Power Law versus Exponential State Transition Dynamics: Application to Sleep-Wake Architecture

BACKGROUND: Despite the common experience that interrupted sleep has a negative impact on waking function, the features of human sleep-wake architecture that best distinguish sleep continuity versus fragmentation remain elusive. In this regard, there is growing interest in characterizing sleep architecture using models of the temporal dynamics of sleep-wake stage transitions. In humans and other mammals, the state transitions defining sleep and wake bout durations have been described with exponential and power law models, respectively. However, sleep-wake stage distributions are often complex, and distinguishing between exponential and power law processes is not always straightforward. Although mono-exponential distributions are distinct from power law distributions, multi-exponential distributions may in fact resemble power laws by appearing linear on a log-log plot. METHODOLOGY/PRINCIPAL FINDINGS: To characterize the parameters that may allow these distributions to mimic one another, we systematically fitted multi-exponential-generated distributions with a power law model, and power law-generated distributions with multi-exponential models. We used the Kolmogorov-Smirnov method to investigate goodness of fit for the "incorrect" model over a range of parameters. The "zone of mimicry" of parameters that increased the risk of mistakenly accepting power law fitting resembled empiric time constants obtained in human sleep and wake bout distributions. CONCLUSIONS/SIGNIFICANCE: Recognizing this uncertainty in model distinction impacts interpretation of transition dynamics (self-organizing versus probabilistic), and the generation of predictive models for clinical classification of normal and pathological sleep architecture

Obstructive Sleep Apnea Alters Sleep Stage Transition Dynamics

Enhanced characterization of sleep architecture, compared with routine polysomnographic metrics such as stage percentages and sleep efficiency, may improve the predictive phenotyping of fragmented sleep. One approach involves using stage transition analysis to characterize sleep continuity.We analyzed hypnograms from Sleep Heart Health Study (SHHS) participants using the following stage designations: wake after sleep onset (WASO), non-rapid eye movement (NREM) sleep, and REM sleep. We show that individual patient hypnograms contain insufficient number of bouts to adequately describe the transition kinetics, necessitating pooling of data. We compared a control group of individuals free of medications, obstructive sleep apnea (OSA), medical co-morbidities, or sleepiness (n = 374) with mild (n = 496) or severe OSA (n = 338). WASO, REM sleep, and NREM sleep bout durations exhibited multi-exponential temporal dynamics. The presence of OSA accelerated the "decay" rate of NREM and REM sleep bouts, resulting in instability manifesting as shorter bouts and increased number of stage transitions. For WASO bouts, previously attributed to a power law process, a multi-exponential decay described the data well. Simulations demonstrated that a multi-exponential process can mimic a power law distribution.OSA alters sleep architecture dynamics by decreasing the temporal stability of NREM and REM sleep bouts. Multi-exponential fitting is superior to routine mono-exponential fitting, and may thus provide improved predictive metrics of sleep continuity. However, because a single night of sleep contains insufficient transitions to characterize these dynamics, extended monitoring of sleep, probably at home, would be necessary for individualized clinical application

Importance of Glycosylation on Function of a Potassium Channel in Neuroblastoma Cells

The Kv3.1 glycoprotein, a voltage-gated potassium channel, is expressed throughout the central nervous system. The role of N-glycans attached to the Kv3.1 glycoprotein on conducting and non-conducting functions of the Kv3.1 channel are quite limiting. Glycosylated (wild type), partially glycosylated (N220Q and N229Q), and unglycosylated (N220Q/N229Q) Kv3.1 proteins were expressed and characterized in a cultured neuronal-derived cell model, B35 neuroblastoma cells. Western blots, whole cell current recordings, and wound healing assays were employed to provide evidence that the conducting and non-conducting properties of the Kv3.1 channel were modified by N-glycans of the Kv3.1 glycoprotein. Electrophoretic migration of the various Kv3.1 proteins treated with PNGase F and neuraminidase verified that the glycosylation sites were occupied and that the N-glycans could be sialylated, respectively. The unglycosylated channel favored a different whole cell current pattern than the glycoform. Further the outward ionic currents of the unglycosylated channel had slower activation and deactivation rates than those of the glycosylated Kv3.1 channel. These kinetic parameters of the partially glycosylated Kv3.1 channels were also slowed. B35 cells expressing glycosylated Kv3.1 protein migrated faster than those expressing partially glycosylated and much faster than those expressing the unglycosylated Kv3.1 protein. These results have demonstrated that N-glycans of the Kv3.1 glycoprotein enhance outward ionic current kinetics, and neuronal migration. It is speculated that physiological changes which lead to a reduction in N-glycan attachment to proteins will alter the functions of the Kv3.1 channel

Cholinergic Modulation of Narcoleptic Attacks in Double Orexin Receptor Knockout Mice

To investigate how cholinergic systems regulate aspects of the sleep disorder narcolepsy, we video-monitored mice lacking both orexin (hypocretin) receptors (double knockout; DKO mice) while pharmacologically altering cholinergic transmission. Spontaneous behavioral arrests in DKO mice were highly similar to those reported in orexin-deficient mice and were never observed in wild-type (WT) mice. A survival analysis revealed that arrest lifetimes were exponentially distributed indicating that random, Markovian processes determine arrest lifetime. Low doses (0.01, 0.03 mg/kg, IP), but not a high dose (0.08 mg/kg, IP) of the cholinesterase inhibitor physostigmine increased the number of arrests but did not alter arrest lifetimes. The muscarinic antagonist atropine (0.5 mg/kg, IP) decreased the number of arrests, also without altering arrest lifetimes. To determine if muscarinic transmission in pontine areas linked to REM sleep control also influences behavioral arrests, we microinjected neostigmine (50 nl, 62.5 µM) or neostigmine + atropine (62.5 µM and 111 µM respectively) into the nucleus pontis oralis and caudalis. Neostigmine increased the number of arrests in DKO mice without altering arrest lifetimes but did not provoke arrests in WT mice. Co-injection of atropine abolished this effect. Collectively, our findings establish that behavioral arrests in DKO mice are similar to those in orexin deficient mice and that arrests have exponentially distributed lifetimes. We also show, for the first time in a rodent narcolepsy model, that cholinergic systems can regulate arrest dynamics. Since perturbations of muscarinic transmission altered arrest frequency but not lifetime, our findings suggest cholinergic systems influence arrest initiation without influencing circuits that determine arrest duration

Role of Homer Proteins in the Maintenance of Sleep-Wake States

Sleep is an evolutionarily conserved process that is linked to diurnal cycles and normal daytime wakefulness. Healthy sleep and wakefulness are integral to a healthy lifestyle; this occurs when an organism is able to maintain long bouts of both sleep and wake. Homer proteins, which function as adaptors for group 1 metabotropic glutamate receptors, have been implicated in genetic studies of sleep in both Drosophila and mouse. Drosophila express a single Homer gene product that is upregulated during sleep. By contrast, vertebrates express Homer as both constitutive and immediate early gene (H1a) forms, and H1a is up-regulated during wakefulness. Genetic deletion of Homer in Drosophila results in fragmented sleep and in failure to sustain long bouts of sleep, even under increased sleep drive. However, deletion of Homer1a in mouse results in failure to sustain long bouts of wakefulness. Further evidence for the role of Homer1a in the maintenance of wake comes from the CREB alpha delta mutant mouse, which displays a reduced wake phenotype similar to the Homer1a knockout and fails to up-regulate Homer1a upon sleep loss. Homer1a is a gene whose expression is induced by CREB. Sustained behaviors of the sleep/wake cycle are created by molecular pathways that are distinct from those for arousal or short bouts, and implicate an evolutionarily-conserved role for Homer in sustaining these behaviors

Rebound Discharge in Deep Cerebellar Nuclear Neurons In Vitro

Neurons of the deep cerebellar nuclei (DCN) play a critical role in defining the output of cerebellum in the course of encoding Purkinje cell inhibitory inputs. The earliest work performed with in vitro preparations established that DCN cells have the capacity to translate membrane hyperpolarizations into a rebound increase in firing frequency. The primary means of distinguishing between DCN neurons has been according to cell size and transmitter phenotype, but in some cases, differences in the firing properties of DCN cells maintained in vitro have been reported. In particular, it was shown that large diameter cells in the rat DCN exhibit two phenotypes of rebound discharge in vitro that may eventually help define their functional roles in cerebellar output. A transient burst and weak burst phenotype can be distinguished based on the frequency and pattern of rebound discharge immediately following a hyperpolarizing stimulus. Work to date indicates that the difference in excitability arises from at least the degree of activation of T-type Ca2+ current during the immediate phase of rebound firing and Ca2+-dependent K+ channels that underlie afterhyperpolarizations. Both phenotypes can be detected following stimulation of Purkinje cell inhibitory inputs under conditions that preserve resting membrane potential and natural ionic gradients. In this paper, we review the evidence supporting the existence of different rebound phenotypes in DCN cells and the ion channel expression patterns that underlie their generation