A Mathematical Model towards Understanding the Mechanism of Neuronal Regulation of Wake-NREMS-REMS States

Abstract

In this study we have constructed a mathematical model of a recently proposed functional model known to be responsible for inducing waking, NREMS and REMS. Simulation studies using this model reproduced sleep-wake patterns as reported in normal animals. The model helps to explain neural mechanism(s) that underlie the transitions between wake, NREMS and REMS as well as how both the homeostatic sleep-drive and the circadian rhythm shape the duration of each of these episodes. In particular, this mathematical model demonstrates and confirms that an underlying mechanism for REMS generation is pre-synaptic inhibition from substantia nigra onto the REM-off terminals that project on REM-on neurons, as has been recently proposed. The importance of orexinergic neurons in stabilizing the wake-sleep cycle is demonstrated by showing how even small changes in inputs to or from those neurons can have a large impact on the ensuing dynamics. The results from this model allow us to make predictions of the neural mechanisms of regulation and patho-physiology of REMS.

Effects of Thermoregulation on Human Sleep Patterns: A Mathematical Model of Sleep–Wake Cycles with REM–NREM Subcircuit

“…5. We note that this REM homeostat differs from the implementation in the model of Kumar et al [24]. Indeed, our REM homeostat also decays during REM and it is built on the inhibitory projection from the sleep-promoting area of the hypothalamus (POAH) to REM-off neurons.…”

“…Neurons that inhibit REM sleep (REM-off) can be found in several nuclei including the locus coeruleus, while neuron populations promoting REM sleep (REM-on) can be found in the laterodorsal/ pedunculopontine tegmentum [36]. REM-on neurons are inhibited by MRF [8,24,27]. The suprachiasmatic nucleus (SCN) of the hypothalamus acts as an endogenous oscillator generating the circadian rhythm; it can be entrained to a 24-h light/dark cycle by inputs from the retina.…”

“…2. The model is based upon the model of Kumar et al [24]; further details concerning the choice of neuronal populations to include and the construction of the mathematical model may be found there. Fig.…”

“…1. Following [24], the mean activity level of each neuron population is modeled using Morris-Lecar (ML) equations [29]: …”

“…In Section 2, a description of the model is given, based on the model of Kumar et al [24]. In Sections 3.1 and 3.2 we first separately analyze the sleep/wake and then REM/NREM circuits of the model without the effects of thermoregulation (i.e.…”