Distribution of single-channel conductances in cultured rat hippocampal neurons

1. The nonhomogeneous spatial distribution of ionic channels in neurons has been implied from intracellular recordings at somatic and dendritic locations. These reports indicate that Na- and Ca-dependent regenerative currents are distributed differently throughout the neuron. Although a variety of K conductances and a noninactivating Na conductance have been described in intracellular studies, little is known about the spatial distribution of inward and outward currents throughout different regions of the neuron. 2. We recorded from cell-attached patches from cultured hippocampal cells from 1-day-old rats. The cells were cultured for 3-21 days. The spatial distribution of a variety of ionic channels was determined by comparing the conductances from somatic and dendritic membranes. Single-channel currents obtained from cell-attached patches were identified by the time course of ensemble (averaged) responses, voltage dependence, and the effect of channel blocking agents. 3. We consistently observed that only the rapidly inactivating inward current was localized to the soma. The other channel types that we studied, including an inward noninactivating, delayed rectifier and transient A-type currents, were observed in both the somatic and dendritic regions. 4. We suggest that the distribution of ionic conductances that we have observed may be functional in limiting excitability during development of neurons.     

Stochastic Ion Channel Gating in Dendritic Neurons: Morphology Dependence and Probabilistic Synaptic Activation of Dendritic Spikes

Neuronal activity is mediated through changes in the probability of stochastic transitions between open and closed states of ion channels. While differences in morphology define neuronal cell types and may underlie neurological disorders, very little is known about influences of stochastic ion channel gating in neurons with complex morphology. We introduce and validate new computational tools that enable efficient generation and simulation of models containing stochastic ion channels distributed across dendritic and axonal membranes. Comparison of five morphologically distinct neuronal cell types reveals that when all simulated neurons contain identical densities of stochastic ion channels, the amplitude of stochastic membrane potential fluctuations differs between cell types and depends on sub-cellular location. For typical neurons, the amplitude of membrane potential fluctuations depends on channel kinetics as well as open probability. Using a detailed model of a hippocampal CA1 pyramidal neuron, we show that when intrinsic ion channels gate stochastically, the probability of initiation of dendritic or somatic spikes by dendritic synaptic input varies continuously between zero and one, whereas when ion channels gate deterministically, the probability is either zero or one. At physiological firing rates, stochastic gating of dendritic ion channels almost completely accounts for probabilistic somatic and dendritic spikes generated by the fully stochastic model. These results suggest that the consequences of stochastic ion channel gating differ globally between neuronal cell-types and locally between neuronal compartments. Whereas dendritic neurons are often assumed to behave deterministically, our simulations suggest that a direct consequence of stochastic gating of intrinsic ion channels is that spike output may instead be a probabilistic function of patterns of synaptic input to dendrites.     

Oscillatory burst discharge generated through conditional backpropagation of dendritic spikes.

Gamma frequencies of burst discharge (>40 Hz) have become recognized in select cortical and non-cortical regions as being important in feature extraction, neural synchrony and oscillatory discharge. Pyramidal cells of the electrosensory lateral line lobe (ELL) of Apteronotus leptorhynchus generate burst discharge in relation to specific features of sensory input in vivo that resemble those recognized as gamma frequency discharge when examined in vitro. We have shown that these bursts are generated by an entirely novel mechanism termed conditional backpropagation that involves an intermittent failure of dendritic Na+ spike conduction. Conditional backpropagation arises from a frequency-dependent broadening of dendritic spikes during repetitive discharge, and a mismatch between the refractory periods of somatic and dendritic spikes. A high threshold class of K+ channel, AptKv3.3, is expressed at high levels and distributed over the entire soma-dendritic axis of pyramidal cells. AptKv3.3 channels are shown to contribute to the repolarization of both somatic and dendritic spikes, with pharmacological blockade of dendritic Kv3 channels revealing an important role in controlling the threshold for burst discharge. The entire process of conditional back-propagation and burst output is successfully simulated using a new compartmental model of pyramidal cells that incorporates a cumulative inactivation of dendritic K+ channels during repetitive discharge. This work is important in demonstrating how the success of spike backpropagation can control the output of a principle sensory neuron, and how this process is regulated by the distribution and properties of voltage-dependent K+ channels.     

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.     

Modeling the attenuation and failure of action potentials in the dendrites of hippocampal neurons.

We modeled two different mechanisms, a shunting conductance and a slow sodium inactivation, to test whether they could modulate the active propagation of a train of action potentials in a dendritic tree. Computer simulations, using a compartmental model of a pyramidal neuron, suggest that each of these two mechanisms could account for the activity-dependent attenuation and failure of the action potentials in the dendrites during the train. Each mechanism is shown to be in good qualitative agreement with experimental findings on somatic or dendritic stimulation and on the effects of hyperpolarization. The conditions under which branch point failures can be observed, and a few experimentally testable predictions, are presented and discussed.     

Direction-selective dendritic action potentials in rabbit retina

Dendritic spikes that propagate toward the soma are well documented, but their physiological role remains uncertain. Our in vitro patch-clamp recordings and two-photon calcium imaging show that direction-selective retinal ganglion cells (DSGCs) utilize orthograde dendritic spikes during physiological activity. DSGCs signal the direction of image motion. Excitatory subthreshold postsynaptic potentials are observed in DSGCs for motion in all directions and provide a weakly tuned directional signal. However, spikes are generated over only a narrow range of motion angles, indicating that spike generation greatly enhances directional tuning. Our results indicate that spikes are initiated at multiple sites within the dendritic arbors of DSGCs and that each dendritic spike initiates a somatic spike. We propose that dendritic spike failure, produced by local inhibitory inputs, might be a critical factor that enhances directional tuning of somatic spikes.     

Location-dependent effects of inhibition on local spiking in pyramidal neuron dendrites

Cortical computations are critically dependent on interactions between pyramidal neurons (PNs) and a menagerie of inhibitory interneuron types. A key feature distinguishing interneuron types is the spatial distribution of their synaptic contacts onto PNs, but the location-dependent effects of inhibition are mostly unknown, especially under conditions involving active dendritic responses. We studied the effect of somatic vs. dendritic inhibition on local spike generation in basal dendrites of layer 5 PNs both in neocortical slices and in simple and detailed compartmental models, with equivalent results: somatic inhibition divisively suppressed the amplitude of dendritic spikes recorded at the soma while minimally affecting dendritic spike thresholds. In contrast, distal dendritic inhibition raised dendritic spike thresholds while minimally affecting their amplitudes. On-the-path dendritic inhibition modulated both the gain and threshold of dendritic spikes depending on its distance from the spike initiation zone. Our findings suggest that cortical circuits could assign different mixtures of gain vs. threshold inhibition to different neural pathways, and thus tailor their local computations, by managing their relative activation of soma- vs. dendrite-targeting interneurons.     

Role of Multiple Calcium and Calcium-Dependent Conductances in Regulation of Hippocampal Dentate Granule Cell Excitability

We have constructed a detailed model of a hippocampal dentate granule (DG) cell that includes nine different channel types. Channel densities and distributions were chosen to reproduce reported physiological responses observed in normal solution and when blockers were applied. The model was used to explore the contribution of each channel type to spiking behavior with particular emphasis on the mechanisms underlying postspike events. T-type calcium current in more distal dendrites contributed prominently to the appearance of the depolarizing after-potential, and its effect was controlled by activation of BK-type calcium-dependent potassium channels. Co-activation and interaction of N-, and/or L-type calcium and AHP currents present in somatic and proximal dendritic regions contributed to the adaptive properties of the model DG cell in response to long-lasting current injection. The model was used to predict changes in channel densities that could lead to epileptogenic burst discharges and to predict the effect of altered buffering capacity on firing behavior. We conclude that the clustered spatial distributions of calcium related channels, the presence of slow delayed rectifier potassium currents in dendrites, and calcium buffering properties, together, might explain the resistance of DG cells to the development of epileptogenic burst discharges.     

Visual Stimuli Evoked Action Potentials Trigger Rapidly Propagating Dendritic Calcium Transients in the Frog Optic Tectum Layer 6 Neurons

The superior colliculus in mammals or the optic tectum in amphibians is a major visual information processing center responsible for generation of orientating responses such as saccades in monkeys or prey catching avoidance behavior in frogs. The conserved structure function of the superior colliculus the optic tectum across distant species such as frogs, birds monkeys permits to draw rather general conclusions after studying a single species. We chose the frog optic tectum because we are able to perform whole-cell voltage-clamp recordings fluorescence imaging of tectal neurons while they respond to a visual stimulus. In the optic tectum of amphibians most visual information is processed by pear-shaped neurons possessing long dendritic branches, which receive the majority of synapses originating from the retinal ganglion cells. Since the first step of the retinal input integration is performed on these dendrites, it is important to know whether this integration is enhanced by active dendritic properties. We demonstrate that rapid calcium transients coinciding with the visual stimulus evoked action potentials in the somatic recordings can be readily detected up to the fine branches of these dendrites. These transients were blocked by calcium channel blockers nifedipine CdCl₂ indicating that calcium entered dendrites via voltage-activated L-type calcium channels. The high speed of calcium transient propagation, >300 μm in <10 ms, is consistent with the notion that action potentials, actively propagating along dendrites, open voltage-gated L-type calcium channels causing rapid calcium concentration transients in the dendrites. We conclude that such activation by somatic action potentials of the dendritic voltage gated calcium channels in the close vicinity to the synapses formed by axons of the retinal ganglion cells may facilitate visual information processing in the principal neurons of the frog optic tectum.     

The Subcellular Distribution of T-Type Ca2+ Channels in Interneurons of the Lateral Geniculate Nucleus

Inhibitory interneurons (INs) in the lateral geniculate nucleus (LGN) provide both axonal and dendritic GABA output to thalamocortical relay cells (TCs). Distal parts of the IN dendrites often enter into complex arrangements known as triadic synapses, where the IN dendrite plays a dual role as postsynaptic to retinal input and presynaptic to TC dendrites. Dendritic GABA release can be triggered by retinal input, in a highly localized process that is functionally isolated from the soma, but can also be triggered by somatically elicited Ca²⁺-spikes and possibly by backpropagating action potentials. Ca²⁺-spikes in INs are predominantly mediated by T-type Ca²⁺-channels (T-channels). Due to the complex nature of the dendritic signalling, the function of the IN is likely to depend critically on how T-channels are distributed over the somatodendritic membrane (T-distribution). To study the relationship between the T-distribution and several IN response properties, we here run a series of simulations where we vary the T-distribution in a multicompartmental IN model with a realistic morphology. We find that the somatic response to somatic current injection is facilitated by a high T-channel density in the soma-region. Conversely, a high T-channel density in the distal dendritic region is found to facilitate dendritic signalling in both the outward direction (increases the response in distal dendrites to somatic input) and the inward direction (the soma responds stronger to distal synaptic input). The real T-distribution is likely to reflect a compromise between several neural functions, involving somatic response patterns and dendritic signalling.     

The capabilities and limitations of conductance-based compartmental neuron models with reduced branched or unbranched morphologies and active dendrites

Conductance-based neuron models are frequently employed to study the dynamics of biological neural networks. For speed and ease of use, these models are often reduced in morphological complexity. Simplified dendritic branching structures may process inputs differently than full branching structures, however, and could thereby fail to reproduce important aspects of biological neural processing. It is not yet well understood which processing capabilities require detailed branching structures. Therefore, we analyzed the processing capabilities of full or partially branched reduced models. These models were created by collapsing the dendritic tree of a full morphological model of a globus pallidus (GP) neuron while preserving its total surface area and electrotonic length, as well as its passive and active parameters. Dendritic trees were either collapsed into single cables (unbranched models) or the full complement of branch points was preserved (branched models). Both reduction strategies allowed us to compare dynamics between all models using the same channel density settings. Full model responses to somatic inputs were generally preserved by both types of reduced model while dendritic input responses could be more closely preserved by branched than unbranched reduced models. However, features strongly influenced by local dendritic input resistance, such as active dendritic sodium spike generation and propagation, could not be accurately reproduced by any reduced model. Based on our analyses, we suggest that there are intrinsic differences in processing capabilities between unbranched and branched models. We also indicate suitable applications for different levels of reduction, including fast searches of full model parameter space.     

DPP6 establishes the A-type K(+) current gradient critical for the regulation of dendritic excitability in CA1 hippocampal neurons

Subthreshold-activating A-type K(+) currents are essential for the proper functioning of the brain, where they act to delay excitation and regulate firing frequency. In CA1 hippocampal pyramidal neuron dendrites, the density of A-type K(+) current increases with distance from the soma, playing an important role in synaptic integration and plasticity. The mechanism underlying this gradient has, however, remained elusive. Here, dendritic recordings from mice lacking the Kv4 transmembrane auxiliary subunit DPP6 revealed that this protein is critical for generating the A-current gradient. Loss of DPP6 led to a decrease in A-type current, specifically in distal dendrites. Decreased current density was accompanied by a depolarizing shift in the voltage dependence of channel activation. Together these changes resulted in hyperexcitable dendrites with enhanced dendritic AP back-propagation, calcium electrogenesis, and induction of synaptic long-term potentiation. Despite enhanced dendritic excitability, firing behavior evoked by somatic current injection was mainly unaffected in DPP6-KO recordings, indicating compartmentalized regulation of neuronal excitability.     

Dendritic Spikes Amplify the Synaptic Signal to Enhance Detection of Motion in a Simulation of the Direction-Selective Ganglion Cell

The On-Off direction-selective ganglion cell (DSGC) in mammalian retinas responds most strongly to a stimulus moving in a specific direction. The DSGC initiates spikes in its dendritic tree, which are thought to propagate to the soma with high probability. Both dendritic and somatic spikes in the DSGC display strong directional tuning, whereas somatic PSPs (postsynaptic potentials) are only weakly directional, indicating that spike generation includes marked enhancement of the directional signal. We used a realistic computational model based on anatomical and physiological measurements to determine the source of the enhancement. Our results indicate that the DSGC dendritic tree is partitioned into separate electrotonic regions, each summing its local excitatory and inhibitory synaptic inputs to initiate spikes. Within each local region the local spike threshold nonlinearly amplifies the preferred response over the null response on the basis of PSP amplitude. Using inhibitory conductances previously measured in DSGCs, the simulation results showed that inhibition is only sufficient to prevent spike initiation and cannot affect spike propagation. Therefore, inhibition will only act locally within the dendritic arbor. We identified the role of three mechanisms that generate directional selectivity (DS) in the local dendritic regions. First, a mechanism for DS intrinsic to the dendritic structure of the DSGC enhances DS on the null side of the cell''s dendritic tree and weakens it on the preferred side. Second, spatially offset postsynaptic inhibition generates robust DS in the isolated dendritic tips but weak DS near the soma. Third, presynaptic DS is apparently necessary because it is more robust across the dendritic tree. The pre- and postsynaptic mechanisms together can overcome the local intrinsic DS. These local dendritic mechanisms can perform independent nonlinear computations to make a decision, and there could be analogous mechanisms within cortical circuitry.     

The Role of Ongoing Dendritic Oscillations in Single-Neuron Dynamics

The dendritic tree contributes significantly to the elementary computations a neuron performs while converting its synaptic inputs into action potential output. Traditionally, these computations have been characterized as both temporally and spatially localized. Under this localist account, neurons compute near-instantaneous mappings from their current input to their current output, brought about by somatic summation of dendritic contributions that are generated in functionally segregated compartments. However, recent evidence about the presence of oscillations in dendrites suggests a qualitatively different mode of operation: the instantaneous phase of such oscillations can depend on a long history of inputs, and under appropriate conditions, even dendritic oscillators that are remote may interact through synchronization. Here, we develop a mathematical framework to analyze the interactions of local dendritic oscillations and the way these interactions influence single cell computations. Combining weakly coupled oscillator methods with cable theoretic arguments, we derive phase-locking states for multiple oscillating dendritic compartments. We characterize how the phase-locking properties depend on key parameters of the oscillating dendrite: the electrotonic properties of the (active) dendritic segment, and the intrinsic properties of the dendritic oscillators. As a direct consequence, we show how input to the dendrites can modulate phase-locking behavior and hence global dendritic coherence. In turn, dendritic coherence is able to gate the integration and propagation of synaptic signals to the soma, ultimately leading to an effective control of somatic spike generation. Our results suggest that dendritic oscillations enable the dendritic tree to operate on more global temporal and spatial scales than previously thought; notably that local dendritic activity may be a mechanism for generating on-going whole-cell voltage oscillations.     

Dendritic slow dynamics enables localized cortical activity to switch between mobile and immobile modes with noisy background input

Mounting lines of evidence suggest the significant computational ability of a single neuron empowered by active dendritic dynamics. This motivates us to study what functionality can be acquired by a network of such neurons. The present paper studies how such rich single-neuron dendritic dynamics affects the network dynamics, a question which has scarcely been specifically studied to date. We simulate neurons with active dendrites networked locally like cortical pyramidal neurons, and find that naturally arising localized activity--called a bump--can be in two distinct modes, mobile or immobile. The mode can be switched back and forth by transient input to the cortical network. Interestingly, this functionality arises only if each neuron is equipped with the observed slow dendritic dynamics and with in vivo-like noisy background input. If the bump activity is considered to indicate a point of attention in the sensory areas or to indicate a representation of memory in the storage areas of the cortex, this would imply that the flexible mode switching would be of great potential use for the brain as an information processing device. We derive these conclusions using a natural extension of the conventional field model, which is defined by combining two distinct fields, one representing the somatic population and the other representing the dendritic population. With this tool, we analyze the spatial distribution of the degree of after-spike adaptation and explain how we can understand the presence of the two distinct modes and switching between the modes. We also discuss the possible functional impact of this mode-switching ability.     

Dendritic sodium spikes endow neurons with inverse firing rate response to correlated synaptic activity

Many neurons possess dendrites enriched with sodium channels and are capable of generating action potentials. However, the role of dendritic sodium spikes remain unclear. Here, we study computational models of neurons to investigate the functional effects of dendritic spikes. In agreement with previous studies, we found that point neurons or neurons with passive dendrites increase their somatic firing rate in response to the correlation of synaptic bombardment for a wide range of input conditions, i.e. input firing rates, synaptic conductances, or refractory periods. However, neurons with active dendrites show the opposite behavior: for a wide range of conditions the firing rate decreases as a function of correlation. We found this property in three types of models of dendritic excitability: a Hodgkin-Huxley model of dendritic spikes, a model with integrate and fire dendrites, and a discrete-state dendritic model. We conclude that fast dendritic spikes confer much broader computational properties to neurons, sometimes opposite to that of point neurons.     

Spatial codes in dendritic BC1 RNA

BC1 RNA is a dendritic untranslated RNA that has been implicated in local translational control mechanisms in neurons. Prerequisite for a functional role of the RNA in synaptodendritic domains is its targeted delivery along the dendritic extent. We report here that the targeting-competent 5' BC1 domain carries two dendritic targeting codes. One code, specifying somatic export, is located in the medial-basal region of the 5' BC1 stem-loop structure. It is defined by an export-determinant stem-bulge motif. The second code, specifying long-range dendritic delivery, is located in the apical part of the 5' stem-loop domain. This element features a GA kink-turn (KT) motif that is indispensable for distal targeting. It specifically interacts with heterogeneous nuclear ribonucleoprotein A2, a trans-acting targeting factor that has previously been implicated in the transport of MBP mRNA in oligodendrocytes and neurons. Our work suggests that a BC1 KT motif encodes distal targeting via the A2 pathway and that architectural RNA elements, such as KT motifs, may function as spatial codes in neural cells.     

Integro-differential equations and the stability of neural networks with dendritic structure

 We analyse the effects of dendritic structure on the stability of a recurrent neural network in terms of a set of coupled, non-linear Volterra integro-differential equations. These, which describe the dynamics of the somatic membrane potentials, are obtained by eliminating the dendritic potentials from the underlying compartmental model or cable equations. We then derive conditions for Turing-like instability as a precursor for pattern formation in a spatially organized network. These conditions depend on the spatial distribution of axo-dendritic connections across the network. Received: 2 November 1994/Accepted in revised form: 7 March 1995