Switching mechanisms and bout times in a pair of reciprocally inhibitory neurons

An integrate-and-fire mathematical model of sleep-wake neuronal networks in the developing mammal

Sleep behavior is present in nearly all animals, and is a vital part of growth, development, and overall health. Infant mammals cycle randomly between short bouts of sleep and wake, and the lengths of these bouts both follow an exponential distribution. As mammals mature into adulthood, the mean sleep and wake bout lengths increase, and we also observe a change in the distribution of wake bout lengths from exponential to power law. Focusing on three regions of the brainstem that are involved in sleep-wake regulation, we develop a novel integrate-and-fire neuronal network model to expand upon previous mathematical models of sleep-wake regulation in mammals, focusing on rats. This model allows fine control over neuronal connectivity while simultaneously increasing the size and complexity of the modeled system to make it more representative of reality. We establish a relationship between neuronal network structure and function that could explain the different sleep-wake behaviors observed in rats as they progress through development. We explore the relationship between three different neuronal populations as well as the overall network behavior of the system. We find that increasing synaptic connectivity strength between the wake-promoting region and the wake-active region accounts for the observed changes in mammalian sleep-wake patterns. This dynamic neuronal connectivity is a possible mechanism that accurately accounts for sleep-wake pattern changes observed during mammalian development.

Development of the sleep-wake switch in rats during the P2-P21 early infancy period

In early infancy, rats randomly alternate between the sleeping and waking states-from postnatal day 2-10 (P2-P10), sleep and wake bouts are both exponentially distributed with increasing means, while from P10-P21 sleep and wake bout means continue to increase, though there is a striking qualitative shift in the distribution of wake bouts from exponential to power law. The behavioral states of sleep and wakefulness correspond to the activity of sleep-active and wake-active neuronal brainstem populations, with reciprocal inhibition between the two ensuring that only one population is active at a time. The locus coeruleus (LC) forms a third component of this circuit that rises in prominence during the P10-P21 period, as experimental evidence shows that an as-of-yet undeciphered interaction of the LC with sleep-active and wake-active populations is responsible for the transformation of the wake bout distribution from exponential to power law. Interestingly, the LC undergoes remarkable physiological changes during the P10-P21 period-gap junctions within the LC are pruned and network-wide oscillatory synchrony declines and vanishes. In this work, we discuss a series of models of sleep-active, wake-active, and the LC populations, and we use these models to postulate the nature of the interaction between these three populations and how these interactions explain empirical observations of sleep and wake bout dynamics. We hypothesize a circuit in which there is reciprocal excitation between the LC and wake-active population with inhibition from the sleep-active population to the LC that suppresses the LC during sleep bouts. During the P2-P10 period, we argue that a noise-based switching mechanism between the sleep-active and wake-active populations provides a simple and natural way to account for exponential bout distributions, and that the locked oscillatory state of the LC prevents it from impacting bout distributions. From P10-P21, we use our models to postulate that, as the LC gradually shifts from a state of synchronized oscillations to a state of continuous firing, reciprocal excitation between the LC and the wake-active population is able to gradually transform the wake bout distribution from exponential to power law.

Deterministic stability regimes and noise-induced quasistable behavior in a pair of reciprocally inhibitory neurons

Reciprocal inhibition is a common motif exploited by neuronal networks; an intuitive and tractable way to examine the behaviors produced by reciprocal inhibition is to consider a pair of neurons that synaptically inhibit each other and receive constant or noisy excitatory driving currents. In this work, we examine reciprocal inhibition using two models (a voltage-based and a current-based integrate-and-fire model with instantaneous or temporally structured input), and we use analytic and computational tools to examine the bifurcations that occur and study the various possible monostable, bistable, and tristable regimes that can exist; we find that, depending on system parameters (and on choice of neuron model), there can exist up to 3 distinct monostable regimes (denoted M0, M1, M2), 3 distinct bistable regimes (denoted B, B1, B2), and a single tristable regime (denoted T). We also find that synaptic inhibition exerts independent control over the two neurons - inhibition from neuron 1 to neuron 2 governs the spiking behavior of neuron 2 but has no impact on the spiking behavior of neuron 1 (and vice versa). The excitatory driving current, however, does not exhibit this property - the excitatory current to neuron 1 affects the spiking behavior of both neurons 1 and 2 (as does the excitatory current to neuron 2). Furthermore, we develop a methodology to examine the behavior of the system when the excitatory driving currents are allowed to be noisy, and we investigate the relationship between the behavior of the noisy system with the stability regime of the corresponding deterministic system.

Role of the locus coeruleus in the emergence of power law wake bouts in a model of the brainstem sleep-wake system through early infancy

Infant rats randomly cycle between the sleeping and waking states, which are tightly correlated with the activity of mutually inhibitory brainstem sleep and wake populations. Bouts of sleep and wakefulness are random; from P2-P10, sleep and wake bout lengths are exponentially distributed with increasing means, while during P10-P21, the sleep bout distribution remains exponential while the distribution of wake bouts gradually transforms to power law. The locus coeruleus (LC), via an undeciphered interaction with sleep and wake populations, has been shown experimentally to be responsible for the exponential to power law transition. Concurrently during P10-P21, the LC undergoes striking physiological changes - the LC exhibits strong global 0.3 Hz oscillations up to P10, but the oscillation frequency gradually rises and synchrony diminishes from P10-P21, with oscillations and synchrony vanishing at P21 and beyond. In this work, we construct a biologically plausible Wilson Cowan-style model consisting of the LC along with sleep and wake populations. We show that external noise and strong reciprocal inhibition can lead to switching between sleep and wake populations and exponentially distributed sleep and wake bout durations as during P2-P10, with the parameters of inhibition between the sleep and wake populations controlling mean bout lengths. Furthermore, we show that the changing physiology of the LC from P10-P21, coupled with reciprocal excitation between the LC and wake population, can explain the shift from exponential to power law of the wake bout distribution. To our knowledge, this is the first study that proposes a plausible biological mechanism, which incorporates the known changing physiology of the LC, for tying the developing sleep-wake circuit and its interaction with the LC to the transformation of sleep and wake bout dynamics from P2-P21.