Activity-independent homeostasis in rhythmically active neurons

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.

The plasticitome of cortical interneurons

Hebb postulated that, to store information in the brain, assemblies of excitatory neurons coding for a percept are bound together via associative long-term synaptic plasticity. In this view, it is unclear what role, if any, is carried out by inhibitory interneurons. Indeed, some have argued that inhibitory interneurons are not plastic. Yet numerous recent studies have demonstrated that, similar to excitatory neurons, inhibitory interneurons also undergo long-term plasticity. Here, we discuss the many diverse forms of long-term plasticity that are found at inputs to and outputs from several types of cortical inhibitory interneuron, including their plasticity of intrinsic excitability and their homeostatic plasticity. We explain key plasticity terminology, highlight key interneuron plasticity mechanisms, extract overarching principles and point out implications for healthy brain functionality as well as for neuropathology. We introduce the concept of the plasticitome - the synaptic plasticity counterpart to the genome or the connectome - as well as nomenclature and definitions for dealing with this rich diversity of plasticity. We argue that the great diversity of interneuron plasticity rules is best understood at the circuit level, for example as a way of elucidating how the credit-assignment problem is solved in deep biological neural networks.

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.

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.

Neuromodulation reduces interindividual variability of neuronal output

In similar states, neural circuits produce similar outputs across individuals despite substantial interindividual variability in neuronal ionic conductances and synapses. Circuit states are largely shaped by neuromodulators that tune ionic conductances. It is therefore possible that, in addition to producing flexible circuit output, neuromodulators also contribute to output similarity despite varying ion channel expression. We studied whether neuromodulation at saturating concentrations can increase the output similarity of a single identified neuron across individual animals. Using the LP neuron of the crab stomatogastric ganglion (STG), we compared the variability of f-I curves and rebound properties in the presence of neuropeptides. The two neuropeptides we used converge to activate the same target current, which increases neuronal excitability. Output variability was lower in the presence of the neuropeptides, regardless of whether the neuropeptides significantly changed the mean of the corresponding parameter or not. However, the addition of the second neuropeptide did not add further to the reduction of variability. With a family of computational LP-like models, we explored how increased excitability and target variability contribute to output similarity and found two mechanisms: Saturation of the responses and a differential increase in baseline activity. Saturation alone can reduce the interindividual variability only if the population shares a similar ceiling for the responses. In contrast, reduction of variability due to the increase in baseline activity is independent of ceiling effects.Significance StatementThe activity of single neurons and neural circuits can be very similar across individuals even though the ionic currents underlying activity are variable. The mechanisms that compensate for the underlying variability and promote output similarity are poorly understood but may involve neuromodulation. Using an identified neuron, we show that neuropeptide modulation of excitability can reduce interindividual variability of response properties at a single-neuron level in two ways. First, the neuropeptide increases baseline excitability in a differential manner, resulting in similar response thresholds. Second, the neuropeptide increases excitability towards a shared saturation level, promoting similar maximal firing rates across individuals. Such tuning of neuronal excitability could be an important mechanism compensating for interindividual variability of ion channel expression.

Mechanisms Driving the Emergence of Neuronal Hyperexcitability in Fragile X Syndrome

Hyperexcitability is a shared neurophysiological phenotype across various genetic neurodevelopmental disorders, including Fragile X syndrome (FXS). Several patient symptoms are associated with hyperexcitability, but a puzzling feature is that their onset is often delayed until their second and third year of life. It remains unclear how and why hyperexcitability emerges in neurodevelopmental disorders. FXS is caused by the loss of FMRP, an RNA-binding protein which has many critical roles including protein synthesis-dependent and independent regulation of ion channels and receptors, as well as global regulation of protein synthesis. Here, we discussed recent literature uncovering novel mechanisms that may drive the progressive onset of hyperexcitability in the FXS brain. We discussed in detail how recent publications have highlighted defects in homeostatic plasticity, providing new insight on the FXS brain and suggest pharmacotherapeutic strategies in FXS and other neurodevelopmental disorders.

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.

Homeostatic Regulation of Motoneuron Properties in Development

Homeostatic plasticity represents a set of compensatory mechanisms that are engaged following a perturbation to some feature of neuronal or network function. Homeostatic mechanisms are most robustly expressed during development, a period that is replete with various perturbations such as increased cell size and the addition/removal of synaptic connections. In this review we look at numerous studies that have advanced our understanding of homeostatic plasticity by taking advantage of the accessibility of developing motoneurons. We discuss the homeostatic regulation of embryonic movements in the living chick embryo and describe the spinal compensatory mechanisms that act to recover these movements (homeostatic intrinsic plasticity) or stabilize synaptic strength (synaptic scaling). We describe the expression and triggering mechanisms of these forms of homeostatic plasticity and thereby gain an understanding of their roles in the motor system. We then illustrate how these findings can be extended to studies of developing motoneurons in other systems including the rodents, zebrafish, and fly. Furthermore, studies in developing drosophila have been critical in identifying some of the molecular signaling cascades and expression mechanisms that underlie homeostatic intrinsic membrane excitability. This powerful model organism has also been used to study a presynaptic form of homeostatic plasticity where increases or decreases in synaptic transmission are associated with compensatory changes in probability of release at the neuromuscular junction. Further, we describe studies that demonstrate homeostatic adjustments of ion channel expression following perturbations to other kinds of ion channels. Finally, we discuss work in xenopus that shows a homeostatic regulation of neurotransmitter phenotype in developing motoneurons following activity perturbations. Together, this work illustrates the importance of developing motoneurons in elucidating the mechanisms and roles of homeostatic plasticity.

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.

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.

Maturation of persistent and hyperpolarization-activated inward currents shapes the differential activation of motoneuron subtypes during postnatal development

The size principle underlies the orderly recruitment of motor units; however, motoneuron size is a poor predictor of recruitment amongst functionally defined motoneuron subtypes. Whilst intrinsic properties are key regulators of motoneuron recruitment, the underlying currents involved are not well defined. Whole-cell patch-clamp electrophysiology was deployed to study intrinsic properties, and the underlying currents, that contribute to the differential activation of delayed and immediate firing motoneuron subtypes. Motoneurons were studied during the first three postnatal weeks in mice to identify key properties that contribute to rheobase and may be important to establish orderly recruitment. We find that delayed and immediate firing motoneurons are functionally homogeneous during the first postnatal week and are activated based on size, irrespective of subtype. The rheobase of motoneuron subtypes becomes staggered during the second postnatal week, which coincides with the differential maturation of passive and active properties, particularly persistent inward currents. Rheobase of delayed firing motoneurons increases further in the third postnatal week due to the development of a prominent resting hyperpolarization-activated inward current. Our results suggest that motoneuron recruitment is multifactorial, with recruitment order established during postnatal development through the differential maturation of passive properties and sequential integration of persistent and hyperpolarization-activated inward currents.

Is prediction nothing more than multi-scale pattern completion of the future?

While the notion of the brain as a prediction machine has been extremely influential and productive in cognitive science, there are competing accounts of how best to model and understand the predictive capabilities of brains. One prominent framework is of a "Bayesian brain" that explicitly generates predictions and uses resultant errors to guide adaptation. We suggest that the prediction-generation component of this framework may involve little more than a pattern completion process. We first describe pattern completion in the domain of visual perception, highlighting its temporal extension, and show how this can entail a form of prediction in time. Next, we describe the forward momentum of entrained dynamical systems as a model for the emergence of predictive processing in non-predictive systems. Then, we apply this reasoning to the domain of language, where explicitly predictive models are perhaps most popular. Here, we demonstrate how a connectionist model, TRACE, exhibits hallmarks of predictive processing without any representations of predictions or errors. Finally, we present a novel neural network model, inspired by reservoir computing models, that is entirely unsupervised and memoryless, but nonetheless exhibits prediction-like behavior in its pursuit of homeostasis. These explorations demonstrate that brain-like systems can get prediction "for free," without the need to posit formal logical representations with Bayesian probabilities or an inference machine that holds them in working memory.

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

The large number of ion channels found in all nervous systems poses fundamental questions concerning how the characteristic intrinsic properties of single neurons are determined by the specific subsets of channels they express. All neurons display many different ion channels with overlapping voltage- and time-dependent properties. We speculate that these overlapping properties promote resilience in neuronal function. Individual neurons of the same cell type show variability in ion channel conductance densities even though they can generate reliable and similar behavior. This complicates a simple assignment of function to any conductance and is associated with variable responses of neurons of the same cell type to perturbations, deletions, and pharmacological manipulation. Ion channel genes often show strong positively correlated expression, which may result from the molecular and developmental rules that determine which ion channels are expressed in a given cell type.

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.

Fragile X mental retardation protein modulates somatic D-type K+ channels and action potential threshold in the mouse prefrontal cortex

Axo-somatic K⁺ channels control action potential output in part by acting in concert with voltage-gated Na⁺ channels to set action potential threshold. Slowly inactivating, D-type K⁺ channels are enriched at the axo-somatic region of cortical pyramidal neurons of the prefrontal cortex, where they regulate action potential firing. We previously demonstrated that D-type K⁺ channels are downregulated in extratelencephalic-projecting (ET) L5 neurons in the medial prefrontal cortex (mPFC) of the Fmr1-knockout mouse model of fragile X syndrome (FX mice), resulting in a hyperpolarized action potential threshold. To test whether K⁺ channel alterations are regulated in a cell-autonomous manner in FXS, we used a virus-mediated approach to restore expression of fragile X mental retardation protein (FMRP) in a small population of prefrontal neurons in male FX mice. Outside-out voltage-clamp recordings revealed a higher D-type K⁺ conductance in FMRP-positive ET neurons compared with nearby FMRP-negative ET neurons. FMRP did not affect either rapidly inactivating A-type or noninactivating K⁺ conductance. ET neuron patches recorded with FMRP_1-298, a truncated form of FMRP that lacks mRNA binding domains, included in the pipette solution had larger D-type K⁺ conductance compared with heat-inactivated controls. Viral expression of FMRP in FX mice depolarized action potential threshold to near-wild-type levels in ET neurons. These results suggest that FMRP influences the excitability of ET neurons in the mPFC by regulating somatic D-type K⁺ channels in a cell-autonomous, protein-protein-dependent manner.NEW & NOTEWORTHY We demonstrate that fragile X mental retardation protein (FMRP), which is absent in fragile X syndrome (FXS), regulates D-type potassium channels in prefrontal cortex L5 pyramidal neurons with subcerebral projections but not in neighboring pyramidal neurons without subcerebral projections. FMRP regulates D-type potassium channels in a protein-protein-dependent manner and rescues action potential threshold in a mouse model of FXS. These findings have implications for how changes in voltage-gated channels contribute to neurodevelopmental disorders.

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.

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.

Molecular mechanisms of homeostatic plasticity in central pattern generator networks

Central pattern generator (CPG) networks rely on a balance of intrinsic and network properties to produce reliable, repeatable activity patterns. This balance is maintained by homeostatic plasticity where alterations in neuronal properties dynamically maintain appropriate neural output in the face of changing environmental conditions and perturbations. However, it remains unclear just how these neurons and networks can both monitor their ongoing activity and use this information to elicit homeostatic physiological responses to ensure robustness of output over time. Evidence exists that CPG networks use a mixed strategy of activity-dependent, activity-independent, modulator-dependent, and synaptically regulated homeostatic plasticity to achieve this critical stability. In this review, we focus on some of the current understanding of the molecular pathways and mechanisms responsible for this homeostatic plasticity in the context of central pattern generator function, with a special emphasis on some of the smaller invertebrate networks that have allowed for extensive cellular-level analyses that have brought recent insights to these questions.

Dimensions of control for subthreshold oscillations and spontaneous firing in dopamine neurons

Dopaminergic neurons (DAs) of the rodent substantia nigra pars compacta (SNc) display varied electrophysiological properties in vitro. Despite this, projection patterns and functional inputs from DAs to other structures are conserved, so in vivo delivery of consistent, well-timed dopamine modulation to downstream circuits must be coordinated. Here we show robust coordination by linear parameter controllers, discovered through powerful mathematical analyses of data and models, and from which consistent control of DA subthreshold oscillations (STOs) and spontaneous firing emerges. These units of control represent coordinated intracellular variables, sufficient to regulate complex cellular properties with radical simplicity. Using an evolutionary algorithm and dimensionality reduction, we discovered metaparameters, which when regressed against STO features, revealed a 2-dimensional control plane for the neuron’s 22-dimensional parameter space that fully maps the natural range of DA subthreshold electrophysiology. This plane provided a basis for spiking currents to reproduce a large range of the naturally occurring spontaneous firing characteristics of SNc DAs. From it we easily produced a unique population of models, derived using unbiased parameter search, that show good generalization to channel blockade and compensatory intracellular mechanisms. From this population of models, we then discovered low-dimensional controllers for regulating spontaneous firing properties, and gain insight into how currents active in different voltage regimes interact to produce the emergent activity of SNc DAs. Our methods therefore reveal simple regulators of neuronal function lurking in the complexity of combined ion channel dynamics.

Electrophysiological activity of the neuronal membrane and concomitant ion channel properties are highly variable within groups of neurons of the same type from the same brain region. Reconciliation of the mechanisms generating neuronal activity is challenging due to the complexity of the interactions between the channel currents involved. Here we present a set of mathematical analyses that uncover the low-dimensional intracellular parameter combinations capable of regulating features of subthreshold oscillations and spontaneous firing in empirically constrained models of nigral dopaminergic neurons. This method generates, from a naive starting point, linear combinations of ion channel properties that are surprisingly capable of reliably controlling a wide variety of emergent electrophysiological activity, thereby predicting drug effects and shedding light on unsuspected compensatory mechanisms that contribute to neuronal function.

Neuromodulation of central pattern generators and its role in the functional recovery of central pattern generator activity

Neuromodulators play an important role in how the nervous system organizes activity that results in behavior. Disruption of the normal patterns of neuromodulatory release or production is known to be related to the onset of severe pathologies such as Parkinson's disease, Rett syndrome, Alzheimer's disease, and affective disorders. Some of these pathologies involve neuronal structures that are called central pattern generators (CPGs), which are involved in the production of rhythmic activities throughout the nervous system. Here I discuss the interplay between CPGs and neuromodulatory activity, with particular emphasis on the potential role of neuromodulators in the recovery of disrupted neuronal activity. I refer to invertebrate and vertebrate model systems and some of the lessons we have learned from research on these systems and propose a few avenues for future research. I make one suggestion that may guide future research in the field: neuromodulators restrict the parameter landscape in which CPG components operate, and the removal of neuromodulators may enable a perturbed CPG in finding a new set of parameter values that can allow it to regain normal function.

Membrane Voltage Is a Direct Feedback Signal That Influences Correlated Ion Channel Expression in Neurons

The number and type of ion channels present in the membrane determines the electrophysiological function of every neuron. In many species, stereotyped output of neurons often persists for years [1], and ion channel dysregulation can change these properties to cause severe neurological disorders [2-4]. Thus, a fundamental question is how do neurons coordinate channel expression to uphold their firing patterns over long timescales [1, 5]? One major hypothesis purports that neurons homeostatically regulate their ongoing activity through mechanisms that link membrane voltage to expression relationships among ion channels [6-10]. However, experimentally establishing this feedback loop for the control of expression relationships has been a challenge: manipulations that aim to test for voltage feedback invariably disrupt trophic signaling from synaptic transmission and neuromodulation in addition to activity [9, 11, 12]. Further, neuronal activity often relies critically on these chemical mediators, obscuring the contribution of voltage activity of the membrane per se in forming the channel relationships that determine neuronal output [6, 13]. To resolve this, we isolated an identifiable neuron in crustaceans and then either kept this neuron silent or used a long-term voltage clamp protocol to artificially maintain activity. We found that physiological voltage activity-independent of all known forms of synaptic and neuromodulatory feedback-maintains most channel mRNA relationships, while metabotropic influences may play a relatively smaller role. Thus, ion channel relationships likely needed to maintain neuronal identity are actively and continually regulated at least in part at the level of channel mRNAs through feedback by membrane voltage.

Dual separable feedback systems govern firing rate homeostasis

Firing rate homeostasis (FRH) stabilizes neural activity. A pervasive and intuitive theory argues that a single variable, calcium, is detected and stabilized through regulatory feedback. A prediction is that ion channel gene mutations with equivalent effects on neuronal excitability should invoke the same homeostatic response. In agreement, we demonstrate robust FRH following either elimination of Kv4/Shal protein or elimination of the Kv4/Shal conductance. However, the underlying homeostatic signaling mechanisms are distinct. Eliminating Shal protein invokes Krüppel-dependent rebalancing of ion channel gene expression including enhanced slo, Shab, and Shaker. By contrast, expression of these genes remains unchanged in animals harboring a CRISPR-engineered, Shal pore-blocking mutation where compensation is achieved by enhanced IK_DR. These different homeostatic processes have distinct effects on homeostatic synaptic plasticity and animal behavior. We propose that FRH includes mechanisms of proteostatic feedback that act in parallel with activity-driven feedback, with implications for the pathophysiology of human channelopathies.

Ionic current correlations are ubiquitous across phyla

Ionic currents, whether measured as conductance amplitude or as ion channel transcript numbers, can vary many-fold within a population of identified neurons. In invertebrate neuronal types multiple currents can be seen to vary while at the same time their magnitudes are correlated. These conductance amplitude correlations are thought to reflect a tight homeostasis of cellular excitability that enhances the robustness and stability of neuronal activity over long stretches of time. Although such ionic conductance correlations are well documented in invertebrates, they have not been reported in vertebrates. Here we demonstrate with two examples, identified mouse hippocampal granule cells (GCs) and cholinergic basal forebrain neurons, that the correlation of ionic conductance amplitudes between different ionic currents also exists in vertebrates, and we argue that it is a ubiquitous phenomenon expressed by many species across phyla. We further demonstrate that in dentate gyrus GCs these conductance correlations are likely regulated in a circadian manner. This is reminiscent of the known conductance regulation by neuromodulators in crustaceans. However, in GCs we observe a more nuanced regulation, where for some conductance pairs the correlations are completely eliminated while for others the correlation is quantitatively modified but not obliterated.

Xolotl: An Intuitive and Approachable Neuron and Network Simulator for Research and Teaching

Conductance-based models of neurons are used extensively in computational neuroscience. Working with these models can be challenging due to their high dimensionality and large number of parameters. Here, we present a neuron and network simulator built on a novel automatic type system that binds object-oriented code written in C++ to objects in MATLAB. Our approach builds on the tradition of uniting the speed of languages like C++ with the ease-of-use and feature-set of scientific programming languages like MATLAB. Xolotl allows for the creation and manipulation of hierarchical models with components that are named and searchable, permitting intuitive high-level programmatic control over all parts of the model. The simulator's architecture allows for the interactive manipulation of any parameter in any model, and for visualizing the effects of changing that parameter immediately. Xolotl is fully featured with hundreds of ion channel models from the electrophysiological literature, and can be extended to include arbitrary conductances, synapses, and mechanisms. Several core features like bookmarking of parameters and automatic hashing of source code facilitate reproducible and auditable research. Its ease of use and rich visualization capabilities make it an attractive option in teaching environments. Finally, xolotl is written in a modular fashion, includes detailed tutorials and worked examples, and is freely available at https://github.com/sg-s/xolotl, enabling seamless integration into the workflows of other researchers.

Inconvenient Truth to Principle of Neuroscience

In 2004, Prinz et al. demonstrated that almost indistinguishable network activity can arise from widely different sets of underlying membrane and synaptic parameters, and, thus, likely arise from different cellular and network mechanisms. This now broadly accepted principle guides research into individual variation in neuronal and synaptic properties, and their homeostatic regulation.

Origin of heterogeneous spiking patterns from continuously distributed ion channel densities: a computational study in spinal dorsal horn neurons

KEY POINTS

Distinct spiking patterns may arise from qualitative differences in ion channel expression (i.e. when different neurons express distinct ion channels) and/or when quantitative differences in expression levels qualitatively alter the spike generation process. We hypothesized that spiking patterns in neurons of the superficial dorsal horn (SDH) of spinal cord reflect both mechanisms. We reproduced SDH neuron spiking patterns by varying densities of KV 1- and A-type potassium conductances. Plotting the spiking patterns that emerge from different density combinations revealed spiking-pattern regions separated by boundaries (bifurcations). This map suggests that certain spiking pattern combinations occur when the distribution of potassium channel densities straddle boundaries, whereas other spiking patterns reflect distinct patterns of ion channel expression. The former mechanism may explain why certain spiking patterns co-occur in genetically identified neuron types. We also present algorithms to predict spiking pattern proportions from ion channel density distributions, and vice versa.

ABSTRACT

Neurons are often classified by spiking pattern. Yet, some neurons exhibit distinct patterns under subtly different test conditions, which suggests that they operate near an abrupt transition, or bifurcation. A set of such neurons may exhibit heterogeneous spiking patterns not because of qualitative differences in which ion channels they express, but rather because quantitative differences in expression levels cause neurons to operate on opposite sides of a bifurcation. Neurons in the spinal dorsal horn, for example, respond to somatic current injection with patterns that include tonic, single, gap, delayed and reluctant spiking. It is unclear whether these patterns reflect five cell populations (defined by distinct ion channel expression patterns), heterogeneity within a single population, or some combination thereof. We reproduced all five spiking patterns in a computational model by varying the densities of a low-threshold (KV 1-type) potassium conductance and an inactivating (A-type) potassium conductance and found that single, gap, delayed and reluctant spiking arise when the joint probability distribution of those channel densities spans two intersecting bifurcations that divide the parameter space into quadrants, each associated with a different spiking pattern. Tonic spiking likely arises from a separate distribution of potassium channel densities. These results argue in favour of two cell populations, one characterized by tonic spiking and the other by heterogeneous spiking patterns. We present algorithms to predict spiking pattern proportions based on ion channel density distributions and, conversely, to estimate ion channel density distributions based on spiking pattern proportions. The implications for classifying cells based on spiking pattern are discussed.

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

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

Developmental Disruption of Recurrent Inhibitory Feedback Results in Compensatory Adaptation in the Renshaw Cell-Motor Neuron Circuit

When activating muscles, motor neurons in the spinal cord also activate Renshaw cells, which provide recurrent inhibitory feedback to the motor neurons. The tight coupling with motor neurons suggests that Renshaw cells have an integral role in movement, a role that is yet to be elucidated. Here we used the selective expression of the nicotinic cholinergic receptor α2 (Chrna2) in mice to genetically target the vesicular inhibitory amino acid transporter (VIAAT) in Renshaw cells. Loss of VIAAT from Chrna2^Cre -expressing Renshaw cells did not impact any aspect of drug-induced fictive locomotion in the neonatal mouse or change gait, motor coordination, or grip strength in adult mice of both sexes. However, motor neurons from neonatal mice lacking VIAAT in Renshaw cells received spontaneous inhibitory synaptic input with a reduced frequency, showed lower input resistance, and had an increased number of proprioceptive glutamatergic and calbindin-labeled putative Renshaw cell synapses on their soma and proximal dendrites. Concomitantly, Renshaw cells developed with increased excitability and a normal number of cholinergic motor neuron synapses, indicating a compensatory mechanism within the recurrent inhibitory feedback circuit. Our data suggest an integral role for Renshaw cell signaling in shaping the excitability and synaptic input to motor neurons.SIGNIFICANCE STATEMENT We here provide a deeper understanding of spinal cord circuit formation and the repercussions for the possible role for Renshaw cells in speed and force control. Our results suggest that while Renshaw cells are not directly required as an integral part of the locomotor coordination machinery, the development of their electrophysiological character is dependent on vesicular inhibitory amino acid transporter-mediated signaling. Further, Renshaw cell signaling is closely associated with the molding of motor neuron character proposing the existence of a concerted maturation process, which seems to endow this particular spinal cord circuit with the plasticity to compensate for loss of the Renshaw cell in adult circuit function.

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.

The transient potassium outward current has different roles in modulating the pyloric and gastric mill rhythms in the stomatogastric ganglion

The crustacean stomatogastric nervous system is a classic model for understanding the effects of modulating ionic currents and synapses at both the cell and network levels. The stomatogastric ganglion in this system contains two distinct central pattern generators: a slow gastric mill network that generates flexible rhythmic outputs (8-20 s) and is often silent, and a fast pyloric network that generates more consistent rhythmic outputs (0.5-2 s) and is always active in vitro. Different ionic conductances contribute to the properties of individual neurons and therefore to the overall dynamics of the pyloric and gastric mill networks. However, the contributions of ionic currents to different dynamics between the pyloric and gastric mill networks are not well understood. The goal of this study is to evaluate how changes in outward potassium current (I _A) in the stomatogastric ganglion affect the dynamics of the pyloric and gastric mill rhythms by interfering with normal I _A activity. We bath-applied the specific I _A blocker 4-aminopyridine to reduce I _A's effect in the stomatogastric ganglion in vitro and evaluated quantitatively the changes in both rhythms. We found that blocking I _A in the stomatogastric ganglion alters the synchronization between pyloric neurons, and consistently activates the gastric mill rhythm in quiescent preparations.

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.

Genetic perturbations suggest a role of the resting potential in regulating the expression of the ion channels of the KCNA and HCN families in octopus cells of the ventral cochlear nucleus

Low-voltage-activated K⁺ (g_KL) and hyperpolarization-activated mixed cation conductances (g_h) mediate currents, I_KL and I_h, through channels of the Kv1 (KCNA) and HCN families respectively and give auditory neurons the temporal precision required for signaling information about the onset, fine structure, and time of arrival of sounds. Being partially activated at rest, g_KL and g_h contribute to the resting potential and shape responses to even small subthreshold synaptic currents. Resting g_KL and g_h also affect the coupling of somatic depolarization with the generation of action potentials. To learn how these important conductances are regulated we have investigated how genetic perturbations affect their expression in octopus cells of the ventral cochlear nucleus (VCN). We report five new findings: First, the magnitude of g_h and g_KL varied over more than two-fold between wild type strains of mice. Second, average resting potentials are not different in different strains of mice even in the face of large differences in average g_KL and g_h. Third, I_KL has two components, one being α-dendrotoxin (α-DTX)-sensitive and partially inactivating and the other being α-DTX-insensitive, tetraethylammonium (TEA)-sensitive, and non-inactivating. Fourth, the loss of Kv1.1 results in diminution of the α-DTX-sensitive I_KL, and compensatory increased expression of an α-DTX-insensitive, tetraethylammonium (TEA)-sensitive I_KL. Fifth, I_h and I_KL are balanced at the resting potential in all wild type and mutant octopus cells even when resting potentials vary in individual cells over nearly 10 mV, indicating that the resting potential influences the expression of g_h and g_KL. The independence of resting potentials on g_KL and g_h shows that g_KL and g_h do not, over days or weeks, determine the resting potential but rather that the resting potential plays a role in regulating the magnitude of either or both g_KL and g_h.

Potassium channels in the heart: structure, function and regulation

This paper is the outcome of the fourth UC Davis Systems Approach to Understanding Cardiac Excitation-Contraction Coupling and Arrhythmias Symposium, a biannual event that aims to bring together leading experts in subfields of cardiovascular biomedicine to focus on topics of importance to the field. The theme of the 2016 symposium was 'K⁺ Channels and Regulation'. Experts in the field contributed their experimental and mathematical modelling perspectives and discussed emerging questions, controversies and challenges on the topic of cardiac K⁺ channels. This paper summarizes the topics of formal presentations and informal discussions from the symposium on the structural basis of voltage-gated K⁺ channel function, as well as the mechanisms involved in regulation of K⁺ channel gating, expression and membrane localization. Given the critical role for K⁺ channels in determining the rate of cardiac repolarization, it is hardly surprising that essentially every aspect of K⁺ channel function is exquisitely regulated in cardiac myocytes. This regulation is complex and highly interrelated to other aspects of myocardial function. K⁺ channel regulatory mechanisms alter, and are altered by, physiological challenges, pathophysiological conditions, and pharmacological agents. An accompanying paper focuses on the integrative role of K⁺ channels in cardiac electrophysiology, i.e. how K⁺ currents shape the cardiac action potential, and how their dysfunction can lead to arrhythmias, and discusses K⁺ channel-based therapeutics. A fundamental understanding of K⁺ channel regulatory mechanisms and disease processes is fundamental to reveal new targets for human therapy.

Deep sequencing of transcriptomes from the nervous systems of two decapod crustaceans to characterize genes important for neural circuit function and modulation

BACKGROUND

Crustaceans have been studied extensively as model systems for nervous system function from single neuron properties to behavior. However, lack of molecular sequence information and tools have slowed the adoption of these physiological systems as molecular model systems. In this study, we sequenced and performed de novo assembly for the nervous system transcriptomes of two decapod crustaceans: the Jonah crab (Cancer borealis) and the American lobster (Homarus americanus).

RESULTS

Forty-two thousand, seven hundred sixty-six and sixty thousand, two hundred seventy-three contigs were assembled from C. borealis and H. americanus respectively, representing 9,489 and 11,061 unique coding sequences. From these transcripts, genes associated with neural function were identified and manually curated to produce a characterization of multiple gene families important for nervous system function. This included genes for 34 distinct ion channel types, 17 biogenic amine and 5 GABA receptors, 28 major transmitter receptor subtypes including glutamate and acetylcholine receptors, and 6 gap junction proteins - the Innexins.

CONCLUSION

With this resource, crustacean model systems are better poised for incorporation of modern genomic and molecular biology technologies to further enhance the interrogation of fundamentals of nervous system function.

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.

K+ channel reorganization and homeostatic plasticity during postembryonic development: biophysical and genetic analyses in acutely dissociated Drosophila central neurons

Intrinsic electric activities of neurons play important roles in establishing and refining neural circuits during development. However, how the underlying ionic currents undergo postembryonic reorganizations remains largely unknown. Using acutely dissociated neurons from larval, pupal, and adult Drosophila brains, we show drastic re-assemblies and compensatory regulations of voltage-gated (IKv) and Ca2+-activated (IK(Ca)) K+ currents during postembryonic development. Larval and adult neurons displayed prominent fast-inactivating IKv, mediated by the Shaker (Sh) channel to a large extent, while in the same neurons IK(Ca) was far smaller in amplitude. In contrast, pupal neurons were characterized by large sustained IKv and prominent IK(Ca), encoded predominantly by the slowpoke (slo) gene. Surprisingly, deletion of Sh in the ShM null mutant removed inactivating, transient IKv from large portions of neurons at all stages. Interestingly, elimination of Sh currents was accompanied by upregulation of non-Sh transient IKv. In comparison, the slo1 mutation abolished the vast majority of IK(Ca), particularly at the pupal stage. Strikingly, the deficiency of IK(Ca) in slo pupae was compensated by the transient component of IKv mediated by Sh channels. Thus, IK(Ca) appears to play critical roles in pupal development and its absence induces functional compensations from a specific transient IKv current. While mutants lacking either Sh or slo currents survived normally, Sh;;slo double mutants deficient in both failed to survive through pupal metamorphosis. Together, our data highlight significant reorganizations and homeostatic compensations of K+ currents during postembryonic development and uncover previously unrecognized roles for Sh and slo in this plastic process.

Consequences of degeneracy in network function

Often distinct elements serve similar functions within a network. However, it is unclear whether this network degeneracy is beneficial, or merely a reflection of tighter regulation of overall network performance relative to individual neuronal properties. We review circumstances where data strongly suggest that degeneracy is beneficial in that it makes network function more robust. Importantly, network degeneracy is likely to have functional consequences that are not widely appreciated. This is likely to be true when network activity is configured by modulators with persistent actions, and the history of network activity potentially impacts subsequent functioning. Data suggest that degeneracy in this context may be important for the creation of latent memories, and for state-dependent task switching.

Firing frequency and entrainment maintained in primary auditory neurons in the presence of combined BDNF and NT3

Primary auditory neurons rely on neurotrophic factors for development and survival. We previously determined that exposure to brain-derived neurotrophic factor (BDNF) and neurotrophin-3 (NT3) alters the activity of hyperpolarization-activated currents (Ih) in this neuronal population. Since potassium channels are sensitive to neurotrophins, and changes in Ih are often accompanied by a shift in voltage-gated potassium currents (IK), this study examined IK with exposure to both BDNF and NT3 and the impact on firing entrainment during high frequency pulse trains. Whole-cell patch-clamp recordings revealed significant changes in action potential latency and duration, but no change in firing adaptation or total outward IK. Dendrotoxin-I (DTX-I), targeting voltage-gated potassium channel subunits KV1.1 and KV1.2, uncovered an increase in the contribution of DTX-I sensitive currents with exposure to neurotrophins. No difference in Phrixotoxin-1 (PaTX-1) sensitive currents, mediated by KV4.2 and KV4.3 subunits, was observed. Further, no difference was seen in firing entrainment. These results show that combined BDNF and NT3 exposure influences the contribution of KV1.1 and KV1.2 to the low voltage-activated potassium current (IKL). Whilst this is accompanied by a shift in spike latency and duration, both firing frequency and entrainment to high frequency pulse trains are preserved.

Transient potassium channels augment degeneracy in hippocampal active dendritic spectral tuning

Hippocampal pyramidal neurons express an intraneuronal map of spectral tuning mediated by hyperpolarization-activated cyclic-nucleotide-gated nonspecific-cation channels. Modeling studies have predicted a critical regulatory role for A-type potassium (KA) channels towards augmenting functional robustness of this map. To test this, we performed patch-clamp recordings from soma and dendrites of rat hippocampal pyramidal neurons, and measured spectral tuning before and after blocking KA channels using two structurally distinct pharmacological agents. Consistent with computational predictions, we found that blocking KA channels resulted in a significant reduction in resonance frequency and significant increases in input resistance, impedance amplitude and action-potential firing frequency across the somato-apical trunk. Furthermore, across all measured locations, blocking KA channels enhanced temporal summation of postsynaptic potentials and critically altered the impedance phase profile, resulting in a significant reduction in total inductive phase. Finally, pair-wise correlations between intraneuronal percentage changes (after blocking KA channels) in different measurements were mostly weak, suggesting differential regulation of different physiological properties by KA channels. Our results unveil a pivotal role for fast transient channels in regulating theta-frequency spectral tuning and intrinsic phase response, and suggest that degeneracy with reference to several coexisting functional maps is mediated by cross-channel interactions across the active dendritic arbor.

Electrophysiological Evidence for Intrinsic Pacemaker Currents in Crayfish Parasol Cells

I used sharp intracellular electrodes to record from parasol cells in the semi-isolated crayfish brain to investigate pacemaker currents. Evidence for the presence of the hyperpolarization-activated inward rectifier potassium current was obtained in about half of the parasol cells examined, where strong, prolonged hyperpolarizing currents generated a slowly-rising voltage sag, and a post-hyperpolarization rebound. The amplitudes of both the sag voltage and the depolarizing rebound were dependent upon the strength of the hyperpolarizing current. The voltage sag showed a definite threshold and was non-inactivating. The voltage sag and rebound depolarization evoked by hyperpolarization were blocked by the presence of 5-10 mM Cs2+ ions, 10 mM tetraethyl ammonium chloride, and 10 mM cobalt chloride in the bathing medium, but not by the drug ZD 7288. Cs+ ions in normal saline in some cells caused a slight increase in mean resting potential and a reduction in spontaneous burst frequency. Many of the neurons expressing the hyperpolarization-activated inward potassium current also provided evidence for the presence of the transient potassium current IA, which was inferred from experimental observations of an increased latency of post-hyperpolarization response to a depolarizing step, compared to the response latency to the depolarization alone. The latency increase was reduced in the presence of 4-aminopyridine (4-AP), a specific blocker of IA. The presence of 4-AP in normal saline also induced spontaneous bursting in parasol cells. It is conjectured that, under normal physiological conditions, these two potassium currents help to regulate burst generation in parasol cells, respectively, by helping to maintain the resting membrane potential near a threshold level for burst generation, and by regulating the rate of rise of membrane depolarizing events leading to burst generation. The presence of post-burst hyperpolarization may depend upon IA channels in parasol cells.

Monoaminergic tone supports conductance correlations and stabilizes activity features in pattern generating neurons of the lobster, Panulirus interruptus

Experimental and computational studies demonstrate that different sets of intrinsic and synaptic conductances can give rise to equivalent activity patterns. This is because the balance of conductances, not their absolute values, defines a given activity feature. Activity-dependent feedback mechanisms maintain neuronal conductance correlations and their corresponding activity features. This study demonstrates that tonic nM concentrations of monoamines enable slow, activity-dependent processes that can maintain a correlation between the transient potassium current (I_A) and the hyperpolarization activated current (I_h) over the long-term (i.e., regulatory change persists for hours after removal of modulator). Tonic 5 nM DA acted through an RNA interference silencing complex (RISC)- and RNA polymerase II-dependent mechanism to maintain a long-term positive correlation between I_A and I_h in the lateral pyloric neuron (LP) but not in the pyloric dilator neuron (PD). In contrast, tonic 5 nM 5HT maintained a RISC-dependent positive correlation between I_A and I_h in PD but not LP over the long-term. Tonic 5 nM OCT maintained a long-term negative correlation between I_A and I_h in PD but not LP; however, it was only revealed when RISC was inhibited. This study also demonstrated that monoaminergic tone can also preserve activity features over the long-term: the timing of LP activity, LP duty cycle and LP spike number per burst were maintained by tonic 5 nM DA. The data suggest that low-level monoaminergic tone acts through multiple slow processes to permit cell-specific, activity-dependent regulation of ionic conductances to maintain conductance correlations and their corresponding activity features over the long-term.

Long-lasting changes in neural networks to compensate for altered nicotinic input

The nervous system must balance excitatory and inhibitory input to constrain network activity levels within a proper dynamic range. This is a demanding requirement during development, when networks form and throughout adulthood as networks respond to constantly changing environments. Defects in the ability to sustain a proper balance of excitatory and inhibitory activity are characteristic of numerous neurological disorders such as schizophrenia, Alzheimer's disease, and autism. A variety of homeostatic mechanisms appear to be critical for balancing excitatory and inhibitory activity in a network. These are operative at the level of individual neurons, regulating their excitability by adjusting the numbers and types of ion channels, and at the level of synaptic connections, determining the relative numbers of excitatory versus inhibitory connections a neuron receives. Nicotinic cholinergic signaling is well positioned to contribute at both levels because it appears early in development, extends across much of the nervous system, and modulates transmission at many kinds of synapses. Further, it is known to influence the ratio of excitatory-to-inhibitory synapses formed on neurons during development. GABAergic inhibitory neurons are likely to be key for maintaining network homeostasis (limiting excitatory output), and nicotinic signaling is known to prominently regulate the activity of several GABAergic neuronal subtypes. But how nicotinic signaling achieves this and how networks may compensate for the loss of such input are important questions remaining unanswered. These issues are reviewed.

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.

Noise-induced plasticity of KCNQ2/3 and HCN channels underlies vulnerability and resilience to tinnitus

Vulnerability to noise-induced tinnitus is associated with increased spontaneous firing rate in dorsal cochlear nucleus principal neurons, fusiform cells. This hyperactivity is caused, at least in part, by decreased Kv7.2/3 (KCNQ2/3) potassium currents. However, the biophysical mechanisms underlying resilience to tinnitus, which is observed in noise-exposed mice that do not develop tinnitus (non-tinnitus mice), remain unknown. Our results show that noise exposure induces, on average, a reduction in KCNQ2/3 channel activity in fusiform cells in noise-exposed mice by 4 days after exposure. Tinnitus is developed in mice that do not compensate for this reduction within the next 3 days. Resilience to tinnitus is developed in mice that show a re-emergence of KCNQ2/3 channel activity and a reduction in HCN channel activity. Our results highlight KCNQ2/3 and HCN channels as potential targets for designing novel therapeutics that may promote resilience to tinnitus.

Voltage-gated ion channels in cancer cell proliferation

Changes of the electrical charges across the surface cell membrane are absolutely necessary to maintain cellular homeostasis in physiological as well as in pathological conditions. The opening of ion channels alter the charge distribution across the surface membrane as they allow the diffusion of ions such as K+, Ca++, Cl.

Spinal circuits for motor learning

Studies of motor learning have largely focussed on the cerebellum, and have provided key concepts about neural circuits required. However, other parts of the nervous system are involved in learning, as demonstrated by the capacity to 'train' spinal circuits to produce locomotion following spinal cord injury. While somatosensory feedback is necessary for spinal motor learning, feed forward circuits within the spinal cord must also contribute. In fact, motoneurons themselves could act as comparators that integrate feed forward and feedback inputs, and thus contribute to motor learning. Application of cerebellar-derived principles to spinal circuitry leads to testable predictions of spinal organization required for motor learning.

Intrinsic plasticity: an emerging player in addiction

Exposure to drugs of abuse, such as cocaine, leads to plastic changes in the activity of brain circuits, and a prevailing view is that these changes play a part in drug addiction. Notably, there has been intense focus on drug-induced changes in synaptic excitability and much less attention on intrinsic excitability factors (that is, excitability factors that are remote from the synapse). Accumulating evidence now suggests that intrinsic factors such as K+ channels are not only altered by cocaine but may also contribute to the shaping of the addiction phenotype.