Propagation of action potentials in the dendrites of neurons from rat spinal cord slice cultures

Investigating the role of axonal ion channel cooperativity in action potential dynamics: Studies on Hodgkin-Huxley's model

Voltage-gated ion channels play an important role in generating action potential in neurons. These ion channels are found to be in localized cluster form on the axonal membrane surface and behave cooperatively. However, in Hodgkin & Huxley's model of action potential the ion channels are considered to function independently. According to some recent reports, the activity of an ion channel is influenced by the neighboring ion channels' activities. We have modified the Hodgkin-Huxley's model based on our previous studies on cooperativity among ion channels. Computational analysis of the proposed model shows that the initiation of the action potential, amplitude and hyperpolarization are affected significantly by the cooperative interactions among the voltage-gated ion channels present on the axonal membrane surface. These results are qualitatively supported by the existing experimental facts.

Feedback inhibition and its control in an insect olfactory circuit

Inhibitory neurons play critical roles in regulating and shaping olfactory responses in vertebrates and invertebrates. In insects, these roles are performed by relatively few neurons, which can be interrogated efficiently, revealing fundamental principles of olfactory coding. Here, with electrophysiological recordings from the locust and a large-scale biophysical model, we analyzed the properties and functions of GGN, a unique giant GABAergic neuron that plays a central role in structuring olfactory codes in the locust mushroom body. Our simulations suggest that depolarizing GGN at its input branch can globally inhibit KCs several hundred microns away. Our in vivorecordings show that GGN responds to odors with complex temporal patterns of depolarization and hyperpolarization that can vary with odors and across animals, leading our model to predict the existence of a yet-undiscovered olfactory pathway. Our analysis reveals basic new features of GGN and the olfactory network surrounding it.

Mechanism-Based and Input-Output Modeling of the Key Neuronal Connections and Signal Transformations in the CA3-CA1 Regions of the Hippocampus

This letter examines the results of input-output (nonparametric) modeling based on the analysis of data generated by a mechanism-based (parametric) model of CA3-CA1 neuronal connections in the hippocampus. The motivation is to obtain biological insight into the interpretation of such input-output (Volterra-equivalent) models estimated from synthetic data. The insights obtained may be subsequently used to interpretat input-output models extracted from actual experimental data. Specifically, we found that a simplified parametric model may serve as a useful tool to study the signal transformations in the hippocampal CA3-CA1 regions. Input-output modeling of model-based synthetic data show that GABAergic interneurons are responsible for regulating neuronal excitation, controlling the precision of spike timing, and maintaining network oscillations, in a manner consistent with previous studies. The input-output model obtained from real data exhibits intriguing similarities with its synthetic-data counterpart, demonstrating the importance of a dynamic resonance in the system/model response around 2 Hz to 3 Hz. Using the input-output model from real data as a guide, we may be able to amend the parametric model by incorporating more mechanisms in order to yield better-matching input-output model. The approach we present can also be applied to the study of other neural systems and pathways.

Firing and intrinsic properties of antennal lobe neurons in the Noctuid moth Agrotis ipsilon

The antennal lobe (AL) of the Noctuid moth Agrotis ipsilon has emerged as an excellent model for studying olfactory processing and its plasticity in the central nervous system. Odor-evoked responses of AL neurons and input-to-output transformations involved in pheromone processing are well characterized in this species. However, the intrinsic electrical properties responsible of the firing of AL neurons are poorly known. To this end, patch-clamp recordings in current- and voltage-clamp mode from neurons located in the two main clusters of cell bodies in the ALs were combined with intracellular staining on A. ipsilon males. Staining indicated that the lateral cluster (LC) is composed of 85% of local neurons (LNs) and 15% of projection neurons (PNs). The medial cluster (MC) contains only PNs. Action potentials were readily recorded from the soma in LNs and PNs located in the LC but not from PNs in the MC where recordings showed small or no action potentials. In the LC, the spontaneous activity of about 20% of the LNs presented irregular bursts while being more regular in PNs. We also identified a small population of LNs lacking voltage-gated Na(+) currents and generating spikelets. We focused on the firing properties of LNs since in about 60% of LNs, but not in PNs, action potentials were followed by depolarizing afterpotentials (DAPs). These DAPs could generate a second action potential, so that the activity was composed of action potential doublets. DAPs depended on voltage, Ca(2+)-channels and possibly on Ca(2+)-activated non-specific cationic channels. During steady state current injection, DAPs occurred after each action potential and did not require high-frequency firing. The amplitude of DAPs increased when the interspike interval was small, typically within bursts, likely arising from a Ca(2+) build up. DAPs were more often found in bursting than in non-bursting LNs but do not support bursting activity. DAPs and spike doublets also occurred during odor-evoked activity suggesting that they can mediate olfactory integration in the AL.

Excitability of type II cochlear afferents

Two types of sensory hair cells in the mammalian cochlea signal through anatomically distinct populations of spiral ganglion afferent neurons. The solitary inner hair cell ribbon synapse uses multivesicular release to trigger action potentials that encode acoustic timing, intensity, and frequency in each type I afferent. In contrast, cochlear outer hair cells (OHCs) have a far weaker effect on their postsynaptic targets, the type II spiral ganglion afferents. OHCs typically release single vesicles with low probability so that extensive summation is required to reach the relatively high action potential initiation threshold. These stark differences in synaptic transfer call into question whether type II neurons contribute to the cognitive perception of sound. Given the sparse and weak synaptic inputs from OHCs, the electrical properties of type II afferents are crucial in determining whether synaptic responses can sum to evoke an action potential to convey information to the cochlear nucleus. In the present work, dual-electrode recordings determined that type II afferents of rats have length constants that exceed the length of the distal, spiral process, enabling spatial summation from widespread OHCs. Focal application of tetrodotoxin localized the spike initiation zone to the type II proximal, radial process, near the spiral ganglion, in agreement with the high voltage threshold measured in the spiral process. These measured membrane properties were incorporated into a compartmental model of the type II neuron to demonstrate that neurotransmitter release from at least six OHCs is required to trigger an action potential in a type II neuron.

Mechanisms underlying subunit independence in pyramidal neuron dendrites

Pyramidal neuron (PN) dendrites compartmentalize voltage signals and can generate local spikes, which has led to the proposal that their dendrites act as independent computational subunits within a multilayered processing scheme. However, when a PN is strongly activated, back-propagating action potentials (bAPs) sweeping outward from the soma synchronize dendritic membrane potentials many times per second. How PN dendrites maintain the independence of their voltage-dependent computations, despite these repeated voltage resets, remains unknown. Using a detailed compartmental model of a layer 5 PN, and an improved method for quantifying subunit independence that incorporates a more accurate model of dendritic integration, we first established that the output of each dendrite can be almost perfectly predicted by the intensity and spatial configuration of its own synaptic inputs, and is nearly invariant to the rate of bAP-mediated "cross-talk" from other dendrites over a 100-fold range. Then, through an analysis of conductance, voltage, and current waveforms within the model cell, we identify three biophysical mechanisms that together help make independent dendritic computation possible in a firing neuron, suggesting that a major subtype of neocortical neuron has been optimized for layered, compartmentalized processing under in-vivo-like spiking conditions.

Motor unit

Movement is accomplished by the controlled activation of motor unit populations. Our understanding of motor unit physiology has been derived from experimental work on the properties of single motor units and from computational studies that have integrated the experimental observations into the function of motor unit populations. The article provides brief descriptions of motor unit anatomy and muscle unit properties, with more substantial reviews of motoneuron properties, motor unit recruitment and rate modulation when humans perform voluntary contractions, and the function of an entire motor unit pool. The article emphasizes the advances in knowledge on the cellular and molecular mechanisms underlying the neuromodulation of motoneuron activity and attempts to explain the discharge characteristics of human motor units in terms of these principles. A major finding from this work has been the critical role of descending pathways from the brainstem in modulating the properties and activity of spinal motoneurons. Progress has been substantial, but significant gaps in knowledge remain.

Statistical computer model analysis of the reciprocal and recurrent inhibitions of the Ia-EPSP in α-motoneurons

We simulate the inhibition of Ia-glutamatergic excitatory postsynaptic potential (EPSP) by preceding it with glycinergic recurrent (REN) and reciprocal (REC) inhibitory postsynaptic potentials (IPSPs). The inhibition is evaluated in the presence of voltage-dependent conductances of sodium, delayed rectifier potassium, and slow potassium in five α-motoneurons (MNs). We distribute the channels along the neuronal dendrites using, alternatively, a density function of exponential rise (ER), exponential decay (ED), or a step function (ST). We examine the change in EPSP amplitude, the rate of rise (RR), and the time integral (TI) due to inhibition. The results yield six major conclusions. First, the EPSP peak and the kinetics depending on the time interval are either amplified or depressed by the REC and REN shunting inhibitions. Second, the mean EPSP peak, its TI, and RR inhibition of ST, ER, and ED distributions turn out to be similar for analogous ranges of G. Third, for identical G, the large variations in the parameters' values can be attributed to the sodium conductance step (g(Na_step)) and the active dendritic area. We find that small g(Na_step) on a few dendrites maintains the EPSP peak, its TI, and RR inhibition similar to the passive state, but high g(Na_step) on many dendrites decrease the inhibition and sometimes generates even an excitatory effect. Fourth, the MN's input resistance does not alter the efficacy of EPSP inhibition. Fifth, the REC and REN inhibitions slightly change the EPSP peak and its RR. However, EPSP TI is depressed by the REN inhibition more than the REC inhibition. Finally, only an inhibitory effect shows up during the EPSP TI inhibition, while there are both inhibitory and excitatory impacts on the EPSP peak and its RR.

Somato-dendritic morphology and dendritic signal transfer properties differentiate between fore- and hindlimb innervating motoneurons in the frog Rana esculenta

Background

The location specific motor pattern generation properties of the spinal cord along its rostro-caudal axis have been demonstrated. However, it is still unclear that these differences are due to the different spinal interneuronal networks underlying locomotions or there are also segmental differences in motoneurons innervating different limbs. Frogs use their fore- and hindlimbs differently during jumping and swimming. Therefore we hypothesized that limb innervating motoneurons, located in the cervical and lumbar spinal cord, are different in their morphology and dendritic signal transfer properties. The test of this hypothesis what we report here.

Results

Discriminant analysis classified segmental origin of the intracellularly labeled and three-dimensionally reconstructed motoneurons 100% correctly based on twelve morphological variables. Somata of lumbar motoneurons were rounder; the dendrites had bigger total length, more branches with higher branching orders and different spatial distributions of branch points. The ventro-medial extent of cervical dendrites was bigger than in lumbar motoneurons. Computational models of the motoneurons showed that dendritic signal transfer properties were also different in the two groups of motoneurons. Whether log attenuations were higher or lower in cervical than in lumbar motoneurons depended on the proximity of dendritic input to the soma. To investigate dendritic voltage and current transfer properties imposed by dendritic architecture rather than by neuronal size we used standardized distributions of transfer variables. We introduced a novel combination of cluster analysis and homogeneity indexes to quantify segmental segregation tendencies of motoneurons based on their dendritic transfer properties. A segregation tendency of cervical and lumbar motoneurons was detected by the rates of steady-state and transient voltage-amplitude transfers from dendrites to soma at all levels of synaptic background activities, modeled by varying the specific dendritic membrane resistance. On the other hand no segregation was observed by the steady-state current transfer except under high background activity.

Conclusions

We found size-dependent and size-independent differences in morphology and electrical structure of the limb moving motoneurons based on their spinal segmental location in frogs. Location specificity of locomotor networks is therefore partly due to segmental differences in motoneurons driving fore-, and hindlimbs.

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.

Interregional synaptic competition in neurons with multiple STDP-inducing signals

Neocortical layer 5 (L5) pyramidal cells have at least two spike initiation zones: Na(+) spikes are generated near the soma, and Ca(2+) spikes at the apical dendritic tuft. These spikes interact with each other and serve as signals for synaptic plasticity. The present computational study explores the implications of having two spike-timing-dependent plasticity (STDP) signals in a neuron, each with its respective regional population of synaptic "pupils." In a detailed model of an L5 pyramidal neuron, competition emerges between synapses belonging to different regions, on top of the competition among synapses within each region, which characterizes the STDP mechanism. Interregional competition results in strengthening of one group of synapses, which ultimately dominates cell firing, at the expense of weakening synapses in other regions. This novel type of competition is inherent to dendrites with multiple regional signals for Hebbian plasticity. Surprisingly, such interregional competition exists even in a simplified model of two identical coupled compartments. We find that in a model of an L5 pyramidal cell, the different synaptic subpopulations "live in peace" when the induction of Ca(2+) spikes requires the back-propagating action potential (BPAP). Thus we suggest a new key role for the BPAP, to maintain the balance between synaptic efficacies throughout the dendritic tree, thereby sustaining the functional integrity of the entire neuron.

Asymmetric electrotonic coupling between the soma and dendrites alters the bistable firing behaviour of reduced models

The goal of the study was to investigate the influence of asymmetric coupling, between the soma and dendrites, on the nonlinear dynamic behaviour of a two-compartment model. We used a recently published method for generating reduced two-compartment models that retain the asymmetric coupling of anatomically reconstructed motor neurons. The passive input-output relationship of the asymmetrically coupled model was analytically compared to the symmetrically coupled case. Predictions based on the analytic comparison were tested using numerical simulations. The simulations evaluated the nonlinear dynamics of the models as a function of coupling parameters. Analytical results showed that the input resistance at the dendrite of the asymmetric model was directly related to the degree of coupling asymmetry. In contrast, a comparable symmetric model had identical input resistances at both the soma and dendrite regardless of coupling strength. These findings lead to predictions that variations in dendritic excitability, subsequent to changes in input resistance, might change the current threshold and onset timing of the plateau potential generated in the dendrite. Since the plateau potential underlies bistable firing, these results further predicted that asymmetric coupling might alter nonlinear (i.e. bistable) firing patterns. The numerical simulations supported analytical predictions, showing that the fully bistable firing pattern of the asymmetric model depended on the degree of coupling asymmetry and its correlated dendritic excitability. The physiological property of asymmetric coupling plays an important role in generating and stabilizing the bistability of motor neurons by interacting with the excitability of dendritic branches.

Statistical computer model analysis of the reciprocal and recurrent inhibitory postsynaptic potentials in alpha-motoneurons

We simulate reconstructed alpha-motoneurons (MNs) under physiological and morphological realistic parameters and compare the modeled reciprocal (REC) and recurrent (REN) inhibitory postsynaptic potentials (IPSPs) containing voltage-dependent channels on the dendrites with the IPSPs of a passive MN model. Three distribution functions of the voltage-dependent channels on the dendrites are applied: a step function (ST) with uniform spatial dispersion; an exponential decay (ED) function, with channels with high density located proximal to the soma; and an exponential rise (ER) with a higher density of channels located distally. The excitatory and REN inhibitory inputs are located as a gaussian function on the dendrites, while the REC inhibitory synapses are located proximal to the soma. Our simulations generate four key results. (1) The distribution pattern of the voltage-dependent channels does not affect the IPSP peak, its time integral (TI), or its rate of rise (RR). However, the IPSP peak decreased in the presence of the active dendrites, while the EPSP peak increased. (2) Proximally located IPSP conductance produces greater IPSP peak, RR, and TI. (3) Increased duration of the IPSP produces greater RR and moderately increased TI and has a small effect on the peak amplitude. (4) The IPSP of both REC and REN models is specific to each MN: its amplitude is proportional to the MNs' input resistance, R(N); the increase of IPSP at the proximal location of the IPSP synapses is inversely related to R(N); and the effect of the IPSP conductance duration is insensitive to R(N).

Voluntary motor output is altered by spike-timing-dependent changes in the human corticospinal pathway

Repeated pairs of timed presynaptic and postsynaptic potentials cause lasting changes in efficacy of transmission at many synapses. The corticospinal tract is the major pathway controlling voluntary movement in humans, and corticospinal neurons have monosynaptic connections to motoneurons of many muscles. We hypothesized that corticospinal transmission in humans could be altered by delivering, to the corticospinal-motoneuronal synapses, timed pairs of presynaptic volleys (produced by cortical stimulation) and antidromic postsynaptic volleys (by peripheral nerve stimulation). To test corticospinal transmission, electrical cervicomedullary stimuli evoked motor responses [cervicomedullary motor-evoked potentials (CMEPs)] in biceps brachii before and for 1 h after conditioning with 50 paired cortical and peripheral nerve stimuli. Seven interstimulus intervals (ISIs) of conditioning stimulus pairs were tested on different days. With one ISI (+3 ms; cortical before peripheral nerve stimulation), CMEPs were significantly increased in size by 33 +/- 30% (mean +/- SD; n = 7) from 4 until 32 min after conditioning. With two other ISIs (-13 ms, +22 ms), CMEPs were decreased from approximately 30 until 60 min after conditioning (by 25 +/- 23% and 27 +/- 32%; n = 8). The remaining ISIs produced no changes. In a second study, subjects performed weak bilateral voluntary elbow flexion contractions before and after conditioning of the right elbow flexors. Conditioning ISIs that increased or decreased CMEPs similarly increased or decreased voluntary force and EMG on the right. Thus, depending on their timing, repeated paired stimuli can potentiate or depress corticospinal transmission, and these changes are functionally relevant. We suggest that bidirectional spike-timing-dependent plasticity can be induced at corticospinal-motoneuronal synapses and can influence voluntary motor output.

Regulation of somatic firing dynamics by backpropagating dendritic spikes

Pyramidal cells of the apteronotid ELL have been shown to display a characteristic mechanism of burst discharge, which has been shown to play an important role in sensory coding. This form of bursting depends on a reciprocal dendro-somatic interaction, in which discharge of a somatic spike causes a dendritic spike, which in turn contributes a dendro-somatic current flow to create a depolarizing afterpotential (DAP) in the soma. We review here our recent work showing how the timing of this DAP influences the somatic firing dynamics, and how the degree of inactivation of dendritic Na(+) currents can cause an increased delay between somatic and dendritic spikes. This ultimately allows the DAP to become more effective at increasing the excitability of the somatic spike generating mechanism. Further, this delay between dendritic and somatic spiking can be regulated by strongly hyperpolarizing GABA(B) mediated dendritic inhibition, allowing the burst dynamics to fall under synaptic regulation. In contrast, a weaker, shunting inhibition due to GABA(A) mediated dendritic inhibition can regulate the dendritic spike waveform to decrease the dendro-somatic current flow and the resulting DAP. We therefore show that the qualitative behaviour of an individual cell can depend on the degree of synaptic input, and the exact timing of events across the spatial extent of the neuron. Thus, our results serve to illustrate the complex dynamics that can be observed in cells with significant dendritic arborisation, a nearly ubiquitous adaptation amongst principal neurons.

Dendritic excitability and synaptic plasticity

Most synaptic inputs are made onto the dendritic tree. Recent work has shown that dendrites play an active role in transforming synaptic input into neuronal output and in defining the relationships between active synapses. In this review, we discuss how these dendritic properties influence the rules governing the induction of synaptic plasticity. We argue that the location of synapses in the dendritic tree, and the type of dendritic excitability associated with each synapse, play decisive roles in determining the plastic properties of that synapse. Furthermore, since the electrical properties of the dendritic tree are not static, but can be altered by neuromodulators and by synaptic activity itself, we discuss how learning rules may be dynamically shaped by tuning dendritic function. We conclude by describing how this reciprocal relationship between plasticity of dendritic excitability and synaptic plasticity has changed our view of information processing and memory storage in neuronal networks.

Analysis of the Interaction Between the Dendritic Conductance Density and Activated Area in Modulating α-Motoneuron EPSP: Statistical Computer Model

Five reconstructed α-motoneurons (MNs) are simulated under physiological and morphological realistic parameters. We compare the resulting excitatory postsynaptic potential (EPSP) of models, containing voltage-dependent channels on the dendrites, with the EPSP of a passive MN and an active soma and axon model. In our simulations, we apply three different distribution functions of the voltage-dependent channels on the dendrites: a step function (ST) with uniform spatial dispersion; an exponential decay (ED) function, with proximal to the soma high-density location; and an exponential rise (ER) with distally located conductance density. In all cases, the synaptic inputs are located as a gaussian function on the dendrites. Our simulations lead to eight key observations. (1) The presence of the voltage-dependent channels conductance (gActive) in the dendrites is vital for obtaining EPSP peak boosting. (2) The mean EPSP peaks of the ST, ER, and ED distributions are similar when the ranges of G (total conductance) are equal. (3) EPSP peak increases monotonically when the magnitude of gNa_step (maximal gNa at a particular run) is increased. (4) EPSP kinetics parameters were differentially affected; time integral was decreased monotonically with increased gNa_step, but the rate of rise (the decay time was not analyzed) does not show clear relations. (5) The total G can be elevated by increasing the number of active dendrites; however, only a small active area of the dendritic tree is sufficient to get the maximal boosting. (6) The sometimes large variations in the parameters values for identical G depend on the gNa_step and active dendritic area. (7) High gNa_step in a few dendrites is more efficient in amplifying the EPSP peak than low gNa_step in many dendrites. (8) The EPSP peak is approximately linear with respect to the MNs' RN (input resistance).

Action potential initiation and propagation in hippocampal mossy fibre axons

Dentate gyrus granule cells transmit action potentials (APs) along their unmyelinated mossy fibre axons to the CA3 region. Although the initiation and propagation of APs are fundamental steps during neural computation, little is known about the site of AP initiation and the speed of propagation in mossy fibre axons. To address these questions, we performed simultaneous somatic and axonal whole-cell recordings from granule cells in acute hippocampal slices of adult mice at approximately 23 degrees C. Injection of short current pulses or synaptic stimulation evoked axonal and somatic APs with similar amplitudes. By contrast, the time course was significantly different, as axonal APs had a higher maximal rate of rise (464 +/- 30 V s(-1) in the axon versus 297 +/- 12 V s(-1) in the soma, mean +/- s.e.m.). Furthermore, analysis of latencies between the axonal and somatic signals showed that APs were initiated in the proximal axon at approximately 20-30 mum distance from the soma, and propagated orthodromically with a velocity of 0.24 m s(-1). Qualitatively similar results were obtained at a recording temperature of approximately 34 degrees C. Modelling of AP propagation in detailed cable models of granule cells suggested that a approximately 4 times higher Na(+) channel density ( approximately 1000 pS mum(-2)) in the axon might account for both the higher rate of rise of axonal APs and the robust AP initiation in the proximal mossy fibre axon. This may be of critical importance to separate dendritic integration of thousands of synaptic inputs from the generation and transmission of a common AP output.

Interval coding. II. Dendrite-dependent mechanisms

The rich temporal structure of neural spike trains provides multiple dimensions to code dynamic stimuli. Popular examples are spike trains from sensory cells where bursts and isolated spikes can serve distinct coding roles. In contrast to analyses of neural coding, the cellular mechanics of burst mechanisms are typically elucidated from the neural response to static input. Bridging the mechanics of bursting with coding of dynamic stimuli is an important step in establishing theories of neural coding. Electrosensory lateral line lobe (ELL) pyramidal neurons respond to static inputs with a complex dendrite-dependent burst mechanism. Here we show that in response to dynamic broadband stimuli, these bursts lack some of the electrophysiological characteristics observed in response to static inputs. A simple leaky integrate-and-fire (LIF)-style model with a dendrite-dependent depolarizing afterpotential (DAP) is sufficient to match both the output statistics and coding performance of experimental spike trains. We use this model to investigate a simplification of interval coding where the burst interspike interval (ISI) codes for the scale of a canonical upstroke rather than a multidimensional stimulus feature. Using this stimulus reduction, we compute a quantization of the burst ISIs and the upstroke scale to show that the mutual information rate of the interval code is maximized at a moderate DAP amplitude. The combination of a reduced description of ELL pyramidal cell bursting and a simplification of the interval code increases the generality of ELL burst codes to other sensory modalities.

Muscle proprioceptive feedback and spinal networks

This review revolves primarily around segmental feedback systems established by muscle spindle and Golgi tendon organ afferents, as well as spinal recurrent inhibition via Renshaw cells. These networks are considered as to their potential contributions to the following functions: (i) generation of anti-gravity thrust during quiet upright stance and the stance phase of locomotion; (ii) timing of locomotor phases; (iii) linearization and correction for muscle nonlinearities; (iv) compensation for muscle lever-arm variations; (v) stabilization of inherently unstable systems; (vi) compensation for muscle fatigue; (vii) synergy formation; (viii) selection of appropriate responses to perturbations; (ix) correction for intersegmental interaction forces; (x) sensory-motor transformations; (xi) plasticity and motor learning. The scope will at times extend beyond the narrow confines of spinal circuits in order to integrate them into wider contexts and concepts.

Dendritic patch-clamp recording

The patch-clamp technique allows investigation of the electrical excitability of neurons and the functional properties and densities of ion channels. Most patch-clamp recordings from neurons have been made from the soma, the largest structure of individual neurons, while their dendrites, which form the majority of the surface area and receive most of the synaptic input, have been relatively neglected. This protocol describes techniques for recording from the dendrites of neurons in brain slices under direct visual control. Although the basic technique is similar to that used for somatic patching, we describe refinements and optimizations of slice quality, microscope optics, setup stability and electrode approach that are required for maximizing the success rate for dendritic recordings. Using this approach, all configurations of the patch-clamp technique (cell-attached, inside-out, whole-cell, outside-out and perforated patch) can be achieved, even for relatively distal dendrites, and simultaneous multiple-electrode dendritic recordings are also possible. The protocol--from the beginning of slice preparation to the end of the first successful recording--can be completed in 3 h.

Synaptic Amplification Versus Bistability in Motoneuron Dendritic Processing: A Top-Down Modeling Approach

Motoneurons have been shown to exhibit both bistable firing and synaptic amplification. Both of these behaviors have generally been attributed to a single mechanism—dendritic plateau potentials based on L-type Ca2+ conductances. However, our recent discovery of a fast-amplification mode calls this into question. Here we examine the possibility that two mechanisms underlie these behaviors, one being a slow-mode bistability mechanism (i.e., the L-type Ca2+-conductance–based dendritic plateaus) and the other being a theoretical fast-mode amplification mechanism. A “top-down” motoneuron model that encapsulated these and other hypotheses was developed in which these mechanisms could be explored. The resulting final model simultaneously exhibits synaptic amplification, plateau potential formation, bistable firing patterns, and current–voltage ( I– V) and frequency–current ( F– I) hystereses. This model suggests that amplification and plateaus are mutually exclusive in the same dendrite/dendritic branch. Thus we predict that plateau generation does not occur in all dendritic branches. This could be readily accomplished by a large degree of variation in the density of L-type Ca2+ channels believed to underlie plateau formation in these cells with the added benefit of spreading plateau onset over a wider voltage range, as is observed experimentally.

Somato-dendritic mechanisms underlying the electrophysiological properties of hypothalamic magnocellular neuroendocrine cells: a multicompartmental model study

Magnocellular neuroendocrine cells (MNCs) of the hypothalamus synthesize the neurohormones vasopressin and oxytocin, which are released into the blood and exert a wide spectrum of actions, including the regulation of cardiovascular and reproductive functions. Vasopressin- and oxytocin-secreting neurons have similar morphological structure and electrophysiological characteristics. A realistic multicompartmental model of a MNC with a bipolar branching structure was developed and calibrated based on morphological and in vitro electrophysiological data in order to explore the roles of ion currents and intracellular calcium dynamics in the intrinsic electrical MNC properties. The model was used to determine the likely distributions of ion conductances in morphologically distinct parts of the MNCs: soma, primary dendrites and secondary dendrites. While reproducing the general electrophysiological features of MNCs, the model demonstrates that the differential spatial distributions of ion channels influence the functional expression of MNC properties, and reveals the potential importance of dendritic conductances in these properties.

Fast Amplification of Dynamic Synaptic Inputs in Spinal Motoneurons In Vivo

The ability of voltage-dependent inward currents (likely Na+) of the adult cat lumbar motoneurons to amplify rapidly changing (i.e., dynamic) synaptic inputs was investigated using in vivo intracellular recording techniques. Fast amplification was assessed by measuring the magnitude of the high-frequency (180 Hz) component of the Ia synaptic input due to tendon vibration as a function of somatic voltage and was compared with the previously observed amplification of steady inputs (steady state response of PICs to slow inputs). Data from 17 experiments show that amplification of the dynamic input indeed occurred and was directly linked to neuromodulatory drive (standard state: decerebrate with intact descending neuromodulatory systems vs. minimal state: pentobarbital with said systems significantly inhibited). Fast amplification factors averaged 2.0 ± 0.7 (mean ± SD) in the standard neuromodulatory state. That is, the effective synaptic current was nearly twice as large at its peak as it was at hyperpolarized levels, ranging as high as 2.6. Although fast amplification was often smaller than the amplification of steady inputs, the difference was not statistically significant. However, the voltage at which fast amplification began was ∼10 mV more depolarized ( P < 0.01). It is concluded that both dynamic and steady inputs can be amplified, but there may be differences in mechanism.

Improved organotypic cell culture model for analysis of the neuronal circuit involved in the monosynaptic stretch reflex

Knowledge regarding neuronal circuit formation is central for the understanding of the vast network making up the brain. It is therefore necessary to find novel ways to analyze the mechanisms involved in well-defined neural circuits. We present an improved in vitro model of the monosynaptic stretch reflex circuit, based on primary organotypic cell cultures. By using limb tissue as a source of muscle fibers instead of circumspinal tissue we could make the in vitro system more in vivo like in the sense that it focuses on the stretch reflex involving limb muscles. Furthermore, our analyses showed that this procedure allows muscle fibers to follow the normal developmental pattern. Particularly interesting was the finding of slow tonic myosin heavy chain expressing muscle fibers, a developmental marker for muscle spindles, in the cultures showing that this system has the potential to contain the complete reflex circuits.

Dendritic spikes and activity-dependent synaptic plasticity

Whereas the regenerative nature of action potential conduction in axons has been known since the late 1940s, neuronal dendrites have been considered as passive cables transferring incoming synaptic activity to the soma. The relatively recent discovery that neuronal dendrites contain active conductances has revolutionized our view of information processing in neurons. In many neuronal cell types, sodium action potentials initiated at the axon initial segment can back-propagate actively into the dendrite thereby serving, for the dendrite, as an indicator of the output activity of the neuron. In addition, the dendrites themselves can initiate action-potential-like regenerative responses, so-called dendritic spikes, that are mediated either by the activation of sodium, calcium, and/or N-methyl-D-aspartate receptor channels. Here, we review the recent experimental and theoretical evidence for a role of regenerative dendritic activity in information processing within neurons and, especially, in activity-dependent synaptic plasticity.

Measuring dendritic distribution of membrane proteins

Neurons perform much of their integrative work in the dendritic tree, and spinal motoneurons have the largest tree of any cell. Electrical excitability is strongly influenced by dendrite membrane properties, which are difficult to measure directly. We describe a method to measure the distribution of ion channel membrane densities along dendritic trajectories. The method combines standard immunohistochemistry with reconstruction procedures for both large-scale and small-scale optical microscopy. Software written for Matlab then extracts the colocalization of the target ion channel with the target dye injected cell, and calculates the relative channel density per square micron of cell surface area, as a function of distance from the cell body. The technique can be used to quantify the localization and distribution of any immunoreactive moiety, and the software provides a flexible vehicle for sensitivity analysis, to validate heuristics for selecting thresholds.

Deterministic multiplicative gain control with active dendrites

Multiplicative gain control is a vital component of many theoretical analyses of neural computations, conferring the ability to scale neuronal firing rate in response to synaptic inputs. Many theories of gain control in single cells have used precisely balanced noisy inputs. Such noisy inputs can degrade signal processing. We demonstrate a deterministic method for the control of gain without the use of noise. We show that a depolarizing afterpotential (DAP), arising from active dendritic spike backpropagation, leads to a multiplicative increase in gain. Reduction of DAP amplitude by dendritic inhibition dilutes the multiplicative effect, allowing for divisive scaling of the firing rate. In contrast, somatic inhibition acts in a subtractive manner, allowing spatially distinct inhibitory inputs to perform distinct computations. The simplicity of this mechanism and the ubiquity of its elementary components suggest that many cell types have the potential to display a dendritic division of neuronal output.

Backpropagating action potentials in neurones: measurement, mechanisms and potential functions

Here we review some properties and functions of backpropagating action potentials in the dendrites of mammalian CNS neurones. We focus on three main aspects: firstly the current techniques available for measuring backpropagating action potentials, secondly the morphological parameters and voltage gated ion channels that determine action potential backpropagation and thirdly the potential functions of backpropagating action potentials in real neuronal networks.

Hyperpolarization of substantia gelatinosa neurons evoked by mu-, kappa-, delta 1-, and delta 2-selective opioids

With whole-cell recordings of substantia gelatinosa (SG) neurons from rat spinal cord slices, we investigated the effects of bath application of highly selective delta(1), delta(2), kappa and mu opioid agonists on membrane potential and conductance. Each agonist was applied at 0.5 to 1 micromol/L and evoked robust hyperpolarizations and conductance increases in a subset of neurons. The response magnitude means were similar across agonists at several concentrations; no excitatory effects were observed. Nine of 55 (16%) were hyperpolarized by delta(1) opioids, 2 of 45 (4%) by delta(2), 8 of 59 (14%) by kappa, and 35 of 67 (52%) by mu opioids. To test the hypothesis that SG neurons may be hyperpolarized by multiple opioid subtype agonists, we applied 2, 3, or 4 selective agonists to individual neurons. Most neurons were hyperpolarized only by mu opioids; however, a minority were hyperpolarized by multiple subtype-selective agonists. These results indicate that delta(1)- and delta(2)-selective opioids can also evoke robust hyperpolarizations in spinal SG neurons, that the relative abundance of hyperpolarizing responses was mu > > delta (1) approximately equal kappa > delta(2), and that some SG neurons can be hyperpolarized by more than 1 opioid subtype-selective agonist. These powerful inhibitory postsynaptic responses likely contribute to analgesia evoked by spinally and systemically administered opioid subtype-selective agonists.

Dendritic Ca2+ transients evoked by action potentials in rat dorsal cochlear nucleus pyramidal and cartwheel neurons

Simultaneous fluorescence imaging and electrophysiologic recordings were used to investigate the Ca(2+) influx initiated by action potentials (APs) into dorsal cochlear nucleus (DCN) pyramidal cell (PC) and cartwheel cell (CWC) dendrites. Local application of Cd(2+) blocked Ca(2+) transients in PC and CWC dendrites, demonstrating that the Ca(2+) influx was initiated by dendritic Ca(2+) channels. In PCs, TTX eliminated the dendritic Ca(2+) transients when APs were completely blocked. However, the Ca(2+) influx could be partially recovered during an incomplete block of APs or when a large depolarization was substituted for the blocked APs. In CWCs, dendritic Ca(2+) transients evoked by individual APs, or simple spikes, were blocked by TTX and could be recovered during an incomplete block of APs or by a large depolarization. In contrast, dendritic Ca(2+) transients evoked by complex spikes, a burst of APs superimposed on a slow depolarization, were not blocked by TTX, despite eliminating the APs superimposed on the slow depolarization. These results suggest two different mechanisms for the retrograde activation of dendritic Ca(2+) channels: the first requires fast Na(+) channel-mediated APs or a large somatic depolarization, whereas the second is independent of Na(+) channel activation, requiring only the slow depolarization underlying complex spikes.

Multiple modes of action potential initiation and propagation in mitral cell primary dendrite

The mitral cell primary dendrite plays an important role in transmitting distal olfactory nerve input from olfactory glomerulus to the soma-axon initial segment. To understand how dendritic active properties are involved in this transmission, we have combined dual soma and dendritic patch recordings with computational modeling to analyze action-potential initiation and propagation in the primary dendrite. In response to depolarizing current injection or distal olfactory nerve input, fast Na(+) action potentials were recorded along the entire length of the primary dendritic trunk. With weak-to-moderate olfactory nerve input, an action potential was initiated near the soma and then back-propagated into the primary dendrite. As olfactory nerve input increased, the initiation site suddenly shifted to the distal primary dendrite. Multi-compartmental modeling indicated that this abrupt shift of the spike-initiation site reflected an independent thresholding mechanism in the distal dendrite. When strong olfactory nerve excitation was paired with strong inhibition to the mitral cell basal secondary dendrites, a small fast prepotential was recorded at the soma, which indicated that an action potential was initiated in the distal primary dendrite but failed to propagate to the soma. As the inhibition became weaker, a "double-spike" was often observed at the dendritic recording site, corresponding to a single action potential at the soma. Simulation demonstrated that, in the course of forward propagation of the first dendritic spike, the action potential suddenly jumps from the middle of the dendrite to the axonal spike-initiation site, leaving the proximal part of primary dendrite unexcited by this initial dendritic spike. As Na(+) conductances in the proximal dendrite are not activated, they become available to support the back-propagation of the evoked somatic action potential to produce the second dendritic spike. In summary, the balance of spatially distributed excitatory and inhibitory inputs can dynamically switch the mitral cell firing among four different modes: axo-somatic initiation with back-propagation, dendritic initiation either with no forward propagation, forward propagation alone, or forward propagation followed by back-propagation.

Dynamic gating of spike propagation in the mitral cell lateral dendrites

A unique feature of the olfactory bulb circuit is the long projection of the mitral cell lateral dendrites. Through dendrodendritic reciprocal synapses, these dendrites connect one olfactory glomerular module to hundreds of others; but the functional principles governing these extensive lateral interactions remain largely unknown. Here we report that the spatial extent of action potential propagation in these dendrites is dynamically regulated by inhibitory synapses distributed along the dendrites. The extent of propagation determines the spatial pattern of Ca(2+) influx and thus the range and number of dendrodendritic synapses to be activated. Accordingly, network control of spike traffic in the mitral cell lateral dendrites can mediate dynamic interaction with different combinations of glomerular modules in response to different odorants.

Influence of dendritic conductances on the input-output properties of neurons

A fundamental problem in neuroscience is understanding how a neuron transduces synaptic input into action potentials. The dendrites form the substrate for consolidating thousands of synaptic inputs and are the first stage for signal processing in the neuron. Traditionally, dendrites are viewed as passive structures whose main function is to funnel synaptic input into the soma. However, dendrites contain a wide variety of voltage- and time-dependent ion channels. When activated, the currents through these channels can alter the amplitude and time course of the synaptic input and under certain conditions even evoke all-or-none regenerative potentials. The synaptic input that ultimately reaches the soma is likely to be a highly transformed version of the original signal. Thus, a key step in understanding the relationship between synaptic input and neuronal firing is to elucidate the signal processing that occurs in the dendrites.

Input-output functions of mammalian motoneurons

Our intent in this review was to consider the relationship between the biophysical properties of motoneurons and the mechanisms by which they transduce the synaptic inputs they receive into changes in their firing rates. Our emphasis has been on experimental results obtained over the past twenty years, which have shown that motoneurons are just as complex and interesting as other central neurons. This work has shown that motoneurons are endowed with a rich complement of active dendritic conductances, and flexible control of both somatic and dendritic channels by endogenous neuromodulators. Although this new information requires some revision of the simple view of motoneuron input-output properties that was prevalent in the early 1980's (see sections 2.3 and 2.10), the basic aspects of synaptic transduction by motoneurons can still be captured by a relatively simple input-output model (see section 2.3, equations 1-3). It remains valid to describe motoneuron recruitment as a product of the total synaptic current delivered to the soma, the effective input resistance of the motoneuron and the somatic voltage threshold for spike initiation (equations 1 and 2). However, because of the presence of active channels activated in the subthreshold range, both the delivery of synaptic current and the effective input resistance depend upon membrane potential. In addition, activation of metabotropic receptors by achetylcholine, glutamate, noradrenaline, serotonin, substance P and thyrotropin releasing factor (TRH) can alter the properties of various voltage- and calcium-sensitive channels and thereby affect synaptic current delivery and input resistance. Once motoneurons are activated, their steady-state rate of repetitive discharge is linearly related to the amount of injected or synaptic current reaching the soma (equation 3). However, the slope of this relation, the minimum discharge rate and the threshold current for repetitive discharge are all subject to neuromodulatory control. There are still a number of unresolved issues concerning the control of motoneuron discharge by synaptic inputs. Under dynamic conditions, when synaptic input is rapidly changing, time- and activity-dependent changes in the state of ionic channels will alter both synaptic current delivery to the spike-generating conductances and the relation between synaptic current and discharge rate. There is at present no general quantitative expression for motoneuron input-output properties under dynamic conditions. Even under steady-state conditions, the biophysical mechanisms underlying the transfer of synaptic current from the dendrites to the soma are not well understood, due to the paucity of direct recordings from motoneuron dendrites. It seems likely that resolving these important issues will keep motoneuron afficiandoes well occupied during the next twenty years.

High I(h) channel density in the distal apical dendrite of layer V pyramidal cells increases bidirectional attenuation of EPSPs

Despite the wealth of recent research on active signal propagation along the dendrites of layer V neocortical pyramidal neurons, there is still little known regarding the traffic of subthreshold synaptic signals. We present a study using three simultaneous whole cell recordings on the apical dendrites of these cells in acute rat brain slices to examine the spread and attenuation of spontaneous excitatory postsynaptic potentials (sEPSPs). Equal current injections at each of a pair of sites separated by approximately 500 microm on the apical dendrite resulted in equal voltage transients at the other site ("reciprocity"), thus disclosing linear behavior of the neuron. The mean apparent "length constants" of the apical dendrite were 273 and 446 microm for somatopetal and somatofugal sEPSPs, respectively. Trains of artificial EPSPs did not show temporal summation. Blockade of the hyperpolarization-activated cation current (I(h)) resulted in less attenuation by 17% for somatopetal and by 47% for somatofugal sEPSPs. A pronounced location-dependent temporal summation of EPSP trains was seen. The subcellular distribution and biophysical properties of I(h) were studied in cell-attached patches. Within less than approximately 400 microm of the soma, a low density of approximately 3 pA/microm(2) was found, which increased to approximately 40 pA/microm(2) in the apical distal dendrite. I(h) showed activation and deactivation kinetics with time constants faster than 40 ms and half-maximal activation at -95 mV. These findings suggest that integration of synaptic input to the apical tuft and the basal dendrites occurs spatially independently. This is due to a high I(h) channel density in the apical tuft that increases the electrotonic distance between these two compartments in comparison to a passive dendrite.

Differentiation of electrical excitability in motoneurons

Investigation of the differentiation of electrical properties of motoneurons has been stimulated by the importance of these neurons for embryonic behavior and facilitated by their experimental accessibility. In this review, we examine the development of different patterns of excitability and their functions, and discuss the emergence of repetitive firing and localization of ion channels in axons and dendrites. Finally, we summarize studies of the role of extrinsic factors in differentiation. These changes associated with differentiation of young motoneurons may presage those occurring later in the context of plasticity in the mature nervous system.

Diversity and dynamics of dendritic signaling

Communication between neurons in the brain occurs primarily through synapses made onto elaborate treelike structures called dendrites. New electrical and optical recording techniques have led to tremendous advances in our understanding of how dendrites contribute to neuronal computation in the mammalian brain. The varied morphology and electrical and chemical properties of dendrites enable a spectrum of local and long-range signaling, defining the input-output relationship of neurons and the rules for induction of synaptic plasticity. In this way, diversity in dendritic signaling allows individual neurons to carry out specialized functions within their respective networks.

Conditional spike backpropagation generates burst discharge in a sensory neuron

Backpropagating dendritic Na(+) spikes generate a depolarizing afterpotential (DAP) at the soma of pyramidal cells in the electrosensory lateral line lobe (ELL) of weakly electric fish. Repetitive spike discharge is associated with a progressive depolarizing shift in somatic spike afterpotentials that eventually triggers a high-frequency spike doublet and subsequent burst afterhyperpolarization (bAHP). The rhythmic generation of a spike doublet and bAHP groups spike discharge into an oscillatory burst pattern. This study examined the soma-dendritic mechanisms controlling the depolarizing shift in somatic spike afterpotentials, and the mechanism by which spike doublets terminate spike discharge. Intracellular recordings were obtained from ELL pyramidal somata and apical dendrites in an in vitro slice preparation. The pattern of spike discharge was equivalent in somatic and dendritic regions, reflecting the backpropagation of spikes from soma to dendrites. There was a clear frequency-dependent threshold in the transition from tonic to burst discharge, with bursts initiated when interspike intervals fell between approximately 3-7 ms. Removal of all backpropagating spikes by dendritic TTX ejection revealed that the isolated somatic AHPs were entirely stable at the interspike intervals that generated burst discharge. As such, the depolarizing membrane potential shift during repetitive discharge could be attributed to a potentiation of DAP amplitude. Potentiation of the DAP was due to a frequency-dependent broadening and temporal summation of backpropagating dendritic Na(+) spikes. Spike doublets were generated with an interspike interval close to, but not within, the somatic spike refractory period. In contrast, the interspike interval of spike doublets always fell within the longer dendritic refractory period, preventing backpropagation of the second spike of the doublet. The dendritic depolarization was thus abruptly removed from one spike to the next, allowing the burst to terminate when the bAHP hyperpolarized the membrane. The transition from tonic to burst discharge was dependent on the number and frequency of spikes invoking dendritic spike summation, indicating that burst threshold depends on the immediate history of cell discharge. Spike frequency thus represents an important condition that determines the success of dendritic spike invasion, establishing an intrinsic mechanism by which backpropagating spikes can be used to generate a rhythmic burst output.

Release-independent short-term synaptic depression in cultured hippocampal neurons

Short-term synaptic plasticity may dramatically influence neuronal information transfer, yet the underlying mechanisms remain incompletely understood. In autapses (self-synapses) formed by cultured hippocampal neurons, short-term synaptic depression (STD) had several unusual features. (1) Reduction of neurotransmitter release probability with Cd(2+), a blocker of voltage-gated calcium channels, did not change depression. (2) Lowering [Ca(2+)](o) and/or raising [Mg(2+)](o) had little effect on STD in cells with strong baseline depression, but in cells with more modest baseline depression, it reduced the depression. (3) Random variations in the size of initial EPSCs did not influence successive EPSC sizes. These findings were inconsistent with release-dependent mechanisms, such as vesicle depletion, post-synaptic receptor desensitization, and autoreceptor inhibition. Instead, other results suggested that changes in action potentials (APs) contributed to depression. The somatic APs declined in amplitude with repetitive stimulation, and modest reduction of AP amplitudes with tetrodotoxin inhibited EPSCs. Notably, tetrodotoxin also increased depression. Similar changes in axonal APs could produce STD in at least two ways. First, decreasing presynaptic spike amplitudes could reduce calcium entry and release probability. Alternatively, APs could fail to propagate through some axonal branches, reducing the number of active synapses. To explore these possibilities, we derived the expected variance of EPSCs for the two scenarios. Experimentally, the variance increased and then decreased on average with successive responses during trains of APs, confirming a unique prediction from the conduction failure scenario. Thus, STD had surprising properties, incompatible with commonly postulated mechanisms but consistent with AP conduction failure at axonal branches.

Synaptic control of motoneuronal excitability

Movement, the fundamental component of behavior and the principal extrinsic action of the brain, is produced when skeletal muscles contract and relax in response to patterns of action potentials generated by motoneurons. The processes that determine the firing behavior of motoneurons are therefore important in understanding the transformation of neural activity to motor behavior. Here, we review recent studies on the control of motoneuronal excitability, focusing on synaptic and cellular properties. We first present a background description of motoneurons: their development, anatomical organization, and membrane properties, both passive and active. We then describe the general anatomical organization of synaptic input to motoneurons, followed by a description of the major transmitter systems that affect motoneuronal excitability, including ligands, receptor distribution, pre- and postsynaptic actions, signal transduction, and functional role. Glutamate is the main excitatory, and GABA and glycine are the main inhibitory transmitters acting through ionotropic receptors. These amino acids signal the principal motor commands from peripheral, spinal, and supraspinal structures. Amines, such as serotonin and norepinephrine, and neuropeptides, as well as the glutamate and GABA acting at metabotropic receptors, modulate motoneuronal excitability through pre- and postsynaptic actions. Acting principally via second messenger systems, their actions converge on common effectors, e.g., leak K(+) current, cationic inward current, hyperpolarization-activated inward current, Ca(2+) channels, or presynaptic release processes. Together, these numerous inputs mediate and modify incoming motor commands, ultimately generating the coordinated firing patterns that underlie muscle contractions during motor behavior.

Macroscopic and subcellular factors shaping population spikes

Population spikes (PS) are built by the extracellular summation of action currents during synchronous action potential (AP) firing. In the hippocampal CA1, active dendritic invasion of APs ensures mixed contribution of somatic and dendritic currents to any extracellular location. We investigated the macroscopic and subcellular factors shaping the antidromic PS by fitting its spatiotemporal map with a multineuronal CA1 model in a volume conductor. Decreased summation by temporal scatter of APs reduced less than expected the PS peak in the stratum pyramidale (st. pyr.) but strongly increased the relative contribution of far dendritic currents. Increasing the number of firing cells also augmented the relative dendritic contribution to the somatic PS, an effect caused by the different waveform of somatic and dendritic unitary transmembrane currents (I(m)). Those from somata are short-lasting and spiky, having smaller temporal summation than those from dendrites, which are smoother and longer. The different shape of compartmental I(m)s is imposed by the fitting of backpropagating APs, which are large and fast at the soma and smaller and longer in dendrites. The maximum sodium conductance ((Na)) strongly affects the unitary APs at the soma, but barely the PS at the stratum pyramidale (st. pyr.). This occurred because somatic I(m) saturated at low (Na) due to the strong reduction of driving force during somatic APs, limiting the current contribution to the extracellular space. On the contrary, (Na) effectively defined the PS amplitude in the st. radiatum. The relative contribution of dendritic currents to the st. pyr. increases during the time span of the PS, from approximately 30-40% at the peak up to 100% at its end, a pattern resultant from the timing of active inward currents along the somatodendritic axis, which delay during backpropagation. Extreme changes imposed on dendritic currents caused only moderate effects on the st. pyr. due to reciprocal shunting of active soma and dendrites that partially counterbalance the net amount of instant current. The amplitude of the PS follows an inverse relation to the internal resistance (R(i)), which turned out to be a most critical factor. Low R(i) facilitated the spread of APs into dendrites and accelerated their speed, increasing temporal overlapping of inward currents along the somatodendritic axis and yielding the best PS reproductions. Model reconstruction of field potentials is a powerful tool to understand the interactions between different levels of complexity. The potential use of this approach to restrain the variability of some experimental measurements is discussed.

The role of dendritic filtering in associative long-term synaptic plasticity

Several forms of synaptic plasticity in the neocortex and hippocampus depend on the temporal coincidence of presynaptic activity and postsynaptic trains of action potentials (APs). This requirement is consistent with the Hebbian, or correlational, type of cellular learning rule used in many studies of associative synaptic plasticity. Recent experimental evidence suggests that APs initiated in the axosomatic area are actively back-propagated to the dendritic arborization of neocortical and pyramidal cells. High-frequency trains of postsynaptic APs that are used as conditioning stimuli for the induction of Hebbian-like plasticity in both neocortical and hippocampal pyramidal cells display attenuation of the dendritic AP amplitude during the train. This attenuation has been shown to be modulated by neurotransmitters and by electrical activity. We suggest here that both spike train attenuation in the dendrite and its modulation by neurotransmitters and electrical activity may have important functional consequences on the magnitude and/or the sign of the synaptic plasticity induced by a Hebbian pairing procedure.

Solution of the nerve cable equation using Chebyshev approximations

The propagation of excitation along the dendrites and the axon of a neurone is described by a partial differential equation which is nonlinear when voltage-gated conductances are present. In this case, numerical methods are employed to obtain a solution: the evolution of the membrane potential in space and time. Even when the membrane is passive (linear), numerical methods might still be preferred to analytical ones that are often too cumbersome to obtain. In this paper, we present the Chebyshev pseudospectral or collocation method as an alternative to the hitherto commonly used finite difference schemes (compartmental models) that are based on sufficiently fine equidistant subdivisions of the spatial structure (dendrites or axon). In the Chebyshev method, solutions are approximated by finite Chebyshev series. The solutions have uniform, usually high, numerical accuracy at any spatial point, not only at the original collocation points. Often, truncation errors become negligible, hence, the total error is essentially the rounding error of the computations. Furthermore, quantities involving spatial derivatives, and in particular the axial current, can be computed exactly from the solution, i.e. the membrane potential. Space-dependent parameter distributions (channel densities, non-uniform dendritic geometries), as well as mixed linear boundary conditions can easily be implemented, and can be chosen from the large class of piecewise smooth functions.

Automatic characterization and classification of ganglion cells from the salamander retina

The classification of retinal ganglion cells according to their morphological features is addressed by using a comprehensive set of shape measures and several clustering strategies. The morphological features considered include many common measures (such as dendritic radii and the number of dendritic segments) and three new quantifiable measures: 1) the area of influence of the dendritic tree as calculated in an operator-independent manner by using Minkowski sausages; 2) the complexity of tortuousity along each dendritic segment as represented by the 3D bending energy; and 3) the coverage factor as calculated by using the Bouligand-Minkowski fractal dimension, which is more accurate than the commonly used box-counting algorithm. We evaluated four clustering approaches including the k-means and Ward's hierarchical clustering methods. By using these highly quantifiable methods to group the cells into classes, the present work has extended and reassessed the analysis of 68 ganglion cells from the tiger salamander previously classified by Toris et al. ([1995] J. Comp. Neurol. 352:535-559). Though substantiating the number of classes (5) previously proposed by Toris et al., the results obtained here indicate a number of discrepancies among the members of each class, especially regarding the border between two classes, originally called the medium simple and the medium complex cells. Such an effect has motivated the proposal of new names for the medium simple and medium complex classes, now called small highly complex and medium cells, respectively. Also included in the present article are comprehensive statistics of each class, correlations among all the adopted shape measures, and examples of the cells from each class. The resultant classes that emerged were compared using their electrotonic characteristics and physiological profiles.

Spinal cord modular organization and rhythm generation: an NMDA iontophoretic study in the frog

Previous work using electrical microstimulation has suggested the existence of modules subserving limb posture in the spinal cord. In this study, the question of modular organization was reinvestigated with the more selective method of chemical microstimulation. N-methyl--aspartate (NMDA) iontophoresis was applied to 229 sites of the lumbar spinal cord gray while monitoring the isometric force output of the ipsilateral hindlimb at the ankle. A force response was elicited from 69 sites. At 18 of these sites, tonic forces were generated and rhythmic forces at 44. In the case of tonic forces, their directions clustered along four orientations: lateral extension, rostral flexion, adduction, and caudal extension. For the entire set of forces (tonic and rhythmic), the same clusters of orientations were found with the addition of a cluster directed as a flexion toward the body. This distribution of force orientations was quite comparable to that obtained with electrical stimulation at the same sites. The map of tonic responses revealed a topographic organization; each type of force orientation was elicited from sites that grouped together in zones at distinct rostrocaudal and depth locations. In the case of rhythmic sequences of force orientations, some were distinctly more common, whereas others were rarely elicited by NMDA. Mapping of the most common rhythms showed that each was elicited from two or three regions of the cord. These regions were close in location to the tonic regions that produced those forces that represented components specific to that rhythm. There was an additional caudal region from which the different rhythms also could be elicited. Taken together, these results support the concept of a modular organization of the motor system in the frog's spinal cord and delineate the topography of these modules. They also suggest that these modules are used by the circuitry underlying rhythmic pattern generation by the spinal cord.