Plasticity of dendritic excitability

Dendrites are equipped with a plethora of voltage-gated ion channels that greatly enrich the computational and storage capacity of neurons. The excitability of dendrites and dendritic function display plasticity under diverse circumstances such as neuromodulation, adaptation, learning and memory, trauma, or disorders. This adaptability arises from alterations in the biophysical properties or the expression levels of voltage-gated ion channels-induced by the activity of neurotransmitters, neuromodulators, and second-messenger cascades. In this review we discuss how this plasticity of dendritic excitability could alter information transfer and processing within dendrites, neurons, and neural networks under physiological and pathological conditions.     

Neuronal firing sensitivity to morphologic and active membrane parameters

Both the excitability of a neuron's membrane, driven by active ion channels, and dendritic morphology contribute to neuronal firing dynamics, but the relative importance and interactions between these features remain poorly understood. Recent modeling studies have shown that different combinations of active conductances can evoke similar firing patterns, but have neglected how morphology might contribute to homeostasis. Parameterizing the morphology of a cylindrical dendrite, we introduce a novel application of mathematical sensitivity analysis that quantifies how dendritic length, diameter, and surface area influence neuronal firing, and compares these effects directly against those of active parameters. The method was applied to a model of neurons from goldfish Area II. These neurons exhibit, and likely contribute to, persistent activity in eye velocity storage, a simple model of working memory. We introduce sensitivity landscapes, defined by local sensitivity analyses of firing rate and gain to each parameter, performed globally across the parameter space. Principal directions over which sensitivity to all parameters varied most revealed intrinsic currents that most controlled model output. We found domains where different groups of parameters had the highest sensitivities, suggesting that interactions within each group shaped firing behaviors within each specific domain. Application of our method, and its characterization of which models were sensitive to general morphologic features, will lead to advances in understanding how realistic morphology participates in functional homeostasis. Significantly, we can predict which active conductances, and how many of them, will compensate for a given age- or development-related structural change, or will offset a morphologic perturbation resulting from trauma or neurodegenerative disorder, to restore normal function. Our method can be adapted to analyze any computational model. Thus, sensitivity landscapes, and the quantitative predictions they provide, can give new insight into mechanisms of homeostasis in any biological system.     

Directional Summation in Non-direction Selective Retinal Ganglion Cells

Retinal ganglion cells receive inputs from multiple bipolar cells which must be integrated before a decision to fire is made. Theoretical studies have provided clues about how this integration is accomplished but have not directly determined the rules regulating summation of closely timed inputs along single or multiple dendrites. Here we have examined dendritic summation of multiple inputs along On ganglion cell dendrites in whole mount rat retina. We activated inputs at targeted locations by uncaging glutamate sequentially to generate apparent motion along On ganglion cell dendrites in whole mount retina. Summation was directional and dependent13 on input sequence. Input moving away from the soma (centrifugal) resulted in supralinear summation, while activation sequences moving toward the soma (centripetal) were linear. Enhanced summation for centrifugal activation was robust as it was also observed in cultured retinal ganglion cells. This directional summation was dependent on hyperpolarization activated cyclic nucleotide-gated (HCN) channels as blockade with ZD7288 eliminated directionality. A computational model confirms that activation of HCN channels can override a preference for centripetal summation expected from cell anatomy. This type of direction selectivity could play a role in coding movement similar to the axial selectivity seen in locust ganglion cells which detect looming stimuli. More generally, these results suggest that non-directional retinal ganglion cells can discriminate between input sequences independent of the retina network.     

Local Plasticity of Dendritic Excitability Can Be Autonomous of Synaptic Plasticity and Regulated by Activity-Based Phosphorylation of Kv4.2

While plasticity is typically associated with persistent modifications of synaptic strengths, recent studies indicated that modulations of dendritic excitability may form the other part of the engram and dynamically affect computational processing and output of neuronal circuits. However it remains unknown whether modulation of dendritic excitability is controlled by synaptic changes or whether it can be distinct from them. Here we report the first observation of the induction of a persistent plastic decrease in dendritic excitability decoupled from synaptic stimulation, which is localized and purely activity-based. In rats this local plasticity decrease is conferred by CamKII mediated phosphorylation of A-type potassium channels upon interaction of a back propagating action potential (bAP) with dendritic depolarization.     

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.     

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.     

Active dendrites,potassium channels and synaptic plasticity

The dendrites of CA1 pyramidal neurons in the hippocampus express numerous types of voltage-gated ion channel, but the distributions or densities of many of these channels are very non-uniform. Sodium channels in the dendrites are responsible for action potential (AP) propagation from the axon into the dendrites (back-propagation); calcium channels are responsible for local changes in dendritic calcium concentrations following back-propagating APs and synaptic potentials; and potassium channels help regulate overall dendritic excitability. Several lines of evidence are presented here to suggest that back-propagating APs, when coincident with excitatory synaptic input, can lead to the induction of either long-term depression (LTD) or long-term potentiation (LTP). The induction of LTD or LTP is correlated with the magnitude of the rise in intracellular calcium. When brief bursts of synaptic potentials are paired with postsynaptic APs in a theta-burst pairing paradigm, the induction of LTP is dependent on the invasion of the AP into the dendritic tree. The amplitude of the AP in the dendrites is dependent, in part, on the activity of a transient, A-type potassium channel that is expressed at high density in the dendrites and correlates with the induction of the LTP. Furthermore, during the expression phase of the LTP, there are local changes in dendritic excitability that may result from modulation of the functioning of this transient potassium channel. The results support the view that the active properties of dendrites play important roles in synaptic integration and synaptic plasticity of these neurons.     

HCN1 channels constrain synaptically evoked Ca2+ spikes in distal dendrites of CA1 pyramidal neurons

HCN1 hyperpolarization-activated cation channels act as an inhibitory constraint of both spatial learning and synaptic integration and long-term plasticity in the distal dendrites of hippocampal CA1 pyramidal neurons. However, as HCN1 channels provide an excitatory current, the mechanism of their inhibitory action remains unclear. Here we report that HCN1 channels also constrain CA1 distal dendritic Ca2+ spikes, which have been implicated in the induction of LTP at distal excitatory synapses. Our experimental and computational results indicate that HCN1 channels provide both an active shunt conductance that decreases the temporal integration of distal EPSPs and a tonic depolarizing current that increases resting inactivation of T-type and N-type voltage-gated Ca2+ channels, which contribute to the Ca2+ spikes. This dual mechanism may provide a general means by which HCN channels regulate dendritic excitability.     

The bacterial K+ channel structure and its implications for neuronal channels.

Voltage-gated K+ (Kv) channels play a central role in generating action potentials and rhythmic patterns, as well as in dendritic signal processing in neurons. Recently, the first structure of a member of the K+ channel family was solved. Although this channel is from bacteria and has a streamlined body plan with no voltage gating, it establishes the architecture of the functional core of the voltage-gated (K+) channels and their relatives. This architecture explains the crucial features of ion permeation and blockade, and gives some strong hints about gating. The bacterial K+ channel structure is the central piece in a puzzle; it remains to be seen how it will fit together with other domains of the Kv channels, with auxiliary subunits, and with other signal transduction molecules.     

On the superposition of currents from ion channels.

We derive a number of statistical properties of the superposition of several independent channels contributing to a patch-clamp recording. Failure of these properties indicates dependence of the channels and may suggest the nature of interactions. We show how properties such as dwell-time distributions of the individual channels may be determined from those of the superposition in the case that the channels are independent.     

Voltage-gated potassium channels: from hyperexcitability to excitement.

The superfamily of voltage-activated potassium channels may express structurally and functionally diverse voltage-activated potassium channels in the nervous system. The roles of some voltage-activated potassium channel types, e.g. rapidly inactivating (transiently active type) channels and muscarine sensitive muscarine sensitive channels, are beginning to be understood. They may significantly influence dendritic action-potential back-propagation, signal to noise ratios in presynaptic excitability or the responsiveness of a neuron to synaptic input. Inherited disorders related to changes in excitability (episodic ataxia, epilepsy, heart arrhythmia) or to defects in sensory perception (hearing loss) have been associated with mutations in a few voltage-activated potassium channel genes. Most likely, more voltage-activated potassium channel genes will be linked to related disorders in the near future.     

Self-influencing synaptic plasticity: Recurrent changes of synaptic weights can lead to specific functional properties

Recent experimental results suggest that dendritic and back-propagating spikes can influence synaptic plasticity in different ways (Holthoff, 2004; Holthoff et al., 2005). In this study we investigate how these signals could interact at dendrites in space and time leading to changing plasticity properties at local synapse clusters. Similar to a previous study (Saudargiene et al., 2004) we employ a differential Hebbian learning rule to emulate spike-timing dependent plasticity and investigate how the interaction of dendritic and back-propagating spikes, as the post-synaptic signals, could influence plasticity. Specifically, we will show that local synaptic plasticity driven by spatially confined dendritic spikes can lead to the emergence of synaptic clusters with different properties. If one of these clusters can drive the neuron into spiking, plasticity may change and the now arising global influence of a back-propagating spike can lead to a further segregation of the clusters and possibly the dying-off of some of them leading to more functional specificity. These results suggest that through plasticity being a spatial and temporal local process, the computational properties of dendrites or complete neurons can be substantially augmented. Action Editor: Wulfram Gerstner     

Parallel Computational Subunits in Dentate Granule Cells Generate Multiple Place Fields

A fundamental question in understanding neuronal computations is how dendritic events influence the output of the neuron. Different forms of integration of neighbouring and distributed synaptic inputs, isolated dendritic spikes and local regulation of synaptic efficacy suggest that individual dendritic branches may function as independent computational subunits. In the present paper, we study how these local computations influence the output of the neuron. Using a simple cascade model, we demonstrate that triggering somatic firing by a relatively small dendritic branch requires the amplification of local events by dendritic spiking and synaptic plasticity. The moderately branching dendritic tree of granule cells seems optimal for this computation since larger dendritic trees favor local plasticity by isolating dendritic compartments, while reliable detection of individual dendritic spikes in the soma requires a low branch number. Finally, we demonstrate that these parallel dendritic computations could contribute to the generation of multiple independent place fields of hippocampal granule cells.     

Specific Sorting and Post-Golgi Trafficking of Dendritic Potassium Channels in Living Neurons

Proper membrane localization of ion channels is essential for the function of neuronal cells. Particularly, the computational ability of dendrites depends on the localization of different ion channels in specific subcompartments. However, the molecular mechanisms that control ion channel localization in distinct dendritic subcompartments are largely unknown. Here, we developed a quantitative live cell imaging method to analyze protein sorting and post-Golgi vesicular trafficking. We focused on two dendritic voltage-gated potassium channels that exhibit distinct localizations: Kv2.1 in proximal dendrites and Kv4.2 in distal dendrites. Our results show that Kv2.1 and Kv4.2 channels are sorted into two distinct populations of vesicles at the Golgi apparatus. The targeting of Kv2.1 and Kv4.2 vesicles occurred by distinct mechanisms as evidenced by their requirement for specific peptide motifs, cytoskeletal elements, and motor proteins. By live cell and super-resolution imaging, we identified a novel trafficking machinery important for the localization of Kv2.1 channels. Particularly, we identified non-muscle myosin II as an important factor in Kv2.1 trafficking. These findings reveal that the sorting of ion channels at the Golgi apparatus and their subsequent trafficking by unique molecular mechanisms are crucial for their specific localizations within dendrites.     

A computational model of dendrite elongation and branching based on MAP2 phosphorylation

We introduce a new computational model of dendritic development in neurons. In contrast to previous models, our model explicitly includes cellular mechanisms involved in dendritic development. It is based on recent experimental data which indicates that the phosphorylation state of microtubule-associated protein 2 (MAP2) may play a key role in controlling dendritic elongation and branching (Audesirk et al., 1997). Dephosphorylated MAP2 favours elongation by promoting microtubule polymerization and bundling, whilst branching is more likely to occur when MAP2 is phosphorylated and microtubules are spaced apart. In the model, the rate of elongation and branching is directly determined by the ratio of phosphorylated to dephosphorylated MAP2. This is regulated by calmodulin-dependent protein kinase II (CaMKII) and calcineurin, which are both dependent on the intracellular calcium concentration. Results from computer simulations of the model suggest that the wide variety of branching patterns observed among different cell types may be generated by the same underlying mechanisms and that elongation and branching are not necessarily independent processes. The model predicts how the branching pattern will change following manipulations with calcium, CaMKII and MAP2 phosphorylation.     

Molecular dynamics simulations of membrane proteins

Membrane proteins control the traffic across cell membranes and thereby play an essential role in cell function from transport of various solutes to immune response via molecular recognition. Because it is very difficult to determine the structures of membrane proteins experimentally, computational methods have been increasingly used to study their structure and function. Here we focus on two classes of membrane proteins—ion channels and transporters—which are responsible for the generation of action potentials in nerves, muscles, and other excitable cells. We describe how computational methods have been used to construct models for these proteins and to study the transport mechanism. The main computational tool is the molecular dynamics (MD) simulation, which can be used for everything from refinement of protein structures to free energy calculations of transport processes. We illustrate with specific examples from gramicidin and potassium channels and aspartate transporters how the function of these membrane proteins can be investigated using MD simulations.     

How to decide whether small samples comply with an equidistribution

The decision whether a measured distribution complies with an equidistribution is a central element of many biostatistical methods. High throughput differential expression measurements, for instance, necessitate to judge possible over-representation of genes. The reliability of this judgement, however, is strongly affected when rarely expressed genes are pooled. We propose a method that can be applied to frequency ranked distributions and that yields a simple but efficient criterion to assess the hypothesis of equiprobable expression levels. By applying our technique to surrogate data we exemplify how the decision criterion can differentiate between a true equidistribution and a triangular distribution. The distinction succeeds even for small sample sizes where standard tests of significance (e.g. chi(2)) fail. Our method will have a major impact on several problems of computational biology where rare events baffle a reliable assessment of frequency distributions. The program package is available upon request from the authors.     

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.