Noise analysis to study unitary properties of transporter-associated ion channels

Excitatory amino acid transporters (EAATs) do not only mediate secondary-active glutamate uptake but also function as anion channels. We recently used macroscopic current recordings and noise analysis to determine unitary current amplitudes of anion channels associated with a neuronal EAAT isoform, EAAT4. We found that, at symmetrical NO(3)(-), EAAT4 anion channels exhibit a single channel conductance of ~1 pS in the absence as well as in the presence of glutamate. These results indicate that glutamate increases EAAT4 anion currents by modifying exclusively open probabilities, however, leaves unitary current amplitudes unaffected. Noise analysis has been developed for ion channels with a single conductance state and limitations might ensue when using this approach for transporter-associated ion channels. We here performed stochastic simulations of EAAT transporter-associated anion channels and noise analysis of simulated currents to assess the reliability and possible limitations of this technique in studying this special class of ion channels.     

Modeling electromagnetic fields detectability in a HH-like neuronal system: stochastic resonance and window behavior

Noise has already been shown to play a constructive role in neuronal processing and reliability, according to stochastic resonance (SR). Here another issue is addressed, concerning noise role in the detectability of an exogenous signal, here representing an electromagnetic (EM) field. A Hodgkin–Huxley like neuronal model describing a myelinated nerve fiber is proposed and validated, excited with a suprathreshold stimulation. EM field is introduced as an additive voltage input and its detectability in neuronal response is evaluated in terms of the output signal-to-noise ratio. Noise intensities maximizing spiking activity coherence with the exogenous EM signal are clearly shown, indicating a stochastic resonant behavior, strictly connected to the model frequency sensitivity. In this study SR exhibits a window of occurrence in the values of field frequency and intensity, which is a kind of effect long reported in bioelectromagnetic experimental studies. The spatial distribution of the modeled structure also allows to investigate possible effects on action potentials saltatory propagation, which results to be reliable and robust over the presence of an exogenous EM field and biological noise. The proposed approach can be seen as assessing biophysical bases of medical applications funded on electric and magnetic stimulation where the role of noise as a cooperative factor has recently gained growing attention. This work investigates the role of noise as a cooperative factor for the detection of an exogenous electromagnetic field in a compartimental model of a myelinated nerve fiber. The occurrence of stochastic resonance is discussed in relation to neuronal frequency sensitivity.     

Variability and coding efficiency of noisy neural spike encoders

Encoding synaptic inputs as a train of action potentials is a fundamental function of nerve cells. Although spike trains recorded in vivo have been shown to be highly variable, it is unclear whether variability in spike timing represents faithful encoding of temporally varying synaptic inputs or noise inherent in the spike encoding mechanism. It has been reported that spike timing variability is more pronounced for constant, unvarying inputs than for inputs with rich temporal structure. This could have significant implications for the nature of neural coding, particularly if precise timing of spikes and temporal synchrony between neurons is used to represent information in the nervous system. To study the potential functional role of spike timing variability, we estimate the fraction of spike timing variability which conveys information about the input for two types of noisy spike encoders--an integrate and fire model with randomly chosen thresholds and a model of a patch of neuronal membrane containing stochastic Na(+) and K(+) channels obeying Hodgkin-Huxley kinetics. The quality of signal encoding is assessed by reconstructing the input stimuli from the output spike trains using optimal linear mean square estimation. A comparison of the estimation performance of noisy neuronal models of spike generation enables us to assess the impact of neuronal noise on the efficacy of neural coding. The results for both models suggest that spike timing variability reduces the ability of spike trains to encode rapid time-varying stimuli. Moreover, contrary to expectations based on earlier studies, we find that the noisy spike encoding models encode slowly varying stimuli more effectively than rapidly varying ones.     

Rat ENaC expressed in Xenopus laevis oocytes is activated by cAMP and blocked by Ni(2+)

We used oocytes of the South African clawed toad Xenopus laevis to express the three subunits of the epithelial Na(+) channel from rat distal colon (rENaC). We combined conventional dual-microelectrode voltage-clamp with continuous capacitance (C(m)) measurements and noise analysis to evaluate the effects of cAMP and Ni(2+) on rENaC. Control oocytes or rENaC-expressing oocytes exhibited no spontaneous fluctuations in current. However, in rENaC-expressing oocytes amiloride induced a marked plateau-shaped rise of the power density spectra. Recordings using four different concentrations of amiloride revealed that the blocker-channel interactions were of the first order. A cocktail of the membrane permeant cAMP analogue chlorophenylthio-cAMP and IBMX (cAMP cocktail) increased amiloride-sensitive current (I(ami)) and conductance (G(ami)). Furthermore, C(m) was also increased following cAMP application, indicating an increase in plasma membrane surface area. Noise analysis showed that cAMP increased the number of active channels in the oocyte membrane while single-channel current decreased. From these data we conclude that cAMP triggered exocytotic delivery of preformed rENaCs to the plasma membrane. Ni(2+) (2.5 mM) inhibited about 60% of the rENaC current and conductance while C(m) remained unaffected. Noise analysis revealed that this inhibition could be attributed to a decrease in the apparent channel density, while single-channel current did not change significantly. These observations argue for direct effects of Ni(2+) on channel activity rather than induction of endocytotic removal of active channels from the plasma membrane.     

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.     

Cell-attached recordings of the volume-sensitive anion channel in rat pancreatic beta-cells.

The cell-attached configuration of the patch-clamp technique was used to study the volume-sensitive anion conductance in isolated rat pancreatic beta-cells at the single-channel level. In unstimulated cells, current level was close to zero. Exposure of cells to a 33% hypotonic solution resulted in the generation of an inward current at 0 mV pipette potential. A similar inward current was elicited by a rise in glucose concentration or by addition of alpha-ketoisocaproate. In contrast, the sulphonylurea tolbutamide was ineffective. The inward current evoked by hypotonic solutions consisted of occasional discreet channel events interspersed with periods of current noise which could not be clearly resolved into unitary channel events. Stimulation with glucose resulted in a predominantly noisy pattern of current. With a reduced [Cl(-)] pipette solution, regular channel openings could be resolved in the presence of a stimulatory glucose concentration, with a calculated conductance of 215 pS. Channel activity could also be recorded in excised inside-out patches, though rapid 'rundown' occurred under such conditions. It is concluded that hypotonic solutions and glucose activate the volume-sensitive anion channel in the cell-attached configuration by increasing channel open probability. This generates an inward current in non-voltage-clamped cells. The channel showed complex kinetics which depended in part upon extracellular [Cl(-)].     

Noise pollution alters ecological services: enhanced pollination and disrupted seed dispersal

Noise pollution is a novel, widespread environmental force that has recently been shown to alter the behaviour and distribution of birds and other vertebrates, yet whether noise has cumulative, community-level consequences by changing critical ecological services is unknown. Herein, we examined the effects of noise pollution on pollination and seed dispersal and seedling establishment within a study system that isolated the effects of noise from confounding stimuli common to human-altered landscapes. Using observations, vegetation surveys and pollen transfer and seed removal experiments, we found that effects of noise pollution can reverberate through communities by disrupting or enhancing these ecological services. Specifically, noise pollution indirectly increased artificial flower pollination by hummingbirds, but altered the community of animals that prey upon and disperse Pinus edulis seeds, potentially explaining reduced P. edulis seedling recruitment in noisy areas. Despite evidence that some ecological services, such as pollination, may benefit indirectly owing to noise, declines in seedling recruitment for key-dominant species such as P. edulis may have dramatic long-term effects on ecosystem structure and diversity. Because the extent of noise pollution is growing, this study emphasizes that investigators should evaluate the ecological consequences of noise alongside other human-induced environmental changes that are reshaping human-altered landscapes worldwide.     

Different behavioural responses to anthropogenic noise by two closely related passerine birds

Anthropogenic noise, now common to many landscapes, can impair acoustic communication for many species, yet some birds compensate for masking by noise by altering their songs. The phylogenetic distribution of these noise-dependent signal adjustments is uncertain, and it is not known whether closely related species respond similarly to noise. Here, we investigated the influence of noise on habitat occupancy rates and vocal frequency in two congeneric vireos with similar song features. Noise exposure did not influence occupancy rates for either species, yet song features of both changed, albeit in different ways. With increases in noise levels, plumbeous vireos (Vireo plumbeus) sang shorter songs with higher minimum frequencies. By contrast, grey vireos (Vireo vicinior) sang longer songs with higher maximum frequencies. These findings support the notion that vocal plasticity may help some species occupy noisy areas, but because there were no commonalities among the signal changes exhibited by these closely related birds, it may be difficult to predict how diverse species may modify their signals in an increasingly noisy world.     

Diversity and noise effects in a model of homeostatic regulation of the sleep-wake cycle

Recent advances in sleep neurobiology have allowed development of physiologically based mathematical models of sleep regulation that account for the neuronal dynamics responsible for the regulation of sleep-wake cycles and allow detailed examination of the underlying mechanisms. Neuronal systems in general, and those involved in sleep regulation in particular, are noisy and heterogeneous by their nature. It has been shown in various systems that certain levels of noise and diversity can significantly improve signal encoding. However, these phenomena, especially the effects of diversity, are rarely considered in the models of sleep regulation. The present paper is focused on a neuron-based physiologically motivated model of sleep-wake cycles that proposes a novel mechanism of the homeostatic regulation of sleep based on the dynamics of a wake-promoting neuropeptide orexin. Here this model is generalized by the introduction of intrinsic diversity and noise in the orexin-producing neurons, in order to study the effect of their presence on the sleep-wake cycle. A simple quantitative measure of the quality of a sleep-wake cycle is introduced and used to systematically study the generalized model for different levels of noise and diversity. The model is shown to exhibit a clear diversity-induced resonance: that is, the best wake-sleep cycle turns out to correspond to an intermediate level of diversity at the synapses of the orexin-producing neurons. On the other hand, only a mild evidence of stochastic resonance is found, when the level of noise is varied. These results show that disorder, especially in the form of quenched diversity, can be a key-element for an efficient or optimal functioning of the homeostatic regulation of the sleep-wake cycle. Furthermore, this study provides an example of a constructive role of diversity in a neuronal system that can be extended beyond the system studied here.     

Computer simulation for studying calcium dependent abnormalities in firing mechanism of molluscan neurones

Computer modelling technique is proposed to assist in physiological research on invertebrate neuronal membranes. The firing mechanism of a single patch of invertebrate neuronal membrane has been studied in dependence on maximum Ca++ conductance. The calculations are based on modification of Hodgkin-Huxley's data completed by a straight line approximation between experimental points of the kinetic parameters of Ca++ current and early transient potassium current. The time course of conductance changes is assumed to be proportional to m2h for Ca++ current. Three distinct potassium currents are involved into the model, viz. transient potassium current, delayed potassium current and Ca++-dependent potassium current. The modified Euler method run on a digital computer has been used for numerical integration of kinetic equations. Significant effects of Ca++ conductance on spike broadening, plateau development and spike afterhyperpolarization are represented. In the range of small Ca++ conductance an infinite spontaneous activity can be triggered by a short (suprathreshold) current pulse which may be considered a model of pacemaker activity. Plateau development resulting from potassium blocking or decreasing potassium equilibrium is facilitated by Ca++ conductance in the range of greater Ca++ conductance. The effects of voltage sensitivity of the coupling coefficient describing the current of Ca++-dependent K+ channels were studied and compared to the voltage independent case. The coupling coefficient seems to be a crucial factor in broadening the range of Ca++ conductance responsible for pacemaker activity. For greater values of Ca++ conductance, a decrease of the coupling coefficient leads to a transition from prolonged bursting to interruption of burst activity by burst-afterhyperpolarization. The blocking effect of 4-aminopyridine on fast outward current has been studied by the model which has a practical significance considering that aminopyridine is known as a convulsive agent. We suppose that it is reasonable to study the convulsive effects of aminopyridine by the model based on the kinetics of the isolated neuronal membrane. The model may help in understanding the ionic background underlying abnormal network activity during epileptic discharges of mammalian neurones.     

Influence of simulated neuromuscular noise on movement variability and fall risk in a 3D dynamic walking model

People at risk of falling exhibit increased gait variability, which may predict future falls. However, the causal mechanisms underlying these correlations are not well known. Increased neuronal noise associated with aging likely leads to increased gait variability, which could in turn lead to increased fall risk. This paper presents a model of how changes in neuromuscular noise independently affect gait variability and probability of falling, and aims to determine the extent to which changes in gait variability directly predict fall risk. We used a dynamic walking model that incorporates a lateral step controller to maintain lateral stability. Noise was applied to this controller to approximate neuromuscular noise in humans. Noise amplitude was varied between low amplitudes that did not induce falls and high amplitudes for which the model always fell. With increases in noise amplitude, the model fell more often and after fewer steps. Gait variability increased with noise amplitude and predicted increased probability of falling. Importantly, these relationships were not linear. At either low gait variability or very high gait variability, small increases in noise and variability affected probability of falling very little. Conversely, at intermediate noise and/or variability levels, the same small increases resulted in large increases in probability of falling. Our results validate the idea that age-related increases in neuromuscular noise likely play a direct contributing role in increasing fall risk. However, neuromuscular noise remains only one of many important factors that need to be considered. These findings have important implications for fall prevention research and practice.     

Noise enhances subthreshold oscillations in injured primary sensory neurons

Noise can play a constructive role in the detection of weak signals in various kinds of peripheral receptors and neurons. What the mechanism underlying the effect of noise is remains unclear. Here, the perforated patch-clamp technique was used on isolated cells from chronic compression of the dorsal root ganglion (DRG) model. Our data provided new insight indicating that, under conditions without external signals, noise can enhance subthreshold oscillations, which was observed in a certain type of neurons with high-frequency (20-100 Hz) intrinsic resonance from injured DRG neurons. The occurrence of subthreshold oscillation considerably decreased the threshold potential for generating repetitive firing. The above effects of noise can be abolished by blocking the persistent sodium current (I(Na, P)). Utilizing a mathematical neuron model we further simulated the effect of noise on subthreshold oscillation and firing, and also found that noise can enhance the electrical activity through autonomous stochastic resonance. Accordingly, we propose a new concept of the effects of noise on neural intrinsic activity, which suggests that noise may be an important factor for modulating the excitability of neurons and generation of chronic pain signals.     

Slope-Based Stochastic Resonance: How Noise Enables Phasic Neurons to Encode Slow Signals

Fundamental properties of phasic firing neurons are usually characterized in a noise-free condition. In the absence of noise, phasic neurons exhibit Class 3 excitability, which is a lack of repetitive firing to steady current injections. For time-varying inputs, phasic neurons are band-pass filters or slope detectors, because they do not respond to inputs containing exclusively low frequencies or shallow slopes. However, we show that in noisy conditions, response properties of phasic neuron models are distinctly altered. Noise enables a phasic model to encode low-frequency inputs that are outside of the response range of the associated deterministic model. Interestingly, this seemingly stochastic-resonance (SR) like effect differs significantly from the classical SR behavior of spiking systems in both the signal-to-noise ratio and the temporal response pattern. Instead of being most sensitive to the peak of a subthreshold signal, as is typical in a classical SR system, phasic models are most sensitive to the signal''s rising and falling phases where the slopes are steep. This finding is consistent with the fact that there is not an absolute input threshold in terms of amplitude; rather, a response threshold is more properly defined as a stimulus slope/frequency. We call the encoding of low-frequency signals with noise by phasic models a slope-based SR, because noise can lower or diminish the slope threshold for ramp stimuli. We demonstrate here similar behaviors in three mechanistic models with Class 3 excitability in the presence of slow-varying noise and we suggest that the slope-based SR is a fundamental behavior associated with general phasic properties rather than with a particular biological mechanism.     

Subthreshold Voltage Noise Due to Channel Fluctuations in Active Neuronal Membranes

Voltage-gated ion channels in neuronal membranes fluctuate randomly between different conformational states due to thermal agitation. Fluctuations between conducting and nonconducting states give rise to noisy membrane currents and subthreshold voltage fluctuations and may contribute to variability in spike timing. Here we study subthreshold voltage fluctuations due to active voltage-gated Na⁺ and K⁺ channels as predicted by two commonly used kinetic schemes: the Mainen et al. (1995) (MJHS) kinetic scheme, which has been used to model dendritic channels in cortical neurons, and the classical Hodgkin-Huxley (1952) (HH) kinetic scheme for the squid giant axon. We compute the magnitudes, amplitude distributions, and power spectral densities of the voltage noise in isopotential membrane patches predicted by these kinetic schemes. For both schemes, noise magnitudes increase rapidly with depolarization from rest. Noise is larger for smaller patch areas but is smaller for increased model temperatures. We contrast the results from Monte Carlo simulations of the stochastic nonlinear kinetic schemes with analytical, closed-form expressions derived using passive and quasi-active linear approximations to the kinetic schemes. For all subthreshold voltage ranges, the quasi-active linearized approximation is accurate within 8% and may thus be used in large-scale simulations of realistic neuronal geometries.     

Contribution of cyclic-nucleotide-gated channels to the resting conductance of olfactory receptor neurons

The basal conductance of unstimulated frog olfactory receptor neurons was investigated using whole-cell and perforated-patch recording. The input conductance, measured between -80 mV and -60 mV, averaged 0.25 nS in physiological saline. Studies were conducted to determine whether part of the input conductance is due to gating of neuronal cyclic-nucleotide-gated (CNG) channels. In support of this idea, the neuronal resting conductance was reduced by each of five treatments that reduce current through CNG channels: external application of divalent cations or amiloride; treatment with either of two adenylate cyclase inhibitors; and application of AMP-PNP, a competitive substrate for adenylate cyclase. The current blocked by divalent cations or by a cyclase inhibitor reversed near 0 mV, as expected for a CNG current. Under physiological conditions, gating of CNG channels contributes approximately 0.06 nS to the resting neuronal conductance. This implies a resting cAMP concentration of 0.1-0.3 micro M. A theoretical model suggests that a neuron containing 0.1-0.3 micro M cAMP is poised to give the largest possible depolarization in response to a very small olfactory stimulus. Although having CNG channels open at rest decreases the voltage change resulting from a given receptor current, it more substantially increases the receptor current resulting from a given increase in [cAMP].     

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.     

Noise Normalizes Firing Output of Mouse Lateral Geniculate Nucleus Neurons

The output of individual neurons is dependent on both synaptic and intrinsic membrane properties. While it is clear that the response of an individual neuron can be facilitated or inhibited based on the summation of its constituent synaptic inputs, it is not clear whether subthreshold activity, (e.g. synaptic “noise”- fluctuations that do not change the mean membrane potential) also serve a function in the control of neuronal output. Here we studied this by making whole-cell patch-clamp recordings from 29 mouse thalamocortical relay (TC) neurons. For each neuron we measured neuronal gain in response to either injection of current noise, or activation of the metabotropic glutamate receptor-mediated cortical feedback network (synaptic noise). As expected, injection of current noise via the recording pipette induces shifts in neuronal gain that are dependent on the amplitude of current noise, such that larger shifts in gain are observed in response to larger amplitude noise injections. Importantly we show that shifts in neuronal gain are also dependent on the intrinsic sensitivity of the neuron tested, such that the gain of intrinsically sensitive neurons is attenuated divisively in response to current noise, while the gain of insensitive neurons is facilitated multiplicatively by injection of current noise- effectively normalizing the output of the dLGN as a whole. In contrast, when the cortical feedback network was activated, only multiplicative gain changes were observed. These network activation-dependent changes were associated with reductions in the slow afterhyperpolarization (sAHP), and were mediated at least in part, by T-type calcium channels. Together, this suggests that TC neurons have the machinery necessary to compute multiple output solutions to a given set of stimuli depending on the current level of network stimulation.     

Surface expression and single channel properties of KCNQ2/KCNQ3, M-type K+ channels involved in epilepsy

Mutations in either KCNQ2 or KCNQ3 underlie benign familial neonatal convulsions (BFNC), an inherited epilepsy. The corresponding proteins are co-expressed in broad regions of the brain and associate to heteromeric K(+) channels. These channels mediate M-type currents that regulate neuronal excitability. We investigated the basis for the increase in currents seen after co-expressing these subunits in Xenopus oocytes. Noise analysis and single channel recordings revealed a conductance of approximately 18 pS for KCNQ2 and approximately 7 pS for KCNQ3. Different conductance levels (ranging from 8 to 22 pS) were seen upon co-expression. Their weighted average is close to that obtained by noise analysis (16 pS). The open probability of heteromeric channels was not increased significantly. Co-expression of both subunits increased the surface expression of KCNQ2 and KCNQ3 by factors of 5 and >10, respectively. A KCNQ2 mutant associated with BFNC that has a truncated cytoplasmic carboxyl terminus did not reach the surface and failed to stimulate KCNQ3 surface expression. By contrast, several BFNC-associated missense mutations in KCNQ2 or KCNQ3 did not alter their surface expression. Thus, the increase in currents seen upon co-expressing KCNQ2 and KCNQ3 is predominantly due to an increase in surface expression, which is dependent on an intact carboxyl terminus.     

Oscillations and synchrony in a cortical neural network

In this paper, the oscillations and synchronization status of two different network connectivity patterns based on Izhikevich model are studied. One of the connectivity patterns is a randomly connected neuronal network, the other one is a small-world neuronal network. This Izhikevich model is a simple model which can not only reproduce the rich behaviors of biological neurons but also has only two equations and one nonlinear term. Detailed investigations reveal that by varying some key parameters, such as the connection weights of neurons, the external current injection, the noise of intensity and the neuron number, this neuronal network will exhibit various collective behaviors in randomly coupled neuronal network. In addition, we show that by changing the number of nearest neighbor and connection probability in small-world topology can also affect the collective dynamics of neuronal activity. These results may be instructive in understanding the collective dynamics of mammalian cortex.