The provided code models the dynamics of the human sleep-wake regulatory network. This model focuses on simulating a typical human sleep cycle, incorporating several key components responsible for regulating wakefulness, non-rapid eye movement (NREM) sleep, and rapid eye movement (REM) sleep. The biological basis underlying this code is rooted in several interconnected aspects of human sleep biology: ### Sleep-Wake Regulation 1. **Neuronal Populations**: The code represents three main sleep-wake promoting neuronal populations: - **Wake**: Neuronal activity associated with maintaining wakefulness. - **NREM**: Neuronal population activity promoting non-REM sleep. - **REM**: Activity controlling REM sleep episodes. - An additional population related to the **Suprachiasmatic Nucleus (SCN)**, which is involved in regulating circadian rhythms. 2. **Homeostatic Sleep Drive**: The variable involved in monitoring 'sleep pressure,' which grows during wakefulness and dissipates during sleep. The dynamics of this drive are modeled using revised parameters from the literature, indicating its significance in determining sleep onset and duration. 3. **Circadian Rhythms**: The model includes a circadian component that is responsible for regulating daily biological rhythms, synchronized to a roughly 24-hour cycle influenced by environmental cues such as light. This is crucial for aligning sleep patterns with the external environment. 4. **State Transitions**: The model includes mechanisms for transitioning between different sleep states: - **Sleep Onset** occurs when the model indicates a transition to NREM sleep. - **Wake Onset** corresponds to transitions from sleep states to wakefulness. - Control of **REM Onset and Offset**, modeled as transitions into and out of REM sleep. 5. **Parameters and Events**: The code uses specific threshold values for firing rates in neuronal populations to trigger transitions between sleep-wake states. Parameters are based on empirical data to reflect realistic neurobiological dynamics. ### Biological Outcomes The primary outcomes assessed by the model include: - **Sleep and Wake Durations**: Calculation of the durations of wakefulness and sleep bouts to yield patterns reflective of human sleep architecture. - **REM Cycles**: Evaluation of REM cycle durations and sequences as a component of restoring essential cognitive functions and processing emotions. - **Phase Relationships**: Analysis of the phase of sleep onsets relative to circadian timing, reflecting how different states of alertness and rest occur within the circadian cycle. In summary, this code models the complex interplay between homeostatic and circadian drives, neuronal population dynamics, and transition mechanisms that together control and modulate the human sleep-wake cycle. The mathematical description provided aligns with empirical neurobiological findings to simulate and analyze typical human sleep physiology.