Ion Channel Degeneracy, Variability, and Covariation in Neuron and Circuit Resilience

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.

Interdependence of cellular and network properties in respiratory rhythm generation

How breathing is generated by the preBötzinger complex (preBötC) remains divided between two ideological frameworks, and a persistent sodium current (INaP) lies at the heart of this debate. Although INaP is widely expressed, the pacemaker hypothesis considers it essential because it endows a small subset of neurons with intrinsic bursting or "pacemaker" activity. In contrast, burstlet theory considers INaP dispensable because rhythm emerges from "preinspiratory" spiking activity driven by feed-forward network interactions. Using computational modeling, we find that small changes in spike shape can dissociate INaP from intrinsic bursting. Consistent with many experimental benchmarks, conditional effects on spike shape during simulated changes in oxygenation, development, extracellular potassium, and temperature alter the prevalence of intrinsic bursting and preinspiratory spiking without altering the role of INaP. Our results support a unifying hypothesis where INaP and excitatory network interactions, but not intrinsic bursting or preinspiratory spiking, are critical interdependent features of preBötC rhythmogenesis.

A synthetic method to assay polycystin channel biophysics

Ion channels are biological transistors that control ionic flux across cell membranes to regulate electrical transmission and signal transduction. They are found in all biological membranes and their conductive states are frequently disrupted in human diseases. Organelle ion channels are among the most resistant to functional and pharmacological interrogation. Traditional channel protein reconstitution methods rely upon exogenous expression and/or purification from endogenous cellular sources which are frequently contaminated by resident ionophores. Here we describe a fully synthetic method to assay the functional properties of the polycystin subfamily of transient receptor potential (TRP) channels that natively traffic to primary cilia and endoplasmic reticulum organelles. Using this method, we characterize their membrane integration, orientation and conductance while comparing these results to their endogenous channel properties. Outcomes define a novel synthetic approach that can be applied broadly to investigate other channels resistant to biophysical analysis and pharmacological characterization.

How do we get from hyperexcitability to excitotoxicity in amyotrophic lateral sclerosis?

Amyotrophic lateral sclerosis is a devastating neurodegenerative disease that, at present, has no effective cure. Evidence of increased circulating glutamate and hyperexcitability of the motor cortex in patients with amyotrophic lateral sclerosis have provided an empirical support base for the 'dying forward' excitotoxicity hypothesis. The hypothesis postulates that increased activation of upper motor neurons spreads pathology to lower motor neurons in the spinal cord in the form of excessive glutamate release, which triggers excitotoxic processes. Many clinical trials have focused on therapies that target excitotoxicity via dampening neuronal activation, but not all are effective. As such, there is a growing tension between the rising tide of evidence for the 'dying forward' excitotoxicity hypothesis and the failure of therapies that target neuronal activation. One possible solution to these contradictory outcomes is that our interpretation of the current evidence requires revision in the context of appreciating the complexity of the nervous system and the limitations of the neurobiological assays we use to study it. In this review we provide an evaluation of evidence relevant to the 'dying forward' excitotoxicity hypothesis and by doing so, identify key gaps in our knowledge that need to be addressed. We hope to provide a road map from hyperexcitability to excitotoxicity so that we can better develop therapies for patients suffering from amyotrophic lateral sclerosis. We conclude that studies of upper motor neuron activity and their synaptic output will play a decisive role in the future of amyotrophic lateral sclerosis therapy.

Similar excitability through different sodium channels and implications for the analgesic efficacy of selective drugs

Nociceptive sensory neurons convey pain-related signals to the CNS using action potentials. Loss-of-function mutations in the voltage-gated sodium channel NaV1.7 cause insensitivity to pain (presumably by reducing nociceptor excitability) but clinical trials seeking to treat pain by inhibiting NaV1.7 pharmacologically have struggled. This may reflect the variable contribution of NaV1.7 to nociceptor excitability. Contrary to claims that NaV1.7 is necessary for nociceptors to initiate action potentials, we show that nociceptors can achieve similar excitability using different combinations of NaV1.3, NaV1.7, and NaV1.8. Selectively blocking one of those NaV subtypes reduces nociceptor excitability only if the other subtypes are weakly expressed. For example, excitability relies on NaV1.8 in acutely dissociated nociceptors but responsibility shifts to NaV1.7 and NaV1.3 by the fourth day in culture. A similar shift in NaV dependence occurs in vivo after inflammation, impacting ability of the NaV1.7-selective inhibitor PF-05089771 to reduce pain in behavioral tests. Flexible use of different NaV subtypes exemplifies degeneracy - achieving similar function using different components - and compromises reliable modulation of nociceptor excitability by subtype-selective inhibitors. Identifying the dominant NaV subtype to predict drug efficacy is not trivial. Degeneracy at the cellular level must be considered when choosing drug targets at the molecular level.

Biophysical modeling of the whole-cell dynamics of C. elegans motor and interneurons families

The nematode Caenorhabditis elegans is a widely used model organism for neuroscience. Although its nervous system has been fully reconstructed, the physiological bases of single-neuron functioning are still poorly explored. Recently, many efforts have been dedicated to measuring signals from C. elegans neurons, revealing a rich repertoire of dynamics, including bistable responses, graded responses, and action potentials. Still, biophysical models able to reproduce such a broad range of electrical responses lack. Realistic electrophysiological descriptions started to be developed only recently, merging gene expression data with electrophysiological recordings, but with a large variety of cells yet to be modeled. In this work, we contribute to filling this gap by providing biophysically accurate models of six classes of C. elegans neurons, the AIY, RIM, and AVA interneurons, and the VA, VB, and VD motor neurons. We test our models by comparing computational and experimental time series and simulate knockout neurons, to identify the biophysical mechanisms at the basis of inter and motor neuron functioning. Our models represent a step forward toward the modeling of C. elegans neuronal networks and virtual experiments on the nematode nervous system.

Futile cycles: Emerging utility from apparent futility

Futile cycles are biological phenomena where two opposing biochemical reactions run simultaneously, resulting in a net energy loss without appreciable productivity. Such a state was presumed to be a biological aberration and thus deemed an energy-wasting "futile" cycle. However, multiple pieces of evidence suggest that biological utilities emerge from futile cycles. A few established functions of futile cycles are to control metabolic sensitivity, modulate energy homeostasis, and drive adaptive thermogenesis. Yet, the physiological regulation, implication, and pathological relevance of most futile cycles remain poorly studied. In this review, we highlight the abundance and versatility of futile cycles and propose a classification scheme. We further discuss the energetic implications of various futile cycles and their impact on basal metabolic rate, their bona fide and tentative pathophysiological implications, and putative drug interactions.

Localization of hyperpolarization-activated cyclic nucleotide-gated channels in the vertebrate retinas across species and their physiological roles

Transmembrane proteins known as hyperpolarization-activated cyclic nucleotide-gated (HCN) channels control the movement of Na+ and K+ ions across cellular membranes. HCN channels are known to be involved in crucial physiological functions in regulating neuronal excitability and rhythmicity, and pacemaker activity in the heart. Although HCN channels have been relatively well investigated in the brain, their distribution and function in the retina have received less attention, remaining their physiological roles to be comprehensively understood. Also, because recent studies reported HCN channels have been somewhat linked with the dysfunction of photoreceptors which are affected by retinal diseases, investigating HCN channels in the retina may offer valuable insights into disease mechanisms and potentially contribute to identifying novel therapeutic targets for retinal degenerative disorders. This paper endeavors to summarize the existing literature on the distribution and function of HCN channels reported in the vertebrate retinas of various species and discuss the potential implications for the treatment of retinal diseases. Then, we recapitulate current knowledge regarding the function and regulation of HCN channels, as well as their relevance to various neurological disorders.

Coupled action potential and calcium dynamics underlie robust spontaneous firing in dopaminergic neurons

Dopaminergic neurons are specialized cells in the substantia nigra, tasked with dopamine secretion. This secretion relies on intracellular calcium signaling coupled to neuronal electrical activity. These neurons are known to display spontaneous calcium oscillationsin-vitroandin-vivo, even in synaptic isolation, controlling the basal dopamine levels. Here we outline a kinetic model for the ion exchange across the neuronal plasma membrane. Crucially, we relax the assumption of constant, cytoplasmic sodium and potassium concentration. We show that sodium-potassium dynamics are strongly coupled to calcium dynamics and are essential for the robustness of spontaneous firing frequency. The model predicts several regimes of electrical activity, including tonic and 'burst' oscillations, and predicts the switch between those in response to perturbations. 'Bursting' correlates with increased calcium amplitudes, while maintaining constant average, allowing for a vast change in the calcium signal responsible for dopamine secretion. All the above traits provide the flexibility to create rich action potential dynamics that are crucial for cellular function.

Evolutionary origin of the nervous system from Ctenophora prospective

Nervous system is one of the key adaptations underlying the evolutionary success of the majority of animal groups. Ctenophores (or comb jellies) are gelatinous marine invertebrates that were probably the first lineage to diverge from the rest of animals. Due to the key phylogenetic position and multiple unique adaptations, the noncentralized nervous system of comb jellies has been in the center of the debate around the origin of the nervous system in the animal kingdom and whether it happened only once or twice. Here, we discuss the latest findings in ctenophore neuroscience and multiple challenges on the way to build a clear evolutionary picture of the origin of the nervous system.

Modulation by Neuropeptides with Overlapping Targets Results in Functional Overlap in Oscillatory Circuit Activation

Neuromodulation lends flexibility to neural circuit operation but the general notion that different neuromodulators sculpt neural circuit activity into distinct and characteristic patterns is complicated by interindividual variability. In addition, some neuromodulators converge onto the same signaling pathways, with similar effects on neurons and synapses. We compared the effects of three neuropeptides on the rhythmic pyloric circuit in the stomatogastric ganglion of male crabs, Cancer borealis Proctolin (PROC), crustacean cardioactive peptide (CCAP), and red pigment concentrating hormone (RPCH) activate the same modulatory inward current, I MI, and have convergent actions on synapses. However, while PROC targets all four neuron types in the core pyloric circuit, CCAP and RPCH target the same subset of only two neurons. After removal of spontaneous neuromodulator release, none of the neuropeptides restored the control cycle frequency, but all restored the relative timing between neuron types. Consequently, differences between neuropeptide effects were mainly found in the spiking activity of different neuron types. We performed statistical comparisons using the Euclidean distance in the multidimensional space of normalized output attributes to obtain a single measure of difference between modulatory states. Across preparations, the circuit output in PROC was distinguishable from CCAP and RPCH, but CCAP and RPCH were not distinguishable from each other. However, we argue that even between PROC and the other two neuropeptides, population data overlapped enough to prevent reliable identification of individual output patterns as characteristic for a specific neuropeptide. We confirmed this notion by showing that blind classifications by machine learning algorithms were only moderately successful.Significance Statement It is commonly assumed that distinct behaviors or circuit activities can be elicited by different neuromodulators. Yet it is unknown to what extent these characteristic actions remain distinct across individuals. We use a well-studied circuit model of neuromodulation to examine the effects of three neuropeptides, each known to produce a distinct activity pattern in controlled studies. We find that, when compared across individuals, the three peptides elicit activity patterns that are either statistically indistinguishable or show too much overlap to be labeled characteristic. We ascribe this to interindividual variability and overlapping subcellular actions of the modulators. Because both factors are common in all neural circuits, these findings have broad significance for understanding chemical neuromodulatory actions while considering interindividual variability.

Diversity-induced trivialization and resilience of neural dynamics

Heterogeneity is omnipresent across all living systems. Diversity enriches the dynamical repertoire of these systems but remains challenging to reconcile with their manifest robustness and dynamical persistence over time, a fundamental feature called resilience. To better understand the mechanism underlying resilience in neural circuits, we considered a nonlinear network model, extracting the relationship between excitability heterogeneity and resilience. To measure resilience, we quantified the number of stationary states of this network, and how they are affected by various control parameters. We analyzed both analytically and numerically gradient and non-gradient systems modeled as non-linear sparse neural networks evolving over long time scales. Our analysis shows that neuronal heterogeneity quenches the number of stationary states while decreasing the susceptibility to bifurcations: a phenomenon known as trivialization. Heterogeneity was found to implement a homeostatic control mechanism enhancing network resilience to changes in network size and connection probability by quenching the system's dynamic volatility.

Differential Neuroanatomical, Neurochemical, and Behavioral Impacts of Early-Age Isolation in a Eusocial Insect

Social experience early in life appears to be necessary for the development of species-typical behavior. Although isolation during critical periods of maturation has been shown to impact behavior by altering gene expression and brain development in invertebrates and vertebrates, workers of some ant species appear resilient to social deprivation and other neurobiological challenges that occur during senescence or due to loss of sensory input. It is unclear if and to what degree neuroanatomy, neurochemistry, and behavior will show deficiencies if social experience in the early adult life of worker ants is compromised. We reared newly-eclosed adult workers of Camponotus floridanus under conditions of social isolation for 2 to 53 days, quantified brain compartment volumes, recorded biogenic amine levels in individual brains, and evaluated movement and behavioral performance to compare the neuroanatomy, neurochemistry, brood-care behavior, and foraging (predatory behavior) of isolated workers with that of workers experiencing natural social contact after adult eclosion. We found that the volume of the antennal lobe, which processes olfactory inputs, was significantly reduced in workers isolated for an average of 40 days, whereas the size of the mushroom bodies, centers of higher-order sensory processing, increased after eclosion and was not significantly different from controls. Titers of the neuromodulators serotonin, dopamine, and octopamine remained stable and were not significantly different in isolation treatments and controls. Brood care, predation, and overall movement were reduced in workers lacking social contact early in life. These results suggest that the behavioral development of isolated workers of C. floridanus is specifically impacted by a reduction in the size of the antennal lobe. Task performance and locomotor ability therefore appear to be sensitive to a loss of social contact through a reduction of olfactory processing ability rather than change in the size of the mushroom bodies, which serve important functions in learning and memory, or the central complex, which controls movement.

Oscillatory network spontaneously recovers both activity and robustness after prolonged removal of neuromodulators

Robustness of neuronal activity is a property necessary for a neuronal network to withstand perturbations, which may otherwise disrupt or destroy the system. The robustness of complex systems has been shown to depend on a number of features of the system, including morphology and heterogeneity of the activity of the component neurons, size of the networks, synaptic connectivity, and neuromodulation. The activity of small networks, such as the pyloric network of the crustacean stomatogastric nervous system, appears to be robust despite some of the factors not being consistent with the expected properties of complex systems, e.g., small size and homogeneity of the synaptic connections. The activity of the pyloric network has been shown to be stable and robust in a neuromodulatory state-dependent manner. When neuromodulatory inputs are severed, activity is initially disrupted, losing both stability and robustness. Over the long term, however, stable activity homeostatically recovers without the restoration of neuromodulatory input. The question we address in this study is whether robustness can also be restored as the network reorganizes itself to compensate for the loss of neuromodulatory input and recovers the lost activity. Here, we use temperature changes as a perturbation to probe the robustness of the network's activity. We develop a simple metric of robustness, i.e., the variances of the network phase relationships, and show that robustness is indeed restored simultaneously along with its stable network activity, indicating that, whatever the reorganization of the network entails, it is deep enough also to restore this important property.

Ih current stabilizes excitability in rodent DRG neurons and reverses hyperexcitability in a nociceptive neuron model of inherited neuropathic pain

We show here that hyperpolarization-activated current (Ih ) unexpectedly acts to inhibit the activity of dorsal root ganglion (DRG) neurons expressing WT Nav1.7, the largest inward current and primary driver of DRG neuronal firing, and hyperexcitable DRG neurons expressing a gain-of-function Nav1.7 mutation that causes inherited erythromelalgia (IEM), a human genetic model of neuropathic pain. In this study we created a kinetic model of Ih and used it, in combination with dynamic-clamp, to study Ih function in DRG neurons. We show, for the first time, that Ih increases rheobase and reduces the firing probability in small DRG neurons, and demonstrate that the amplitude of subthreshold oscillations is reduced by Ih . Our results show that Ih , due to slow gating, is not deactivated during action potentials (APs) and has a striking damping action, which reverses from depolarizing to hyperpolarizing, close to the threshold for AP generation. Moreover, we show that Ih reverses the hyperexcitability of DRG neurons expressing a gain-of-function Nav1.7 mutation that causes IEM. In the aggregate, our results show that Ih unexpectedly has strikingly different effects in DRG neurons as compared to previously- and well-studied cardiac cells. Within DRG neurons where Nav1.7 is present, Ih reduces depolarizing sodium current inflow due to enhancement of Nav1.7 channel fast inactivation and creates additional damping action by reversal of Ih direction from depolarizing to hyperpolarizing close to the threshold for AP generation. These actions of Ih limit the firing of DRG neurons expressing WT Nav1.7 and reverse the hyperexcitability of DRG neurons expressing a gain-of-function Nav1.7 mutation that causes IEM. KEY POINTS: Hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, the molecular determinants of hyperpolarization-activated current (Ih ) have been characterized as a 'pain pacemaker', and thus considered to be a potential molecular target for pain therapeutics. Dorsal root ganglion (DRG) neurons express Nav1.7, a channel that is not present in central neurons or cardiac tissue. Gain-of-function mutations (GOF) of Nav1.7 identified in inherited erythromelalgia (IEM), a human genetic model of neuropathic pain, produce DRG neuron hyperexcitability, which in turn produces severe pain. We found that Ih increases rheobase and reduces firing probability in small DRG neurons expressing WT Nav1.7, and demonstrate that the amplitude of subthreshold oscillations is reduced by Ih . We also demonstrate that Ih reverses the hyperexcitability of DRG neurons expressing a GOF Nav1.7 mutation (L858H) that causes IEM. Our results show that, in contrast to cardiac cells and CNS neurons, Ih acts to stabilize DRG neuron excitability and prevents excessive firing.

The enigmatic HCN channels: A cellular neurophysiology perspective

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

A universal workflow for creation, validation, and generalization of detailed neuronal models

Detailed single-neuron modeling is widely used to study neuronal functions. While cellular and functional diversity across the mammalian cortex is vast, most of the available computational tools focus on a limited set of specific features characteristic of a single neuron. Here, we present a generalized automated workflow for the creation of robust electrical models and illustrate its performance by building cell models for the rat somatosensory cortex. Each model is based on a 3D morphological reconstruction and a set of ionic mechanisms. We use an evolutionary algorithm to optimize neuronal parameters to match the electrophysiological features extracted from experimental data. Then we validate the optimized models against additional stimuli and assess their generalizability on a population of similar morphologies. Compared to the state-of-the-art canonical models, our models show 5-fold improved generalizability. This versatile approach can be used to build robust models of any neuronal type.

Thermal acclimation and habitat-dependent differences in temperature robustness of a crustacean motor circuit

Introduction

At the cellular level, acute temperature changes alter ionic conductances, ion channel kinetics, and the activity of entire neuronal circuits. This can result in severe consequences for neural function, animal behavior and survival. In poikilothermic animals, and particularly in aquatic species whose core temperature equals the surrounding water temperature, neurons experience rather rapid and wide-ranging temperature fluctuations. Recent work on pattern generating neural circuits in the crustacean stomatogastric nervous system have demonstrated that neuronal circuits can exhibit an intrinsic robustness to temperature fluctuations. However, considering the increased warming of the oceans and recurring heatwaves due to climate change, the question arises whether this intrinsic robustness can acclimate to changing environmental conditions, and whether it differs between species and ocean habitats.

Methods

We address these questions using the pyloric pattern generating circuits in the stomatogastric nervous system of two crab species, Hemigrapsus sanguineus and Carcinus maenas that have seen a worldwide expansion in recent decades.

Results and discussion

Consistent with their history as invasive species, we find that pyloric activity showed a broad temperature robustness (>30°C). Moreover, the temperature-robust range was dependent on habitat temperature in both species. Warm-acclimating animals shifted the critical temperature at which circuit activity breaks down to higher temperatures. This came at the cost of robustness against cold stimuli in H. sanguineus, but not in C. maenas. Comparing the temperature responses of C. maenas from a cold latitude (the North Sea) to those from a warm latitude (Spain) demonstrated that similar shifts in robustness occurred in natural environments. Our results thus demonstrate that neuronal temperature robustness correlates with, and responds to, environmental temperature conditions, potentially preparing animals for changing ecological conditions and shifting habitats.

Estimating the probability of early afterdepolarizations and predicting arrhythmic risk associated with long QT syndrome type 1 mutations

Early afterdepolarizations (EADs) are action potential (AP) repolarization abnormalities that can trigger lethal arrhythmias. Simulations using biophysically detailed cardiac myocyte models can reveal how model parameters influence the probability of these cellular arrhythmias; however, such analyses can pose a huge computational burden. We have previously developed a highly simplified approach in which logistic regression models (LRMs) map parameters of complex cell models to the probability of ectopic beats. Here, we extend this approach to predict the probability of EADs (P(EAD)) as a mechanistic metric of arrhythmic risk. We use the LRM to investigate how changes in parameters of the slow-activating delayed rectifier current (IKs) affect P(EAD) for 17 different long QT syndrome type 1 (LQTS1) mutations. In this LQTS1 clinical arrhythmic risk prediction task, we compared P(EAD) for these 17 mutations with two other recently published model-based arrhythmia risk metrics (AP morphology metric across populations of myocyte models and transmural repolarization prolongation based on a one-dimensional [1D] tissue-level model). These model-based risk metrics yield similar prediction performance; however, each fails to stratify clinical risk for a significant number of the 17 studied LQTS1 mutations. Nevertheless, an interpretable ensemble model using multivariate linear regression built by combining all of these model-based risk metrics successfully predicts the clinical risk of 17 mutations. These results illustrate the potential of computational approaches in arrhythmia risk prediction.

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.

Distinctive biophysical features of human cell-types: insights from studies of neurosurgically resected brain tissue

Electrophysiological characterization of live human tissue from epilepsy patients has been performed for many decades. Although initially these studies sought to understand the biophysical and synaptic changes associated with human epilepsy, recently, it has become the mainstay for exploring the distinctive biophysical and synaptic features of human cell-types. Both epochs of these human cellular electrophysiological explorations have faced criticism. Early studies revealed that cortical pyramidal neurons obtained from individuals with epilepsy appeared to function "normally" in comparison to neurons from non-epilepsy controls or neurons from other species and thus there was little to gain from the study of human neurons from epilepsy patients. On the other hand, contemporary studies are often questioned for the "normalcy" of the recorded neurons since they are derived from epilepsy patients. In this review, we discuss our current understanding of the distinct biophysical features of human cortical neurons and glia obtained from tissue removed from patients with epilepsy and tumors. We then explore the concept of within cell-type diversity and its loss (i.e., "neural homogenization"). We introduce neural homogenization to help reconcile the epileptogenicity of seemingly "normal" human cortical cells and circuits. We propose that there should be continued efforts to study cortical tissue from epilepsy patients in the quest to understand what makes human cell-types "human".

A biophysical perspective on the resilience of neuronal excitability across timescales

Neuronal membrane excitability must be resilient to perturbations that can take place over timescales from milliseconds to months (or even years in long-lived animals). A great deal of attention has been paid to classes of homeostatic mechanisms that contribute to long-term maintenance of neuronal excitability through processes that alter a key structural parameter: the number of ion channel proteins present at the neuronal membrane. However, less attention has been paid to the self-regulating 'automatic' mechanisms that contribute to neuronal resilience by virtue of the kinetic properties of ion channels themselves. Here, we propose that these two sets of mechanisms are complementary instantiations of feedback control, together enabling resilience on a wide range of temporal scales. We further point to several methodological and conceptual challenges entailed in studying these processes - both of which involve enmeshed feedback control loops - and consider the consequences of these mechanisms of resilience.

Perturbed Information Processing Complexity in Experimental Epilepsy

Comorbidities, such as cognitive deficits, which often accompany epilepsies, constitute a basal state, while seizures are rare and transient events. This suggests that neural dynamics, in particular those supporting cognitive function, are altered in a permanent manner in epilepsy. Here, we test the hypothesis that primitive processes of information processing at the core of cognitive function (i.e., storage and sharing of information) are altered in the hippocampus and the entorhinal cortex in experimental epilepsy in adult, male Wistar rats. We find that information storage and sharing are organized into substates across the stereotypic states of slow and theta oscillations in both epilepsy and control conditions. However, their internal composition and organization through time are disrupted in epilepsy, partially losing brain state selectivity compared with controls, and shifting toward a regimen of disorder. We propose that the alteration of information processing at this algorithmic level of computation, the theoretical intermediate level between structure and function, may be a mechanism behind the emergent and widespread comorbidities associated with epilepsy, and perhaps other disorders.SIGNIFICANCE STATEMENT Comorbidities, such as cognitive deficits, which often accompany epilepsies, constitute a basal state, while seizures are rare and transient events. This suggests that neural dynamics, in particular those supporting cognitive function, are altered in a permanent manner in epilepsy. Here, we show that basic processes of information processing at the core of cognitive function (i.e., storage and sharing of information) are altered in the hippocampus and the entorhinal cortex (two regions involved in memory processes) in experimental epilepsy. Such disruption of information processing at the algorithmic level itself could underlie the general performance impairments in epilepsy.

Molecular profiling of CO2/pH-sensitive neurons in the locus coeruleus of bullfrogs reveals overlapping noradrenergic and glutamatergic cell identity

Locus coeruleus (LC) neurons regulate breathing by sensing CO2/pH. Neurons within the vertebrate LC are the main source of norepinephrine within the brain. However, they also use glutamate and GABA for fast neurotransmission. Although the amphibian LC is recognized as a site involved in central chemoreception for the control of breathing, the neurotransmitter phenotype of these neurons is unknown. To address this question, we combined electrophysiology and single-cell quantitative PCR to detect mRNA transcripts that define norepinephrinergic, glutamatergic, and GABAergic phenotypes in LC neurons activated by hypercapnic acidosis (HA) in American bullfrogs. Most LC neurons activated by HA had overlapping expression of noradrenergic and glutamatergic markers but did not show strong support for GABAergic transmission. Genes that encode the pH-sensitive K+ channel, TASK2, and acid-sensing cation channel, ASIC2, were most abundant, while Kir5.1 was present in 1/3 of LC neurons. The abundance of transcripts related to norepinephrine biosynthesis linearly correlated with those involved in pH sensing. These results suggest that noradrenergic neurons in the amphibian LC also use glutamate as a neurotransmitter and that CO2/pH sensitivity may be linkedto the noradrenergic cell identity.

Comodulation reduces interindividual variability of circuit output

Ionic current levels of identified neurons vary substantially across individual animals. Yet, under similar conditions, neural circuit output can be remarkably similar, as evidenced in many motor systems. All neural circuits are influenced by multiple neuromodulators which provide flexibility to their output. These neuromodulators often overlap in their actions by modulating the same channel type or synapse, yet have neuron-specific actions resulting from distinct receptor expression. Because of this different receptor expression pattern, in the presence of multiple convergent neuromodulators, a common downstream target would be activated more uniformly in circuit neurons across individuals. We therefore propose that a baseline tonic (non-saturating) level of comodulation by convergent neuromodulators can reduce interindividual variability of circuit output. We tested this hypothesis in the pyloric circuit of the crab, Cancer borealis. Multiple excitatory neuropeptides converge to activate the same voltage-gated current in this circuit, but different subsets of pyloric neurons have receptors for each peptide. We quantified the interindividual variability of the unmodulated pyloric circuit output by measuring the activity phases, cycle frequency and intraburst spike number and frequency. We then examined the variability in the presence of different combinations and concentrations of three neuropeptides. We found that at mid-level concentration (30 nM) but not at near-threshold (1 nM) or saturating (1 μM) concentrations, comodulation by multiple neuropeptides reduced the circuit output variability. Notably, the interindividual variability of response properties of an isolated neuron was not reduced by comodulation, suggesting that the reduction of output variability may emerge as a network effect.

Cell anatomy and network input explain differences within but not between leech touch cells at two different locations

Mechanosensory cells in the leech share several common features with mechanoreceptors in the human glabrous skin. Previous studies showed that the six T (touch) cells in each body segment of the leech are highly variable in their responses to somatic current injection and change their excitability over time. Here, we investigate three potential reasons for this variability in excitability by comparing the responses of T cells at two soma locations (T2 and T3): (1) Differential effects of time-dependent changes in excitability, (2) divergent synaptic input from the network, and (3) different anatomical structures. These hypotheses were explored with a combination of electrophysiological double recordings, 3D reconstruction of neurobiotin-filled cells, and compartmental model simulations. Current injection triggered significantly more spikes with shorter latency and larger amplitudes in cells at soma location T2 than at T3. During longer recordings, cells at both locations increased their excitability over time in the same way. T2 and T3 cells received the same amount of synaptic input from the unstimulated network, and the polysynaptic connections between both T cells were mutually symmetric. However, we found a striking anatomical difference: While in our data set all T2 cells innervated two roots connecting the ganglion with the skin, 50% of the T3 cells had only one root process. The sub-sample of T3 cells with one root process was significantly less excitable than the T3 cells with two root processes and the T2 cells. To test if the additional root process causes higher excitability, we simulated the responses of 3D reconstructed cells of both anatomies with detailed multi-compartment models. The anatomical subtypes do not differ in excitability when identical biophysical parameters and a homogeneous channel distribution are assumed. Hence, all three hypotheses may contribute to the highly variable T cell responses, but none of them is the only factor accounting for the observed systematic difference in excitability between cells at T2 vs. T3 soma location. Therefore, future patch clamp and modeling studies are needed to analyze how biophysical properties and spatial distribution of ion channels on the cell surface contribute to the variability and systematic differences of electrophysiological phenotypes.

Intrinsic neural diversity quenches the dynamic volatility of neural networks

Heterogeneity is the norm in biology. The brain is no different: Neuronal cell types are myriad, reflected through their cellular morphology, type, excitability, connectivity motifs, and ion channel distributions. While this biophysical diversity enriches neural systems' dynamical repertoire, it remains challenging to reconcile with the robustness and persistence of brain function over time (resilience). To better understand the relationship between excitability heterogeneity (variability in excitability within a population of neurons) and resilience, we analyzed both analytically and numerically a nonlinear sparse neural network with balanced excitatory and inhibitory connections evolving over long time scales. Homogeneous networks demonstrated increases in excitability, and strong firing rate correlations-signs of instability-in response to a slowly varying modulatory fluctuation. Excitability heterogeneity tuned network stability in a context-dependent way by restraining responses to modulatory challenges and limiting firing rate correlations, while enriching dynamics during states of low modulatory drive. Excitability heterogeneity was found to implement a homeostatic control mechanism enhancing network resilience to changes in population size, connection probability, strength and variability of synaptic weights, by quenching the volatility (i.e., its susceptibility to critical transitions) of its dynamics. Together, these results highlight the fundamental role played by cell-to-cell heterogeneity in the robustness of brain function in the face of change.

M-current modulation of cortical slow oscillations: Network dynamics and computational modeling

The slow oscillation is a synchronized network activity expressed by the cortical network in slow wave sleep and under anesthesia. Waking up requires a transition from this synchronized brain state to a desynchronized one. Cholinergic innervation is critical for the transition from slow-wave-sleep to wakefulness, and muscarinic action is largely exerted through the muscarinic-sensitive potassium current (M-current) block. We investigated the dynamical impact of blocking the M-current on slow oscillations, both in cortical slices and in a cortical network computational model. Blocking M-current resulted in an elongation of Up states (by four times) and in a significant firing rate increase, reflecting an increased network excitability, albeit no epileptiform discharges occurred. These effects were replicated in a biophysical cortical model, where a parametric reduction of the M-current resulted in a progressive elongation of Up states and firing rate. All neurons, and not only those modeled with M-current, increased their firing rates due to network recurrency. Further increases in excitability induced even longer Up states, approaching the microarousals described in the transition towards wakefulness. Our results bridge an ionic current with network modulation, providing a mechanistic insight into network dynamics of awakening.

Biological complexity facilitates tuning of the neuronal parameter space

The electrical and computational properties of neurons in our brains are determined by a rich repertoire of membrane-spanning ion channels and elaborate dendritic trees. However, the precise reason for this inherent complexity remains unknown, given that simpler models with fewer ion channels are also able to functionally reproduce the behaviour of some neurons. Here, we stochastically varied the ion channel densities of a biophysically detailed dentate gyrus granule cell model to produce a large population of putative granule cells, comparing those with all 15 original ion channels to their reduced but functional counterparts containing only 5 ion channels. Strikingly, valid parameter combinations in the full models were dramatically more frequent at -6% vs. -1% in the simpler model. The full models were also more stable in the face of perturbations to channel expression levels. Scaling up the numbers of ion channels artificially in the reduced models recovered these advantages confirming the key contribution of the actual number of ion channel types. We conclude that the diversity of ion channels gives a neuron greater flexibility and robustness to achieve a target excitability.

Single Neuron Modeling Identifies Potassium Channel Modulation as Potential Target for Repetitive Head Impacts

Traumatic brain injury (TBI) and repetitive head impacts can result in a wide range of neurological symptoms. Despite being the most common neurological disorder in the world, repeat head impacts and TBI do not have any FDA-approved treatments. Single neuron modeling allows researchers to extrapolate cellular changes in individual neurons based on experimental data. We recently characterized a model of high frequency head impact (HFHI) with a phenotype of cognitive deficits associated with decreases in neuronal excitability of CA1 neurons and synaptic changes. While the synaptic changes have been interrogated in vivo, the cause and potential therapeutic targets of hypoexcitability following repetitive head impacts are unknown. Here, we generated in silico models of CA1 pyramidal neurons from current clamp data of control mice and mice that sustained HFHI. We use a directed evolution algorithm with a crowding penalty to generate a large and unbiased population of plausible models for each group that approximated the experimental features. The HFHI neuron model population showed decreased voltage gated sodium conductance and a general increase in potassium channel conductance. We used partial least squares regression analysis to identify combinations of channels that may account for CA1 hypoexcitability after HFHI. The hypoexcitability phenotype in models was linked to A- and M-type potassium channels in combination, but not by any single channel correlations. We provide an open access set of CA1 pyramidal neuron models for both control and HFHI conditions that can be used to predict the effects of pharmacological interventions in TBI models.

Modulation by neuropeptides with overlapping targets results in functional overlap in oscillatory circuit activation

Neuromodulation lends flexibility to neural circuit operation but the general notion that different neuromodulators sculpt neural circuit activity into distinct and characteristic patterns is complicated by interindividual variability. In addition, some neuromodulators converge onto the same signaling pathways, with similar effects on neurons and synapses. We compared the effects of three neuropeptides on the rhythmic pyloric circuit in the crab Cancer borealis stomatogastric nervous system. Proctolin (PROC), crustacean cardioactive peptide (CCAP), and red pigment concentrating hormone (RPCH) all activate the same modulatory inward current, IMI, and have convergent actions on synapses. However, while PROC targets all four neuron types in the core pyloric circuit, CCAP and RPCH target the same subset of only two neurons. After removal of spontaneous neuromodulator release, none of the neuropeptides restored the control cycle frequency, but all restored the relative timing between neuron types. Consequently, differences between neuropeptide effects were mainly found in the spiking activity of different neuron types. We performed statistical comparisons using the Euclidean distance in the multidimensional space of normalized output attributes to obtain a single measure of difference between modulatory states. Across preparations, circuit output in PROC was distinguishable from CCAP and RPCH, but CCAP and RPCH were not distinguishable from each other. However, we argue that even between PROC and the other two neuropeptides, population data overlapped enough to prevent reliable identification of individual output patterns as characteristic for a specific neuropeptide. We confirmed this notion by showing that blind classifications by machine learning algorithms were only moderately successful.

Homeostatic regulation of neuronal function: importance of degeneracy and pleiotropy

Neurons maintain their average firing rate and other properties within narrow bounds despite changing conditions. This homeostatic regulation is achieved using negative feedback to adjust ion channel expression levels. To understand how homeostatic regulation of excitability normally works and how it goes awry, one must consider the various ion channels involved as well as the other regulated properties impacted by adjusting those channels when regulating excitability. This raises issues of degeneracy and pleiotropy. Degeneracy refers to disparate solutions conveying equivalent function (e.g., different channel combinations yielding equivalent excitability). This many-to-one mapping contrasts the one-to-many mapping described by pleiotropy (e.g., one channel affecting multiple properties). Degeneracy facilitates homeostatic regulation by enabling a disturbance to be offset by compensatory changes in any one of several different channels or combinations thereof. Pleiotropy complicates homeostatic regulation because compensatory changes intended to regulate one property may inadvertently disrupt other properties. Co-regulating multiple properties by adjusting pleiotropic channels requires greater degeneracy than regulating one property in isolation and, by extension, can fail for additional reasons such as solutions for each property being incompatible with one another. Problems also arise if a perturbation is too strong and/or negative feedback is too weak, or because the set point is disturbed. Delineating feedback loops and their interactions provides valuable insight into how homeostatic regulation might fail. Insofar as different failure modes require distinct interventions to restore homeostasis, deeper understanding of homeostatic regulation and its pathological disruption may reveal more effective treatments for chronic neurological disorders like neuropathic pain and epilepsy.

Heterogeneity of voltage gated sodium current density between neurons decorrelates spiking and suppresses network synchronization in Scn1b null mouse models

Voltage gated sodium channels (VGSCs) are required for action potential initiation and propagation in mammalian neurons. As with other ion channel families, VGSC density varies between neurons. Importantly, sodium current (INa) density variability is reduced in pyramidal neurons of Scn1b null mice. Scn1b encodes the VGSC β1/ β1B subunits, which regulate channel expression, trafficking, and voltage dependent properties. Here, we investigate how variable INa density in cortical layer 6 and subicular pyramidal neurons affects spike patterning and network synchronization. Constitutive or inducible Scn1b deletion enhances spike timing correlations between pyramidal neurons in response to fluctuating stimuli and impairs spike-triggered average current pattern diversity while preserving spike reliability. Inhibiting INa with a low concentration of tetrodotoxin similarly alters patterning without impairing reliability, with modest effects on firing rate. Computational modeling shows that broad INa density ranges confer a similarly broad spectrum of spike patterning in response to fluctuating synaptic conductances. Network coupling of neurons with high INa density variability displaces the coupling requirements for synchronization and broadens the dynamic range of activity when varying synaptic strength and network topology. Our results show that INa heterogeneity between neurons potently regulates spike pattern diversity and network synchronization, expanding VGSC roles in the nervous system.

Low-dimensional models of single neurons: a review

The classical Hodgkin-Huxley (HH) point-neuron model of action potential generation is four-dimensional. It consists of four ordinary differential equations describing the dynamics of the membrane potential and three gating variables associated to a transient sodium and a delayed-rectifier potassium ionic currents. Conductance-based models of HH type are higher-dimensional extensions of the classical HH model. They include a number of supplementary state variables associated with other ionic current types, and are able to describe additional phenomena such as subthreshold oscillations, mixed-mode oscillations (subthreshold oscillations interspersed with spikes), clustering and bursting. In this manuscript we discuss biophysically plausible and phenomenological reduced models that preserve the biophysical and/or dynamic description of models of HH type and the ability to produce complex phenomena, but the number of effective dimensions (state variables) is lower. We describe several representative models. We also describe systematic and heuristic methods of deriving reduced models from models of HH type.

Target cell-specific synaptic dynamics of excitatory to inhibitory neuron connections in supragranular layers of human neocortex

Rodent studies have demonstrated that synaptic dynamics from excitatory to inhibitory neuron types are often dependent on the target cell type. However, these target cell-specific properties have not been well investigated in human cortex, where there are major technical challenges in reliably obtaining healthy tissue, conducting multiple patch-clamp recordings on inhibitory cell types, and identifying those cell types. Here, we take advantage of newly developed methods for human neurosurgical tissue analysis with multiple patch-clamp recordings, post-hoc fluorescent in situ hybridization (FISH), machine learning-based cell type classification and prospective GABAergic AAV-based labeling to investigate synaptic properties between pyramidal neurons and PVALB- vs. SST-positive interneurons. We find that there are robust molecular differences in synapse-associated genes between these neuron types, and that individual presynaptic pyramidal neurons evoke postsynaptic responses with heterogeneous synaptic dynamics in different postsynaptic cell types. Using molecular identification with FISH and classifiers based on transcriptomically identified PVALB neurons analyzed by Patch-seq, we find that PVALB neurons typically show depressing synaptic characteristics, whereas other interneuron types including SST-positive neurons show facilitating characteristics. Together, these data support the existence of target cell-specific synaptic properties in human cortex that are similar to rodent, thereby indicating evolutionary conservation of local circuit connectivity motifs from excitatory to inhibitory neurons and their synaptic dynamics.

Loss or gain of function? Effects of ion channel mutations on neuronal firing depend on the neuron type

Introduction

Clinically relevant mutations to voltage-gated ion channels, called channelopathies, alter ion channel function, properties of ionic currents, and neuronal firing. The effects of ion channel mutations are routinely assessed and characterized as loss of function (LOF) or gain of function (GOF) at the level of ionic currents. However, emerging personalized medicine approaches based on LOF/GOF characterization have limited therapeutic success. Potential reasons are among others that the translation from this binary characterization to neuronal firing is currently not well-understood-especially when considering different neuronal cell types. In this study, we investigate the impact of neuronal cell type on the firing outcome of ion channel mutations.

Methods

To this end, we simulated a diverse collection of single-compartment, conductance-based neuron models that differed in their composition of ionic currents. We systematically analyzed the effects of changes in ion current properties on firing in different neuronal types. Additionally, we simulated the effects of known mutations in KCNA1 gene encoding the K_V1.1 potassium channel subtype associated with episodic ataxia type 1 (EA1).

Results

These simulations revealed that the outcome of a given change in ion channel properties on neuronal excitability depends on neuron type, i.e., the properties and expression levels of the unaffected ionic currents.

Discussion

Consequently, neuron-type specific effects are vital to a full understanding of the effects of channelopathies on neuronal excitability and are an important step toward improving the efficacy and precision of personalized medicine approaches.

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.

Syncytial nerve net in a ctenophore adds insights on the evolution of nervous systems

A fundamental breakthrough in neurobiology has been the formulation of the neuron doctrine by Santiago Ramón y Cajal, which stated that the nervous system is composed of discrete cells. Electron microscopy later confirmed the doctrine and allowed the identification of synaptic connections. In this work, we used volume electron microscopy and three-dimensional reconstructions to characterize the nerve net of a ctenophore, a marine invertebrate that belongs to one of the earliest-branching animal lineages. We found that neurons in the subepithelial nerve net have a continuous plasma membrane that forms a syncytium. Our findings suggest fundamental differences of nerve net architectures between ctenophores and cnidarians or bilaterians and offer an alternative perspective on neural network organization and neurotransmission.

A general pattern of non-spiking neuron dynamics under the effect of potassium and calcium channel modifications

Electrical activity of excitable cells results from ion exchanges through cell membranes, so that genetic or epigenetic changes in genes encoding ion channels are likely to affect neuronal electrical signaling throughout the brain. There is a large literature on the effect of variations in ion channels on the dynamics of spiking neurons that represent the main type of neurons found in the vertebrate nervous systems. Nevertheless, non-spiking neurons are also ubiquitous in many nervous tissues and play a critical role in the processing of some sensory systems. To our knowledge, however, how conductance variations affect the dynamics of non-spiking neurons has never been assessed. Based on experimental observations reported in the biological literature and on mathematical considerations, we first propose a phenotypic classification of non-spiking neurons. Then, we determine a general pattern of the phenotypic evolution of non-spiking neurons as a function of changes in calcium and potassium conductances. Furthermore, we study the homeostatic compensatory mechanisms of ion channels in a well-posed non-spiking retinal cone model. We show that there is a restricted range of ion conductance values for which the behavior and phenotype of the neuron are maintained. Finally, we discuss the implications of the phenotypic changes of individual cells at the level of neuronal network functioning of the C. elegans worm and the retina, which are two non-spiking nervous tissues composed of neurons with various phenotypes.

Neuron populations use variable combinations of short-term feedback mechanisms to stabilize firing rate

Neurons tightly regulate firing rate and a failure to do so leads to multiple neurological disorders. Therefore, a fundamental question in neuroscience is how neurons produce reliable activity patterns for decades to generate behavior. Neurons have built-in feedback mechanisms that allow them to monitor their output and rapidly stabilize firing rate. Most work emphasizes the role of a dominant feedback system within a neuronal population for the control of moment-to-moment firing. In contrast, we find that respiratory motoneurons use 2 activity-dependent controllers in unique combinations across cells, dynamic activation of an Na+ pump subtype, and rapid potentiation of Kv7 channels. Both systems constrain firing rate by reducing excitability for up to a minute after a burst of action potentials but are recruited by different cellular signals associated with activity, increased intracellular Na+ (the Na+ pump), and membrane depolarization (Kv7 channels). Individual neurons do not simply contain equal amounts of each system. Rather, neurons under strong control of the Na+ pump are weakly regulated by Kv7 enhancement and vice versa along a continuum. Thus, each motoneuron maintains its characteristic firing rate through a unique combination of the Na+ pump and Kv7 channels, which are dynamically regulated by distinct feedback signals. These results reveal a new organizing strategy for stable circuit output involving multiple fast activity sensors scaled inversely across a neuronal population.

Microcircuit Synchronization and Heavy-Tailed Synaptic Weight Distribution Augment preBötzinger Complex Bursting Dynamics

The preBötzinger Complex (preBötC) encodes inspiratory time as rhythmic bursts of activity underlying each breath. Spike synchronization throughout a sparsely connected preBötC microcircuit initiates bursts that ultimately drive the inspiratory motor patterns. Using minimal microcircuit models to explore burst initiation dynamics, we examined the variability in probability and latency to burst following exogenous stimulation of a small subset of neurons, mimicking experiments. Among various physiologically plausible graphs of 1000 excitatory neurons constructed using experimentally determined synaptic and connectivity parameters, directed Erdős-Rényi graphs with a broad (lognormal) distribution of synaptic weights best captured the experimentally observed dynamics. preBötC synchronization leading to bursts was regulated by the efferent connectivity of spiking neurons that are optimally tuned to amplify modest preinspiratory activity through input convergence. Using graph-theoretic and machine learning-based analyses, we found that input convergence of efferent connectivity at the next-nearest neighbor order was a strong predictor of incipient synchronization. Our analyses revealed a crucial role of synaptic heterogeneity in imparting exceptionally robust yet flexible preBötC attractor dynamics. Given the pervasiveness of lognormally distributed synaptic strengths throughout the nervous system, we postulate that these mechanisms represent a ubiquitous template for temporal processing and decision-making computational motifs.SIGNIFICANCE STATEMENT Mammalian breathing is robust, virtually continuous throughout life, yet is inherently labile: to adapt to rapid metabolic shifts (e.g., fleeing a predator or chasing prey); for airway reflexes; and to enable nonventilatory behaviors (e.g., vocalization, breathholding, laughing). Canonical theoretical frameworks-based on pacemakers and intrinsic bursting-cannot account for the observed robustness and flexibility of the preBötzinger Complex rhythm. Experiments reveal that network synchronization is the key to initiate inspiratory bursts in each breathing cycle. We investigated preBötC synchronization dynamics using network models constructed with experimentally determined neuronal and synaptic parameters. We discovered that a fat-tailed (non-Gaussian) synaptic weight distribution-a manifestation of synaptic heterogeneity-augments neuronal synchronization and attractor dynamics in this vital rhythmogenic network, contributing to its extraordinary reliability and responsiveness.

Machine learning provides insight into models of heterogeneous electrical activity in human beta-cells

Understanding how heterogeneous cellular responses emerge from cell-to-cell variations in expression and function of subcellular components is of general interest. Here, we focus on human insulin-secreting beta-cells, which are believed to constitute a population in which heterogeneity is of physiological importance. We exploit recent single-cell electrophysiological data that allow biologically realistic population modeling of human beta-cells that accounts for cellular heterogeneity and correlation between ion channel parameters. To investigate how ion channels influence the dynamics of our updated mathematical model of human pancreatic beta-cells, we explore several machine learning techniques to determine which model parameters are important for determining the qualitative patterns of electrical activity of the model cells. As expected, K^＋ channels promote absence of activity, but once a cell is active, they increase the likelihood of having action potential firing. HERG channels were of great importance for determining cell behavior in most of the investigated scenarios. Fast bursting is influenced by the time scales of ion channel activation and, interestingly, by the type of Ca^2＋ channels coupled to BK channels in BK-CaV complexes. Slow, metabolically driven oscillations are promoted mostly by K(ATP) channels. In summary, combining population modeling with machine learning analysis provides insight into the model and generates new hypotheses to be investigated both experimentally, via simulations and through mathematical analysis.

Reprogramming the topology of the nociceptive circuit in C. elegans reshapes sexual behavior

The effect of the detailed connectivity of a neural circuit on its function and the resulting behavior of the organism is a key question in many neural systems. Here, we study the circuit for nociception in C. elegans, which is composed of the same neurons in the two sexes that are wired differently. We show that the nociceptive sensory neurons respond similarly in the two sexes, yet the animals display sexually dimorphic behaviors to the same aversive stimuli. To uncover the role of the downstream network topology in shaping behavior, we learn and simulate network models that replicate the observed dimorphic behaviors and use them to predict simple network rewirings that would switch behavior between the sexes. We then show experimentally that these subtle synaptic rewirings indeed flip behavior. Interestingly, when presented with aversive cues, rewired males were compromised in finding mating partners, suggesting that network topologies that enable efficient avoidance of noxious cues have a reproductive "cost." Our results present a deconstruction of the design of a neural circuit that controls sexual behavior and how to reprogram it.

Efficient information coding and degeneracy in the nervous system

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

Representational drift: Emerging theories for continual learning and experimental future directions

Recent work has revealed that the neural activity patterns correlated with sensation, cognition, and action often are not stable and instead undergo large scale changes over days and weeks-a phenomenon called representational drift. Here, we highlight recent observations of drift, how drift is unlikely to be explained by experimental confounds, and how the brain can likely compensate for drift to allow stable computation. We propose that drift might have important roles in neural computation to allow continual learning, both for separating and relating memories that occur at distinct times. Finally, we present an outlook on future experimental directions that are needed to further characterize drift and to test emerging theories for drift's role in computation.

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.

Breathing Rhythm and Pattern and Their Influence on Emotion

Breathing is a vital rhythmic motor behavior with a surprisingly broad influence on the brain and body. The apparent simplicity of breathing belies a complex neural control system, the breathing central pattern generator (bCPG), that exhibits diverse operational modes to regulate gas exchange and coordinate breathing with an array of behaviors. In this review, we focus on selected advances in our understanding of the bCPG. At the core of the bCPG is the preBötzinger complex (preBötC), which drives inspiratory rhythm via an unexpectedly sophisticated emergent mechanism. Synchronization dynamics underlying preBötC rhythmogenesis imbue the system with robustness and lability. These dynamics are modulated by inputs from throughout the brain and generate rhythmic, patterned activity that is widely distributed. The connectivity and an emerging literature support a link between breathing, emotion, and cognition that is becoming experimentally tractable. These advances bring great potential for elucidating function and dysfunction in breathing and other mammalian neural circuits.

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.

Vulnerability of Human Cerebellar Neurons to Degeneration in Ataxia-Causing Channelopathies

Mutations in ion channel genes underlie a number of human neurological diseases. Historically, human mutations in ion channel genes, the so-called channelopathies, have been identified to cause episodic disorders. In the last decade, however, mutations in ion channel genes have been demonstrated to result in progressive neurodegenerative and neurodevelopmental disorders in humans, particularly with ion channels that are enriched in the cerebellum. This was unexpected given prior rodent ion channel knock-out models that almost never display neurodegeneration. Human ataxia-causing channelopathies that result in even haploinsufficiency can result in cerebellar atrophy and cerebellar Purkinje neuron loss. Rodent neurons with ion channel loss-of-function appear to, therefore, be significantly more resistant to neurodegeneration compared to human neurons. Fundamental differences in susceptibility of human and rodent cerebellar neurons in ataxia-causing channelopathies must therefore be present. In this review, we explore the properties of human neurons that may contribute to their vulnerability to cerebellar degeneration secondary to ion channel loss-of-function mutations. We present a model taking into account the known allometric scaling of neuronal ion channel density in humans and other mammals that may explain the preferential vulnerability of human cerebellar neurons to degeneration in ataxia-causing channelopathies. We also speculate on the vulnerability of cerebellar neurons to degeneration in mouse models of spinocerebellar ataxia (SCA) where ion channel transcript dysregulation has recently been implicated in disease pathogenesis.