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Abstract. Unlike equilibrium statistical mechanics, with its well-established foundations, a similar widely-accepted framework for non-equilibrium statistical mechanics (NESM) remains elusive. Here, we review some of the many recent activities on NESM, focusing on some of the fundamental issues and general aspects. Using the language of stochastic Markov processes, we emphasize general properties of the evolution of configurational probabilities, as described by master equations. Of particular interest are systems in which the dynamics violate detailed balance, since such systems serve to model a wide variety of phenomena in nature. We next review two distinct approaches for investigating such problems. One approach focuses on models sufficiently simple to allow us to find exact, analytic, non-trivial results. We provide detailed mathematical analyses of a onedimensional continuous-time lattice gas, the totally asymmetric exclusion process (TASEP). It is regarded as a paradigmatic model for NESM, much like the role the Ising model played for equilibrium statistical mechanics. It is also the starting point for the second approach, which attempts to include more realistic ingredients in order to be more applicable to systems in nature. Restricting ourselves to the area of biophysics and cellular biology, we review a number of models that are relevant for transport phenomena. Successes and limitations of these simple models are also highlighted.

The neuropeptide orexin (also known as hypocretin) is hypothesized to play a critical role in the regulation of sleep-wake behavior. Lack of orexin produces narcolepsy, which is characterized by poor maintenance of wakefulness and intrusions of rapid eye movement (REM) sleep or REM sleep-like phenomena into wakefulness. Orexin neurons heavily innervate many aminergic nuclei that promote wakefulness and inhibit REM sleep. We hypothesized that orexin neurons should be relatively active during wakefulness and inactive during sleep. To determine the pattern of activity of orexin neurons, we recorded sleep-wake behavior, body temperature, and locomotor activity under various conditions and used double-label immunohistochemistry to measure the expression of Fos in orexin neurons of the perifornical region. In rats maintained on a 12 hr light/ dark cycle, more orexin neurons had Fos immunoreactive nuclei during the night period; in animals housed in constant darkness, this activation still occurred during the subjective night. Sleep deprivation or treatment with methamphetamine also increased Fos expression in orexin neurons. In each of these experiments, Fos expression in orexin neurons correlated positively with the amount of wakefulness and correlated negatively with the amounts of non-REM and REM sleep during the preceding 2 hr. In combination with previous work, these results suggest that activation of orexin neurons may contribute to the promotion or maintenance of wakefulness. Conversely, relative inactivity of orexin neurons may allow the expression of sleep. Key words: orexin; hypocretin; Fos; wake; wakefulness; sleep; REM; lateral hypothalamus; perifornical region; hypothalamus; thermoregulation; ratThe neuropeptide orexin (also known as hypocretin) is hypothesized to play a critical role in the regulation of wakefulness and sleep. Orexin is synthesized in neurons of the perifornical region and lateral hypothalamic area, and orexin fibers innervate brain regions known to regulate behavioral state such as the raphe nuclei, the locus coeruleus, the tuberomammillary nucleus, and the cholinergic neurons of the basal forebrain and pons (Peyron et al., 1998;Chemelli et al., 1999;Date et al., 1999). Orexin increases the firing rate of postsynaptic neurons via OX1 and OX2 receptors (Sakurai et al., 1998;Hagan et al., 1999). Recent observations demonstrate that impaired orexin transmission may result in narcolepsy, which is characterized by poor maintenance of wakefulness and intrusions of rapid eye movement (REM) sleep or REM sleep-like phenomena into wakefulness (for review, see Siegel, 1999). The brains of narcoleptics exhibit a nearly complete loss of neurons expressing orexin mRNA or peptide (Peyron et al., 2000;Thannickal et al., 2000), and individuals with narcolepsy often have unmeasurably low orexin levels in CSF . Canine narcolepsy is caused by mutations of the OX2 receptor (Lin et al., 1999), and orexin knock-out mice have a phenotype very similar to canine and human narcolepsy (Chemelli et al., 1999). Addi...

The suprachiasmatic nucleus (SCN) contains the brain's circadian pacemaker, but mechanisms by which it controls circadian rhythms of sleep and related behaviors are poorly understood. Previous anatomic evidence has implicated the dorsomedial hypothalamic nucleus (DMH) in circadian control of sleep, but this hypothesis remains untested. We now show that excitotoxic lesions of the DMH reduce circadian rhythms of wakefulness, feeding, locomotor activity, and serum corticosteroid levels by 78-89% while also reducing their overall daily levels. We also show that the DMH receives both direct and indirect SCN inputs and sends a mainly GABAergic projection to the sleep-promoting ventrolateral preoptic nucleus, and a mainly glutamate-thyrotropin-releasing hormone projection to the wake-promoting lateral hypothalamic area, including orexin (hypocretin) neurons. Through these pathways, the DMH may influence a wide range of behavioral circadian rhythms.

All known eukaryotic organisms exhibit physiological and behavioral rhythms termed circadian rhythms that cycle with a near-24-hour period; in mammals, light is the most potent stimulus for entraining endogenous rhythms to the daily light cycle. Photic information is transmitted via the retinohypothalamic tract (RHT) to the suprachiasmatic nucleus (SCN) in the hypothalamus, where circadian rhythms are generated, but the retinal photopigment that mediates circadian entrainment has remained elusive. Here we show that most retinal ganglion cells (RGCs) that project to the SCN express the photopigment melanopsin.

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Sleep is influenced by diverse factors such as circadian time, affective states, ambient temperature, pain, etc., but pathways mediating these influences are unknown. To identify pathways that may influence sleep, we examined afferents to the ventrolateral preoptic nucleus (VLPO), an area critically implicated in promoting sleep. Injections of the retrograde tracer cholera toxin B subunit (CTB) into the VLPO produced modest numbers of CTB-labeled monoaminergic neurons in the tuberomammillary nucleus, raphe nuclei, and ventrolateral medulla, as well as a few neurons in the locus coeruleus. Immunohistochemistry for monoaminergic markers showed dense innervation of the VLPO by histaminergic, noradrenergic, and serotonergic fibers. Along with previous findings, these results suggest that the VLPO and monoaminergic nuclei may be reciprocally connected. Retrograde and anterograde tracing showed moderate or heavy inputs to the VLPO from hypothalamic regions including the median preoptic nucleus, lateral hypothalamic area, and dorsomedial hypothalamic nucleus (DMH), autonomic regions including the infralimbic cortex and parabrachial nucleus, and limbic regions including the lateral septal nucleus and ventral subiculum. Light to moderate inputs arose from orexin and melanin concentrating hormone neurons, but cholinergic or dopaminergic inputs were extremely sparse. Suprachiasmatic nucleus (SCN) projections to the VLPO were sparse, but the heavy input to the VLPO from the DMH, which receives direct and indirect SCN inputs, could provide an alternate pathway regulating the circadian timing of sleep. These robust pathways suggest candidate mechanisms by which sleep may be influenced by brain systems regulating arousal, autonomic, limbic, and circadian functions.

Orexins (also called hypocretins) are peptide neurotransmitters expressed in neurons of the lateral hypothalamic area (LHA). Mice lacking the orexin peptides develop narcolepsy-like symptoms, whereas mice with a selective loss of the orexin neurons develop hypophagia and severe obesity in addition to the narcolepsy phenotype. These different phenotypes suggest that orexin neurons may contain neurotransmitters besides orexin that regulate feeding and energy balance. Dynorphin neurons are common in the LHA, and dynorphin has been shown to influence feeding; hence, we studied whether dynorphin and orexin are colocalized. In rats, double-label in situ hybridization revealed that nearly all (94%) neurons expressing prepro-orexin mRNA also expressed prodynorphin mRNA. The converse was also true: 96% of neurons in the LHA containing prodynorphin mRNA also expressed prepro-orexin mRNA. Double-label immunohistochemistry confirmed that orexin-A and dynorphin-A peptides were highly colocalized in the LHA. Wild-type mice and orexin knock-out mice showed abundant prodynorphin mRNA-expressing neurons in the LHA, but orexin/ataxin-3 mice with a selective loss of the orexin neurons completely lacked prodynorphin mRNA in this area, further confirming that within the LHA, dynorphin expression is restricted to the orexin neurons. These findings suggest that dynorphin-A may play an important role in the function of the orexin neurons.