Effects of fractal gating of potassium channels on neuronal behaviours

The classical model of voltage-gated ion channels assumes that according to a Markov process ion channels switch among a small number of states without memory, but a bunch of experimental papers show that some ion channels exhibit significant memory effects, and this memory effects can take the form of kinetic rate constant that is fractal. Obviously the gating character of ion channels will affect generation and propagation of action potentials, furthermore, affect generation, coding and propagation of neural information. However, there is little previous research on this series of interesting issues. This paper investigates effects of fractal gating of potassium channel subunits switching from closed state to open state on neuronal behaviours. The obtained results show that fractal gating of potassium channel subunits switching from closed state to open state has important effects on neuronal behaviours, increases excitability, rest potential and spiking frequency of the neuronal membrane, and decreases threshold voltage and threshold injected current of the neuronal membrane. So fractal gating of potassium channel subunits switching from closed state to open state can improve the sensitivity of the neuronal membrane, and enlarge the encoded strength of neural information.     

Voltage-gated sodium channels in taste bud cells

Background  

Taste bud cells transmit information regarding the contents of food from taste receptors embedded in apical microvilli to gustatory nerve fibers innervating basolateral membranes. In particular, taste cells depolarize, activate voltage-gated sodium channels, and fire action potentials in response to tastants. Initial cell depolarization is attributable to sodium influx through TRPM5 in sweet, bitter, and umami cells and an undetermined cation influx through an ion channel in sour cells expressing PKD2L1, a candidate sour taste receptor. The molecular identity of the voltage-gated sodium channels that sense depolarizing signals and subsequently initiate action potentials coding taste information to gustatory nerve fibers is unknown.     

Brain-derived neurotrophic factor modulation of Kv1.3 channel is disregulated by adaptor proteins Grb10 and nShc

Background  

Neurotrophins are important regulators of growth and regeneration, and acutely, they can modulate the activity of voltage-gated ion channels. Previously we have shown that acute brain-derived neurotrophic factor (BDNF) activation of neurotrophin receptor tyrosine kinase B (TrkB) suppresses the Shaker voltage-gated potassium channel (Kv1.3) via phosphorylation of multiple tyrosine residues in the N and C terminal aspects of the channel protein. It is not known how adaptor proteins, which lack catalytic activity, but interact with members of the neurotrophic signaling pathway, might scaffold with ion channels or modulate channel activity.     

Field-effect transistor with recombinant potassium channels: fast and slow response by electrical and chemical interactions

Electrical interfacing of semiconductor devices with ion channels is the basis for a development of neuroelectronic systems and of cell-based biospecific electronic sensors. To elucidate the mechanism of cell–chip coupling, we studied the voltage-gated potassium channel Kv1.3 in HEK 293 cells on field-effect transistors in silicon with a metal-free gate of silicon dioxide. Upon intracellular depolarization there is a positive change of the effective extracellular voltage on the transistor with an amplitude that correlates with the gating of Kv1.3 channels, but with a dynamics that is far slower than channel gating. After repolarization there is a fast negative change of the transistor signal followed by a slow relaxation dynamics without any membrane current. To rationalize the involved transistor response, we propose a concept that combines the electrodiffusion of ions in the cell–chip junction with selective ion binding in the electrical double layer of silicon dioxide. The model implies (i) an electrical charging and discharging of the cell–chip capacitance within a microsecond, (ii) a changing K⁺ concentration in the cell–chip junction within a millisecond and (iii) a changing adsorption of K⁺ and Na⁺ ions within tens of milliseconds. The total transistor signal is a superposition of the changed electrical potential in the extracellular space between cell and chip and of the changed surface potential at the chip surface. PACS 73.40.Mr; 82.45.Vp; 85.30.Tv; 87.16.Uv; 87.19.Nn     

Nonlinearities in cochlear receptor potentials and their origins

Using intracellular recording methods in vivo [P. Dallos, J. Neurosci. 5, 1591-1608 (1985)], various nonlinear characteristics of receptor potentials from hair cells located in the low-frequency region of the guinea pig cochlea have been examined. Patterns of saturation for ac and dc response components obtained from Fourier analysis and directly from averaged waveforms are studied. Growth patterns of lower harmonic components are investigated and the interesting nonmonotonic properties of even harmonics noted. The latter are seen in both inner and outer hair cell responses, primarily with stimuli near the cells' best frequency. Fundamental ac and the dc potentials occasionally exhibit nonmonotonic growth. These patterns are studied and their occurrence in inner and outer hair cell responses considered.     

Effects of channel noise on firing coherence of small-world Hodgkin-Huxley neuronal networks

We investigate the effects of channel noise on firing coherence of Watts-Strogatz small-world networks consisting of biophysically realistic HH neurons having a fraction of blocked voltage-gated sodium and potassium ion channels embedded in their neuronal membranes. The intensity of channel noise is determined by the number of non-blocked ion channels, which depends on the fraction of working ion channels and the membrane patch size with the assumption of homogeneous ion channel density. We find that firing coherence of the neuronal network can be either enhanced or reduced depending on the source of channel noise. As shown in this paper, sodium channel noise reduces firing coherence of neuronal networks; in contrast, potassium channel noise enhances it. Furthermore, compared with potassium channel noise, sodium channel noise plays a dominant role in affecting firing coherence of the neuronal network. Moreover, we declare that the observed phenomena are independent of the rewiring probability.     

Influence of direct current on dc receptor potentials from cochlear inner hair cells in the guinea pig

Inner hair cell responses to sound were monitored while direct current was applied across the membranous labyrinth in the first turn of the guinea pig cochlea. The current injection electrodes were positioned in the scala vestibuli and on the round window membrane. Positive and negative current (less than 100 microA) caused changes in the sound-evoked dc receptor potentials which were dependent on the sound frequency and intensity. The frequencies most affected by this extracellular current were those comprising the "tip" portion of the inner hair cell frequency tuning characteristic (FTC). The influence of current increased with increasing frequency. Positive current increased the amount of dc receptor potential for the affected frequencies while negative current decreased the potential. Current-induced changes (on a percentage basis) were greater for low intensity sounds and the negative current direction. These frequency specific changes are evidenced as a loss in sensitivity for the tip area of the FTC and a downward shift of the inner hair cell characteristic frequency. Larger current levels (greater than 160 microA) cause more complex changes including unrecoverable loss of cell performance. In separate experiments positive and negative currents (less than 1.1 microA) were injected into the inner hair cell from the recording electrode during simultaneous measurement of the sound-evoked dc receptor potential. This condition caused a shift in IHC sensitivity that was independent of sound frequency and intensity. Positive current decreased the sensitivity of the level of the cell while negative current increased the responses. The effect of current level on sound-evoked dc receptor potential was nonlinear, as comparatively greater increases in cell response were observed for negative than decreases for positive current. The intracellular current injection results are accounted for by the mechano-resistive model of hair cell transduction, where nonlinear responses with current level may reflect outward rectification. Response changes induced by extracellular current are evidence of current effects on both inner and outer hair cells. The frequency and intensity dependences are hypothesized to represent voltage mediated control of inner hair cell response by the outer hair cells.     

Frequency-dependent self-induced bias of the basilar membrane and its potential for controlling sensitivity and tuning in the mammalian cochlea

A displacement-sensitive capacitive probe technique was used in the first turn of guinea pig cochleas to examine whether the motion of the basilar membrane includes a displacement component analogous to the dc receptor potentials of the hair cells. Such a "dc" component apparently exists. At a given location on the basilar membrane, its direction toward scala vestibuli (SV) or scala tympani (ST) varies systematically with frequency of the acoustic stimulus. Furthermore, it appears to consist of two parts: a small asymmetric offset response to each gated tone burst plus a progressive shift of the basilar membrane from its previous position. The mean position shift is cumulative, increasing with successive tone bursts. The amplitude of the immediate offset response, when plotted as a function of frequency, appears to exhibit a trimodal pattern. This displacement offset is toward SV at the characteristic frequency (CF) of the location of the probe, while at frequencies either above or below the CF the offset is relatively larger, and toward ST. The mechanical motion of the basilar membrane therefore appears to contain the basis for lateral suppression. The cumulative mean position shift, however, appears to peak toward ST at the apical end of the traveling wave envelope and appears to be associated with a resonance, not of the basilar membrane motion directly, but coupled to it. The summating potential, measured concurrently at the round window, shows a more broadly tuned peak just above the CF of the position of the probe. This seems to correspond to the peak at the CF of the mechanical bias. As the preparation deteriorates, the best frequency of the vibratory displacement response decreases to about a half-octave below the original CF. There is a corresponding decrease in the frequency of the peaks of the trimodal pattern of the asymmetric responses to tone bursts. The trimodal pattern also broadens. In previous experiments the basilar membrane has been forced to move in response to a low-frequency biasing tone. The sensitivity to high-frequency stimuli varies in phase with the biasing tone. The amplitudes of slow movement in these earlier experiments and in the present experiments are of the same order of magnitude. This suggests strongly that the cumulative shift toward ST to a high-frequency acoustic stimulus constitutes a substantial controlling bias on the sensitivity of the cochlea in that same high-frequency region. Its effect will be to reduce the slope of neural rate-level functions on the high-frequency side of CF.     

Effect of current stimulus on in vivo cochlear mechanics

In this paper, the influence of direct current stimulation on the acoustic impulse response of the basilar membrane (BM) is studied. A positive current applied in the scala vestibuli relative to a ground electrode in the scala tympani is found to enhance gain and increase the best frequency at a given location on the BM. An opposite effect is found for a negative current. Also, the amplitude of low-frequency cochlear microphonic at high sound levels is found to change with the concurrent application of direct current stimulus. BM vibrations in response to pure tone acoustic excitation are found to possess harmonics whose levels relative to the fundamental increase with the application of positive current and decrease with the application of negative current. A model for outer hair cell activity that couples changes in length and stiffness to transmembrane potential is used to interpret the results of these experiments and others in the literature. The importance of the in vivo mechanical and electrical loading is emphasized. Simulation results show the somewhat paradoxical finding that for outer hair cells under tension, hyperpolarization causes shortening of the cell length due to the dominance of voltage dependent stiffness changes.     

Influence of fixed electric charges on potential profile across the squid axon membrane

The potential profile for a model of squid axon membrane has been determined for two physiological states: resting and action states. The non-linear Poisson-Boltzmann equation has been solved by considering the volumetric charge densities due to charges dissolved in an electrolytic solution and fixed on both glycocalyx and cytoplasmatic proteins. Results showing the features of the potential profile along the outer electrolytic region are similar for both resting and action states. However, the potential fall along glycocalyx at action state is lower than at resting. A small variation in the Na⁺ concentration drastically affects the surface membrane potentials and vice versa. We conclude that effects on the potential profile due to surface lipidic bilayer charge and contiguous electric double layers are more relevant than those provoked by fixed charges distributed along the cell cytoplasm.     

Dynamical response of a neuron–astrocyte coupling system under electromagnetic induction and external stimulation

Previous studies have observed that electromagnetic induction can seriously affect the electrophysiological activity of the nervous system. Considering the role of astrocytes in regulating neural firing, we studied a simple neuron–astrocyte coupled system under electromagnetic induction in response to different types of external stimulation. Both the duration and intensity of the external stimulus can induce different modes of electrical activity in this system, and thus the neuronal firing patterns can be subtly controlled. When the external stimulation ceases, the neuron will continue to fire for a long time and then reset to its resting state. In this study, "delay" is defined as the delayed time from the firing state to the resting state, and it is highly sensitive to changes in the duration or intensity of the external stimulus. Meanwhile, the self-similarity embodied in the aforementioned sensitivity can be quantified by fractal dimension. Moreover, a hysteresis loop of calcium activity in the astrocyte is observed in the specific interval of the external stimulus when the stimulus duration is extended to infinity, since astrocytic calcium or neuron electrical activity in the resting state or during periodic oscillation depends on the initial state. Finally, the regulating effect of electromagnetic induction in this system is considered. It is clarified that the occurrence of "delay" depends purely on the existence of electromagnetic induction. This model can reveal the dynamic characteristics of the neuron–astrocyte coupling system with magnetic induction under external stimulation. These results can provide some insights into the effects of electromagnetic induction and stimulation on neuronal activity.     

Qualitative interpretation of resonance effects in vibrational excitation cross sections of diatomic molecules by slow electrons

It is suggested to solve the problem of resonance vibrational excitation of diatomic molecules colliding with slow electrons without using a formal expansion in wave functions with complex eigenvalues. The main point is to overcome the difficulties associated with the necessity of considering at the same time a large number of inelastic channels so as to account for the long range part of the interaction potential. In the model proposed inelastic scattering is determined by the parameters of a single interaction potential, determining also elastic scattering. As a result we obtain as a special case an equation similar in structure to that of Herzenberg and Mandl [1] for evaluating cross sections. As an example numerical calculations were performed for spherical square well potentials, indicating the presence of characteristic resonance cross sections already in this simplest case.Translated from Izvestiya VUZ. Fizika, No. 12 pp. 7–13 December, 1971.     

Cardiac Excitation Waves under Strong Hyperkalemia Condition

Normal blood levels of potassium are critical for maintaining normal heart electrical rhythm. Both low blood potassium levels (hypokalemia) and high blood potassium levels (hyperkalemia) can lead to abnormal heart rhythms. The aim of the work presented is to study the effect of potassium concentration on the excitation wave in the cardiac tissue. Results have been obtained both in the experimental model, which is a monolayer of neonatal rat cardiomyocytes, and in the modified Korhonen computer model, designed for ventricular rat neonatal cardiomyocytes. The existence of non-sodium excitation waves under a strong hyperkalemia (more than 10 mM K + in the extracellular environment) in the cardiomyocyte monolayer has been found and has also be confirmed by inactivation of sodium channels with a specific channel blocker.     

A comparison between basilar membrane and inner hair cell receptor potential input-output functions in the guinea pig cochlea

Intracellular recordings were made from inner hair cells and basilar membrane motion was measured at a similar place, but in different preparations, in the first turn of the guinea pig cochlea. Potential recordings were made using glass microelectrodes and mechanical measurements were made using the M?ssbauer technique. Intensity functions of DC receptor potential and basilar membrane velocity in animals with good and poor thresholds are presented. In animals with good thresholds, stimuli at and above the characteristic frequency produce similarly compressive input-output functions for both inner hair cell receptor potentials and basilar membrane motion. However, for frequencies lower than the characteristic frequency, receptor potential input-output functions obtained from animals in good and poor condition show saturation at high stimulus intensities at which basilar membrane motion is linear. This discrepancy is believed to be due to a nonlinear inner hair cell transduction mechanism. We propose that nonlinearity observed in receptor potential input-output functions is a consequence of the simple cascading of a frequency-dependent nonlinear mechanical input and a frequency-independent nonlinear transduction process.     

Phase resetting and dynamics in isolated atrioventricular nodal cell clusters

In the heart, the AV node is the primary conduction pathway between the atria and ventricles and subserves an important function by virtue of its rate-dependent properties. Cell clusters isolated from the rabbit atrioventricular (AV) node beat with a stable rhythm (cycle length: 300-520 ms) and are characterized by slow action potential upstroke velocities (7 to 30 V/s). The goal of this study is to better characterize the phase resetting and the rhythms during periodic stimulation of this slow inward current system. Single or periodic depolarizing pulses (20 ms in duration) were injected into AV nodal cell clusters using glass microelectrodes. Phase resetting curves of both strong, weak as well as discontinuous types were obtained by applying single current pulses of different intensities and latencies following every ten action potentials. Graded responses were elicited in a wide range of stimulus phases and amplitudes. A single premature stimulus caused a transient prolongation of the cycle length. Sustained periodic stimulation, at rates faster than the intrinsic beat rate, resulted in various N:M (stimulus frequency: action potential frequency) entrainment rhythms as well as periodic or irregular changes in action potential morphology. The changes in action potential characteristics were evaluated by computing the area under the action potential trace and above a fixed threshold (-45 mV). We show that the variations in action potential morphology play a major role in the onset of complicated dynamics observed in this experimental preparation. In this context, the prediction of entrainment rhythms using techniques based on the iteration of phase resetting curves (PRCs) is inadequate since the PRC does not carry information directly related to the changes in action potential morphology. This study demonstrates the need to consider graded events which, though not propagated, have important implications in the understanding of dynamical diseases of the heart. (c) 1995 American Institute of Physics.     

Chaotic states in a random world: Relationship between the nonlinear differential equations of excitability and the stochastic properties of ion channels

Excitable membranes allow cells to generate and propagate electrical signals. In the nervous system these signals transmit information, in muscle they trigger contraction, and in heart they regulate spontaneous beating. A central question in excitability theory concerns the relationship between the aggregate properties of membranes (marcoscopic) and the properties of channels in the membranes (mircoscopic). Hodgkin and Huxley (1952) laid the foundations of membrane excitability, and Neher and Sakmann (1976) developed techniques to study individual channels. This article focuses on the relationship between the macroscopic domain, in which non-linear differential equations determine the electrical properties of cells, and the microscopic domain, in which the probabilistic nature of channels establishes the pattern of activity. Using nerve cell membranes as an example, we examine how information in one domain predicts behavior in the other. We conclude that the probabilistic nature of channels generates virtually all macroscopic electrical properties, including resting potentials, action potentials, spontaneous firing, and chaos.     

Manganese-enhanced auditory tract-tracing MRI with cochlear injection

Recent studies have demonstrated the use of manganese ion (Mn2+)) as an in vivo neuronal tract tracer. In contrast to histological approaches, manganese tracing can be performed repeatedly on the same living animal. In this study, we describe the neuroaxonal tracing of the auditory pathway in the living guinea pig, relying on the fact that Mn2+ ion enters excitable cells through voltage-gated calcium channels and is an excellent MRI paramagnetic tract-tracing agent. Small focal injections of Mn2+ ion into the cochlea produced significant contrast enhancement along the known neuronal circuitry. This in vivo approach, allowing repeated measures, is expected to open new vistas to study auditory physiology and to provide new insights on in vivo axonal transport and neuronal activity in the central auditory system.     

Spontaneous dynamics and response properties of a Hodgkin-Huxley-type neuron model driven by harmonic synaptic noise

We study statistical properties, response dynamics, and information transmission in a Hodgkin-Huxley–type neuron system, modeling peripheral electroreceptors in paddlefish. In addition to sodium and potassium currents, the neuron model includes fast calcium and slow afterhyperpolarization (AHP) potassium currents. The synaptic transmission from sensory epithelium is modeled by a Poission process with a rate modulated by narrow-band noise, mimicking stochastic epithelial oscillations observed experimentally. We study how the interplay of parameters of AHP current and synaptic noise affects the statistics of spontaneous dynamics and response properties of the system. In particular, we confirm predictions made earlier with perfect integrate and fire and phase neuron models that epithelial oscillations enhance stimulus–response coherence and thus information transmission in electroreceptor system. In addition, we consider a strong stimulus regime and show that coherent epithelial oscillations may reduce variability of electroreceptor responses to time-varying stimuli.