Compensation for variable intrinsic neuronal excitability by circuit-synaptic interactions

Degenerate neuronal and circuit mechanisms important for generating rhythmic motor patterns

In 1996, we published a review article (Marder E, Calabrese RL. Physiol Rev 76: 687-717, 1996) describing the state of knowledge about the structure and function of the central pattern-generating circuits important for producing rhythmic behaviors. Although many of the core questions persist, much has changed since 1996. Here, we focus on newer studies that reveal ambiguities that complicate understanding circuit dynamics, despite the enormous technical advances of the recent past. In particular, we highlight recent studies of animal-to-animal variability and our understanding that circuit rhythmicity may be supported by multiple state-dependent mechanisms within the same animal and that robustness and resilience in the face of perturbation may depend critically on the presence of modulators and degenerate circuit mechanisms. Additionally, we highlight the use of computational models to ask whether there are generalizable principles about circuit motifs that can be found across rhythmic motor systems in different animal species.

Daily light-induced transcription in visual cortex neurons drives downward firing rate homeostasis and stabilizes sensory processing

Balancing plasticity and stability in neural circuits is essential for an animal's ability to learn from its environment while preserving proper processing and perception of sensory information. However, unlike the mechanisms that drive plasticity in neural circuits, the activity-induced molecular mechanisms that convey functional stability remain poorly understood. Focusing on the visual cortex of adult mice and combining transcriptomics, electrophysiology, and in vivo calcium imaging, we find that the daily appearance of light induces, in excitatory neurons, a large gene program along with rapid and transient increases in the ratio of excitation and inhibition (E/I ratio) and neural activity. Furthermore, we find that the light-induced transcription factor NPAS4 drives these daily normalizations of the E/I ratio and neural activity rates and that it stabilizes the neurons' response properties. These findings indicate that daily sensory-induced transcription normalizes the E/I ratio and drives downward firing rate homeostasis to maintain proper sensory processing and perception.

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.

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.

Predicting the Behavior of Sparsely-Sampled Systems Across Neurobiology and Epidemiology

Inference is a term that encompasses many techniques including statistical data assimilation (SDA). Unlike machine learning, which is designed to harness predictive power from extremely large data sets, SDA is designed for sparsely-sampled systems. This is the realm of study of nonlinear dynamical systems in nature. Formulated as an optimization procedure, SDA can be considered a path-integral approach to state and parameter estimation. Within this formulation, we can use the physical principle of least action to identify optimal solutions: solutions that are consistent with both measurements and a dynamical model assumed to give rise to those measurements. I review examples from neurobiology and an epidemiological model tailored to the coronavirus SARS-CoV-2, to demonstrate the versatility of SDA across the sciences, and how these distinct applications possess commonalities that can inform one another.

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.

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.

Energy-efficient network activity from disparate circuit parameters

Neural circuits can produce similar activity patterns from vastly different combinations of channel and synaptic conductances. These conductances are tuned for specific activity patterns but might also reflect additional constraints, such as metabolic cost or robustness to perturbations. How do such constraints influence the range of permissible conductances? Here we investigate how metabolic cost affects the parameters of neural circuits with similar activity in a model of the pyloric network of the crab Cancer borealis . We present a machine learning method that can identify a range of network models that generate activity patterns matching experimental data and find that neural circuits can consume largely different amounts of energy despite similar circuit activity. Furthermore, a reduced but still significant range of circuit parameters gives rise to energy-efficient circuits. We then examine the space of parameters of energy-efficient circuits and identify potential tuning strategies for low metabolic cost. Finally, we investigate the interaction between metabolic cost and temperature robustness. We show that metabolic cost can vary across temperatures but that robustness to temperature changes does not necessarily incur an increased metabolic cost. Our analyses show that despite metabolic efficiency and temperature robustness constraining circuit parameters, neural systems can generate functional, efficient, and robust network activity with widely disparate sets of conductances.

New insights from small rhythmic circuits

Small rhythmic circuits, such as those found in invertebrates, have provided fundamental insights into how circuit dynamics depend on individual neuronal and synaptic properties. Degenerate circuits are those with different network parameters and similar behavior. New work on degenerate circuits and their modulation illustrates some of the rules that help maintain stable and robust circuit function despite environmental perturbations. Advances in neuropeptide isolation and identification provide enhanced understanding of the neuromodulation of circuits for behavior. The advent of molecular studies of mRNA expression provides new insight into animal-to-animal variability and the homeostatic regulation of excitability in neurons and networks.

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.

Compensatory variability in network parameters enhances memory performance in the Drosophila mushroom body

Neural circuits use homeostatic compensation to achieve consistent behavior despite variability in underlying intrinsic and network parameters. However, it remains unclear how compensation regulates variability across a population of the same type of neurons within an individual and what computational benefits might result from such compensation. We address these questions in the Drosophila mushroom body, the fly's olfactory memory center. In a computational model, we show that under sparse coding conditions, memory performance is degraded when the mushroom body's principal neurons, Kenyon cells (KCs), vary realistically in key parameters governing their excitability. However, memory performance is rescued while maintaining realistic variability if parameters compensate for each other to equalize KC average activity. Such compensation can be achieved through both activity-dependent and activity-independent mechanisms. Finally, we show that correlations predicted by our model's compensatory mechanisms appear in the Drosophila hemibrain connectome. These findings reveal compensatory variability in the mushroom body and describe its computational benefits for associative memory.

Cholinergic modulation of hierarchical inhibitory control over cortical resting state dynamics: Local circuit modeling of schizophrenia-related hypofrontality

Nicotinic acetylcholine receptors (nAChRs) modulate the cholinergic drive to a hierarchy of inhibitory neurons in the superficial layers of the PFC, critical to cognitive processes. It has been shown that genetic deletions of the various types of nAChRs impact the properties of ultra-slow transitions between high and low PFC activity states in mice during quiet wakefulness. The impact characteristics depend on specific interneuron populations expressing the manipulated receptor subtype. In addition, recent data indicate that a genetic mutation of the α5 nAChR subunit, located on vasoactive intestinal polypeptide (VIP) inhibitory neurons, the rs16969968 single nucleotide polymorphism (α5 SNP), plays a key role in the hypofrontality observed in schizophrenia patients carrying the SNP. Data also indicate that chronic nicotine application to α5 SNP mice relieves the hypofrontality. We developed a computational model to show that the activity patterns recorded in the genetically modified mice can be explained by changes in the dynamics of the local PFC circuit. Notably, our model shows that these altered PFC circuit dynamics are due to changes in the stability structure of the activity states. We identify how this stability structure is differentially modulated by cholinergic inputs to the parvalbumin (PV), somatostatin (SOM) or the VIP inhibitory populations. Our model uncovers that a change in amplitude, but not duration of the high activity states can account for the lowered pyramidal (PYR) population firing rates recorded in α5 SNP mice. We demonstrate how nicotine-induced desensitization and upregulation of the β2 nAChRs located on SOM interneurons, as opposed to the activation of α5 nAChRs located on VIP interneurons, is sufficient to explain the nicotine-induced activity normalization in α5 SNP mice. The model further implies that subsequent nicotine withdrawal may exacerbate the hypofrontality over and beyond one caused by the SNP mutation.

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Prefrontal cortex shows ultra-slow alterations between low and high activity states at rest. This activity is characteristically decreased in schizophrenia patients.

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Model identifies local circuit origin of hypofrontality associated with schizophrenia and a5 nicotinic receptor malfunction.

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Decrease in PFC VIP-interneuron excitability drives decrease in high-activity-state stability and overall hypofrontality.

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Model shows desensitization/upregulation of SOM-expressed β2-NAChRs drive nicotine-induced renormalization of PFC activity.

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

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

Comodulation of h- and Na+/K+ Pump Currents Expands the Range of Functional Bursting in a Central Pattern Generator by Navigating between Dysfunctional Regimes

Central pattern generators (CPGs), specialized oscillatory neuronal networks controlling rhythmic motor behaviors such as breathing and locomotion, must adjust their patterns of activity to a variable environment and changing behavioral goals. Neuromodulation adjusts these patterns by orchestrating changes in multiple ionic currents. In the medicinal leech, the endogenous neuromodulator myomodulin speeds up the heartbeat CPG by reducing the electrogenic Na+/K+ pump current and increasing h-current in pairs of mutually inhibitory leech heart interneurons (HNs), which form half-center oscillators (HN HCOs). Here we investigate whether the comodulation of two currents could have advantages over a single current in the control of functional bursting patterns of a CPG. We use a conductance-based biophysical model of an HN HCO to explain the experimental effects of myomodulin. We demonstrate that, in the model, comodulation of the Na+/K+ pump current and h-current expands the range of functional bursting activity by avoiding transitions into nonfunctional regimes, such as asymmetric bursting and plateau-containing seizure-like activity. We validate the model by finding parameters that reproduce temporal bursting characteristics matching experimental recordings from HN HCOs under control, three different myomodulin concentrations, and Cs+ treated conditions. The matching cases are located along the border of an asymmetric regime away from the border with more dangerous seizure-like activity. We found a simple comodulation mechanism with an inverse relation between the pump and h-currents makes a good fit of the matching cases and comprises a general mechanism for the robust and flexible control of oscillatory neuronal networks.SIGNIFICANCE STATEMENT Rhythm-generating neuronal circuits adjust their oscillatory patterns to accommodate a changing environment through neuromodulation. In different species, chemical messengers participating in such processes may target two or more membrane currents. In medicinal leeches, the neuromodulator myomodulin speeds up the heartbeat central pattern generator by reducing Na+/K+ pump current and increasing h-current. In a computational model, we show that this comodulation expands the range of central pattern generator's functional activity by navigating the circuit between dysfunctional regimes resulting in a much wider range of cycle period. This control would not be attainable by modulating only one current, emphasizing the synergy of combined effects. Given the prevalence of h-current and Na+/K+ pump current in neurons, similar comodulation mechanisms may exist across species.

Intrinsic plasticity and birdsong learning

Although information processing and storage in the brain is thought to be primarily orchestrated by synaptic plasticity, other neural mechanisms such as intrinsic plasticity are available. While a number of recent studies have described the plasticity of intrinsic excitability in several types of neurons, the significance of non-synaptic mechanisms in memory and learning remains elusive. After reviewing plasticity of intrinsic excitation in relation to learning and homeostatic mechanisms, we focus on the intrinsic properties of a class of basal-ganglia projecting song system neurons in zebra finch, how these related to each bird's unique learned song, how these properties change over development, and how they are maintained dynamically to rapidly change in response to auditory feedback perturbations. We place these results in the broader theme of learning and changes in intrinsic properties, emphasizing the computational implications of this form of plasticity, which are distinct from synaptic plasticity. The results suggest that exploring reciprocal interactions between intrinsic and network properties will be a fruitful avenue for understanding mechanisms of birdsong learning.

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.

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.

Differential neuropeptide modulation of premotor and motor neurons in the lobster cardiac ganglion

The American lobster, Homarus americanus, cardiac neuromuscular system is controlled by the cardiac ganglion (CG), a central pattern generator consisting of four premotor and five motor neurons. Here, we show that the premotor and motor neurons can establish independent bursting patterns when decoupled by a physical ligature. We also show that mRNA encoding myosuppressin, a cardioactive neuropeptide, is produced within the CG. We thus asked whether myosuppressin modulates the decoupled premotor and motor neurons, and if so, how this modulation might underlie the role(s) that these neurons play in myosuppressin's effects on ganglionic output. Although myosuppressin exerted dose-dependent effects on burst frequency and duration in both premotor and motor neurons in the intact CG, its effects on the ligatured ganglion were more complex, with different effects and thresholds on the two types of neurons. These data suggest that the motor neurons are more important in determining the changes in frequency of the CG elicited by low concentrations of myosuppressin, whereas the premotor neurons have a greater impact on changes elicited in burst duration. A single putative myosuppressin receptor (MSR-I) was previously described from the Homarus nervous system. We identified four additional putative MSRs (MSR-II-V) and investigated their individual distributions in the CG premotor and motor neurons using RT-PCR. Transcripts for only three receptors (MSR-II-IV) were amplified from the CG. Potential differential distributions of the receptors were observed between the premotor and motor neurons; these differences may contribute to the distinct physiological responses of the two neuron types to myosuppressin.NEW & NOTEWORTHY Premotor and motor neurons of the Homarus americanus cardiac ganglion (CG) are normally electrically and chemically coupled, and generate rhythmic bursting that drives cardiac contractions; we show that they can establish independent bursting patterns when physically decoupled by a ligature. The neuropeptide myosuppressin modulates different aspects of the bursting pattern in these neuron types to determine the overall modulation of the intact CG. Differential distribution of myosuppressin receptors may underlie the observed responses to myosuppressin.

Computational model of the distributed representation of operant reward memory: combinatoric engagement of intrinsic and synaptic plasticity mechanisms

Operant reward learning of feeding behavior in Aplysia increases the frequency and regularity of biting, as well as biases buccal motor patterns (BMPs) toward ingestion-like BMPs (iBMPs). The engram underlying this memory comprises cells that are part of a central pattern generating (CPG) circuit and includes increases in the intrinsic excitability of identified cells B30, B51, B63, and B65, and increases in B63-B30 and B63-B65 electrical synaptic coupling. To examine the ways in which sites of plasticity (individually and in combination) contribute to memory expression, a model of the CPG was developed. The model included conductance-based descriptions of cells CBI-2, B4, B8, B20, B30, B31, B34, B40, B51, B52, B63, B64, and B65, and their synaptic connections. The model generated patterned activity that resembled physiological BMPs, and implementation of the engram reproduced increases in frequency, regularity, and bias. Combined enhancement of B30, B63, and B65 excitabilities increased BMP frequency and regularity, but not bias toward iBMPs. Individually, B30 increased regularity and bias, B51 increased bias, B63 increased frequency, and B65 decreased all three BMP features. Combined synaptic plasticity contributed primarily to regularity, but also to frequency and bias. B63-B30 coupling contributed to regularity and bias, and B63-B65 coupling contributed to all BMP features. Each site of plasticity altered multiple BMP features simultaneously. Moreover, plasticity loci exhibited mutual dependence and synergism. These results indicate that the memory for operant reward learning emerged from the combinatoric engagement of multiple sites of plasticity.

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

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

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

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

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

Automatic Adaptation of Model Neurons and Connections to Build Hybrid Circuits with Living Networks

Hybrid circuits built by creating mono- or bi-directional interactions among living cells and model neurons and synapses are an effective way to study neuron, synaptic and neural network dynamics. However, hybrid circuit technology has been largely underused in the context of neuroscience studies mainly because of the inherent difficulty in implementing and tuning this type of interactions. In this paper, we present a set of algorithms for the automatic adaptation of model neurons and connections in the creation of hybrid circuits with living neural networks. The algorithms perform model time and amplitude scaling, real-time drift adaptation, goal-driven synaptic and model tuning/calibration and also automatic parameter mapping. These algorithms have been implemented in RTHybrid, an open-source library that works with hard real-time constraints. We provide validation examples by building hybrid circuits in a central pattern generator. The results of the validation experiments show that the proposed dynamic adaptation facilitates closed-loop communication among living and artificial model neurons and connections, and contributes to characterize system dynamics, achieve control, automate experimental protocols and extend the lifespan of the preparations.

Statistical data assimilation for estimating electrophysiology simultaneously with connectivity within a biological neuronal network

A method of data assimilation (DA) is employed to estimate electrophysiological parameters of neurons simultaneously with their synaptic connectivity in a small model biological network. The DA procedure is cast as an optimization, with a cost function consisting of both a measurement error and a model error term. An iterative reweighting of these terms permits a systematic method to identify the lowest minimum, within a local region of state space, on the surface of a nonconvex cost function. In the model, two sets of parameter values are associated with two particular functional modes of network activity: simultaneous firing of all neurons and a pattern-generating mode wherein the neurons burst in sequence. The DA procedure is able to recover these modes if: (i) the stimulating electrical currents have chaotic waveforms and (ii) the measurements consist of the membrane voltages of all neurons in the circuit. Further, this method is able to prune a model of unnecessarily high dimensionality to a representation that contains the maximum dimensionality required to reproduce the provided measurements. This paper offers a proof-of-concept that DA has the potential to inform laboratory designs for estimating properties in small and isolatable functional circuits.

Degeneracy in hippocampal physiology and plasticity

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

RTHybrid: A Standardized and Open-Source Real-Time Software Model Library for Experimental Neuroscience

Closed-loop technologies provide novel ways of online observation, control and bidirectional interaction with the nervous system, which help to study complex non-linear and partially observable neural dynamics. These protocols are often difficult to implement due to the temporal precision required when interacting with biological components, which in many cases can only be achieved using real-time technology. In this paper we introduce RTHybrid (www.github.com/GNB-UAM/RTHybrid), a free and open-source software that includes a neuron and synapse model library to build hybrid circuits with living neurons in a wide variety of experimental contexts. In an effort to encourage the standardization of real-time software technology in neuroscience research, we compared different open-source real-time operating system patches, RTAI, Xenomai 3 and Preempt-RT, according to their performance and usability. RTHybrid has been developed to run over Linux operating systems supporting both Xenomai 3 and Preempt-RT real-time patches, and thus allowing an easy implementation in any laboratory. We report a set of validation tests and latency benchmarks for the construction of hybrid circuits using this library. With this work we want to promote the dissemination of standardized, user-friendly and open-source software tools developed for open- and closed-loop experimental neuroscience.

Two central pattern generators from the crab, Cancer borealis, respond robustly and differentially to extreme extracellular pH

The activity of neuronal circuits depends on the properties of the constituent neurons and their underlying synaptic and intrinsic currents. We describe the effects of extreme changes in extracellular pH – from pH 5.5 to 10.4 – on two central pattern generating networks, the stomatogastric and cardiac ganglia of the crab, Cancer borealis. Given that the physiological properties of ion channels are known to be sensitive to pH within the range tested, it is surprising that these rhythms generally remained robust from pH 6.1 to pH 8.8. The pH sensitivity of these rhythms was highly variable between animals and, unexpectedly, between ganglia. Animal-to-animal variability was likely a consequence of similar network performance arising from variable sets of underlying conductances. Together, these results illustrate the potential difficulty in generalizing the effects of environmental perturbation across circuits, even within the same animal.

Graded Transmission without Action Potentials Sustains Rhythmic Activity in Some But Not All Modulators That Activate the Same Current

Neurons in the central pattern-generating circuits in the crustacean stomatogastric ganglion (STG) release neurotransmitter both as a graded function of presynaptic membrane potential that persists in TTX and in response to action potentials. In the STG of the male crab Cancer borealis, the modulators oxotremorine, C. borealis tachykinin-related peptide Ia (CabTRP1a), red pigment concentrating hormone (RPCH), proctolin, TNRNFLRFamide, and crustacean cardioactive peptide (CCAP) produce and sustain robust pyloric rhythms by activating the same modulatory current (I _MI), albeit on different subsets of pyloric network targets. The muscarinic agonist oxotremorine, and the peptides CabTRP1a and RPCH elicited rhythmic triphasic intracellular alternating fluctuations of activity in the presence of TTX. Intracellular waveforms of pyloric neurons in oxotremorine and CabTRP1a in TTX were similar to those in the intact rhythm, and phase relationships among neurons were conserved. Although cycle frequency was conserved in oxotremorine and TTX, it was altered in CabTRP1a in the presence of TTX. Both rhythms were primarily driven by the pacemaker kernel consisting of the Anterior Burster and Pyloric Dilator neurons. In contrast, in TTX the circuit remained silent in proctolin, TNRNFLRFamide, and CCAP. These experiments show that graded synaptic transmission in the absence of voltage-gated Na⁺ current is sufficient to sustain rhythmic motor activity in some, but not other, modulatory conditions, even when each modulator activates the same ionic current. This further demonstrates that similar rhythmic motor patterns can be produced by qualitatively different mechanisms, one that depends on the activity of voltage-gated Na⁺ channels, and one that can persist in their absence.SIGNIFICANCE STATEMENT The pyloric rhythm of the crab stomatogastric ganglion depends both on spike-mediated and graded synaptic transmission. We activate the pyloric rhythm with a wide variety of different neuromodulators, all of which converge on the same voltage-dependent inward current. Interestingly, when action potentials and spike-mediated transmission are blocked using TTX, we find that the muscarinic agonist oxotremorine and the neuropeptide CabTRP1a sustain rhythmic alternations and appropriate phases of activity in the absence of action potentials. In contrast, TTX blocks rhythmic activity in the presence of other modulators. This demonstrates fundamental differences in the burst-generation mechanisms in different modulators that would not be suspected on the basis of their cellular actions at the level of the targeted current.

The Dynamic Basis of Respiratory Rhythm Generation: One Breath at a Time

Rhythmicity is a universal timing mechanism in the brain, and the rhythmogenic mechanisms are generally dynamic. This is illustrated for the neuronal control of breathing, a behavior that occurs as a one-, two-, or three-phase rhythm. Each breath is assembled stochastically, and increasing evidence suggests that each phase can be generated independently by a dedicated excitatory microcircuit. Within each microcircuit, rhythmicity emerges through three entangled mechanisms: ( a) glutamatergic transmission, which is amplified by ( b) intrinsic bursting and opposed by ( c) concurrent inhibition. This rhythmogenic triangle is dynamically tuned by neuromodulators and other network interactions. The ability of coupled oscillators to reconfigure and recombine may allow breathing to remain robust yet plastic enough to conform to nonventilatory behaviors such as vocalization, swallowing, and coughing. Lessons learned from the respiratory network may translate to other highly dynamic and integrated rhythmic systems, if approached one breath at a time.

Network oscillation rules imposed by species-specific electrical coupling

Electrical junctions are widespread within the mammalian CNS. Yet, their role in organizing neuronal ensemble activity remains incompletely understood. Here, in a functionally well-characterized system – neuroendocrine tuberoinfundibular dopamine (TIDA) neurons - we demonstrate a striking species difference in network behavior: rat TIDA cells discharge in highly stereotyped, robust, synchronized slow oscillations, whereas mouse oscillations are faster, flexible and show substantial cell-to-cell variability. We show that these distinct operational modes are explained by the presence of strong TIDA-TIDA gap junction coupling in the rat, and its complete absence in the mouse. Both species, however, encompass a similar heterogeneous range of intrinsic resonance frequencies, suggesting similar network building blocks. We demonstrate that gap junctions select and impose the slow network rhythm. These data identify a role for electrical junctions in determining oscillation frequency and show how related species can rely on distinct network strategies to accomplish adaptive control of hormone release.

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

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

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

A Dynamic Connectome Supports the Emergence of Stable Computational Function of Neural Circuits through Reward-Based Learning

Synaptic connections between neurons in the brain are dynamic because of continuously ongoing spine dynamics, axonal sprouting, and other processes. In fact, it was recently shown that the spontaneous synapse-autonomous component of spine dynamics is at least as large as the component that depends on the history of pre- and postsynaptic neural activity. These data are inconsistent with common models for network plasticity and raise the following questions: how can neural circuits maintain a stable computational function in spite of these continuously ongoing processes, and what could be functional uses of these ongoing processes? Here, we present a rigorous theoretical framework for these seemingly stochastic spine dynamics and rewiring processes in the context of reward-based learning tasks. We show that spontaneous synapse-autonomous processes, in combination with reward signals such as dopamine, can explain the capability of networks of neurons in the brain to configure themselves for specific computational tasks, and to compensate automatically for later changes in the network or task. Furthermore, we show theoretically and through computer simulations that stable computational performance is compatible with continuously ongoing synapse-autonomous changes. After reaching good computational performance it causes primarily a slow drift of network architecture and dynamics in task-irrelevant dimensions, as observed for neural activity in motor cortex and other areas. On the more abstract level of reinforcement learning the resulting model gives rise to an understanding of reward-driven network plasticity as continuous sampling of network configurations.

Conserved neural circuit structure across Drosophila larval development revealed by comparative connectomics

During postembryonic development, the nervous system must adapt to a growing body. How changes in neuronal structure and connectivity contribute to the maintenance of appropriate circuit function remains unclear. Previously , we measured the cellular neuroanatomy underlying synaptic connectivity in Drosophila (Schneider-Mizell et al., 2016). Here, we examined how neuronal morphology and connectivity change between first instar and third instar larval stages using serial section electron microscopy. We reconstructed nociceptive circuits in a larva of each stage and found consistent topographically arranged connectivity between identified neurons. Five-fold increases in each size, number of terminal dendritic branches, and total number of synaptic inputs were accompanied by cell type-specific connectivity changes that preserved the fraction of total synaptic input associated with each pre-synaptic partner. We propose that precise patterns of structural growth act to conserve the computational function of a circuit, for example determining the location of a dangerous stimulus.

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

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

A stable brain from unstable components: Emerging concepts and implications for neural computation

Neuroscientists have often described the adult brain in similar terms to an electronic circuit board- dependent on fixed, precise connectivity. However, with the advent of technologies allowing chronic measurements of neural structure and function, the emerging picture is that neural networks undergo significant remodeling over multiple timescales, even in the absence of experimenter-induced learning or sensory perturbation. Here, we attempt to reconcile the parallel observations that critical brain functions are stably maintained, while synapse- and single-cell properties appear to be reformatted regularly throughout adult life. In this review, we discuss experimental evidence at multiple levels ranging from synapses to neuronal ensembles, suggesting that many parameters are maintained in a dynamic equilibrium. We highlight emerging hypotheses that could explain how stable brain functions may be generated from dynamic elements. Furthermore, we discuss the impact of dynamic circuit elements on neural computations, and how they could provide living neural circuits with computational abilities a fixed structure cannot offer. Taken together, recent evidence indicates that continuous dynamics are a fundamental property of neural circuits compatible with macroscopically stable behaviors. In addition, they may be a unique advantage imparting robustness and flexibility throughout life.

Homeostatic plasticity of excitability in crustacean central pattern generator networks

Plasticity of excitability can come in two general forms: changes in excitability that alter neuronal output (e.g. long-term potentiation of intrinsic excitability) or excitability changes that stabilize neuronal output (homeostatic plasticity). Here we discuss the latter form of plasticity in the context of the crustacean stomatogastric nervous system, and a second central pattern generator circuit, the cardiac ganglion. We discuss this plasticity at three levels: rapid homeostatic changes in membrane conductance, longer-term effects of neuromodulation on excitability, and the impacts of activity-dependent feedback on steady-state channel mRNA levels. We then conclude with thoughts on the implications of plasticity of excitability for variability of conductance levels across populations of motor neurons.

Nonreciprocal homeostatic compensation in Drosophila potassium channel mutants

Homeostatic control of intrinsic excitability is important for long-term regulation of neuronal activity. In conjunction with many other forms of plasticity, intrinsic homeostasis helps neurons maintain stable activity regimes in the face of external input variability and destabilizing genetic mutations. In this study, we report a mechanism by which Drosophila melanogaster larval motor neurons stabilize hyperactivity induced by the loss of the delayed rectifying K⁺ channel Shaker cognate B (Shab), by upregulating the Ca²⁺-dependent K⁺ channel encoded by the slowpoke (slo) gene. We also show that loss of SLO does not trigger a reciprocal compensatory upregulation of SHAB, implying that homeostatic signaling pathways utilize compensatory pathways unique to the channel that was mutated. SLO upregulation due to loss of SHAB involves nuclear Ca²⁺ signaling and dCREB, suggesting that the slo homeostatic response is transcriptionally mediated. Examination of the changes in gene expression induced by these mutations suggests that there is not a generic transcriptional response to increased excitability in motor neurons, but that homeostatic compensations are influenced by the identity of the lost conductance.NEW & NOTEWORTHY The idea that activity-dependent homeostatic plasticity is driven solely by firing has wide credence. In this report we show that homeostatic compensation after loss of an ion channel conductance is tailored to identity of the channel lost, not its properties.

When complex neuronal structures may not matter

Much work has explored animal-to-animal variability and compensation in ion channel expression. Yet, little is known regarding the physiological consequences of morphological variability. We quantify animal-to-animal variability in cable lengths (CV = 0.4) and branching patterns in the Gastric Mill (GM) neuron, an identified neuron type with highly-conserved physiological properties in the crustacean stomatogastric ganglion (STG) of Cancer borealis. We examined passive GM electrotonic structure by measuring the amplitudes and apparent reversal potentials (E_revs) of inhibitory responses evoked with focal glutamate photo-uncaging in the presence of TTX. Apparent E_revs were relatively invariant across sites (mean CV ± SD = 0.04 ± 0.01; 7–20 sites in each of 10 neurons), which ranged between 100–800 µm from the somatic recording site. Thus, GM neurons are remarkably electrotonically compact (estimated λ > 1.5 mm). Electrotonically compact structures, in consort with graded transmission, provide an elegant solution to observed morphological variability in the STG.

DOI:http://dx.doi.org/10.7554/eLife.23508.001

Synchronous Infra-Slow Bursting in the Mouse Accessory Olfactory Bulb Emerge from Interplay between Intrinsic Neuronal Dynamics and Network Connectivity

Rhythmic neuronal activity of multiple frequency bands has been described in many brain areas and attributed to numerous brain functions. Among these, little is known about the mechanism and role of infra-slow oscillations, which have been demonstrated recently in the mouse accessory olfactory bulb (AOB). Along with prolonged responses to stimuli and distinct network connectivity, they inexplicably affect the AOB processing of social relevant stimuli. Here, we show that assemblies of AOB mitral cells are synchronized by lateral interactions through chemical and electrical synapses. Using a network model, we demonstrate that the synchronous oscillations in these assemblies emerge from interplay between intrinsic membrane properties and network connectivity. As a consequence, the AOB network topology, in which each mitral cell receives input from multiple glomeruli, enables integration of chemosensory stimuli over extended time scales by interglomerular synchrony of infra-slow bursting. These results provide a possible functional significance for the distinct AOB physiology and topology. Beyond the AOB, this study presents a general model for synchronous infra-slow bursting in neuronal networks.SIGNIFICANCE STATEMENT Infra-slow rhythmic neuronal activity with a very long (>10 s) duration has been described in many brain areas, but little is known about the role of this activity and the mechanisms that produce it. Here, we combine experimental and computational methods to show that synchronous infra-slow bursting activity in mitral cells of the mouse accessory olfactory bulb (AOB) emerges from interplay between intracellular dynamics and network connectivity. In this novel mechanism, slow intracellular Na⁺ dynamics endow AOB mitral cells with a weak tendency to burst, which is further enhanced and stabilized by chemical and electrical synapses between them. Combined with the unique topology of the AOB network, infra-slow bursting enables integration and binding of multiple chemosensory stimuli over a prolonged time scale.

Ih Equalizes Membrane Input Resistance in a Heterogeneous Population of Fusiform Neurons in the Dorsal Cochlear Nucleus

In a neuronal population, several combinations of its ionic conductances are used to attain a specific firing phenotype. Some neurons present heterogeneity in their firing, generally produced by expression of a specific conductance, but how additional conductances vary along in order to homeostatically regulate membrane excitability is less known. Dorsal cochlear nucleus principal neurons, fusiform neurons, display heterogeneous spontaneous action potential activity and thus represent an appropriate model to study the role of different conductances in establishing firing heterogeneity. Particularly, fusiform neurons are divided into quiet, with no spontaneous firing, or active neurons, presenting spontaneous, regular firing. These modes are determined by the expression levels of an intrinsic membrane conductance, an inwardly rectifying potassium current (I_Kir). In this work, we tested whether other subthreshold conductances vary homeostatically to maintain membrane excitability constant across the two subtypes. We found that I_h expression covaries specifically with I_Kir in order to maintain membrane resistance constant. The impact of I_h on membrane resistance is dependent on the level of I_Kir expression, being much smaller in quiet neurons with bigger I_Kir, but I_h variations are not relevant for creating the quiet and active phenotypes. Finally, we demonstrate that the individual proportion of each conductance, and not their absolute conductance, is relevant for determining the neuronal firing mode. We conclude that in fusiform neurons the variations of their different subthreshold conductances are limited to specific conductances in order to create firing heterogeneity and maintain membrane homeostasis.

Dynamic compensation mechanism gives rise to period and duty-cycle level sets in oscillatory neuronal models

Rhythmic oscillation in neurons can be characterized by various attributes, such as the oscillation period and duty cycle. The values of these features depend on the amplitudes of the participating ionic currents, which can be characterized by their maximum conductance values. Recent experimental and theoretical work has shown that the values of these attributes can be maintained constant for different combinations of two or more ionic currents of varying conductances, defining what is known as level sets in conductance space. In two-dimensional conductance spaces, a level set is a curve, often a line, along which a particular oscillation attribute value is conserved. In this work, we use modeling, dynamical systems tools (phase-space analysis), and numerical simulations to investigate the possible dynamic mechanisms responsible for the generation of period and duty-cycle levels sets in simplified (linearized and FitzHugh-Nagumo) and conductance-based (Morris-Lecar) models of neuronal oscillations. A simplistic hypothesis would be that the tonic balance between ionic currents with the same or opposite effective signs is sufficient to create level sets. According to this hypothesis, the dynamics of each ionic current during a given cycle are well captured by some constant quantity (e.g., maximal conductances), and the phase-plane diagrams are identical or are almost identical (e.g., cubic-like nullclines with the same maxima and minima) for different combinations of these maximal conductances. In contrast, we show that these mechanisms are dynamic and involve the complex interaction between the nonlinear voltage dependencies and the effective time scales at which the ionic current's dynamical variables operate.

Synergistic plasticity of intrinsic conductance and electrical coupling restores synchrony in an intact motor network

Motor neurons of the crustacean cardiac ganglion generate virtually identical, synchronized output despite the fact that each neuron uses distinct conductance magnitudes. As a result of this variability, manipulations that target ionic conductances have distinct effects on neurons within the same ganglion, disrupting synchronized motor neuron output that is necessary for proper cardiac function. We hypothesized that robustness in network output is accomplished via plasticity that counters such destabilizing influences. By blocking high-threshold K⁺ conductances in motor neurons within the ongoing cardiac network, we discovered that compensation both resynchronized the network and helped restore excitability. Using model findings to guide experimentation, we determined that compensatory increases of both G_A and electrical coupling restored function in the network. This is one of the first direct demonstrations of the physiological regulation of coupling conductance in a compensatory context, and of synergistic plasticity across cell- and network-level mechanisms in the restoration of output.

DOI:http://dx.doi.org/10.7554/eLife.16879.001

Neurons can communicate with each other by releasing chemicals called neurotransmitters, or by forming direct connections with each other known as gap junctions. These direct connections allow electrical impulses to flow from one neuron to another via pores in the membranes between the cells. Unlike communication via neurotransmitters, gap junctions are usually thought to be hard-wired and unchanging over the life of the animal.

Lane et al. recorded electrical activity in a network of neurons that generates rhythmic heart contractions in the Jonah crab. Neurons in this network usually all fire an electrical impulse at the same time, which is crucial to make sure that the whole heart contracts at the same time. The experiments show that drugs that block potassium channel pores in the membrane cause the neurons to fire too much and at different times to each other.

However, the network of neurons soon adapted to the changes caused by the drugs and returned to working as normal. Mimicking these changes in a computer model of the neuron network, together with experimental data, showed that changes to the gap junctions play a major role in restoring normal activity to the network.

The next step following on from this research is to understand how a network of neurons ‘senses’ that it is not working normally and changes its electrical activity.

DOI:http://dx.doi.org/10.7554/eLife.16879.002

The complexity of small circuits: the stomatogastric nervous system

The crustacean stomatogastric nervous system is a long-standing test bed for studies of circuit dynamics and neuromodulation. We give a brief update on the most recent work on this system, with an emphasis on the broader implications for understanding neural circuits. In particular, we focus on new findings underlining that different levels of dynamics taking place at different time scales all interact in multiple ways. Dynamics due to synaptic and intrinsic neuronal properties, neuromodulation, and long-term gene expression-dependent regulation are not independent, but influence each other. Extensive research on the stomatogastric system shows that these dynamic interactions convey robustness to circuit operation, while facilitating the flexibility of producing multiple circuit outputs.

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

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

Implications of Epigenetic Variability within a Cell Population for "Cell Type" Classification

Here, we propose a new approach to defining nerve “cell types” in reaction to recent advances in single cell analysis. Among cells previously thought to be equivalent, considerable differences in global gene expression and biased tendencies among differing developmental fates have been demonstrated within multiple lineages. The model of classifying cells into distinct types thus has to be revised to account for this intrinsic variability. A “cell type” could be a group of cells that possess similar, but not necessarily identical properties, variable within a spectrum of epigenetic adjustments that permit its developmental path toward a specific function to be achieved. Thus, the definition of a cell type is becoming more similar to the definition of a species: sharing essential properties with other members of its group, but permitting a certain amount of deviation in aspects that do not seriously impact function. This approach accommodates, even embraces the spectrum of natural variation found in various cell populations and consequently avoids the fallacy of false equivalence. For example, developing neurons will react to their microenvironments with epigenetic changes resulting in slight changes in gene expression and morphology. Addressing the new questions implied here will have significant implications for developmental neurobiology.

Network Plasticity as Bayesian Inference

General results from statistical learning theory suggest to understand not only brain computations, but also brain plasticity as probabilistic inference. But a model for that has been missing. We propose that inherently stochastic features of synaptic plasticity and spine motility enable cortical networks of neurons to carry out probabilistic inference by sampling from a posterior distribution of network configurations. This model provides a viable alternative to existing models that propose convergence of parameters to maximum likelihood values. It explains how priors on weight distributions and connection probabilities can be merged optimally with learned experience, how cortical networks can generalize learned information so well to novel experiences, and how they can compensate continuously for unforeseen disturbances of the network. The resulting new theory of network plasticity explains from a functional perspective a number of experimental data on stochastic aspects of synaptic plasticity that previously appeared to be quite puzzling.

Feedback control of variability in the cycle period of a central pattern generator

We address how feedback to a bursting biological pacemaker with intrinsic variability in cycle length can affect that variability. Specifically, we examine a hybrid circuit constructed of an isolated crab anterior burster (AB)/pyloric dilator (PD) pyloric pacemaker receiving virtual feedback via dynamic clamp. This virtual feedback generates artificial synaptic input to PD with timing determined by adjustable phase response dynamics that mimic average burst intervals generated by the lateral pyloric neuron (LP) in the intact pyloric network. Using this system, we measure network period variability dependence on the feedback element's phase response dynamics and find that a constant response interval confers minimum variability. We further find that these optimal dynamics are characteristic of the biological pyloric network. Building upon our previous theoretical work mapping the firing intervals in one cycle onto the firing intervals in the next cycle, we create a theoretical map of the distribution of all firing intervals in one cycle to the distribution of firing intervals in the next cycle. We then obtain an integral equation for a stationary self-consistent distribution of the network periods of the hybrid circuit, which can be solved numerically given the uncoupled pacemaker's distribution of intrinsic periods, the nature of the network's feedback, and the phase resetting characteristics of the pacemaker. The stationary distributions obtained in this manner are strongly predictive of the experimentally observed distributions of hybrid network period. This theoretical framework can provide insight into optimal feedback schemes for minimizing variability to increase reliability or maximizing variability to increase flexibility in central pattern generators driven by pacemakers with feedback.

Animal-to-Animal Variability in Neuromodulation and Circuit Function

Each animal alive in the world is different from all other individuals, while sharing most attributes of form and function with others of the same species. Still other attributes are shared within a phylum, and still others are common to most eukaryotic organisms. All animals have mechanisms that modulate the strength of their synapses or alter the intrinsic excitability of component neurons. What animal-to-animal variability in behavior arises from differences in neuronal structure, ion channel expression, or connectivity, and what variability arises from neuromodulation of brain states? Conversely, can robust behavior be maintained despite variability in circuit components by the action of neuromodulatory inputs? These are fundamental issues relevant to all nervous systems that have been illuminated by many years of study of the small, rhythmic motor circuits found in the crustacean stomatogastric nervous system.

Robust circuit rhythms in small circuits arise from variable circuit components and mechanisms

Small central pattern generating circuits found in invertebrates have significant advantages for the study of the circuit mechanisms that generate brain rhythms. Experimental and computational studies of small oscillatory circuits reveal that similar rhythms can arise from disparate mechanisms. Animal-to-animal variation in the properties of single neurons and synapses may underly robust circuit performance, and can be revealed by perturbations. Neuromodulation can produce altered circuit performance but also ensure reliable circuit function.

Elevated serotonergic signaling amplifies synaptic noise and facilitates the emergence of epileptiform network oscillations

Serotonin fibers densely innervate the cortical sheath to regulate neuronal excitability, but its role in shaping network dynamics remains undetermined. We show that serotonin provides an excitatory tone to cortical neurons in the form of spontaneous synaptic noise through 5-HT3 receptors, which is persistent and can be augmented using fluoxetine, a selective serotonin re-uptake inhibitor. Augmented serotonin signaling also increases cortical network activity by enhancing synaptic excitation through activation of 5-HT2 receptors. This in turn facilitates the emergence of epileptiform network oscillations (10-16 Hz) known as fast runs. A computational model of cortical dynamics demonstrates that these two combined mechanisms, increased background synaptic noise and enhanced synaptic excitation, are sufficient to replicate the emergence fast runs and their statistics. Consistent with these findings, we show that blocking 5-HT2 receptors in vivo significantly raises the threshold for convulsant-induced seizures.

Neural and genetic degeneracy underlies Caenorhabditis elegans feeding behavior

Degenerate networks, in which structurally distinct elements can perform the same function or yield the same output, are ubiquitous in biology. Degeneracy contributes to the robustness and adaptability of networks in varied environmental and evolutionary contexts. However, how degenerate neural networks regulate behavior in vivo is poorly understood, especially at the genetic level. Here, we identify degenerate neural and genetic mechanisms that underlie excitation of the pharynx (feeding organ) in the nematode Caenorhabditis elegans using cell-specific optogenetic excitation and inhibition. We show that the pharyngeal neurons MC, M2, M4, and I1 form multiple direct and indirect excitatory pathways in a robust network for control of pharyngeal pumping. I1 excites pumping via MC and M2 in a state-dependent manner. We identify nicotinic and muscarinic receptors through which the pharyngeal network regulates feeding rate. These results identify two different mechanisms by which degeneracy is manifest in a neural circuit in vivo.