Axonal Noise as a Source of Synaptic Variability

Post-synaptic potential (PSP) variability is typically attributed to mechanisms inside synapses, yet recent advances in experimental methods and biophysical understanding have led us to reconsider the role of axons as highly reliable transmission channels. We show that in many thin axons of our brain, the action potential (AP) waveform and thus the Ca⁺⁺ signal controlling vesicle release at synapses will be significantly affected by the inherent variability of ion channel gating. We investigate how and to what extent fluctuations in the AP waveform explain observed PSP variability. Using both biophysical theory and stochastic simulations of central and peripheral nervous system axons from vertebrates and invertebrates, we show that channel noise in thin axons (<1 µm diameter) causes random fluctuations in AP waveforms. AP height and width, both experimentally characterised parameters of post-synaptic response amplitude, vary e.g. by up to 20 mV and 0.5 ms while a single AP propagates in C-fibre axons. We show how AP height and width variabilities increase with a ¾ power-law as diameter decreases and translate these fluctuations into post-synaptic response variability using biophysical data and models of synaptic transmission. We find for example that for mammalian unmyelinated axons with 0.2 µm diameter (matching cerebellar parallel fibres) axonal noise alone can explain half of the PSP variability in cerebellar synapses. We conclude that axonal variability may have considerable impact on synaptic response variability. Thus, in many experimental frameworks investigating synaptic transmission through paired-cell recordings or extracellular stimulation of presynaptic neurons, causes of variability may have been confounded. We thereby show how bottom-up aggregation of molecular noise sources contributes to our understanding of variability observed at higher levels of biological organisation.     

Stochastic simulations on the reliability of action potential propagation in thin axons

It is generally assumed that axons use action potentials (APs) to transmit information fast and reliably to synapses. Yet, the reliability of transmission along fibers below 0.5 μm diameter, such as cortical and cerebellar axons, is unknown. Using detailed models of rodent cortical and squid axons and stochastic simulations, we show how conduction along such thin axons is affected by the probabilistic nature of voltage-gated ion channels (channel noise). We identify four distinct effects that corrupt propagating spike trains in thin axons: spikes were added, deleted, jittered, or split into groups depending upon the temporal pattern of spikes. Additional APs may appear spontaneously; however, APs in general seldom fail (<1%). Spike timing is jittered on the order of milliseconds over distances of millimeters, as conduction velocity fluctuates in two ways. First, variability in the number of Na channels opening in the early rising phase of the AP cause propagation speed to fluctuate gradually. Second, a novel mode of AP propagation (stochastic microsaltatory conduction), where the AP leaps ahead toward spontaneously formed clusters of open Na channels, produces random discrete jumps in spike time reliability. The combined effect of these two mechanisms depends on the pattern of spikes. Our results show that axonal variability is a general problem and should be taken into account when considering both neural coding and the reliability of synaptic transmission in densely connected cortical networks, where small synapses are typically innervated by thin axons. In contrast we find that thicker axons above 0.5 μm diameter are reliable.     

Modulatory effects of acid-sensing ion channels on action potential generation in hippocampal neurons

Extracellular acidification has been shown to generate action potentials (APs) in several types of neurons. In this study, we investigated the role of acid-sensing ion channels (ASICs) in acid-induced AP generation in brain neurons. ASICs are neuronal Na⁺ channels that belong to the epithelial Na⁺ channel/degenerin family and are transiently activated by a rapid drop in extracellular pH. We compared the pharmacological and biophysical properties of acid-induced AP generation with those of ASIC currents in cultured hippocampal neurons. Our results show that acid-induced AP generation in these neurons is essentially due to ASIC activation. We demonstrate for the first time that the probability of inducing APs correlates with current entry through ASICs. We also show that ASIC activation in combination with other excitatory stimuli can either facilitate AP generation or inhibit AP bursts, depending on the conditions. ASIC-mediated generation and modulation of APs can be induced by extracellular pH changes from 7.4 to slightly <7. Such local extracellular pH values may be reached by pH fluctuations due to normal neuronal activity. Furthermore, in the plasma membrane, ASICs are localized in close proximity to voltage-gated Na⁺ and K⁺ channels, providing the conditions necessary for the transduction of local pH changes into electrical signals. cellular excitability; neuronal signaling; pH     

A small fraction of strongly cooperative sodium channels boosts neuronal encoding of high frequencies

Generation of action potentials (APs) is a crucial step in neuronal information processing. Existing biophysical models for AP generation almost universally assume that individual voltage-gated sodium channels operate statistically independently, and their avalanche-like opening that underlies AP generation is coordinated only through the transmembrane potential. However, biological ion channels of various types can exhibit strongly cooperative gating when clustered. Cooperative gating of sodium channels has been suggested to explain rapid onset dynamics and large threshold variability of APs in cortical neurons. It remains however unknown whether these characteristic properties of cortical APs can be reproduced if only a fraction of channels express cooperativity, and whether the presence of cooperative channels has an impact on encoding properties of neuronal populations. To address these questions we have constructed a conductance-based neuron model in which we continuously varied the size of a fraction [Formula: see text] of sodium channels expressing cooperativity and the strength of coupling between cooperative channels [Formula: see text]. We show that starting at a critical value of the coupling strength [Formula: see text], the activation curve of sodium channels develops a discontinuity at which opening of all coupled channels becomes an all-or-none event, leading to very rapid AP onsets. Models with a small fraction, [Formula: see text], of strongly cooperative channels generate APs with the most rapid onset dynamics. In this regime APs are triggered by simultaneous opening of the cooperative channel fraction and exhibit a pronounced biphasic waveform often observed in cortical neurons. We further show that presence of a small fraction of cooperative Na+ channels significantly improves the ability of neuronal populations to phase-lock their firing to high frequency input fluctuation. We conclude that presence of a small fraction of strongly coupled sodium channels can explain characteristic features of cortical APs and has a functional impact of enhancing the spike encoding of rapidly varying signals.     

Effect of channel block on the spiking activity of excitable membranes in a stochastic Hodgkin-Huxley model

The influence of intrinsic channel noise on the spontaneous spiking activity of poisoned excitable membrane patches is studied by use of a stochastic generalization of the Hodgkin-Huxley model. Internal noise stemming from the stochastic dynamics of individual ion channels is known to affect the collective properties of the whole ion channel cluster. For example, there exists an optimal size of the membrane patch for which the internal noise alone causes a regular spontaneous generation of action potentials. In addition to varying the size of ion channel clusters, living organisms may adapt the densities of ion channels in order to optimally regulate the spontaneous spiking activity. The influence of a channel block on the excitability of a membrane patch of a certain size is twofold: first, a variation of ion channel densities primarily yields a change of the conductance level; second, a down-regulation of working ion channels always increases the channel noise. While the former effect dominates in the case of sodium channel block resulting in a reduced spiking activity, the latter enhances the generation of spontaneous action potentials in the case of a tailored potassium channel blocking. Moreover, by blocking some portion of either potassium or sodium ion channels, it is possible to either increase or decrease the regularity of the spike train.     

Molecular dynamics of alamethicin transmembrane channels from open-channel current noise analysis.

Conductance noise measurement of the open states of alamethicin transmembrane channels reveals excess noise attributable to cooperative low-frequency molecular dynamics that can generate fluctuations approximately 1 A rms in the effective channel pore radius. Single-channel currents through both persistent and nonpersistent channels with multiple conductance states formed by purified polypeptide alamethicin in artificial phospholipid bilayers isolated onto micropipettes with gigaohm seals were recorded using a voltage-clamp technique with low background noise (rms noise < 3 pA up to 20 kHz). Current noise power spectra between 100 Hz and 20 kHz of each open channel state showed little frequency dependence. Noise from undetected conductance state transitions was insignificant. Johnson and shot noises were evaluated. Current noise caused by electrolyte concentration fluctuation via diffusion was isolated by its dependence on buffer concentration. After removing these contributions, significant current noise remains in all persistent channel states and increases in higher conductance states. In nonpersistent channels, remaining noise occurs primarily in the lowest two states. These fluctuations of channel conductance are attributed to thermal oscillations of the channel molecular conformation and are modeled as a Langevin translational oscillation of alamethicin molecules moving radially from the channel pore, damped mostly by lipid bilayer viscosity.     

Interaction between voltage-gated sodium channels and the neurotoxin,tetrodotoxin

Tetrodotoxin (TTX) is a potent toxin that specifically binds to voltage gated sodium channels. TTX binding physically blocks the flow of sodium ions through the channel, thereby preventing action potential (AP) generation and propagation. TTX has different binding affinities for different sodium channel isoforms. These differences are imparted by amino acid substitutions. Such substitutions confer TTX resistance to a variety of species. Tetrodotoxin resistance, however, may come at a cost to performance caused by changes in the biophysical properties and/or ion selectivity of the TTX resistant sodium channels. We here review the properties of sodium channels and their interaction with TTX, and look at some special examples of TTX resistant channels wherein the benefit of toxin resistance may be offset by other behavioral costs.     

Understanding LTP in pain pathways

Background

Small neurons of the dorsal root ganglion (DRG) express five of the nine known voltage-gated sodium channels. Each channel has unique biophysical characteristics which determine how it contributes to the generation of action potentials (AP). To better understand how AP amplitude is maintained in nociceptive DRG neurons and their centrally projecting axons, which are subjected to depolarization within the dorsal horn, we investigated the dependence of AP amplitude on membrane potential, and how that dependence is altered by the presence or absence of sodium channel Na_v1.8.

Results

In small neurons cultured from wild type (WT) adult mouse DRG, AP amplitude decreases as the membrane potential is depolarized from -90 mV to -30 mV. The decrease in amplitude is best fit by two Boltzmann equations, having V_1/2 values of -73 and -37 mV. These values are similar to the V_1/2 values for steady-state fast inactivation of tetrodotoxin-sensitive (TTX-s) sodium channels, and the tetrodotoxin-resistant (TTX-r) Na_v1.8 sodium channel, respectively. Addition of TTX eliminates the more hyperpolarized V_1/2 component and leads to increasing AP amplitude for holding potentials of -90 to -60 mV. This increase is substantially reduced by the addition of potassium channel blockers. In neurons from Na_v1.8(-/-) mice, the voltage-dependent decrease in AP amplitude is characterized by a single Boltzmann equation with a V_1/2 value of -55 mV, suggesting a shift in the steady-state fast inactivation properties of TTX-s sodium channels. Transfection of Na_v1.8(-/-) DRG neurons with DNA encoding Na_v1.8 results in a membrane potential-dependent decrease in AP amplitude that recapitulates WT properties.

Conclusion

We conclude that the presence of Na_v1.8 allows AP amplitude to be maintained in DRG neurons and their centrally projecting axons even when depolarized within the dorsal horn.     

Mouse models for studying pacemaker channel function and sinus node arrhythmia

Pacemaker activity of the heart is generated by a small group of cells forming the sinoatrial node (SAN). Cells of the SAN are spontaneously active and generate action potentials with remarkable regularity and stability under all physiological conditions. The exact molecular mechanisms underlying pacemaker potentials in the SAN have not yet been fully elucidated. Several voltage-dependent ion channels as well as intracellular calcium cycling processes are thought to contribute to the pacemaker activity. Hyperpolarization-activated cation channels, which generate the I_f current, have biophysical properties which seem ideally suited for the initiation of spontaneous electrical activity. This review describes recent work on several transgenic mice lacking different cardiac HCN channel subtypes. The role of I_f for normal pacemaking and sinus node arrhythmia as revealed by these genetic models will be discussed. In addition, a new mouse line is described which enables gene targeting in a temporally-controlled manner selectively in SAN cells. Elucidating the function of HCN and other ion channels in well-controlled mouse models should ultimately lead to a better understanding of the mechanisms underlying human sinoatrial arrhythmias.     

Gain-of-function mutation of Nav1.5 in atrial fibrillation enhances cellular excitability and lowers the threshold for action potential firing

Genetic mutations of the cardiac sodium channel (SCN5A) specific only to the phenotype of atrial fibrillation have recently been described. However, data on the biophysical properties of SCN5A variants associated with atrial fibrillation are scarce. In a mother and son with lone atrial fibrillation, we identified a novel SCN5A coding variant, K1493R, which altered a highly conserved residue in the DIII-IV linker and was located six amino acids downstream from the fast inactivation motif of sodium channels. Biophysical studies of K1493R in tsA201 cells demonstrated a significant positive shift in voltage-dependence of inactivation and a large ramp current near resting membrane potential, indicating a gain-of-function. Enhanced cellular excitability was observed in transfected HL-1 atrial cardiomyocytes, including spontaneous action potential depolarizations and a lower threshold for action potential firing. These novel biophysical observations provide molecular evidence linking cellular “hyperexcitability” as a mechanism inducing vulnerability to this common arrhythmia.     

Spontaneous action potential generation due to persistent sodium channel currents in simulated carotid body afferent fibers.

The mechanism by which action potentials (APs) are generated in afferent nerve fibers in the carotid body is unknown, but it is generally speculated to be release of an excitatory transmitter and synaptic depolarizing events. However, previous results suggested that Na(+) channels in the afferent nerve fibers play an important role in this process. To better understand the potential mechanism by which Na(+) channels may generate APs, a mathematical model of chemoreceptor nerve fibers that incorporated Hodgkin-Huxley-type Na(+) channels with kinetics of activation and inactivation, as determined previously from recordings of petrosal chemoreceptor neurons, was constructed. While the density of Na(+) channels was kept constant, spontaneous APs arose in nerve terminals as the axonal diameter was reduced to that in rat carotid body. AP excitability and pattern were similar to those observed in chemoreceptor recordings: 1) a random pattern at low- and high-frequency discharge rates, 2) a high sensitivity to reductions in extracellular Na(+) concentration, and 3) a variation in excitability that increased with AP generation rate. Taken together, the results suggest that an endogenous process in chemoreceptor nerve terminals may underlie AP generation, a process independent of synaptic depolarizing events.     

TRPV4 links inflammatory signaling and neuroglial swelling

The activity of voltage-gated sodium channels contributes to onset and duration of the cardiac action potential through an intricate balance with the activity of other ion channels. Activation of sodium channels leads to membrane depolarization and Phase 0 of the cardiac action potential. Sodium channel fast inactivation contributes to Phase 1, the initial repolarization. Slow inactivation and closed state fast inactivation determine channel availability and, thus, overall membrane excitability. Defects in any of these biophysical states or transitions between them, imparted by (over 170 reported thus far, including both Long QT3 and Brugada syndromes) mutations in the (over 2000) amino acids that compose the sodium channel protein, can lead to channel dysfunction that manifests as an abnormal cardiac action potential and electrocardiogram. A causal relationship between several such abnormalities and the panoply of sodium channel mutations have led to a greater understanding of the molecular underpinnings of cardiac arrhythmias as well as a deeper appreciation for the intricacies of sodium channel function. Here, we review the literature regarding these causal relationships from a perspective of the biophysical properties of sodium channels.     

Biophysical defects in voltage.gated sodium channels associated with long QT and Brugada syndromes

The activity of voltage-gated sodium channels contributes to onset and duration of the cardiac action potential through an intricate balance with the activity of other ion channels. Activation of sodium channels leads to membrane depolarization and Phase 0 of the cardiac action potential. Sodium channel fast inactivation contributes to Phase 1, the initial repolarization. Slow inactivation and closed state fast inactivation determine channel availability and, thus, overall membrane excitability. Defects in any of these biophysical states or transitions between them, imparted by (over 170 reported thus far, including both Long QT3 and Brugada syndromes) mutations in the (over 2000) amino acids that compose the sodium channel protein, can lead to channel dysfunction that manifests as an abnormal cardiac action potential and electrocardiogram. A causal relationship between several such abnormalities and the panoply of sodium channel mutations have led to a greater understanding of the molecular underpinnings of cardiac arrhythmias as well as a deeper appreciation for the intricacies of sodium channel function. Here, we review the literature regarding these causal relationships from a perspective of the biophysical properties of sodium channels.     

How noisy adaptation of neurons shapes interspike interval histograms and correlations

Channel noise is the dominant intrinsic noise source of neurons causing variability in the timing of action potentials and interspike intervals (ISI). Slow adaptation currents are observed in many cells and strongly shape response properties of neurons. These currents are mediated by finite populations of ionic channels and may thus carry a substantial noise component. Here we study the effect of such adaptation noise on the ISI statistics of an integrate-and-fire model neuron by means of analytical techniques and extensive numerical simulations. We contrast this stochastic adaptation with the commonly studied case of a fast fluctuating current noise and a deterministic adaptation current (corresponding to an infinite population of adaptation channels). We derive analytical approximations for the ISI density and ISI serial correlation coefficient for both cases. For fast fluctuations and deterministic adaptation, the ISI density is well approximated by an inverse Gaussian (IG) and the ISI correlations are negative. In marked contrast, for stochastic adaptation, the density is more peaked and has a heavier tail than an IG density and the serial correlations are positive. A numerical study of the mixed case where both fast fluctuations and adaptation channel noise are present reveals a smooth transition between the analytically tractable limiting cases. Our conclusions are furthermore supported by numerical simulations of a biophysically more realistic Hodgkin-Huxley type model. Our results could be used to infer the dominant source of noise in neurons from their ISI statistics.     

Channel density regulation of firing patterns in a cortical neuron model

Modifying the density and distribution of ion channels in a neuron (by natural up- and downregulation or by pharmacological intervention or by spontaneous mutations) changes its activity pattern. In this investigation we analyzed how the impulse patterns are regulated by the density of voltage-gated channels in a neuron model based on voltage-clamp measurements of hippocampal interneurons. At least three distinct oscillatory patterns, associated with three distinct regions in the Na-K channel density plane, were found. A stability analysis showed that the different regions are characterized by saddle-node, double-orbit, and Hopf-bifurcation threshold dynamics, respectively. Single, strongly graded action potentials occur in an area outside the oscillatory regions, but less graded action potentials occur together with repetitive firing over a considerable range of channel densities. The relationship found here between channel densities and oscillatory behavior may partly explain the difference between the principal spiking patterns previously described for crab axons (class 1 and 2) and cortical neurons (regular firing and fast spiking).     

ATP-sensitive potassium channels exhibit variance in the number of open channels below the limit predicted for identical and independent gating

In small cells containing small numbers of ion channels, noise due to stochastic channel opening and closing can introduce a substantial level of variability into the cell's membrane potential. Negatively cooperative interactions that couple a channel's gating conformational change to the conformation of its neighbor(s) provide a potential mechanism for mitigating this variability, but such interactions have not previously been directly observed. Here we show that heterologously expressed ATP-sensitive potassium channels generate noise (i.e., variance in the number of open channels) below the level possible for identical and independent channels. Kinetic analysis with single-molecule resolution supports the interpretation that interchannel negative cooperativity (specifically, the presence of an open channel making a closed channel less likely to open) contributes to the decrease in noise. Functional coupling between channels may be important in modulating stochastic fluctuations in cellular signaling pathways.     

Presynaptic action potential amplification by voltage-gated Na+ channels in hippocampal mossy fiber boutons

Action potentials in central neurons are initiated near the axon initial segment, propagate into the axon, and finally invade the presynaptic terminals, where they trigger transmitter release. Voltage-gated Na(+) channels are key determinants of excitability, but Na(+) channel density and properties in axons and presynaptic terminals of cortical neurons have not been examined yet. In hippocampal mossy fiber boutons, which emerge from parent axons en passant, Na(+) channels are very abundant, with an estimated number of approximately 2000 channels per bouton. Presynaptic Na(+) channels show faster inactivation kinetics than somatic channels, suggesting differences between subcellular compartments of the same cell. Computational analysis of action potential propagation in axon-multibouton structures reveals that Na(+) channels in boutons preferentially amplify the presynaptic action potential and enhance Ca(2+) inflow, whereas Na(+) channels in axons control the reliability and speed of propagation. Thus, presynaptic and axonal Na(+) channels contribute differentially to mossy fiber synaptic transmission.     

Dynamic compartmentalization of the voltage-gated sodium channels in axons

One of the major physiological roles of the neuronal voltage-gated sodium channel is to generate action potentials at the axon hillock/initial segment and to ensure propagation along myelinated or unmyelinated fibers to nerve terminal. These processes require a precise distribution of sodium channels accumulated at high density in discrete subdomains of the nerve membrane. In neurons, information relevant to ion channel trafficking and compartmentalization into sub-domains of the plasma membrane is far from being elucidated. Besides, whereas information on dendritic targeting is beginning to emerge, less is known about the mechanisms leading to the polarized distribution of proteins in axon. To obtain a better understanding of how neurons selectively target sodium channels to discrete subdomains of the nerve, we addressed the question as to whether any of the large intracellular regions of Nav1.2 contain axonal sorting and/or clustering signals. We first obtained evidence showing that addition of the cytoplasmic carboxy-terminal region of Nav1.2 restricted the distribution of a dendritic-axonal reporter protein to axons of hippocampal neurons. The analysis of mutants revealed that a di-leucine-based motif mediates chimera compartmentalization in axons and its elimination in soma and dendrites by endocytosis. The analysis of the others generated chimeras showed that the determinant conferring sodium channel clustering at the axonal initial segment is contained within the cytoplasmic loop connecting domains II-III of Nav1.2. Expression of a soluble Nav1.2 II-III linker protein led to the disorganization of endogenous sodium channels. The motif was sufficient to redirect a somatodendritic potassium channel to the axonal initial segment, a process involving association with ankyrin G. Thus, it is conceivable that concerted action of the two determinants is required for sodium channel compartmentalization in axons.     

Electrophysiology of mammalian Schwann cells

Schwann cells are the satellite cell of the peripheral nervous system, and they surround axons and motor nerve terminals. The review summarises evidence for the ion channels expressed by mammalian Schwann cells, their molecular nature and known or speculated functions. In addition, the recent evidence for gap junctions and cytoplasmic diffusion pathways within the myelin and the functional consequences of a lower-resistance myelin sheath are discussed.

The main types of ion channel expressed by Schwann cells are K⁺ channels, Cl⁻ channels, Na⁺ channels and Ca²⁺ channels. Each is represented by a variety of sub-types. The molecular and biophysical characteristics of the cation channels expressed by Schwann cells are closely similar or identical to those of channels expressed in peripheral axons and elsewhere. In addition, Schwann cells express P₂X ligand-gated ion channels. Possible in vivo roles for each ion channel type are discussed. Ion channel expression in culture could have a special function in driving or controlling cell proliferation and recent evidence indicates that some Ca²⁺ channel and Kir channel expression in culture is dependent upon the presence of neurones and local electrical activity.     

Ca2+ current activation rate correlates with alpha 1 subunit density.

We report here that L-type Ca2+ channels activate rapidly in myotubes expressing current at high density and slowly in myotubes expressing current at low density. Partial block of the current in individual cells does not slow activation, indicating that Ca2+ influx does not link activation rate to current density. Activation rate is positively correlated with the density of gating charge (Qmax) associated with the L-type Ca2+ channels. The range of values for Qmax, and the relationship between activation rate and Qmax, are similar for myotubes expressing native or recombinant L-type Ca2+ channels, whereas peak Ca2+ current density is approximately 3-fold higher for native channels. Taken together, these results suggest that Ca2+ channel density can govern activation kinetics. Our findings have important important implications for studies of ion channel function because they suggest that biophysical properties can be significantly influenced by channel density, both in heterologous expression systems and in native tissues.