Transmission Of Action Potentials Research Articles

Six Networks on a Universal Neuromorphic Computing Substrate

In this study, we present a highly configurable neuromorphic computing substrate and use it for emulating several types of neural networks. At the heart of this system lies a mixed-signal chip, with analog implementations of neurons and synapses and digital transmission of action potentials. Major advantages of this emulation device, which has been explicitly designed as a universal neural network emulator, are its inherent parallelism and high acceleration factor compared to conventional computers. Its configurability allows the realization of almost arbitrary network topologies and the use of widely varied neuronal and synaptic parameters. Fixed-pattern noise inherent to analog circuitry is reduced by calibration routines. An integrated development environment allows neuroscientists to operate the device without any prior knowledge of neuromorphic circuit design. As a showcase for the capabilities of the system, we describe the successful emulation of six different neural networks which cover a broad spectrum of both structure and functionality.

Impact of The Ion Channel Blockage on the Collective Spiking Regularity of a Scale-Free Neuronal Network

The voltage-gated ion channels embedded in biological membranes play crucial roles on the generation and transmission of action potentials. Therefore, understanding of impacts of each ion channel is of great importance for the dynamics of neuronal networks. Among the others, one method on this way is to block a specific ion channel type while keeping the remaining ion channel types active across the membrane and to observe their impact on neuronal dynamics. In this study, we study the effects of sodium and potassium channels blockage on the collective spiking regularity of a scale-free neuronal network with stochastic Hodgkin-Huxley neurons, and investigate how the dependence of the collective spiking regularity on the membrane area or cell size varies with the coupling constant between neurons. Results reveal that the collective spiking regularity exhibits coherence resonance (CR) depending on the channel blockage scaling factor and the cell size, where potassium channel blockage enhances the collective spiking regularity whereas sodium channel blockage decreases it. We show that there is a lower limit for the coupling constant which warrants the CR behavior. We also show that the maximal regularity is obtained for a smaller cell size with the increasing the value of the coupling constant.

Functional and histopathological identification of the respiratory failure in a DMSXL transgenic mouse model of Myotonic Dystrophy

SUMMARYAcute and chronic respiratory failure is one of the major and potentially life-threatening features in individuals with myotonic dystrophy type 1 (DM1). Despite several clinical demonstrations showing respiratory problems in DM1 patients, the mechanisms are still not completely understood. This study was designed to investigate whether the DMSXL transgenic mouse model for DM1 exhibits respiratory disorders and, if so, to identify the pathological changes underlying these respiratory problems. Using pressure plethysmography, we assessed the breathing function in control mice and DMSXL mice generated after large expansions of the CTG repeat in successive generations of DM1 transgenic mice. Statistical analysis of breathing function measurements revealed a significant decrease in the most relevant respiratory parameters in DMSXL mice, indicating impaired respiratory function. Histological and morphometric analysis showed pathological changes in diaphragmatic muscle of DMSXL mice, characterized by an increase in the percentage of type I muscle fibers, the presence of central nuclei, partial denervation of end-plates (EPs) and a significant reduction in their size, shape complexity and density of acetylcholine receptors, all of which reflect a possible breakdown in communication between the diaphragmatic muscles fibers and the nerve terminals. Diaphragm muscle abnormalities were accompanied by an accumulation of mutant DMPK RNA foci in muscle fiber nuclei. Moreover, in DMSXL mice, the unmyelinated phrenic afferents are significantly lower. Also in these mice, significant neuronopathy was not detected in either cervical phrenic motor neurons or brainstem respiratory neurons. Because EPs are involved in the transmission of action potentials and the unmyelinated phrenic afferents exert a modulating influence on the respiratory drive, the pathological alterations affecting these structures might underlie the respiratory impairment detected in DMSXL mice. Understanding mechanisms of respiratory deficiency should guide pharmaceutical and clinical research towards better therapy for the respiratory deficits associated with DM1.

Ginsenoside Rb3 exerts antidepressant-like effects in several animal models

Total ginsenosides have been shown to have therapeutic actions as antidepressants. We report a major active ingredient of total ginsenosides, the ginsenoside Rb3 (Rb3), which may have antidepressant-like effects. Using the forced swim test, tail suspension test, and learned helplessness procedure, we found that Rb3 had significant anti-immobility effects in mice in the forced swim and tail suspension tests and reduced the number of escape failures in the learned helplessness procedure. In a reserpine-induced syndrome model, Rb3 attenuated hypothermia, palpebral ptosis, and akinesia. In the chronic mild stress model, chronic Rb3 administration reversed the decrease in locomotor activity, novelty-suppressed feeding, and sucrose preference. Furthermore, neurochemical tests were performed to support our hypothesis that biochemical variations (i.e. brain-derived neurotrophic factor and the monoamine neurotransmitters 5-hydroxytryptamine, dopamine, and norepinephrine) are involved in Rb3's antidepressant-like effects. Finally, we found, using whole-cell patch-clamp recordings, that the action potential transmission in neurons within the somatosensory cortex was excited by Rb3 perfusion and blocked with Panax notoginseng total saponins extracted from leaves. This study provides evidence for the mechanism of action of the antidepressant-like effects of Rb3.

Axonal Transmission in the Retina Introduces a Small Dispersion of Relative Timing in the Ganglion Cell Population Response

BackgroundVisual stimuli elicit action potentials in tens of different retinal ganglion cells. Each ganglion cell type responds with a different latency to a given stimulus, thus transforming the high-dimensional input into a temporal neural code. The timing of the first spikes between different retinal projection neurons cells may further change along axonal transmission. The purpose of this study is to investigate if intraretinal conduction velocity leads to a synchronization or dispersion of the population signal leaving the eye.Methodology/Principal FindingsWe ‘imaged’ the initiation and transmission of light-evoked action potentials along individual axons in the rabbit retina at micron-scale resolution using a high-density multi-transistor array. We measured unimodal conduction velocity distributions (1.3±0.3 m/sec, mean ± SD) for axonal populations at all retinal eccentricities with the exception of the central part that contains myelinated axons. The velocity variance within each piece of retina is caused by ganglion cell types that show narrower and slightly different average velocity tuning. Ganglion cells of the same type respond with similar latency to spatially homogenous stimuli and conduct with similar velocity. For ganglion cells of different type intraretinal conduction velocity and response latency to flashed stimuli are negatively correlated, indicating that differences in first spike timing increase (up to 10 msec). Similarly, the analysis of pair-wise correlated activity in response to white-noise stimuli reveals that conduction velocity and response latency are negatively correlated.Conclusion/SignificanceIntraretinal conduction does not change the relative spike timing between ganglion cells of the same type but increases spike timing differences among ganglion cells of different type. The fastest retinal ganglion cells therefore act as indicators of new stimuli for postsynaptic neurons. The intraretinal dispersion of the population activity will not be compensated by variability in extraretinal conduction times, estimated from data in the literature.

Wireless cardiac action potential transmission with ultrasonically inserted silicon microprobes

This paper reports on the integration of ultrasonically inserted horn-shaped cardiac probes with wireless transmission of 3D cardiac action potential measurement for applications in ex vivo preparations such as monitoring the onset of ventricular fibrillation. Ultrasonically inserted silicon horn probes permit reduced penetration force during insertion, allowing silicon, a brittle material, to penetrate cardiac tissue. The probes also allow recording from multiple sites that are lithographically defined. An application-specific integrated circuit has been designed with a 40 dB amplifying stage and a frequency modulating oscillator at 95 MHz to wirelessly transmit the recorded action potentials. This ultrasonically inserted microprobe wireless system demonstrates the initial results in wireless monitoring of 3D action potential propagation, and the extraction of parameters of interest including the action potential duration and diastolic interval.

Active Generation and Propagation of Ca 2+ Signals within Tunneling Membrane Nanotubes

A new mechanism of cell-cell communication was recently proposed after the discovery of tunneling nanotubes (TNTs) between cells. TNTs are membrane protrusions with lengths of tens of microns and diameters of a few hundred nanometers that permit the exchange of membrane and cytoplasmic constituents between neighboring cells. TNTs have been reported to mediate intercellular Ca 2+ signaling; however, our simulations indicate that passive diffusion of Ca 2+ ions alone would be inadequate for efficient transmission between cells. Instead, we observed spontaneous and inositol trisphosphate (IP 3)-evoked Ca 2+ signals within TNTs between cultured mammalian cells, which sometimes remained localized and in other instances propagated as saltatory waves to evoke Ca 2+ signals in a connected cell. Consistent with this, immunostaining showed the presence of both endoplasmic reticulum and IP 3 receptors along the TNT. We propose that IP 3 receptors may actively propagate intercellular Ca 2+ signals along TNTs via Ca 2+-induced Ca 2+ release, acting as amplification sites to overcome the limitations of passive diffusion in a chemical analog of electrical transmission of action potentials.

Desensitization of neurotransmitter‐gated ion channels during high‐frequency stimulation: a comparative study of Cys‐loop, AMPA and purinergic receptors

Changes in synaptic strength allow synapses to regulate the flow of information in the neural circuits in which they operate. In particular, changes lasting from milliseconds to minutes (‘short-term changes') underlie a variety of computational operations and, ultimately, behaviours. Most studies thus far have attributed the short-term type of plasticity to activity-dependent changes in the dynamics of neurotransmitter release (a presynaptic mechanism) while largely dismissing the role of the loss of responsiveness of postsynaptic receptor channels to neurotransmitter owing to entry into desensitization. To better define the response of the different neurotransmitter-gated ion channels (NGICs) to repetitive stimulation without interference from presynaptic variables, we studied eight representative members of all three known superfamilies of NGICs in fast-perfused outside-out patches of membrane. We found that the responsiveness of all tested channels (two nicotinic acetylcholine receptors, two glycine receptors, one GABA receptor, two AMPA-type glutamate receptors and one purinergic receptor) declines along trains of brief neurotransmitter pulses delivered at physiologically relevant frequencies to an extent that suggests that the role of desensitization in the synaptic control of action-potential transmission may be more general than previously thought. Furthermore, our results indicate that a sizable fraction (and, for some NGICs, most) of this desensitization occurs during the neurotransmitter-free interpulse intervals. Clearly, an incomplete clearance of neurotransmitter from the synaptic cleft between vesicle-fusion events need not be invoked to account for NGIC desensitization upon repetitive stimulation.

Independent and joint modulation of rat Nav1.6 voltage-gated sodium channels by coexpression with the auxiliary β1 and β2 subunits

The Nav1.6 voltage-gated sodium channel α subunit isoform is the most abundant isoform in the brain and is implicated in the transmission of high frequency action potentials. Purification and immunocytochemical studies imply that Nav1.6 exist predominantly as Nav1.6+β1+β2 heterotrimeric complexes. We assessed the independent and joint effects of the rat β1 and β2 subunits on the gating and kinetic properties of rat Nav1.6 channels by recording whole-cell currents in the two-electrode voltage clamp configuration following transient expression in Xenopus oocytes. The β1 subunit accelerated fast inactivation of sodium currents but had no effect on the voltage dependence of their activation and steady-state inactivation and also prevented the decline of currents following trains of high-frequency depolarizing prepulses. The β2 subunit selectively retarded the fast phase of fast inactivation and shifted the voltage dependence of activation towards depolarization without affecting other gating properties and had no effect on the decline of currents following repeated depolarization. The β1 and β2 subunits expressed together accelerated both kinetic phases of fast inactivation, shifted the voltage dependence of activation towards hyperpolarization, and gave currents with a persistent component typical of those recorded from neurons expressing Nav1.6 sodium channels. These results identify unique effects of the β1 and β2 subunits and demonstrate that joint modulation by both auxiliary subunits gives channel properties that are not predicted by the effects of individual subunits.

Delayed functional maturation of human neuronal progenitor cells in vitro

Introduction Differentiation of neuronal progenitor cells (NPCs) in vitro into functional neurons is dependent on a complex cascade of molecular signaling pathways, many of which remain unknown. More specifically, in human NPCs the relationship between the expression of typical neuronal marker proteins and functional properties, such as firing action potential and synaptic transmission, is not well understood. In the present report, the immunocytochemical, morphological and electrophysiological changes that human NPCs undergo during neuronal differentiation in vitro were investigated. Methods Human NPCs were differentiated toward a neuronal phenotype. The time course of the expression of neuronal markers and morphological cell changes was mapped and passive and active electrophysiological membrane properties assessed, throughout the neuronal maturation process. Results The acquisition of neuronal markers preceded functional physiological maturation by several weeks. Cell input resistance decreased in the first 2 weeks as cells became less sensitive to input current, while cell capacitance progressively increased with continued neuronal process growth. Functional maturation was observed only by the fifth/sixth week, preceded by a marked increase in Na + and K + currents. In contrast, electrophysiological maturation of rodent precursor cells was observed at the end of the first week in vitro. Functionally, human neuronal cells became capable of firing action potentials and forming active synaptic contacts. Many features of the firing pattern however remained immature. Conclusions The results showed that human NPCs develop remarkably slowly and retain immature neuronal features for a prolonged period. The importance of Na-dependent activity for proper neuronal maturation is emphasized.

Robust Observer-Based Tracking Control of Hodgkin-Huxley Neuron Systems Under Environmental Disturbances

A nervous system consists of a large number of highly interconnected nerve cells. Nerve cells communicate by generation and transmission of short electrical pulses (action potential). In addition, membrane voltage is the only measurable state in nervous systems. A robust observer-based model reference tracking control is proposed for Hodgkin-Huxley (HH) neuron systems to generate a desired reference response in spite of environmental noises, uncertain initial values, and diffusion currents from other interconnected nerve cells. In order to simplify the robust tracking control design of nonlinear stochastic HH neuron systems, a fuzzy interpolation method is employed to interpolate several linear stochastic systems to approximate a nonlinear stochastic HH neuron system so that the nonlinear robust tracking control problem can be solved by the linear matrix inequality (LMI) technique with the help of Robust Control Toolbox in Matlab. The proposed robust observer-based tracking control scheme can provide new methods for desired action potential generation, suppression of oscillations, and blockage of action potential transmission under environmental noise and diffusion currents. These new methods are useful for patients with different neuron system dysfunctions. Finally, three simulation examples of tracking control of nervous systems are given to illustrate the design procedure and confirm the tracking performance of the proposed method.

Electrotonic Coupling between Pyramidal Neurons in the Neocortex

Electrotonic couplings (i.e., electrical synapses or gap junctions) are fundamental to neuronal synchronization, and thus essential for many physiological functions and pathological disorders. Interneuron electrical synapses have been studied intensively. Although studies on electrotonic couplings between pyramidal cells (PCs) are emerging, particularly in the hippocampus, evidence is still rare in the neocortex. The electrotonic coupling of PCs in the neocortex is therefore largely unknown in terms of electrophysiological, anatomical and synaptological properties. Using multiple patch-clamp recording with differential interference contrast infrared videomicroscopy (IR-DIC) visualization, histochemical staining, and 3D-computer reconstruction, electrotonic coupling was recorded between close PCs, mainly in the medial prefrontal cortex as well as in the visual cortical regions of ferrets and rats. Compared with interneuron gap junctions, these electrotonic couplings were characterized by several special features. The recording probability of an electrotonic coupling between PCs is extremely low; but the junctional conductance is notably high, permitting the direct transmission of action potentials (APs) and even tonic firing between coupled neurons. AP firing is therefore perfectly synchronized between coupled PCs; Postjunctional APs and spikelets alternate following slight changes of membrane potentials; Postjunctional spikelets, especially at high frequencies, are summated and ultimately reach AP-threshold to fire. These properties of pyramidal electrotonic couplings largely fill the needs, as predicted by simulation studies, for the synchronization of a neuronal assembly. It is therefore suggested that the electrotonic coupling of PCs plays a unique role in the generation of neuronal synchronization in the neocortex.

Tunneling membrane nanotubes generate local calcium signals and may actively propagate calcium signals between cells

Cells have long been known to employ gap junctions and synapses to communicate with their neighbors. A new mechanism has recently been proposed following the discovery of tunneling membrane nanotubes (TNTs) between cells [1]. TNTs are dynamic membrane protrusions with lengths up to several tens of microns and diameters of 50–800nm, which permit the exchange of membrane components and cytoplasmic molecules between neighboring cells. Ca2+ diffusion along TNTs has been proposed as a means of intercellular communication [2], yet our modeling simulations show that passive diffusion alone is insufficient to account for efficient transmission of Ca2+ between cells. Instead, we observe local spontaneous and inositol trisphosphate (IP3)‐evoked mediated Ca2+ signals within the length of TNTs formed between cultured SHSY‐5Y neuroblastoma cells. Moreover, immunostaining demonstrates the presence of both ER and IP3 receptors along the TNT. We propose that IP3Rs are involved in actively propagating intercellular Ca2+ signals along TNTs, acting as amplification sites to overcome limitations of passive diffusion in a chemical analog of electrical transmission of action potentials along axons.Supported by grants NIH GM 40871 and GM65830.

Molecular Dynamics Simulations of the GABA Type A Receptor

The type A GABA-receptors (GABARs) are chloride ion channels found in the brain and are the major inhibitory neurotransmitter receptors. Upon binding of an agonist, the GABAR opens and increases the intraneuronal concentration of chloride ions, thus hyperpolarizing the cell and inhibiting the transmission of the nerve action potential. GABARs can also be modulated by a variety of pharmacologically important drugs, such as diazepam and also other regularly abused drugs such as ethanol. Here, we present homology models (based upon the 4 A resolution EM acetylcholine receptor structure) and simulations of the most abundant GABAR subtype (γ2α1β2), and also the alcohol-sensitive subtype (δα6β3). As well as GABA itself, a variety of ligands were docked to the proteins to assess the potential binding sites, and also the affect of ligand binding on the properties of the structure. Through the modeling and simulation of the two different receptor subtypes, and comparison of the ligand effects upon each one, we are able to gain greater insight into the specific residues important in binding, and also details of the different behavior of the subtypes. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. Release number LLNL-ABS-417208.

Tunneling Membrane Nanotubes Generate Local Calcium Signals and May Actively Propagate Calcium Signals Between Cells

Cells have long been known to employ gap junctions and synapses to communicate with their neighbors. A new mechanism has recently been proposed following the discovery of tunneling membrane nanotubes (TNTs) between cells [1]. TNTs are dynamic membrane protrusions with lengths up to several tens of microns and diameters of 50-800nm, which permit the exchange of membrane components and cytoplasmic molecules between neighboring cells. Ca2+ diffusion along TNTs has been proposed as a means of intercellular communication [2], yet our modeling simulations show that passive diffusion alone is insufficient to account for efficient transmission of Ca2+ between cells. Instead, we observe local spontaneous and inositol trisphosphate (IP3)-evoked mediated Ca2+ signals within the length of TNTs formed between cultured SHSY-5Y neuroblastoma cells. Moreover, immunostaining demonstrates the presence of both ER and IP3 receptors along the TNT. We propose that IP3Rs are involved in actively propagating intercellular Ca2+ signals along TNTs, acting as amplification sites to overcome limitations of passive diffusion in a chemical analog of electrical transmission of action potentials along axons.Supported by grants NIH GM 40871 and GM65830.1. Rustom, A. et al. (2004) Science. 303, 1007-10102. Watkins, S. C. and Salter, R. D. (2005) Immunity. 23, 309-318.

Corrigendum

CorrigendaCorrigendumPublished Online:01 Nov 2009https://doi.org/10.1152/jn.z9k-9775-corr.2009Original articleMoreSectionsPDF (152 KB)Download PDF ToolsExport citationAdd to favoritesGet permissionsTrack citations ShareShare onFacebookTwitterLinkedInWeChat Volume 102, August 2009Tolnai S, Englitz B, Scholbach J, Jost J, and Rübsamen R. Spike Transmission Delay at the Calyx of Held In Vivo: Rate Dependence, Phenomenological Modeling, and Relevance for Sound Localization. J Neurophysiol 102: , 2009. First published June 10, 2009; doi:10.1152/jn.00275.2009; http://jn.physiology.org/cgi/content/full/102/2/1206.During production, parts of Fig. 1 were shifted and gave a misleading illustration of the measurements depicted. The corrected version of Fig. 1 appears here.Fig. 1.Measuring the action potential transmission delay (ATD). A: extracellular recordings of responses to acoustic stimulations of principal cells of the medial nucleus of the trapezoid body (MNTB) and their presynaptic input, the calyces of Held in the Mongolian gerbil. Due to the size of the calyx, extracellular recordings resemble complex waveforms that consist of the discharge of the calyx (prepotential) and the action potential (AP) of the principal cell. ATD was measured as the distance between the positive peak amplitudes of prepotential and postsynaptic AP. B: ATD measured under silent condition depends on the spontaneous discharge rate of a given MNTB unit. Significantly higher ATDspont are found in units with higher spontaneous rates. C: extracellular recording (top) of a unit's response to a sequence of pure tones (bottom, duration: 100 ms, interstimulus interval: 100 ms, stimulus amplitudes in decreasing order, not to scale). D: mean complex waveforms of the same unit as in C for 5 different ATDs (380–460 μs, black to red) aligned to the prepotential (top) and to the postsynaptic AP (bottom). Individual complex waveforms of ATDs in a 10 μs bin were pooled into each mean complex waveform. E and F: changes in ATD and firing rate correlate (same unit as in C). ATD (E) changes as a function of intensity and frequency of the acoustic stimulus and the firing rate (F) show a very similar profile.Download figureDownload PowerPointThis article has no references to display. Download PDF Previous Back to Top FiguresReferencesRelatedInformationRelated ArticlesSpike Transmission Delay at the Calyx of Held In Vivo: Rate Dependence, Phenomenological Modeling, and Relevance for Sound Localization 01 Aug 2009Journal of Neurophysiology More from this issue > Volume 102Issue 5November 2009Pages 3077-3077 Copyright & PermissionsCopyright © 2009 the American Physiological Societyhttps://doi.org/10.1152/jn.z9k-9775-corr.2009History Published online 1 November 2009 Published in print 1 November 2009 Metrics

Reliability of Synaptic Transmission at the Synapses of Held In Vivo under Acoustic Stimulation

BackgroundThe giant synapses of Held play an important role in high-fidelity auditory processing and provide a model system for synaptic transmission at central synapses. Whether transmission of action potentials can fail at these synapses has been investigated in recent studies. At the endbulbs of Held in the anteroventral cochlear nucleus (AVCN) a consistent picture emerged, whereas at the calyx of Held in the medial nucleus of the trapezoid body (MNTB) results on the reliability of transmission remain inconsistent. In vivo this discrepancy could be due to the difficulty in identifying failures of transmission.Methods/FindingsWe introduce a novel method for detecting unreliable transmission in vivo. Based on the temporal relationship between a cells' waveform and other potentials in the recordings, a statistical test is developed that provides a balanced decision between the presence and the absence of failures. Its performance is quantified using simulated voltage recordings and found to exhibit a high level of accuracy. The method was applied to extracellular recordings from the synapses of Held in vivo. At the calyces of Held failures of transmission were found only rarely. By contrast, at the endbulbs of Held in the AVCN failures were found under spontaneous, excited, and suppressed conditions. In accordance with previous studies, failures occurred most abundantly in the suppressed condition, suggesting a role for inhibition.Conclusions/SignificanceUnder the investigated activity conditions/anesthesia, transmission seems to remain largely unimpeded in the MNTB, whereas in the AVCN the occurrence of failures is related to inhibition and could be the basis/result of computational mechanisms for temporal processing. More generally, our approach provides a formal tool for studying the reliability of transmission with high statistical accuracy under typical in vivo recording conditions.

Spike Transmission Delay at the Calyx of Held In Vivo: Rate Dependence, Phenomenological Modeling, and Relevance for Sound Localization

Transmission at central synapses exhibits rapid changes in response amplitude under different patterns of stimulation. Whether the delay associated with the transmission of action potentials is similarly modifiable is important for temporally precise computations. We address this question at the calyx of Held of the medial nucleus of the trapezoid body (MNTB) in Mongolian gerbils in vivo using extracellular recordings. Here the pre- and postsynaptic activity can be observed simultaneously, allowing the definition of an action potential transmission delay (ATD) from the pre- to the postsynaptic side. We find the ATD to increase as a function of spike rate (10-40%). The temporal dynamics of the ATD increase exhibit an exponential shape with activity-dependent time constants ( approximately 15-25 ms). Recovery dynamics of ATD were mono- (20-70 ms) or biexponential with fast (3-20 ms) and slow time constants (50-500 ms). Using a phenomenological model to capture ATD dynamics, we estimated DeltaATD = 5-30 micros per transmitted action potential. Using vocalizations and cage noise stimuli, we confirm that substantial changes in ATD occur in natural situations. Because the ATD changes cover the behaviorally relevant range of interaural time differences in gerbils, these results could provide constraints for models of sound localization.

A multiscale approach to modelling electrochemical processes occurring across the cell membrane with application to transmission of action potentials

By application of matched asymptotic expansions, a simplified partial differential equation (PDE) model for the dynamic electrochemical processes occurring in the vicinity of a membrane, as ions selectively permeate across it, is formally derived from the Poisson-Nernst-Planck equations of electrochemistry. It is demonstrated that this simplified model reduces itself, in the limit of a long thin axon, to the cable equation used by Hodgkin and Huxley to describe the propagation of action potentials in the unmyelinated squid giant axon. The asymptotic reduction from the simplified PDE model to the cable equation leads to insights that are not otherwise apparent; these include an explanation of why the squid giant axon attains a diameter in the region of 1 mm. The simplified PDE model has more general application than the Hodgkin-Huxley cable equation and can, e.g. be used to describe action potential propagation in myelinated axons and neuronal cell bodies.

Odor-Evoked Oxygen Consumption by Action Potential and Synaptic Transmission in the Olfactory Bulb

The relationship between metabolism of neuronal activity, microvascular organization, and blood flow dynamics is critical for interpreting functional brain imaging. Here we used the rat dorsal olfactory bulb as a model to determine in vivo the correlation between action potential propagation, synaptic transmission, oxygen consumption, and capillary density during odor stimulation. We find that capillary lumen occupies approximately 3% of the glomerular volume, where synaptic transmission occurs, and only 0.1% of the overlying nerve layer. In glomeruli, odor triggers a local early decrease in tissue oxygen partial pressure that results principally from dendritic activation rather than from firing of axon terminals, transmitter release or astrocyte activation. In the nerve layer, action potential propagation does not generate local changes in tissue oxygen partial pressure. We conclude that capillary density is tightly correlated with the oxidative metabolism of synaptic transmission, and suggest that action potential propagation operates mainly anaerobically.