Dendritic Conductances Research Articles

Computational models reveal how chloride dynamics determine the optimal distribution of inhibitory synapses to minimise dendritic excitability.

Many neurons in the mammalian central nervous system have complex dendritic arborisations and active dendritic conductances that enable these cells to perform sophisticated computations. How dendritically targeted inhibition affects local dendritic excitability is not fully understood. Here we use computational models of branched dendrites to investigate where GABAergic synapses should be placed to minimise dendritic excitability over time. To do so, we formulate a metric we term the "Inhibitory Level" (IL), which quantifies the effectiveness of synaptic inhibition for reducing the depolarising effect of nearby excitatory input. GABAergic synaptic inhibition is dependent on the reversal potential for GABAA receptors (EGABA), which is primarily set by the transmembrane chloride ion (Cl-) concentration gradient. We, therefore, investigated how variable EGABA and dynamic chloride affects dendritic inhibition. We found that the inhibitory effectiveness of dendritic GABAergic synapses combines at an encircled branch junction. The extent of this inhibitory accumulation is dependent on the number of branches and location of synapses but is independent of EGABA. This inhibitory accumulation occurs even for very distally placed inhibitory synapses when they are hyperpolarising-but not when they are shunting. When accounting for Cl- fluxes and dynamics in Cl- concentration, we observed that Cl- loading is detrimental to inhibitory effectiveness. This enabled us to determine the most inhibitory distribution of GABAergic synapses which is close to-but not at-a shared branch junction. This distribution balances a trade-off between a stronger combined inhibitory influence when synapses closely encircle a branch junction with the deleterious effects of increased Cl- by loading that occurs when inhibitory synapses are co-located.

Non-uniform distribution of dendritic nonlinearities differentially engages thalamostriatal and corticostriatal inputs onto cholinergic interneurons.

The tonic activity of striatal cholinergic interneurons (CINs) is modified differentially by their afferent inputs. Although their unitary synaptic currents are identical, in most CINs cortical inputs onto distal dendrites only weakly entrain them, whereas proximal thalamic inputs trigger abrupt pauses in discharge in response to salient external stimuli. To test whether the dendritic expression of the active conductances that drive autonomous discharge contribute to the CINs' capacity to dissociate cortical from thalamic inputs, we used an optogenetics-based method to quantify dendritic excitability in mouse CINs. We found that the persistent sodium (NaP) current gave rise to dendritic boosting, and that the hyperpolarization-activated cyclic nucleotide-gated (HCN) current gave rise to a subhertz membrane resonance. This resonance may underlie our novel finding of an association between CIN pauses and internally-generated slow wave events in sleeping non-human primates. Moreover, our method indicated that dendritic NaP and HCN currents were preferentially expressed in proximal dendrites. We validated the non-uniform distribution of NaP currents: pharmacologically; with two-photon imaging of dendritic back-propagating action potentials; and by demonstrating boosting of thalamic, but not cortical, inputs by NaP currents. Thus, the localization of active dendritic conductances in CIN dendrites mirrors the spatial distribution of afferent terminals and may promote their differential responses to thalamic vs. cortical inputs.

Do Biological Constraints Impair Dendritic Computation?

Computations on the dendritic trees of neurons have important constraints. Voltage dependent conductances in dendrites are not similar to arbitrary direct-current generation, they are the basis for dendritic nonlinearities and they do not allow converting positive currents into negative currents. While it has been speculated that the dendritic tree of a neuron can be seen as a multi-layer neural network and it has been shown that such an architecture could be computationally strong, we do not know if that computational strength is preserved under these biological constraints. Here we simulate models of dendritic computation with and without these constraints. We find that dendritic model performance on interesting machine learning tasks is not hurt by these constraints but may benefit from them. Our results suggest that single real dendritic trees may be able to learn a surprisingly broad range of tasks.

Mechanisms of Supralinear Calcium Integration in Dendrites of Hippocampal CA1 Fast-Spiking Cells.

In fast-spiking (FS), parvalbumin-expressing interneurons of the CA1 hippocampus, activation of the GluA2-lacking Ca2+-permeable AMPA receptors (CP-AMPARs) in basal dendrites is coupled to Ca2+-induced Ca2+-release (CICR), and can result in a supralinear summation of postsynaptic Ca2+-transients (post-CaTs). While this mechanism is important in controlling the direction of long-term plasticity, it is still unknown whether it can operate at all excitatory synapses converging onto FS cells or at a set of synapses receiving a particular input. Using a combination of patch-clamp recordings and two-photon Ca2+ imaging in acute mouse hippocampal slices with computational simulations, here we compared the generation of supralinear post-CaTs between apical and basal dendrites of FS cells. We found that, similar to basal dendrites, apical post-CaTs summated supralinearly and relied mainly on the activation of the CP-AMPARs, with a variable contribution of other Ca2+ sources, such as NMDA receptors, L-type voltage-gated Ca2+-channels and Ca2+ release. In addition, supralinear post-CaTs generated in apical dendrites had a slower decay time and a larger cumulative charge than those in basal, and were associated with a stronger level of somatic depolarization. The model predicted that modulation of ryanodine receptors and of the Ca2+ extrusion mechanisms, such as the Na+/Ca2+-exchanger and SERCA pump, had a major impact on the magnitude of supralinear post-CaTs. These data reveal that supralinear Ca2+ summation is a common mechanism of Ca2+ signaling at CP-AMPAR-containing synapses. Shaped in a location-specific manner through modulation of ryanodine receptors and Ca2+ extrusion mechanisms, CP-AMPAR/CICR signaling is suitable for synapse-specific bidirectional modification of incoming inputs in the absence of active dendritic conductances.

Pre-synaptic Muscarinic Excitation Enhances the Discrimination of Looming Stimuli in a Collision-Detection Neuron

SUMMARYVisual neurons that track objects on a collision course are often finely tuned to their target stimuli because this is critical for survival. The presynaptic neural networks converging on these neurons and their role in tuning them remain poorly understood. We took advantage of well-known characteristics of one such neuron in the grasshopper visual system to investigate the properties of its presynaptic input network. We find the structure more complex than hitherto realized. In addition to dynamic lateral inhibition used to filter out background motion, presynaptic circuits include normalizing inhibition and excitatory interactions mediated by muscarinic acetylcholine receptors. These interactions preferentially boost responses to coherently expanding visual stimuli generated by colliding objects, as opposed to spatially incoherent controls, helping to discriminate between them. Hence, in addition to active dendritic conductances within collision-detecting neurons, multiple layers of inhibitory and excitatory presynaptic connections are needed to finely tune neural circuits for collision detection.

Active dendritic integration as a mechanism for robust and precise grid cell firing.

Understanding how active dendrites are exploited for behaviorally relevant computations is a fundamental challenge in neuroscience. Grid cells in medial entorhinal cortex are an attractive model system for addressing this question, as the computation they perform is clear: they convert synaptic inputs into spatially modulated, periodic firing. Whether active dendrites contribute to the generation of the dual temporal and rate codes characteristic of grid cell output is unknown. We show that dendrites of medial entorhinal cortex neurons are highly excitable and exhibit a supralinear input-output function in vitro, while in vivo recordings reveal membrane potential signatures consistent with recruitment of active dendritic conductances. By incorporating these nonlinear dynamics into grid cell models, we show that they can sharpen the precision of the temporal code and enhance the robustness of the rate code, thereby supporting a stable, accurate representation of space under varying environmental conditions. Our results suggest that active dendrites may therefore constitute a key cellular mechanism for ensuring reliable spatial navigation.

Active subthreshold dendritic conductances shape the local field potential.

Key points The local field potential (LFP), the low‐frequency part of extracellular potentials recorded in neural tissue, is often used for probing neural circuit activity. Interpreting the LFP signal is difficult, however.While the cortical LFP is thought mainly to reflect synaptic inputs onto pyramidal neurons, little is known about the role of the various subthreshold active conductances in shaping the LFP.By means of biophysical modelling we obtain a comprehensive qualitative understanding of how the LFP generated by a single pyramidal neuron depends on the type and spatial distribution of active subthreshold currents.For pyramidal neurons, the h‐type channels probably play a key role and can cause a distinct resonance in the LFP power spectrum.Our results show that the LFP signal can give information about the active properties of neurons and imply that preferred frequencies in the LFP can result from those cellular properties instead of, for example, network dynamics. The main contribution to the local field potential (LFP) is thought to stem from synaptic input to neurons and the ensuing subthreshold dendritic processing. The role of active dendritic conductances in shaping the LFP has received little attention, even though such ion channels are known to affect the subthreshold neuron dynamics. Here we used a modelling approach to investigate the effects of subthreshold dendritic conductances on the LFP. Using a biophysically detailed, experimentally constrained model of a cortical pyramidal neuron, we identified conditions under which subthreshold active conductances are a major factor in shaping the LFP. We found that, in particular, the hyperpolarization‐activated inward current, I h, can have a sizable effect and cause a resonance in the LFP power spectral density. To get a general, qualitative understanding of how any subthreshold active dendritic conductance and its cellular distribution can affect the LFP, we next performed a systematic study with a simplified model. We found that the effect on the LFP is most pronounced when (1) the synaptic drive to the cell is asymmetrically distributed (i.e. either basal or apical), (2) the active conductances are distributed non‐uniformly with the highest channel densities near the synaptic input and (3) when the LFP is measured at the opposite pole of the cell relative to the synaptic input. In summary, we show that subthreshold active conductances can be strongly reflected in LFP signals, opening up the possibility that the LFP can be used to characterize the properties and cellular distributions of active conductances.

NMDA Receptors Multiplicatively Scale Visual Signals and Enhance Directional Motion Discrimination in Retinal Ganglion Cells

Postsynaptic responses in many CNS neurons are typically small and variable, often making it difficult to distinguish physiologically relevant signals from background noise. To extract salient information, neurons are thought to integrate multiple synaptic inputs and/or selectively amplify specific synaptic activation patterns. Here, we present evidence for a third strategy: directionally selective ganglion cells (DSGCs) in the mouse retina multiplicatively scale visual signals via a mechanism that requires both nonlinear NMDA receptor (NMDAR) conductances in DSGC dendrites and directionally tuned inhibition provided by the upstream retinal circuitry. Postsynaptic multiplication enables DSGCs to discriminate visual motion more accurately in noisy visual conditions without compromising directional tuning. These findings demonstrate a novel role for NMDARs in synaptic processing and provide new insights into how synaptic and network features interact to accomplish physiologically relevant neural computations.

Neuron Morphology Influences Axon Initial Segment Plasticity.

In most vertebrate neurons, action potentials are initiated in the axon initial segment (AIS), a specialized region of the axon containing a high density of voltage-gated sodium and potassium channels. It has recently been proposed that neurons use plasticity of AIS length and/or location to regulate their intrinsic excitability. Here we quantify the impact of neuron morphology on AIS plasticity using computational models of simplified and realistic somatodendritic morphologies. In small neurons (e.g., dentate granule neurons), excitability was highest when the AIS was of intermediate length and located adjacent to the soma. Conversely, neurons having larger dendritic trees (e.g., pyramidal neurons) were most excitable when the AIS was longer and/or located away from the soma. For any given somatodendritic morphology, increasing dendritic membrane capacitance and/or conductance favored a longer and more distally located AIS. Overall, changes to AIS length, with corresponding changes in total sodium conductance, were far more effective in regulating neuron excitability than were changes in AIS location, while dendritic capacitance had a larger impact on AIS performance than did dendritic conductance. The somatodendritic influence on AIS performance reflects modest soma-to-AIS voltage attenuation combined with neuron size-dependent changes in AIS input resistance, effective membrane time constant, and isolation from somatodendritic capacitance. We conclude that the impact of AIS plasticity on neuron excitability will depend largely on somatodendritic morphology, and that, in some neurons, a shorter or more distally located AIS may promote, rather than limit, action potential generation.

Contributions from active dendritic conductances to the Local Field Potential

The Local Field Potential (LFP) is typically assumed to mainly stem from synaptic inputs and their subthreshold dendritic processing. The role of active dendritic conductances in shaping the LFP has often been ignored, even though several ion channels are active in the subthreshold voltage regime. Here we use biophysical modeling to investigate the impact of active conductances and their spatial distributions on the LFP in the subthreshold voltage regime. We used models of neocortical pyramidal neurons with realistic morphologies and systematically varied the spatial distributions of active conductances and synaptic inputs. We linearized the active conductances -- yielding the so-called quasi-active description -- thereby reducing the number of model parameters and highlighting that active currents can be divided into two classes: regenerative and restorative. In terms of the filtering properties of the cell membrane, regenerative conductances amplify low frequencies of the synaptic input current, whereas restorative conductances dampen them. The low-frequency components of the synaptic input current give the largest contributions to the LFP, due to their larger distance between synaptic currents and associated return currents. Since active conductances can enhance or diminish a neuron's response to low frequencies, they are also expected to affect the LFP. We indeed found that the effect of active conductances on the single-neuron LFP is strongest for the lowest frequencies (< 10-30 Hz). The impact was most pronounced when 1) the synaptic input is asymmetric (i.e., either basal or apical), 2) the active conductances are distributed non-uniformly with the highest channel densities near the synaptic input, and 3) when the LFP is measured at the opposite pole of the cell relative to the synaptic input. Restorative conductances are typically expressed in the LFP as resonance peaks. However, these are considerably smaller than the corresponding peaks for the membrane potentials and transmembrane currents. We compared the findings from our quasi-active models with published, experimentally constrained pyramidal cell models that display various active conductances. We found that in particular the hyperpolarization-activated inward current, IH, can have a sizable impact on the shape of the LFP, since it is a restorative current, strong in the apical dendrite, and active at subthreshold voltages. We conclude that subthreshold contributions of active currents to the LFP of detailed pyramidal cell models can be very well captured by quasi-active models containing one or two voltage-dependent currents, and that their contribution can be a major factor in shaping the LFP for the lowest frequencies.

Impact of single-site axonal GABAergic synaptic events on cerebellar interneuron activity.

Axonal ionotropic receptors are present in a variety of neuronal types, and their function has largely been associated with the modulation of axonal activity and synaptic release. It is usually assumed that activation of axonal GABA(A)Rs comes from spillover, but in cerebellar molecular layer interneurons (MLIs) the GABA source is different: in these cells, GABA release activates presynaptic GABA(A) autoreceptors (autoRs) together with postsynaptic targets, producing an autoR-mediated synaptic event. The frequency of presynaptic, autoR-mediated miniature currents is twice that of their somatodendritic counterparts, suggesting that autoR-mediated responses have an important effect on interneuron activity. Here, we used local Ca(2+) photolysis in MLI axons of juvenile rats to evoke GABA release from individual varicosities to study the activation of axonal autoRs in single release sites. Our data show that single-site autoR conductances are similar to postsynaptic dendritic conductances. In conditions of high [Cl(-)](i), autoR-mediated conductances range from 1 to 5 nS; this corresponds to ∼30-150 GABA(A) channels per presynaptic varicosity, a value close to the number of channels in postsynaptic densities. Voltage responses produced by the activation of autoRs in single varicosities are amplified by a Na(v)-dependent mechanism and propagate along the axon with a length constant of 91 µm. Immunolabeling determination of synapse location shows that on average, one third of the synapses produce autoR-mediated signals that are large enough to reach the axon initial segment. Finally, we show that single-site activation of presynaptic GABA(A) autoRs leads to an increase in MLI excitability and thus conveys a strong feedback signal that contributes to spiking activity.

Active dendrites mediate stratified gamma-range coincidence detection in hippocampal model neurons.

Quantitative metrics for the temporal window of integration/coincidence detection, based on the spike-triggered average, were employed to assess the emergence and dependence of gamma-range coincidence detection in hippocampal pyramidal neurons on various ion channel combinations. The presence of hyperpolarization-activated cyclic nucleotide-gated (HCN) channels decreased the coincidence detection window (CDW) of the neuronal compartment to the gamma frequency range. Interaction of HCN channels with T-type calcium channels and persistent sodium channels further reduced the CDW, whereas interaction with A-type potassium channels broadened the CDW. When multiple channel gradients were co-expressed, the high density of resonating conductances in the distal dendrites led to a slow gamma CDW in the proximal dendrites and a fast-gamma CDW in the distal dendrites. The presence of resonating and spike-generating conductances serve as a mechanism underlying the emergence of stratified gamma-range coincidence detection in the dendrites of CA1 pyramidal neurons, enabling them to perform behaviour- and state-dependent gamma frequency multiplexing. Hippocampal pyramidal neurons exhibit gamma-phase preference in their spikes, selectively route inputs through gamma frequency multiplexing and are considered part of gamma-bound cell assemblies. How do these neurons exhibit gamma-frequency coincidence detection capabilities, a feature that is essential for the expression of these physiological observations, despite their slow membrane time constant? In this conductance-based modelling study, we developed quantitative metrics for the temporal window of integration/coincidence detection based on the spike-triggered average (STA) of the neuronal compartment. We employed these metrics in conjunction with quantitative measures for spike initiation dynamics to assess the emergence and dependence of coincidence detection and STA spectral selectivity on various ion channel combinations. We found that the presence of resonating conductances (hyperpolarization-activated cyclic nucleotide-gated or T-type calcium), either independently or synergistically when expressed together, led to the emergence of spectral selectivity in the spike initiation dynamics and a significant reduction in the coincidence detection window (CDW). The presence of A-type potassium channels, along with resonating conductances, reduced the STA characteristic frequency and broadened the CDW, but persistent sodium channels sharpened the CDW by strengthening the spectral selectivity in the STA. Finally, in a morphologically precise model endowed with experimentally constrained channel gradients, we found that somatodendritic compartments expressed functional maps of strong theta-frequency selectivity in spike initiation dynamics and gamma-range CDW. Our results reveal the heavy expression of resonating and spike-generating conductances as the mechanism underlying the robust emergence of stratified gamma-range coincidence detection in the dendrites of hippocampal and cortical pyramidal neurons.

Dendritic orientation and branching distinguish a class of multifunctional turtle spinal interneurons.

Spinal interneurons can integrate diverse propriospinal and supraspinal inputs that trigger or modulate locomotion and other limb movements. These synaptic inputs can occur on distal dendrites and yet must remain effective at the soma. Active dendritic conductances may amplify distal dendritic inputs, but appear to play a minimal role during scratching, at least. Another possibility is that spinal interneurons that integrate inputs on distal dendrites have unusually simple dendritic trees that effectively funnel current to the soma. We previously described a class of spinal interneurons, called transverse interneurons (or T neurons), in adult turtles. T neurons were defined as having dendrites that extend further in the transverse plane than rostrocaudally and a soma that extends further mediolaterally than rostrocaudally. T neurons are multifunctional, as they were activated during both swimming and scratching motor patterns. T neurons had higher peak firing rates and larger membrane potential oscillations during scratching than scratch-activated interneurons with different dendritic morphologies (“non-T” neurons). These characteristics make T neurons good candidates to play an important role in integrating diverse inputs and generating or relaying rhythmic motor patterns. Here, we quantitatively investigated additional dendritic morphological characteristics of T neurons as compared to non-T neurons. We found that T neurons have less total dendritic length, a greater proportion of dendritic length in primary dendrites, and dendrites that are oriented more mediolaterally. Thus, T neuron dendritic trees extend far mediolaterally, yet are unusually simple, which may help channel synaptic current from distal dendrites in the lateral and ventral funiculi to the soma. In combination with T neuron physiological properties, these dendritic properties may help integrate supraspinal and propriospinal inputs and generate and/or modulate rhythmic limb movements.

Activity-Dependent Gating of Calcium Spikes by A-type K+ Channels Controls Climbing Fiber Signaling in Purkinje Cell Dendrites

SummaryIn cerebellar Purkinje cell dendrites, heterosynaptic calcium signaling induced by the proximal climbing fiber (CF) input controls plasticity at distal parallel fiber (PF) synapses. The substrate and regulation of this long-range dendritic calcium signaling are poorly understood. Using high-speed calcium imaging, we examine the role of active dendritic conductances. Under basal conditions, CF stimulation evokes T-type calcium signaling displaying sharp proximodistal decrement. Combined mGluR1 receptor activation and depolarization, two activity-dependent signals, unlock P/Q calcium spikes initiation and propagation, mediating efficient CF signaling at distal sites. These spikes are initiated in proximal smooth dendrites, independently from somatic sodium action potentials, and evoke high-frequency bursts of all-or-none fast-rising calcium transients in PF spines. Gradual calcium spike burst unlocking arises from increasing inactivation of mGluR1-modulated low-threshold A-type potassium channels located in distal dendrites. Evidence for graded activity-dependent CF calcium signaling at PF synapses refines current views on cerebellar supervised learning rules.

Glutamate-bound NMDARs arising from in vivo-like network activity extend spatio-temporal integration in a L5 cortical pyramidal cell model.

In vivo, cortical pyramidal cells are bombarded by asynchronous synaptic input arising from ongoing network activity. However, little is known about how such ‘background’ synaptic input interacts with nonlinear dendritic mechanisms. We have modified an existing model of a layer 5 (L5) pyramidal cell to explore how dendritic integration in the apical dendritic tuft could be altered by the levels of network activity observed in vivo. Here we show that asynchronous background excitatory input increases neuronal gain and extends both temporal and spatial integration of stimulus-evoked synaptic input onto the dendritic tuft. Addition of fast and slow inhibitory synaptic conductances, with properties similar to those from dendritic targeting interneurons, that provided a ‘balanced’ background configuration, partially counteracted these effects, suggesting that inhibition can tune spatio-temporal integration in the tuft. Excitatory background input lowered the threshold for NMDA receptor-mediated dendritic spikes, extended their duration and increased the probability of additional regenerative events occurring in neighbouring branches. These effects were also observed in a passive model where all the non-synaptic voltage-gated conductances were removed. Our results show that glutamate-bound NMDA receptors arising from ongoing network activity can provide a powerful spatially distributed nonlinear dendritic conductance. This may enable L5 pyramidal cells to change their integrative properties as a function of local network activity, potentially allowing both clustered and spatially distributed synaptic inputs to be integrated over extended timescales.

A Quantitative Description of Dendritic Conductances and Its Application to Dendritic Excitation in Layer 5 Pyramidal Neurons

Postsynaptic integration is a complex function of passive membrane properties and nonlinear activation of voltage-gated channels. Some cortical neurons express many voltage-gated channels, with each displaying heterogeneous dendritic conductance gradients. This complexity has hindered the construction of experimentally based mechanistic models of cortical neurons. Here we show that it is possible to overcome this obstacle. We recorded the membrane potential from the soma and apical dendrite of layer 5 (L5) pyramidal neurons of the rat somatosensory cortex. A combined experimental and numerical parameter peeling procedure was implemented to optimize a detailed ionic mechanism for the generation and propagation of dendritic spikes in neocortical L5 pyramidal neurons. In the optimized model, the density of voltage-gated Ca(2+) channels decreased linearly from the soma, and leveled at the distal apical dendrite. The density of the small-conductance Ca(2+)-activated channel decreased along the apical dendrite, whereas the density of the large-conductance Ca(2+)-gated K(+) channel was uniform throughout the apical dendrite. The model predicted an ionic mechanism for the generation of a dendritic spike, the interaction of this spike with the backpropagating action potential, the mechanism responsible for the ability of the proximal apical dendrite to control the coupling between the axon and the dendrite, and the generation of NMDA spikes in the distal apical tuft. Moreover, in addition to faithfully predicting many experimental results recorded from the apical dendrite of L5 pyramidal neurons, the model validates a new methodology for mechanistic modeling of neurons in the CNS.

Dendritic Generation of mGluR-Mediated Slow Afterdepolarization in Layer 5 Neurons of Prefrontal Cortex

Many prefrontal cortex (PFC)-dependent tasks require individual neurons to fire persistently in response to brief stimuli. Persistent activity is proposed to involve changes in intrinsic properties, resulting in an increased sensitivity to inputs. The dendrite is particularly relevant to this hypothesis because it receives the majority of synaptic inputs and is enriched for conductances implicated in persistent firing. We provide evidence that dendritic conductances contribute to persistent activity-related changes in intrinsic properties. The effects of Group 1 metabotropic glutamate receptor (mGluR) activation on persistent activity-related properties were tested in two classes of rat L5 neurons with distinct membrane properties: those projecting to the pons (CPn) and those projecting across the commissure to the contralateral cortex (COM). mGluR activation produced long-term changes in the subthreshold properties of CPn, but not COM neurons. These changes were indicative of a decrease in hyperpolarization-activated cation nonselective current (I(h)) at the soma and dendrite. mGluR activation also transiently increased the amplitude of the postburst slow afterdepolarization potential (sADP) at the soma of both neuron types. Interestingly, the sADP occurred along the extent of the apical dendrite in CPn and COM neurons. Simultaneous somatic/dendritic recordings revealed that the dendritic sADP does not result solely from passive propagation of the somatic sADP. Focal mGluR activation in L5, near the soma or at the border of L1/L2, near the tuft, generates a local sADP. This dendritic depolarization may act synergistically with synaptic input to regulate mnemonic activity in PFC.

Interspike intervals under the constraint of linear synaptic integration and background synaptic activity

Previous work [1] using a one-compartment steady-state computer model of a neuron shows how combinations of two active dendritic conductances can produce a linear dendritic response over a voltage range of ca. 15 to 22 mV. Here we extend this linearization issue to a dynamic, non-steady state situation for a neuron model with a soma, dendrite and distal compartment. It is known that synaptically-induced voltage pulses that originate in distal compartments will be both attenuated and broader by the time they reach the soma due to the passive cable properties of neurons. Additionally, neurons in intact brains are not isolated but are under constant synaptic bombardment. While a single synaptic event will not significantly affect the cell properties, thousands of such events will significantly change the integrative properties of neurons [2]. Due to the reduction in membrane resistance caused by synaptic activity, attenuation of individual voltage pulses is even stronger in the presence of background synaptic activity. This study shows that the presence of active conductances distributed along the cell membrane can mitigate some of the effects of electrical filtering on voltage pulses propagating to the soma, even in the presence of background synaptic activity. We consider three uniformly distributed conductances found in pyramidal cells of the forebrain: persistent sodium current (INaP) [3,4], hyperpolarization-activated mixed cation current (Ih) [5], and A-type potassium current (IKA) [6]. Added to an otherwise passive cell, select combinations of these voltage-activated ion channels can generate linear synaptic integration over the entire interspike interval (ISI) membrane potential range, that is from rest (here -72 mV) to threshold (here roughly -45 mV). In the presence of various levels of background synaptic activity, the ratio of these active conductances changes and contributes to the inverse ISI effect. Under the constraint of linear synaptic integration, the length of the ISI is seen to be inversely related to the intensity of the background synaptic activity. This inverse relationship results from a decrease of the effective time constant of the cell by increased levels of membrane conductance induced by the combination of synaptic activity and active conductances.

Preserving axosomatic spiking features despite diverse dendritic morphology

Throughout the nervous system, cells belonging to a certain electrical class (e-class)-sharing high similarity in firing response properties-may nevertheless have widely variable dendritic morphologies. To quantify the effect of this morphological variability on the firing of layer 5 thick-tufted pyramidal cells (TTCs), a detailed conductance-based model was constructed for a three-dimensional reconstructed exemplar TTC. The model exhibited spike initiation in the axon and reproduced the characteristic features of individual spikes, as well as of the firing properties at the soma, as recorded in a population of TTCs in young Wistar rats. When using these model parameters over the population of 28 three-dimensional reconstructed TTCs, both axonal and somatic ion channel densities had to be scaled linearly with the conductance load imposed on each of these compartments. Otherwise, the firing of model cells deviated, sometimes very significantly, from the experimental variability of the TTC e-class. The study provides experimentally testable predictions regarding the coregulation of axosomatic membrane ion channels density for cells with different dendritic conductance load, together with a simple and systematic method for generating reliable conductance-based models for the whole population of modeled neurons belonging to a particular e-class, with variable morphology as found experimentally.

Vestibular integrator neurons have quadratic functions due to voltage dependent conductances

The nonlinear properties of the dendrites of the prepositus hypoglossi nucleus (PHN) neurons are essential for the operation of the vestibular neural integrator that converts a head velocity signal to one that controls eye position. A novel system of frequency probing, namely quadratic sinusoidal analysis (QSA), was used to decode the intrinsic nonlinear behavior of these neurons under voltage clamp conditions. Voltage clamp currents were measured at harmonic and interactive frequencies using specific nonoverlapping stimulation frequencies. Eigenanalysis of the QSA matrix reduces it to a remarkably compact processing unit, composed of just one or two dominant components (eigenvalues). The QSA matrix of rat PHN neurons provides signatures of the voltage dependent conductances for their particular dendritic and somatic distributions. An important part of the nonlinear response is due to the persistent sodium conductance (gNaP), which is likely to be essential for sustained effects needed for a neural integrator. It was found that responses in the range of 10mV peak to peak could be well described by quadratic nonlinearities suggesting that effects of higher degree nonlinearities would add only marginal improvement. Therefore, the quadratic response is likely to sufficiently capture most of the nonlinear behavior of neuronal systems except for extremely large synaptic inputs. Thus, neurons have two distinct linear and quadratic functions, which shows that piecewise linear + quadratic analysis is much more complete than just piecewise linear analysis; in addition quadratic analysis can be done at a single holding potential. Furthermore, the nonlinear neuronal responses contain more frequencies over a wider frequency band than the input signal. As a consequence, they convert limited amplitude and bandwidth input signals to wider bandwidth and more complex output responses. Finally, simulations at subthreshold membrane potentials with realistic PHN neuron models suggest that the quadratic functions are fundamentally dominated by active dendritic structures and persistent sodium conductances.