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.     

Frequency-dependent membrane impedance inChara corallina estimated by Fourier analysis

Summary The white noise method of measuring membrane impedance has been applied to internodal cells ofChara corallina. Fourier analysis of a white noise transmembrane current signal and the voltage response has been used to obtain the frequency-dependent impedance of the in-series combination of the plasmalemma and tonoplast membranes. The results are similar to those of other workers who have measured membrane impedances by different techniques. At very low frequencies the equivalent capacitance of the membrane treated as an RC-circuit becomes negative, indicating a pseudoinductive effect.Membrane impedance has been measured over a range of pH values from pH 5.2 to pH 11; impedance magnitude reaches a maximum at pH 7. At interesting effect of fusicoccin at pH 11 has been observed, in which a decrease in membrane conductance occurs simultaneously with a small hyperpolarization of membrane PD.     

Effects of Music on the Recovery of Autonomic and Electrocortical Activity After Stress Induced by Aversive Visual Stimuli

The purpose of this study was to compare the effects of music and white noise on the recovery of physiological measures after stressful visual stimulation. Twenty-nine participants took part in the experiment. Visual stimulation with slides eliciting disgust was followed by subjectively pleasant music, sad music, and white noise in three consecutive sessions. The spectral power of the frontal and temporal EEG, skin conductance, heart rate, heart period variability, facial capillary blood flow, and respiration rate were recorded and analyzed. Aversive visual stimulation evoked heart rate deceleration, increased high frequency component of heart period variability, increased skin conductance level and skin conductance response frequency, decreased facial blood flow and velocity, decreased temporal slow alpha and increased frontal fast beta power in all three sessions. Both subjectively pleasant and sad music led to the restoration of baseline levels on most parameters; while white noise did not enhance the recovery process. The effects of pleasant music on post-stress recovery, when compared to white noise, were significantly different on heart rate, respiration rate, and peripheral blood flow. Both positive and negative music exerted positive modulatory effects on cardiovascular and respiratory activity, namely increased heart rate, balanced heart period variability, increased vascular blood flow and respiration rate during the post-stress recovery. Data only partially supported the “undoing” hypothesis, which states that positive emotions may facilitate the process of physiological recovery following negative emotions.     

Noise-induced divisive gain control in neuron models

A recent computational study of gain control via shunting inhibition has shown that the slope of the frequency-versus-input (f-I) characteristic of a neuron can be decreased by increasing the noise associated with the inhibitory input (Neural Comput. 13, 227-248). This novel noise-induced divisive gain control relies on the concommittant increase of the noise variance with the mean of the total inhibitory conductance. Here we investigate this effect using different neuronal models. The effect is shown to occur in the standard leaky integrate-and-fire (LIF) model with additive Gaussian white noise, and in the LIF with multiplicative noise acting on the inhibitory conductance. The noisy scaling of input currents is also shown to occur in the one-dimensional theta-neuron model, which has firing dynamics, as well as a large scale compartmental model of a pyramidal cell in the electrosensory lateral line lobe of a weakly electric fish. In this latter case, both the inhibition and the excitatory input have Poisson statistics; noise-induced divisive inhibition is thus seen in f-I curves for which the noise increases along with the input I. We discuss how the variation of the noise intensity along with inputs is constrained by the physiological context and the class of model used, and further provide a comparison of the divisive effect across models.     

On the thermal noise limit of cellular membranes

Comparison of thermal noise limits and the effects of low frequency electromagnetic fields (LFEMF) on the cellular membrane have important implications for the study of bioelectro-magnetism in this regime. Over a decade ago, Weaver and Astumian developed a model to show that thermal noise can limit the efficacy of LFEMF. A recent report by Kaune [Kaune (2002) Bioelectromagnetics 23:622-628], however, contradicted their findings. Kaune assumes that the conductance noise current of cell membrane can be decomposed into two components, where one of them is identical regarding all segments (coherent), while the other is different (incoherent). Besides, this decomposition is not unequivocal and contradicts to the statistical independence of the segment noise currents, and therefore to the second law of thermodynamics as well. We suggest the procedure based on the method of symmetrical components, by the means of which we can re-interpret the result of Kaune in a correct way.     

High-resolution intracellular recordings using a real-time computational model of the electrode

Intracellular recordings of neuronal membrane potential are a central tool in neurophysiology. In many situations, especially in vivo, the traditional limitation of such recordings is the high electrode resistance and capacitance, which may cause significant measurement errors during current injection. We introduce a computer-aided technique, Active Electrode Compensation (AEC), based on a digital model of the electrode interfaced in real time with the electrophysiological setup. The characteristics of this model are first estimated using white noise current injection. The electrode and membrane contribution are digitally separated, and the recording is then made by online subtraction of the electrode contribution. Tests performed in vitro and in vivo demonstrate that AEC enables high-frequency recordings in demanding conditions, such as injection of conductance noise in dynamic-clamp mode, not feasible with a single high-resistance electrode until now. AEC should be particularly useful to characterize fast neuronal phenomena intracellularly in vivo.     

White-noise analysis of nonlinear behavior in an insect sensory neuron: Kernel and cascade approaches

A functional expansion was used to model the relationship between a Gaussian white noise stimulus current and the resulting action potential output in the single sensory neuron of the cockroach femoral tactile spine. A new precise procedure was used to measure the kernels of the functional expansion. Very similar kernel estimates were obtained from separate sections of the data produced by the same neuron with the same input noise power level, although some small time-varying effects were detectable in moving through the data. Similar kernel estimates were measured using different input noise power levels for a given cell, or when comparing different cells under similar stimulus conditions. The kernels were used to identify a model for sensory encoding in the neuron, comprising a cascade of dynamic linear, static nonlinear, and dynamic linear elements. Only a single slice of the estimated experimental second-order kernel was used in identifying the cascade model. However, the complete second-order kernel of the cascade model closely resembled the estimated experimental kernel. Moreover, the model could closely predict the experimental action potential train obtained with novel white noise inputs.     

Residue ionization and ion transport through OmpF channels

Single trimeric channels of the general bacterial porin, OmpF, were reconstituted into planar lipid membranes and their conductance, selectivity, and open-channel noise were studied over a wide range of proton concentrations. From pH 1 to pH 12, channel transport properties displayed three characteristic regimes. First, in acidic solutions, channel conductance is a strong function of pH; it increases by approximately threefold as the proton concentration decreases from pH 1 to pH 5. This rise in conductance is accompanied by a sharp increase in cation transport number and by pronounced open-channel low-frequency current noise with a peak at ~pH 2.5. Random stepwise transients with amplitudes at ~1/5 of the monomer conductance are major contributors to this noise. Second, over the middle range (pH 5 ÷ pH 9), channel conductance and selectivity stay virtually constant; open channel noise is at its minimum. Third, over the basic range (pH 9 ÷ pH 12), channel conductance and cation selectivity start to grow again with an onset of a higher frequency open-channel noise. We attribute these effects to the reversible protonation of channel residues whose pH-dependent charge influences transport by direct interactions with ions passing through the channel.     

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.     

Interspike interval correlations in neuron models with adaptation and correlated noise

The generation of neural action potentials (spikes) is random but nevertheless may result in a rich statistical structure of the spike sequence. In particular, contrary to the popular renewal assumption of theoreticians, the intervals between adjacent spikes are often correlated. Experimentally, different patterns of interspike-interval correlations have been observed and computational studies have identified spike-frequency adaptation and correlated noise as the two main mechanisms that can lead to such correlations. Analytical studies have focused on the single cases of either correlated (colored) noise or adaptation currents in combination with uncorrelated (white) noise. For low-pass filtered noise or adaptation, the serial correlation coefficient can be approximated as a single geometric sequence of the lag between the intervals, providing an explanation for some of the experimentally observed patterns. Here we address the problem of interval correlations for a widely used class of models, multidimensional integrate-and-fire neurons subject to a combination of colored and white noise sources and a spike-triggered adaptation current. Assuming weak noise, we derive a simple formula for the serial correlation coefficient, a sum of two geometric sequences, which accounts for a large class of correlation patterns. The theory is confirmed by means of numerical simulations in a number of special cases including the leaky, quadratic, and generalized integrate-and-fire models with colored noise and spike-frequency adaptation. Furthermore we study the case in which the adaptation current and the colored noise share the same time scale, corresponding to a slow stochastic population of adaptation channels; we demonstrate that our theory can account for a nonmonotonic dependence of the correlation coefficient on the channel’s time scale. Another application of the theory is a neuron driven by network-noise-like fluctuations (green noise). We also discuss the range of validity of our weak-noise theory and show that by changing the relative strength of white and colored noise sources, we can change the sign of the correlation coefficient. Finally, we apply our theory to a conductance-based model which demonstrates its broad applicability.     

Mechanotransduction by Membrane Proteins: The speed of the hair cell mechanotransducer channel revealed by fluctuation analysis

Although mechanoelectrical transducer (MET) channels have been extensively studied, uncertainty persists about their molecular architecture and single-channel conductance. We made electrical measurements from mouse cochlear outer hair cells (OHCs) to reexamine the MET channel conductance comparing two different methods. Analysis of fluctuations in the macroscopic currents showed that the channel conductance in apical OHCs determined from nonstationary noise analysis was about half that of single-channel events recorded after tip link destruction. We hypothesized that this difference reflects a bandwidth limitation in the noise analysis, which we tested by simulations of stochastic fluctuations in modeled channels. Modeling indicated that the unitary conductance depended on the relative values of the channel activation time constant and the applied low-pass filter frequency. The modeling enabled the activation time constant of the channel to be estimated for the first time, yielding a value of only a few microseconds. We found that the channel conductance, assayed with both noise and recording of single-channel events, was reduced by a third in a new deafness mutant, Tmc1 p.D528N. Our results indicate that noise analysis is likely to underestimate MET channel amplitude, which is better characterized from recordings of single-channel events.     

Single-channel properties of a volume-sensitive anion conductance. Current activation occurs by abrupt switching of closed channels to an open state

Swelling-induced loss of organic osmolytes from cells is mediated by an outwardly rectified, volume-sensitive anion channel termed VSOAC (Volume-Sensitive Organic osmolyte/Anion Channel). Similar swelling- activated anion channels have been described in numerous cell types. The unitary conductance and gating kinetics of VSOAC have been uncertain, however. Stationary noise analysis and single-channel measurements have produced estimates for the unitary conductance of swelling-activated, outwardly rectified anion channels that vary by > 15-fold. We used a combination of stationary and nonstationary noise analyses and single-channel measurements to estimate the unitary properties of VSOAC. Current noise was analyzed initially by assuming that graded changes in macroscopic current were due to graded changes in channel open probability. Stationary noise analysis predicts that the unitary conductance of VSOAC is approximately 1 pS at 0 mV. In sharp contrast, nonstationary noise analysis demonstrates that VSOAC is a 40-50 pS channel at +120 mV (approximately 15 pS at 0 mV). Measurement of single-channel events in whole-cell currents and outside- out membrane patches confirmed the nonstationary noise analysis results. The discrepancy between stationary and nonstationary noise analyses and single-channel measurements indicates that swelling- induced current activation is not mediated by a graded increase in channel open probability as assumed initially. Instead, activation of VSOAC appears to involve an abrupt switching of single channels from an OFF state, where channel open probability is zero, to an ON state, where open probability is near unity.     

Membrane Operational Impedance Spectra in Chara corallina Estimated by Laplace Transforms Analysis

The membrane operational impedance spectrum of Chara corallina Klein ex Willd. (R. Brown) cells is investigated using Laplace transform analysis. The spectrum changes with both amplitude and sign of the electrical stimulation when time- and voltage-dependent K⁺ channels contribute to the membrane conductance. We compare the advantages and disadvantage of this technique for studying membrane impedance with those of the alternating current method and the white noise method.     

A nonlinear cascade model for action potential encoding in an insect sensory neuron.

Action potential encoding in the cockroach tactile spine neuron can be represented as a single-input single-output nonlinear dynamic process. We have used a new functional expansion method to characterize the nonlinear behavior of the neural encoder. This method, which yields similar kernels to the Wiener method, is more accurate than the latter and is efficient enough to obtain reasonable kernels in less than 15 min using a personal computer. The input stimulus was band-limited white Gaussian noise and the output consisted of the resulting train of action potentials, which were unitized to give binary values. The kernels and the system input-output signals were used to identify a model for encoding comprising a cascade of dynamic linear, static nonlinear, and dynamic linear components. The two dynamic linear components had repeatable and distinctive forms with the first being low-pass and the second being high-pass. The static nonlinearity was fitted with a fifth-order polynomial function over several input amplitude ranges and had the form of a half-wave rectifier. The complete model gave a good approximation to the output of the neuron when both were subjected to the same novel white noise input signal.     

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.     

Ozone‐induced stomatal sluggishness changes stomatal parameters of Jarvis‐type model in white birch and deciduous oak

• Stomatal ozone flux is closely related to ozone injury to plants. Jarvis‐type multiplicative model has been recommended for estimating stomatal ozone flux in forest trees. Ozone can change stomatal conductance by both stomatal closure and less efficient stomatal control (stomatal sluggishness). However, current Jarvis‐type models do not account for these ozone effects on stomatal conductance in forest trees.
• We examined seasonal course of stomatal conductance in two common deciduous tree species native to northern Japan (white birch: Betula platyphylla var. japonica ; deciduous oak: Quercus mongolica var. crispula ) grown under free‐air ozone exposure. We innovatively considered stomatal sluggishness in the Jarvis‐type model using a simple parameter, s , relating to cumulative ozone uptake (defined as POD : phytotoxic ozone dose).
• We found that ozone decreased stomatal conductance of white birch leaves after full expansion (?28%). However, such a reduction of stomatal conductance by ozone fell in late summer (?10%). At the same time, ozone reduced stomatal sensitivity of white birch to VPD and increased stomatal conductance under low light conditions. In contrast, in deciduous oak, ozone did not clearly change the model parameters.
• The consideration of both ozone‐induced stomatal closure and stomatal sluggishness improved the model performance to estimate stomatal conductance and to explain the dose–response relationship on ozone‐induced decline of photosynthesis of white birch. Our results indicate that ozone effects on stomatal conductance (i.e . stomatal closure and stomatal sluggishness) are crucial for modelling studies to determine stomatal response in deciduous trees, especially in species sensitive to ozone.

     

Hidden Markov analysis of mechanosensitive ion channel gating

Patch clamp data from the large conductance mechanosensitive channel (MscL) in E. coli was studied with the aim of developing a strategy for statistical analysis based on hidden Markov models (HMMs) and determining the number of conductance levels of the channel, together with mean current, mean dwell time and equilibrium probability of occupancy for each level. The models incorporated state-dependent white noise and moving average adjustment for filtering, with maximum likelihood parameter estimates obtained using an EM (expectation-maximisation) based iteration. Adjustment for filtering was included as it could be expected that the electronic filter used in recording would have a major effect on obviously brief intermediate conductance level sojourns. Preliminary data analysis revealed that the brevity of intermediate level sojourns caused difficulties in assignment of data points to levels as a result of over-estimation of noise variances. When reasonable constraints were placed on these variances using the better determined noise variances for the closed and fully open levels, idealisation anomalies were eliminated. Nevertheless, simulations suggested that mean sojourn times for the intermediate levels were still considerably over-estimated, and that recording bandwidth was a major limitation; improved results were obtained with higher bandwidth data (10 kHz sampled at 25 kHz). The simplest model consistent with these data had four open conductance levels, intermediate levels being approximately 20%, 51% and 74% of fully open. The mean lifetime at the fully open level was about 1 ms; estimates for the three intermediate levels were 54-92 micros, probably still over-estimates.     

Growth environment determines light sensitivity of shoot hydraulic conductance

Acclimation of light sensitivity of hydraulic conductance of shoots of silver birch (Betula pendula) and hybrid aspen (Populus × wettsteinii) to growth environments with three different air humidities was studied. Hydraulic conductance of shoots kept for 1–2 h in darkness (D) or in light (L) was measured by the pressure chamber method, and light sensitivity was defined as a significant difference between D and L shoots. Light sensitivity of shoots grown in three different air humidities was found to vary. Amongst shoots grown in current natural air, only the hydraulic conductance of the whole shoot and that of the leaf blades of birch upper foliage were significantly light sensitive. Amongst shoots grown in decreased air humidity, hydraulic conductance of the whole shoot, the leaf blades, and the stem and petioles of birch upper foliage, the conductance of the whole shoot and the leaf blades of birch lower foliage, and the conductance of the whole shoot of aspen upper foliage were light sensitive. None of the shoots grown in increased air humidity were significantly light sensitive. We predict that light sensitivity will become more widespread among species in regions where air humidity decreases as a result of global climate change, and vice versa. Low white light always caused the same increase in hydraulic conductance as high white light, and blue and white light always caused an increase in conductance about two times greater than red light, indicating that growth environment did not markedly modify the mechanism of light sensitivity.     

Noise analysis of the glutamate-activated current in photoreceptors.

The glutamate-activated current in photoreceptors has been attributed both to a sodium/glutamate transporter and to a glutamate-activated chloride channel. We have further studied the glutamate-activated current in single, isolated photoreceptors from the tiger salamander using noise analysis on whole-cell patch-clamp recordings. In cones, the current is generated by chloride channels with a single-channel conductance of 0.7 pS and an open lifetime of 2.4 ms. The number of channels per cell is in the range of 10,000-20,000. Activation of the channels requires the presence of both glutamate and sodium. The single-channel conductance and the open lifetime of the channel are independent of the external concentration of glutamate and sodium. External glutamate and sodium affect only the opening rate of the channels. D,L-Threo-3-hydroxyaspartate (THA), a glutamate-transport blocker, is shown to be a partial agonist for the channel. The single-channel conductance is the same regardless of whether glutamate or THA is the ligand, but the open lifetime of the channel is only 0.8 ms with THA as ligand. The glutamate-activated current in rods has a similar single-channel conductance (0.74 pS) and open lifetime (3 ms). We propose a kinetic model, consistent with these results, to explain how a transporter can simultaneously act both as a sodium/glutamate-gated chloride channel and a glutamate/sodium cotransporter.     

Noise analysis of ion channels in non-space-clamped cables: estimates of channel parameters in olfactory cilia.

Ion channels in the cilia of olfactory neurons are part of the transduction machinery of olfaction. Odorant stimuli have been shown to induce a biphasic current response, consisting of a cAMP-activated current and a Ca(2+)-activated Cl- current. We have developed a noise analysis method to study ion channels in leaky cables, such as the olfactory cilium, under non-space-clamp conditions. We performed steady-state noise analysis on ligand-induced currents in excised cilia, voltage-clamped at input and internally perfused with cAMP or Ca2+. The cAMP-activated channels analyzed by this method gave results similar to those of single-channel recordings (gamma = 8.3 pS). Single-channel currents have not yet been recorded for the Ca(2+)-activated Cl- channels. Using our noise analysis method, we estimate a unit conductance, gamma = 0.8 pS, for these channels. The density of channels was found to be approximately 70 channels/micron2 for both channel species.