A minimal physiologically based model of the HPA axis under influence of the sleep-wake cycles.

The hypothalamic-pituitary-adrenal axis (also called the HPA or stress axis) exhibits distinct circadian and ultradian rhythms in cortisol release that cannot be explained solely by the feedback loops from cortisol to the control systems in the paraventricular nucleus (PVN) and pituitary gland. The HPA axis is intimately connected with other brain functions. In particular, it is strongly affected by the sleep-wake cycles via direct and indirect effects of the circadian and homeostatic mechanisms. For example, the HPA axis has direct inputs from the master circadian clock in the suprachiasmatic nuclei (SCN), and from the various sleep-wake related neuronal populations, which themselves are under the effects of the circadian and homeostatic processes. In this paper a first step towards a physiologically based mathematical model of the HPA-axis under effects of the sleep-wake cycles is presented. This model accounts for 3 major characteristics of daily cortisol profile in the blood: i) abrupt increase of cortisol concentration in response to awakening, the so-called cortisol-awakening response (CAR); ii) reduced cortisol levels during daytime with underlying ultradian oscillations; and iii) suppression of cortisol release during sleep.

Neurones and synapses for systemic models of psychiatric disorders.

We propose a mechanism-based modelling approach which brings together the most relevant features of neural dynamics and synaptic transmission for clinically valuable simulations of psychiatric disorders and their pharmaceutical treatment. It is based on a minimal, but physiologically justified concept, which allows to account for a great diversity of neuronal dynamics and synaptic mechanisms. It can simulate ionotropic as well as metabotropic receptors in addition to the effects of eventual co-transmitters and external neuromodulators. The proposed model can mimic the clinically most important aspects of synaptic disturbances, such as impaired transmitter availability or reduced number of postsynaptic receptors, for example due to their internalization as a function of transmitter concentration. It also allows evaluation of the effects of drugs with specific actions such as receptor agonists and antagonists or reuptake inhibitors. It is a major advantage of this physiologically based approach that it can be adjusted to different types of neurons and synapses, and also can be extended to more elaborate physiological situations, e. g. by including additional receptors or ion channels, whenever this is indicated by clinical or experimental data.

Influence of time-delayed feedback in the firing pattern of thermally sensitive neurons.

We explore the dynamics of a Hodgkin-Huxley-type model for thermally sensitive neurons that exhibit intrinsic oscillatory activity. The model is modified to include a feedback loop that is represented by two parameters: the synaptic strength and the transmission delay time. We analyze the dynamics of the neuron depending on the temperature, the synaptic strength, and the delay time. We find parameter regions where the effect of the recurrent connexion is excitatory, inducing spikes or trains of spikes, and regions where it is inhibitory, reducing or eliminating completely the spiking behavior. We characterize the complex interplay of the intrinsic dynamics of the neuron with the recurrent feedback input and a noisy input.

Noise-induced impulse pattern modifications at different dynamical period-one situations in a computer model of temperature encoding.

We used a minimal Hodgkin-Huxley type model of cold receptor discharges to examine how noise interferes with the non-linear dynamics of the ionic mechanisms of neuronal stimulus encoding. The model is based on the assumption that spike-generation depends on subthreshold oscillations. With physiologically plausible temperature scaling, it passes through different impulse patterns which, with addition of noise, are in excellent agreement with real experimental data. The interval distributions of purely deterministic simulations, however, exhibit considerable differences compared to the noisy simulations especially at the bifurcations of deterministically period-one discharges. We, therefore, analyzed the effects of noise in different situations of deterministically regular period-one discharges: (1) at high-temperatures near the transition to subthreshold oscillations and to burst discharges, and (2) at low-temperatures close to and more far away from the bifurcations to chaotic dynamics. The data suggest that addition of noise can considerably extend the dynamical behavior of the system with coexistence of different dynamical situations at deterministically fixed parameter constellations. Apart from well-described coexistence of spike-generating and subthreshold oscillations also mixtures of tonic and bursting patterns can be seen and even transitions to unstable period-one orbits seem to appear. The data indicate that cooperative effects between low- and high-dimensional dynamics have to be considered as qualitatively important factors in neuronal encoding.

On the impact of episode sensitization on the course of recurrent affective disorders.

Sensitization of an organism by recurrent disease episodes is postulated as a key mechanism governing the progressive long-term course of affective disorders. The particular significance is that episode sensitization could underly the transition from externally triggered disease episodes to autonomous episode generation. Functionally, this transition might be explained by positive feedback between a disease episode and the activity state of an organism which includes the introduction of a memory trace for generated disease episodes. Here we consider the functional consequences of episode sensitization for the course of recurrent affective disorders. We use a computational approach and extend our previously introduced model for the course of affective disorders by a feedback mechanism for episode sensitization. Depending on sensitization timescale and amount, triggered episodes leave the model in a sustained sensitized state or induce autonomous disease progression. Runaway activation can end in saturation. Remarkably, however, over a broad parametric range the progression ends in intermediate states with fluctuating disease patterns. This behavior results from the model's nonlinear dynamics and represents a situation where the feedback intermittently changes between positive and negative directions. Our simulations strongly support episode sensitization as an important disease mechanism for affective disorders. From a nonlinear standpoint, this mechanism offers an explanation not only for autonomous disease progression but also for occurence and stability of irregular rapid-cycling disease states.

Phase-space structure of a thermoreceptor.

We analyze the phase-space structure of a model for thermoreceptors in fish and mammals. As a function of the temperature we identify a period doubling scenario at low temperatures, a regime where an unstable stationary fixed point collides with the attractor and blocks the thermoreceptor, and a transition from period n+1 to period n as the temperature is further increased. The period reduction phenomenon is due to an autoresonance between fast and slow ion channels and shows the features typical for mode locking.

Effects of noise on different disease states of recurrent affective disorders.

BACKGROUND: Nonlinear dynamics are currently proposed to explain the course of recurrent affective disorders. Such a nonlinear disease model predicts complex interactions with stochastic influences, in particular, because both disease dynamics and stochastic influences, such as psychosocial stressors, will vary during the course of the disease. We approach this problem by investigating general effects of noise intensity on different disease states of a nonlinear model for recurrent affective disorders. METHODS: A recently developed neurodynamic model is studied numerically. RESULTS: Noise can cause unstructured randomness or can maximize periodic order. The frequency of episode occurrence can increase with noise but it can also remain unaffected or even can decrease. The observed effects, thereby, depend critically on both the noise intensity and the internal nonlinear dynamics of the disease model. CONCLUSIONS: Our findings indicate that altered stochastic influences can significantly affect the outcome of a dynamic disease. To evaluate the effects of noise, it is essential to know about the underlying dynamics of respective disease states. Therefore, characterization of low-dimensional dynamics might become valuable for disease prediction and control.

Low-dimensional dynamics in sensory biology 2: facial cold receptors of the rat.

We report the results of a search for evidence of unstable periodic orbits in the sensory afferents of the facial cold receptors of the rat. Cold receptors are unique in that they exhibit a diversity of action potential firing patterns as well as pronounced transients in firing rate following rapid temperature changes. These characteristics are the result of an internal oscillator operating at the level of the membrane potential. If such oscillators have three or more degree of freedom, and at least one of which also exhibits a nonlinearity, they are potentially capable of complex activity. By detecting the existence of unstable periodic orbits, we demonstrate low-dimensional dynamical behavior whose characteristics depend on the temperature range, impulse pattern, and temperature transients.

Consequences of deterministic and random dynamics for the course of affective disorders.

BACKGROUND: Uni- and bipolar affective disorders tend to be recurrent and progressive. Illness patterns can evolve from isolated episodes to more rapid, rhythmic, and "chaotic" mood patterns. Nonlinear deterministic dynamics are currently proposed to explain this progression. However, most natural systems are nonlinear and noisy, and cooperative behavior of possible clinical relevance can result. METHODS: The latter issue has been studied with a mathematical model for progression of disease patterns in affective disorders. RESULTS: Deterministic dynamics can reproduce a progression from stable, to periodic, to chaotic patterns. Noise increases the spectrum of dynamic behaviors, enhances the responsiveness to weak activations, and facilitates the occurrence of aperiodic patterns. CONCLUSIONS: Noise might amplify subclinical vulnerabilities into disease onset and could induce transitions to rapid-changing dysrhythmic mood patterns. We suggest that noise-mediated cooperative behavior, including stochastic resonance, should be considered in appropriate models for affective illness.

Stimulus sensitivity and neuromodulatory properties of noisy intrinsic neuronal oscillators.

Intrinsic subthreshold oscillations in the membrane potential are a common property of many neurons in the peripheral and central nervous system. When such oscillations are combined with noise, interesting signal encoding and neuromodulatory properties are obtained which allow, for example, sensitivity adjustment or differential encoding of stimuli. Here we demonstrate that a noisy Hodgkin/Huxley-model for subthreshold oscillations, when tuned to maximum sensitivity, can be significantly modulated by even minor physiological changes in the oscillation parameters amplitude or frequency. Given the ubiquity of subthreshold oscillating neurons, it can be assumed that these findings reflect principle encoding properties which are relevant for an understanding of sensitivity and neuromodulation in peripheral and central neurons.

Low-dimensional dynamics in sensory biology. 1: Thermally sensitive electroreceptors of the catfish.

We report the results of a search for evidence of periodic unstable orbits in the electroreceptors of the catfish. The function of these receptor organs is to sense weak external electric fields. In addition, they respond to the ambient temperature and to the ionic composition of the water. These quantities are encoded by receptors that make use of an internal oscillator operating at the level of the membrane potential. If such oscillators have three or more degrees of freedom, and at least one of which also exhibits a nonlinearity, they are potentially capable of chaotic dynamics. By detecting the existence of stable and unstable periodic orbits, we demonstrate bifurcations between noisy stable and chaotic behavior using the ambient temperature as a parameter. We suggest that the technique developed herein be regarded as an additional tool for the analysis of data in sensory biology and thus can be potentially useful in studies of functional responses to external stimuli. We speculate that the appearance of unstable orbits may be indicative of a state of heightened sensory awareness by the animal.

Periodic firing pattern in afferent discharges from electroreceptor organs of catfish.

Spontaneous afferent activity was recorded from 26 single ampullary electroreceptive organs of freshwater catfish (Ictalurus nebulosus LeS) at various temperatures. Regular grouping of action potentials was apparent in this secondary sensory system at 35 degrees C and occasionally at 30 degrees C. Impulse groups consisted of up to seven impulses. The precise timing of impulse generation and the temporal sequence of impulses indicated that oscillating processes are involved. Expectation density functions were calculated for records of afferent activity obtained at various temperatures below 35 degrees C. In the majority of records the function was periodic. Impulse grouping and expectation density functions became more distinct in units exhibiting extremely high thresholds (i.e. being insensitive) to electrical stimuli. The results suggest that the oscillations originate from the postsynaptic membrane. The temporal pattern of impulse generation within impulse groups of ampullary electroreceptor organs and of specific warm and cold receptors was compared and found to be similar. Application of cadmium and menthol, which both reduce calcium entry, suppressed spontaneous activity in normal and insensitive electroreceptor systems, attenuated the sensitivity of normal receptors and modified the periodic pattern. This indicates that calcium is implicated in sensory transduction and in postsynaptic mechanisms. The data suggest that an oscillating process is one component of signal transmission in ampullary electroreceptor organs of teleost fish.

Oscillation and noise determine signal transduction in shark multimodal sensory cells.

Oscillating membrane potentials that generate rhythmic impulse patterns are considered to be of particular significance for neuronal information processing. In contrast, noise is usually seen as a disturbance which limits the accuracy of information transfer. We show here, however, that noise in combination with intrinsic oscillations can provide neurons with particular encoding properties, a discovery we made when recording from single electro-sensory afferents of a fish. The temporal sequence of the impulse trains indicates oscillations that operate near the spike-triggering threshold. The oscillation frequency determines the basic rhythm of impulse generation, but whether or not an impulse is actually triggered essentially depends on superimposed noise. The probability of impulse generation can be altered considerably by minor modifications of oscillation baseline and amplitude, which may underlie the exquisite sensitivity of these receptors to thermal and electrical stimuli. Additionally, thermal, but not electrical, stimuli alter the oscillation frequency, allowing dual sensory messages to be conveyed in a single spike train. These findings demonstrate novel properties of sensory transduction which may be relevant for neuronal signalling in general.

Actions of dalargin upon single unit activity in the ampullae of Lorenzini of the skate Raja clavata.

In the present study we have shown by single afferent unit recording in electroreceptors of skates (the ampullae of Lorenzini) that the synthetic analogue of leu-enkephalin, dalargin (DAL) at concentrations between 10(-6)-10(-10) M cause a concentration-dependent decrease in the resting discharge frequency as well as a decrease in stimulus evoked responses. The specific opiate antagonist naloxone (NAL, 10(-6) M) antagonizes responses induced by DAL. DAL depresses the excitatory action of L-glutamate (L-GLU). The data obtained speak in favour of the presence of opiate receptors at the synaptic membrane of the ampullae of Lorenzini.

Modulation of cutaneous cold receptor function by electrolytes, hormones and thermal adaptation.

The response properties of feline cold receptors were analyzed under control conditions, during conditions of altered external calcium concentrations and during application of menthol, catecholamines and ouabain. Afferent activity was extracellularly recorded from cold fibres of an isolated preparation of the tongue. Reduced calcium levels (0.5 mM) generally enhanced and elevated calcium levels (5.0 mM) suppressed cold fibre activity. The effects of menthol (10(-5) M) on cold receptors were qualitatively similar to those of reduced calcium. Application of adrenaline and noradrenaline (10(-6) M) were predominantly inhibiting. In cold receptors, the mean discharge rate is determined by the frequency of an oscillating receptor process and the probability of each cycle of this process to initiate afferent impulses. All measures mainly affected the probability of impulse generation rather than the oscillation frequency. Application of ouabain (10(-6) M) resulted in excitatory responses, caused by an increase of both probability of impulse generation and frequency of the oscillating receptor process. It is concluded that cold receptor function is based on a specific combination of common neuronal elements rather than on specific sensory processes.

Discharge pattern analysis suggests existence of a low-threshold calcium channel in cold receptors.

The regular periodic activity patterns of mammalian cold receptors have been quantitatively studied. Analysis of the timing of either single impulses or impulse groups demonstrated that the periodic receptor process is maintained independently of impulse generation and continues to operate under conditions when afferent impulses are not initiated. These results imply that the underlying conductances must be operational at threshold potentials related to impulse generation. In addition to temperature, the periodic process is considerably sensitive to calcium, which affects mainly the probability of impulse generation during each cycle. Reduction of external calcium and application of calcium entry blockers with relative selectivity for low-threshold calcium channels are similarly effective in modulating cold receptor activity. The data imply the existence of a low-threshold calcium conductance at the sensory terminal.

Modulation of periodic cold receptor activity by ouabain.

The effect of ouabain on the periodic discharge pattern of feline cold receptors was studied in order to substantiate a possible contribution of Na/K pump activity to signal transduction. Afferent activity was recorded from the cold fibres of an isolated preparation of the tongue. The periodic pattern consisted of beating activity and of grouped discharges and was characterized by two parameters, the oscillation frequency and the number of impulses initiated per cycle. Ouabain (10(-7)-10(-6)M) induced in all receptors excitatory responses, consisting of a short vigorous increase of activity followed by inhibition. Thus the receptors never stabilized to or maintained a new static level of activity. The ouabain-induced responses occurred repeatedly in several receptors and were produced by remarkable stereotyped modifications of both the oscillation frequency and the number of impulses per cycle. The oscillation frequency attained peak values which increased monotonically with higher static temperatures and which were considerably greater than peak control values. The data indicate that an electrogenic Na/K pump contributes to the transducer process of cold receptors and that inhibition of this pump evidently gives rise to a depolarizing imbalance of the membrane potential, accelerating the oscillation frequency to a maximum value. Thus the oscillation frequency seems to be controlled by temperature and by membrane potential in cold receptors.

Ampullary electroreceptors in catfish (Teleostei): temperature dependence of stimulus transduction.

The response properties of ampullary electroreceptors have been studied in the catfish Ictalurus nebulosus at skin temperatures between 5 and 35 degrees C. A unimodal relationship between spontaneous activity and temperature was obtained. Mean (+/- SEM) peak discharge rate was 57.3 +/- 1.8 impulses s-1 at 25 degrees C; the receptors were active at 5 degrees C (15.0 impulses s-1) and at 35 degrees C (31.5 impulses s-1). There were no dynamic responses to temperature changes in either the warming or cooling direction. The shape of the frequency characteristic depended on temperature: the peak of the gain curve shifted to low frequencies at low temperatures. There was a concomitant change of the phase characteristic: the intersection at zero degree phase angle shifted to higher frequencies with an increase of temperature, thus increasing the lead at lower frequencies and decreasing the lag at higher frequencies. Latency after combined excitatory and inhibitory impulse stimulation was temperature dependent, ranging from 16.4 ms (5 degrees C) to 5.6 ms (35 degrees C). Application of the specific calcium channel blocker menthol (0.2 mM) suppressed spontaneous activity, the effect becoming more prominent at higher temperatures. Sensitivity to sinusoidal electrical stimulation was also impaired, but to a lesser degree and mainly at lower temperatures. We conclude that the filter properties of the receptor organ can be modelled by a band-pass filter in series with a latency, both of which are temperature dependent. These filter properties might be partially based on the activation kinetics of the transduction channels.

Analysis of facial cold receptor activity in the rat.

Afferent activity of single facial cold receptors was extracellularly recorded from infraorbital nerve fibers in the rat, and the response properties of 28 receptors to thermal stimulation were quantitatively studied. Generally, on repeated stimulation, the afferent activity was highly reproducible and was not dependent on previous adapting temperatures. At constant temperatures, a periodic pattern was apparent in the discharges of 24 receptors; in the remaining 4 receptors periodic elements could not reliably be detected. The temperature dependence of the cyclic pattern corresponded to that observed in other mammalian cold receptor populations: we observed regular impulse groups (bursts) at lower and beating activity at higher adapting temperatures. Rapid changes of temperature induced transient alterations of activity. The dynamic response to cooling was biphasic, indicating a complex sequence of receptor events. A transient acceleration of impulse frequency was followed by a dynamic burst discharge which was characterized by longer pauses and a greater number of impulses per burst compared with the steady-state activity at the same temperature. This indicates a deceleration of the periodic receptor events during the adaptation process following dynamic responses, which is accompanied by a concomitant shift of these processes to a more pronounced suprathreshold condition. In an additional series of experiments, parameters of the periodic activity in the rat were compared with corresponding data of facial and lingual cold receptors in the cat. Whereas the number of impulses per cycle was similar in the 3 receptor populations, the frequency of the periodic pattern proved to be considerably higher in the rat than in the cat.