Influence fields: a quantitative framework for representation and analysis of active dendrites

The enigmatic HCN channels: A cellular neurophysiology perspective

What physiological role does a slow hyperpolarization-activated ion channel with mixed cation selectivity play in the fast world of neuronal action potentials that are driven by depolarization? That puzzling question has piqued the curiosity of physiology enthusiasts about the hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, which are widely expressed across the body and especially in neurons. In this review, we emphasize the need to assess HCN channels from the perspective of how they respond to time-varying signals, while also accounting for their interactions with other co-expressing channels and receptors. First, we illustrate how the unique structural and functional characteristics of HCN channels allow them to mediate a slow negative feedback loop in the neurons that they express in. We present the several physiological implications of this negative feedback loop to neuronal response characteristics including neuronal gain, voltage sag and rebound, temporal summation, membrane potential resonance, inductive phase lead, spike triggered average, and coincidence detection. Next, we argue that the overall impact of HCN channels on neuronal physiology critically relies on their interactions with other co-expressing channels and receptors. Interactions with other channels allow HCN channels to mediate intrinsic oscillations, earning them the "pacemaker channel" moniker, and to regulate spike frequency adaptation, plateau potentials, neurotransmitter release from presynaptic terminals, and spike initiation at the axonal initial segment. We also explore the impact of spatially non-homogeneous subcellular distributions of HCN channels in different neuronal subtypes and their interactions with other channels and receptors. Finally, we discuss how plasticity in HCN channels is widely prevalent and can mediate different encoding, homeostatic, and neuroprotective functions in a neuron. In summary, we argue that HCN channels form an important class of channels that mediate a diversity of neuronal functions owing to their unique gating kinetics that made them a puzzle in the first place.

Heterogeneous off-target impact of ion-channel deletion on intrinsic properties of hippocampal model neurons that self-regulate calcium

How do neurons that implement cell-autonomous self-regulation of calcium react to knockout of individual ion-channel conductances? To address this question, we used a heterogeneous population of 78 conductance-based models of hippocampal pyramidal neurons that maintained cell-autonomous calcium homeostasis while receiving theta-frequency inputs. At calcium steady-state, we individually deleted each of the 11 active ion-channel conductances from each model. We measured the acute impact of deleting each conductance (one at a time) by comparing intrinsic electrophysiological properties before and immediately after channel deletion. The acute impact of deleting individual conductances on physiological properties (including calcium homeostasis) was heterogeneous, depending on the property, the specific model, and the deleted channel. The underlying many-to-many mapping between ion channels and properties pointed to ion-channel degeneracy. Next, we allowed the other conductances (barring the deleted conductance) to evolve towards achieving calcium homeostasis during theta-frequency activity. When calcium homeostasis was perturbed by ion-channel deletion, post-knockout plasticity in other conductances ensured resilience of calcium homeostasis to ion-channel deletion. These results demonstrate degeneracy in calcium homeostasis, as calcium homeostasis in knockout models was implemented in the absence of a channel that was earlier involved in the homeostatic process. Importantly, in reacquiring homeostasis, ion-channel conductances and physiological properties underwent heterogenous plasticity (dependent on the model, the property, and the deleted channel), even introducing changes in properties that were not directly connected to the deleted channel. Together, post-knockout plasticity geared towards maintaining homeostasis introduced heterogenous off-target effects on several channels and properties, suggesting that extreme caution be exercised in interpreting experimental outcomes involving channel knockouts.

Simulations predict differing phase responses to excitation vs. inhibition in theta-resonant pyramidal neurons

Rhythmic activity is ubiquitous in neural systems, with theta-resonant pyramidal neurons integrating rhythmic inputs in many cortical structures. Impedance analysis has been widely used to examine frequency-dependent responses of neuronal membranes to rhythmic inputs, but it assumes that the neuronal membrane is a linear system, requiring the use of small signals to stay in a near-linear regime. However, postsynaptic potentials are often large and trigger nonlinear mechanisms (voltage-gated ion channels). The goals of this work were to 1) develop an analysis method to evaluate membrane responses in this nonlinear domain and 2) explore phase relationships between rhythmic stimuli and subthreshold and spiking membrane potential (Vmemb) responses in models of theta-resonant pyramidal neurons. Responses in these output regimes were asymmetrical, with different phase shifts during hyperpolarizing and depolarizing half-cycles. Suprathreshold theta-rhythmic stimuli produced nonstationary Vmemb responses. Sinusoidal inputs produced "phase retreat": action potentials occurred progressively later in cycles of the input stimulus, resulting from adaptation. Sinusoidal current with increasing amplitude over cycles produced "phase advance": action potentials occurred progressively earlier. Phase retreat, phase advance, and subthreshold phase shifts were modulated by multiple ion channel conductances. Our results suggest differential responses of cortical neurons depending on the frequency of oscillatory input, which will play a role in neuronal responses to shifts in network state. We hypothesize that intrinsic cellular properties complement network properties and contribute to in vivo phase-shift phenomena such as phase precession, seen in place and grid cells, and phase roll, also observed in hippocampal CA1 neurons.NEW & NOTEWORTHY We augmented electrical impedance analysis to characterize phase shifts between large-amplitude current stimuli and nonlinear, asymmetric membrane potential responses. We predict different frequency-dependent phase shifts in response excitation vs. inhibition, as well as shifts in spike timing over multiple input cycles, in theta-resonant pyramidal neurons. We hypothesize that these effects contribute to navigation-related phenomena such as phase precession and phase roll. Our neuron-level hypothesis complements, rather than falsifies, prior network-level explanations of these phenomena.

The impact of Hodgkin-Huxley models on dendritic research

For the past seven decades, the Hodgkin-Huxley (HH) formalism has been an invaluable tool in the arsenal of neuroscientists, allowing for robust and reproducible modelling of ionic conductances and the electrophysiological phenomena they underlie. Despite its apparent age, its role as a cornerstone of computational neuroscience has not waned. The discovery of dendritic regenerative events mediated by ionic and synaptic conductances has solidified the importance of HH-based models further, yielding new predictions concerning dendritic integration, synaptic plasticity and neuronal computation. These predictions are often validated through in vivo and in vitro experiments, advancing our understanding of the neuron as a biological system and emphasizing the importance of HH-based detailed computational models as an instrument of dendritic research. In this article, we discuss recent studies in which the HH formalism is used to shed new light on dendritic function and its role in neuronal phenomena.

Ion-channel degeneracy: Multiple ion channels heterogeneously regulate intrinsic physiology of rat hippocampal granule cells

Degeneracy, the ability of multiple structural components to elicit the same characteristic functional properties, constitutes an elegant mechanism for achieving biological robustness. In this study, we sought electrophysiological signatures for the expression of ion-channel degeneracy in the emergence of intrinsic properties of rat hippocampal granule cells. We measured the impact of four different ion-channel subtypes-hyperpolarization-activated cyclic-nucleotide-gated (HCN), barium-sensitive inward rectifier potassium (Kir ), tertiapin-Q-sensitive inward rectifier potassium, and persistent sodium (NaP) channels-on 21 functional measurements employing pharmacological agents, and report electrophysiological data on two characteristic signatures for the expression of ion-channel degeneracy in granule cells. First, the blockade of a specific ion-channel subtype altered several, but not all, functional measurements. Furthermore, any given functional measurement was altered by the blockade of many, but not all, ion-channel subtypes. Second, the impact of blocking each ion-channel subtype manifested neuron-to-neuron variability in the quantum of changes in the electrophysiological measurements. Specifically, we found that blocking HCN or Ba-sensitive Kir channels enhanced action potential firing rate, but blockade of NaP channels reduced firing rate of granule cells. Subthreshold measures of granule cell intrinsic excitability (input resistance, temporal summation, and impedance amplitude) were enhanced by blockade of HCN or Ba-sensitive Kir channels, but were not significantly altered by NaP channel blockade. We confirmed that the HCN and Ba-sensitive Kir channels independently altered sub- and suprathreshold properties of granule cells through sequential application of pharmacological agents that blocked these channels. Finally, we found that none of the sub- or suprathreshold measurements of granule cells were significantly altered upon treatment with tertiapin-Q. Together, the heterogeneous many-to-many mapping between ion channels and single-neuron intrinsic properties emphasizes the need to account for ion-channel degeneracy in cellular- and network-scale physiology.

Effects of Ih and TASK-like shunting current on dendritic impedance in layer 5 pyramidal-tract neurons

Pyramidal neurons in neocortex have complex input-output relationships that depend on their morphologies, ion channel distributions, and the nature of their inputs, but which cannot be replicated by simple integrate-and-fire models. The impedance properties of their dendritic arbors, such as resonance and phase shift, shape neuronal responses to synaptic inputs and provide intraneuronal functional maps reflecting their intrinsic dynamics and excitability. Experimental studies of dendritic impedance have shown that neocortical pyramidal tract neurons exhibit distance-dependent changes in resonance and impedance phase with respect to the soma. We, therefore, investigated how well several biophysically detailed multicompartment models of neocortical layer 5 pyramidal tract neurons reproduce the location-dependent impedance profiles observed experimentally. Each model tested here exhibited location-dependent impedance profiles, but most captured either the observed impedance amplitude or phase, not both. The only model that captured features from both incorporates hyperpolarization-activated cyclic nucleotide-gated (HCN) channels and a shunting current, such as that produced by Twik-related acid-sensitive K+ (TASK) channels. TASK-like channel density in this model was proportional to local HCN channel density. We found that although this shunting current alone is insufficient to produce resonance or realistic phase response, it modulates all features of dendritic impedance, including resonance frequencies, resonance strength, synchronous frequencies, and total inductive phase. We also explored how the interaction of HCN channel current (Ih) and a TASK-like shunting current shape synaptic potentials and produce degeneracy in dendritic impedance profiles, wherein different combinations of Ih and shunting current can produce the same impedance profile.NEW & NOTEWORTHY We simulated chirp current stimulation in the apical dendrites of 5 biophysically detailed multicompartment models of neocortical pyramidal tract neurons and found that a combination of HCN channels and TASK-like channels produced the best fit to experimental measurements of dendritic impedance. We then explored how HCN and TASK-like channels can shape the dendritic impedance as well as the voltage response to synaptic currents.

Ion-channel regulation of response decorrelation in a heterogeneous multi-scale model of the dentate gyrus

Heterogeneities in biological neural circuits manifest in afferent connectivity as well as in local-circuit components such as neuronal excitability, neural structure and local synaptic strengths. The expression of adult neurogenesis in the dentate gyrus (DG) amplifies local-circuit heterogeneities and guides heterogeneities in afferent connectivity. How do neurons and their networks endowed with these distinct forms of heterogeneities respond to perturbations to individual ion channels, which are known to change under several physiological and pathophysiological conditions? We sequentially traversed the ion channels-neurons-network scales and assessed the impact of eliminating individual ion channels on conductance-based neuronal and network models endowed with disparate local-circuit and afferent heterogeneities. We found that many ion channels differentially contributed to specific neuronal or network measurements, and the elimination of any given ion channel altered several functional measurements. We then quantified the impact of ion-channel elimination on response decorrelation, a well-established metric to assess the ability of neurons in a network to convey complementary information, in DG networks endowed with different forms of heterogeneities. Notably, we found that networks constructed with structurally immature neurons exhibited functional robustness, manifesting as minimal changes in response decorrelation in the face of ion-channel elimination. Importantly, the average change in output correlation was dependent on the eliminated ion channel but invariant to input correlation. Our analyses suggest that neurogenesis-driven structural heterogeneities could assist the DG network in providing functional resilience to molecular perturbations.

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Perturbations at one scale result in a cascading impact on physiology across scales.

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Heterogeneous multi-scale models used to assess the impact of ion-channel deletion.

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Mapping of structural components to functional outcomes is many-to-many.

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Differential & variable impact of ion channel deletion on response decorrelation.

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Neurogenesis-induced structural heterogeneity confers resilience to perturbations.

Heterogeneities in intrinsic excitability and frequency-dependent response properties of granule cells across the blades of the rat dentate gyrus

The dentate gyrus (DG), the input gate to the hippocampus proper, is anatomically segregated into three different sectors, namely, the suprapyramidal blade, the crest region, and the infrapyramidal blade. Although there are well-established differences between these sectors in terms of neuronal morphology, connectivity patterns, and activity levels, differences in electrophysiological properties of granule cells within these sectors have remained unexplored. Here, employing somatic whole cell patch-clamp recordings from the rat DG, we demonstrate that granule cells in these sectors manifest considerable heterogeneities in their intrinsic excitability, temporal summation, action potential characteristics, and frequency-dependent response properties. Across sectors, these neurons showed positive temporal summation of their responses to inputs mimicking excitatory postsynaptic currents and showed little to no sag in their voltage responses to pulse currents. Consistently, the impedance amplitude profile manifested low-pass characteristics and the impedance phase profile lacked positive phase values at all measured frequencies and voltages and for all sectors. Granule cells in all sectors exhibited class I excitability, with broadly linear firing rate profiles, and granule cells in the crest region fired significantly fewer action potentials compared with those in the infrapyramidal blade. Finally, we found weak pairwise correlations across the 18 different measurements obtained individually from each of the three sectors, providing evidence that these measurements are indeed reporting distinct aspects of neuronal physiology. Together, our analyses show that granule cells act as integrators of afferent information and emphasize the need to account for the considerable physiological heterogeneities in assessing their roles in information encoding and processing.NEW & NOTEWORTHY We employed whole cell patch-clamp recordings from granule cells in the three subregions of the rat dentate gyrus to demonstrate considerable heterogeneities in their intrinsic excitability, temporal summation, action potential characteristics, and frequency-dependent response properties. Across sectors, granule cells did not express membrane potential resonance, and their impedance profiles lacked inductive phase leads at all measured frequencies. Our analyses also show that granule cells manifest class I excitability characteristics, categorizing them as integrators of afferent information.

Degeneracy in hippocampal physiology and plasticity

Degeneracy, defined as the ability of structurally disparate elements to perform analogous function, has largely been assessed from the perspective of maintaining robustness of physiology or plasticity. How does the framework of degeneracy assimilate into an encoding system where the ability to change is an essential ingredient for storing new incoming information? Could degeneracy maintain the balance between the apparently contradictory goals of the need to change for encoding and the need to resist change towards maintaining homeostasis? In this review, we explore these fundamental questions with the mammalian hippocampus as an example encoding system. We systematically catalog lines of evidence, spanning multiple scales of analysis that point to the expression of degeneracy in hippocampal physiology and plasticity. We assess the potential of degeneracy as a framework to achieve the conjoint goals of encoding and homeostasis without cross-interferences. We postulate that biological complexity, involving interactions among the numerous parameters spanning different scales of analysis, could establish disparate routes towards accomplishing these conjoint goals. These disparate routes then provide several degrees of freedom to the encoding-homeostasis system in accomplishing its tasks in an input- and state-dependent manner. Finally, the expression of degeneracy spanning multiple scales offers an ideal reconciliation to several outstanding controversies, through the recognition that the seemingly contradictory disparate observations are merely alternate routes that the system might recruit towards accomplishment of its goals.

Stores, Channels, Glue, and Trees: Active Glial and Active Dendritic Physiology

Glial cells and neuronal dendrites were historically assumed to be passive structures that play only supportive physiological roles, with no active contribution to information processing in the central nervous system. Research spanning the past few decades has clearly established this assumption to be far from physiological realities. Whereas the discovery of active channel conductances and their localized plasticity was the turning point for dendritic structures, the demonstration that glial cells release transmitter molecules and communicate across the neuroglia syncytium through calcium wave propagation constituted path-breaking discoveries for glial cell physiology. An additional commonality between these two structures is the ability of calcium stores within their endoplasmic reticulum (ER) to support active propagation of calcium waves, which play crucial roles in the spatiotemporal integration of information within and across cells. Although there have been several demonstrations of regulatory roles of glial cells and dendritic structures in achieving common physiological goals such as information propagation and adaptability through plasticity, studies assessing physiological interactions between these two active structures have been few and far. This lacuna is especially striking given the strong connectivity that is known to exist between these two structures through several complex and tightly intercoupled mechanisms that also recruit their respective ER structures. In this review, we present brief overviews of the parallel literatures on active dendrites and active glial physiology and make a strong case for future studies to directly assess the strong interactions between these two structures in regulating physiology and pathophysiology of the brain.

Active dendrites regulate the spatiotemporal spread of signaling microdomains

Microdomains that emerge from spatially constricted spread of biochemical signaling components play a central role in several neuronal computations. Although dendrites, endowed with several voltage-gated ion channels, form a prominent structural substrate for microdomain physiology, it is not known if these channels regulate the spatiotemporal spread of signaling microdomains. Here, we employed a multiscale, morphologically realistic, conductance-based model of the hippocampal pyramidal neuron that accounted for experimental details of electrical and calcium-dependent biochemical signaling. We activated synaptic N-Methyl-d-Aspartate receptors through theta-burst stimulation (TBS) or pairing (TBP) and assessed microdomain propagation along a signaling pathway that included calmodulin, calcium/calmodulin-dependent protein kinase II (CaMKII) and protein phosphatase 1. We found that the spatiotemporal spread of the TBS-evoked microdomain in phosphorylated CaMKII (pCaMKII) was amplified in comparison to that of the corresponding calcium microdomain. Next, we assessed the role of two dendritically expressed inactivating channels, one restorative (A-type potassium) and another regenerative (T-type calcium), by systematically varying their conductances. Whereas A-type potassium channels suppressed the spread of pCaMKII microdomains by altering the voltage response to TBS, T-type calcium channels enhanced this spread by modulating TBS-induced calcium influx without changing the voltage. Finally, we explored cross-dependencies of these channels with other model components, and demonstrated the heavy mutual interdependence of several biophysical and biochemical properties in regulating microdomains and their spread. Our conclusions unveil a pivotal role for dendritic voltage-gated ion channels in actively amplifying or suppressing biochemical signals and their spatiotemporal spread, with critical implications for clustered synaptic plasticity, robust information transfer and efficient neural coding.

The spatiotemporal spread of biochemical signals in neurons and other cells regulate signaling specificity, tuning of signal propagation, along with specificity and clustering of adaptive plasticity. Theoretical and experimental studies have demonstrated a critical role for cellular morphology and the topology of signaling networks in regulating this spread. In this study, we add a significantly complex dimension to this narrative by demonstrating that voltage-gated ion channels on the plasma membrane could actively amplify or suppress the strength and spread of downstream signaling components. Given the expression of different ion channels with wide-ranging heterogeneity in gating kinetics, localization and density, our results point to an increase in complexity of and degeneracy in signaling spread, and unveil a powerful mechanism for regulating biochemical-signaling pathways across different cell types.

Spatially dispersed synapses yield sharply-tuned place cell responses through dendritic spike initiation

KEY POINTS

The generation of dendritic spikes and the consequent sharp tuning of neuronal responses are together attainable even when iso-feature synapses are randomly dispersed across the dendritic arbor. Disparate combinations of channel conductances with distinct configurations of randomly dispersed place field synapses concomitantly yield similar sharp tuning profiles and similar functional maps of several intrinsic properties. Targeted synaptic plasticity converts silent cells to place cells for specific place fields in models with disparate channel combinations that receive dispersed synaptic inputs from multiple place field locations. Dispersed localization of iso-feature synapses is a strong candidate for achieving sharp feature selectivity in neurons across sensory-perceptual systems, with several degrees of freedom in relation to synaptic locations. Quantitative evidence for the possibility that degeneracy (i.e. the ability of disparate structural components to yield similar functional outcomes) could act as a broad framework that effectively accomplishes the twin goals of input-feature encoding and homeostasis of intrinsic properties without cross interferences.

ABSTRACT

A prominent hypothesis spanning several sensory-perceptual systems implicates spatially clustered synapses in the generation of dendritic spikes that mediate sharply-tuned neuronal responses to input features. In this conductance-based morphologically-precise computational study, we tested this hypothesis by systematically analysing the impact of distinct synaptic and channel localization profiles on sharpness of spatial tuning in hippocampal pyramidal neurons. We found that the generation of dendritic spikes, the emergence of an excitatory ramp in somatic voltage responses, the expression of several intrinsic somatodendritic functional maps and sharp tuning of place-cell responses were all attainable even when iso-feature synapses are randomly dispersed across the dendritic arbor of models with disparate channel combinations. Strikingly, the generation and propagation of dendritic spikes, reliant on dendritic sodium channels and N-methyl-d-asparate receptors, mediated the sharpness of spatial tuning achieved with dispersed synaptic localization. To ensure that our results were not artefacts of narrow parametric choices, we confirmed these conclusions with independent multiparametric stochastic search algorithms spanning thousands of unique models for each synaptic localization scenario. Next, employing virtual knockout models, we demonstrated a vital role for dendritically expressed voltage-gated ion channels, especially the transient potassium channels, in maintaining sharpness of place-cell tuning. Importantly, we established that synaptic potentiation targeted to afferents from one specific place field was sufficient to impart place field selectivity even when intrinsically disparate neurons received randomly dispersed afferents from multiple place field locations. Our results provide quantitative evidence for disparate combinations of channel and synaptic localization profiles to concomitantly yield similar tuning and similar intrinsic properties.

Increased transient Na+ conductance and action potential output in layer 2/3 prefrontal cortex neurons of the fmr1-/y mouse

KEY POINTS

Layer 2/3 neurons of the prefrontal cortex display higher gain of somatic excitability, responding with a higher number of action potentials for a given stimulus, in fmr1^-/y mice. In fmr1^-/y L2/3 neurons, action potentials are taller, faster and narrower. Outside-out patch clamp recordings revealed that the maximum Na⁺ conductance density is higher in fmr1^-/y L2/3 neurons. Measurements of three biophysically distinct K⁺ currents revealed a depolarizing shift in the activation of a rapidly inactivating (A-type) K⁺ conductance. Realistic neuronal simulations of the biophysical observations recapitulated the elevated action potential and repetitive firing phenotype.

ABSTRACT

Fragile X syndrome is the most common form of inherited mental impairment and autism. The prefrontal cortex is responsible for higher order cognitive processing, and prefrontal dysfunction is believed to underlie many of the cognitive and behavioural phenotypes associated with fragile X syndrome. We recently demonstrated that somatic and dendritic excitability of layer (L) 5 pyramidal neurons in the prefrontal cortex of the fmr1^-/y mouse is significantly altered due to changes in several voltage-gated ion channels. In addition to L5 pyramidal neurons, L2/3 pyramidal neurons play an important role in prefrontal circuitry, integrating inputs from both lower brain regions and the contralateral cortex. Using whole-cell current clamp recording, we found that L2/3 pyramidal neurons in prefrontal cortex of fmr1^-/y mouse fired more action potentials for a given stimulus compared with wild-type neurons. In addition, action potentials in fmr1^-/y neurons were significantly larger, faster and narrower. Voltage clamp of outside-out patches from L2/3 neurons revealed that the transient Na⁺ current was significantly larger in fmr1^-/y neurons. Furthermore, the activation curve of somatic A-type K⁺ current was depolarized. Realistic conductance-based simulations revealed that these biophysical changes in Na⁺ and K⁺ channel function could reliably reproduce the observed increase in action potential firing and altered action potential waveform. These results, in conjunction with our prior findings on L5 neurons, suggest that principal neurons in the circuitry of the medial prefrontal cortex are altered in distinct ways in the fmr1^-/y mouse and may contribute to dysfunctional prefrontal cortex processing in fragile X syndrome.

Strings on a Violin: Location Dependence of Frequency Tuning in Active Dendrites

Strings on a violin are tuned to generate distinct sound frequencies in a manner that is firmly dependent on finger location along the fingerboard. Sound frequencies emerging from different violins could be very different based on their architecture, the nature of strings and their tuning. Analogously, active neuronal dendrites, dendrites endowed with active channel conductances, are tuned to distinct input frequencies in a manner that is dependent on the dendritic location of the synaptic inputs. Further, disparate channel expression profiles and differences in morphological characteristics could result in dendrites on different neurons of the same subtype tuned to distinct frequency ranges. Alternately, similar location-dependence along dendritic structures could be achieved through disparate combinations of channel profiles and morphological characteristics, leading to degeneracy in active dendritic spectral tuning. Akin to strings on a violin being tuned to different frequencies than those on a viola or a cello, different neuronal subtypes exhibit distinct channel profiles and disparate morphological characteristics endowing each neuronal subtype with unique location-dependent frequency selectivity. Finally, similar to the tunability of musical instruments to elicit distinct location-dependent sounds, neuronal frequency selectivity and its location-dependence are tunable through activity-dependent plasticity of ion channels and morphology. In this morceau, we explore the origins of neuronal frequency selectivity, and survey the literature on the mechanisms behind the emergence of location-dependence in distinct forms of frequency tuning. As a coda to this composition, we present some future directions for this exciting convergence of biophysical mechanisms that endow a neuron with frequency multiplexing capabilities.

Degeneracy in the regulation of short-term plasticity and synaptic filtering by presynaptic mechanisms

KEY POINTS

We develop a new biophysically rooted, physiologically constrained conductance-based synaptic model to mechanistically account for short-term facilitation and depression, respectively through residual calcium and transmitter depletion kinetics. We address the specific question of how presynaptic components (including voltage-gated ion channels, pumps, buffers and release-handling mechanisms) and interactions among them define synaptic filtering and short-term plasticity profiles. Employing global sensitivity analyses (GSAs), we show that near-identical synaptic filters and short-term plasticity profiles could emerge from disparate presynaptic parametric combinations with weak pairwise correlations. Using virtual knockout models, a technique to address the question of channel-specific contributions within the GSA framework, we unveil the differential and variable impact of each ion channel on synaptic physiology. Our conclusions strengthen the argument that parametric and interactional complexity in biological systems should not be viewed from the limited curse-of-dimensionality standpoint, but from the evolutionarily advantageous perspective of providing functional robustness through degeneracy.

ABSTRACT

Information processing in neurons is known to emerge as a gestalt of pre- and post-synaptic filtering. However, the impact of presynaptic mechanisms on synaptic filters has not been quantitatively assessed. Here, we developed a biophysically rooted, conductance-based model synapse that was endowed with six different voltage-gated ion channels, calcium pumps, calcium buffer and neurotransmitter-replenishment mechanisms in the presynaptic terminal. We tuned our model to match the short-term plasticity profile and band-pass structure of Schaffer collateral synapses, and performed sensitivity analyses to demonstrate that presynaptic voltage-gated ion channels regulated synaptic filters through changes in excitability and associated calcium influx. These sensitivity analyses also revealed that calcium- and release-control mechanisms were effective regulators of synaptic filters, but accomplished this without changes in terminal excitability or calcium influx. Next, to perform global sensitivity analysis, we generated 7000 randomized models spanning 15 presynaptic parameters, and computed eight different physiological measurements in each of these models. We validated these models by applying experimentally obtained bounds on their measurements, and found 104 (∼1.5%) models to match the validation criteria for all eight measurements. Analysing these valid models, we demonstrate that analogous synaptic filters emerge from disparate combinations of presynaptic parameters exhibiting weak pairwise correlations. Finally, using virtual knockout models, we establish the variable and differential impact of different presynaptic channels on synaptic filters, underlining the critical importance of interactions among different presynaptic components in defining synaptic physiology. Our results have significant implications for protein-localization strategies required for physiological robustness and for degeneracy in long-term synaptic plasticity profiles.

Variability in State-Dependent Plasticity of Intrinsic Properties during Cell-Autonomous Self-Regulation of Calcium Homeostasis in Hippocampal Model Neurons

How do neurons reconcile the maintenance of calcium homeostasis with perpetual switches in patterns of afferent activity? Here, we assessed state-dependent evolution of calcium homeostasis in a population of hippocampal pyramidal neuron models, through an adaptation of a recent study on stomatogastric ganglion neurons. Calcium homeostasis was set to emerge through cell-autonomous updates to 12 ionic conductances, responding to different types of synaptically driven afferent activity. We first assessed the impact of theta-frequency inputs on the evolution of ionic conductances toward maintenance of calcium homeostasis. Although calcium homeostasis emerged efficaciously across all models in the population, disparate changes in ionic conductances that mediated this emergence resulted in variable plasticity to several intrinsic properties, also manifesting as significant differences in firing responses across models. Assessing the sensitivity of this form of plasticity, we noted that intrinsic neuronal properties and the firing response were sensitive to the target calcium concentration and to the strength and frequency of afferent activity. Next, we studied the evolution of calcium homeostasis when afferent activity was switched, in different temporal sequences, between two behaviorally distinct types of activity: theta-frequency inputs and sharp-wave ripples riding on largely silent periods. We found that the conductance values, intrinsic properties, and firing response of neurons exhibited differential robustness to an intervening switch in the type of afferent activity. These results unveil critical dissociations between different forms of homeostasis, and call for a systematic evaluation of the impact of state-dependent switches in afferent activity on neuronal intrinsic properties during neural coding and homeostasis.

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

KEY POINTS

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.

ABSTRACT

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 atrophy constricts functional maps in resonance and impedance properties of hippocampal model neurons

A gradient in the density of hyperpolarization-activated cyclic-nucleotide gated (HCN) channels is necessary for the emergence of several functional maps within hippocampal pyramidal neurons. Here, we systematically analyzed the impact of dendritic atrophy on nine such functional maps, related to input resistance and local/transfer impedance properties, using conductance-based models of hippocampal pyramidal neurons. We introduced progressive dendritic atrophy in a CA1 pyramidal neuron reconstruction through a pruning algorithm, measured all functional maps in each pruned reconstruction, and arrived at functional forms for the dependence of underlying measurements on dendritic length. We found that, across frequencies, atrophied neurons responded with higher efficiency to incoming inputs, and the transfer of signals across the dendritic tree was more effective in an atrophied reconstruction. Importantly, despite the presence of identical HCN-channel density gradients, spatial gradients in input resistance, local/transfer resonance frequencies and impedance profiles were significantly constricted in reconstructions with dendritic atrophy, where these physiological measurements across dendritic locations converged to similar values. These results revealed that, in atrophied dendritic structures, the presence of an ion channel density gradient alone was insufficient to sustain homologous functional maps along the same neuronal topograph. We assessed the biophysical basis for these conclusions and found that this atrophy-induced constriction of functional maps was mediated by an enhanced spatial spread of the influence of an HCN-channel cluster in atrophied trees. These results demonstrated that the influence fields of ion channel conductances need to be localized for channel gradients to express themselves as homologous functional maps, suggesting that ion channel gradients are necessary but not sufficient for the emergence of functional maps within single neurons.

High-conductance states and A-type K+ channels are potential regulators of the conductance-current balance triggered by HCN channels

An increase in the hyperpolarization-activated cyclic nucleotide-gated (HCN) channel conductance reduces input resistance, whereas the consequent increase in the inward h current depolarizes the membrane. This results in a delicate and unique conductance-current balance triggered by the expression of HCN channels. In this study, we employ experimentally constrained, morphologically realistic, conductance-based models of hippocampal neurons to explore certain aspects of this conductance-current balance. First, we found that the inclusion of an experimentally determined gradient in A-type K+ conductance, but not in M-type K+ conductance, tilts the HCN conductance-current balance heavily in favor of conductance, thereby exerting an overall restorative influence on neural excitability. Next, motivated by the well-established modulation of neuronal excitability by synaptically driven high-conductance states observed under in vivo conditions, we inserted thousands of excitatory and inhibitory synapses with different somatodendritic distributions. We measured the efficacy of HCN channels, independently and in conjunction with other channels, in altering resting membrane potential (RMP) and input resistance ( Rin) when the neuron received randomized or rhythmic synaptic bombardments through variable numbers of synaptic inputs. We found that the impact of HCN channels on average RMP, Rin, firing frequency, and peak-to-peak voltage response was severely weakened under high-conductance states, with the impinging synaptic drive playing a dominant role in regulating these measurements. Our results suggest that the debate on the role of HCN channels in altering excitability should encompass physiological and pathophysiological neuronal states under in vivo conditions and the spatiotemporal interactions of HCN channels with other channels.

Activation of InsP₃ receptors is sufficient for inducing graded intrinsic plasticity in rat hippocampal pyramidal neurons

The synaptic plasticity literature has focused on establishing necessity and sufficiency as two essential and distinct features in causally relating a signaling molecule to plasticity induction, an approach that has been surprisingly lacking in the intrinsic plasticity literature. In this study, we complemented the recently established necessity of inositol trisphosphate (InsP3) receptors (InsP3R) in a form of intrinsic plasticity by asking if InsP3R activation was sufficient to induce intrinsic plasticity in hippocampal neurons. Specifically, incorporation of d-myo-InsP3 in the recording pipette reduced input resistance, maximal impedance amplitude, and temporal summation but increased resonance frequency, resonance strength, sag ratio, and impedance phase lead. Strikingly, the magnitude of plasticity in all these measurements was dependent on InsP3 concentration, emphasizing the graded dependence of such plasticity on InsP3R activation. Mechanistically, we found that this InsP3-induced plasticity depended on hyperpolarization-activated cyclic nucleotide-gated channels. Moreover, this calcium-dependent form of plasticity was critically reliant on the release of calcium through InsP3Rs, the influx of calcium through N-methyl-d-aspartate receptors and voltage-gated calcium channels, and on the protein kinase A pathway. Our results delineate a causal role for InsP3Rs in graded adaptation of neuronal response dynamics, revealing novel regulatory roles for the endoplasmic reticulum in neural coding and homeostasis.

Homeostasis of functional maps in active dendrites emerges in the absence of individual channelostasis

The maintenance of ion channel homeostasis, or channelostasis, is a complex puzzle in neurons with extensive dendritic arborization, encompassing a combinatorial diversity of proteins that encode these channels and their auxiliary subunits, their localization profiles, and associated signaling machinery. Despite this, neurons exhibit amazingly stereotypic, topographically continuous maps of several functional properties along their active dendritic arbor. Here, we asked whether the membrane composition of neurons, at the level of individual ion channels, is constrained by this structural requirement of sustaining several functional maps along the same topograph. We performed global sensitivity analysis on morphologically realistic conductance-based models of hippocampal pyramidal neurons that coexpressed six well-characterized functional maps along their trunk. We generated randomized models by varying 32 underlying parameters and constrained these models with quantitative experimental measurements from the soma and dendrites of hippocampal pyramidal neurons. Analyzing valid models that satisfied experimental constraints on all six functional maps, we found topographically analogous functional maps to emerge from disparate model parameters with weak pairwise correlations between parameters. Finally, we derived a methodology to assess the contribution of individual channel conductances to the various functional measurements, using virtual knockout simulations on the valid model population. We found that the virtual knockout of individual channels resulted in variable, measurement- and location-specific impacts across the population. Our results suggest collective channelostasis as a mechanism behind the robust emergence of analogous functional maps and have significant ramifications for the localization and targeting of ion channels and enzymes that regulate neural coding and homeostasis.

Active dendrites regulate spectral selectivity in location-dependent spike initiation dynamics of hippocampal model neurons

How does the presence of plastic active dendrites in a pyramidal neuron alter its spike initiation dynamics? To answer this question, we measured the spike-triggered average (STA) from experimentally constrained, conductance-based hippocampal neuronal models of various morphological complexities. We transformed the STA computed from these models to the spectral and the spectrotemporal domains and found that the spike initiation dynamics exhibited temporally localized selectivity to a characteristic frequency. In the presence of the hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, the STA characteristic frequency strongly correlated with the subthreshold resonance frequency in the theta frequency range. Increases in HCN channel density or in input variance increased the STA characteristic frequency and its selectivity strength. In the absence of HCN channels, the STA exhibited weak delta frequency selectivity and the characteristic frequency was related to the repolarization dynamics of the action potentials and the recovery kinetics of sodium channels from inactivation. Comparison of STA obtained with inputs at various dendritic locations revealed that nonspiking and spiking dendrites increased and reduced the spectrotemporal integration window of the STA with increasing distance from the soma as direct consequences of passive filtering and dendritic spike initiation, respectively. Finally, the presence of HCN channels set the STA characteristic frequency in the theta range across the somatodendritic arbor and specific STA measurements were strongly related to equivalent transfer-impedance-related measurements. Our results identify explicit roles for plastic active dendrites in neural coding and strongly recommend a dynamically reconfigurable multi-STA model to characterize location-dependent input feature selectivity in pyramidal neurons.

Age- and location-dependent differences in store depletion-induced h-channel plasticity in hippocampal pyramidal neurons

Disruptions of endoplasmic reticulum (ER) Ca(2+) homeostasis are heavily linked to neuronal pathology. Depletion of ER Ca(2+) stores can result in cellular dysfunction and potentially cell death, although adaptive processes exist to aid in survival. We examined the age and region dependence of one postulated, adaptive response to ER store-depletion (SD), hyperpolarization-activated cation-nonspecific (h)-channel plasticity in neurons of the dorsal and ventral hippocampus (DHC and VHC, respectively) from adolescent and adult rats. With the use of whole-cell patch-clamp recordings from the soma and dendrites of CA1 pyramidal neurons, we observed a change in h-sensitive measurements in response to SD, induced by treatment with cyclopiazonic acid, a sarcoplasmic reticulum/ER Ca(2+)-ATPase blocker. We found that whereas DHC and VHC neurons in adolescent animals respond to SD with a perisomatic expression of SD h plasticity, adult animals express SD h plasticity with a dendritic and somatodendritic locus of plasticity in DHC and VHC neurons, respectively. Furthermore, SD h plasticity in adults was dependent on membrane potential and on the activation of L-type voltage-gated Ca(2+) channels. These results suggest that cellular responses to the impairment of ER function, or ER stress, are dependent on brain region and age and that the differential expression of SD h plasticity could provide a neural basis for region- and age-dependent disease vulnerabilities.

Functional maps within a single neuron

The presence and plasticity of dendritic ion channels are well established. However, the literature is divided on what specific roles these dendritic ion channels play in neuronal information processing, and there is no consensus on why neuronal dendrites should express diverse ion channels with different expression profiles. In this review, we present a case for viewing dendritic information processing through the lens of the sensory map literature, where functional gradients within neurons are considered as maps on the neuronal topograph. Under such a framework, drawing analogies from the sensory map literature, we postulate that the formation of intraneuronal functional maps is driven by the twin objectives of efficiently encoding inputs that impinge along different dendritic locations and of retaining homeostasis in the face of changes that are required in the coding process. In arriving at this postulate, we relate intraneuronal map physiology to the vast literature on sensory maps and argue that such a metaphorical association provides a fresh conceptual framework for analyzing and understanding single-neuron information encoding. We also describe instances where the metaphor presents specific directions for research on intraneuronal maps, derived from analogous pursuits in the sensory map literature. We suggest that this perspective offers a thesis for why neurons should express and alter ion channels in their dendrites and provides a framework under which active dendrites could be related to neural coding, learning theory, and homeostasis.

Inactivating ion channels augment robustness of subthreshold intrinsic response dynamics to parametric variability in hippocampal model neurons

Voltage-gated ion channels play a critical role in regulating neuronal intrinsic response dynamics (IRD). Here, we computationally analysed the roles of the two inactivating subthreshold conductances (A and T), individually and in various combinations with the non-inactivating h conductance, in regulating several physiological IRD measurements in the theta frequency range. We found that the independent presence of a T conductance, unlike that of an h conductance, was unable to sustain an inductive phase lead in the theta frequency range, despite its ability to mediate theta frequency resonance. The A conductance, on the other hand, when expressed independently, acted in a manner similar to a leak conductance with reference to most IRD measurements. Next, analysing the impact of pair-wise coexpression of these channels, we found that the coexpression of the h and T conductances augmented the range of parameters over which they sustained resonance and inductive phase lead. Additionally, coexpression of the A conductance with the h or the T conductance elicited changes in IRD measurements that were similar to those obtained with the expression of a leak conductance with a resonating conductance. Finally, to understand the global sensitivity of IRD measurements to all parameters associated with models expressing all three channels, we generated 100,000 neuronal models, each built with a unique set of parametric values. We categorized valid models among these by matching their IRD measurements with experimental counterparts, and found that functionally similar models could be achieved even when underlying parameters displayed tremendous variability and exhibited weak pair-wise correlations. Our results suggest that the three prominent subthreshold conductances contribute differently to intrinsic excitability and to phase coding. We postulate that the differential expression and activity-dependent plasticity of these conductances contribute to robustness of subthreshold IRD, whereby response homeostasis is achieved by recruiting several non-unique combinations of these channel parameters.