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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.