic pattern of high SCN population activity during the light period and low SCN population activity during the dark period. GABA release from the SCN followed this activity profile (figure 5). Peptide concentration levels, in contrast, were higher on average during the dark period when wake was the dominant state (see below).
Simulations of the CTP model produce appropriate circadian modulation of sleep–wake patterning (table 2) with shorter wake bouts and increased frequency of NREM and REM sleep bouts during the light period and opposite effects during the dark period (electronic supplementary material, figure S3a,b). As in the TPDO model, the inclusion of both GABA and peptide provides mechanisms for SCN-mediated promotion of both wake and sleep. When SCN firing rates are relatively high, high levels of GABA concentration dominate SCN-mediated effects to promote sleep states through the mechanisms discussed above. When SCN firing rates are low, promotion of wake by peptide is realized through a network effect: low SCN firing rates produce low levels of GABA release that permit relative increases in wake durations, and the positive feedback loop formed by the synaptic feedback projections to the SCN further promotes peptide release, which can maintain wake bouts. Thus, the differential timing of GABA and peptide expression promotes wake and sleep at different circadian phases. Since excitation levels to the wake-promoting populations remain sufficiently low during the dark period in the CTP model, REM bouts continue to regularly occur at transitions from NREM sleep to wake.
(d) Parameter sensitivity of model results
Values of free parameters in each of the models were tuned to optimize agreement with experimentally recorded summary statistics in the light and dark periods, and, for the TPDO and CTP models, agreement with SCN lesion statistics was also taken into account. The majority of model parameter values are consistent across all three models, and those that differ are primarily parameters associated with the interaction terms between the SCN and the sleep–wake regulatory populations (all parameter values are listed in the electronic supplementary material). In particular, all parameters associated with the sleep–wake network are identical for the TPDO and CTP models. Previous parameter sensitivity analysis of the sleep–wake regulatory network model indicated that state transition patterning is qualitatively robust to changes in parameter values, with 10 per cent changes in parameter values resulting in less than 10 per cent changes in per cent time spent in each state [30,34]. Given this general robustness of model dynamics to parameters associated with sleep–wake regulatory populations, we concentrated on analysing sensitivity of circadian modulation of sleep–wake patterning to variation in parameters associated with the interaction projections between the SCN and the sleep–wake populations.
In all three models, a ±10 per cent variation in the values of most of the weighting parameters gi,X associated with the projections between the SCN and the sleep–wake regulatory populations resulted in a less than 12 per cent change in per cent time spent in waking and NREM sleep in both the light and dark periods, and in per cent time spent in REM sleep in the light period. Per cent time spent in REM sleep during the dark period showed a greater sensitivity (less than 22%), but since its value is 7 per cent or less in each model, this variation in results was still minor. Per cent time in wake and NREM sleep was most sensitive to variations in the strengths of the GABA- and peptide-mediated projections from the SCN to VLPO (gG(SCN),VLPO, gPEP,VLPO), with 10 per cent parameter variation resulting in much larger percentage changes, particularly in the CTP model. Per cent time in REM sleep in the STO and TPDO models was sensitive to variations in the strength of the GABA- and peptide-mediated projections from the SCN to the LC and DR (gG(SCN),LC, gG(SCN),DR, gPEP,LC, gPEP,DR), and, in the CTP model, REM sleep per cent was sensitive to the strength of the GABA-mediated SCN projection to the REM-promoting population (gG(SCN),R). In our sleep–wake regulatory network, REM bout durations are determined by activation dynamics of the LC and DR [30,34], hence it is not surprising that SCN-mediated modulation of these populations can affect REM sleep percentages.
Some parameter variations that did not significantly affect per cent time in any state altered mean bout durations and numbers of bouts. However, the changes in the temporal architecture of sleep–wake behaviour were compensatory, so per cent time in state remained relatively unchanged. For example, in both the STO and CTP models, ±10 per cent variation in the strength of the cholinergic feedback projection from the LDT/PPT subpopulations to the SCN (gA,SCN) increased (decreased) mean wake bout durations by up to 50 per cent, but decreased (increased) the number of wake bouts such that per cent time spent in wake varied by less than 12 per cent. Thus, optimizing parameters to agree with all three summary statistics constrained their values, although these summary statistics do not reflect all of the fine temporal dynamics of rat sleep–wake behaviour (§4).
Most importantly, while per cent times spent in each state showed some sensitivity to variations in these parameters associated with SCN interaction pathways, circadian modulation of sleep–wake patterning was robust to parameter variation. Specifically, under ±10 per cent variation in each parameter, the per cent time in each state was significantly different between the light and dark periods (paired t-test, p<0.05). Thus, the circadian modulation of per cent time spent in wake, NREM sleep and REM sleep was preserved under parameter variation in each model.
(e) Simulating suprachiasmatic nucleus lesions in the transmitter–peptide dual oscillator and collocalized transmitter–peptide models
We simulated SCN lesions in the TPDO and CTP models by removing both GABA- and peptide-mediated inputs from the SCN to the sleep–wake network. For both models, the per cent time in each state over 24 h was preserved by the TPDO and CTP models (figure 6). In addition, the resulting simulated sleep–wake behaviour displayed patterning reflecting intermediate bout durations and frequencies (table 2, figure 6 and electronic supplementary material, figures S2c and S3c) consistent with experimental data. Although the TPDO model produced more brief awakenings and fewer REM bouts compared with the CTP model, the simulated SCN lesion behaviour associated with the two models was qualitatively similar (figure 6b,c).
(f) Model predictions
The main prediction of the STO model is that, although a single sleep- or wake-promoting role for the SCN can produce baseline circadian modulation of sleep–wake behaviour, it is not sufficient to account for the intermediate pattern of behaviour associated with SCN lesions in the rat. Both the TPDO and CTP models provide potential physiologically based mechanisms for dual wake- and sleep-promoting roles of the SCN.
Differences in the mechanisms implemented in these two models lead to different predictions regarding the physiology of SCN neurons and the patterns of release of GABA and peptide. The TPDO model is based on the assumption that distinct subpopulations of the SCN separately, and at different times, release GABA and peptide. Furthermore, the intracellular circadian clock regulating peptide release is assumed to be phase-shifted relative to the clock modulating GABA release, so GABA and peptide expression peak at different times of day, with peptide release highest during the dark period (figure 7).
The CTP model reflects the assumption that peptide is released by the SCN population in response to excitatory synaptic inputs, while GABA release depends directly on SCN firing rate as it is modulated by the circadian drive and synaptic inputs. This model permits distinct GABAergic and peptidergic subpopulations as well as SCN neurons in which GABA and peptide are collocalized. As in the STO and TPDO models, GABA release peaks during the light period and falls during the dark period (figure 7a). Like the TPDO model, the CTP model predicts that peptide concentration levels are on average higher during the dark period. This occurs because, during the dark period, wake is the dominant state and maintained synaptic feedback to the SCN from the wake-active DR provides for more sustained peptide release. However, the CTP model predicts that maximum peptide expression occurs during dawn and dusk ‘transition’ hours (figure 7b). This can be understood by considering the function governing the steady-state firing rate of the SCN population (equation (2.4)). When SCN firing rate is low or high, excitatory synaptic inputs on the feedback projections produce small changes in SCN firing rate owing to saturation properties at either end of this sigmoidal steady-state curve. These small changes in firing rate result in lower levels of peptide release. However, when the circadian drive is at intermediate levels and SCN firing rate is operating in the activation portion of its sigmoidal steady-state response function, the excitatory synaptic inputs result in larger increases in firing rate that drive higher levels of peptide release. Thus, while no model components are tuned to respond specifically at dawn or dusk phases, the generic mechanism of saturating neuronal activity profiles generates differential activity at these phases.
Although both models generate sleep–wake behaviour that is consistent with experimental characterizations of rat sleep–wake behaviour as measured by standard summary statistics (per cent time in each state, mean bout durations and bout frequency), the key differences in the fine architecture and 24 h organization of sleep–wake behaviour associated with each model constitute testable model predictions. The main differences in the organization of sleep–wake behaviour between the two models are the circadian organization of REM sleep and the predicted timing of the longest wake bouts. In the TPDO model, there is an interval during the dark period, near the peak of peptide expression, when REM sleep does not occur. This is a result of the increased peptide-mediated excitation to the wake-promoting populations that inhibit the REM-promoting populations. By contrast, although the frequency of REM sleep during the dark period is reduced in the CTP model, there is no extended interval in which REM sleep does not occur. In the light period, the frequency of REM sleep is much higher in the TPDO model compared with the CTP model and experimental data. This reflects an increased probability of an NREM–REM transition and a decreased probability of a direct NREM–wake transition in the TPDO model. These differences can be understood by considering the circadian modulation of (REM-promoting) peptide in both models: in the TPDO model, peptide levels are low but non-zero throughout the light period; by contrast, in the CTP model, peptide levels are zero during NREM sleep. Hence, the persistent level of peptide in the TPDO model plays an important role in promoting transitions from NREM sleep to REM sleep.
In the TPDO model, the peak of peptide expression in the middle of the dark period, coinciding with the trough of GABA release, governs the timing of the longest wake bouts. The CTP model, on the other hand, predicts that the longest wake bouts are produced during dawn and dusk ‘transition’ hours, in a crepuscular pattern. This effect is the result of peak peptide levels occurring during the transitions between light and dark phases, as described above. These peak peptide levels provide for higher excitatory inputs to the wake-promoting populations that act to sustain and lengthen wake bouts.
In this work, we have simulated the interactions between the circadian and sleep–wake regulatory systems through three separate models: the STO model, the TPDO model and the CTP model. State-dependent, 24 h variation in SCN firing rate in each model is consistent with experimental results , and each of these models produces dynamic circadian modulation of sleep–wake behaviour consistent with experimental data from nocturnal rats . However, the STO model, with its purely sleep-promoting circadian effect, cannot account for the behaviour of SCN-lesioned rats. By contrast, the proposed mechanisms in the TPDO and CTP models offer two possibilities by which the SCN can differentially exert a sleep- and wake-promoting signal that provides realistic circadian modulation of sleep–wake behaviour and accurately captures the intermediate behaviour associated with SCN lesion data.
(a) Model advantages and limitations
The key advantages of the modelling approaches presented here are the physiological basis for the models and the dynamic nature of the interactions involving bidirectional projections between the SCN and the sleep–wake regulatory network. By maintaining close links to the physiology, each model generates experimentally testable predictions. These predictions include mechanistic proposals as well as features of the fine temporal architecture of sleep–wake behaviour, the firing profiles for neuronal populations and neurotransmitter-expression profiles for key neurotransmitters. To assess the patterning of sleep–wake behaviour in the model, we compared the per cent time in each state, mean bout durations and number of bouts with published data describing these summary statistics in rats during 12 h light and dark periods . These statistics provide a general characterization of sleep–wake patterning; however, owing to the non-Gaussian distribution of wake and sleep bouts across species [71–74], more detailed characterization of the fine architecture of sleep–wake behaviour is desirable. Future work examining circadian differences in sleep–wake behaviour should consider variation in these detailed measures as well as the basic summary statistics.
Our general model structure includes several simplifications of physiology. We assumed specific excitatory or inhibitory actions of neurotransmitters on neuronal populations. It should be noted that the actual data regarding these interactions are often less clear than these simple models convey, and heterogeneity of neurotransmitter action may represent an important consideration for future modelling work. For indirect projections from the SCN to sleep–wake regulatory populations, we have described net effects without explicitly modelling the activity of relay populations such as the SPZ, the DMH and orexin neurons in the lateral hypothalamus [11,18,51,75–80]. In the nocturnal rat, the indirect synaptic pathway has been implicated in an inversion of the SCN circadian signal, most probably occurring in the DMH [10,45]. Therefore, to investigate the differences between nocturnal and diurnal species, it may be important to explicitly include this indirect signalling pathway. This and other physiological differences between nocturnal and diurnal animals may contribute to the mechanisms that result in different 24 h distributions of behaviour .
Another potential physiological simplification is the network structure used for REM sleep regulation. We incorporated the classical reciprocal-interaction structure [32,82], but recent work suggests that other populations may be involved in REM sleep regulation [83–86]. Since the timing of REM sleep is under circadian control and feedback projections to the SCN increase the firing of SCN neurons during REM sleep, the network structure for REM sleep regulation may have significant implications for the interactions between the circadian and sleep–wake regulatory systems and should be examined in future work.
By taking into consideration dynamic bidirectional projections, these models provide insights into the role of feedback mechanisms that have not been addressed by prior modelling approaches focusing on unidirectional modulation of sleep–wake regulation by the circadian system [30,33–35,37–39,87]. In addition to their role in network interactions, there is evidence that these feedback mechanisms may be involved in shifting the intracellular circadian clock in SCN neurons [88–90]. By assuming a fixed waveform for our modelled circadian clock, we fail to capture the heterogeneity of neuronal behaviours found within the SCN and investigated in recent mathematical models of individual SCN neurons [5–7,28,29,65]. Furthermore, we have not been able to consider phase-shifting effects on the clock . Since sleep–wake behaviour is directly involved in providing or gating these inputs, these effects have important implications for interactions between sleep and circadian systems. Similarly, the fixed waveform for our modelled circadian clock has prevented investigation of explicit nonlinear interactions between the circadian clock and the homeostatic sleep drive [26,92,93]. In future work, analysis of these inputs to the clock could suggest novel mechanisms by which these systems interact under non-entrained conditions.
(b) Inter-model comparisons and model implications
All three of the models presented herein can produce circadian modulation of sleep–wake behaviour in the nocturnal rat. However, they incorporate different mechanisms and generate different predictions regarding the physiology of SCN neurons, profiles of SCN transmitter and peptide expression levels and the fine temporal architecture and 24 h organization of sleep and wake patterning. In addition, there are significant differences between the simulations of behaviour in SCN-lesioned rats among the three models.
As previously discussed, the STO interaction model assumes a solely sleep-promoting effect of the SCN in nocturnal rats and predicts that high SCN activity promotes sleep during the light period, and low SCN activity gates wake during the dark period. However, this purely sleep-promoting role cannot account for data from SCN-lesioned rats [40,42,43]. We note that a model postulating a solely wake-promoting effect of the SCN would have the same limitations, and, therefore, an SCN model with a single oscillator and a single transmitter cannot accurately represent behaviour of both wild-type and SCN-lesioned rats. Physiologically, this implies that the SCN must work to differentially promote both wake and sleep in nocturnal rodents, rather than solely promoting either state. Although the balance between wake- and sleep-promoting roles for the SCN may vary across species, resulting in species-specific responses to SCN lesions, this idea is consistent with experimental evidence from both rodent and human studies (reviewed in ). However, the physiological mechanisms that achieve such a dual role through standard neural pathways are not clear.
In the TPDO and CTP models, we propose two possible mechanisms for relaying multiple circadian signals. Both of these mechanisms rely on signalling by a neuropeptide that exerts a post-synaptic action opposite to that of GABA. There are several neuropeptides in the SCN that could play such a role [8,13–15]. For example, VIP propagates opposite net effects on the activity of target populations in the SPZ compared with GABA . Thus, while GABA exerts a sleep-promoting effect in the nocturnal rat, VIP promotes wake and REM sleep [17,94–96]. Interestingly, anatomical and physiological constraints dictated that the role of peptide action in our model schematic must include the promotion of both wake and REM sleep. Although network effects seem to be more important than peptide expression for driving the 24 h profile of REM sleep in our model, such a REM-promoting peptide action would be consistent with experiments involving intraventricular application of VIP [94–96].
The TPDO model accounts for behaviour in both intact and SCN-lesioned rats by describing circadian modulation that exploits phase-shifted SCN firing profiles to promote sleep during the light period and promote wake during the dark period. This mechanism relies on heterogeneity in the activity of SCN subpopulations [6,7,65] and assumes that the release of the wake-promoting peptide is controlled by one of these subpopulations. For example, an assumption that VIP is released by a population whose activity peaks during the dark period would be consistent with experimental results suggesting that the release of VIP in the SCN may be under the control of a distinct oscillator with peak activity during the dark period of the 12 L:12 D cycle [16,19,20,97]. This expression profile, contrasting with the expression profile of GABA that peaks during the inactive (light) period, provides a mechanism for the SCN to differentially promote wake and sleep at different circadian phases . Examining the extra-SCN expression profiles for VIP and other peptides expressed by SCN neurons could help to establish a physiological substrate for our model peptide.
Rather than assuming that peptide expression is under the control of a distinct oscillator, the CTP model employs a mechanism based on differential transmitter and peptide release that allows for collocalization of both substrates in the same population of SCN neurons. This assumption is a key feature of the CTP model since there is evidence that VIP, GRP or NPY may be collocalized with GABA in SCN neurons [14,15,18,99].
Differential release profiles for collocalized transmitters and peptides have been observed experimentally. For example, in neurons in the cat submandibularis that synthesize both ACh and VIP, measurable release of VIP first occurs at stimulation frequencies of about 2 Hz, while ACh release is already significant at stimulation frequencies below 0.5 Hz . In addition to this general firing-rate-dependent phenomenon, experiments support an SCN firing-pattern-dependent inhibitory action of SCN peptide signalling on VLPO activity: while single-pulse SCN stimulation evoked standard fast inhibitory and excitatory post-synaptic potentials in the VLPO, longer duration stimulus trains to the SCN evoked a long-lasting inhibition that suppressed action potential firing . The necessity of train stimulation in evoking the long-lasting inhibition suggests that the response may involve peptide release, which often depends on higher firing rates, or even burst firing [66,67].
Although the CTP model does not include a mechanism to explicitly modulate the phase dependence of peptide release, the interactions between GABA, peptide and vigilance state result in a 24 h expression profile for peptide that is higher overall in the dark period, consistent with the experimental data previously discussed [16,19,20]. The resulting differential release profiles for GABA and peptide propagate through the network to promote sleep during the light period and wake during the dark period. Interestingly, peptide expression peaks during the transitions between light and dark periods, rather than in the middle of the dark period, consistent with the expression of NPY under 12 L:12 D conditions . Peak peptide expression helps to reinforce waking behaviour, so the longest wake bouts occur at these transitions, consistent with the crepuscular pattern of activity observed in multiple species [101,102].
Previously developed models have produced crepuscular behaviour by the coordination of two distinct oscillators . In the CTP model, however, the crepuscular behaviour is produced by a different mechanism. During the mid-day, or mid-night, SCN activity is saturated at high or low levels, respectively, such that incoming feedback signals have little effect on neurotransmitter release. By contrast, at dawn and dusk, the model is more sensitive to these signals, and this sensitivity results in increased release of peptide associated with state-dependent feedback. This model is consistent with recent data on SCN firing which show that certain SCN neurons are in a highly active state or a highly inactive state during the mid-day or mid-night, respectively . Further work is needed to incorporate the observations reported by Belle and colleagues into a population-level model of SCN activity.
In summary, the inability of the STO model to account for behaviour under both intact and SCN lesion conditions provides theoretical support for the hypothesis that the SCN exerts both wake- and sleep-promoting effects in the nocturnal rat. The TPDO and CTP models propose two mechanisms by which the SCN may achieve this dual role: the TPDO model predicts that different subpopulations of the SCN separately, and at different circadian times, release GABA and peptide; and the CTP model predicts that GABA and peptide are collocalized and that peptide is released when SCN neurons undergo fast increases in firing rate, while GABA release depends directly on firing-rate magnitude. Experimental investigations of SCN release of GABA and other peptides that are able to characterize their time-varying profiles on short time scales, their dependence on SCN activity and their effects on post-synaptic targets would allow evaluation of the mechanistic and observable predictions of each model. However, these modelling results bring us one step closer to understanding the interactions between the SCN and sleep–wake regulatory systems and the implications of these interactions for sleep disorders, jet lag and shift work.
The authors wish to thank Theresa Lee and members of the Lee laboratory for critical readings of the manuscript. This work was supported by Air Force Office of Scientific Research (AFOSR) grant FA9550-08-1-0111 and AFOSR Young Investigator grant FA 9550-08-01-0076 (D.B.F.).
One contribution of 11 to a Theme Issue ‘The complexity of sleep’.
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