Attenuation of current and voltage noise signals recorded from epithelia

Transepithelially recorded current and voltage fluctuations are filtered by the impedance of the electrical equivalent parameters of the preparation, in series or in parallel, with the noise source. Fluctuations in voltage and current are assumed to be caused by fluctuations in conductance of the apical membrane. In order to obtain an estimation of the intrinsic noise amplitudes, calculations are presented to correct the transepithelial fluctuations. The influence of different model parameters on the recorded noise spectra is investigated. It is shown that the shape of the transepithelially recorded noise spectra may differ from the intrinsic ones, e.g. “peaking” in the power spectra may be explained by the assumption of a positive (referred to cell inside) e.m.f. at the basolateral membrane or a polarization impedance in series with the epithelium. Furthermore it is demonstrated that the ratio of voltage to current noise power may differ from the squared magnitude of the impedance.     

Noise analysis of ion current through the open and the sugar-induced closed state of the LamB channel of Escherichia coli outer membrane: evaluation of the sugar binding kinetics to the channel interior.

LamB, a sugar-specific channel of Escherichia coli outer membrane was reconstituted into lipid bilayer membranes and the current noise was investigated using fast Fourier transformation. The current noise through the open channels had a rather small spectral density, which was a function of the inverse frequency up to about 100 Hz. The spectral density of the noise of the open LamB channels was a quadratic function of the applied voltage. Its magnitude was not correlated to the number of channels in the lipid bilayer membrane. Upon addition of sugars to the aqueous phase the current decreased in a dose-dependent manner. Simultaneously, the spectral density of the current noise increased drastically, which indicated interaction of the sugars with the binding site inside the channel. The frequency dependence of the spectral density was of Lorentzian type, although the power of its frequency dependence was not identical to -2. Analysis of the power density spectra using a previously proposed simple model (Benz, R., A. Schmid, and G. H. Vos-Scheperkeuter. 1987. J. Membr. Biol. 100: 12-29), allowed the evaluation of the on- and the off-rate constants for the maltopentaose binding to the binding site inside the LamB channels. This means also that the maltopentaose flux through the LamB channel could be estimated by assuming a simple one-site, two-barrier model for the sugar transport from the results of the noise analysis.     

Basolateral K channels in an insect epithelium. Channel density, conductance, and block by barium

K channels in the basolateral membrane of insect hindgut were studied using current fluctuation analysis and microelectrodes. Locust recta were mounted in Ussing-type chambers containing Cl-free saline and cyclic AMP (cAMP). A transepithelial K current was induced by raising serosal [K] under short-circuit conditions. Adding Ba to the mucosal (luminal) side under these conditions had no effect; however, serosal Ba reversibly inhibited the short-circuit current (Isc), increased transepithelial resistance (Rt), and added a Lorentzian component to power density spectra of the Isc. A nonlinear relationship between corner frequency and serosal [Ba] was observed, which suggests that the rate constant for Ba association with basolateral channels increased as [Ba] was elevated. Microelectrode experiments revealed that the basolateral membrane hyperpolarized when Ba was added: this change in membrane potential could explain the nonlinearity of the 2 pi fc vs. [Ba] relationship if external Ba sensed about three-quarters of the basolateral membrane field. Conventional microelectrodes were used to determine the correspondence between transepithelially measured current noise and basolateral membrane conductance fluctuations, and ion-sensitive microelectrodes were used to measure intracellular K activity (acK). From the relationship between the net electrochemical potential for K across the basolateral membrane and the single channel current calculated from noise analysis, we estimate that the conductance of basolateral K channels is approximately 60 pS, and that there are approximately 180 million channels per square centimeter of tissue area.     

Calcium-activated potassium conductance noise in snail neurons

Current fluctuations were measured in small, 3-6 micrometers-diameter patches of soma membrane in bursting neurons of the snail, Helix pomatia. The fluctuations dramatically increased in magnitude with depolarization of the membrane potential under voltage clamp conditions. Two components of conductance noise were identified in the power spectra calculated from the membrane currents. One component had a corner frequency which increased with depolarization. This component was blocked by intracellular injection of TEA and was relatively insensitive to extracellular calcium levels (as long as the total number of effective divalent cations remained constant). It was identified as fluctuations of the voltage-dependent component of delayed outward current. The second component of conductance noise had a corner frequency which decreased with depolarization. It was relatively unaffected by TEA injection and was reversibly blocked by substitution of extracellular calcium with magnesium, cobalt, or nickel. This second component of noise was identified as fluctuations of the calcium-dependent potassium current. The results suggest that the two components of delayed outward current are conducted through physically distinct channels.     

Excess electrical noise during current flow through porous membranes separating ionic solutions.

Spectral analysis of electrical noise from various artificial membrane systems suggests that excess noise of an f-n spectral form, where n is approximately unity, is not primarily a bulk phenomenon simply dependent on the number of charge carriers. Measurements from aqueous and nonaqueous electrolytic resistors, comprised of several different ionic species, show only flat power density spectra under applied currents, even at extreme dilutions. Excess noise of f-n form is observed under applied d-c current in single pore membranes, as previously reported, but is also seen in multipore and polymer mesh membranes. Calculations based on single pore membrane noise data are in significant variance with the bulk charge carrier model proposed by Hooge. These observations suggest that such excess noise occurs in conjunction with anisotropic constraints to ion flow.     

Conductance versus current noise in a neuronal model for noisy subthreshold oscillations and related spike generation

Biological systems are notoriously noisy. Noise, therefore, also plays an important role in many models of neural impulse generation. Noise is not only introduced for more realistic simulations but also to account for cooperative effects between noisy and nonlinear dynamics. Often, this is achieved by a simple noise term in the membrane equation (current noise). However, there are ongoing discussions whether such current noise is justified or whether rather conductance noise should be introduced because it is closer to the natural origin of noise. Therefore, we have compared the effects of current and conductance noise in a neuronal model for subthreshold oscillations and action potential generation. We did not see any significant differences in the model behavior with respect to voltage traces, tuning curves of interspike intervals, interval distributions or frequency responses when the noise strength is adjusted. These findings indicate that simple current noise can give reasonable results in neuronal simulations with regard to physiological relevant noise effects.     

Propagation effects of current and conductance noise in a model neuron with subthreshold oscillations

We have examined the effects of current and conductance noise in a single-neuron model which can generate a variety of physiologically important impulse patterns. Current noise enters the membrane equation directly while conductance noise is propagated through the activation variables. Additive Gaussian white noise which is implemented as conductance noise appears in the voltage equations as an additive and a multiplicative term. Moreover, the originally white noise is turned into colored noise. The noise correlation time is a function of the system's control parameters which may explain the different effects of current and conductance noise in different dynamic states. We have found the most significant, qualitative differences between different noise implementations in a pacemaker-like, tonic firing regime at the transition to chaotic burst discharges. This reflects a dynamic state of high physiological relevance.     

Power Laws from Linear Neuronal Cable Theory: Power Spectral Densities of the Soma Potential,Soma Membrane Current and Single-Neuron Contribution to the EEG

Power laws, that is, power spectral densities (PSDs) exhibiting behavior for large frequencies f, have been observed both in microscopic (neural membrane potentials and currents) and macroscopic (electroencephalography; EEG) recordings. While complex network behavior has been suggested to be at the root of this phenomenon, we here demonstrate a possible origin of such power laws in the biophysical properties of single neurons described by the standard cable equation. Taking advantage of the analytical tractability of the so called ball and stick neuron model, we derive general expressions for the PSD transfer functions for a set of measures of neuronal activity: the soma membrane current, the current-dipole moment (corresponding to the single-neuron EEG contribution), and the soma membrane potential. These PSD transfer functions relate the PSDs of the respective measurements to the PSDs of the noisy input currents. With homogeneously distributed input currents across the neuronal membrane we find that all PSD transfer functions express asymptotic high-frequency power laws with power-law exponents analytically identified as for the soma membrane current, for the current-dipole moment, and for the soma membrane potential. Comparison with available data suggests that the apparent power laws observed in the high-frequency end of the PSD spectra may stem from uncorrelated current sources which are homogeneously distributed across the neural membranes and themselves exhibit pink () noise distributions. While the PSD noise spectra at low frequencies may be dominated by synaptic noise, our findings suggest that the high-frequency power laws may originate in noise from intrinsic ion channels. The significance of this finding goes beyond neuroscience as it demonstrates how power laws with a wide range of values for the power-law exponent α may arise from a simple, linear partial differential equation.     

White-noise stimulation of the Hodgkin–Huxley model

 We studied the combined influence of noise and constant current stimulations on the Hodgkin–Huxley neuron model through time and frequency analysis of the membrane-potential dynamics. We observed that, in agreement with experimental data (Guttman et al. 1974), at low noise and low constant current stimulation the behavior of the model is well approximated by that of the linearized Hodgkin–Huxley system. Conversely, nonlinearities due to firing dominate at large noise or current stimulations. The transition between the two regimes is abrupt, and takes place in the same range of noise and current intensities as the noise-induced transition characterized by the qualitative change in the stationary distribution of the membrane potential (Tanabe and Pakdaman 2001a). The implications of these results are discussed. Received: 27 July 2001 / Accepted in revised form: 18 December 2001     

Noise effects on spike propagation in the stochastic Hodgkin-Huxley models

Effects of membrane current noise on spike propagation along a nerve fiber are studied. Additive current noise and channel noise are considered by using stochastic versions of the Hodgkin-Huxley model. The results of computer simulation show that the membrane noise causes considerable variation of the propagation time of a spike (thus changes in interspike intervals) for a small unmyelinated fiber of radius 0.1 approximately 1 micron.     

Potassium-ion conduction noise in squid axon membrane.

Spectral analysis (1-1000 Hz) of spontaneous fluctuations of potential and current in small areas of squid (Loligo pealei) axon shows two forms of noise: f-1 noise occurs in both excitable and inexcitable axons with an intensity which depends upon the driving force for potassium ions. The other noise has a spectral form corresponding to a relaxation process, i.e. its asymptotic behavior at low frequencies is constant, and at high frequencies it declines with a slope of -2. This latter noise occurs only in excitable axons and was identified in spectra by (1) its disappearance after reduction of K+ current by internal perfusion with solutions containing tetraethylammonium (TEA+), Cs+ or reduced [Ki+] and (2) its insensitivity to block of Na+ conduction and active transport. The transition frequency of relaxation spectra are also voltage and temperature dependent and relate to the kinetics of K+-conduction in the Hodgkin-Huxley formulation. These data strongly suggest that the relaxation noise component arises from the kinetic properties of K+ channels. The f-1 noise is attributed to restricted diffusion in conducting K+ channels and/or leakage pathways. In addition, an induced K+ conduction noise associated with the binding of TEA+ and triethyldecylammonium ion to membrane sites is described. Measurement of the induced noise may provide an alternative means of characterizing the kinetics of interaction of these molecules with the membrane and also suggests that these and other pharmacological agents may not be useful in identifying noise components related to the sodium conduction mechanism which, in these experiments, appears to be much lower in intensity than either the normal K conduction or induced noise components.     

Voltage Noise in Acer pseudoplatanus Cells : Basic Cellular Noise and Gramicidin a Induced Noise

The present contribution is devoted to studying the electrical noise of Acer pseudoplatanus cells in culture suspensions. Spontaneous voltage noise of the cells was recorded by means of a microelectrode inserted in the vacuole. The small signal impedance of the cell was measured so that it was possible to study the intensity spectra of the noise. We recorded intensity spectra with cells incubated in 10⁻³ molar gramicidin A. Difference spectra showed characteristics of a channel noise. By using the calculated conductance of gramicidin A in an artificial membrane, and by simplifying assumptions for the ionic transports through plasmalemma and tonoplast, we were able to estimate the electrochemical potential difference for K⁺ ions across the plasmalemma (3.2 ± 1 millivolt).     

Correlation analysis of electrical noise in lipid bilayer membranes: kinetics of gramicidin A channels.

If a membrane contains ion-conducting channels which form and disappear in a random fashion, an electric current which is passed through the membrane under constant voltage shows statistical fluctuations. Information on the kinetics of channel formation and on the conductance of the single channel may be obtained by analyzing the electrical noise generated in a membrane containing a great number of channels. For this purpose the autocorrelation function of the current noise is measured at different concentrations of the channel-forming substance. As a test system for the application of this technique we have used lipid bilayer membranes doped with gramicidin A. From the correlation time of the current noise generated by the membrane, the rate constants of formation (k-R) and dissociation (k-D) of the channels could be determined. In addition, the mean square of the current fluctuations yielded the single-channel conductance lambda. The values of k-R, k-D, and lambda obtained from the noise analysis agreed closely with the values determined by relaxation measurments and single-channel experiments.     

Excess electrical noise during current flow through porous membranes separating ionic solutions

Summary Spectral analysis of electrical noise from various artificial membrane systems suggests that excess noise of anf ^–n spectral form, wheren is approximately unity, is not primarily a bulk phenomenon simply dependent on the number of charge carriers. Measurements from aqueous and nonaqueous electrolytic resistors, comprised of several different ionic species, show only flat power density spectra under applied currents, even at extreme dilutions. Excess noise off ^–n form is observed under applied d-c current in single pore membranes, as previously reported, but is also seen in multipore and polymer mesh membranes. Calculations based on single pore membrane noise data are in significant variance with the bulk charge carrier model proposed by Hooge. These observations suggest that such excess noise occurs in conjunction with anisotropic constraints to ion flow.1 Fishman, H. M., Moore, L. E., Poussart, D. J. M. 1975. Potassium ion conduction noise in squid axon membrane.J. Membrane Biol. (Submitted for publication).     

Non-equilibrium voltage noise generated by ion transport through pores

In this paper, we describe a systematic approach to the theoretical analysis of non-equilibrium voltage noise that arises from ions moving through pores in membranes. We assume that an ion must cross one or two barriers in the pore in order to move from one side of the membrane to the other. In our analysis, we consider the following factors: a) surface charge as a variable in the kinetic equations, b) linearization of the kinetic equations, c) master equation approach to fluctuations. To analyze the voltage noise arising from ion movement through a two barrier (i.e., one binding site) pore, we included the effects of ions in the channel's interior on the voltage noise. The current clamp is considered as a white noise generating additional noise in the system. In contrast to what is found for current noise, at low frequencies the voltage noise intensity is reduced by increasing voltage across the membrane. With this approach, we demonstrate explicity for the examples treated that, apart from additional noise generated by the current clamp, the non-equilibrium voltage fluctuations can be related to the current fluctuations by the complex admittance.     

Evidence for interactions between batrachotoxin-modified channels in hybrid neuroblastoma cells.

Current records from voltage-clamped membrane patches containing two batrachotoxin-modified sodium channels were analyzed to determine whether these channels are identical and independent. In most two-channel patches, the experimentally observed probabilities that zero, one, or two channels are open differ from the binomial distribution, demonstrating that the two channels are nonidentical or nonindependent or both. From the same current records, we also determined the rate for the transition from two open channels to one open channel and for the transition from one open channel to zero open channels. These data are consistent with closing rates for the two channels that are equal and independent. Both probability and closing rate data can be fit by a model wherein the channels are identical, the closing rates are independent, and the opening rate is greater when the other channel is closed than when it is open. The implications of this model for analyzing noise spectra and current variance are examined.     

Kinetics of light-sensitive channels in vertebrate photoreceptors

We have studied the ion channels mediating the light response of vertebrate rod photoreceptors by analysing fluctuations in the current across the rod membrane, using the whole cell patch-clamp technique on rods isolated from the axolotl retina. Light decreases the membrane current fluctuations. Noise analysis reveals two components to this decrease: a low frequency component due to biochemical noise in the transduction mechanism, and a high frequency component we attribute to the random opening and closing of the ion channels in the dark. The probability of any one channel being open in the dark is low. The spectrum of the high frequency component of the current fluctuations indicates that the current through an open channel is 4 X 10(-15)A, that the mean channel open time is 2 ms, and that about 10000 channels are open in each rod in the dark. The effect of light is to reduce the opening rate constant of these channels, with no effect on the closing rate constant.     

1/f Membrane noise generated by diffusion processes in unstirred solution layers.

A mathematical treatment is given for 1/f noise observed in the ion transport through membranes. It is shown that this noise can be generated by current or voltage fluctuations which occur after step changes of the membrane permeability. Due to diffusion polarization in the unstirred solution layers near the membrane these fluctuations exhibit a 1 square root of t time course which produces noise with a 1/f frequency dependence. The spectral density of 1/f noise is calculated for porous membranes with random switches between a finite and zero pore permeability. A wide frequency range and a magnitude of 1/f noise are obtained which are compatible with experimental data of 1/f noise reported for nerve membranes.     

Ion channels activated by L-glutamate and GABA in cultured cerebellar neurons of the rat

Glutamate and GABA-receptor channels were investigated in explants of rat cerebellum grown in cell culture. The patch-clamp technique was used to examine neurons under whole cell clamp and the properties of channels were derived by analysis of glutamate and GABA-evoked current noise. In addition, single channel currents activated by glutamate were recorded from isolated outside-out patches of membrane. We found evidence for at least two types of glutamate receptor-channels in cerebellar cells. Some neurons exhibited a channel of 50 pS conductance with a Lorentzian noise spectrum of 5.9 ms time constant. Single channels were readily resolved both in whole cell clamp and excised patches. Other neurons possessed low conductance channels which produced two component spectra. Estimates of the single channel conductance gave a value of about 140 fS. GABA channel noise obtained from these cells was also fitted by two component spectra which gave single channel conductance of 16 pS.