Physiologically based quantitative modeling of unihemispheric sleep

Journal of Theoretical Biology 314 (2012) 109–119

Contents lists available at SciVerse ScienceDirect

Journal of Theoretical Biology journal homepage: www.elsevier.com/locate/yjtbi

Physiologically based quantitative modeling of unihemispheric sleep D.J. Kedziora a,n, R.G. Abeysuriya a, A.J.K. Phillips a,b, P.A. Robinson a,c,d a

School of Physics, University of Sydney, New South Wales 2006, Australia Division of Sleep Medicine, Brigham & Women’s Hospital, Harvard Medical School, 221 Longwood Avenue, Boston, MA 02115, USA Brain Dynamics Center, Sydney Medical School — Western, University of Sydney, Westmead, New South Wales 2145, Australia d Center for Integrated Research and Understanding of Sleep, 431 Glebe Point Road, New South Wales 2037, Australia b c

H I G H L I G H T S c

c

c

c

c

G R A P H I C A L

A B S T R A C T

A physiology-based quantitative model of unihemispheric sleep compared with experimental data. Contralateral inhibitory VLPO connections promote unihemispheric sleep. Ipsilateral inhibitory VLPO connections promote bihemispheric sleep. Decreasing homeostatic time constant increases interhemispheric switching frequency. Seal sleep pattern replicated by perturbation in contralateral connection strength.

a r t i c l e i n f o

abstract

Article history: Received 2 February 2012 Received in revised form 23 July 2012 Accepted 25 August 2012 Available online 1 September 2012

Unihemispheric sleep has been observed in numerous species, including birds and aquatic mammals. While knowledge of its functional role has been improved in recent years, the physiological mechanisms that generate this behavior remain poorly understood. Here, unihemispheric sleep is simulated using a physiologically based quantitative model of the mammalian ascending arousal system. The model includes mutual inhibition between wake-promoting monoaminergic nuclei (MA) and sleep-promoting ventrolateral preoptic nuclei (VLPO), driven by circadian and homeostatic drives as well as cholinergic and orexinergic input to MA. The model is extended here to incorporate two distinct hemispheres and their interconnections. It is postulated that inhibitory connections between VLPO nuclei in opposite hemispheres are responsible for unihemispheric sleep, and it is shown that contralateral inhibitory connections promote unihemispheric sleep while ipsilateral inhibitory connections promote bihemispheric sleep. The frequency of alternating unihemispheric sleep bouts is chiefly determined by sleep homeostasis and its corresponding time constant. It is shown that the model reproduces dolphin sleep, and that the sleep regimes of humans, cetaceans, and fur seals, the latter both terrestrially and in a marine environment, require only modest changes in contralateral connection strength and homeostatic time constant. It is further demonstrated that fur seals can potentially switch between their terrestrial bihemispheric and aquatic unihemispheric sleep patterns by varying just the contralateral connection strength. These results provide experimentally testable predictions regarding the differences between species that sleep bihemispherically and unihemispherically. & 2012 Elsevier Ltd. All rights reserved.

Keywords: Sleep dynamics Mammalian sleep Cetacean sleep Unihemispheric arousal Simulations

1. Introduction

n

Corresponding author. Tel.: þ61425360248. E-mail addresses: [email protected], [email protected] (D.J. Kedziora). 0022-5193/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jtbi.2012.08.031

Unihemispheric sleep is the phenomenon in which various marine mammals and birds have been found to sleep with only one half of the brain at a time (Rattenborg et al., 2000; Siegel, 2008). The physiological mechanism underlying this behavior is unknown,

110

D.J. Kedziora et al. / Journal of Theoretical Biology 314 (2012) 109–119

although several potential mechanisms and functions have been proposed (Borbe´ly and Achermann, 1999; Manger et al., 2004; Lyamin et al., 2008b). Understanding this phenomenon would potentially provide new insight into brain structure and dynamics, as well as a deeper understanding of sleep function and evolution. In this paper, we investigate a recently proposed mechanism for unihemispheric sleep in depth by introducing interhemispheric connections into a physiologically based model of mammalian sleep (Phillips et al., 2010). We demonstrate that this model is able to reproduce the salient features of unihemispheric sleep for multiple species, including the ability of fur seals to switch between unihemispheric and bihemispheric sleep modes, by comparing model simulations with biological data (Lyamin et al., 2008a). Unihemispheric sleep (UHS) is typified by interhemispheric asymmetry in electroencephalographic (EEG) recordings and other unilateral sleep behavior (Mukhametov et al., 1985; Lyamin et al., 2002). It has not been consistently reported to involve rapid eye movement (REM) sleep and is therefore sometimes termed unihemispheric slow wave sleep (SWS). The phenomenon can be completely absent from the sleep of a given species, such as humans, or may be the predominant mode of sleep, as for dolphins (Mukhametov et al., 1988). In certain species, such as fur seals, bihemispheric sleep (BHS) and UHS are both possible, and occur when the seal sleeps on land and in water, respectively (Lyamin et al., 2008a). Birds also appear to sleep unihemispherically as noted many centuries ago (Chaucer, 1380), although these periods are often brief and difficult to ascertain (Rattenborg et al., 2004; Low et al., 2008). There is also growing speculation that reptiles may be capable of UHS (Mathews et al., 2006), and new evidence shows that walruses may also exhibit it (Pryaslova et al., 2009). The reasons for the existence of UHS have been widely debated (Rattenborg et al., 2000; Siegel, 2005, 2009) and the dominant theory is that it developed in some species in response to the need to avoid drowning and other dangers specific to aquatic environments (Rattenborg et al., 1999). However, little is understood of the mechanism behind UHS, despite extensive reviews of neurobiological factors that could be involved (Lyamin et al., 2008b). Such is the practical importance of this knowledge that there has been military interest in extended alertness (Ridgway et al., 2006) and sleep deprivation rebound in cetaceans (Oleksenko et al., 1992). It has even been speculated that hemispheric interactions could be related to other biological rhythms; for example the nasal cycle (Werntz et al., 1983) or sleep disorders that involve hemispheric differences such as apnea (Huupponen et al., 2006). Investigations of UHS have traditionally used statistical analysis of experimental data (Huszagh and Infante, 1989). The present work investigates UHS by modeling it using a generalization of a recent physiologically based mathematical model of the sleep–wake switch, which was previously calibrated to the physiology of humans (Phillips and Robinson, 2008) and recently used successfully to simulate the sleep of other mammals (Phillips et al., 2010). As seen in Fig. 1, the ascending arousal system is a collection of brainstem and hypothalamic nuclei that diffusely project to the cerebrum, governing its arousal state. It consists of two primary groups, known as the monoaminergic (MA) and the cholinergic (ACh) nuclei. The former has high firing rates during wake and is subdued during sleep, whereas the latter is generally most active in REM (Vazquez and Baghdoyan, 2001). The neural populations of the MA and hypothalamic ventrolateral preoptic area (VLPO) mutually inhibit each other, generating flip-flop behavior in which the MA is wake-active and the VLPO is sleep-active. Orexin inputs stabilize the switch and promote wake (Saper et al., 2001). Finer details have been added to this picture of the basic sleep/ wake circuitry over the last decade, but we use a simplified model of the basic elements. Despite the known existence of non-photic zeitgebers such as food intake and temperature, there is

Fig. 1. Schematic of our two-hemisphere model of the sleep–wake switch (details in Section 2). The shaded area corresponds to the structures included in the original model (Phillips and Robinson, 2007). The monoaminergic group (MA) consists of the locus ceruleus, dorsal raphe and tuberomamillary nucleus. The ventrolateral preoptic area (VLPO) receives homeostatic (H) and circadian (C) drives. Inhibitory connections are represented by open arrow heads and excitatory inputs by solid ones. The MA receives excitatory input from the acetylcholine and orexin groups (ACh/Orx). MA activity is high in wake and low in sleep, so it is used as a proxy for arousal state when estimating the rate of buildup of the corresponding homeostatic drive H. Hypothesized ipsilateral (ci) and contralateral (cc) connections are shown.

experimental evidence suggesting that the VLPO plays a dominant role in sleep/wake regulation (Szymusiak et al., 1998; Lu et al., 2000) and that this simplified mechanism is sufficient to describe the large-scale dynamics of sleep and wake. This point is discussed further in Section 4. The VLPO receives input from circadian and homeostatic drives. The former is generated in the suprachiasmatic nucleus (SCN), which is entrained to the 24 h day primarily by light (Czeisler et al., 1999). The physical mechanism for the homeostatic drive is poorly understood, although some evidence suggests that accumulation of adenosine or other somnogens in the basal forebrain plays a key role, with the effect relayed to the VLPO (Hobson and Pace-Schott, 2002; Kalinchuk et al., 2008). The accumulated somnogens are then cleared during sleep when metabolism and corresponding somnogen production slows (Diaz-Munoz et al., 1999; Porkka-Heiskanen et al., 2000). In the present context, the precise identity of the homeostatic drive is not critical. Although the ascending arousal system has been well investigated in land mammals, the connectivity of hypothalamic and brainstem nuclei involved in sleep-regulation has not yet been mapped in the dolphin or other animals that sleep unihemispherically. However, we recently proposed that a mutually inhibitory contralateral connection between VLPO nuclei could stop BHS states occurring by preventing both nuclei from activating simultaneously (Phillips et al., 2010). This simple, experimentally testable, hypothesis is motivated by the fact that the VLPO and MA nuclei are bilaterally paired, aside from the dorsal raphe, which lies on the brainstem midline (Kandel et al., 2000; Chou et al., 2002). Here, we explore the consequences of our proposed mechanism in detail, including the effects of both ipsilateral and contralateral connections.

2. Theory We now introduce the model used to simulate unihemispheric sleep. In constructing any mathematical model, it is necessary to introduce some restrictions regarding the physiology to be modeled. In this instance, we have restricted our model to encompass the large-scale regulation of sleep by hypothalamic and brainstem control systems. In doing so, we do not deny the potential importance of local sleep phenomena; rather, we use our model to test whether bihemispheric and unihemispheric sleep can be accounted for by the circuitry of large-scale sleep control systems. In Section 2.1 we briefly review our sleep–wake switch model (Phillips and Robinson, 2007), and describe its extension to two distinct hemispheres. Then in

D.J. Kedziora et al. / Journal of Theoretical Biology 314 (2012) 109–119

Section 2.2, we describe how circadian and homeostatic drives are modeled in this context. 2.1. Model populations To generate UHS, we extend our prior neural mass neuronal population model (Phillips and Robinson, 2007), which treats the MA and VLPO nuclei by assigning average properties to each population (Nunez, 1995; Robinson et al., 1997). These populations are each subdivided into two parts to represent their bilateral division, as shown schematically in Fig. 1. Each MA and VLPO population is assigned a mean cell body voltage relative to resting of Vj(t) and a mean firing rate of Qj(t), where j ¼ v1 ,m1 and j ¼ v2 ,m2 for the VLPO and MA nuclei of the left and right hemispheres, respectively, as shown in Fig. 1. The relationship between Vj and Qj is described by a sigmoid function (Freeman, 1975), Q j ¼ SðV j Þ ¼

Q max , 1 þ exp½ðV j yÞ=s0 

ð1Þ

where Q max is the maximum possible firing pffiffiffi rate, y is the mean firing threshold relative to resting, and s0 p= 3 is the threshold’s standard deviation, which determines the sigmoid width (Robinson et al., 1997, 2004). The dynamics of all populations are represented by differential equations (Phillips and Robinson, 2007). The MA equations are

tm

dV m1 þ V m1 ¼ A þ nmv Q v1 , dt

ð2Þ

tm

dV m2 þ V m2 ¼ A þ nmv Q v2 , dt

ð3Þ

where tm is the average decay time following voltage perturbations, njk is the strength of input to population j from k measured in units of voltage divided by those of the quantity that njk multiplies (V s here, but appropriately modified in some cases below), and A represents an average excitatory input from acetylcholine and orexin (Phillips and Robinson, 2007). Variations in A are omitted to simplify the model, thereby smoothing out ultradian dynamics and restricting the model’s arousal states to sleep and wake. This is not a severe limitation here since UHS appears to be solely SWS (Rattenborg et al., 2000; Siegel, 2005). Interhemispheric interactions between cholinergic populations and the dorsal raphe’s placement on the brainstem midline may play a role in explaining why this SWS restriction exists, but we do not pursue this further here. Similarly, the VLPO equations are

tv

dV v1 þ V v1 ¼ nvm Q m1 þ L1 þ D1 , dt

ð4Þ

tv

dV v2 þ V v2 ¼ nvm Q m2 þ L2 þ D2 , dt

ð5Þ

where D1 and D2 are functions of the homeostatic and circadian drives, discussed in Section 2.2 below, and L1 and L2 represent hypothetical GABAergic connections between the two VLPOs, which are expected to be inhibitory (Phillips et al., 2010). Both L1 and L2 are functions of V v1 and V v2 , and each includes both an ipsilateral (self) connection and a contralateral (cross) connection, as shown schematically in Fig. 1. We thus use the forms L1 ¼ cc Q v2 þ ci Q v1 ,

ð6Þ

L2 ¼ cc Q v1 þ ci Q v2 ,

ð7Þ

where cc ¼ nv1 v2 ¼ nv2 v1 and ci ¼ nv1 v1 ¼ nv2 v2 are the respective weights of contralateral and ipsilateral connections, and are negative if inhibitory and positive if excitatory. The effects of varying these two parameters are investigated in Sections 3.1 and 3.2, respectively. For simplicity, we assume that all parameter values are identical between hemispheres.

111

This model assumes that the VLPO is central to sleep/wake regulation, as indicated by the drive inputs in Eqs. (4) and (5). Secondary regulatory mechanisms can be incorporated into this framework, but experimental evidence suggests that sleep is primarily determined by the VLPO (Hobson and Pace-Schott, 2002; Kalinchuk et al., 2008), which justifies the parsimony applied here. We discuss this point further in Section 4. 2.2. Model drives The drives to the respective VLPOs are D1 ¼ nvc C þ nvh H1 ,

ð8Þ

D2 ¼ nvc C þ nvh H2 ,

ð9Þ

where nvc and nvh are weighted strengths of the circadian (C) and homeostatic (H) drives, respectively, as shown schematically in Fig. 1. We model a separate homeostatic drive for each hemisphere, based on well documented effects of localized homeostasis in multiple species (Kattler et al., 1994; Vyazovskiy et al., 2000; Huber et al., 2004). Moreover, the lateralization of cortical acetylcholine in unihemispheric sleepers (Lapierre et al., 2007) suggests similar divisions may exist with monoamines (excluding those that originate from the dorsal raphe). Together, this evidence provides experimental justification for at least a bilateral division of the homeostatic drive, even in animals that sleep bihemispherically. We model C as a sinusoidal input to both hemispheres, as it is reasonable to assume each hemisphere is independently well entrained by exposure to environmental light, with CðtÞ ¼ c0 þ cos½OðtaÞ,

ð10Þ

where O ¼ 2p=ð24 hÞ is the angular frequency of Earth’s rotation, a is the phase, and c0 is the mean circadian drive. However, cases of hemispheric differences in entrained phase may exist due to both the complete crossing over of optic nerves in dolphins, known as complete decussation (Tarpley et al., 1994), and the tendency to use monocular vision (Delfour and Marten, 2006). This could motivate a lateralization of the model circadian drive in future studies because it suggests that environmental light signals project from each eye to only the contralateral SCN in dolphins. In contrast, this decussation is only partial in humans, allowing light signals to project from each eye to the SCN of both hemispheres. As mentioned in Section 1, the exact physiological mechanism of the homeostatic drive is still unclear, but the simplest physical assumptions are that somnogen clearance rate is proportional to concentration, and MA activity is well correlated with arousal and hence somnogen production (Aston-Jones et al., 1991). For the two hemispheres, this yields

w

dH1 þ H1 ¼ mQ m1 , dt

ð11Þ

w

dH2 þ H2 ¼ mQ m2 , dt

ð12Þ

where w is the homeostatic time constant and m is a constant determining the rate of production (Phillips and Robinson, 2007). We note a minor difference from previous work in the fact that we have modified the notation so that there is no reference to chemical concentration in the homeostatic drive. 2.3. Parameters The parameters for the original bilateral model were calibrated to reproduce human sleep patterns (Phillips and Robinson, 2007, 2008), and nominal values are given in Table 1. Variations in w and c0 have been shown to generate sleep patterns for many other mammals (Phillips et al., 2010). We show here that varying

112

D.J. Kedziora et al. / Journal of Theoretical Biology 314 (2012) 109–119

equilibriums lie in regions of low V_ v . We label these by the state of each hemisphere, thus defining the sleep–sleep state (SS) to be when VLPO voltages are high in both hemispheres. Similarly we establish equilibriums for wake–wake (WW), sleep–wake (SW; left hemisphere asleep, right awake), and wake–sleep (WS) states. To illustrate how the system evolves between its equilibrium states, Fig. 2(a) and (b) shows the time evolution for BHS with cc ¼0, and Fig. 2(c)–(e) shows UHS with cc ¼ 6 mV s. The system never rests permanently in any state because the circadian and homeostatic drives are continually changing. The circadian component can be described as pushing the state of the system along the V v1 ¼ V v2 line, whereas interhemispheric asymmetry in homeostatic drives pushes the system transverse to this line, driving the system towards SW for H1 4 H2 and towards WS for H2 4 H1 . To further analytically investigate the equilibriums of the system, we set dV mj =dt ¼ 0 for j ¼1,2, reducing Eqs. (2)–(5) to

Table 1 Nominal human parameters used in the model (Phillips and Robinson, 2008). Parameter

Human Nominal

Units

nvc nvh w m

2.9 1.0 45 4.4 4.5 100 10 3 1.3 2.1 1.8 10 10

mV mV h s 1 s1 mV mV mV mV s mV s s s

c0 Q max

y

s0 A nvm nmv

tm tv

contralateral connection strength cc is sufficient to generate UHS, while w modulates the rate of cycling between sleep bouts. The ipsilateral connection strength ci is shown to effect finer control of sleep patterns by inhibiting UHS, while affecting total sleep time and minimum population voltages. Finally, c0 affects total sleep duration with little effect on other dynamics.

3. Results We now describe the basic sleep patterns generated by the model and examine, both analytically and numerically, the effect of cc in Section 3.1. This is followed in Section 3.2 by numerical analysis of how ci affects the dynamics. In Section 3.3 we examine the effects of varying w, then in Section 3.4 we examine the effects of varying c0. Finally, we compare the model simulations with experiment in Section 3.5. Because the relationship between the parameters is complex, we focus on exploring two-dimensional subspaces of parameter space in Sections 3.2–3.4. All other parameters are fixed at their nominal values. 3.1. Contralateral connections The solution of the differential equations (2)–(5) for ci ¼ cc ¼ 0, with other parameters taking the values given in Table 1, describes standard human sleep patterns as demonstrated previously (Phillips and Robinson, 2007). Here, wake is defined to occur when Q m \ 3 s1 , during which Vm is high, Vv is low and H is increasing. Sleep occurs when Q m t3 s1 , Vm is low, Vv is high and H is decreasing. According to Eq. (1), this firing rate corresponds to a numerical threshold of about  0.5 mV, chosen due to MA sleep voltages occasionally dipping slightly below 0 mV. Due to the flip-flop nature of the system, the precise cut-off value does not significantly affect the analysis. Transitions between wake and sleep are rapid, on the order of 10 min. We now show that the contralateral connection strength, cc, is critical in determining whether a sleep pattern is unihemispheric or bihemispheric: sufficiently strong inhibitory connections result in UHS. A useful measure of the system dynamics is the rate of voltage changes. Hence, to help probe the structure of state space, we consider the quantity V_ v ¼ ½ðdV v1 =dtÞ2 þ ðdV v2 =dtÞ2 1=2

ð13Þ

for fixed values of cc, with ci ¼0 and all other parameters as listed in Table 1. A contour plot of this quantity is shown in Fig. 2, where

tv

dV v1 ¼ nvm Sðnmv Q v1 þ AÞ þD þcc Q v2 þci Q v1 V v1 , dt

ð14Þ

tv

dV v2 ¼ nvm Sðnmv Q v2 þ AÞ þD þcc Q v1 þci Q v2 V v2 , dt

ð15Þ

where we have assumed D ¼ D1 ¼ D2 and thus H1 ¼ H2 . This simplification is reasonable because the two homeostatic drives are almost synchronized in practice; both increase monotonically during the day and then alternately decrease across left and right UHS bouts during the night. All four stable states can be generated for physiologically realistic values of the parameters, D, cc, and ci. However, with ci ¼0, the UHS states (SW and WS) only exist when cc is more negative than a certain threshold strength. Decreasing cc further causes the SS state to become less stable relative to SW and WS, leading to less time spent in SS. Once cc falls beyond another threshold, dependent on parameters discussed later, the BHS state is no longer accessed and sleep becomes purely unihemispheric, as shown in Fig. 2(c)–(e). The WW and SS states lie on the V v1 ¼ V v2 diagonal, so we can begin to explore how the SS state loses stability by setting V v1 ¼ V v2 in Eqs. (14) and (15), which further reduces the dimensionality of the system and yields

tv

dV v þV v ¼ nvm Sðnmv Q v þ AÞ þD þðcc þci ÞQ v : dt

ð16Þ

With the above analytical assumptions, the reduced system is found to bifurcate from having stable SS and WW states to having only a stable WW state on the diagonal for combined coupling strength values of cc þ ci o11 mV s. This calculation is done with 5 mV r D r 10 mV, beyond which resulting neural group voltages tend to be unphysiological according to a conservative range established in Section 3.2 below. However, while the above analysis provides an absolute bound on the existence of a stable SS state and thus a threshold for BHS no longer being possible, UHS patterns can still be generated for less negative values of cc þ ci due to the system preferentially accessing the WS and SW states (V v1 aV v2 ) over the SS state (V v1 ¼ V v2 ). It is also possible to determine the type of sleep pattern from the path shape through V v1 V v2 space. For default values of w ¼ 45 h and c0 ¼4.5, with ci ¼0, the model predicts BHS for cc 40:9 mV s, mixed BHS/UHS for 3:5 mV s occ o0:9 mV s, and UHS for cc o 3:5 mV s, as shown in Fig. 3(a)–(c). Our finding that negative cc can induce unihemispheric sleep accords with the behavior expected of mutually inhibitory nuclei. At the onset of bihemispheric sleep, both VLPO nuclei increase in activity. However, a substantial contralateral inhibition, combined with any firing rate asymmetry, will result in one VLPO nucleus suppressing the activation of the other. Consequently, only the MA nucleus in the VLPO-active hemisphere is inhibited, resulting in unihemispheric sleep. Once the VLPO-active hemisphere is

D.J. Kedziora et al. / Journal of Theoretical Biology 314 (2012) 109–119

113

SS Vv2(mV)

Vv2(mV)

SS

WW WW Vv1(mV)

Vv1(mV)

WS

Vv2(mV)

Vv2(mV)

WS

WW

WW

SW

SW

Vv1(mV)

Vv1(mV)

Vv2(mV)

WS

WW

SW

Vv1(mV) Fig. 2. Snapshots from the evolution of V_ v and a corresponding trajectory of VLPO voltages in V v1 V v2 space. (a) and (b) show evolution between bihemispheric wake (WW) and sleep (SS), and (c)–(e) show UHS. (a) System transitions to a WW state. (b) System returns to SS state. (c) VLPO voltages deviate from the V v1 ¼ V v2 line, signifying onset of a UHS state SW (left hemisphere S, right W). (d) Interhemispheric asymmetry in homeostatic pressure causes a rapid transition from SW to WS. (e) Bout of UHS ends with a return to WW, possibly after several cycles between SW and WS states.

sufficiently cleared of somnogens, the higher sleep homeostatic pressure in the other hemisphere triggers an inversion in the activity of the two VLPO nuclei. This inter-hemispheric cycle of VLPO activation and inhibition continues until the somnogens in both hemispheres are sufficiently diminished and/or the circadian drive for wakefulness becomes sufficiently strong to induce bihemispheric wakefulness. If cc is positive (i.e., the contralateral connection is excitatory), then synchronization between VLPO nuclei is strengthened and bihemispheric sleep is promoted. 3.2. Ipsilateral connections We now explore the effects of ipsilateral VLPO self-connections on sleep, motivated by the fact that if GABAergic contralateral connections exist, then the existence of self-connections is at least plausible.

We simulate 400 h of sleep for a range of cc and ci values, by which point all patterns enter a stable repetitive cycle. For each run, the amounts of BHS, UHS, and wake are calculated for the final 24 h, along with the frequency of hemispheric switching and the length of the last unbroken sleep episode in either hemisphere. This is done for the default human values of w ¼ 45 h and c0 ¼4.5 (Phillips and Robinson, 2008), and repeated for w ¼ 10 h, as this value was found to generate sleep patterns typical of cetaceans (Phillips et al., 2010), discussed in Section 3.3. In Fig. 4, the contours of constant UHS duration indicate that, in general, inhibitory cc can be classified as UHS-promoting and inhibitory ci as UHS-opposing. The explanation for this latter result is complicated by the fact that UHS is an interhemispheric phenomenon, whereas selfconnections are intrinsically intrahemispheric. Without inhibitory

114

D.J. Kedziora et al. / Journal of Theoretical Biology 314 (2012) 109–119

−5

Right

Vv (mV)

5 Left

0

0

Vm (mV)

−15

−10

−10

−20

−20

16

16

14

14

12 0

6

12

12 18 24 30 36 42 48 54 60 66 72 t (h)

0

6 12 18 24 30 36 42 48 54 60 66 72 t (h)

0

6 12 18 24 30 36 42 48 54 60 66 72 t (h)

5 Vv (mV)

10 Vv (mV)

−5

−15

H

H

Vm (mV)

Vv (mV)

5

0 −10 −20

−5 −15

Vm (mV)

Vm (mV)

5 0 −20

−5 −15

−40

20 H

H

16 15

14 0

6

12 18 24 30 36 42 48 54 60 66 72 t (h)

10

Vv (mV)

5 −5

Vm (mV)

−15

0

−10 −20

H

20 15 10

0

6 12 18 24 30 36 42 48 54 60 66 72 t (h)

Fig. 3. Time series for different sleep regimes. (a) Consolidated BHS for cc ¼ 0 and w ¼ 45 h (left- and right-hemisphere curves overlap). (b) The effect of lowering cc to 3 mV s within the mixed BHS/UHS regime. (c) Pure low-frequency UHS for cc ¼ 6 mV s and w ¼ 45 h. (d) Polyphasic BHS for cc ¼ 0 and w ¼ 10 h (left- and right-hemisphere curves overlap). (e) Pure high-frequency UHS for cc ¼ 3 mV s and w ¼ 10 h.

D.J. Kedziora et al. / Journal of Theoretical Biology 314 (2012) 109–119

12 10 0

1

Within the above bounds, cc and ci affect the system dynamics in similar but opposing ways; negative ci promotes BHS. This does not necessarily contradict the result in Section 3.1 that cc þ ci o 11 mV s leaves only one stable state on the VLPO diagonal, because a sufficiently strong inhibitory ipsilateral connection will increase the VLPO voltage of the WW state until it more closely resembles a SS state. However, this scenario occurs in a region of parameter space that is likely to be physiologically unrealistic. Thus, to simplify analysis, we set ci ¼0 in all following sections.

9 2 3 4 5 6 8 10 11 7

-ci (μV s)

8

12

6

115

4

2

12

-ci (μV s)

10

3.3. Interhemispheric switching frequency

13

2

1 3 2 5 6 4 7

12

6 -cc (μV s)

8

9

8 10 6 4

11

2 2

6 -cc (μV s)

12

Fig. 4. Contour plots of the total daily duration of UHS (WS and SW) in hours and its dependency on coupling for (a) w ¼ 45 h and (b) w ¼ 10 h.

Referring to Fig. 2(d), the frequency of hemispheric switching is determined by the length of time the system spends in an offdiagonal state (WS or SW) before transitioning to the other. We find that this frequency is strongly affected by the homeostatic time constant. Lower w values result in greater frequency of hemispheric alternation, because each hemisphere accumulates and clears somnogens more rapidly. The experimental observation that mammals undergoing UHS rarely sleep with one hemisphere for more than 2 h at a time (Mukhametov et al., 1988; Lyamin et al., 2002; Siegel, 2005) thus sets an upper bound on w (see below for further discussion). Fig. 5 shows how the type of sleep depends on cc and w. As with ci in Section 3.2, regions of parameter space are deemed unphysiological if MA voltages go beyond the bounds of  40 mV and  6 mV in sleep, thus preventing contralateral coupling from being significantly excitatory. Consolidated bihemispheric sleep (BHSC) shown in Fig. 3(a) consists of one SS bout every 24 h and exists for w \15 h. Defined

100 90

70 60

Unphysical

80

χ (h)

cc to set up contrasting behavior between hemispheres, changing ci alone cannot induce UHS. However, ipsilateral inhibition suppresses each VLPO nucleus in proportion to its current rate of firing. This self-inhibition tends to counteract any firing rate asymmetry and thus reduces the amount of inhibition received by the less active nucleus. A negative value of ci therefore suppresses unihemispheric sleep by reducing the effect of contralateral inhibition, meaning a stronger contralateral connection would be required to induce unihemispheric sleep. Conversely, a positive value of ci promotes unihemispheric sleep. Another result of the parameter space exploration is that ipsilateral connections affect the minimum MA voltage amplitude more significantly than do contralateral connections, particularly for positive excitatory values of ci. Parameter bounds can thus be found by excluding pathologically low or high values of V mj , for j ¼1,2. Although it is difficult to determine the acceptable range for all species, conservative (i.e. broad) estimates for the lower and upper bounds of MA firing rates during sleep are approximately 6 mHz and 0.5 Hz, which leads to a derived feasible MA voltage range of  40 mV to  6 mV relative to resting. These criteria yield 12 mV s o ci o þ1 mV s (where the positive sign indicates excitatory coupling) for cc ¼0 and the nominal human values of w ¼ 45 h and c0 ¼4.5. However, because the minimum MA voltage values drop much more suddenly for excitatory ci, it appears that the upper bound is much better defined than the lower bound across a broad range of w values. Therefore, if the ipsilateral connection were to be excitatory, it would have to be proportionally much weaker than the corresponding inhibitory contralateral connection.

UHSL BHSC BHS/UHS

50 3b

3a

40

3c

30 20 10 3.5

3d

BHSP 1.5

0

3e −2.5

UHSH −5

−7.5

cc (μV s) Fig. 5. Phase diagram of sleep regimes vs. w and cc for ci ¼0. The dashed line divides contralateral coupling between excitatory (cc 4 0) and inhibitory (cc o 0). Regions of BHS and UHS are marked where less than 10% and more than 90% of total sleep is unihemispheric, respectively. The intermediate region is the transitional regime (BHS/UHS). Polyphasic bihemispheric sleep (BHSP) is distinguished from consolidated bihemispheric sleep (BHSC) by having two or more bilateral sleep bouts per 24 h. Low (UHSL) and high (UHSH) frequency unihemispheric sleep is denoted by the average sleep bout duration being greater or less than 2 h, respectively. Black denotes physiologically unrealistic regimes for which MA voltages pass outside the bounds of 40 mV and 6 mV during sleep. Crosses mark the parameters at which the sleep patterns in Fig. 3 arise.

D.J. Kedziora et al. / Journal of Theoretical Biology 314 (2012) 109–119

3.4. Wake duration This section investigates the effect on system dynamics of variations in c0, the mean input to the VLPO, which has previously been shown to modify total daily wake duration with little effect on other dynamics (Phillips and Robinson, 2007; Phillips et al., 2010). In Fig. 6(a), the amount of bihemispheric wake is shown as a function of cc and c0. For BHSC and BHS/UHS (cc \ 3:5 mV s), there is an approximately linear relationship between c0 and the duration of bihemispheric wake: increasing c0 from 1.5 to 7 monotonically increases wake duration from 0 to 20 h. Similarly for UHSL (cc t 3:5 mV s), there is an approximately linear relationship: increasing c0 from 2 to 7 monotonically increases wake duration from 0 to 20 h. Therefore, the effect of c0 on wake duration appears qualitatively similar regardless of the value of cc, provided that changes in cc do not cause a transition between UHS and BHS. Fig. 6(b) shows the effect of c0 on sleep and wake durations to be nearly independent of changes in ci (the contours are nearly horizontal). Likewise, Fig. 6(c) shows that variations in w have little effect on wake duration except for the low values that mark the UHSH regime, where the relationship to c0 is nonetheless still monotonic. 3.5. Comparisons with data We now show that the model can reproduce the salient features of experimental data. In the spirit of parsimony, we change as few parameters as possible from previously calibrated human values

7

20

18

16 14 12 10

4.5

c0

6 2

2

8 4

-0.5 -3

2

4

6

8

10

12

8

10

12

-cc (μV s)

7

20 18 16

4.5

14 12

c0

here to have more than 90% of total sleep as bilateral, BHSC only exists if cc 4 1:7 mV s. However, as w decreases, the duration of bouts decreases while the corresponding frequency increases. Thus, w o 15 h results in polyphasic bihemispheric sleep (BHSP ), shown in Fig. 3(d), in which there are multiple SS bouts per day. This regime has been examined in detail elsewhere (Phillips et al., 2010) and can account for the diverse sleep patterns of numerous terrestrial mammals. Low frequency unihemispheric sleep (UHSL ) shown in Fig. 3(c) also appears for w \15 h in Fig. 5. With UHS defined here to have less than 10% of total sleep as bilateral, it exists for cc o3:5 mV s. Separating BHSC and UHSL is the intermediate mode of sleep (BHS/UHS) shown in Fig. 3(b). As with BHSP , decreased values of w promote more rapid cycling of UHS. The low frequency pattern in Fig. 3(c) has only two UHS bouts per night; one in the SW state and one in the WS state. By contrast, the high frequency pattern in Fig. 3(e) has eight UHS bouts per night; four in the SW state and four in the WS state. Roughly the same total amount of time is spent asleep in both cases, but the average unihemispheric bout duration is shorter in the latter case, as calculated by dividing the total time spent in SW and WS by the number of distinct SW and WS bouts. Here we define high frequency unihemispheric sleep (UHSH ) for patterns where the average bout length is less than 2 h, and low frequency unihemispheric sleep (UHSL ) for patterns where the average bout length is greater than 2 h. The threshold of 2 h is motivated by the fact that all UHS patterns observed to date satisfy the UHSH definition. Given this distinction, UHSH requires w t15 h and cc o 1:5 mV s, as shown in Fig. 5. We henceforth use w ¼ 10 h as an estimate of a marine mammal’s somnogen clearance time. In Section 3.2, it was shown that strengthened ipsilateral coupling required strengthened contralateral coupling for UHSL to occur. Consistent with this observation, a greatly decreased value of ci ¼ 10 mV s reproduces a similar diagram to Fig. 5, except with all regions stretched along the cc axis. In contrast, the boundary for UHSH remains at w  15 h, regardless of ci.

10

2

8 4

-0.5 -3

7

2

4

6 2

6 -ci (μV s)

20

18

16 14

4.5

12

c0

116

10

2

8 6 2

-0.5

-3

10

20

4

30

40

50

χ(h) Fig. 6. Daily time spent in bihemispheric wake (WW) as a function of c0 with contour labels for hours. (a) Time in WW as a function of c0 and cc (with w ¼ 45 h and ci ¼0). (b) Time in WW as a function of c0 and ci (with cc ¼ 3 mV s and w ¼ 45 h). (c) Time in WW as a function of c0 and w (with cc ¼ 3 mV s and ci ¼0).

(Phillips and Robinson, 2008) shown in Table 1. Figs. 4(a) and 5 showed that these nominal parameter values yield BHS for weak values of cc \ 1 mV s, with only a small change in this threshold at lower levels of ci. In Section 3.3, we identified the five distinct regimes of BHSC, BHSP, BHS/UHS, UHSL, and UHSH. From the sleep data available, the UHSL region does not appear to represent any mammal that has yet been studied (Mukhametov et al., 1988; Lyamin et al., 2002; Siegel, 2005). This implies w o 15 h for marine mammals such as dolphins and seals. Some mammals such as whales may have higher values of w because of scaling related to their physical size (Phillips et al., 2010). The parameter c0 can easily be constrained based on its relationship with bihemispheric wake, as described in Section 3.4. We can also estimate the value of cc þ ci for each species based on whether the primary mode of sleep is bihemispheric or unihemispheric. However, without additional data, it is not possible to constrain the values of cc and ci separately. We thus assume ci ¼0 for simplicity.

D.J. Kedziora et al. / Journal of Theoretical Biology 314 (2012) 109–119

Vv (mV)

0 −10 −20

5 −5 −15

Vm (mV)

Vm (mV)

10

117

12

18

0 −10 −20

H

20 15 10 0

6

12

18

24

30

36

42

t (h)

Fig. 7. Sleep data from the literature and its comparison with a simulated sleep pattern. (a) 12-h sleep pattern recorded from a dolphin, underneath legend describing three possible states denoted by bar amplitude. Brief moments of wake (I) are marked by an absence of bars. Small (II) and large (III) amplitude bars indicate periods of moderate-frequency and delta electrocorticographic synchronization, respectively, where the former includes sleep spindles and slow-wave patterns with a delta index below 50%, while the latter involves slow peak amplitude waves with a delta index above 50%. The standard delta band comprises frequencies below 4 Hz. Bars above or below baseline denote that the state describes the left (L) or right (R) hemisphere, respectively. Adapted with kind permission from Springer Science+Business Media: Mukhametov et al. (1988). (b) Simulated pattern uses c0 ¼4.5, w ¼ 12 h, cc ¼ 3 mV s and ci ¼0. Both the experiment and model yield a 12 h sleep period with six interhemispheric sleep transitions. (c) 12-h EEG of a unihemispherically sleeping beluga whale. Reprinted by permission from Macmillan Publishers Ltd: Siegel (2005).

Fig. 7 compares a model simulation of dolphin sleep with experimental data (Mukhametov et al., 1988; Siegel, 2005). Using c0 ¼4.5, w ¼ 12 h and cc ¼ 3 mV s, the model replicates a fast cycling rate with seven unilateral sleep bouts, each under 2 h duration, as well as the absence of a SS state. When we change cc, the model transitions between UHS and BHS (Phillips et al., 2010), mimicking the change in sleep patterns of the fur seal, which is able to transition between sleep regimes depending on whether it is in a terrestrial or marine environment (Mukhametov et al., 1985). Fig. 8(a) shows interhemispheric asymmetry in the EEG of a seal undergoing bilateral terrestrial sleep. The appearance is very similar to the mixed BHS/UHS state discussed in Section 3.1. Fig. 8(a) also demonstrates that fur seals appear to sleep polyphasically while on land, corresponding to BHSP. In fact most land mammals sleep polyphasically (Tobler and Schwierin, 1996). This fact suggests that it is possible to model the seal transition from UHSH to BHS using a low unchanged w value and varying contralateral coupling strength alone, as hypothesized previously (Phillips et al., 2010). An example of such sleep patterns is shown in Fig. 8(b), with w ¼ 10 h, c0 ¼ 4:5, ci ¼ 0 and cc shifting from 6 mV s to 0 after 6 h, before returning to its original value at 30 h. The transitions between BHSP synchronization and UHSH antisynchronization at these two respective times are very rapid, supporting the utility of this model in describing fur seal sleep transitions.

Fig. 8. Seal sleep patterns. (a) 3 h of seal terrestrial sleep in both hemispheres via EEG, with unshaded regions representing wake (1), shaded regions noting moderate (2) or delta synchronization (3), and PS standing for paradoxical sleep. Moderate-frequency synchronization includes theta- and delta-waves as well as sleep spindles, while delta synchronization involves over 50% of a scoring epoch (20 seconds) consisting of maximal amplitude delta-waves. The standard delta band comprises frequencies below 4 Hz. Reprinted with kind permission from Springer Science+Business Media: Mukhametov et al. (1985). (b) Simulation of UHS in a marine environment with cc ¼ 6 mV s. Between 6 and 30 h, the seal undergoes terrestrial fragmented BHS with a cc of 0. All other parameters are default human, except for w ¼ 10 h.

4. Summary and discussion We have generalized and applied an existing model of sleep physiology (Phillips and Robinson, 2007) to generate unihemispheric sleep patterns by dividing each neural population into two and including contralateral and ipsilateral connections between VLPO nuclei. The model’s dynamics were explored numerically and found to reproduce a wide variety of unihemispheric and bihemispheric sleep dynamics, as summarized below. In Section 3.1, we showed that a zero, weak inhibitory or weak excitatory contralateral connection strength between VLPO nuclei reproduces normal human sleep patterns, demonstrating consistency with previous forms of the model (Phillips and Robinson, 2008). We then used bifurcation analysis to determine the absolute bound for the existence of the BHS state. When combined with the fact that ci cannot be higher than þ 1 mV s for feasible MA voltages, cc þ ci 411 mV s limits the allowable range of connection strengths for species that sleep bihemispherically. However, simulations with default parameters revealed that higher values of cc þci were sufficient to prevent the model accessing the SS state. With ci ¼0, cc 4 0:9 mV s generates BHS, cc o 3:5 mV s generates UHS, and the region between generates mixed BHS/UHS. These results arise from a model of unihemispheric sleep that is based on the VLPO sleep/wake switch, considered central to sleep/wake regulation (Saper et al., 2001, 2010). Given this, it must be noted that sleep is regulated on multiple biological scales and that the existence of local sleep shows that some phenomena associated with sleep and wake states can be locally generated. However, without large scale coordination, it is difficult to account for

118

D.J. Kedziora et al. / Journal of Theoretical Biology 314 (2012) 109–119

the sleep/wake synchrony of all brain regions in bihemispheric sleep, and it is even more difficult to account for the anti-phase oscillation of the two brain halves in unihemispheric sleep. These phenomena require higher level orchestration, which, based on current understanding, is likely provided by hypothalamic and brainstem control systems. Bilateral loss of 70% of VLPO neurons in the rat causes a 50–60% reduction in NREM sleep (Lu et al., 2000), and the degree of proportionality in this finding suggests a dominant role for the VLPO regarding sleep patterns. Moreover, adenosine, a major sleep homeostatic factor, is known to act directly on the VLPO and on nuclei that connect to the VLPO (Morairty et al., 2004; Huang et al., 2007). The VLPO has therefore been interpreted by us and others (Hobson and Pace-Schott, 2002; Saper et al., 2010) to be an integrator of homeostatic and circadian drives. Without further study involving total lesions, the possibility of sleep regulatory mechanisms secondary to the VLPO cannot be ruled out, e.g., circadian and homeostatic inputs to neuronal populations in the MA, basal forebrain, thalamus, and cortex. Nonetheless, in the intact animal, the VLPO appears to be the primary determinant of sleep (Szymusiak et al., 1998). This function is analogous to that of the SCN; the SCN times the sleep/wake cycle in the intact animal by promoting sleep or wake at certain phases, but both sleep and wake are still present in animals with bilateral SCN lesions, albeit in different amounts (Edgar et al., 1993). The locus for the mechanism which determines whether sleep is bihemispheric or unihemispheric is currently unknown. Here, we hypothesized that the mechanism could be at the level of the sleep/wake switch. We then showed that a contralateral VLPO connection is a plausible mechanism for promoting unihemispheric sleep, while an ipsilateral VLPO connection is a plausible mechanism for promoting bihemispheric sleep. Three pieces of experimental evidence support our hypothesis. First, there are many more ipsilateral than contralateral VLPO-VLPO connections in the rat, which sleeps bihemispherically (Chou et al., 2002). It might be naively thought that weak or absent contralateral connectivity would lead to hemispheric independence and a predilection for unihemispheric sleep, but this case indicates that this is not true and that our model dynamics are consistent with the observed connectivity. Second, the loss of inter-cortical connections in the case of acallosal humans does not result in unihemispheric sleep (Nielsen et al., 1992). Third, bisection of the brainstem in the cat results in the independence of the sleep/wake state between the two hemispheres, allowing for the accessibility of both bihemispheric and unihemispheric sleep states along with the standard wake state (Michel and Roffwarg, 1967). Even so, the resolution of this hypothesis may rest with further study of fur seals, which have likely evolved coupling with borderline strength, susceptible to controlled perturbation. In Section 3.2, we explored the possibility of ipsilateral VLPO connections, and found that they serve to suppress UHS in contrast to contralateral connections. In Section 3.3, we elucidated the importance of the homeostatic time constant w in determining the rate of cycling between UHS bouts. Regardless of the value of ci, there are two distinct regions for w 4 15 h: a consolidated BHS regime representative of humans and other primates for weak contralateral connections, and a low-frequency UHS regime, not yet found in nature, for strong contralateral connections. In contrast, the w o15 h region consists of high-frequency UHS and, for negligible inhibitory (or excitatory) contralateral connection strength, a polyphasic BHS regime, as seen previously (Phillips et al., 2010). This may help to explain how fur seals are capable of shifting between fragmented bihemispheric terrestrial sleep and marine UHS with ease. It is probable that, due to their w value, they require only minor variations in coupling strength to transition between polyphasic BHS and high frequency UHS. By contrast, humans, who have a high value of w  45 h, would require substantial modifications in coupling strength to achieve UHS.

Our preliminary results (Phillips et al., 2010) previously showed that, in the absence of ipsilateral connections, inhibitory contralateral connections would have to be very weak to permit BHS. The present results demonstrate that ipsilateral connections can counterbalance the effects of strong contralateral connections, consistent with the finding that bihemispheric sleepers have ipsilateral connections (Chou et al., 2002). A consequence of this is that transitions between UHS and BHS can potentially be achieved by modulating either contralateral or ipsilateral connection strengths, or both. In Section 3.4, we demonstrated that the mean VLPO drive c0 modifies total sleep duration nearly independently of variations in ci and cc that do not induce a sleep regime transition. We then further demonstrated the plausibility of our model in Section 3.5, by simulating the sleep of dolphins and fur seals, including UHSBHS transitions in the latter. A comprehensive calibration of the model to the sleep of a particular marine mammal awaits more detailed quantitative studies of UHS. Complexities arise in gathering data from marine animals, and EEG experiments to date have only been carried out in artificial environments (Lyamin et al., 2008a). Extending the model beyond mammals to birds and other species is another potential application, with different phenomena to address. For example, while UHS has been confirmed in birds, hypotheses such as the existence of prolonged UHS during migration have not yet been tested or modeled (Rattenborg et al., 2004). Our hypothesis that contralateral inhibitory connections exist is experimentally testable, and it may be that supporting commissures exist at multiple levels of the neural architecture, such as the thalamus and cortex. These ideas might be tested through combining VLPO retrograde tracing with zoological brain studies (Chou et al., 2002; Tarpley et al., 1994). In addition, the model allows for parameter values to be varied separately for each hemisphere, with future potential for studying hemispheric asymmetries. Whether there is a propensity for one hemisphere or the other to be the first to sleep in UHS, what the effects of unihemispheric sleep deprivation or insomnia are, and other similar questions, can potentially be addressed in this way. A key aim of this research area is not just to study the sleep patterns of cetaceans but also to relate them to humans and determine whether human sleep can be better understood and/or modified in useful ways (Siegel, 2008). In that respect, studies about prolonged cetacean vigilance under sleep deprivation (Ridgway et al., 2006) can be aided by incorporating relevant components into the model and investigating the simulated effects. We speculate that sleep pathologies that sometimes have lateralized or unihemispheric effects, such as apnea (Huupponen et al., 2006) and some parasomnias, could also potentially be explored in the future using this framework.

Acknowledgments The Australian Research Council, The National Health and Medical Research Council, and the Westmead Millennium Institute supported this work. References Aston-Jones, G., Chiang, C., Alexinsky, T., 1991. Discharge of noradrenergic locus coeruleus neurons in behaving rats and monkeys suggests a role in vigilance. Prog. Brain Res. 88, 501–520. Borbe´ly, A.A., Achermann, P., 1999. Sleep homeostasis and models of sleep regulation. J. Biol. Rhythms 14, 559–568. Chaucer, G., c. 1380. The Canterbury Tales, The Prologue. Chou, T.C., Bjorkum, A.A., Gaus, S.E., Lu, J., Scammell, T.E., Saper, C.B., 2002. Afferents to the ventrolateral preoptic nucleus. J. Neurosci. 22, 977–990.

D.J. Kedziora et al. / Journal of Theoretical Biology 314 (2012) 109–119

Czeisler, C.A., Duffy, J.F., Shanahan, T.L., Brown, E.N., Mitchell, J.F., Rimmer, D.W., Ronda, J.M., Silva, E.J., Allan, J.S., Emens, J.S., Dijk, D.J., Kronauer, R.E., 1999. Stability, precision, and near-24-hour period of the human circadian pacemaker. Science 284, 2177–2181. Delfour, F., Marten, K., 2006. Lateralized visual behavior in bottlenose dolphins (Tursiops truncatus) performing audio-visual tasks: The right visual field advantage. Behav. Proc. 71, 41–50. Diaz-Munoz, M., Hernandez-Munoz, R., Suarez, J., Vidrio, S., Yaanez, L., AguilarRoblero, R., Rosenthal, L., Villalobos, L., Fernandez-Cancino, F., Drucker-Colin, R., Sanchez, V.C.D., 1999. Correlation between blood adenosine metabolism and sleep in humans. Sleep Res. 2, 33–41. Edgar, D., Dement, W., Fuller, C., 1993. Effect of SCN lesions on sleep in squirrel monkeys: evidence for opponent processes in sleep-wake regulation. J. Neurosci. 13, 1065–1079. Freeman, W.J., 1975. Mass Action in the Nervous System. Academic Press, New York. Hobson, J.A., Pace-Schott, E.F., 2002. The cognitive neuroscience of sleep: Neuronal systems, consciousness and learning. Nat. Rev. Neurosci. 3, 679–693. Huang, Z.L., Urade, Y., Hayaishi, O., 2007. Prostaglandins and adenosine in the regulation of sleep and wakefulness. Curr. Opin. Pharmacol. 7, 33–38. Huber, R., Ghilardi, M.F., Massimini, M., Tononi, G., 2004. Local sleep and learning. Nature 430, 78–81. Huszagh, V.A., Infante, J.P., 1989. The hypothetical way of progress. Nature 338, 109. Huupponen, E., Saastamoinen, A., Eskelinen, V., Vaerri, A., Hasan, J., Himanen, S.L., 2006. Apnea patients show a frontopolar inter-hemispheric spindle frequency difference. Neurosci. Lett. 403, 186–189. Kalinchuk, A., McCarley, R., Stenberg, D., Porkka-Heiskanen, T., Basheer, R., 2008. The role of cholinergic basal forebrain neurons in adenosine-mediated homeostatic control of sleep: lessons from 192 IgG-saporin lesions. Neuroscience 157, 238–253. Kandel, E., Schwartz, J., Jessell, T., 2000. Principles of Neural Science, 4th edition McGraw-Hill Medical. Kattler, H., Dijk, D.J., Borbe´ly, A.A., 1994. Effect of unilateral somatosensory stimulation prior to sleep on the sleep EEG in humans. J. Sleep Res. 3, 159–164. Lapierre, J.L., Kosenko, P.O., Lyamin, O.I., Kodama, T., Mukhametov, L.M., Siegel, J.M., 2007. Cortical acetylcholine release is lateralized during asymmetrical slow-wave sleep in northern fur seals. J. Neurosci. 27, 11999–12006. Low, P.S., Shank, S.S., Sejnowski, T.J., Margoliash, D., 2008. Mammalian-like features of sleep structure in zebra finches. Proc. Natl. Acad. Sci. U.S.A. 105, 9081–9086. Lu, J., Greco, M.A., Shiromani, P., Saper, C.B., 2000. Effect of lesions of the ventrolateral preoptic nucleus on NREM and REM sleep. J. Neurosci. 20, 3830–3842. Lyamin, O.I., Kosenko, P.O., Lapierre, J.L., Mukhametov, L.M., Siegel, J.M., 2008a. Fur seals display a strong drive for bilateral slow-wave sleep while on land. J. Neurosci. 28, 12614–12621. Lyamin, O.I., Manger, P.R., Ridgway, S.H., Mukhametov, L.M., Siegel, J.M., 2008b. Cetacean sleep: an unusual form of mammalian sleep. Neurosci. Biobehav. Rev. 32, 1451–1484. Lyamin, O.I., Mukhametov, L.M., Siegel, J.M., Nazarenko, E.A., Polyakova, I.G., Shpak, O.V., 2002. Unihemispheric slow wave sleep and the state of the eyes in a white whale. Behav. Brain Res. 129, 125–129. Manger, P.R., Fuxe, K., Ridgway, S.H., Siegel, J.M., 2004. The distribution and morphological characteristics of catecholaminergic cells in the diencephalon and midbrain of the bottlenose dolphin (Tursiops truncatus). Brain Behav. Evol. 64, 42–60. Mathews, C.G., Lesku, J.A., Lima, S.L., Amlaner, C.J., 2006. Asynchronous eye closure as an anti-predator behavior in the western fence lizard (Sceloporus occidentalis). Ethology 112, 286–292. Michel, F., Roffwarg, H., 1967. Chronic split brain stem preparation: effect on the sleep-waking cycle. Cell. Mol. Life Sci. 23, 126–128. Morairty, S., Rainnie, D., McCarley, R., Greene, R., 2004. Disinhibition of ventrolateral preoptic area sleep-active neurons by adenosine: a new mechanism for sleep promotion. Neuroscience 123, 451–457. Mukhametov, L.M., Lyamin, O.I., Polyakova, I.G., 1985. Interhemispheric asynchrony of the sleep EEG in northern fur seals. Experientia 41, 1034–1035.

119

Mukhametov, L.M., Oleksenko, A.I., Polyakova, I.G., 1988. Quantification of ECoG stages of sleep in the bottlenose dolphin. Neurophysiology 20, 398–403. Nielsen, T., Montplaisir, J., Lassonde, M., 1992. Sleep architecture in agenesis of the corpus callosum: laboratory assessment of four cases. J. Sleep Res. 1, 197–200. Nunez, P.L., 1995. Neocortical Dynamics and Human EEG Rhythms. Oxford University Press, New York. Oleksenko, A.I., Mukhametov, L.M., Polyakova, I.G., Supin, A.Y., Kovalzon, V.M., 1992. Unihemispheric sleep deprivation in bottlenose dolphins. J. Sleep Res. 1, 40–44. Phillips, A.J.K., Robinson, P.A., 2007. A quantitative model of sleep-wake dynamics based on the physiology of the brainstem ascending arousal system. J. Biol. Rhythms 22, 167–179. Phillips, A.J.K., Robinson, P.A., 2008. Sleep deprivation in a quantitative physiologically based model of the ascending arousal system. J. Theor. Biol. 255, 413–423. Phillips, A.J.K., Robinson, P.A., Kedziora, D.J., Abeysuriya, R.G., 2010. Mammalian sleep dynamics: How diverse features arise from a common physiological framework. PLoS Comput. Biol. 6, e1000826. Porkka-Heiskanen, T., Strecker, R.E., McCarley, R.W., 2000. Brain site-specificity of extracellular adenosine concentration changes during sleep deprivation and spontaneous sleep: an in vivo microdialysis study. Neuroscience 99, 507–517. Pryaslova, J.P., Lyamin, O.I., Siegel, J.M., Mukhametov, L.M., 2009. Behavioral sleep in the walrus. Behav. Brain Res. 201, 80–87. Rattenborg, N.C., Amlaner, C.J., Lima, S.L., 2000. Behavioral, neurophysiological and evolutionary perspectives on unihemispheric sleep. Neurosci. Biobehav. Rev. 24, 817–842. Rattenborg, N.C., Lima, S.L., Amlaner, C.J., 1999. Half-awake to the risk of predation. Nature 397, 397–398. Rattenborg, N.C., Mandt, B.H., Obermeyer, W.H., Winsauer, P.J., Huber, R., Wikelski, M., Benca, R.M., 2004. Migratory sleeplessness in the white-crowned sparrow (Zonotrichia leucophrys gambelii). PLoS Biol. 2, 0924–0936. Ridgway, S., Carder, D., Finneran, J., Keogh, M., Kamolnick, T., Todd, M., Goldblatt, A., 2006. Dolphin continuous auditory vigilance for five days. J. Exp. Biol. 209, 3621–3628. Robinson, P.A., Rennie, C.J., Rowe, D.L., O’Connor, S.C., 2004. Estimation of multiscale neurophysiologic parameters by electroencephalographic means. Human Brain Mapp. 23, 53–72. Robinson, P.A., Rennie, C.J., Wright, J.J., 1997. Propagation and stability of waves of electrical activity in the cerebral cortex. Phys. Rev. E 56, 826–840. Saper, C.B., Chou, T.C., Scammell, T.E., 2001. The sleep switch: hypothalamic control of sleep and wakefulness. Trends Neurosci. 24, 726–731. Saper, C.B., Fuller, P.M., Pedersen, N.P., Lu, J., Scammell, T.E., 2010. Sleep state switching. Neuron 68, 1023–1042. Siegel, J.M., 2005. Clues to the functions of mammalian sleep. Nature 437, 1264–1271. Siegel, J.M., 2008. Do all animals sleep? Trends Neurosci. 31, 208–213. Siegel, J.M., 2009. Sleep viewed as a state of adaptive inactivity. Nat. Rev. Neurosci. 10, 747–753. Szymusiak, R., Alam, N., Steininger, T.L., McGinty, D., 1998. Sleep-waking discharge patterns of ventrolateral preoptic/anterior hypothalamic neurons in rats. Brain Res. 803, 178–188. Tarpley, R.J., Gelderd, J.B., Bauserman, S., Ridgway, S.H., 1994. Dolphin peripheral visual pathway in chronic unilateral ocular atrophy: complete decussation apparent. J. Morphol. 222, 91–102. Tobler, I., Schwierin, B., 1996. Behavioural sleep in the giraffe (Giraffa camelopardalis) in a zoological garden. J. Sleep Res. 5, 21–32. Vazquez, J., Baghdoyan, H.A., 2001. Basal forebrain acetylcholine release during REM sleep is significantly greater than during waking. Am. J. Physiol. Regul. Integr. Comp. Physiol. 280, R598–R601. Vyazovskiy, V., Borbely, A.A., Tobler, I., 2000. Unilateral vibrissae stimulation during waking induces interhemispheric EEG asymmetry during subsequent sleep in the rat. J. Sleep Res. 9, 367–371. Werntz, D.A., Bickford, R.G., Bloom, F.E., Shannahoff-Khalsa, D.S., 1983. Alternating cerebral hemispheric activity and the lateralization of autonomic nervous function. Human Neurobiol. 2, 39–43.