Parametric spectral analysis of nonstationary fluctuations of excitatory synaptic currents

We assessed on Monte-Carlo simulated excitatory post-synaptic currents the ability of autoregressive (AR)-model fitting to evaluate their fluctuations. AR-model fitting consists of a linear filter describing the process that generates the fluctuations when driven with a white noise. Its fluctuations provide a filtered version of the signal and have a spectral density depending on the properties of the linear filter. When the spectra of the non-stationary fluctuations of excitatory post-synaptic currents were estimated by fitting AR-models to the segments of current fluctuations, assumed to be stationary and independent, the parameter and spectral estimates were scattered. The scatter was much reduced if the time-variant AR-models were fitted using stochastic adaptive estimators (Kalman, recursive least squares and least mean squares). The ability of time-variant AR-models to accurately fit the current fluctuations was monitored by comparing the fluctuations with predicted fluctuations, and by evaluating the model-learning rate. The median frequency of current fluctuations, which could be rapidly tracked and estimated from the individual quantal events (either Monte-Carlo simulated or recorded from pyramidal neurons of rat hippocampus), rose during the rise phase, before declining to a lower steady-state level during the decay phase of quantal event, whereas the variance showed a broad peak. The closing rate of AMPA channels directly affects the steady-state median frequency, whereas the transient peak can be modulated by a variety of factors—number of molecules released, ability of glutamate molecules to re-enter the synaptic cleft, diffusion constant of glutamate in the cleft and opening rate of AMPA channels. In each case, the effect on the amplitude and decay time of mEPSCs and on the current fluctuations differs. Each factor thus leaves its own kinetic fingerprint arguing that the contribution of such factors can be inferred from the combined kinetic properties of individual mEPSCs.     

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.     

Analysis of calcium activated chloride current fluctuations in Xenopus laevis oocytes.

Fluctuations of calcium activated chloride currents were investigated in oocytes of Xenopus laevis. The method of noise analysis and the model of chloride channels activation by calcium ions were used to estimate the chloride channels lifetime and the average frequency of current fluctuations, which depends on changes of cytoplasmic calcium concentration. This current fluctuations can be evoked by activation of cholinergic receptors or inhibition by Na3VO4 of plasma membrane Ca(2+)-ATPase. The average opening lifetime of chloride channels was approximately 100 ms. The frequency of fluctuations increased with the increasing extracellular calcium concentrations and external ACh concentrations. Caffeine in 2 mmol/l concentration changed the current fluctuations into oscillations with a period of about 18-20s. Ten mmol/l caffeine fully inhibited the oscillation activity.     

Open channel noise. II. A test for coupling between current fluctuations and conformational transitions in the acetylcholine receptor.

The first paper of this series demonstrated that the open-channel currents in the acetylcholine receptors in cultured rat muscle show fluctuations on a time scale of approximately 1 ms. In this paper the hypothesis is tested that these fluctuations are coupled to the gating mechanism that opens and closes the channel. Such a coupling could arise if the channel current and the energy barrier for gating transitions both showed fluctuations having a common origin such as a motion of part of the receptor molecule. A test for coupled fluctuations is made by averaging approximately 1,000 channel opening or closing transitions to search for the small relaxation in the current that is predicted. At a resolution of approximately 1% of the single-channel current amplitude, no such relaxation is observed. It is concluded that any coupled fluctuations are small; fluctuations in the energy barrier for the open-closed conformational transition must be smaller than about 0.3 kT.     

Interpreting power spectra from nonstationary membrane current fluctuations

It is often desirable to characterize membrane current fluctuations from ionic channels under conditions in which the mean current and the variance of the fluctuations change with time. A simple theory is developed that relates the power spectrum to the channel characteristics under such nonstationary conditions, assuming that the mean current time-course has been removed from the fluctuation records. Strategies for removing the mean time-course are discussed, the spectra are calculated from simulated channel fluctuations for comparison with the theory.     

Modification of sodium inactivation in myelinated nerve by Anemonia toxin II and iodate. Analysis of current fluctuations and current relaxations

(1) Na+ currents and Na+ current fluctuations were measured in single myelinated nerve fibres of Rana esculenta under voltage-clamp conditions. The process of Na+ inactivation was modified by external treatment with 7 microM Anemonia Toxin II or by internal application of 20 or 40 mM IO3(-). (2) At depolarization of 24 and 32 mV the spectral density of Na+ current fluctuations could be described as the sum of two contributions, Sh(f) and Sm(f), representing the spectrum from fluctuations of the inactivation (h) and activation (m) gates, respectively. At higher depolarizations of 40 and 48 mV the low frequency (h) fluctuations could be better fitted by the sum, Sh1(f)+Sh2(f), of two separate Lorentzian functions. (3) The Na+ current and the variance of Na+ current fluctuations between 150 and 450 ms after depolarization are increased by one order of magnitude after application of Anemonia Toxin II or IO3(-). (4) The kinetics of Na+ current inactivation were described as A1 x exp(-t/tau h1) + A2 x exp(-t/tau h2) + B. The constant, tau h1, of fast Na+ inactivation was the same in normal and modified nerve fibres. The slow inactivation time constant, tau h2, increased with increasing depolarizations in modified fibres but decreased under control conditions. In all cases tau h2 showed a similar voltage dependence as the time constant found by fitting the low frequency fluctuations of Na+ current with one Lorentzian function, Sh(f). (5) It is concluded that Anemonia Toxin II and IO3(-) modify a fraction of Na+ channels in an all-or-none manner. A lower limit of the number of modified Na+ channels is estimated from the Na+ current and the variance Na+ current fluctuations. 7 microM external Anemonia Toxin II modifies more than 17% and 20 or 40 mM internal IO3(-) more than 8% of all Na+ channels. The inactivation gates in modified channels experience an electric field different from that in normal fibres.     

Open channel noise. I. Noise in acetylcholine receptor currents suggests conformational fluctuations.

The random passage of ions through an open channel is expected to result in shot noise fluctuations in the channel current. The patch-clamp technique now allows fluctuations of this size to be observed in single-channel currents. In the experiments reported here the acetylcholine-induced currents in cultured rat muscle cells were analyzed; fluctuations were found that were considerably larger than expected for shot noise. A low-frequency component, which was fitted with a Lorentzian, was examined in detail; it appears to arise from fluctuations in channel conductance of approximately 3% on a time scale of 1 ms. The characteristic relaxation time is voltage dependent and temperature dependent (Q10 approximately equal to 3) suggesting that the fluctuations arise from conformational fluctuations in the channel protein.     

A model for characterizing residential ground current and magnetic field fluctuations

The current through the residential grounding circuit is an important source for magnetic fields; field variations near the grounding circuit accurately track fluctuations in this ground current. In this paper, a model is presented which permits calculation of the range of these fluctuations. A discrete network model is used to simulate a local distribution system for a single street, and a statistical model to simulate unbalanced currents in the system. Simulations of three-house and ten-house networks show that random appliance operation leads to ground current fluctuations which can be quite large, on the order of 600%. This is consistent with measured fluctuations in an actual house. © 1994 Wiley-Liss, Inc.     

Fluctuations of the Ca2+-activated K+ current in Aplysia neurones

Fluctuations of the Ca2+-activated K+ current were measured in identified Aplysia neurones under voltage clamp conditions. The amplitude of IK,Ca was manipulated by ionophoretic injections of Ca2+. At small amplitudes of Ca2+-activated outward currents the variance of the Ca2+-activated current fluctuations increases linearly with the mean outward current. The single-channel conductance estimated from the variance of the fluctuations and the mean outward current is 11 +/- 3 pS at -30 mV. Power spectra of the Ca2+-activated K+ current can be fitted by the sum of two Lorentzian components with corner frequencies of about 10 Hz and 120 Hz.     

Electrical Fluctuations Associated with Active Transport

Measurements were made of the spectrum of the voltage fluctuations developed in the 0.025-10 Hz band during active transport by frog abdominal skin with Ringer's solution on both sides. Decreasing the potential across the skin by an external supply of current diminishes the voltage fluctuations, but they do not disappear, reaching a minimum finite value. Thus, fluctuations in both the resistance of the skin and the electric current attendant to the active transport of sodium contribute to the voltage fluctuations. Ouabain eliminates the current fluctuations but not those of the resistance. At 20°C, the spectral intensities of the resistance and current fluctuations are nearly identical, varying as 1/f^a, where f is frequency and a = 1.6-2.0. At 32°C, the spectrum of the voltage fluctuations is sigmoid shaped, evidencing a relaxation process with a time constant of 0.6 sec. The fluctuations can be accounted for by stochastic variations in the concentration of a complex formed between a carrier molecule, fixed or mobile, and the actively transported species, sodium.     

Conductivity noise in transmembrane ion channels due to ion concentration fluctuations via diffusion.

A Green's function approach is developed from first principles to evaluate the power spectral density of conductance fluctuations caused by ion concentration fluctuations via diffusion in an electrolyte system. This is applied to simple geometric models of transmembrane ion channels to obtain an estimate of the magnitude of ion concentration fluctuation noise in the channel current. Pure polypeptide alamethicin forms stable ion channels with multiple conductance states in artificial phospholipid bilayers isolated onto tips of micropipettes with gigaohm seals. In the single-channel current recorded by voltage-clamp techniques, excess noise was found after the background instrumental noise and the intrinsic Johnson and shot noises were removed. The noise que to ion concentration fluctuations via diffusion was isolated by the dependence of the excess current noise on buffer ion concentration. The magnitude of the concentration fluctuation noise derived from experimental data lies within limits estimated using our simple geometric channel models. Variation of the noise magnitude for alamethicin channels in various conductance states agrees with theoretical prediction.     

Structure of fluctuations in the floating potential and ion saturation current in the edge plasma of the L-2M stellarator

Results are presented from the measurements of the ion saturation current, the floating potential, and their fluctuations in the edge plasma of the L-2M stellarator. Distinguishing features in the distribution of the ion saturation current and the floating potential near the separatrix are revealed and examined. Based on the cross correlation measurements with probes positioned at different toroidal angles, it is concluded that fluctuations in the ion saturation current are related to fast vertical displacements of the plasma column, whereas fluctuations in the floating potential have the form of waves propagating in the radial direction.     

Dynamical behavior of lipid bilayer membranes for taste substances under random membrane-potential fluctuations

The dynamical behavior of the lipid bilayer membranes was experimentally studied under superposition of random or periodic membrane-potential fluctuations. The analysis of the mutual information has revealed that, in less than 10 Hz of random fluctuations, each of the time series of the mutual information of the transmembrane current for the five chemical substances (taste substances) has its inherent pattern, but not in a periodic fluctuation. On the other hand, the analysis of the power spectrum of the frequency could not distinguish those five basic taste substances in both random and periodic fluctuations. We provide the new detection idea of chemical substances by random fluctuations.     

Phase-State Dependent Current Fluctuations in Pure Lipid Membranes

Current fluctuations in pure lipid membranes have been shown to occur under the influence of transmembrane electric fields (electroporation) as well as a result from structural rearrangements of the lipid bilayer during phase transition (soft perforation). We demonstrate that the ion permeability during lipid phase transition exhibits the same qualitative temperature dependence as the macroscopic heat capacity of a D15PC/DOPC vesicle suspension. Microscopic current fluctuations show distinct characteristics for each individual phase state. Although current fluctuations in the fluid phase show spikelike behavior of short timescales (∼2 ms) with a narrow amplitude distribution, the current fluctuations during lipid phase transition appear in distinct steps with timescales of ∼20 ms. We propose a theoretical explanation for the origin of timescales and permeability based on a linear relationship between lipid membrane susceptibilities and relaxation times near the phase transition.     

Nonstationary fluctuation analysis of the delayed rectifier K channel in cardiac Purkinje fibers. Actions of norepinephrine on single-channel current.

We have studied the large increase in macroscopic potassium channel current caused by catecholamines in mammalian cardiac cells. An increase in macroscopic K current could result from either an increase in the single-channel current or by an increase in the number of channels that are open. Therefore, we have measured nonstationary potassium current fluctuations under voltage clamp conditions to determine whether norepinephrine increases the current through this channel. The single-channel current (at a potential of -30 mV in 4 mM external [K]) was estimated to be 3.7 pA and was not altered by concentrations of norepinephrine up to 2 microM. The spectral density of the current fluctuations were fitted well by a sum of 2 Lorentzians with corner frequencies that correspond with the measured time constants for deactivation of the macroscopic K current tails. We conclude that the increase in macroscopic K current caused by norepinephrine in these cells is not the result of an increase in single-channel conductance and therefore must involve an increase in the number of open K channels.     

Current fluctuations across the bilayer membrane in the presence of prostaglandin F2 alpha

The prostaglandin F2 alpha (in concentration 1,4 or 14 microM) has been shown to induce the current fluctuations across the bilayers under the action on the planar bilayer membranes from the soya total phospholipids. The current fluctuations depend on the potential, their number expresses indistinctly and corresponds to the conductivity jumps across the bilayer about 5 pSm.     

Fluctuations in membrane current driven by intracellular calcium in cardiac Purkinje fibers

Spontaneous oscillatory fluctuations in membrane potential are often observed in heart cells, but their basis remains controversial. Such activity is enhanced in cardiac Purkinje fibers by exposure to digitalis or K-free solutions. Under these conditions, we find that voltage noise is generated by current fluctuations that persist when membrane potential is voltage clamped. Power spectra of current signals are not made up of single time-constant components, as expected from gating of independent channels, but are dominated by resonant characteristics between 0.5 and 2 HZ. Our evidence suggests that the periodicity arises from oscillatory variations in intracellular free Ca that control ion movements across the surface membrane. The current fluctuations are strongly cross-correlated with oscillatory fluctuations in contractile force, and are inhibited by removing extracellular Ca or exposure to D600. Chelating intracellular Ca with injected EGTA also abolishes the current fluctuations. The oscillatory mechanism may involve cycles of Ca (or Sr) movement between sarcoplasmic reticulum and myoplasm, as previously suggested for skinned cardiac preparations. Our experiments in intact cells indicate that changes in surface membrane potential can modulate cytoplasmic Ca oscillations in frequency and perhaps amplitude as well. A two-way interaction between surface membrane potential and intracellular Ca stores may be a common feature of heart, neuron, and other cell types.     

Transduction noise induced by 4-hydroxy retinals in rod photoreceptors.

New visual pigments were formed with 4-hydroxy retinals in isolated vertebrate rod photoreceptors by exposing bleached rods from the tiger salamander, Ambystoma tigrinum, to lipid vesicles containing the analogues. Formation of physiologically active pigment was demonstrated by the restoration of sensitivity and by a shift of approximately 50 nm in the peak of both the visual pigment absorptance spectrum and rod spectral sensitivity spectrum from approximately 520 to approximately 470 nm for 11-cis 4-hydroxy retinal. Membrane current recordings from the inner segments of isolated rods revealed excess fluctuations in membrane current after formation of the new pigment in bleached cells or after exposure of unbleached cells to flashes in the presence of the analogue. The excess current fluctuations are similar to the fluctuations elicited by steady light producing a few discrete responses per second, a rate approximately 100 times greater than the normal rate of spontaneous events in darkness. These results suggest that analogues of retinal can produce alterations in the frequency of production of discrete responses in darkness in rod photoreceptors.     

Fluctuations of the electrical characteristics of a membrane in stress states

The general scheme of calculation of current and voltage fluctuations obtained in [4] was applied to the definite theoretical membrane model based on the experimental data. Spectra for the extreme conditions of current and voltage fixation were obtained. The estimation of some parameters of the theory was carried out.     

Theory of single-file noise.

A general theoretical approach to the analysis of electric fluctuations generated by the so-called single-file diffusion through narrow channels is presented. The formalism is a slight extension of an approach to electric fluctuations in discrete transport systems with negligible interactions between the particles recently developed by one of the authors. In the single-file transport mechanism interactions between the particles must be taken into account. Three main results of principal interest are: (a) the electric fluctuations around stationary states (at equilibrium and non-equilibrium) are determined by the time-dependent solutions of the macroscopic single-file transport equations, (b) as a direct consquence of the interactions between the ions in the single-file transport the macroscopic time-dependent current and the autocorrelation function of the microscopic current fluctuations can exhibit damped oscillatory behavior, and the current noise spectrum can show peaking, (c) the number of binding sites for the ions within the pores seems to have a strong influence on the oscillatory behavior: with increasing number of binding sites the damping of the oscillations decreases and the peaking of the spectrum becomes stronger.