Periodic forcing of a K+ channel at various temperatures

A dynamics model of neuron-astrocyte network accounting for febrile seizures

Febrile seizure (FS) is a full-body convulsion caused by a high body temperature that affect young kids, however, how these most common of human seizures are generated by fever has not been known. One common observation is that cortical neurons become overexcited with abnormal running of sodium and potassium ions cross membrane in raised body temperature condition, Considering that astrocyte Kir4.1 channel play a critical role in maintaining extracellular homeostasis of ionic concentrations and electrochemical potentials of neurons by fast depletion of extracellular potassium ions, we examined here the potential role of temperature-dependent Kir4.1 channel in astrocytes in causing FS. We first built up a temperature-dependent computational model of the Kir4.1 channel in astrocytes and validated with experiments. We have then built up a neuron-astrocyte network and examine the role of the Kir4.1 channel in modulating neuronal firing dynamics as temperature increase. The numerical experiment demonstrated that the Kir4.1 channel function optimally in the body temperature around 37 °C in cleaning 'excessive' extracellular potassium ions during neuronal firing process, however, higher temperature deteriorates its cleaning function, while lower temperature slows down its cleaning efficiency. With the increase of temperature, neurons go through different stages of spiking dynamics from spontaneous slow oscillations, to tonic spiking, fast bursting oscillations, and eventually epileptic bursting. Thus, our study may provide a potential new mechanism that febrile seizures may be happened due to temperature-dependent functional disorders of Kir4.1 channel in astrocytes.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-021-09706-w.

Low-frequency noise induced by cation exchange fluctuation on the wall of silicon nitride nanopore

Nanopore-based biosensors have attracted attention as highly sensitive microscopes for detecting single molecules in aqueous solutions. However, the ionic current noise through a nanopore degrades the measurement accuracy. In this study, the magnitude of the low-frequency noise in the ionic current through a silicon nitride nanopore was found to change depending on the metal ion species in the aqueous solution. The order of the low-frequency noise magnitudes of the alkali metal ionic current was consistent with the order of the adsorption affinities of the metal ions for the silanol surface of the nanopore (Li <Na <K < Rb <Cs). For the more adsorptive alkaline earth metal ions (Mg and Ca), the low-frequency noise magnitudes were as low as those for Li ions. This tendency, i.e., metal ions having a very high or low adsorption affinity causing a reduction in low-frequency noise, suggests that the low-frequency noise was induced by the exchange reactions between protons and metal ions occurring on the silanol surface. In addition, the low-frequency noise in the ionic current remained low even after replacing the CaCl₂ aqueous solution with a CsCl aqueous solution, indicating that Ca ions continued being adsorbed onto silanol groups even after removing the aqueous solution.

Quantum stochastic dynamics in the presence of a time-periodic rapidly oscillating potential: nonadiabatic escape rate

Escape from a metastable state in the presence of a high-frequency field (where the driving becomes nonadiabatic) underlies a broad range of phenomena of physics and chemistry, and thus its understanding is of paramount importance. We study the problem of intermediate-to-high-damping escape from a metastable state of a dissipative system driven by a rapidly oscillating field, one of the most important classes of nonequilibrium systems, in a broad range of field driving frequencies (ω) and amplitudes (a). We construct a Langevin equation using quantum gauge transformation in the light of Floquet theorem and exploiting a systematic perturbative expansion in powers of 1/ω using "Kapitza-Landau time window". The quantum dynamics in a high-frequency field are found to be described by an effective time-independent potential. The temperature dependence of escape rate and the change of its form with varying parameters of the field have been analyzed. It may decrease upon increasing the temperature which is contingent on the effects of intricate interplay between external modulation and dissipation. The crossover temperature between tunnelling and thermal hopping increases with an increase in external modulation so that quantum effects in the escape are relevant at higher temperatures. These observations are uncommon and counterintuitive and, therefore, of considerable interest. Our results might be valuable for the exploration of the dynamics of cold atoms in electromagnetic fields.

Thermally enhanced stability in fluctuating bistable potentials

Overdamped motion of Brownian particles in an asymmetric double-well potential driven by an additive nonequilibrium three-level noise and a thermal noise is considered. In the stationary regime, an exact formula for the mean occupancy of the metastable state is derived, and the phenomenon of enhancement of stability versus temperature is investigated. It is established that in a certain region of the system parameters the mean occupancy can be either multiply enhanced or suppressed by variations of temperature. We show that this effect is due to the involvement of different time scales in the problem. The necessary conditions for several different behaviors of the mean occupancy as a function of temperature are also discussed. The effect is more pronounced when the kurtosis of the three-level noise tends to -2 , i.e., in the case of dichotomous noise.

Stimulus-response curves of a neuronal model for noisy subthreshold oscillations and related spike generation

We investigate the stimulus-dependent tuning properties of a noisy ionic conductance model for intrinsic subthreshold oscillations in membrane potential and associated spike generation. Upon depolarization by an applied current, the model exhibits subthreshold oscillatory activity with an occasional spike generation when oscillations reach the spike threshold. We consider how the amount of applied current, the noise intensity, variation of maximum conductance values, and scaling to different temperature ranges alter the responses of the model with respect to voltage traces, interspike intervals and their statistics, and the mean spike frequency curves. We demonstrate that subthreshold oscillatory neurons in the presence of noise can sensitively and also selectively be tuned by the stimulus-dependent variation of model parameters.

Effects of patch temperature on spontaneous action potential train due to channel fluctuations: Coherence resonance

Based on the Hodgkin-Huxley (HH) model, the effects of patch temperature as a control parameter on the spontaneous action potentials for finite size of membrane patch are studied. With increasing patch temperature, it is found that the mean open rates of sodium and potassium channels of the HH neuron are decreased, and the mean duration of spikes of membrane potential is also decreased, which are qualitatively consistent with previous experimental results of single ion channel. Under moderate patch size, the mean interspike interval of membrane potential first decreases, reaches a minimum, and then increases with increasing patch temperature. It is shown that for both low and high temperatures, the channels fluctuation-induced spontaneous action potentials appear to be rather irregular, while for moderate patch temperature, relatively coherent oscillations observed. By defining a measure parameter beta, we show that there is a maximal region for the measure beta in the patch temperature and patch size parameter plane where the coherence resonance phenomena are very remarkable, and the characteristic correlation time of the output also confirm our result.

Non-Markovian stochastic resonance: three-state model of ion channel gating

Stochastic resonance in single voltage-dependent ion channels is investigated within a three-state non-Markovian modeling of the ion channel conformational dynamics. In contrast to a two-state description one assumes the presence of an additional closed state for the ion channel which mimics the manifold of voltage-independent closed subconformations (inactivated "state"). The conformational transition into the open state occurs through a domain of voltage-dependent closed subconformations (closed "state"). At distinct variance with the standard two-state and also the three-state Markovian approach, the inactivated state is characterized by a broad, nonexponential probability distribution of corresponding residence times. The linear response to a periodic voltage signal is determined for arbitrary distributions of the channel's recovery times. Analytical results are obtained for the spectral amplification of the applied signal and the corresponding signal-to-noise ratio. Alternatively, these results are also derived by use of a corresponding two-state non-Markovian theory which is based on driven integral renewal equations [I. Goychuk and P. Hänggi, Phys. Rev. E 69, 021104 (2004)]. The non-Markovian features of stochastic resonance are studied for a power law distribution of the residence time intervals in the inactivated state which exhibits a large variance. A comparison with the case of biexponentially distributed residence times possessing the same mean value, i.e., the simplest non-Markovian two-state description, is also presented.

Theory of non-Markovian stochastic resonance

We consider a two-state model of non-Markovian stochastic resonance (SR) within the framework of the theory of renewal processes. Residence time intervals are assumed to be mutually independent and characterized by some arbitrary nonexponential residence time distributions which are modulated in time by an externally applied signal. Making use of a stochastic path integral approach we obtain general integral equations governing the evolution of conditional probabilities in the presence of an input signal. These equations generalize earlier integral renewal equations by Cox and others to the case of driving-induced nonstationarity. On the basis of these equations a response theory of two-state renewal processes is formulated beyond the linear response approximation. Moreover, a general expression for the linear response function is derived. The connection of the developed approach with the phenomenological theory of linear response for manifest non-Markovian SR put forward [I. Goychuk and P. Hänggi, Phys. Rev. Lett. 91, 070601 (2003)] is clarified and its range of validity is scrutinized. The theory is then applied to SR in symmetric non-Markovian systems and to the class of single ion channels possessing a fractal kinetics.

On episode sensitization in recurrent affective disorders: the role of noise

Episode sensitization is postulated as a key mechanism underlying the long-term course of recurrent affective disorders. Functionally, episode sensitization represents positive feedback between a disease process and its disease episodes resulting in a transition from externally triggered to autonomous episode generation. Recently, we introduced computational approaches to elucidate the functional properties of sensitization. Specifically, we considered the dynamics of episode sensitization with a simple computational model. The present study extends this work by investigating how naturally occurring, internal or external, random influences ("noise") affect episode sensitization. Our simulations demonstrate that actions of noise differ qualitatively in dependence on both the model's activity state as well as the noise intensity. Thereby induction as well as suppression of sensitization can be observed. Most interestingly, externally triggered sensitization development can be minimized by tuning the noise to intermediate intensities. Our findings contribute to the conceptual understanding of the clinical kindling model for affective disorders and also indicate interesting roles for random fluctuations in kindling and sensitization at the neuronal level.

Detecting subthreshold events in noisy data by symbolic dynamics

We show that a symmetric threshold crossing detector can be described by a symbolic dynamics of a static three-symbol encoding which is highly efficient to detect subthreshold events in noisy nonstationary data. After computing instantaneous word statistics and running cylinder entropies, we introduce a mean-field transformation of the three-symbol dynamics considered as a Potts-spin lattice onto a distribution of two symbols. This transformed word statistics enables one to derive an estimator of the signal-to-noise ratio (SNR). Subthreshold events are then proven by a prominent peak of the SNR estimator as a function of the noise intensity.

Stochastic resonance in two-state model of membrane channel with comparable opening and closing rates

Voltage-gated ion channels in biological membranes can be modeled as two-state stochastic systems with inter-state transition probabilities that depend on external stimulus. We study analytically the passage of a signal through such a system in the presence of external noise in the case when the above dependence is arbitrary, and illustrate our approach using the two models of ion channels known in the literature. The explicit expressions for the spectral density of the output signal and noise, the signal-to-noise ratio, and the coherence function are obtained for rectangular periodic signal and dichotomous noise in a wide range of parameters. The dependence of the above quantities on the bias and on the noise amplitude demonstrates strong resonant behavior in the regions where the probabilities of channel closing and opening become equal. This resonance results from additional symmetry between channel states and differs from conventional stochastic resonance studied earlier.

Behavioral stochastic resonance: how the noise from a Daphnia swarm enhances individual prey capture by juvenile paddlefish

Zooplankton emit weak electric fields into the surrounding water that originate from their own muscular activities associated with swimming and feeding. Juvenile paddlefish prey upon single zooplankton by detecting and tracking these weak electric signatures. The passive electric sense in this fish is provided by an elaborate array of electroreceptors, Ampullae of Lorenzini, spread over the surface of an elongated rostrum. We have previously shown that the fish use stochastic resonance to enhance prey capture near the detection threshold of their sensory system. However, stochastic resonance requires an external source of electrical noise in order to function. A swarm of plankton, for example Daphnia, can provide the required noise. We hypothesize that juvenile paddlefish can detect and attack single Daphnia as outliers in the vicinity of the swarm by using noise from the swarm itself. From the power spectral density of the noise plus the weak signal from a single Daphnia, we calculate the signal-to-noise ratio, Fisher information and discriminability at the surface of the paddlefish's rostrum. The results predict a specific attack pattern for the paddlefish that appears to be experimentally testable.

Effective rate equations for the overdamped motion in fluctuating potentials

We discuss physical and mathematical aspects of the overdamped motion of a Brownian particle in fluctuating potentials. It is shown that such a system can be described quantitatively by fluctuating rates if the potential fluctuations are slow compared to relaxation within the minima of the potential, and if the position of the minima does not fluctuate. Effective rates can be calculated; they describe the long-time dynamics of the system. Furthermore, we show the existence of a stationary solution of the Fokker-Planck equation that describes the motion within the fluctuating potential under some general conditions. We also show that a stationary solution of the rate equations with fluctuating rates exists.

Stochastic resonance in a Hodgkin-Huxley neuron in the absence of external noise

We study numerically nonlinear responses of a periodically forced Hodgkin-Huxley neuron. The coherence of the system in the absence of external noise, namely, the "intrinsic stochastic resonance," is evidenced by the multimodal aperiodic firing pattern, a bell-shaped curve in the signal-to-noise ratio, and the statistical features of the mean firing rate. The subthreshold intrinsic oscillations enhance the signal transduction in a manner different from that in models studied previously.

Noise induced stability in fluctuating, bistable potentials

The overdamped motion of a Brownian particle in an asymmetric, bistable, fluctuating potential shows noise induced stability: For intermediate fluctuation rates the mean occupancy of minima with an energy above the absolute minimum is enhanced. The model works as a detector for potential fluctuations being not too fast and not too slow. This effect occurs due to the different time scales in the problem. We present a detailed analysis of this effect using the exact solution of the Fokker-Planck equation for a simple model. Further we show that for not too fast fluctuations the system can be well described by effective rate equations. The results of the rate equations agree quantitatively with the exact results.

Effect of syncytium structure of receptor systems on stochastic resonance induced by chaotic potential fluctuation

To study a role of syncytium structure of sensory receptor systems in the detection of weak signals through stochastic resonance, we present a model of a receptor system with syncytium structure in which receptor cells are interconnected by gap junctions. The apical membrane of each cell includes two kinds of ion channels whose gating processes are described by the deterministic model. The membrane potential of each cell fluctuates chaotically or periodically, depending on the dynamical state of collective channel gating. The chaotic fluctuation of membrane potential acts as internal noise for the stochastic resonance. The detection ability of the system increases as the electric conductance between adjacent cells generated by the gap junction increases. This effect of gap junctions arises mainly from the fact that the synchronization of chaotic fluctuation of membrane potential between the receptor cells is strengthened as the density of gap junctions is increased.

Amplification of electromagnetic signals by ion channels

Cells may respond to the exposure of low-frequency electromagnetic fields with changes in cell division, ion influx, chemical reaction rates, etc. The chain of events leading to such responses is difficult to study, mainly because of extremely small energies associated with low-frequency fields, usually much smaller than the thermal noise level. However, the presence of stochastic systems (for instance, ion channels) provides a basis for signal amplification, and could therefore, despite the low signal-to-noise ratio of the primary response, lead to the transmission of weak signals along the signaling pathways of cells. We have explored this possibility for an ion channel model, and we present a theory, based on the formalism of stochastically driven processes, that relates the time averages of the ion channel currents to the amplitude and frequency of the applied signal. It is concluded from this theory that the signal-to-noise ratio increases with the number of channels, the magnitude of the rate constants, and the frequency response of the intracellular sensing system (for instance, a calcium oscillator). The amplification properties of the stochastic system are further deduced from numerical simulations carried out on the model, which consists of multiple identical two-state channels, and the behavior for different parameters is examined. Numerical estimates of the parameters show that under optimum conditions, even very weak low-frequency electromagnetic signals (<100 Hz and down to 100 microT) may be detected in a cellular system with a large number of ion channels.

Noise-induced enhancement of signal transduction across voltage-dependent ion channels

The presence of noise in a signal transduction system usually interferes with its ability to transfer information reliably. But many nonlinear systems can use noise to enhance performance, and this phenomenon, called stochastic resonance, may underlie the extraordinary ability of some biological systems to detect and amplify small signals in noisy environments. Previous work has demonstrated the occurrence of stochastic resonance in a complex system of biological transducers and neural signal pathways, but the possibility that it could occur at the sub-cellular level has remained open. Here we report the observation of stochastic resonance in a system of voltage-dependent ion channels formed by the peptide alamethicin. A hundred-fold increase in signal transduction induced by external noise is accompanied by a growth in the output signal-to-noise ratio. The system of ion channels considered here represents the simplest biological system yet known to exhibit stochastic resonance.