Computation of action potential propagation and presynaptic bouton activation in terminal arborizations of different geometries

Axons compensate for biophysical constraints of variable size to uniformize their action potentials

Active conductances tune the kinetics of axonal action potentials (APs) to support specialized functions of neuron types. However, the temporal characteristics of voltage signals strongly depend on the size of neuronal structures, as capacitive and resistive effects slow down voltage discharges in the membranes of small elements. Axonal action potentials are particularly sensitive to these inherent biophysical effects because of the large diameter variabilities within individual axons, potentially implying bouton size-dependent synaptic effects. However, using direct patch-clamp recordings and voltage imaging in small hippocampal axons in acute slices from rat brains, we demonstrate that AP shapes remain uniform within the same axons, even across an order of magnitude difference in caliber. Our results show that smaller axonal structures have more Kv1 potassium channels that locally re-accelerate AP repolarization and contribute to size-independent APs, while they do not preclude the plasticity of AP shapes. Thus, size-independent axonal APs ensure consistent digital signals for each synapse within axons of same types.

Functional Connectivity Favors Aberrant Visual Network c-Fos Expression Accompanied by Cortical Synapse Loss in a Mouse Model of Alzheimer's Disease

Background

While Alzheimer's disease (AD) has been extensively studied with a focus on cognitive networks, visual network dysfunction has received less attention despite compelling evidence of its significance in AD patients and mouse models. We recently reported c-Fos and synaptic dysregulation in the primary visual cortex of a pre-amyloid plaque AD-model.

Objective

We test whether c-Fos expression and presynaptic density/dynamics differ in cortical and subcortical visual areas in an AD-model. We also examine whether aberrant c-Fos expression is inherited through functional connectivity and shaped by light experience.

Methods

c-Fos+ cell density, functional connectivity, and their experience-dependent modulation were assessed for visual and whole-brain networks in both sexes of 4-6-month-old J20 (AD-model) and wildtype (WT) mice. Cortical and subcortical differences in presynaptic vulnerability in the AD-model were compared using ex vivo and in vivo imaging.

Results

Visual cortical, but not subcortical, networks show aberrant c-Fos expression and impaired experience-dependent modulation. The average functional connectivity of a brain region in WT mice significantly predicts aberrant c-Fos expression, which correlates with impaired experience-dependent modulation in the AD-model. We observed a subtle yet selective weakening of excitatory visual cortical synapses. The size distribution of cortical boutons in the AD-model is downscaled relative to those in WT mice, suggesting a synaptic scaling-like adaptation of bouton size.

Conclusions

Visual network structural and functional disruptions are biased toward cortical regions in pre-plaque J20 mice, and the cellular and synaptic dysregulation in the AD-model represents a maladaptive modification of the baseline physiology seen in WT conditions.

The structure of sensory afferent compartments in health and disease

Primary sensory neurons are a heterogeneous population of cells able to respond to both innocuous and noxious stimuli. Like most neurons they are highly compartmentalised, allowing them to detect, convey and transfer sensory information. These compartments include specialised sensory endings in the skin, the nodes of Ranvier in myelinated axons, the cell soma and their central terminals in the spinal cord. In this review, we will highlight the importance of these compartments to primary afferent function, describe how these structures are compromised following nerve damage and how this relates to neuropathic pain.

Voltage-Gated Potassium Channels Ensure Action Potential Shape Fidelity in Distal Axons

The initiation and propagation of the action potential (AP) along an axon allows neurons to convey information rapidly and across distant sites. Although AP properties have typically been characterized at the soma and proximal axon, knowledge of the propagation of APs toward distal axonal domains of mammalian CNS neurons remains limited. We used genetically encoded voltage indicators (GEVIs) to image APs with submillisecond temporal resolution simultaneously at different locations along the long axons of dissociated hippocampal neurons from rat embryos of either sex. We found that APs became sharper and showed remarkable fidelity as they traveled toward distal axons, even during a high-frequency train. Blocking voltage-gated potassium channels (Kv) with 4-AP resulted in an increase in AP width in all compartments, which was stronger at distal locations and exacerbated during AP trains. We conclude that the higher levels of Kv channel activity in distal axons serve to sustain AP fidelity, conveying a reliable digital signal to presynaptic boutons.SIGNIFICANCE STATEMENT The AP represents the electrical signal carried along axons toward distant presynaptic boutons where it culminates in the release of neurotransmitters. The nonlinearities involved in this process are such that small changes in AP shape can result in large changes in neurotransmitter release. Since axons are remarkably long structures, any distortions that APs suffer along the way have the potential to translate into a significant modulation of synaptic transmission, particularly in distal domains. To avoid these issues, distal axons have ensured that signals are kept remarkably constant and insensitive to modulation during a train, despite the long distances traveled. Here, we uncover the mechanisms that allow distal axonal domains to provide a reliable and faithful digital signal to presynaptic terminals.

The physiological function of different voltage-gated sodium channels in pain

Evidence from human genetic pain disorders shows that voltage-gated sodium channel α-subtypes Nav1.7, Nav1.8 and Nav1.9 are important in the peripheral signalling of pain. Nav1.7 is of particular interest because individuals with Nav1.7 loss-of-function mutations are congenitally insensitive to acute and chronic pain, and there is considerable hope that phenocopying these effects with a pharmacological antagonist will produce a new class of analgesic drug. However, studies in these rare individuals do not reveal how and where voltage-gated sodium channels contribute to pain signalling, which is of critical importance for drug development. More than a decade of research utilizing rodent genetic models and pharmacological tools to study voltage-gated sodium channels in pain has begun to unravel the role of different subtypes. Here, we review the contribution of individual channel subtypes in three key physiological processes necessary for transmission of sensory information to the CNS: transduction of stimuli at peripheral nerve terminals, axonal transmission of action potentials and neurotransmitter release from central terminals. These data suggest that drugs seeking to recapitulate the analgesic effects of loss of function of Nav1.7 will need to be brain-penetrant - which most of those developed to date are not.

Action potential propagation recorded from single axonal arbors using multielectrode arrays

We report the presence of co-occurring extracellular action potentials (eAPs) from cultured mouse hippocampal neurons among groups of planar electrodes on multielectrode arrays (MEAs). The invariant sequences of eAPs among coactive electrode groups, repeated co-occurrences, and short interelectrode latencies are consistent with action potential propagation in unmyelinated axons. Repeated eAP codetection by multiple electrodes was widespread in all our data records. Codetection of eAPs confirms they result from the same neuron and allows these eAPs to be isolated from all other spikes independently of spike sorting algorithms. We averaged co-occurring events and revealed additional electrodes with eAPs that would otherwise be below detection threshold. We used these eAP cohorts to explore the temperature sensitivity of action potential propagation and the relationship between voltage-gated sodium channel density and propagation velocity. The sequence of eAPs among coactive electrodes "fingerprints" neurons giving rise to these events and identifies them within neuronal ensembles. We used this property and the noninvasive nature of extracellular recording to monitor changes in excitability at multiple points in single axonal arbors simultaneously over several hours, demonstrating independence of axonal segments. Over several weeks, we recorded changes in interelectrode propagation latencies and ongoing changes in excitability in different regions of single axonal arbors. Our work illustrates how repeated eAP co-occurrences can be used to extract physiological data from single axons with low-density MEAs. However, repeated eAP co-occurrences lead to oversampling spikes from single neurons and thus can confound traditional spike-train analysis. NEW & NOTEWORTHY We studied action potential propagation in single axons using low-density multielectrode arrays. We unambiguously identified the neuronal sources of propagating action potentials and recorded extracellular action potentials from several positions within single axonal arbors. We found a surprisingly high density of axonal voltage-gated sodium channels responsible for a high propagation safety factor. Our experiments also demonstrate that excitability in different segments of single axons is regulated independently on timescales from hours to weeks.

Branching morphology determines signal propagation dynamics in neurons

Computational modeling of signal propagation in neurons is critical to our understanding of basic principles underlying brain organization and activity. Exploring these models is used to address basic neuroscience questions as well as to gain insights for clinical applications. The seminal Hodgkin Huxley model is a common theoretical framework to study brain activity. It was mainly used to investigate the electrochemical and physical properties of neurons. The influence of neuronal structure on activity patterns was explored, however, the rich dynamics observed in neurons with different morphologies is not yet fully understood. Here, we study signal propagation in fundamental building blocks of neuronal branching trees, unbranched and branched axons. We show how these simple axonal elements can code information on spike trains, and how asymmetric responses can emerge in axonal branching points. This asymmetric phenomenon has been observed experimentally but until now lacked theoretical characterization. Together, our results suggest that axonal morphological parameters are instrumental in activity modulation and information coding. The insights gained from this work lay the ground for better understanding the interplay between function and form in real-world complex systems. It may also supply theoretical basis for the development of novel therapeutic approaches to damaged nervous systems.

Synapse-Level Determination of Action Potential Duration by K(+) Channel Clustering in Axons

In axons, an action potential (AP) is thought to be broadcast as an unwavering binary pulse over its arbor, driving neurotransmission uniformly at release sites. Yet by recording from axons of cerebellar stellate cell (SC) interneurons, we show that AP width varies between presynaptic bouton sites, even within the same axon branch. The varicose geometry of SC boutons alone does not impose differences in spike duration. Rather, axonal patching revealed heterogeneous peak conductance densities of currents mediated mainly by fast-activating Kv3-type potassium channels, with clustered hotspots at boutons and restricted expression at adjoining shafts. Blockade of Kv channels at individual boutons indicates that currents immediately local to a release site direct spike repolarization at that location. Thus, the clustered arrangement and variable expression density of Kv3 channels at boutons are key determinants underlying compartmentalized control of AP width in a near synapse-by-synapse manner, multiplying the signaling capacity of these structures.

Identifying critical regions for spike propagation in axon segments

Morphological reconstructions of axon segments reveal the abundance of geometrical ultrastructures that can dramatically affect the propagation of Action Potentials (AP). Moreover, deformations and swellings in axons resulting from brain traumas are associated to many neural dysfunctions and disorders. Our aim is to develop a computational framework to distinguish between geometrical enlargements that lead to minor changes in propagation from those that result in critical phenomenon such as reflection or blockage of the original traveling spike. We use a few geometrical parameters to model a prototypical shaft enlargement and explore the parameter space characterizing all possible propagation regimes and dynamics in an unmylienated AP model. Contrary to earlier notions that large diameter increases mostly lead to blocking, we demonstrate transmission is stable provided the geometrical changes occur in a slow manner. Our method also identifies a narrow range of parameters leading to a reflection regime. The distinction between these three regimes can be evaluated by a simple function of the geometrical parameters inferred through numerical simulations. We suggest that evaluating this function along axon segments can detect regions most susceptible to (i) transmission failure due to perturbations, (ii) structural plasticity, (iii) critical swellings caused by brain traumas and/or (iv) neurological disorders associated with the break down of spike train propagation.

Spine calcium transients induced by synaptically-evoked action potentials can predict synapse location and establish synaptic democracy

CA1 pyramidal neurons receive hundreds of synaptic inputs at different distances from the soma. Distance-dependent synaptic scaling enables distal and proximal synapses to influence the somatic membrane equally, a phenomenon called “synaptic democracy”. How this is established is unclear. The backpropagating action potential (BAP) is hypothesised to provide distance-dependent information to synapses, allowing synaptic strengths to scale accordingly. Experimental measurements show that a BAP evoked by current injection at the soma causes calcium currents in the apical shaft whose amplitudes decay with distance from the soma. However, in vivo action potentials are not induced by somatic current injection but by synaptic inputs along the dendrites, which creates a different excitable state of the dendrites. Due to technical limitations, it is not possible to study experimentally whether distance information can also be provided by synaptically-evoked BAPs. Therefore we adapted a realistic morphological and electrophysiological model to measure BAP-induced voltage and calcium signals in spines after Schaffer collateral synapse stimulation. We show that peak calcium concentration is highly correlated with soma-synapse distance under a number of physiologically-realistic suprathreshold stimulation regimes and for a range of dendritic morphologies. Peak calcium levels also predicted the attenuation of the EPSP across the dendritic tree. Furthermore, we show that peak calcium can be used to set up a synaptic democracy in a homeostatic manner, whereby synapses regulate their synaptic strength on the basis of the difference between peak calcium and a uniform target value. We conclude that information derived from synaptically-generated BAPs can indicate synapse location and can subsequently be utilised to implement a synaptic democracy.

Neurons receive information from other neurons via hundreds of contacts (synapses) spread across their dendritic branches. Input signals from synapses propagate along a dendrite to the cell body (soma), where the neuron decides whether or not to produce an action potential. Signals that travel further decay more. Were all synapses equally strong, a synapse far from the soma would have less influence on the decision than a synapse close by. However, neurons in the hippocampus, which are involved in learning and memory, have synapses far from the soma that are stronger than those close by, so that all synapses have an equal voice (“synaptic democracy”). But how can a synapse “know” how far it is from the soma? Using a computational model of a hippocampal neuron, we show that the action potential, which propagates from the soma back into the dendrites, contains information with which synapses can estimate their somatic distance. Specifically, the calcium concentration at the synapse, which is modulated by the backpropagating action potential, decreases with distance from the soma. We show that when the strength of a synapse is adapted in a self-organising manner based on calcium concentration, synaptic democracy is obtained.

Cholesterol-independent effects of methyl-β-cyclodextrin on chemical synapses

The cholesterol chelating agent, methyl-β-cyclodextrin (MβCD), alters synaptic function in many systems. At crayfish neuromuscular junctions, MβCD is reported to reduce excitatory junctional potentials (EJPs) by impairing impulse propagation to synaptic terminals, and to have no postsynaptic effects. We examined the degree to which physiological effects of MβCD correlate with its ability to reduce cholesterol, and used thermal acclimatization as an alternative method to modify cholesterol levels. MβCD impaired impulse propagation and decreased EJP amplitude by 40% (P<0.05) in preparations from crayfish acclimatized to 14 °C but not from those acclimatized to 21 °C. The reduction in EJP amplitude in the cold-acclimatized group was associated with a 49% reduction in quantal content (P<0.05). MβCD had no effect on input resistance in muscle fibers but decreased sensitivity to the neurotransmitter L-glutamate in both warm- and cold-acclimatized groups. This effect was less pronounced and reversible in the warm-acclimatized group (90% reduction in cold, P<0.05; 50% reduction in warm, P<0.05). MβCD reduced cholesterol in isolated nerve and muscle from cold- and warm-acclimatized groups by comparable amounts (nerve: 29% cold, 25% warm; muscle: 20% cold, 18% warm; P<0.05). This effect was reversed by cholesterol loading, but only in the warm-acclimatized group. Thus, effects of MβCD on glutamate-sensitivity correlated with its ability to reduce cholesterol, but effects on impulse propagation and resulting EJP amplitude did not. Our results indicate that MβCD can affect both presynaptic and postsynaptic properties, and that some effects of MβCD are unrelated to cholesterol chelation.

Axon Physiology

Axons are generally considered as reliable transmission cables in which stable propagation occurs once an action potential is generated. Axon dysfunction occupies a central position in many inherited and acquired neurological disorders that affect both peripheral and central neurons. Recent findings suggest that the functional and computational repertoire of the axon is much richer than traditionally thought. Beyond classical axonal propagation, intrinsic voltage-gated ionic currents together with the geometrical properties of the axon determine several complex operations that not only control signal processing in brain circuits but also neuronal timing and synaptic efficacy. Recent evidence for the implication of these forms of axonal computation in the short-term dynamics of neuronal communication is discussed. Finally, we review how neuronal activity regulates both axon morphology and axonal function on a long-term time scale during development and adulthood.

Multiple spike initiation zones in a neuron implicated in learning in the leech: a computational model

Sensitization of the defensive shortening reflex in the leech has been linked to a segmentally repeated tri-synaptic positive feedback loop. Serotonin from the R-cell enhances S-cell excitability, S-cell impulses cross an electrical synapse into the C-interneuron, and the C-interneuron excites the R-cell via a glutamatergic synapse. The C-interneuron has two unusual characteristics. First, impulses take longer to propagate from the S soma to the C soma than in the reverse direction. Second, impulses recorded from the electrically unexcitable C soma vary in amplitude when extracellular divalent cation concentrations are elevated, with smaller impulses failing to induce synaptic potentials in the R-cell. A compartmental, computational model was developed to test the sufficiency of multiple, independent spike initiation zones in the C-interneuron to explain these observations. The model displays asymmetric delays in impulse propagation across the S-C electrical synapse and graded impulse amplitudes in the C-interneuron in simulated high divalent cation concentrations.

The H-current secures action potential transmission at high frequencies in rat cerebellar parallel fibers

Most axons in the mammalian brain are unmyelinated and thin with pre-synaptic specializations (boutons) along their entire paths. The parallel fibers in the cerebellum are examples of such axons. Unlike most thin axons they have only one branch point. The granule cell soma, where they originate, can fire bursts of action potentials with spike intervals of about 2 ms. An important question is whether the axons are able to propagate spikes with similarly short intervals. By using extracellular single-unit and population-recording methods we showed that parallel fibers faithfully conduct spikes at high frequencies over long distances. However, when adding 20 microm ZD7288 or 1 mm Cs(+), or reducing the temperature from 35 to 24 degrees C, the action potentials often failed even when successfully initiated. Ba(2+)(1 mm), which blocks Kir channels, did not reproduce these effects. The conduction velocity was reduced by ZD7288 but not by Ba(2+). This suggests that the parallel fibers have an H-current that is active at rest and that is important for their frequency-following properties. Interestingly, failures occurred only when the action potential had to traverse the axonal branch point, suggesting that the branch point is the weakest point in these axons.

Fidelity of complex spike-mediated synaptic transmission between inhibitory interneurons

Complex spikes are high-frequency bursts of Na+ spikes, often riding on a slower Ca2+-dependent waveform. Although complex spikes may propagate into axons, given their unusual shape it is not clear how reliably these bursts reach nerve terminals, whether their spikes are efficiently transmitted as a cluster of postsynaptic responses, or what function is served by such a concentrated postsynaptic signal. We examined these questions by recording from synaptically coupled pairs of cartwheel cells, neurons which fire complex spikes and form an inhibitory network in the dorsal cochlear nucleus. Complex spikes in the presynaptic soma were reliably propagated to nerve terminals and elicited powerful, temporally precise postsynaptic responses. Single presynaptic neurons could prevent their postsynaptic partner from firing complex but not simple spikes, dramatically reducing dendritic Ca2+ signals in the postsynaptic neuron. We suggest that rapid transmission of complex spikes may control the susceptibility of neighboring neurons to Ca2+-dependent plasticity.

Electrophysiological events recorded at presynaptic terminals of the crayfish neuromuscular junction with a voltage indicator

The water-soluble voltage indicator JPW1114 was used to stain thin axons and terminal varicosities of the crayfish neuromuscular junction. A slow, overnight injection protocol was developed to brightly stain fine structures without cytotoxicity. Fluorescence transients filtered at 2 kHz showed that the duration of terminal action potentials was shorter than that of those recorded in the main trunk of the axons. In addition, the repolarization phases of the terminal and axonal action potentials overlapped in time, suggesting that the entire axonal arborization repolarizes simultaneously. Manipulating resting membrane potential, +/-15-20 mV, did not alter the peak level or duration of action potentials if they fired in isolation. A prolongation of action potential, by 23%, could be induced if a 10-spike burst at 100 Hz was fired from depolarized membrane potential. No such change was observed when the high frequency train was fired from resting or hyperpolarized levels. Microelectrodes in the main trunk of axons typically recorded a depolarizing after-potential (DAP) following an action potential initiated from resting membrane potential. The DAP could be inverted and enlarged by depolarization and hyperpolarization, respectively. Fluorescence transients recorded from terminals exhibited similar DAP characteristics. The ratio of DAP to action potential amplitude recorded from terminals was similar to that recorded from the main axon. Thus, the entire axonal arborization returned to resting level in a spatially uniform manner during the DAP. The functional significance of DAP is discussed in the light of these observations.

Three-dimensional reconstruction of the axon arbor of a CA3 pyramidal cell recorded and filled in vivo

The three-dimensional intrahippocampal distribution of axon collaterals of an in vivo filled CA3c pyramidal cell was investigated. The neuron was filled with biocytin in an anesthetized rat and the collaterals were reconstructed with the aid of a NeuroLucida program from 48 coronal sections. The total length of the axon collaterals exceeded 0.5 m, with almost 40,000 synaptic boutons. The majority of the collaterals were present in the CA1 region (70.0%), whereas 27.6% constituted CA3 recurrent collaterals with the remaining minority of axons returning to the dentate gyrus. The axon arbor covered more than two thirds of the longitudinal axis of the hippocampus, and the terminals were randomly distributed both locally and distally from the soma. We suggest that the CA3 system can be conceptualized as a single-module, in which nearby and distant targets are contacted by the same probability (similar to a mathematically defined random graph). This arrangement, in combination with the parallel input granule cells and parallel output CA1 pyramidal cells, appears ideal for segregation and integration of information and memories.

Coding with spike shapes and graded potentials in cortical networks

In cortical neurones, analogue dendritic potentials are thought to be encoded into patterns of digital spikes. According to this view, neuronal codes and computations are based on the temporal patterns of spikes: spike times, bursts or spike rates. Recently, we proposed an 'action potential waveform code' for cortical pyramidal neurones in which the spike shape carries information. Broader somatic action potentials are reliably produced in response to higher conductance input, allowing for four times more information transfer than spike times alone. This information is preserved during synaptic integration in a single neurone, as back-propagating action potentials of diverse shapes differentially shunt incoming postsynaptic potentials and so participate in the next round of spike generation. An open question has been whether the information in action potential waveforms can also survive axonal conduction and directly influence synaptic transmission to neighbouring neurones. Several new findings have now brought new light to this subject, showing cortical information processing that transcends the classical models.

Simulator for neural networks and action potentials

A key challenge for neuroinformatics is to devise methods for representing, accessing, and integrating vast amounts of diverse and complex data. A useful approach to represent and integrate complex data sets is to develop mathematical models [Arbib (The Handbook of Brain Theory and Neural Networks, pp. 741-745, 2003); Arbib and Grethe (Computing the Brain: A Guide to Neuroinformatics, 2001); Ascoli (Computational Neuroanatomy: Principles and Methods, 2002); Bower and Bolouri (Computational Modeling of Genetic and Biochemical Networks, 2001); Hines et al. (J. Comput. Neurosci. 17, 7-11, 2004); Shepherd et al. (Trends Neurosci. 21, 460-468, 1998); Sivakumaran et al. (Bioinformatics 19, 408-415, 2003); Smolen et al. (Neuron 26, 567-580, 2000); Vadigepalli et al. (OMICS 7, 235-252, 2003)]. Models of neural systems provide quantitative and modifiable frameworks for representing data and analyzing neural function. These models can be developed and solved using neurosimulators. One such neurosimulator is simulator for neural networks and action potentials (SNNAP) [Ziv (J. Neurophysiol. 71, 294-308, 1994)]. SNNAP is a versatile and user-friendly tool for developing and simulating models of neurons and neural networks. SNNAP simulates many features of neuronal function, including ionic currents and their modulation by intracellular ions and/or second messengers, and synaptic transmission and synaptic plasticity. SNNAP is written in Java and runs on most computers. Moreover, SNNAP provides a graphical user interface (GUI) and does not require programming skills. This chapter describes several capabilities of SNNAP and illustrates methods for simulating neurons and neural networks. SNNAP is available at http://snnap.uth.tmc.edu .

Three dimensional transport lattice model for describing action potentials in axons stimulated by external electrodes

Conditions that stimulate action potentials in one or more nerves is of widespread interest. Axon and nerve models are usually based on two dimensional pre-specified lumped equivalents that assume where currents will flow. In contrast, here we illustrate creation of three dimensional (3D) system models with a transport lattice of interconnected local models for external and internal electrolyte and axon membrane. The transport lattice solves Laplace's equation in the extracellular medium and is coupled to the Hodgkin-Huxley model at local membrane sites. These space-filling models incorporate the geometric scale, which allows explicit representation of confined axons and external electrodes. The present results demonstrate feasibility of the basic approach. These models are spatially coarse and approximate, but can be straightforwardly improved. The transport lattice system models are modular and multiscale (spatial scales ranging from the membrane thickness of 5 nm to the axon segment length of 2 cm).

Homeostatic regulation of glutamate release in response to depolarization

Proper nervous system function requires a balance between excitation and inhibition. Systems of homeostasis may have evolved in neurons to help maintain or restore balance between excitation and inhibition, presumably because excessive excitation can cause dysfunction and cell death. This article reviews evidence for homeostatic mechanisms within the hippocampus that lead to differential regulation of glutamate and gamma-aminobutyric acid release in response to conditions of excess depolarization. We recently found differential effects on glutamate release at the level of action potential coupling to transmitter release, vesicular release probability, and vesicle availability. Such differential regulation may help to prevent excitotoxicity and runaway excitation.

Rallian "equivalent" cylinders reconsidered: comparisons with literal compartments

In Rall's "equivalent" cylinder morphological-to-electrical transformation, neuronal arborizations are reduced to single unbranched core-conductors. The conventional assumption that such an "equivalent" reconstructs the electrical properties of the fibers it represents was tested directly; electrical properties and responses of "equivalent" cylinders were compared with those of their literal branch constituents for fibers with a single symmetrical bifurcation. The numerical solution methods were validated independently by their accurate reconstruction of the responses of an analog circuit configured with compartmental architecture to solve the cable equation for passive fibers with a symmetrical bifurcation. In passive fibers, "equivalent" cylinders misestimated the spatial distribution of voltage amplitudes and steady-state input resistance, partly due to the lack of axial current bifurcation. In active fibers with a single propagating action potential, the spatial distributions of point-to-point conduction velocity values (measured in meters/second) for a literal branch point differed significantly from those of their "equivalent" cylinders. "Equivalent" cylinders also underestimated the diameter-dependent delay in propagation through the branch point and branches, due to the larger "equivalent" diameter. Corrections to the "equivalent" cylinder did not reconcile differences between "equivalent" and literal models. However, "equivalent" and literal branch fibers had the same (a) steady-state resistance "looking into" an isolated symmetrical branch point and (b) geometry-independent point-to-point propagation velocity when measured in space constants per millisecond except within +/-1 space constant from the geometrical inhomogeneity. In summary, Rall's "equivalent" cylinders did not accurately reconstruct all passive or active electrophysiological properties and responses of their literal compartments. For the modeling of individual neurons, the requirement of single-branch resolution is discussed.

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.

Presynaptic K+ channels: electrifying regulators of synaptic terminal excitability

Potassium channels are crucial regulators of neuronal excitability, setting resting membrane potentials and firing thresholds, repolarizing action potentials and limiting excitability. Although most of our understanding of K+ channels is based on somatic recordings, there is good evidence that these channels are present in synaptic terminals. In recent years the improved access to presynaptic compartments afforded by direct recording techniques has indicated diverse roles for native K+ channels, from suppression of aberrant firing to action potential repolarization and activity-dependent modulation of synaptic activity. This article reviews the growing evidence for multiple roles and discrete localization of distinct K+ channels at presynaptic terminals.

Activity-dependent increase of the AHP amplitude in T sensory neurons of the leech

We identified a new form of activity-dependent modulation of the afterhyperpolarization (AHP) in tactile (T) sensory neurons of the leech Hirudo medicinalis. Repetitive intracellular stimulation with 30 trains of depolarizing impulses at 15-s inter-stimulus interval (ISI) led to an increase of the AHP amplitude (~60% of the control). The enhancement of AHP lasted for >/=15 min. The AHP increase was also elicited when a T neuron was activated by repetitive stimulation of its receptive field. The ISI was a critical parameter for the induction and maintenance of AHP enhancement. ISI duration had to fit within a time window with the upper limit of 20 s to make the training effective to induce an enhancement of the AHP amplitude. After recovery from potentiation, AHP amplitude could be enhanced once again by delivering another training session. The increase of AHP amplitude persisted in high Mg(2+) saline, suggesting an intrinsic cellular mechanism for its induction. Previous investigations reported that AHP of leech T neurons was mainly due to the activity of the Na(+)/K(+) ATPase and to a Ca(2+)-dependent K(+) current (I(K/Ca)). In addition, it has been demonstrated that serotonin (5HT) reduces AHP amplitude through the inhibition of the Na(+)/K(+) ATPase. By blocking the I(K/Ca) with pharmacological agents, such as cadmium and apamin, we still observed an increase of the AHP amplitude after repetitive stimulation, whereas 5HT application completely inhibited the AHP increment. These data indicate that the Na(+)/K(+) ATPase is involved in the induction and maintenance of the AHP increase after repetitive stimulation. Moreover, the AHP increase was affected by the level of serotonin in the CNS. Finally, the increase of the AHP amplitude produced a lasting depression of the synaptic connection between two T neurons, suggesting that this activity-dependent phenomenon might be involved in short-term plasticity associated with learning processes.

The use of elevated divalent cation solutions to isolate monosynaptic components of sensorimotor connections in Aplysia

A commonly used method to remove polysynaptic components of test PSPs is to elevate action potential threshold of interneurons with high extracellular concentrations of divalent cations ('Hi-Di'). Extrapolation to normal conditions requires that Hi-Di have negligible effects on synaptic transmission. We examined effects of Hi-Di on EPSPs from sensory neurons (SNs) onto motor neurons (MNs) of Aplysia in the pleural-pedal and abdominal ganglia, and in dissociated cell culture. In ganglia, standard Hi-Di solutions eliminated spontaneous input from interneurons as well as polysynaptic components of PSPs evoked by single action potentials in single SNs, but failed to block polysynaptic PSPs evoked by nerve stimulation. Hi-Di solutions had no effect on activity-dependent synaptic depression or posttetanic potentiation, or facilitation by serotonin (5-HT). Unexpectedly, standard Hi-Di solutions substantially reduced sensorimotor EPSPs in all preparations, whereas a solution containing 2.2x[Ca(2+)] and 2x[Mg(2+)] blocked the polysynaptic component of EPSPs without obvious changes to the monosynaptic component. In contrast to previous observations in Aplysia, and to predictions of the (J. Physiol. 193 (1967) 419) model, tripling the normal extracellular concentrations of Ca(2+) and Mg(2+) failed to increase sensorimotor EPSPs. Depression of EPSPs by these Hi-Di solutions may result from reduced spike invasion into presynaptic terminals.

Synaptic inhibition of pyramidal cells evoked by different interneuronal subtypes in layer v of rat visual cortex

Properties of GABA(A) receptor-mediated unitary inhibitory postsynaptic currents (uIPSCs) in pyramidal (P) cells, evoked by fast spiking (FS) and low-threshold spike (LTS) subtypes of interneurons in layer V of rat visual cortex slices were examined using dual whole cell recordings. uIPSCs evoked by FS cells were larger and faster rising than those evoked by LTS cells, consistent with the known primary projections of FS and LTS cell axons to perisomatic and distal dendritic areas of layer V pyramidal cells, respectively, and the resulting electrotonic attenuation for LTS-P synaptic events. Unexpectedly, the decay time constants for LTS-P and FS-P uIPSCs were not significantly different. Modeling results were consistent with differences in the underlying GABA(A) receptor-mediated conductance at LTS-P and FS-P synapses. Paired-pulse depression (PPD), present at both synapses, was associated with an increase in failure rate and a decrease in coefficient of variation, indicating that presynaptic mechanisms were involved. Furthermore, the second and first uIPSC amplitudes during PPD were not inversely correlated, suggesting that PPD at both synapses is independent of previous release and might not result from depletion of the releasable pool of synaptic vesicles. Short, 20-Hz trains of action potentials in presynaptic interneurons evoked trains of uIPSCs with exponentially decreasing amplitudes at both FS-P and LTS-P synapses. FS-P uIPSC amplitudes declined more slowly than those of LTS-P uIPSCs. Thus FS and LTS cells, with their differences in firing properties, synaptic connectivity with layer V P cells, and short-term synaptic dynamics, might play distinct roles in regulating the input-output relationship of the P cells.

Propagation of action potentials in dendrites depends on dendritic morphology

Action potential propagation links information processing in different regions of the dendritic tree. To examine the contribution of dendritic morphology to the efficacy of propagation, simulations were performed in detailed reconstructions of eight different neuronal types. With identical complements of voltage-gated channels, different dendritic morphologies exhibit distinct patterns of propagation. Remarkably, the range of backpropagation efficacies observed experimentally can be reproduced by the variations in dendritic morphology alone. Dendritic geometry also determines the extent to which modulation of channel densities can affect propagation. Thus in Purkinje cells and dopamine neurons, backpropagation is relatively insensitive to changes in channel densities, whereas in pyramidal cells, backpropagation can be modulated over a wide range. We also demonstrate that forward propagation of dendritically initiated action potentials is influenced by morphology in a similar manner. We show that these functional consequences of the differences in dendritic geometries can be explained quantitatively using simple anatomical measures of dendritic branching patterns, which are captured in a reduced model of dendritic geometry. These findings indicate that differences in dendritic geometry act in concert with differences in voltage-gated channel density and kinetics to generate the diversity in dendritic action potential propagation observed between neurons. They also suggest that changes in dendritic geometry during development and plasticity will critically affect propagation. By determining the spatial pattern of action potential signaling, dendritic morphology thus helps to define the size and interdependence of functional compartments in the neuron.

Calcium dynamics associated with action potentials in single nerve terminals of pyramidal cells in layer 2/3 of the young rat neocortex

Calcium dynamics associated with a single action potential (AP) were studied in single boutons of the axonal arbor of layer 2/3 pyramidal cells in the neocortex of young (P14-16) rats. We used fluorescence imaging with two-photon excitation and Ca2+-selective fluorescence indicators to measure volume-averaged Ca2+ signals. These rapidly reached a peak (in about 1 ms) and then decayed more slowly (tens to hundreds of milliseconds). Single APs and trains of APs reliably evoked Ca2+ transients in en passant boutons located on axon collaterals in cortical layers 2/3, 4 and 5, indicating that APs propagate actively and reliably throughout the axonal arbor. Branch point failures are unlikely to contribute to differences in synaptic efficacy and reliability in the connections made by layer 2/3 pyramidal cells. AP-evoked Ca2+ transients in boutons were mediated by voltage-dependent Ca2+ channels (VDCCs), predominantly by the P/Q- and N-subtypes. Ca2+ transients were, on average, of significantly larger amplitude in boutons than in the flanking segments of the axon collateral. Large amplitude Ca2+ transients in boutons were spatially restricted to within <= 3 m of axonal length. Single AP-evoked Ca2+ transients varied up to 10-fold across different boutons even if they were located on the same axon collateral. In contrast, variation of Ca2+ transients evoked by successive APs in a given single bouton was small (coefficient of variation, c.v. <= 0.21). Amplitudes of AP-evoked Ca2+ signals did not correlate with the distance of boutons from the soma. In contrast, AP-evoked Ca2+ signals in spines of basal dendrites decreased slightly (correlation coefficient, r2 = -0.27) with distance from the soma. Measurements with the low-affinity Ca2+ indicator Magnesium Green suggest that the volume-averaged residual free [Ca2+]i in a bouton increases on average by 500 nM following a single AP. Higher concentrations of indicator caused, on average, a decrease in the amplitude and an increase in the decay time constant of Ca2+ transients. Assuming a single-compartment model the concentration dependence of decay time constants suggests a low endogenous Ca2+ binding ratio close to 140, indicating that of the total Ca2+ influx ( approximately 2 fC) less than 1% remained free. The indicator concentration dependence of decay time constants further suggests that the residual free Delta[Ca2+]i associated with an AP decays with a time constant of about 60 ms (35 C) reflecting a high Ca2+ extrusion rate of about 2600 s(-1). The results show that AP-evoked volume-averaged Ca2+ transients in single boutons are evoked reliably and, on average, have larger amplitudes than Ca2+ transients in other subcellular compartments of layer 2/3 pyramidal cells. A major functional signature is the large variation in the amplitude of Ca2+ transients between different boutons. This could indicate that local interactions between boutons and different target cells modify the spatiotemporal Ca2+ dynamics in boutons and cause target cell-specific differences in their transmitter release properties.

Calcium dynamics associated with action potentials in single nerve terminals of pyramidal cells in layer 2/3 of the young rat neocortex

Calcium dynamics associated with a single action potential (AP) were studied in single boutons of the axonal arbor of layer 2/3 pyramidal cells in the neocortex of young (P14-16) rats. We used fluorescence imaging with two-photon excitation and Ca2+-selective fluorescence indicators to measure volume-averaged Ca2+ signals. These rapidly reached a peak (in about 1 ms) and then decayed more slowly (tens to hundreds of milliseconds). Single APs and trains of APs reliably evoked Ca2+ transients in en passant boutons located on axon collaterals in cortical layers 2/3, 4 and 5, indicating that APs propagate actively and reliably throughout the axonal arbor. Branch point failures are unlikely to contribute to differences in synaptic efficacy and reliability in the connections made by layer 2/3 pyramidal cells. AP-evoked Ca2+ transients in boutons were mediated by voltage-dependent Ca2+ channels (VDCCs), predominantly by the P/Q- and N-subtypes. Ca2+ transients were, on average, of significantly larger amplitude in boutons than in the flanking segments of the axon collateral. Large amplitude Ca2+ transients in boutons were spatially restricted to within <= 3 m of axonal length. Single AP-evoked Ca2+ transients varied up to 10-fold across different boutons even if they were located on the same axon collateral. In contrast, variation of Ca2+ transients evoked by successive APs in a given single bouton was small (coefficient of variation, c.v. <= 0.21). Amplitudes of AP-evoked Ca2+ signals did not correlate with the distance of boutons from the soma. In contrast, AP-evoked Ca2+ signals in spines of basal dendrites decreased slightly (correlation coefficient, r2 = -0.27) with distance from the soma. Measurements with the low-affinity Ca2+ indicator Magnesium Green suggest that the volume-averaged residual free [Ca2+]i in a bouton increases on average by 500 nM following a single AP. Higher concentrations of indicator caused, on average, a decrease in the amplitude and an increase in the decay time constant of Ca2+ transients. Assuming a single-compartment model the concentration dependence of decay time constants suggests a low endogenous Ca2+ binding ratio close to 140, indicating that of the total Ca2+ influx ( approximately 2 fC) less than 1% remained free. The indicator concentration dependence of decay time constants further suggests that the residual free Delta[Ca2+]i associated with an AP decays with a time constant of about 60 ms (35 C) reflecting a high Ca2+ extrusion rate of about 2600 s(-1). The results show that AP-evoked volume-averaged Ca2+ transients in single boutons are evoked reliably and, on average, have larger amplitudes than Ca2+ transients in other subcellular compartments of layer 2/3 pyramidal cells. A major functional signature is the large variation in the amplitude of Ca2+ transients between different boutons. This could indicate that local interactions between boutons and different target cells modify the spatiotemporal Ca2+ dynamics in boutons and cause target cell-specific differences in their transmitter release properties.

Neurochemical and electrophysiological studies on the functional significance of burst firing in serotonergic neurons

We have previously described a population of 5-hydroxytryptamine neurons which repetitively fires bursts of usually two (but occasionally three or four) action potentials, with a short (<20 ms) interspike interval within a regular low-frequency firing pattern. Here we used a paradigm of electrical stimulation comprising twin pulses (with 7- or 10-ms inter-pulse intervals) to mimic this burst firing pattern, and compared the effects of single- and twin-pulse electrical stimulations in models of pre- and postsynaptic 5-hydroxytryptamine function. Firstly, we measured the effect of direct electrical stimulation (2 Hz for 2 min) of rat brain slices on efflux of preloaded [3H]5-hydroxytryptamine. In this in vitro model, twin-pulse stimulation increased the efflux of tritium by about twice as much as did single-pulse stimulation. This effect was evident in the medial prefrontal cortex (area under the curve: 2. 59+/-0.34 vs 1.28+/-0.22% relative fractional release), as well as in the caudate-putamen (3.93+/-0.65 vs 2.17+/-0.51%) and midbrain raphe nuclei (5.42+/-1.05 vs 2.51+/-0.75%). Secondly, we used in vivo microdialysis to monitor changes in endogenous extracellular 5-hydroxytryptamine in rat medial prefrontal cortex in response to electrical stimulation (3 Hz for 10 min) of the dorsal raphe nucleus. In this model, twin-pulse stimulation of the dorsal raphe nucleus increased 5-hydroxytryptamine by approximately twice as much as did single-pulse stimulation at the same frequency (area under the curve: 50.4+/-9.0 vs 24.2+/-4.4 fmol). Finally, we used in vivo extracellular recording to follow the response of postsynaptic neurons in the rat medial prefrontal cortex to 5-hydroxytryptamine released by dorsal raphe stimulation. Electrical stimulation of the dorsal raphe nucleus (1 Hz) induced a clear-cut poststimulus inhibition in the majority of cortical neurons tested. In these experiments, the duration of poststimulus inhibition following twin-pulse stimulation was markedly longer than that induced by single-pulse stimulation (200+/-21 vs 77+/-18.5 ms). Taken together, the present in vitro and in vivo data suggest that in 5-hydroxytryptamine neurons, short bursts of action potentials will propagate along the axon to the nerve terminal and will enhance both the release of 5-hydroxytryptamine and its postsynaptic effect.

Efficacy and stability of quantal GABA release at a hippocampal interneuron-principal neuron synapse

We have examined factors that determine the strength and dynamics of GABAergic synapses between interneurons [dentate gyrus basket cells (BCs)] and principal neurons [dentate gyrus granule cells (GCs)] using paired recordings in rat hippocampal slices at 34 degrees C. Unitary IPSCs recorded from BC-GC pairs in high intracellular Cl(-) concentration showed a fast rise and a biexponential decay, with mean time constants of 2 and 9 msec. The mean quantal conductance change, determined directly at reduced extracellular Ca(2+)/Mg(2+) concentration ratios, was 1.7 nS. Quantal release at the BC-GC synapse occurred with short delay and was highly synchronized. Analysis of IPSC peak amplitudes and numbers of failures by multiple probability compound binomial analysis indicated that synaptic transmission at the BC-GC synapse involves three to seven release sites, each of which releases transmitter with high probability ( approximately 0.5 in 2 mm Ca(2+)/1 mm Mg(2+)). Unitary BC-GC IPSCs showed paired-pulse depression (PPD); maximal depression, measured for 10 msec intervals, was 37%, and recovery from depression occurred with a time constant of 2 sec. Paired-pulse depression was mainly presynaptic in origin but appeared to be independent of previous release. Synaptic transmission at the BC-GC synapse showed frequency-dependent depression, with half-maximal decrease at 5 Hz after a series of 1000 presynaptic action potentials. The relative stability of transmission at the BC-GC synapse is consistent with a model in which an activity-dependent gating mechanism reduces release probability and thereby prevents depletion of the releasable pool of synaptic vesicles. Thus several mechanisms converge on the generation of powerful and sustained transmission at interneuron-principal neuron synapses in hippocampal circuits.

Efficacy and stability of quantal GABA release at a hippocampal interneuron-principal neuron synapse

We have examined factors that determine the strength and dynamics of GABAergic synapses between interneurons [dentate gyrus basket cells (BCs)] and principal neurons [dentate gyrus granule cells (GCs)] using paired recordings in rat hippocampal slices at 34 degrees C. Unitary IPSCs recorded from BC-GC pairs in high intracellular Cl(-) concentration showed a fast rise and a biexponential decay, with mean time constants of 2 and 9 msec. The mean quantal conductance change, determined directly at reduced extracellular Ca(2+)/Mg(2+) concentration ratios, was 1.7 nS. Quantal release at the BC-GC synapse occurred with short delay and was highly synchronized. Analysis of IPSC peak amplitudes and numbers of failures by multiple probability compound binomial analysis indicated that synaptic transmission at the BC-GC synapse involves three to seven release sites, each of which releases transmitter with high probability ( approximately 0.5 in 2 mm Ca(2+)/1 mm Mg(2+)). Unitary BC-GC IPSCs showed paired-pulse depression (PPD); maximal depression, measured for 10 msec intervals, was 37%, and recovery from depression occurred with a time constant of 2 sec. Paired-pulse depression was mainly presynaptic in origin but appeared to be independent of previous release. Synaptic transmission at the BC-GC synapse showed frequency-dependent depression, with half-maximal decrease at 5 Hz after a series of 1000 presynaptic action potentials. The relative stability of transmission at the BC-GC synapse is consistent with a model in which an activity-dependent gating mechanism reduces release probability and thereby prevents depletion of the releasable pool of synaptic vesicles. Thus several mechanisms converge on the generation of powerful and sustained transmission at interneuron-principal neuron synapses in hippocampal circuits.

Visual inter-hemispheric processing: constraints and potentialities set by axonal morphology

The largest bundle of axonal fibers in the entire mammalian brain, namely the corpus callosum, is the pathway through which almost half a billion neurons scattered over all neocortical areas can exert an influence on their contralateral targets. These fibers are thus crucial participants in the numerous cortical functions requiring collaborative processing of information across the hemispheres. One of such operations is to combine the two partial cortical maps of the visual field into a single, coherent representation. This paper reviews recent anatomical, computational and electrophysiological studies on callosal connectivity in the cat visual system. We analyzed the morphology of individual callosal axons linking primary visual cortices using three-dimensional light-microscopic techniques. While only a minority of callosal axons seem to perform a strict 'point-to-point' mapping between retinotopically corresponding sites in both hemispheres, many others have widespread arbors and terminate into a handful of distant, radially oriented tufts. Therefore, the firing of a single callosal neuron might influence several cortical columns within the opposite hemisphere. Computer simulation was then applied to investigate how the intricate geometry of these axons might shape the spatio-temporal distribution of trans-callosal inputs. Based on the linear relation between diameter and conduction velocity of myelinated fibers, the theoretical delays required for a single action potential to reach all presynaptic boutons of a given arbor were derived from the caliber, g-ratio and length of successive axonal segments. This analysis suggests that the architecture of callosal axons is, in principle, suitable to promote the synchronous activation of multiple targets located across distant columns in the opposite hemisphere. Finally, electrophysiological recordings performed in several laboratories have shown the existence of stimulus-dependent synchronization of visual responses across the two hemispheres. Possible implications of these findings are discussed in the context of temporal tagging of neuronal assemblies.

Transmitter release modulation in nerve terminals of rat neocortical pyramidal cells by intracellular calcium buffers

1. Dual whole-cell voltage recordings were made from synaptically connected layer 5 (L5) pyramidal neurones in slices of the young (P14-P16) rat neocortex. The Ca2+ buffers BAPTA or EGTA were loaded into the presynaptic neurone via the pipette recording from the presynaptic neurone to examine their effect on the mean and the coefficient of variation (c.v.) of single fibre EPSP amplitudes, referred to as unitary EPSPs. 2. The fast Ca2+ buffer BAPTA reduced unitary EPSP amplitudes in a concentration dependent way. With 0.1 mM BAPTA in the pipette, the mean EPSP amplitude was reduced by 14 +/- 2.8% (mean +/- s.e.m., n = 7) compared with control pipette solution, whereas with 1.5 mM BAPTA, the mean EPSP amplitude was reduced by 72 +/- 1.5% (n = 5). The concentration of BAPTA that reduced mean EPSP amplitudes to one-half of control was close to 0.7 mM. 3. Saturation of BAPTA during evoked release was tested by comparing the effect of loading the presynaptic neurone with 0.1 mM BAPTA at 2 and 1 mM [Ca2+]o. Reducing [Ca2+]o from 2 to 1 mM, thereby reducing Ca2+ influx into the terminals, decreased the mean EPSP amplitude by 60 +/- 2.2% with control pipette solution and by 62 +/- 1.9% after loading with 0.1 mM BAPTA (n = 7). 4. The slow Ca2+ buffer EGTA at 1 mM reduced mean EPSP amplitudes by 15 +/- 2.5% (n = 5). With 10 mM EGTA mean EPSP amplitudes were reduced by 56 +/- 2.3 % (n = 4). 5. With both Ca2+ buffers, the reduction in mean EPSP amplitudes was associated with an increase in the c.v. of peak EPSP amplitudes, consistent with a reduction of the transmitter release probability as the major mechanism underlying the reduction of the EPSP amplitude. 6. The results suggest that in nerve terminals of thick tufted L5 pyramidal cells the endogenous mobile Ca2+ buffer is equivalent to less than 0.1 mM BAPTA and that at many release sites of pyramidal cell terminals the Ca2+ channel domains overlap, a situation comparable with that at large calyx-type terminals in the brainstem.

Modeling action potential initiation and back-propagation in dendrites of cultured rat motoneurons

Regardless of the site of current injection, action potentials usually originate at or near the soma and propagate decrementally back into the dendrites. This phenomenon has been observed in neocortical pyramidal cells as well as in cultured motoneurons. Here we show that action potentials in motoneurons can be initiated in the dendrite as well, resulting in a biphasic dendritic action potential. We present a model of spinal motoneurons that is consistent with observed physiological properties of spike initiation in the initial segment/axon hillock region and action potential back-propagation into the dendritic tree. It accurately reproduces the results presented by Larkum et al. on motoneurons in organotypic rat spinal cord slice cultures. A high Na+-channel density of Na = 700 mS/cm2 at the axon hillock/initial segment region was required to secure antidromic invasion of the somato-dendritic membrane, whereas for the orthodromic direction, a Na+-channel density of Na = 1,200 mS/cm2 was required. A "weakly" excitable (Na = 3 mS/cm2) dendritic membrane most accurately describes the experimentally observed attenuation of the back-propagated action potential. Careful analysis of the threshold conditions for action potential initiation at the initial segment or the dendrites revealed that, despite the lower voltage threshold for spike initiation in the initial segment, an action potential can be initiated in the dendrite before the initial segment fires a spike. Spike initiation in the dendrite depends on the passive cable properties of the dendritic membrane, its Na+-channel density, and local structural properties, mainly the diameter of the dendrites. Action potentials are initiated more easily in distal than in proximal dendrites. Whether or not such a dendritic action potential invades the soma with a subsequent initiation of a second action potential in the initial segment depends on the actual current source-load relation between the action potential approaching the soma and the electrical load of the soma together with the attached dendrites.

Maxsim, software for the analysis of multiple axonal arbors and their simulated activation

In order to analyze the structural organization of complex axonal arbors reconstructed from histological serial sections, and to investigate the functional implications of their geometrical properties, we developed software providing the following facilities: (1) direct importation of data files generated by a commercially available 3-D light-microscopic reconstruction system, including routine procedures for identification and correction of data acquisition errors; (2) real-time 3-D rotations of the arbors in the stack of serial sections; (3) multiple interactive display modes; (4) possibility of modifying diameter and/or connectivity of different branches; (5) simulation of the invasion of the arbor by a single action potential initiated at any chosen point, and visualization of spatio-temporal profiles of activation; (6) extraction of quantitative data converted to standard file formats compatible with available mathematical software. All these tools can be applied to single or multiple axons, individually or simultaneously. The software, called Maxsim, is a highly flexible C-written program running on graphical workstations using the UNIX operating system and X-Window environment.

Backpropagation of action potentials generated at ectopic axonal loci: hypothesis that axon terminals integrate local environmental signals

This review deals with the fascinating complexity of presynaptic axon terminals that are characterized by a high degree of functional distinctiveness. In vertebrate and invertebrate neurons, all-or-none APs can take off not only from the axon hillock, but also from ectopic axonal loci including terminals. Invertebrate neurons display EAPs, for instance alternating with somatic APs, during survival functions. In vertebrate, EAPs have been recorded in the peripheral and central nervous systems in time relationship with physiological or pathological neuronal activities. In motor or sensory axon, EAP generation may be the cause of motor dysfunctioning or sensory perceptions and pain respectively. Locomotion is associated with rhythmic depolarizations of the presynaptic axonal membrane of primary afferents, which are ridden by robust EAP bursts. In central axons lying within an epileptic tissue EAP discharges, coinciding with paroxysmal ECoG waves, get longer as somatic discharges get shorter during seizure progression. Once invaded by an orthodromic burst, an ectopic axonal locus can display an EAP after discharge. Such loci can also fire during hyperpolarization or the postinhibitory excitatory period of the parent somata, but not during their tonic excitation. Neurons are thus endowed with electrophysiological intrinsic properties making possible the alternate discharges of somatic APs and EAPs. In invertebrate and vertebrate neurons, ectopic axonal loci fire while the parent somata stop firing, further suggesting that axon terminal networks are unique and individual functional entities. The functional importance of EAPs in the nervous systems is, however, not yet well understood. Ectopically generated axonal APs propagate backwards and forwards along the axon, thus acting as a retrograde and anterograde signal. In invertebrate neurons, somatically and ectopically generated APs cannot have the same effect on the postsynaptic membrane. As suggested by studies related to the dorsal root reflex, EAPs may not only be implied in the presynaptic modulation of transmitter release but also contribute significantly during their backpropagation to a powerful control (collision process) of incoming volleys. From experimental data related to epileptiform activities it is proposed that EAPs, once orthodromically conducted, might potentiate synapses, initiate, spread or maintain epileptic cellular processes. For instance, paroxysmal discharges of EAPs would exert, like a booster-driver, a powerful synchronizing synaptic drive upon a large number of excitatory and inhibitory postsynaptic neurons. We have proposed that, once backpropagated, EAPs are likewise capable of initiating (and anticipating) threshold and low-threshold somatodendritic depolarizations. Interestingly, an antidromic EAP can modulate the excitability of the parent soma.(ABSTRACT TRUNCATED AT 400 WORDS)

An in vivo electrophysiological investigation of group Ia afferent fibres and ventral horn terminations in the cat spinal cord

An extracellular microstimulation technique has been used to investigate and compare the properties of group I primary afferent myelinated fibres in the dorsal column and group Ia unmyelinated terminations in the lumbar spinal cord of cats anaesthetised with pentobarbitone sodium. Fibres were distinguished from terminations on the basis of location, anodic blocking factor and sensitivity to GABAA mimetics. The recovery curves of threshold following an orthodromic impulse provided an estimate of both action potential duration and rate of repolarization. The action potentials of group Ia terminations were of briefer duration (by a factor of approximately 2) with more rapid rates of repolarization (factor of approximately 3) than those of the myelinated fibres. The prolongation of termination but not fibre action potentials by microelectrophoretic tetraethylammonium and 4-aminopyridine indicated the presence of voltage-activated potassium channels in the termination membrane. Differences in the effects on Ia termination action potentials of depolarizations (reductions in threshold) associated with a preceding action potential, synaptically released GABA, microelectrophoretic piperidine-4-sulphonic acid or DL-homocysteic acid suggest that an increase in termination membrane conductance is the major factor in the reduction of transmitter release during the activation of presynaptic GABAA receptors.

Computational structure of visual callosal axons

We analysed the activation profiles obtained by simulating invasion of an orthodromic action potential in eleven anterogradely filled and serially reconstructed terminal arbors of callosal axons originating and terminating in areas 17 and 18 of the adult cat. This was done in order to understand how geometry relates to computational properties of axons. In the simulation, conduction from the callosal midline to the first bouton caused activation latencies of 0.9-3.2 ms, compatible with published electrophysiological values. Activation latencies of the total set of terminal boutons varied across arbors between 0.3 and 2.7 ms. Arbors distributed boutons in tangentially segregated terminal columns spanning one or, more often, several layers. Individual columns of one axon were frequently activated synchronously or else with a few hundred microseconds of each other. Synchronous activation of spatially separate columns is achieved by: (i) long primary or secondary branches of similar calibre running nearly parallel to each other for several millimetres; (ii) variations in the calibre of branches serially fed to separate columns by the same primary or secondary branch; (iii) exchange of high-order or preterminal branches across columns. The long, parallel branches blatantly violate principles of axonal economy. Simulated alterations of the axonal arbors indicate that similar spatiotemporal patterns of activity could, in principle, be obtained by less axon-costly architectures. The structure of axonal arbors, therefore, may not be determined solely by the type of spatiotemporal activation profiles it achieves in the cortex but also by other constraints, in particular those imposed by developmental mechanisms.

Simulation study on effects of channel noise on differential conduction at an axon branch

Effects of membrane channel noise (random opening and closing of ion channels) are studied on spike conduction at a branching point on an axon. Computer simulation is done on the basis of a stochastic version of the Hodgkin-Huxley cable model, into which the channel noise is incorporated. It is shown that the channel noise makes conduction of spikes into daughter branches random; spikes randomly succeed or fail in conduction into daughter branches. The conduction is then randomly differential even though the forms and properties of daughter branches are the same. The randomness is considerable when the radius of an axon is small (approximately 1 microns).

Modeling the neuron-microtransducer junction: from extracellular to patch recording

This paper is devoted to a detailed characterization of the neuron-to-microtransducer junction, based on the equivalent electric-circuit approach. As a result, recording of action potentials can be simulated with the general-purpose network-analysis program SPICE. Both noble-metal microelectrodes and insulated-gate FET's are considered. The responses of such devices are characterized as functions of several parameters, e.g., sealing impedance, density of ionic currents in the cell membrane, and spatial discontinuities of the adhesion process. It is shown that the various signal shapes reported in the literature can be reproduced and interpreted in terms of time derivatives of the action potential. In this way, the shape of any experimental signal can be interpreted on the basis of a specific sealing condition. Possible future improvements in microtransducer design, based on the proposed approach, are also suggested.

Propagation of action potentials along complex axonal trees. Model and implementation

Axonal trees are typically morphologically and physiologically complicated structures. Because of this complexity, axonal trees show a large repertoire of behavior: from transmission lines with delay, to frequency filtering devices in both temporal and spatial domains. Detailed theoretical exploration of the electrical behavior of realistically complex axonal trees is notably lacking, mainly because of the absence of a simple modeling tool. AXONTREE is an attempt to provide such a simulator. It is written in C for the SUN workstation and implements both a detailed compartmental modeling of Hodgkin and Huxley-like kinetics, and a more abstract, event-driven, modeling approach. The computing module of AXONTREE is introduced together with its input/output features. These features allow graphical construction of arbitrary trees directly on the computer screen, and superimposition of the results on the simulated structure. Several numerical improvements that increase the computational efficiency by a factor of 5-10 are presented; most notable is a novel method of dynamic lumping of the modeled tree into simpler representations ("equivalent cables"). AXONTREE's performance is examined using a reconstructed terminal of an axon from a Y cell in cat visual cortex. It is demonstrated that realistically complicated axonal trees can be handled efficiently. The application of AXONTREE for the study of propagation delays along axonal trees is presented in the companion paper (Manor et al., 1991).

Effect of geometrical irregularities on propagation delay in axonal trees

Multiple successive geometrical inhomogeneities, such as extensive arborization and terminal varicosities, are usual characteristics of axons. Near such regions the velocity of the action potential (AP) changes. This study uses AXONTREE, a modeling tool developed in the companion paper for two purposes: (a) to gain insights into the consequence of these irregularities for the propagation delay along axons, and (b) to simulate the propagation of APs along a reconstructed axon from a cortical cell, taking into account information concerning the distribution of boutons (release sites) along such axons to estimate the distribution of arrival times of APs to the axons release sites. We used Hodgkin and Huxley (1952) like membrane properties at 20 degrees C. Focusing on the propagation delay which results from geometrical changes along the axon (and not from the actual diameters or length of the axon), the main results are: (a) the propagation delay at a region of a single geometrical change (a step change in axon diameter or a branch point) is in the order of a few tenths of a millisecond. This delay critically depends on the kinetics and the density of the excitable channels; (b) as a general rule, the lag imposed on the AP propagation at a region with a geometrical ratio GR greater than 1 is larger than the lead obtained at a region with a reciprocal of that GR value; (c) when the electronic distance between two successive geometrical changes (Xdis) is small, the delay is not the sum of the individual delays at each geometrical change, when isolated. When both geometrical changes are with GR greater than 1 or both with GR less than 1, this delay is supralinear (larger than the sum of individual delays). The two other combinations yield a sublinear delay; and (d) in a varicose axon, where the diameter changes frequently from thin to thick and back to thin, the propagation velocity may be slower than the velocity along a uniform axon with the thin diameter. Finally, we computed propagation delays along a morphologically characterized axon from layer V of the somatosensory cortex of the cat. This axon projects mainly to area 4 but also sends collaterals to areas 3b and 3a. The model predicts that, for this axon, areas 3a, 3b, and the proximal part of area 4 are activated approximately 2 ms before the activation of the distal part of area 4.

Simulation of action potential propagation in complex terminal arborizations

Action potential propagation in complex terminal arborizations was simulated using SPICE, a general purpose circuit simulation program. The Hodgkin-Huxley equations were used to simulate excitable membrane compartments. Conduction failure was common at branch points and regularly spaced boutons en passant. More complex arborizations had proportionally more inactive synapses than less complex arborizations. At lower temperature the safety factor for impulse propagation increased, reducing the number of silent synapses in a particular arborization. Small structural differences as well as minute changes in the discharge frequency of the action potential resulted in very different activation patterns of the arborization and terminal boutons. The results suggest that the structural diversity of terminal arborizations allows a wide range of presynaptic information processing. The results from this simulation study are discussed in the context of experimental results on the modulation of synaptic transmission.