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

The Brain's Best Kept Secret Is Its Degenerate Structure

Degeneracy is defined as multiple sets of solutions that can produce very similar system performance. Degeneracy is seen across phylogenetic scales, in all kinds of organisms. In neuroscience, degeneracy can be seen in the constellation of biophysical properties that produce a neuron's characteristic intrinsic properties and/or the constellation of mechanisms that determine circuit outputs or behavior. Here, we present examples of degeneracy at multiple levels of organization, from single-cell behavior, small circuits, large circuits, and, in cognition, drawing conclusions from work ranging from bacteria to human cognition. Degeneracy allows the individual-to-individual variability within a population that creates potential for evolution.

Ion-channel degeneracy and heterogeneities in the emergence of signature physiological characteristics of dentate gyrus granule cells

Complex systems are neither fully determined nor completely random. Biological complex systems, including single neurons, manifest intermediate regimes of randomness that recruit integration of specific combinations of functionally specialized subsystems. Such emergence of biological function provides the substrate for the expression of degeneracy, the ability of disparate combinations of subsystems to yield similar function. Here, we present evidence for the expression of degeneracy in morphologically realistic models of dentate gyrus granule cells (GCs) through functional integration of disparate ion-channel combinations. We performed a 45-parameter randomized search spanning 16 active and passive ion channels, each biophysically constrained by their gating kinetics and localization profiles, to search for valid GC models. Valid models were those that satisfied 17 sub- and suprathreshold cellular-scale electrophysiological measurements from rat GCs. A vast majority (>99%) of the 15,000 random models were not electrophysiologically valid, demonstrating that arbitrarily random ion-channel combinations would not yield GC functions. The 141 valid models (0.94% of 15,000) manifested heterogeneities in and cross-dependencies across local and propagating electrophysiological measurements, which matched with their respective biological counterparts. Importantly, these valid models were widespread throughout the parametric space and manifested weak cross-dependencies across different parameters. These observations together showed that GC physiology could neither be obtained by entirely random ion-channel combinations nor is there an entirely determined single parametric combination that satisfied all constraints. The complexity, the heterogeneities in measurement and parametric spaces, and degeneracy associated with GC physiology should be rigorously accounted for while assessing GCs and their robustness under physiological and pathological conditions.NEW & NOTEWORTHY A recent study from our laboratory had demonstrated pronounced heterogeneities in a set of 17 electrophysiological measurements obtained from a large population of rat hippocampal granule cells. Here, we demonstrate the manifestation of ion-channel degeneracy in a heterogeneous population of morphologically realistic conductance-based granule cell models that were validated against these measurements and their cross-dependencies. Our analyses show that single neurons are complex entities whose functions emerge through intricate interactions among several functionally specialized subsystems.

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.

Voltage-Gated Ion Channels and the Variability in Information Transfer

The prerequisites for neurons to function within a circuit and be able to contain and transfer information efficiently and reliably are that they need to be homeostatically stable and fire within a reasonable range, characteristics that are governed, among others, by voltage-gated ion channels (VGICs). Nonetheless, neurons entail large variability in the expression levels of VGICs and their corresponding intrinsic properties, but the role of this variability in information transfer is not fully known. In this study, we aimed to investigate how this variability of VGICs affects information transfer. For this, we used a previously derived population of neuronal model neurons, each with the variable expression of five types of VGICs, fast Na+, delayed rectifier K+, A-type K+, T-type Ca++, and HCN channels. These analyses showed that the model neurons displayed variability in mutual information transfer, measured as the capability of neurons to successfully encode incoming synaptic information in output firing frequencies. Likewise, variability in the expression of VGICs caused variability in EPSPs and IPSPs amplitudes, reflected in the variability of output firing frequencies. Finally, using the virtual knockout methodology, we show that among the ion channels tested, the A-type K+ channel is the major regulator of information processing and transfer.

Dominant role of adult neurogenesis-induced structural heterogeneities in driving plasticity heterogeneity in dentate gyrus granule cells

Neurons and synapses manifest pronounced variability in the amount of plasticity induced by identical activity patterns. The mechanisms underlying such plasticity heterogeneity, which have been implicated in context‐specific resource allocation during encoding, have remained unexplored. Here, we employed a systematic physiologically constrained parametric search to identify the cellular mechanisms behind plasticity heterogeneity in dentate gyrus granule cells. We used heterogeneous model populations to ensure that our conclusions were not biased by parametric choices in a single hand‐tuned model. We found that each of intrinsic, synaptic, and structural heterogeneities independently yielded heterogeneities in synaptic plasticity profiles obtained with two different induction protocols. However, among the disparate forms of neural‐circuit heterogeneities, our analyses demonstrated the dominance of neurogenesis‐induced structural heterogeneities in driving plasticity heterogeneity in granule cells. We found that strong relationships between neuronal intrinsic excitability and plasticity emerged only when adult neurogenesis‐induced heterogeneities in neural structure were accounted for. Importantly, our analyses showed that it was not imperative that the manifestation of neural‐circuit heterogeneities must translate to heterogeneities in plasticity profiles. Specifically, despite the expression of heterogeneities in structural, synaptic, and intrinsic neuronal properties, similar plasticity profiles were attainable across all models through synergistic interactions among these heterogeneities. We assessed the parametric combinations required for the manifestation of such degeneracy in the expression of plasticity profiles. We found that immature cells showed physiological plasticity profiles despite receiving afferent inputs with weak synaptic strengths. Thus, the high intrinsic excitability of immature granule cells was sufficient to counterbalance their low excitatory drive in the expression of plasticity profile degeneracy. Together, our analyses demonstrate that disparate forms of neural‐circuit heterogeneities could mechanistically drive plasticity heterogeneity, but also caution against treating neural‐circuit heterogeneities as proxies for plasticity heterogeneity. Our study emphasizes the need for quantitatively characterizing the relationship between neural‐circuit and plasticity heterogeneities across brain regions.

Reciprocally inhibitory circuits operating with distinct mechanisms are differently robust to perturbation and modulation

Reciprocal inhibition is a building block in many sensory and motor circuits. We studied the features that underly robustness in reciprocally inhibitory two neuron circuits. We used the dynamic clamp to create reciprocally inhibitory circuits from pharmacologically isolated neurons of the crab stomatogastric ganglion by injecting artificial graded synaptic (I_Syn) and hyperpolarization-activated inward (I_H) currents. There is a continuum of mechanisms in circuits that generate antiphase oscillations, with ‘release’ and ‘escape’ mechanisms at the extremes, and mixed mode oscillations between these extremes. In release, the active neuron primarily controls the off/on transitions. In escape, the inhibited neuron controls the transitions. We characterized the robustness of escape and release circuits to alterations in circuit parameters, temperature, and neuromodulation. We found that escape circuits rely on tight correlations between synaptic and H conductances to generate bursting but are resilient to temperature increase. Release circuits are robust to variations in synaptic and H conductances but fragile to temperature increase. The modulatory current (I_MI) restores oscillations in release circuits but has little effect in escape circuits. Perturbations can alter the balance of escape and release mechanisms and can create mixed mode oscillations. We conclude that the same perturbation can have dramatically different effects depending on the circuits’ mechanism of operation that may not be observable from basal circuit activity.

Degeneracy in the nervous system: from neuronal excitability to neural coding

Degeneracy is ubiquitous across biological systems where structurally different elements can yield a similar outcome. Degeneracy is of particular interest in neuroscience too. On the one hand, degeneracy confers robustness to the nervous system and facilitates evolvability: Different elements provide a backup plan for the system in response to any perturbation or disturbance. On the other, a difficulty in the treatment of some neurological disorders such as chronic pain is explained in light of different elements all of which contribute to the pathological behavior of the system. Under these circumstances, targeting a specific element is ineffective because other elements can compensate for this modulation. Understanding degeneracy in the physiological context explains its beneficial role in the robustness of neural circuits. Likewise, understanding degeneracy in the pathological context opens new avenues of discovery to find more effective therapies.

Stable continual learning through structured multiscale plasticity manifolds

Biological plasticity is ubiquitous. How does the brain navigate this complex plasticity space, where any component can seemingly change, in adapting to an ever-changing environment? We build a systematic case that stable continuous learning is achieved by structured rules that enforce multiple, but not all, components to change together in specific directions. This rule-based low-dimensional plasticity manifold of permitted plasticity combinations emerges from cell type-specific molecular signaling and triggers cascading impacts that span multiple scales. These multiscale plasticity manifolds form the basis for behavioral learning and are dynamic entities that are altered by neuromodulation, metaplasticity, and pathology. We explore the strong links between heterogeneities, degeneracy, and plasticity manifolds and emphasize the need to incorporate plasticity manifolds into learning-theoretical frameworks and experimental designs.

Resonating neurons stabilize heterogeneous grid-cell networks

A central theme that governs the functional design of biological networks is their ability to sustain stable function despite widespread parametric variability. Here, we investigated the impact of distinct forms of biological heterogeneities on the stability of a two-dimensional continuous attractor network (CAN) implicated in grid-patterned activity generation. We show that increasing degrees of biological heterogeneities progressively disrupted the emergence of grid-patterned activity and resulted in progressively large perturbations in low-frequency neural activity. We postulated that targeted suppression of low-frequency perturbations could ameliorate heterogeneity-induced disruptions of grid-patterned activity. To test this, we introduced intrinsic resonance, a physiological mechanism to suppress low-frequency activity, either by adding an additional high-pass filter (phenomenological) or by incorporating a slow negative feedback loop (mechanistic) into our model neurons. Strikingly, CAN models with resonating neurons were resilient to the incorporation of heterogeneities and exhibited stable grid-patterned firing. We found CAN models with mechanistic resonators to be more effective in targeted suppression of low-frequency activity, with the slow kinetics of the negative feedback loop essential in stabilizing these networks. As low-frequency perturbations (1/f noise) are pervasive across biological systems, our analyses suggest a universal role for mechanisms that suppress low-frequency activity in stabilizing heterogeneous biological networks.

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.

Circuit Stability to Perturbations Reveals Hidden Variability in the Balance of Intrinsic and Synaptic Conductances

Neurons and circuits each with a distinct balance of intrinsic and synaptic conductances can generate similar behavior but sometimes respond very differently to perturbation. Examining a large family of circuit models with non-identical neurons and synapses underlying rhythmic behavior, we analyzed the circuits' response to modifications in single and multiple intrinsic conductances in the individual neurons. To summarize these changes over the entire range of perturbed parameters, we quantified circuit output by defining a global stability measure. Using this measure, we identified specific subsets of conductances that when perturbed generate similar behavior in diverse individuals of the population. Our unbiased clustering analysis enabled us to quantify circuit stability when simultaneously perturbing multiple conductances as a nonlinear combination of single conductance perturbations. This revealed surprising conductance combinations that can predict the response to specific perturbations, even when the remaining intrinsic and synaptic conductances are unknown. Therefore, our approach can expose hidden variability in the balance of intrinsic and synaptic conductances of the same neurons across different versions of the same circuit solely from the circuit response to perturbations. Developed for a specific family of model circuits, our quantitative approach to characterizing high-dimensional degenerate systems provides a conceptual and analytic framework to guide future theoretical and experimental studies on degeneracy and robustness.

SIGNIFICANCE STATEMENT Neural circuits can generate nearly identical behavior despite neuronal and synaptic parameters varying several-fold between individual instantiations. Yet, when these parameters are perturbed through channel deletions and mutations or environmental disturbances, seemingly identical circuits can respond very differently. What distinguishes inconsequential perturbations that barely alter circuit behavior from disruptive perturbations that drastically disturb circuit output remains unclear. Focusing on a family of rhythmic circuits, we propose a computational approach to reveal hidden variability in the intrinsic and synaptic conductances in seemingly identical circuits based solely on circuit output to different perturbations. We uncover specific conductance combinations that work similarly to maintain stability and predict the effect of changing multiple conductances simultaneously, which often results from neuromodulation or injury.

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 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.

Conditioning by subthreshold synaptic input changes the intrinsic firing pattern of CA3 hippocampal neurons

Unlike synaptic strength, intrinsic excitability is assumed to be a stable property of neurons. For example, learning of somatic conductances is generally not incorporated into computational models, and the discharge pattern of neurons in response to test stimuli is frequently used as a basis for phenotypic classification. However, it is increasingly evident that signal processing properties of neurons are more generally plastic on the timescale of minutes. Here we demonstrate that the intrinsic firing patterns of CA3 neurons of the rat hippocampus in vitro undergo rapid long-term plasticity in response to a few minutes of only subthreshold synaptic conditioning. This plasticity on the spike timing could also be induced by intrasomatic injection of subthreshold depolarizing pulses and was blocked by kinase inhibitors, indicating that discharge dynamics are modulated locally. Cluster analysis of firing patterns before and after conditioning revealed systematic transitions toward adapting and intrinsic burst behaviors, irrespective of the patterns initially exhibited by the cells. We used a conductance-based model to decide appropriate pharmacological blockade and found that the observed transitions are likely due to recruitment of low-voltage calcium and Kv7 potassium conductances. We conclude that CA3 neurons adapt their conductance profile to the subthreshold activity of their input, so that their intrinsic firing pattern is not a static signature, but rather a reflection of their history of subthreshold activity. In this way, recurrent output from CA3 neurons may collectively shape the temporal dynamics of their embedding circuits.NEW & NOTEWORTHY Although firing patterns are widely conserved across the animal phyla, it is still a mystery why nerve cells present such diversity of discharge dynamics upon somatic step currents. Adding a new timing dimension to the intrinsic plasticity literature, here we show that CA3 neurons rapidly adapt through the space of known firing patterns in response to the subthreshold signals that they receive from their embedding circuit, potentially adjusting their network processing to the temporal statistics of their circuit.

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.

Disparate forms of heterogeneities and interactions among them drive channel decorrelation in the dentate gyrus: Degeneracy and dominance

The ability of a neuronal population to effectuate channel decorrelation, which is one form of response decorrelation, has been identified as an essential prelude to efficient neural encoding. To what extent are diverse forms of local and afferent heterogeneities essential in accomplishing channel decorrelation in the dentate gyrus (DG)? Here, we incrementally incorporated four distinct forms of biological heterogeneities into conductance-based network models of the DG and systematically delineate their relative contributions to channel decorrelation. First, to effectively incorporate intrinsic heterogeneities, we built physiologically validated heterogeneous populations of granule (GC) and basket cells (BC) through independent stochastic search algorithms spanning exhaustive parametric spaces. These stochastic search algorithms, which were independently constrained by experimentally determined ion channels and by neurophysiological signatures, revealed cellular-scale degeneracy in the DG. Specifically, in GC and BC populations, disparate parametric combinations yielded similar physiological signatures, with underlying parameters exhibiting significant variability and weak pair-wise correlations. Second, we introduced synaptic heterogeneities through randomization of local synaptic strengths. Third, in including adult neurogenesis, we subjected the valid model populations to randomized structural plasticity and matched neuronal excitability to electrophysiological data. We assessed networks comprising different combinations of these three local heterogeneities with identical or heterogeneous afferent inputs from the entorhinal cortex. We found that the three forms of local heterogeneities were independently and synergistically capable of mediating significant channel decorrelation when the network was driven by identical afferent inputs. However, when we incorporated afferent heterogeneities into the network to account for the divergence in DG afferent connectivity, the impact of all three forms of local heterogeneities was significantly suppressed by the dominant role of afferent heterogeneities in mediating channel decorrelation. Our results unveil a unique convergence of cellular- and network-scale degeneracy in the emergence of channel decorrelation in the DG, whereby disparate forms of local and afferent heterogeneities could synergistically drive input discriminability.

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.

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.

Theta-frequency selectivity in the somatic spike-triggered average of rat hippocampal pyramidal neurons is dependent on HCN channels

The ability to distill specific frequencies from complex spatiotemporal patterns of afferent inputs is a pivotal functional requirement for neurons residing in networks receiving frequency-multiplexed inputs. Although the expression of theta-frequency subthreshold resonance is established in hippocampal pyramidal neurons, it is not known if their spike initiation dynamics manifest spectral selectivity, or if their intrinsic properties are tuned to process gamma-frequency inputs. Here, we measured the spike-triggered average (STA) of rat hippocampal pyramidal neurons through electrophysiological recordings and quantified spectral selectivity in their spike initiation dynamics and their coincidence detection window (CDW). Our results revealed strong theta-frequency selectivity in the STA, which was also endowed with gamma-range CDW, with prominent neuron-to-neuron variability that manifested distinct pairwise dissociations and correlations with different intrinsic measurements. Furthermore, we demonstrate that the STA and its measurements substantially adapted to the state of the neuron defined by its membrane potential and to the statistics of its afferent inputs. Finally, we tested the effect of pharmacologically blocking the hyperpolarization-activated cyclic-nucleotide-gated (HCN) channels on the STA and found that the STA characteristic frequency reduced significantly to the delta-frequency band after HCN channel blockade. This delta-frequency selectivity in the STA emerged in the absence of subthreshold resonance, which was abolished by HCN channel blockade, thereby confirming computational predictions on the dissociation between these two forms of spectral selectivity. Our results expand the roles of HCN channels to theta-frequency selectivity in the spike initiation dynamics, apart from underscoring the critical role of interactions among different ion channels in regulating neuronal physiology.NEW & NOTEWORTHY We had previously predicted, using computational analyses, that the spike-triggered average (STA) of hippocampal neurons would exhibit theta-frequency (4-10 Hz) spectral selectivity and would manifest coincidence detection capabilities for inputs in the gamma-frequency band (25-150 Hz). Here, we confirmed these predictions through direct electrophysiological recordings of STA from rat CA1 pyramidal neurons and demonstrate that blocking HCN channels reduces the frequency of STA spectral selectivity to the delta-frequency range (0.5-4 Hz).

A balance of outward and linear inward ionic currents is required for generation of slow-wave oscillations

Regenerative inward currents help produce slow oscillations through a negative-slope conductance region of their current-voltage relationship that is well approximated by a linear negative conductance. We used dynamic-clamp injections of a linear current with such conductance, I_NL, to explore why some neurons can generate intrinsic slow oscillations whereas others cannot. We addressed this question in synaptically isolated neurons of the crab Cancer borealis after blocking action potentials. The pyloric network consists of a distinct pacemaker and follower neurons, all of which express the same complement of ionic currents. When the pyloric dilator (PD) neuron, a member of the pacemaker group, was injected with I_NL with dynamic clamp, it consistently produced slow oscillations. In contrast, all follower neurons failed to oscillate with I_NL To understand these distinct behaviors, we compared outward current levels of PD with those of follower lateral pyloric (LP) and ventral pyloric (VD) neurons. We found that LP and VD neurons had significantly larger high-threshold potassium currents (I_HTK) than PD and LP had lower-transient potassium current (I_A). Reducing I_HTK pharmacologically enabled both LP and VD neurons to produce I_NL-induced oscillations, whereas modifying I_A levels did not affect I_NL-induced oscillations. Using phase-plane and bifurcation analysis of a simplified model cell, we demonstrate that large levels of I_HTK can block I_NL-induced oscillatory activity whereas generation of oscillations is almost independent of I_A levels. These results demonstrate the general importance of a balance between inward pacemaking currents and high-threshold K⁺ current levels in determining slow oscillatory activity.NEW & NOTEWORTHY Pacemaker neuron-generated rhythmic activity requires the activation of at least one inward and one outward current. We have previously shown that the inward current can be a linear current (with negative conductance). Using this simple mechanism, here we demonstrate that the inward current conductance must be in relative balance with the outward current conductances to generate oscillatory activity. Surprisingly, an excess of outward conductances completely precludes the possibility of achieving such a balance.

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.

Computational implications of biophysical diversity and multiple timescales in neurons and synapses for circuit performance

Despite advances in experimental and theoretical neuroscience, we are still trying to identify key biophysical details that are important for characterizing the operation of brain circuits. Biological mechanisms at the level of single neurons and synapses can be combined as 'building blocks' to generate circuit function. We focus on the importance of capturing multiple timescales when describing these intrinsic and synaptic components. Whether inherent in the ionic currents, the neuron's complex morphology, or the neurotransmitter composition of synapses, these multiple timescales prove crucial for capturing the variability and richness of circuit output and enhancing the information-carrying capacity observed across nervous systems.