Homeostasis, failure of homeostasis and degenerate ion channel regulation

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.

Network motifs in cellular neurophysiology

Concepts from network science and graph theory, including the framework of network motifs, have been frequently applied in studying neuronal networks and other biological complex systems. Network-based approaches can also be used to study the functions of individual neurons, where cellular elements such as ion channels and membrane voltage are conceptualized as nodes within a network, and their interactions are denoted by edges. Network motifs in this context provide functional building blocks that help to illuminate the principles of cellular neurophysiology. In this review we build a case that network motifs operating within neurons provide tools for defining the functional architecture of single-neuron physiology and neuronal adaptations. We highlight the presence of such computational motifs in the cellular mechanisms underlying action potential generation, neuronal oscillations, dendritic integration, and neuronal plasticity. Future work applying the network motifs perspective may help to decipher the functional complexities of neurons and their adaptation during health and disease.

Alterations in network robustness upon simultaneous temperature and pH perturbations

Nervous systems have evolved to function consistently in the face of the normal environmental fluctuations experienced by animals. The stomatogastric nervous system (STNS) of the crab, Cancer borealis, produces a motor output that has been studied for its remarkable robustness in response to single global perturbations. Changes in environments, however, are often complex and multifactorial. Therefore, we studied the robustness of the pyloric network in the stomatogastric ganglion (STG) in response to simultaneous perturbations of temperature and pH. We compared the effects of elevated temperatures on the pyloric rhythm at control, acid, or base pHs. In each pH recordings were made at 11°C, and then the temperature was increased until the rhythms became disorganized ("crashed"). Pyloric burst frequencies and phase relationships showed minor differences between pH groups until reaching close to the crash temperatures. However, the temperatures at which the rhythms were disrupted were lower in the two extreme pH conditions. This indicates that one environmental stress can make an animal less resilient to a second stressor.NEW & NOTEWORTHY Resilience to environmental fluctuations is important for all animals. It is common that animals encounter multiple stressful events at the same time, the cumulative impacts of which are largely unknown. This study examines the effects of temperature and pH on the nervous system of crabs that live in the fluctuating environments of the Northern Atlantic Ocean. The ranges of tolerance to one perturbation, temperature, are reduced under the influence of a second, pH.

Genetically engineered HEK cells as a valuable tool for studying electroporation in excitable cells

Electric pulses used in electroporation-based treatments have been shown to affect the excitability of muscle and neuronal cells. However, understanding the interplay between electroporation and electrophysiological response of excitable cells is complex, since both ion channel gating and electroporation depend on dynamic changes in the transmembrane voltage (TMV). In this study, a genetically engineered human embryonic kidney cells expressing NaV1.5 and Kir2.1, a minimal complementary channels required for excitability (named S-HEK), was characterized as a simple cell model used for studying the effects of electroporation in excitable cells. S-HEK cells and their non-excitable counterparts (NS-HEK) were exposed to 100 µs pulses of increasing electric field strength. Changes in TMV, plasma membrane permeability, and intracellular Ca2+ were monitored with fluorescence microscopy. We found that a very mild electroporation, undetectable with the classical propidium assay but associated with a transient increase in intracellular Ca2+, can already have a profound effect on excitability close to the electrostimulation threshold, as corroborated by multiscale computational modelling. These results are of great relevance for understanding the effects of pulse delivery on cell excitability observed in context of the rapidly developing cardiac pulsed field ablation as well as other electroporation-based treatments in excitable tissues.

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.

Flexible circuit mechanisms for context-dependent song sequencing

Sequenced behaviours, including locomotion, reaching and vocalization, are patterned differently in different contexts, enabling animals to adjust to their environments. How contextual information shapes neural activity to flexibly alter the patterning of actions is not fully understood. Previous work has indicated that this could be achieved via parallel motor circuits, with differing sensitivities to context1,2. Here we demonstrate that a single pathway operates in two regimes dependent on recent sensory history. We leverage the Drosophila song production system3 to investigate the role of several neuron types4-7 in song patterning near versus far from the female fly. Male flies sing 'simple' trains of only one mode far from the female fly but complex song sequences comprising alternations between modes when near her. We find that ventral nerve cord (VNC) circuits are shaped by mutual inhibition and rebound excitability8 between nodes driving the two song modes. Brief sensory input to a direct brain-to-VNC excitatory pathway drives simple song far from the female, whereas prolonged input enables complex song production via simultaneous recruitment of functional disinhibition of VNC circuitry. Thus, female proximity unlocks motor circuit dynamics in the correct context. We construct a compact circuit model to demonstrate that the identified mechanisms suffice to replicate natural song dynamics. These results highlight how canonical circuit motifs8,9 can be combined to enable circuit flexibility required for dynamic communication.

Uncovering circuit mechanisms of current sinks and sources with biophysical simulations of primary visual cortex

Local field potential (LFP) recordings reflect the dynamics of the current source density (CSD) in brain tissue. The synaptic, cellular, and circuit contributions to current sinks and sources are ill-understood. We investigated these in mouse primary visual cortex using public Neuropixels recordings and a detailed circuit model based on simulating the Hodgkin-Huxley dynamics of >50,000 neurons belonging to 17 cell types. The model simultaneously captured spiking and CSD responses and demonstrated a two-way dissociation: firing rates are altered with minor effects on the CSD pattern by adjusting synaptic weights, and CSD is altered with minor effects on firing rates by adjusting synaptic placement on the dendrites. We describe how thalamocortical inputs and recurrent connections sculpt specific sinks and sources early in the visual response, whereas cortical feedback crucially alters them in later stages. These results establish quantitative links between macroscopic brain measurements (LFP/CSD) and microscopic biophysics-based understanding of neuron dynamics and show that CSD analysis provides powerful constraints for modeling beyond those from considering spikes.

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.

IGF-1 receptor regulates upward firing rate homeostasis via the mitochondrial calcium uniporter

An emerging hypothesis is that neuronal circuits homeostatically maintain a stable spike rate despite continuous environmental changes. This firing rate homeostasis is believed to confer resilience to neurodegeneration and cognitive decline. We show that insulin-like growth factor-1 receptor (IGF-1R) is necessary for homeostatic response of mean firing rate to inactivity, termed “upward firing rate homeostasis.” We show that its mechanism of action is to couple spike bursts with downstream mitochondrial Ca²⁺ influx via the mitochondrial calcium uniporter complex (MCUc). We propose that MCUc is a homeostatic Ca²⁺ sensor that triggers the integrated homeostatic response. Firing rate homeostasis may be the principal mechanism by which IGF-1R regulates aging and neurodevelopmental and neurodegenerative disorders.

Regulation of firing rate homeostasis constitutes a fundamental property of central neural circuits. While intracellular Ca²⁺ has long been hypothesized to be a feedback control signal, the molecular machinery enabling a network-wide homeostatic response remains largely unknown. We show that deletion of insulin-like growth factor-1 receptor (IGF-1R) limits firing rate homeostasis in response to inactivity, without altering the distribution of baseline firing rates. The deficient firing rate homeostatic response was due to disruption of both postsynaptic and intrinsic plasticity. At the cellular level, we detected a fraction of IGF-1Rs in mitochondria, colocalized with the mitochondrial calcium uniporter complex (MCUc). IGF-1R deletion suppressed transcription of the MCUc members and burst-evoked mitochondrial Ca²⁺ (mitoCa²⁺) by weakening mitochondria-to-cytosol Ca²⁺ coupling. Overexpression of either mitochondria-targeted IGF-1R or MCUc in IGF-1R–deficient neurons was sufficient to rescue the deficits in burst-to-mitoCa²⁺ coupling and firing rate homeostasis. Our findings indicate that mitochondrial IGF-1R is a key regulator of the integrated homeostatic response by tuning the reliability of burst transfer by MCUc. Based on these results, we propose that MCUc acts as a homeostatic Ca²⁺ sensor. Faulty activation of MCUc may drive dysregulation of firing rate homeostasis in aging and in brain disorders associated with aberrant IGF-1R/MCUc signaling.

Pareto optimality, economy-effectiveness trade-offs and ion channel degeneracy: improving population modelling for single neurons

Neurons encounter unavoidable evolutionary trade-offs between multiple tasks. They must consume as little energy as possible while effectively fulfilling their functions. Cells displaying the best performance for such multi-task trade-offs are said to be Pareto optimal, with their ion channel configurations underpinning their functionality. Ion channel degeneracy, however, implies that multiple ion channel configurations can lead to functionally similar behaviour. Therefore, instead of a single model, neuroscientists often use populations of models with distinct combinations of ionic conductances. This approach is called population (database or ensemble) modelling. It remains unclear, which ion channel parameters in the vast population of functional models are more likely to be found in the brain. Here we argue that Pareto optimality can serve as a guiding principle for addressing this issue by helping to identify the subpopulations of conductance-based models that perform best for the trade-off between economy and functionality. In this way, the high-dimensional parameter space of neuronal models might be reduced to geometrically simple low-dimensional manifolds, potentially explaining experimentally observed ion channel correlations. Conversely, Pareto inference might also help deduce neuronal functions from high-dimensional Patch-seq data. In summary, Pareto optimality is a promising framework for improving population modelling of neurons and their circuits.

Minimal requirements for a neuron to co-regulate many properties and the implications for ion channel correlations and robustness

Neurons regulate their excitability by adjusting their ion channel levels. Degeneracy – achieving equivalent outcomes (excitability) using different solutions (channel combinations) – facilitates this regulation by enabling a disruptive change in one channel to be offset by compensatory changes in other channels. But neurons must coregulate many properties. Pleiotropy – the impact of one channel on more than one property – complicates regulation because a compensatory ion channel change that restores one property to its target value often disrupts other properties. How then does a neuron simultaneously regulate multiple properties? Here, we demonstrate that of the many channel combinations producing the target value for one property (the single-output solution set), few combinations produce the target value for other properties. Combinations producing the target value for two or more properties (the multioutput solution set) correspond to the intersection between single-output solution sets. Properties can be effectively coregulated only if the number of adjustable channels (n_in) exceeds the number of regulated properties (n_out). Ion channel correlations emerge during homeostatic regulation when the dimensionality of solution space (n_in − n_out) is low. Even if each property can be regulated to its target value when considered in isolation, regulation as a whole fails if single-output solution sets do not intersect. Our results also highlight that ion channels must be coadjusted with different ratios to regulate different properties, which suggests that each error signal drives modulatory changes independently, despite those changes ultimately affecting the same ion channels.

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.

Optimal plasticity for memory maintenance during ongoing synaptic change

Synaptic connections in many brain circuits fluctuate, exhibiting substantial turnover and remodelling over hours to days. Surprisingly, experiments show that most of this flux in connectivity persists in the absence of learning or known plasticity signals. How can neural circuits retain learned information despite a large proportion of ongoing and potentially disruptive synaptic changes? We address this question from first principles by analysing how much compensatory plasticity would be required to optimally counteract ongoing fluctuations, regardless of whether fluctuations are random or systematic. Remarkably, we find that the answer is largely independent of plasticity mechanisms and circuit architectures: compensatory plasticity should be at most equal in magnitude to fluctuations, and often less, in direct agreement with previously unexplained experimental observations. Moreover, our analysis shows that a high proportion of learning-independent synaptic change is consistent with plasticity mechanisms that accurately compute error gradients.

Biophysical models of intrinsic homeostasis: Firing rates and beyond

In view of ever-changing conditions both in the external world and in intrinsic brain states, maintaining the robustness of computations poses a challenge, adequate solutions to which we are only beginning to understand. At the level of cell-intrinsic properties, biophysical models of neurons permit one to identify relevant physiological substrates that can serve as regulators of neuronal excitability and to test how feedback loops can stabilize crucial variables such as long-term calcium levels and firing rates. Mathematical theory has also revealed a rich set of complementary computational properties arising from distinct cellular dynamics and even shaping processing at the network level. Here, we provide an overview over recently explored homeostatic mechanisms derived from biophysical models and hypothesize how multiple dynamical characteristics of cells, including their intrinsic neuronal excitability classes, can be stably controlled.

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.

Gene Editing and Modulation: the Holy Grail for the Genetic Epilepsies?

Epilepsy is a complex neurological disorder for which there are a large number of monogenic subtypes. Monogenic epilepsies are often severe and disabling, featuring drug-resistant seizures and significant developmental comorbidities. These disorders are potentially amenable to a precision medicine approach, of which genome editing using CRISPR/Cas represents the holy grail. Here we consider mutations in some of the most 'common' rare epilepsy genes and discuss the different CRISPR/Cas approaches that could be taken to cure these disorders. We consider scenarios where CRISPR-mediated gene modulation could serve as an effective therapeutic strategy and discuss whether a single gene corrective approach could hold therapeutic potential in the context of homeostatic compensation in the developing, highly dynamic brain. Despite an incomplete understanding of the mechanisms of the genetic epilepsies and current limitations of gene editing tools, CRISPR-mediated approaches have game-changing potential in the treatment of genetic epilepsy over the next decade.

Turnover and activity-dependent transcriptional control of NompC in the Drosophila ear

Across their lives, biological sensors maintain near-constant functional outputs despite countless exogenous and endogenous perturbations. This sensory homeostasis is the product of multiple dynamic equilibria, the breakdown of which contributes to age-related decline. The mechanisms of homeostatic maintenance, however, are still poorly understood. The ears of vertebrates and insects are characterized by exquisite sensitivities but also by marked functional vulnerabilities. Being under the permanent load of thermal and acoustic noise, auditory transducer channels exemplify the homeostatic challenge. We show that (1) NompC-dependent mechanotransducers in the ear of the fruit fly Drosophila melanogaster undergo continual replacement with estimated turnover times of 9.1 hr; (2) a de novo synthesis of NompC can restore transducer function in the adult ears of congenitally hearing-impaired flies; (3) key components of the auditory transduction chain, including NompC, are under activity-dependent transcriptional control, likely forming a transducer-operated mechanosensory gain control system that extends beyond hearing organs.

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De novo NompC synthesis restores auditory transduction in congenitally deafened flies.

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Complete turnover of NompC mechanotransducers within less than 24 hr.

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Activity-dependent transcriptional control of transducers controls auditory function.

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.

Neuronal oscillator robustness to multiple global perturbations

Neuronal activity depends on ion channels and biophysical processes that are strongly and differentially sensitive to physical variables such as temperature and pH. Nonetheless, neuronal oscillators can be surprisingly resilient to perturbations in these variables. We study a three-neuron pacemaker ensemble that drives the pyloric rhythm of the crab, Cancer borealis. These crabs routinely experience a number of global perturbations, including changes in temperature and pH. Although pyloric oscillations are robust to such changes, for sufficiently large deviations the rhythm reversibly breaks down. As temperature increases beyond a tipping point, oscillators transition to silence. Acidic pH deviations also show tipping points, with a reliable transition first to tonic spiking, then to silence. Surprisingly, robustness to perturbations in pH only moderately affects temperature robustness. Consistent with high animal-to-animal variability in biophysical circuit parameters, tipping points in temperature and pH vary across animals. However, the ordering and discrete classes of transitions at critical points are conserved. This implies that qualitative oscillator dynamics are preserved across animals despite high quantitative parameter variability. A universal model of bursting dynamics predicts the existence of these transition types and the order in which they occur.

Activity-dependent compensation of cell size is vulnerable to targeted deletion of ion channels

In many species, excitable cells preserve their physiological properties despite significant variation in physical size across time and in a population. For example, neurons in crustacean central pattern generators generate similar firing patterns despite several-fold increases in size between juveniles and adults. This presents a biophysical problem because the electrical properties of cells are highly sensitive to membrane area and channel density. It is not known whether specific mechanisms exist to sense membrane area and adjust channel expression to keep a consistent channel density, or whether regulation mechanisms that sense activity alone are capable of compensating cell size. We show that destabilising effects of growth can be specifically compensated by feedback mechanism that senses average calcium influx and jointly regulate multiple conductances. However, we further show that this class of growth-compensating regulation schemes is necessarily sensitive to perturbations that alter the expression of subsets of ion channel types. Targeted perturbations of specific ion channels can trigger a pathological response of the regulation mechanism and a failure of homeostasis. Our findings suggest that physiological regulation mechanisms that confer robustness to growth may be specifically vulnerable to deletions or mutations that affect subsets of ion channels.

Training deep neural density estimators to identify mechanistic models of neural dynamics

Mechanistic modeling in neuroscience aims to explain observed phenomena in terms of underlying causes. However, determining which model parameters agree with complex and stochastic neural data presents a significant challenge. We address this challenge with a machine learning tool which uses deep neural density estimators-trained using model simulations-to carry out Bayesian inference and retrieve the full space of parameters compatible with raw data or selected data features. Our method is scalable in parameters and data features and can rapidly analyze new data after initial training. We demonstrate the power and flexibility of our approach on receptive fields, ion channels, and Hodgkin-Huxley models. We also characterize the space of circuit configurations giving rise to rhythmic activity in the crustacean stomatogastric ganglion, and use these results to derive hypotheses for underlying compensation mechanisms. Our approach will help close the gap between data-driven and theory-driven models of neural dynamics.

Rapid adaptation to elevated extracellular potassium in the pyloric circuit of the crab, Cancer borealis

Elevated potassium concentration ([K⁺]) is often used to alter excitability in neurons and networks by shifting the potassium equilibrium potential (E_K) and, consequently, the resting membrane potential. We studied the effects of increased extracellular [K⁺] on the well-described pyloric circuit of the crab Cancer borealis. A 2.5-fold increase in extracellular [K⁺] (2.5×[K⁺]) depolarized pyloric dilator (PD) neurons and resulted in short-term loss of their normal bursting activity. This period of silence was followed within 5-10 min by the recovery of spiking and/or bursting activity during continued superfusion of 2.5×[K⁺] saline. In contrast, when PD neurons were pharmacologically isolated from pyloric presynaptic inputs, they exhibited no transient loss of spiking activity in 2.5×[K⁺], suggesting the presence of an acute inhibitory effect mediated by circuit interactions. Action potential threshold in PD neurons hyperpolarized during an hour-long exposure to 2.5×[K⁺] concurrent with the recovery of spiking and/or bursting activity. Thus the initial loss of activity appears to be mediated by synaptic interactions within the network, but the secondary adaptation depends on changes in the intrinsic excitability of the pacemaker neurons. The complex sequence of events in the responses of pyloric neurons to elevated [K⁺] demonstrates that electrophysiological recordings are necessary to determine both the transient and longer term effects of even modest alterations of K⁺ concentrations on neuronal activity.NEW & NOTEWORTHY Solutions with elevated extracellular potassium are commonly used as a depolarizing stimulus. We studied the effects of high potassium concentration ([K⁺]) on the pyloric circuit of the crab stomatogastric ganglion. A 2.5-fold increase in extracellular [K⁺] caused a transient loss of activity that was not due to depolarization block, followed by a rapid increase in excitability and recovery of spiking within minutes. This suggests that changing extracellular potassium can have complex and nonstationary effects on neuronal circuits.

Dynamic clamp constructed phase diagram for the Hodgkin and Huxley model of excitability

Excitability-a threshold-governed transient in transmembrane voltage-is a fundamental physiological process that controls the function of the heart, endocrine, muscles, and neuronal tissues. The 1950s Hodgkin and Huxley explicit formulation provides a mathematical framework for understanding excitability, as the consequence of the properties of voltage-gated sodium and potassium channels. The Hodgkin-Huxley model is more sensitive to parametric variations of protein densities and kinetics than biological systems whose excitability is apparently more robust. It is generally assumed that the model's sensitivity reflects missing functional relations between its parameters or other components present in biological systems. Here we experimentally assembled excitable membranes using the dynamic clamp and voltage-gated potassium ionic channels (Kv1.3) expressed in Xenopus oocytes. We take advantage of a theoretically derived phase diagram, where the phenomenon of excitability is reduced to two dimensions defined as combinations of the Hodgkin-Huxley model parameters, to examine functional relations in the parameter space. Moreover, we demonstrate activity dependence and hysteretic dynamics over the phase diagram due to the impacts of complex slow inactivation kinetics. The results suggest that maintenance of excitability amid parametric variation is a low-dimensional, physiologically tenable control process. In the context of model construction, the results point to a potentially significant gap between high-dimensional models that capture the full measure of complexity displayed by ion channel function and the lower dimensionality that captures physiological function.

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.

Theories of rhythmogenesis

Rhythmogenesis is the process that develops the capacity for rhythmic activity in a non-rhythmic system. Theoretical works suggested a wide array of possible mechanisms for rhythmogenesis ranging from the regulation of cellular properties to top-down control. Here we discuss theories of rhythmogenesis with an emphasis on spike timing-dependent plasticity. We argue that even though the specifics of different mechanisms vary greatly they all share certain key features. Namely, rhythmogenesis can be described as a flow on the phase diagram leading the system into a rhythmic region and stabilizing it on a specific manifold characterized by the desired rhythmic activity. Functionality is retained despite biological diversity by forcing the system into a specific manifold, but allowing fluctuations within that manifold.

Cellular function given parametric variation in the Hodgkin and Huxley model of excitability

How is reliable physiological function maintained in cells despite considerable variability in the values of key parameters of multiple interacting processes that govern that function? Here, we use the classic Hodgkin-Huxley formulation of the squid giant axon action potential to propose a possible approach to this problem. Although the full Hodgkin-Huxley model is very sensitive to fluctuations that independently occur in its many parameters, the outcome is in fact determined by simple combinations of these parameters along two physiological dimensions: structural and kinetic (denoted S and K, respectively). Structural parameters describe the properties of the cell, including its capacitance and the densities of its ion channels. Kinetic parameters are those that describe the opening and closing of the voltage-dependent conductances. The impacts of parametric fluctuations on the dynamics of the system-seemingly complex in the high-dimensional representation of the Hodgkin-Huxley model-are tractable when examined within the S-K plane. We demonstrate that slow inactivation, a ubiquitous activity-dependent feature of ionic channels, is a powerful local homeostatic control mechanism that stabilizes excitability amid changes in structural and kinetic parameters.