A Mathematical Model to Explore the Interdependence Between the Serotonin and Orexin/Hypocretin Systems

Among their multitude of physiological and behavioral effects, the neurochemicals serotonin (5-HT) and orexin (Ox) have been closely linked to major depressive disorders (MDD) and sleep alterations. The dorsal raphe nucleus (DRN) and the later hypothalamus area (LHA) are brain regions that are sources of 5-HT and Ox, and there is evidence that suggests a reciprocal interaction between them. This lends support to the hypothesis of a close relationship between MDD and sleeping disorder. Based on various experimental data, and appropriate assumptions, we construct a mathematical model of the coupled DRN-LHA neural circuit. Our model relates the dynamics of four important variables that can be experimentally measured: (i) the firing rate of 5-HT-containing neurons in DRN, (ii) the firing rate of Ox-containing neurons in the LHA, (iii) 5-HT concentration level in LHA, and (iv) Ox concentration level in DRN. Simulations show that our model supports the co-existence of baseline activities and concentration levels as observed in various separate experiments. It also allows circuit-level exploration of various parameters not yet identified experimentally, e.g. the rise and decay of Ox concentration levels due to Ox neural activity, and the exact dependence of Ox neural activity on 5-HT level. Finally we have made some model predictions regarding the effects of the 5-HT antagonist on the circuit. Our model, which can be subjected to verification and refinement as new experimental data accumulates, provides unified quantitative relationships and predictions between two important connected brain regions strongly tied to MDD and sleep disorders.