Modeling the effect of sleep regulation on a neural mass model

Development of Mechanistic Neural Mass (mNM) Models that Link Physiology to Mean-Field Dynamics

Brain rhythms emerge from the mean-field activity of networks of neurons. There have been many efforts to build mathematical and computational embodiments in the form of discrete cell-group activities-termed neural masses-to understand in particular the origins of evoked potentials, intrinsic patterns of activities such as theta, regulation of sleep, Parkinson's disease related dynamics, and mimic seizure dynamics. As originally utilized, standard neural masses convert input through a sigmoidal function to a firing rate, and firing rate through a synaptic alpha function to other masses. Here we define a process to build mechanistic neural masses (mNMs) as mean-field models of microscopic membrane-type (Hodgkin Huxley type) models of different neuron types that duplicate the stability, firing rate, and associated bifurcations as function of relevant slow variables - such as extracellular potassium - and synaptic current; and whose output is both firing rate and impact on the slow variables - such as transmembrane potassium flux. Small networks composed of just excitatory and inhibitory mNMs demonstrate expected dynamical states including firing, runaway excitation and depolarization block, and these transitions change in biologically observed ways with changes in extracellular potassium and excitatory-inhibitory balance.

Computational Modeling of Information Propagation during the Sleep–Waking Cycle

Simple Summary

During the deep phases of sleep we do not normally wake up by a thunder, but we nevertheless notice it when awake. The exact same sound gets to our ears and cortex through the thalamus and still, it triggers two very different responses. There is growing experimental evidence that these two states of the brain—sleep and wakefulness—distribute sensory information in different ways across the cortex. In particular, during sleep, neuronal responses remain local and do not spread out across distant synaptically connected regions. On the contrary, during wakefulness, stimuli are able to elicit a wider spatial response. We have used a computational model of coupled cortical columns to study how these two propagation modes arise. Moreover, the transition from sleep-like to waking-like dynamics occurs in agreement with the synaptic homeostasis hypothesis and only requires the increase of excitatory conductances. We have found that, in order to reproduce the aforementioned observations, this parameter change has to be selectively applied: synaptic conductances between distinct columns have to be potentiated over local ones.

Abstract

Non-threatening familiar sounds can go unnoticed during sleep despite the fact that they enter our brain by exciting the auditory nerves. Extracellular cortical recordings in the primary auditory cortex of rodents show that an increase in firing rate in response to pure tones during deep phases of sleep is comparable to those evoked during wakefulness. This result challenges the hypothesis that during sleep cortical responses are weakened through thalamic gating. An alternative explanation comes from the observation that the spatiotemporal spread of the evoked activity by transcranial magnetic stimulation in humans is reduced during non-rapid eye movement (NREM) sleep as compared to the wider propagation to other cortical regions during wakefulness. Thus, cortical responses during NREM sleep remain local and the stimulus only reaches nearby neuronal populations. We aim at understanding how this behavior emerges in the brain as it spontaneously shifts between NREM sleep and wakefulness. To do so, we have used a computational neural-mass model to reproduce the dynamics of the sensory auditory cortex and corresponding local field potentials in these two brain states. Following the synaptic homeostasis hypothesis, an increase in a single parameter, namely the excitatory conductance g¯AMPA, allows us to place the model from NREM sleep into wakefulness. In agreement with the experimental results, the endogenous dynamics during NREM sleep produces a comparable, even higher, response to excitatory inputs to the ones during wakefulness. We have extended the model to two bidirectionally connected cortical columns and have quantified the propagation of an excitatory input as a function of their coupling. We have found that the general increase in all conductances of the cortical excitatory synapses that drive the system from NREM sleep to wakefulness does not boost the effective connectivity between cortical columns. Instead, it is the inter-/intra-conductance ratio of cortical excitatory synapses that should raise to facilitate information propagation across the brain.

Computational Evidence for a Competitive Thalamocortical Model of Spikes and Spindle Activity in Rolandic Epilepsy

Rolandic epilepsy (RE) is the most common idiopathic focal childhood epilepsy syndrome, characterized by sleep-activated epileptiform spikes and seizures and cognitive deficits in school age children. Recent evidence suggests that this disease may be caused by disruptions to the Rolandic thalamocortical circuit, resulting in both an abundance of epileptiform spikes and a paucity of sleep spindles in the Rolandic cortex during non-rapid eye movement sleep (NREM); electrographic features linked to seizures and cognitive symptoms, respectively. The neuronal mechanisms that support the competitive shared thalamocortical circuitry between pathological epileptiform spikes and physiological sleep spindles are not well-understood. In this study we introduce a computational thalamocortical model for the sleep-activated epileptiform spikes observed in RE. The cellular and neuronal circuits of this model incorporate recent experimental observations in RE, and replicate the electrophysiological features of RE. Using this model, we demonstrate that: (1) epileptiform spikes can be triggered and promoted by either a reduced NMDA current or h-type current; and (2) changes in inhibitory transmission in the thalamic reticular nucleus mediates an antagonistic dynamic between epileptiform spikes and spindles. This work provides the first computational model that both recapitulates electrophysiological features and provides a mechanistic explanation for the thalamocortical switch between the pathological and physiological electrophysiological rhythms observed during NREM sleep in this common epileptic encephalopathy.

NMMGenerator: an automatic neural mass model generator from population graphs

Neural mass models are among the most popular mathematical models of brain activity, since they enable the rapid simulation of large-scale networks involving different neural types at a spatial scale compatible with electrophysiological experiments (e.g. local field potentials). However, establishing neural mass model (NMM) equations associated with specific neuronal network architectures can be tedious and is an error-prone process, restricting their use to scientists who are familiar with mathematics. In order to overcome this challenge, we have developed a user-friendly software that enables a user to construct rapidly, under the form of a graph, a neuronal network with its populations and connectivity patterns. The resulting graph is then automatically translated into the corresponding set of differential equations, which can be solved and displayed within the same software environment. The software is proposed as open access, and should assist in offering the possibility for a wider audience of scientists to develop NMM corresponding to their specific neuroscience research questions.

Pathway-Dependent Regulation of Sleep Dynamics in a Network Model of the Sleep-Wake Cycle

Sleep is a fundamental homeostatic process within the animal kingdom. Although various brain areas and cell types are involved in the regulation of the sleep-wake cycle, it is still unclear how different pathways between neural populations contribute to its regulation. Here we address this issue by investigating the behavior of a simplified network model upon synaptic weight manipulations. Our model consists of three neural populations connected by excitatory and inhibitory synapses. Activity in each population is described by a firing-rate model, which determines the state of the network. Namely wakefulness, rapid eye movement (REM) sleep or non-REM (NREM) sleep. By systematically manipulating the synaptic weight of every pathway, we show that even this simplified model exhibits non-trivial behaviors: for example, the wake-promoting population contributes not just to the induction and maintenance of wakefulness, but also to sleep induction. Although a recurrent excitatory connection of the REM-promoting population is essential for REM sleep genesis, this recurrent connection does not necessarily contribute to the maintenance of REM sleep. The duration of NREM sleep can be shortened or extended by changes in the synaptic strength of the pathways from the NREM-promoting population. In some cases, there is an optimal range of synaptic strengths that affect a particular state, implying that the amount of manipulations, not just direction (i.e., activation or inactivation), needs to be taken into account. These results demonstrate pathway-dependent regulation of sleep dynamics and highlight the importance of systems-level quantitative approaches for sleep-wake regulatory circuits.

KCNT1 epilepsy with migrating focal seizures shows a temporal sequence with poor outcome, high mortality and SUDEP

Data on KCNT1 epilepsy of infancy with migrating focal seizures are heterogeneous and incomplete. Kuchenbuch et al. refine the syndrome phenotype, showing a three-step temporal sequence, poor prognosis with acquired microcephaly, high prevalence of extra-neurological manifestations and early mortality, particularly due to SUDEP. Refining the electro-clinical spectrum should facilitate early diagnosis.

Sleep Modelling across Physiological Levels

Sleep and circadian rhythms are regulated across multiple functional, spatial and temporal levels: from genes to networks of coupled neurons and glial cells, to large scale brain dynamics and behaviour. The dynamics at each of these levels are complex and the interaction between the levels is even more so, so research have mostly focused on interactions within the levels to understand the underlying mechanisms—the so-called reductionist approach. Mathematical models were developed to test theories of sleep regulation and guide new experiments at each of these levels and have become an integral part of the field. The advantage of modelling, however, is that it allows us to simulate and test the dynamics of complex biological systems and thus provides a tool to investigate the connections between the different levels and study the system as a whole. In this paper I review key models of sleep developed at different physiological levels and discuss the potential for an integrated systems biology approach for sleep regulation across these levels. I also highlight the necessity of building mechanistic connections between models of sleep and circadian rhythms across these levels.

Instantaneous voltage as an alternative to power- and phase-based interpretation of oscillatory brain activity

For decades, oscillatory brain activity has been characterized primarily by measurements of power and phase. While many studies have linked those measurements to cortical excitability, their relationship to each other and to the physiological underpinnings of excitability is unclear. The recently proposed Function-through-Biased-Oscillations (FBO) hypothesis (Schalk, 2015) addressed these issues by suggesting that the voltage potential at the cortical surface directly reflects the excitability of cortical populations, that this voltage is rhythmically driven away from a low resting potential (associated with depolarized cortical populations) towards positivity (associated with hyperpolarized cortical populations). This view explains how oscillatory power and phase together influence the instantaneous voltage potential that directly regulates cortical excitability. This implies that the alternative measurement of instantaneous voltage of oscillatory activity should better predict cortical excitability compared to either of the more traditional measurements of power or phase. Using electrocorticographic (ECoG) data from 28 human subjects, the results of our study confirm this prediction: compared to oscillatory power and phase, the instantaneous voltage explained 20% and 31% more of the variance in broadband gamma, respectively, and power and phase together did not produce better predictions than the instantaneous voltage. These results synthesize the previously separate power- and phase-based interpretations and associate oscillatory activity directly with a physiological interpretation of cortical excitability. This alternative view has implications for the interpretation of studies of oscillatory activity and for current theories of cortical information transmission.

Sleep regulation of the distribution of cortical firing rates

Sleep is thought to mediate both mnemonic and homeostatic functions. However, the mechanism by which this brain state can simultaneously implement the 'selective' plasticity needed to consolidate novel memory traces and the 'general' plasticity necessary to maintain a well-functioning neuronal system is unclear. Recent findings show that both of these functions differentially affect neurons based on their intrinsic firing rate, a ubiquitous neuronal heterogeneity. Furthermore, they are both implemented by the NREM slow oscillation, which also distinguishes neurons based on firing rate during sequential activity at the DOWN→UP transition. These findings suggest a mechanism by which spiking activity during the slow oscillation acts to maintain network statistics that promote a skewed distribution of neuronal firing rates, and perturbation of that activity by hippocampal replay acts to integrate new memory traces into the existing cortical network.

Wake-sleep transition as a noisy bifurcation

A recent physiologically based model of the ascending arousal system is used to analyze the dynamics near the transition from wake to sleep, which corresponds to a saddle-node bifurcation at a critical point. A normal form is derived by approximating the dynamics by those of a particle in a parabolic potential well with dissipation. This mechanical analog is used to calculate the power spectrum of fluctuations in response to a white noise drive, and the scalings of fluctuation variance and spectral width are derived versus distance from the critical point. The predicted scalings are quantitatively confirmed by numerical simulations, which show that the variance increases and the spectrum undergoes critical slowing, both in accord with theory. These signals can thus serve as potential precursors to indicate imminent wake-sleep transition, with potential application to safety-critical occupations in transport, air-traffic control, medicine, and heavy industry.