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

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.

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.

Targeting aberrant dendritic integration to treat cognitive comorbidities of epilepsy

Memory deficits are a debilitating symptom of epilepsy, but little is known about mechanisms underlying cognitive deficits. Here, we describe a Na+ channel-dependent mechanism underlying altered hippocampal dendritic integration, degraded place coding and deficits in spatial memory. Two-photon glutamate uncaging experiments revealed a marked increase in the fraction of hippocampal first-order CA1 pyramidal cell dendrites capable of generating dendritic spikes in the kainate model of chronic epilepsy. Moreover, in epileptic mice dendritic spikes were generated with lower input synchrony, and with a lower threshold. The Nav1.3/1.1 selective Na+ channel blocker ICA-121431 reversed dendritic hyperexcitability in epileptic mice, while the Nav1.2/1.6 preferring anticonvulsant S-Lic did not. We used in vivo two-photon imaging to determine if aberrant dendritic excitability is associated with altered place-related firing of CA1 neurons. We show that ICA-121431 improves degraded hippocampal spatial representations in epileptic mice. Finally, behavioural experiments show that reversing aberrant dendritic excitability with ICA-121431 reverses hippocampal memory deficits. Thus, a dendritic channelopathy may underlie cognitive deficits in epilepsy and targeting it pharmacologically may constitute a new avenue to enhance cognition.

Degeneracy in epilepsy: multiple routes to hyperexcitable brain circuits and their repair

Due to its complex and multifaceted nature, developing effective treatments for epilepsy is still a major challenge. To deal with this complexity we introduce the concept of degeneracy to the field of epilepsy research: the ability of disparate elements to cause an analogous function or malfunction. Here, we review examples of epilepsy-related degeneracy at multiple levels of brain organisation, ranging from the cellular to the network and systems level. Based on these insights, we outline new multiscale and population modelling approaches to disentangle the complex web of interactions underlying epilepsy and to design personalised multitarget therapies.

Efficient information coding and degeneracy in the nervous system

Efficient information coding (EIC) is a universal biological framework rooted in the fundamental principle that system responses should match their natural stimulus statistics for maximizing environmental information. Quantitatively assessed through information theory, such adaptation to the environment occurs at all biological levels and timescales. The context dependence of environmental stimuli and the need for stable adaptations make EIC a daunting task. We argue that biological complexity is the principal architect that subserves deft execution of stable EIC. Complexity in a system is characterized by several functionally segregated subsystems that show a high degree of functional integration when they interact with each other. Complex biological systems manifest heterogeneities and degeneracy, wherein structurally different subsystems could interact to yield the same functional outcome. We argue that complex systems offer several choices that effectively implement EIC and homeostasis for each of the different contexts encountered by the system.

Active Dendrites and Local Field Potentials: Biophysical Mechanisms and Computational Explorations

Neurons and glial cells are endowed with membranes that express a rich repertoire of ion channels, transporters, and receptors. The constant flux of ions across the neuronal and glial membranes results in voltage fluctuations that can be recorded from the extracellular matrix. The high frequency components of this voltage signal contain information about the spiking activity, reflecting the output from the neurons surrounding the recording location. The low frequency components of the signal, referred to as the local field potential (LFP), have been traditionally thought to provide information about the synaptic inputs that impinge on the large dendritic trees of various neurons. In this review, we discuss recent computational and experimental studies pointing to a critical role of several active dendritic mechanisms that can influence the genesis and the location-dependent spectro-temporal dynamics of LFPs, spanning different brain regions. We strongly emphasize the need to account for the several fast and slow dendritic events and associated active mechanisms - including gradients in their expression profiles, inter- and intra-cellular spatio-temporal interactions spanning neurons and glia, heterogeneities and degeneracy across scales, neuromodulatory influences, and activitydependent plasticity - towards gaining important insights about the origins of LFP under different behavioral states in health and disease. We provide simple but essential guidelines on how to model LFPs taking into account these dendritic mechanisms, with detailed methodology on how to account for various heterogeneities and electrophysiological properties of neurons and synapses while studying LFPs.

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.

Spatial information transfer in hippocampal place cells depends on trial-to-trial variability, symmetry of place-field firing, and biophysical heterogeneities

The relationship between the feature-tuning curve and information transfer profile of individual neurons provides vital insights about neural encoding. However, the relationship between the spatial tuning curve and spatial information transfer of hippocampal place cells remains unexplored. Here, employing a stochastic search procedure spanning thousands of models, we arrived at 127 conductance-based place-cell models that exhibited signature electrophysiological characteristics and sharp spatial tuning, with parametric values that exhibited neither clustering nor strong pairwise correlations. We introduced trial-to-trial variability in responses and computed model tuning curves and information transfer profiles, using stimulus-specific (SSI) and mutual (MI) information metrics, across locations within the place field. We found spatial information transfer to be heterogeneous across models, but to reduce consistently with increasing levels of variability. Importantly, whereas reliable low-variability responses implied that maximal information transfer occurred at high-slope regions of the tuning curve, increase in variability resulted in maximal transfer occurring at the peak-firing location in a subset of models. Moreover, experience-dependent asymmetry in place-field firing introduced asymmetries in the information transfer computed through MI, but not SSI, and the impact of activity-dependent variability on information transfer was minimal compared to activity-independent variability. We unveiled ion-channel degeneracy in the regulation of spatial information transfer, and demonstrated critical roles for N-methyl-d-aspartate receptors, transient potassium and dendritic sodium channels in regulating information transfer. Our results demonstrate that trial-to-trial variability, tuning-curve shape and biological heterogeneities critically regulate the relationship between the spatial tuning curve and spatial information transfer in hippocampal place cells.

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.

Theta resonance and synaptic modulation scale activity patterns in the medial entorhinal cortex stellate cells

Stellate cells (SCs) of the medial entorhinal cortex (MEC) are rich in hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, which are known to effectively shape their activity patterns. The explanatory mechanisms, however, have remained elusive. One important but previously unassessed possibility is that HCN channels control the gain of synaptic inputs to these cells. Here, we test this possibility in rat brain slices, while subjecting SCs to a stochastic synaptic bombardment using the dynamic clamp. We show that in the presence of synaptic noise, HCN channels mainly exert their influence by increasing the relative signal gain in the theta frequency through the theta modulation of stochastic synaptic inputs. This subthreshold synaptic modulation then translates into a spiking resonance, which steepens with excitation in the presence of HCN channels. We present here a systematic assessment of synaptic theta modulation and trace its implications to the suprathreshold control of firing rate motifs. Such analysis was yet lacking in the SC literature. Furthermore, we assess the impact of noise statistics on this gain modulation and indicate possible mechanisms for the emergence of membrane theta oscillations and synaptic ramps, as observed in vivo. We support the data with a computational model that further unveils a competing role of inhibition, suggesting important implications for MEC computations.

Efficient phase coding in hippocampal place cells

Neural codes have been postulated to build efficient representations of the external world. The hippocampus, an encoding system, employs neuronal firing rates and spike phases to encode external space. Although the biophysical origin of such codes is at a single neuronal level, the role of neural components in efficient coding is not understood. The complexity of this problem lies in the dimensionality of the parametric space encompassing neural components, and is amplified by the enormous biological heterogeneity observed in each parameter. A central question that spans encoding systems therefore is how neurons arrive at efficient codes in the face of widespread biological heterogeneities. To answer this, we developed a conductance-based spiking model for phase precession, a phase code of external space exhibited by hippocampal place cells. Our model accounted for several experimental observations on place cell firing and electrophysiology: the emergence of phase precession from exact spike timings of conductance-based models with neuron-specific ion channels and receptors; biological heterogeneities in neural components and excitability; the emergence of subthreshold voltage ramp, increased firing rate, enhanced theta power within the place field; a signature reduction in extracellular theta frequency compared to its intracellular counterpart; and experience-dependent asymmetry in firing-rate profile. We formulated phase-coding efficiency, using Shannon's information theory, as an information maximization problem with spike phase as the response and external space within a single place field as the stimulus. We employed an unbiased stochastic search spanning an 11-dimensional neural space, involving thousands of iterations that accounted for the biophysical richness and neuron-to-neuron heterogeneities. We found a small subset of models that exhibited efficient spatial information transfer through the phase code, and investigated the distinguishing features of this subpopulation at the parametric and functional scales. At the parametric scale, which spans the molecular components that defined the neuron, several nonunique parametric combinations with weak pairwise correlations yielded models with similar high phase-coding efficiency. Importantly, placing additional constraints on these models in terms of matching other aspects of hippocampal neural responses did not hamper parametric degeneracy. We provide quantitative evidence demonstrating this parametric degeneracy to be a consequence of a many-to-one relationship between the different parameters and phase-coding efficiency. At the functional scale, involving the cellular-scale neural properties, our analyses revealed an important higher-order constraint that was exclusive to models exhibiting efficient phase coding. Specifically, we found a counterbalancing negative correlation between neuronal gain and the strength of external synaptic inputs as a critical functional constraint for the emergence of efficient phase coding. These observations implicate intrinsic neural properties as important contributors in effectuating such counterbalance, which can be achieved by recruiting nonunique parametric combinations. Finally, we show that a change in afferent statistics, manifesting as input asymmetry onto these neuronal models, induced an adaptive shift in the phase code that preserved its efficiency. Together, our analyses unveil parametric degeneracy as a mechanism to harness widespread neuron-to-neuron heterogeneity towards accomplishing stable and efficient encoding, provided specific higher-order functional constraints on the relationship of neural gain to external inputs are satisfied.

Illuminating dendritic function with computational models

Dendrites have always fascinated researchers: from the artistic drawings by Ramon y Cajal to the beautiful recordings of today, neuroscientists have been striving to unravel the mysteries of these structures. Theoretical work in the 1960s predicted important dendritic effects on neuronal processing, establishing computational modelling as a powerful technique for their investigation. Since then, modelling of dendrites has been instrumental in driving neuroscience research in a targeted manner, providing experimentally testable predictions that range from the subcellular level to the systems level, and their relevance extends to fields beyond neuroscience, such as machine learning and artificial intelligence. Validation of modelling predictions often requires - and drives - new technological advances, thus closing the loop with theory-driven experimentation that moves the field forward. This Review features the most important, to our understanding, contributions of modelling of dendritic computations, including those pending experimental verification, and highlights studies of successful interactions between the modelling and experimental neuroscience communities.

Degeneracy in the emergence of spike-triggered average of hippocampal pyramidal neurons

Hippocampal pyramidal neurons are endowed with signature excitability characteristics, exhibit theta-frequency selectivity - manifesting as impedance resonance and as a band-pass structure in the spike-triggered average (STA) - and coincidence detection tuned for gamma-frequency inputs. Are there specific constraints on molecular-scale (ion channel) properties in the concomitant emergence of cellular-scale encoding (feature detection and selectivity) and excitability characteristics? Here, we employed a biophysically-constrained unbiased stochastic search strategy involving thousands of conductance-based models, spanning 11 active ion channels, to assess the concomitant emergence of 14 different electrophysiological measurements. Despite the strong biophysical and physiological constraints, we found models that were similar in terms of their spectral selectivity, operating mode along the integrator-coincidence detection continuum and intrinsic excitability characteristics. The parametric combinations that resulted in these functionally similar models were non-unique with weak pair-wise correlations. Employing virtual knockout of individual ion channels in these functionally similar models, we found a many-to-many relationship between channels and physiological characteristics to mediate this degeneracy, and predicted a dominant role for HCN and transient potassium channels in regulating hippocampal neuronal STA. Our analyses reveals the expression of degeneracy, that results from synergistic interactions among disparate channel components, in the concomitant emergence of neuronal excitability and encoding characteristics.

Robust emergence of sharply tuned place-cell responses in hippocampal neurons with structural and biophysical heterogeneities

Hippocampal pyramidal neurons sustain propagation of fast electrical signals and are electrotonically non-compact structures exhibiting cell-to-cell variability in their complex dendritic arborization. In this study, we demonstrate that sharp place-field tuning and several somatodendritic functional maps concomitantly emerge despite the presence of geometrical heterogeneities in these neurons. We establish this employing an unbiased stochastic search strategy involving thousands of models that spanned several morphologies and distinct profiles of dispersed synaptic localization and channel expression. Mechanistically, employing virtual knockout models (VKMs), we explored the impact of bidirectional modulation in dendritic spike prevalence on place-field tuning sharpness. Consistent with the prior literature, we found that across all morphologies, virtual knockout of either dendritic fast sodium channels or N-methyl-D-aspartate receptors led to a reduction in dendritic spike prevalence, whereas A-type potassium channel knockouts resulted in a non-specific increase in dendritic spike prevalence. However, place-field tuning sharpness was critically impaired in all three sets of VKMs, demonstrating that sharpness in feature tuning is maintained by an intricate balance between mechanisms that promote and those that prevent dendritic spike initiation. From the functional standpoint of the emergence of sharp feature tuning and intrinsic functional maps, within this framework, geometric variability was compensated by a combination of synaptic democracy, the ability of randomly dispersed synapses to yield sharp tuning through dendritic spike initiation, and ion-channel degeneracy. Our results suggest electrotonically non-compact neurons to be endowed with several degrees of freedom, encompassing channel expression, synaptic localization and morphological microstructure, in achieving sharp feature encoding and excitability homeostasis.

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.

Degeneracy in the robust expression of spectral selectivity, subthreshold oscillations, and intrinsic excitability of entorhinal stellate cells

Biological heterogeneities are ubiquitous and play critical roles in the emergence of physiology at multiple scales. Although neurons in layer II (LII) of the medial entorhinal cortex (MEC) express heterogeneities in channel properties, the impact of such heterogeneities on the robustness of their cellular-scale physiology has not been assessed. Here, we performed a 55-parameter stochastic search spanning nine voltage- or calcium-activated channels to assess the impact of channel heterogeneities on the concomitant emergence of 10 in vitro electrophysiological characteristics of LII stellate cells (SCs). We generated 150,000 models and found a heterogeneous subpopulation of 449 valid models to robustly match all electrophysiological signatures. We employed this heterogeneous population to demonstrate the emergence of cellular-scale degeneracy in SCs, whereby disparate parametric combinations expressing weak pairwise correlations resulted in similar models. We then assessed the impact of virtually knocking out each channel from all valid models and demonstrate that the mapping between channels and measurements was many-to-many, a critical requirement for the expression of degeneracy. Finally, we quantitatively predict that the spike-triggered average of SCs should be endowed with theta-frequency spectral selectivity and coincidence detection capabilities in the fast gamma-band. We postulate this fast gamma-band coincidence detection as an instance of cellular-scale-efficient coding, whereby SC response characteristics match the dominant oscillatory signals in LII MEC. The heterogeneous population of valid SC models built here unveils the robust emergence of cellular-scale physiology despite significant channel heterogeneities, and forms an efficacious substrate for evaluating the impact of biological heterogeneities on entorhinal network function.

NEW & NOTEWORTHY We assessed the impact of heterogeneities in channel properties on the robustness of cellular-scale physiology of medial entorhinal cortical stellate neurons. We demonstrate that neuronal models with disparate channel combinations were endowed with similar physiological characteristics, as a consequence of the many-to-many mapping between channel properties and the physiological characteristics that they modulate. We predict that the spike-triggered average of stellate cells should be endowed with theta-frequency spectral selectivity and fast gamma-band coincidence detection capabilities.