Diversity and noise effects in a model of homeostatic regulation of the sleep-wake cycle.

Recent advances in sleep neurobiology have allowed development of physiologically based mathematical models of sleep regulation that account for the neuronal dynamics responsible for the regulation of sleep-wake cycles and allow detailed examination of the underlying mechanisms. Neuronal systems in general, and those involved in sleep regulation in particular, are noisy and heterogeneous by their nature. It has been shown in various systems that certain levels of noise and diversity can significantly improve signal encoding. However, these phenomena, especially the effects of diversity, are rarely considered in the models of sleep regulation. The present paper is focused on a neuron-based physiologically motivated model of sleep-wake cycles that proposes a novel mechanism of the homeostatic regulation of sleep based on the dynamics of a wake-promoting neuropeptide orexin. Here this model is generalized by the introduction of intrinsic diversity and noise in the orexin-producing neurons, in order to study the effect of their presence on the sleep-wake cycle. A simple quantitative measure of the quality of a sleep-wake cycle is introduced and used to systematically study the generalized model for different levels of noise and diversity. The model is shown to exhibit a clear diversity-induced resonance: that is, the best wake-sleep cycle turns out to correspond to an intermediate level of diversity at the synapses of the orexin-producing neurons. On the other hand, only a mild evidence of stochastic resonance is found, when the level of noise is varied. These results show that disorder, especially in the form of quenched diversity, can be a key-element for an efficient or optimal functioning of the homeostatic regulation of the sleep-wake cycle. Furthermore, this study provides an example of a constructive role of diversity in a neuronal system that can be extended beyond the system studied here.

Temperature-dependent stochastic dynamics of the Huber-Braun neuron model.

The response of a four-dimensional mammalian cold receptor model to different implementations of noise is studied across a wide temperature range. It is observed that for noisy activation kinetics, the parameter range decomposes into two regions in which the system reacts qualitatively completely different to small perturbations through noise, and these regions are separated by a homoclinic bifurcation. Noise implemented as an additional current yields a substantially different system response at low temperature values, while the response at high temperatures is comparable to activation-kinetic noise. We elucidate how this phenomenon can be understood in terms of state space dynamics and gives quantitative results on the statistics of interspike interval distributions across the relevant parameter range.

Noise-induced precursors of tonic-to-bursting transitions in hypothalamic neurons and in a conductance-based model.

The dynamics of neurons is characterized by a variety of different spiking patterns in response to external stimuli. One of the most important transitions in neuronal response patterns is the transition from tonic firing to burst discharges, i.e., when the neuronal activity changes from single spikes to the grouping of spikes. An increased number of interspike-interval sequences of specific temporal correlations was detected in anticipation of temperature induced tonic-to-bursting transitions in both, experimental impulse recordings from hypothalamic brain slices and numerical simulations of a stochastic model. Analysis of the modelling data elucidates that the appearance of such patterns can be related to particular system dynamics in the vicinity of the period-doubling bifurcation. It leads to a nonlinear response on de- and hyperpolarizing perturbations introduced by noise. This explains why such particular patterns can be found as reliable precursors of the neurons' transition to burst discharges.

On the role of subthreshold currents in the Huber-Braun cold receptor model.

We study the role of the strength of subthreshold currents in a four-dimensional Hodgkin-Huxley-type model of mammalian cold receptors. Since a total diminution of subthreshold activity corresponds to a decomposition of the model into a slow, subthreshold, and a fast, spiking subsystem, we first elucidate their respective dynamics separately and draw conclusions about their role for the generation of different spiking patterns. These results motivate a numerical bifurcation analysis of the effect of varying the strength of subthreshold currents, which is done by varying a suitable control parameter. We work out the key mechanisms which can be attributed to subthreshold activity and furthermore elucidate the dynamical backbone of different activity patterns generated by this model.

Inhibition of human 5-HT(3A) and 5-HT(3AB) receptors by etomidate, propofol and pentobarbital.

The actions of intravenous anaesthetics on 5-HT(3AB) receptors have not been studied. Using oocyte electrophysiology, the effects of etomidate, propofol, and pentobarbital on human 5-HT(3A) and 5-HT(3AB) receptors were studied and compared. Inhibition of peak currents by all three compounds in both receptor subtypes was anaesthetic concentration-dependant and non-competitive. Because the half-maximal inhibitory concentrations for etomidate, propofol and pentobarbital in 5-HT(3A) and 5-HT(3AB) receptors were all above their respective anaesthetic concentrations, the results of our study suggest that neither 5-HT(3) receptor subtype contributes to the anaesthetic actions of etomidate, propofol or pentobarbital.

Methodological Problems on the Way to Integrative Human Neuroscience.

Neuroscience is a multidisciplinary effort to understand the structures and functions of the brain and brain-mind relations. This effort results in an increasing amount of data, generated by sophisticated technologies. However, these data enhance our descriptive knowledge, rather than improve our understanding of brain functions. This is caused by methodological gaps both within and between subdisciplines constituting neuroscience, and the atomistic approach that limits the study of macro- and mesoscopic issues. Whole-brain measurement technologies do not resolve these issues, but rather aggravate them by the complexity problem. The present article is devoted to methodological and epistemic problems that obstruct the development of human neuroscience. We neither discuss ontological questions (e.g., the nature of the mind) nor review data, except when it is necessary to demonstrate a methodological issue. As regards intradisciplinary methodological problems, we concentrate on those within neurobiology (e.g., the gap between electrical and chemical approaches to neurophysiological processes) and psychology (missing theoretical concepts). As regards interdisciplinary problems, we suggest that core disciplines of neuroscience can be integrated using systemic concepts that also entail human-environment relations. We emphasize the necessity of a meta-discussion that should entail a closer cooperation with philosophy as a discipline of systematic reflection. The atomistic reduction should be complemented by the explicit consideration of the embodiedness of the brain and the embeddedness of humans. The discussion is aimed at the development of an explicit methodology of integrative human neuroscience, which will not only link different fields and levels, but also help in understanding clinical phenomena.

Oscillations, resonances and noise: basis of flexible neuronal pattern generation.

Modulation of neuronal impulse pattern is examined by means of a simplified Hodgkin-Huxley type computer model which refers to experimental recordings of cold receptor discharges. This model essentially consists of two potentially oscillating subsystems: a spike generator and a subthreshold oscillator. With addition of noise the model successfully mimics the major types of experimentally recorded impulse patterns and thereby elucidate different resonance behaviors. (1) There is a range of rhythmic spiking or bursting where the spike generator is strongly coupled to the subthreshold oscillator. (2) There is a pacemaker activity of more complex interactions where the spike generator has overtaken part of the control. (3) There is a situation where the two subsystems are decoupled and only resonate with the help of noise.

Modeling neuronal activity in relation to experimental voltage-/patch-clamp recordings.

A mechanism-based, Hodgkin-Huxley-type modeling approach is proposed that allows connecting the key parameters of experimental voltage-/patch-clamp data directly to the major control values of the model. The objective of this paper is to facilitate the use of mathematical modeling in supplement to electrophysiological recordings. Typical recordings from current-clamp, whole-cell voltage-clamp, and single-channel patch-clamp experiments are illustrated by means of a simplified computer model designed for life science education. These examples demonstrate that the "rate constants", on which the original Hodgkin-Huxley equations are built up, are difficult, in most experiments even impossible, to extract from experimental data. As the combination of the two exponential rate constants leads to sigmoid activation curves, they can be replaced by sigmoid voltage dependencies, mostly presented in form of Boltzmann functions. Conversely, connecting whole-cell and single-channel patch-clamp simulations, the Boltzmann functions, can be related to exponentially voltage dependent probability factors of ion channel transition rates. The thereby introduced small variability of the activation values suggests that the power functions of the activation variables in the current equations can be neglected. Eliminating the rate constants and the power functions can be physiologically justified and makes the model easier to handle, especially in context with experimental data. Further possibilities of dimension reduction as well as model extensions are discussed. This article is part of a Special Issue entitled Neural Coding 2012.

A computational study of the interdependencies between neuronal impulse pattern, noise effects and synchronization.

Alterations of individual neurons dynamics and associated changes of the activity pattern, especially the transition from tonic firing (single-spikes) to bursts discharges (impulse groups), play an important role for neuronal information processing and synchronization in many physiological processes (sensory encoding, information binding, hormone release, sleep-wake cycles) as well as in disease (Parkinson, epilepsy). We have used Hodgkin-Huxley-type model neurons with subthreshold oscillations to examine the impact of noise on neuronal encoding and thereby have seen significant differences depending on noise implementation as well as on the neuron's dynamic state. The importance of the individual neurons' dynamics is further elucidated by simulation studies with electrotonically coupled model neurons which revealed mutual interdependencies between the alterations of the network's coupling strength and neurons' activity patterns with regard to synchronization. Remarkably, a pacemaker-like activity pattern which revealed to be much more noise sensitive than the bursting patterns also requires much higher coupling strengths for synchronization. This seemingly simple pattern is obviously governed by more complex dynamics than expected from a conventional pacemaker which may explain why neurons more easily synchronize in the bursting than in the tonic firing mode.

Comparison of different methods for the evaluation of treatment effects from the sleep EEG of patients with major depression.

In healthy subjects, sleep has a typical structure of three to five cyclic transitions between different sleep states. In major depression, this regular pattern is often destroyed but can be reestablished during successful treatment. The differences between healthy and abnormal sleep are generally assessed in a time-consuming process, which consists of determining the nightly variations of the sleep states (the hypnogram) based on visual inspection of the electroencephalogram (EEG), electrooculogram, and electromyogram. In this study, three different methods of sleep EEG analysis (spectrum, outlier, and recurrence analysis) have been examined with regard to their ability to extract information about treatment effects in patients with major depression. Our data suggest that improved sleep patterns during treatment with antidepressant medication can be identified with an appropriate analysis of the EEG. By comparing different methods, we have found that many treatment effects identified by spectrum analysis can be reproduced by the much simpler technique of outlier analysis. Finally, the cyclic structure of sleep and its modification by antidepressant treatment is best illustrated by a non-linear approach, the so-called recurrence method.

Neural synchronization at tonic-to-bursting transitions.

We studied the synchronous behavior of two electrically-coupled model neurons as a function of the coupling strength when the individual neurons are tuned to different activity patterns that ranged from tonic firing via chaotic activity to burst discharges. We observe asynchronous and various synchronous states such as out-of-phase, in-phase and almost in-phase chaotic synchronization. The highest variety of synchronous states occurs at the transition from tonic firing to chaos where the highest coupling strength is also needed for in-phase synchronization which is, essentially, facilitated towards the bursting range. This demonstrates that tuning of the neuron's internal dynamics can have significant impact on the synchronous states especially at the physiologically relevant tonic-to-bursting transitions.

Interactions of temperature and angiotensin II in paraventricular neurons of rats in vitro.

We recorded extracellular impulse activity of hypothalamic paraventricular neurons ( n=75) in rat brain slices during application of angiotensin II (ANG II, 10(-9)-10(-6) M) and/or temperature changes (32-42 degrees C). ANG II, with a threshold concentration of 10(-8) M, increased the firing rate in more than 80% of the neurons with strongest excitations occurring in bursting neurons. Increasing the temperature also raised the discharge rate in the majority of the neurons, often together with enhanced burst discharges. When ANG II was applied during ongoing sinusoidal temperature changes, its effects were more pronounced at elevated temperatures. These electrophysiological data illustrate that stimulus-encoding properties at the neuronal level can contribute to the interactions between osmoregulatory and thermoregulatory mechanisms including mutual sensitization when different stimuli (here: ANG II and temperature changes) are applied simultaneously.