  Recent advances in sleep neurobiology have allowed development of
physiologically based mathematical models of sleep regulation that account for
the neuronal dynamics responsible for the regulation of sleep-wake cycles and
allow detailed examination of the underlying mechanisms. Neuronal systems in
general, and those involved in sleep regulation in particular, are noisy and
heterogeneous by their nature. It has been shown in various systems that
certain levels of noise and diversity can significantly improve signal
encoding. However, these phenomena, especially the effects of diversity, are
rarely considered in the models of sleep regulation. The present paper is
focused on a neuron-based physiologically motivated model of sleep-wake cycles
that proposes a novel mechanism of the homeostatic regulation of sleep based on
the dynamics of a wake-promoting neuropeptide orexin. Here this model is
generalized by the introduction of intrinsic diversity and noise in the
orexin-producing neurons in order to study the effect of their presence on the
sleep-wake cycle. A quantitative measure of the quality of a sleep-wake cycle
is introduced and used to systematically study the generalized model for
different levels of noise and diversity. The model is shown to exhibit a clear
diversity-induced resonance: that is, the best wake-sleep cycle turns out to
correspond to an intermediate level of diversity at the synapses of the
orexin-producing neurons. On the other hand only a mild evidence of stochastic
resonance is found when the level of noise is varied. These results show that
disorder, especially in the form of quenched diversity, can be a key-element
for an efficient or optimal functioning of the homeostatic regulation of the
sleep-wake cycle. Furthermore, this study provides an example of constructive
role of diversity in a neuronal system that can be extended beyond the system
studied here.
