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A primary goal of sleep research is to understand the molecular basis of sleep. Although some sleep/wake-promoting circuits and secreted substances have been identified, the detailed molecular mechanisms underlying the regulation of sleep duration have been elusive. Here, to address these mechanisms, we developed a simple computational model of a cortical neuron with five channels and a pump, which recapitulates the cortical electrophysiological characteristics of slow-wave sleep (SWS) and wakefulness. Comprehensive bifurcation and detailed mathematical analyses predicted that leak K channels play a role in generating the electrophysiological characteristics of SWS, leading to a hypothesis that leak K channels play a role in the regulation of sleep duration. To test this hypothesis experimentally, we comprehensively generated and analyzed 14 KO mice, and found that impairment of the leak K channel () decreased sleep duration. Based on these results, we hypothesize that leak K channels regulate sleep duration in mammals.

A theory is given to account for the CROMWELL Current-the Equatorial Undercurrent. The equatorial upwelling is closely related to the Current, and a remarkable similarity between the equatorial circulation and the circulation in the coastal upwelling regions. The widths of the equatorial upwelling as well as of the CROMWELL Current the maximum speeds of the upwelling and of the CROMWELL Current, the depth of the core and the thickness of the CROMWELL Current, are all found to be explained quantitatively. The rate of change in the CORIOLIS parameter with latitude and the mean vertical stability of the waters are essential to determine those length scales of the phenomena. The easterly wind stress over the equatorial region is responsible for the processes.

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