Channel density distributions explain spiking variability in the globus pallidus: a combined physiology and computer simulation database approach

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

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

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.

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.

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

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

Biophysical and Architectural Mechanisms of Subthalamic Theta under Response Conflict

The cortico-basal ganglia circuit is needed to suppress prepotent actions and to facilitate controlled behavior. Under conditions of response conflict, the frontal cortex and subthalamic nucleus (STN) exhibit increased spiking and theta band power, which are linked to adaptive regulation of behavioral output. The electrophysiological mechanisms underlying these neural signatures of impulse control remain poorly understood. To address this lacuna, we constructed a novel large-scale, biophysically principled model of the subthalamopallidal (STN-globus pallidus externus) network and examined the mechanisms that modulate theta power and spiking in response to cortical input. Simulations confirmed that theta power does not emerge from intrinsic network dynamics but is robustly elicited in response to cortical input as burst events representing action selection dynamics. Rhythmic burst events of multiple cortical populations, representing a state of conflict where cortical motor plans vacillate in the theta range, led to prolonged STN theta and increased spiking, consistent with empirical literature. Notably, theta band signaling required NMDA, but not AMPA, currents, which were in turn related to a triphasic STN response characterized by spiking, silence, and bursting periods. Finally, theta band resonance was also strongly modulated by architectural connectivity, with maximal theta arising when multiple cortical populations project to individual STN "conflict detector" units because of an NMDA-dependent supralinear response. Our results provide insights into the biophysical principles and architectural constraints that give rise to STN dynamics during response conflict, and how their disruption can lead to impulsivity and compulsivity.SIGNIFICANCE STATEMENT The subthalamic nucleus exhibits theta band power modulation related to cognitive control over motor actions during conditions of response conflict. However, the mechanisms of such dynamics are not understood. Here we developed a novel biophysically detailed and data-constrained large-scale model of the subthalamopallidal network, and examined the impacts of cellular and network architectural properties that give rise to theta dynamics. Our investigations implicate an important role for NMDA receptors and cortico-subthalamic nucleus topographical connectivities in theta power modulation.

Initial Variability and Time-Dependent Changes of Neuronal Response Features Are Cell-Type-Specific

Different cell types are commonly defined by their distinct response features. But several studies proved substantial variability between cells of the same type, suggesting rather the appraisal of response feature distributions than a limitation to "typical" responses. Moreover, there is growing evidence that time-dependent changes of response features contribute to robust and functional network output in many neuronal systems. The individually characterized Touch (T), Pressure (P), and Retzius (Rz) cells in the medicinal leech allow for a rigid analysis of response features, elucidating differences between and variability within cell types, as well as their changes over time. The initial responses of T and P cells to somatic current injection cover a wide range of spike counts, and their first spike is generated with a high temporal precision after a short latency. In contrast, all Rz cells elicit very similar low spike counts with variable, long latencies. During prolonged electrical stimulation the resting membrane potential of all three cell types hyperpolarizes. At the same time, Rz cells reduce their spiking activity as expected for a departure from the spike threshold. In contrast, both mechanoreceptor types increase their spike counts during repeated stimulation, consistent with previous findings in T cells. A control experiment reveals that neither a massive current stimulation nor the hyperpolarization of the membrane potential is necessary for the mechanoreceptors' increase in excitability over time. These findings challenge the previously proposed involvement of slow K+-channels in the time-dependent activity changes. We also find no indication for a run-down of HCN channels over time, and a rigid statistical analysis contradicts several potential experimental confounders as the basis of the observed variability. We conclude that the time-dependent change in excitability of T and P cells could indicate a cell-type-specific shift between different spiking regimes, which also could explain the high variability in the initial responses. The underlying mechanism needs to be further investigated in more naturalistic experimental situations to disentangle the effects of varying membrane properties versus network interactions. They will show if variability in individual response features serves as flexible adaptation to behavioral contexts rather than just "randomness".

BOLD Monitoring in the Neural Simulator ANNarchy

Multi-scale network models that simultaneously simulate different measurable signals at different spatial and temporal scales, such as membrane potentials of single neurons, population firing rates, local field potentials, and blood-oxygen-level-dependent (BOLD) signals, are becoming increasingly popular in computational neuroscience. The transformation of the underlying simulated neuronal activity of these models to simulated non-invasive measurements, such as BOLD signals, is particularly relevant. The present work describes the implementation of a BOLD monitor within the neural simulator ANNarchy to allow an on-line computation of simulated BOLD signals from neural network models. An active research topic regarding the simulation of BOLD signals is the coupling of neural processes to cerebral blood flow (CBF) and cerebral metabolic rate of oxygen (CMRO2). The flexibility of ANNarchy allows users to define this coupling with a high degree of freedom and thus, not only allows to relate mesoscopic network models of populations of spiking neurons to experimental BOLD data, but also to investigate different hypotheses regarding the coupling between neural processes, CBF and CMRO2 with these models. In this study, we demonstrate how simulated BOLD signals can be obtained from a network model consisting of multiple spiking neuron populations. We first demonstrate the use of the Balloon model, the predominant model for simulating BOLD signals, as well as the possibility of using novel user-defined models, such as a variant of the Balloon model with separately driven CBF and CMRO2 signals. We emphasize how different hypotheses about the coupling between neural processes, CBF and CMRO2 can be implemented and how these different couplings affect the simulated BOLD signals. With the BOLD monitor presented here, ANNarchy provides a tool for modelers who want to relate their network models to experimental MRI data and for scientists who want to extend their studies of the coupling between neural processes and the BOLD signal by using modeling approaches. This facilitates the investigation and model-based analysis of experimental BOLD data and thus improves multi-scale understanding of neural processes in humans.

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

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

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

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

On the Role of Arkypallidal and Prototypical Neurons for Phase Transitions in the External Pallidum

The external pallidum (globus pallidus pars externa [GPe]) plays a central role for basal ganglia functions and dynamics and, consequently, has been included in most computational studies of the basal ganglia. These studies considered the GPe as a homogeneous neural population. However, experimental studies have shown that the GPe contains at least two distinct cell types (prototypical and arkypallidal cells). In this work, we provide in silico insight into how pallidal heterogeneity modulates dynamic regimes inside the GPe and how they affect the GPe response to oscillatory input. We derive a mean-field model of the GPe system from a microscopic spiking neural network of recurrently coupled prototypical and arkypallidal neurons. Using bifurcation analysis, we examine the influence of dopamine-dependent changes of intrapallidal connectivity on the GPe dynamics. We find that increased self-inhibition of prototypical cells can induce oscillations, whereas increased inhibition of prototypical cells by arkypallidal cells leads to the emergence of a bistable regime. Furthermore, we show that oscillatory input to the GPe, arriving from striatum, leads to characteristic patterns of cross-frequency coupling observed at the GPe. Based on these findings, we propose two different hypotheses of how dopamine depletion at the GPe may lead to phase-amplitude coupling between the parkinsonian beta rhythm and a GPe-intrinsic γ rhythm. Finally, we show that these findings generalize to realistic spiking neural networks of sparsely coupled Type I excitable GPe neurons.SIGNIFICANCE STATEMENT Our work provides (1) insight into the theoretical implications of a dichotomous globus pallidus pars externa (GPe) organization, and (2) an exact mean-field model that allows for future investigations of the relationship between GPe spiking activity and local field potential fluctuations. We identify the major phase transitions that the GPe can undergo when subject to static or periodic input and link these phase transitions to the emergence of synchronized oscillations and cross-frequency coupling in the basal ganglia. Because of the close links between our model and experimental findings on the structure and dynamics of prototypical and arkypallidal cells, our results can be used to guide both experimental and computational studies on the role of the GPe for basal ganglia dynamics in health and disease.

Ion-channel degeneracy: Multiple ion channels heterogeneously regulate intrinsic physiology of rat hippocampal granule cells

Degeneracy, the ability of multiple structural components to elicit the same characteristic functional properties, constitutes an elegant mechanism for achieving biological robustness. In this study, we sought electrophysiological signatures for the expression of ion-channel degeneracy in the emergence of intrinsic properties of rat hippocampal granule cells. We measured the impact of four different ion-channel subtypes-hyperpolarization-activated cyclic-nucleotide-gated (HCN), barium-sensitive inward rectifier potassium (Kir ), tertiapin-Q-sensitive inward rectifier potassium, and persistent sodium (NaP) channels-on 21 functional measurements employing pharmacological agents, and report electrophysiological data on two characteristic signatures for the expression of ion-channel degeneracy in granule cells. First, the blockade of a specific ion-channel subtype altered several, but not all, functional measurements. Furthermore, any given functional measurement was altered by the blockade of many, but not all, ion-channel subtypes. Second, the impact of blocking each ion-channel subtype manifested neuron-to-neuron variability in the quantum of changes in the electrophysiological measurements. Specifically, we found that blocking HCN or Ba-sensitive Kir channels enhanced action potential firing rate, but blockade of NaP channels reduced firing rate of granule cells. Subthreshold measures of granule cell intrinsic excitability (input resistance, temporal summation, and impedance amplitude) were enhanced by blockade of HCN or Ba-sensitive Kir channels, but were not significantly altered by NaP channel blockade. We confirmed that the HCN and Ba-sensitive Kir channels independently altered sub- and suprathreshold properties of granule cells through sequential application of pharmacological agents that blocked these channels. Finally, we found that none of the sub- or suprathreshold measurements of granule cells were significantly altered upon treatment with tertiapin-Q. Together, the heterogeneous many-to-many mapping between ion channels and single-neuron intrinsic properties emphasizes the need to account for ion-channel degeneracy in cellular- and network-scale physiology.

A new reduced-morphology model for CA1 pyramidal cells and its validation and comparison with other models using HippoUnit

Modeling long-term neuronal dynamics may require running long-lasting simulations. Such simulations are computationally expensive, and therefore it is advantageous to use simplified models that sufficiently reproduce the real neuronal properties. Reducing the complexity of the neuronal dendritic tree is one option. Therefore, we have developed a new reduced-morphology model of the rat CA1 pyramidal cell which retains major dendritic branch classes. To validate our model with experimental data, we used HippoUnit, a recently established standardized test suite for CA1 pyramidal cell models. The HippoUnit allowed us to systematically evaluate the somatic and dendritic properties of the model and compare them to models publicly available in the ModelDB database. Our model reproduced (1) somatic spiking properties, (2) somatic depolarization block, (3) EPSP attenuation, (4) action potential backpropagation, and (5) synaptic integration at oblique dendrites of CA1 neurons. The overall performance of the model in these tests achieved higher biological accuracy compared to other tested models. We conclude that, due to its realistic biophysics and low morphological complexity, our model captures key physiological features of CA1 pyramidal neurons and shortens computational time, respectively. Thus, the validated reduced-morphology model can be used for computationally demanding simulations as a substitute for more complex models.

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.

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.

Neuronal population model of globular bushy cells covering unit-to-unit variability

Computations of acoustic information along the central auditory pathways start in the cochlear nucleus. Bushy cells in the anteroventral cochlear nucleus, which innervate monaural and binaural stations in the superior olivary complex, process and transfer temporal cues relevant for sound localization. These cells are categorized into two groups: spherical and globular bushy cells (SBCs/GBCs). Spontaneous rates of GBCs innervated by multiple auditory nerve (AN) fibers are generally lower than those of SBCs that receive a small number of large AN synapses. In response to low-frequency tonal stimulation, both types of bushy cells show improved phase-locking and entrainment compared to AN fibers. When driven by high-frequency tones, GBCs show primary-like-with-notch or onset-L peristimulus time histograms and relatively irregular spiking. However, previous in vivo physiological studies of bushy cells also found considerable unit-to-unit variability in these response patterns. Here we present a population of models that can simulate the observed variation in GBCs. We used a simple coincidence detection model with an adaptive threshold and systematically varied its six parameters. Out of 567000 parameter combinations tested, 7520 primary-like-with-notch models and 4094 onset-L models were selected that satisfied a set of physiological criteria for a GBC unit. Analyses of the model parameters and output measures revealed that the parameters of the accepted model population are weakly correlated with each other to retain major GBC properties, and that the output spiking patterns of the model are affected by a combination of multiple parameters. Simulations of frequency-dependent temporal properties of the model GBCs showed a reasonable fit to empirical data, supporting the validity of our population modeling. The computational simplicity and efficiency of the model structure makes our approach suitable for future large-scale simulations of binaural information processing that may involve thousands of GBC units.

In the auditory system, specialized neuronal circuits process various types of acoustic information. A group of neurons, called globular bushy cells (GBCs), faithfully transfer timing information of acoustic signals to their downstream neurons responsible for the perception of sound location. Previous physiological studies found representative activity patterns of GBCs, but with substantial individual variations among them. In this study, we present a population of models, instead of creating one best model, to account for the observed variations of GBCs. We varied all six parameters of a simple auditory neuron model and selected the combinations of parameters that led to acceptable activity patterns of GBCs. In total, we tested more than half a million combinations and accepted ~11600 GBC models. Temporal spiking patterns of real GBCs depend on the sound frequency, and our model population was able to replicate this trend. The model used here is computationally efficient and can thus serve as a building block for future large-scale simulations of auditory information processing.

Beta-Band Resonance and Intrinsic Oscillations in a Biophysically Detailed Model of the Subthalamic Nucleus-Globus Pallidus Network

Increased beta-band oscillatory activity in the basal ganglia network is associated with Parkinsonian motor symptoms and is suppressed with medication and deep brain stimulation (DBS). The origins of the beta-band oscillations, however, remains unclear with both intrinsic oscillations arising within the subthalamic nucleus (STN)-external globus pallidus (GPe) network and exogenous beta-activity, originating outside the network, proposed as potential sources of the pathological activity. The aim of this study was to explore the relative contribution of autonomous oscillations and exogenous oscillatory inputs in the generation of pathological oscillatory activity in a biophysically detailed model of the parkinsonian STN-GPe network. The network model accounts for the integration of synaptic currents and their interaction with intrinsic membrane currents in dendritic structures within the STN and GPe. The model was used to investigate the development of beta-band synchrony and bursting within the STN-GPe network by changing the balance of excitation and inhibition in both nuclei, and by adding exogenous oscillatory inputs with varying phase relationships through the hyperdirect cortico-subthalamic and indirect striato-pallidal pathways. The model showed an intrinsic susceptibility to beta-band oscillations that was manifest in weak autonomously generated oscillations within the STN-GPe network and in selective amplification of exogenous beta-band synaptic inputs near the network's endogenous oscillation frequency. The frequency at which this resonance peak occurred was determined by the net level of excitatory drive to the network. Intrinsic or endogenously generated oscillations were too weak to support a pacemaker role for the STN-GPe network, however, they were considerably amplified by sparse cortical beta inputs and were further amplified by striatal beta inputs that promoted anti-phase firing of the cortex and GPe, resulting in maximum transient inhibition of STN neurons. The model elucidates a mechanism of cortical patterning of the STN-GPe network through feedback inhibition whereby intrinsic susceptibility to beta-band oscillations can lead to phase locked spiking under parkinsonian conditions. These results point to resonance of endogenous oscillations with exogenous patterning of the STN-GPe network as a mechanism of pathological synchronization, and a role for the pallido-striatal feedback loop in amplifying beta oscillations.

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.

Cellular and Synaptic Dysfunctions in Parkinson's Disease: Stepping out of the Striatum

The basal ganglia (BG) are a collection of interconnected subcortical nuclei that participate in a great variety of functions, ranging from motor programming and execution to procedural learning, cognition, and emotions. This network is also the region primarily affected by the degeneration of midbrain dopaminergic neurons localized in the substantia nigra pars compacta (SNc). This degeneration causes cellular and synaptic dysfunctions in the BG network, which are responsible for the appearance of the motor symptoms of Parkinson’s disease. Dopamine (DA) modulation and the consequences of its loss on the striatal microcircuit have been extensively studied, and because of the discrete nature of DA innervation of other BG nuclei, its action outside the striatum has been considered negligible. However, there is a growing body of evidence supporting functional extrastriatal DA modulation of both cellular excitability and synaptic transmission. In this review, the functional relevance of DA modulation outside the striatum in both normal and pathological conditions will be discussed.

Thinking Outside the Box (and Arrow): Current Themes in Striatal Dysfunction in Movement Disorders

The basal ganglia are an intricately connected assembly of subcortical nuclei, forming the core of an adaptive network connecting cortical and thalamic circuits. For nearly three decades, researchers and medical practitioners have conceptualized how the basal ganglia circuit works, and how its pathology underlies motor disorders such as Parkinson's and Huntington's diseases, using what is often referred to as the "box-and-arrow model": a circuit diagram showing the broad strokes of basal ganglia connectivity and the pathological increases and decreases in the weights of specific connections that occur in disease. While this model still has great utility and has led to groundbreaking strategies to treat motor disorders, our evolving knowledge of basal ganglia function has made it clear that this classic model has several shortcomings that severely limit its predictive and descriptive abilities. In this review, we will focus on the striatum, the main input nucleus of the basal ganglia. We describe recent advances in our understanding of the rich microcircuitry and plastic capabilities of the striatum, factors not captured by the original box-and-arrow model, and provide examples of how such advances inform our current understanding of the circuit pathologies underlying motor disorders.

The physiological variability of channel density in hippocampal CA1 pyramidal cells and interneurons explored using a unified data-driven modeling workflow

Every neuron is part of a network, exerting its function by transforming multiple spatiotemporal synaptic input patterns into a single spiking output. This function is specified by the particular shape and passive electrical properties of the neuronal membrane, and the composition and spatial distribution of ion channels across its processes. For a variety of physiological or pathological reasons, the intrinsic input/output function may change during a neuron's lifetime. This process results in high variability in the peak specific conductance of ion channels in individual neurons. The mechanisms responsible for this variability are not well understood, although there are clear indications from experiments and modeling that degeneracy and correlation among multiple channels may be involved. Here, we studied this issue in biophysical models of hippocampal CA1 pyramidal neurons and interneurons. Using a unified data-driven simulation workflow and starting from a set of experimental recordings and morphological reconstructions obtained from rats, we built and analyzed several ensembles of morphologically and biophysically accurate single cell models with intrinsic electrophysiological properties consistent with experimental findings. The results suggest that the set of conductances expressed in any given hippocampal neuron may be considered as belonging to two groups: one subset is responsible for the major characteristics of the firing behavior in each population and the other is responsible for a robust degeneracy. Analysis of the model neurons suggests several experimentally testable predictions related to the combination and relative proportion of the different conductances that should be expressed on the membrane of different types of neurons for them to fulfill their role in the hippocampus circuitry.

Parameter Optimization Using Covariance Matrix Adaptation-Evolutionary Strategy (CMA-ES), an Approach to Investigate Differences in Channel Properties Between Neuron Subtypes

Computational models in neuroscience can be used to predict causal relationships between biological mechanisms in neurons and networks, such as the effect of blocking an ion channel or synaptic connection on neuron activity. Since developing a biophysically realistic, single neuron model is exceedingly difficult, software has been developed for automatically adjusting parameters of computational neuronal models. The ideal optimization software should work with commonly used neural simulation software; thus, we present software which works with models specified in declarative format for the MOOSE simulator. Experimental data can be specified using one of two different file formats. The fitness function is customizable as a weighted combination of feature differences. The optimization itself uses the covariance matrix adaptation-evolutionary strategy, because it is robust in the face of local fluctuations of the fitness function, and deals well with a high-dimensional and discontinuous fitness landscape. We demonstrate the versatility of the software by creating several model examples of each of four types of neurons (two subtypes of spiny projection neurons and two subtypes of globus pallidus neurons) by tuning to current clamp data. Optimizations reached convergence within 1,600-4,000 model evaluations (200-500 generations × population size of 8). Analysis of the parameters of the best fitting models revealed differences between neuron subtypes, which are consistent with prior experimental results. Overall our results suggest that this easy-to-use, automatic approach for finding neuron channel parameters may be applied to current clamp recordings from neurons exhibiting different biochemical markers to help characterize ionic differences between other neuron subtypes.

T2N as a new tool for robust electrophysiological modeling demonstrated for mature and adult-born dentate granule cells

Compartmental models are the theoretical tool of choice for understanding single neuron computations. However, many models are incomplete, built ad hoc and require tuning for each novel condition rendering them of limited usability. Here, we present T2N, a powerful interface to control NEURON with Matlab and TREES toolbox, which supports generating models stable over a broad range of reconstructed and synthetic morphologies. We illustrate this for a novel, highly detailed active model of dentate granule cells (GCs) replicating a wide palette of experiments from various labs. By implementing known differences in ion channel composition and morphology, our model reproduces data from mouse or rat, mature or adult-born GCs as well as pharmacological interventions and epileptic conditions. This work sets a new benchmark for detailed compartmental modeling. T2N is suitable for creating robust models useful for large-scale networks that could lead to novel predictions. We discuss possible T2N application in degeneracy studies.

Logarithmic distributions prove that intrinsic learning is Hebbian

In this paper, we present data for the lognormal distributions of spike rates, synaptic weights and intrinsic excitability (gain) for neurons in various brain areas, such as auditory or visual cortex, hippocampus, cerebellum, striatum, midbrain nuclei. We find a remarkable consistency of heavy-tailed, specifically lognormal, distributions for rates, weights and gains in all brain areas examined. The difference between strongly recurrent and feed-forward connectivity (cortex vs. striatum and cerebellum), neurotransmitter (GABA (striatum) or glutamate (cortex)) or the level of activation (low in cortex, high in Purkinje cells and midbrain nuclei) turns out to be irrelevant for this feature. Logarithmic scale distribution of weights and gains appears to be a general, functional property in all cases analyzed. We then created a generic neural model to investigate adaptive learning rules that create and maintain lognormal distributions. We conclusively demonstrate that not only weights, but also intrinsic gains, need to have strong Hebbian learning in order to produce and maintain the experimentally attested distributions. This provides a solution to the long-standing question about the type of plasticity exhibited by intrinsic excitability.

Logarithmic distributions prove that intrinsic learning is Hebbian

In this paper, we document lognormal distributions for spike rates, synaptic weights and intrinsic excitability (gain) for neurons in various brain areas, such as auditory or visual cortex, hippocampus, cerebellum, striatum, midbrain nuclei. We find a remarkable consistency of heavy-tailed, specifically lognormal, distributions for rates, weights and gains in all brain areas. The difference between strongly recurrent and feed-forward connectivity (cortex vs. striatum and cerebellum), neurotransmitter (GABA (striatum) or glutamate (cortex)) or the level of activation (low in cortex, high in Purkinje cells and midbrain nuclei) turns out to be irrelevant for this feature. Logarithmic scale distribution of weights and gains appears as a functional property that is present everywhere.  Secondly, we created a generic neural model to show that Hebbian learning will create and maintain lognormal distributions. We could prove with the model that not only weights, but also intrinsic gains, need to have strong Hebbian learning in order to produce and maintain the experimentally attested distributions. This settles a long-standing question about the type of plasticity exhibited by intrinsic excitability.

Computational Model of Recurrent Subthalamo-Pallidal Circuit for Generation of Parkinsonian Oscillations

Parkinson's disease is a movement disorder caused by dopamine depletion in the basal ganglia. Abnormally synchronized neuronal oscillations between 8 and 15 Hz in the basal ganglia are implicated in motor symptoms of Parkinson's disease. However, how these abnormal oscillations are generated and maintained in the dopamine-depleted state is unknown. Based on neural recordings in a primate model of Parkinson's disease and other experimental and computational evidence, we hypothesized that the recurrent circuit between the subthalamic nucleus (STN) and the external segment of the globus pallidus (GPe) generates and maintains parkinsonian oscillations, and that the cortical excitatory input to the STN amplifies them. To investigate this hypothesis through computer simulations, we developed a spiking neuron model of the STN-GPe circuit by incorporating electrophysiological properties of neurons and synapses. A systematic parameter search by computer simulation identified regions in the space of the intrinsic excitability of GPe neurons and synaptic strength from the GPe to the STN that reproduce normal and parkinsonian states. In the parkinsonian state, reduced firing of GPe neurons and increased GPe-STN inhibition trigger burst activities of STN neurons with strong post-inhibitory rebound excitation, which is usually subject to short-term depression. STN neuronal bursts are shaped into the 8–15 Hz, synchronous oscillations via recurrent interactions of STN and GPe neurons. Furthermore, we show that cortical excitatory input to the STN can amplify or suppress pathological STN oscillations depending on their phase and strength, predicting conditions of cortical inputs to the STN for suppressing oscillations.

Optimizing computer models of corticospinal neurons to replicate in vitro dynamics

Corticospinal neurons (SPI), thick-tufted pyramidal neurons in motor cortex layer 5B that project caudally via the medullary pyramids, display distinct class-specific electrophysiological properties in vitro: strong sag with hyperpolarization, lack of adaptation, and a nearly linear frequency-current (F-I) relationship. We used our electrophysiological data to produce a pair of large archives of SPI neuron computer models in two model classes: 1) detailed models with full reconstruction; and 2) simplified models with six compartments. We used a PRAXIS and an evolutionary multiobjective optimization (EMO) in sequence to determine ion channel conductances. EMO selected good models from each of the two model classes to form the two model archives. Archived models showed tradeoffs across fitness functions. For example, parameters that produced excellent F-I fit produced a less-optimal fit for interspike voltage trajectory. Because of these tradeoffs, there was no single best model but rather models that would be best for particular usages for either single neuron or network explorations. Further exploration of exemplar models with strong F-I fit demonstrated that both the detailed and simple models produced excellent matches to the experimental data. Although dendritic ion identities and densities cannot yet be fully determined experimentally, we explored the consequences of a demonstrated proximal to distal density gradient of I_h, demonstrating that this would lead to a gradient of resonance properties with increased resonant frequencies more distally. We suggest that this dynamical feature could serve to make the cell particularly responsive to major frequency bands that differ by cortical layer.

NEW & NOTEWORTHY

We developed models of motor cortex corticospinal neurons that replicate in vitro dynamics, including hyperpolarization-induced sag and realistic firing patterns. Models demonstrated resonance in response to synaptic stimulation, with resonance frequency increasing in apical dendrites with increasing distance from soma, matching the increasing oscillation frequencies spanning deep to superficial cortical layers. This gradient may enable specific corticospinal neuron dendrites to entrain to relevant oscillations in different cortical layers, contributing to appropriate motor output commands.

Using a Semi-Automated Strategy to Develop Multi-Compartment Models That Predict Biophysical Properties of Interneuron-Specific 3 (IS3) Cells in Hippocampus

Determining how intrinsic cellular properties govern and modulate neuronal input–output processing is a critical endeavor for understanding microcircuit functions in the brain. However, lack of cellular specifics and nonlinear interactions prevent experiments alone from achieving this. Building and using cellular models is essential in these efforts. We focus on uncovering the intrinsic properties of mus musculus hippocampal type 3 interneuron-specific (IS3) cells, a cell type that makes GABAergic synapses onto specific interneuron types, but not pyramidal cells. While IS3 cell morphology and synaptic output have been examined, their voltage-gated ion channel profile and distribution remain unknown. We combined whole-cell patch-clamp recordings and two-photon dendritic calcium imaging to examine IS3 cell membrane and dendritic properties. Using these data as a target reference, we developed a semi-automated strategy to obtain multi-compartment models for a cell type with unknown intrinsic properties. Our approach is based on generating populations of models to capture determined features of the experimental data, each of which possesses unique combinations of channel types and conductance values. From these populations, we chose models that most closely resembled the experimental data. We used these models to examine the impact of specific ion channel combinations on spike generation. Our models predict that fast delayed rectifier currents should be present in soma and proximal dendrites, and this is confirmed using immunohistochemistry. Further, without A-type potassium currents in the dendrites, spike generation is facilitated at more distal synaptic input locations. Our models will help to determine the functional role of IS3 cells in hippocampal microcircuits.

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

Distinct current modules shape cellular dynamics in model neurons

Numerous intrinsic currents are known to collectively shape neuronal membrane potential dynamics, or neuronal signatures. Although how sets of currents shape specific signatures such as spiking characteristics or oscillations has been studied individually, it is less clear how a neuron's suite of currents jointly shape its entire set of signatures. Biophysical conductance-based models of neurons represent a viable tool to address this important question. We hypothesized that currents are grouped into distinct modules that shape specific neuronal characteristics or signatures, such as resting potential, sub-threshold oscillations, and spiking waveforms, for several classes of neurons. For such a grouping to occur, the currents within one module should have minimal functional interference with currents belonging to other modules. This condition is satisfied if the gating functions of currents in the same module are grouped together on the voltage axis; in contrast, such functions are segregated along the voltage axis for currents belonging to different modules. We tested this hypothesis using four published example case models and found it to be valid for these classes of neurons. This insight into the neurobiological organization of currents also suggests an intuitive, systematic, and robust methodology to develop biophysical single-cell models with multiple biological characteristics applicable for both hand- and automated-tuning approaches. We illustrate the methodology using two example case rodent pyramidal neurons, from the lateral amygdala and the hippocampus. The methodology also helped reveal that a single-core compartment model could capture multiple neuronal properties. Such biophysical single-compartment models have potential to improve the fidelity of large network models.

Automated evolutionary optimization of ion channel conductances and kinetics in models of young and aged rhesus monkey pyramidal neurons

Conductance-based compartment modeling requires tuning of many parameters to fit the neuron model to target electrophysiological data. Automated parameter optimization via evolutionary algorithms (EAs) is a common approach to accomplish this task, using error functions to quantify differences between model and target. We present a three-stage EA optimization protocol for tuning ion channel conductances and kinetics in a generic neuron model with minimal manual intervention. We use the technique of Latin hypercube sampling in a new way, to choose weights for error functions automatically so that each function influences the parameter search to a similar degree. This protocol requires no specialized physiological data collection and is applicable to commonly-collected current clamp data and either single- or multi-objective optimization. We applied the protocol to two representative pyramidal neurons from layer 3 of the prefrontal cortex of rhesus monkeys, in which action potential firing rates are significantly higher in aged compared to young animals. Using an idealized dendritic topology and models with either 4 or 8 ion channels (10 or 23 free parameters respectively), we produced populations of parameter combinations fitting the target datasets in less than 80 hours of optimization each. Passive parameter differences between young and aged models were consistent with our prior results using simpler models and hand tuning. We analyzed parameter values among fits to a single neuron to facilitate refinement of the underlying model, and across fits to multiple neurons to show how our protocol will lead to predictions of parameter differences with aging in these neurons.

Sparse pallidal connections shape synchrony in a network model of the basal ganglia

Neural synchrony in the basal ganglia, especially in the beta frequency band (13-30 Hz), is a hallmark of Parkinson's disease and considered as antikinetic. In contrast, the healthy basal ganglia show low levels of synchrony. It is currently unknown where synchrony and oscillations arise in the parkinsonian brain and how they are transmitted through the basal ganglia, as well as what makes them dependent on dopamine. The external part of the globus pallidus has recently been identified as a hub nucleus in the basal ganglia, possessing intrinsic inhibitory connections and possibly also gap junctions. In this study, we show that in a conductance-based network model of the basal ganglia, the combination of sparse, high-conductance inhibitory synapses and sparse, low-conductance gap junctions in the external part of the globus pallidus could effectively desynchronize the whole network. However, when gap junction coupling became strong enough, the effect was impeded and activity synchronized. In particular, sustained periods of beta coherence occurred between some neuron pairs. As gap junctions can change their conductance with the dopamine level, we suggest pallidal gap junction coupling as a mechanism contributing to the development of beta synchrony in the parkinsonian basal ganglia.

Frequency Responses of Rat Retinal Ganglion Cells

There are 15–20 different types of retinal ganglion cells (RGC) in the mammalian retina, each encoding different aspects of the visual scene. The mechanism by which post-synaptic signals from the retinal network generate spikes is determined by each cell’s intrinsic electrical properties. Here we investigate the frequency responses of morphologically identified rat RGCs using intracellular injection of sinusoidal current waveforms, to assess their intrinsic capabilities with minimal contributions from the retinal network. Recorded cells were classified according to their morphological characteristics (A, B, C or D-type) and their stratification (inner (i), outer (o) or bistratified) in the inner plexiform layer (IPL). Most cell types had low- or band-pass frequency responses. A2, C1 and C4o cells were band-pass with peaks of 15–30 Hz and low-pass cutoffs above 56 Hz (A2 cells) and ~42 Hz (C1 and C4o cells). A1 and C2i/o cells were low-pass with peaks of 10–15 Hz (cutoffs 19–25 Hz). Bistratified D1 and D2 cells were also low-pass with peaks of 5–10 Hz (cutoffs ~16 Hz). The least responsive cells were the B2 and C3 types (peaks: 2–5 Hz, cutoffs: 8–11 Hz). We found no difference between cells stratifying in the inner and outer IPL (i.e., ON and OFF cells) or between cells with large and small somas or dendritic fields. Intrinsic physiological properties (input resistance, spike width and sag) had little impact on frequency response at low frequencies, but account for 30–40% of response variability at frequencies >30 Hz.

The external globus pallidus: progress and perspectives

The external globus pallidus (GPe) of the basal ganglia is in a unique and powerful position to influence processing of motor information by virtue of its widespread projections to all basal ganglia nuclei. Despite the clinical importance of the GPe in common motor disorders such as Parkinson's disease, there is only limited information about its cellular composition and organizational principles. In this review, recent advances in the understanding of the diversity in the molecular profile, anatomy, physiology and corresponding behaviour during movement of GPe neurons are described. Importantly, this study attempts to build consensus and highlight commonalities of the cellular classification based on existing but contentious literature. Additionally, an analysis of the literature concerning the intricate reciprocal loops formed between the GPe and major synaptic partners, including both the striatum and the subthalamic nucleus, is provided. In conclusion, the GPe has emerged as a crucial node in the basal ganglia macrocircuit. While subtleties in the cellular makeup and synaptic connection of the GPe create new challenges, modern research tools have shown promise in untangling such complexity, and will provide better understanding of the roles of the GPe in encoding movements and their associated pathologies.

From global to local: exploring the relationship between parameters and behaviors in models of electrical excitability

Models of electrical activity in excitable cells involve nonlinear interactions between many ionic currents. Changing parameters in these models can produce a variety of activity patterns with sometimes unexpected effects. Further more, introducing new currents will have different effects depending on the initial parameter set. In this study we combined global sampling of parameter space and local analysis of representative parameter sets in a pituitary cell model to understand the effects of adding K (+) conductances, which mediate some effects of hormone action on these cells. Global sampling ensured that the effects of introducing K (+) conductances were captured across a wide variety of contexts of model parameters. For each type of K (+) conductance we determined the types of behavioral transition that it evoked. Some transitions were counterintuitive, and may have been missed without the use of global sampling. In general, the wide range of transitions that occurred when the same current was applied to the model cell at different locations in parameter space highlight the challenge of making accurate model predictions in light of cell-to-cell heterogeneity. Finally, we used bifurcation analysis and fast/slow analysis to investigate why specific transitions occur in representative individual models. This approach relies on the use of a graphics processing unit (GPU) to quickly map parameter space to model behavior and identify parameter sets for further analysis. Acceleration with modern low-cost GPUs is particularly well suited to exploring the moderate-sized (5-20) parameter spaces of excitable cell and signaling models.

Parvalbumin+ Neurons and Npas1+ Neurons Are Distinct Neuron Classes in the Mouse External Globus Pallidus

Compelling evidence suggests that pathological activity of the external globus pallidus (GPe), a nucleus in the basal ganglia, contributes to the motor symptoms of a variety of movement disorders such as Parkinson's disease. Recent studies have challenged the idea that the GPe comprises a single, homogenous population of neurons that serves as a simple relay in the indirect pathway. However, we still lack a full understanding of the diversity of the neurons that make up the GPe. Specifically, a more precise classification scheme is needed to better describe the fundamental biology and function of different GPe neuron classes. To this end, we generated a novel multicistronic BAC (bacterial artificial chromosome) transgenic mouse line under the regulatory elements of the Npas1 gene. Using a combinatorial transgenic and immunohistochemical approach, we discovered that parvalbumin-expressing neurons and Npas1-expressing neurons in the GPe represent two nonoverlapping cell classes, amounting to 55% and 27% of the total GPe neuron population, respectively. These two genetically identified cell classes projected primarily to the subthalamic nucleus and to the striatum, respectively. Additionally, parvalbumin-expressing neurons and Npas1-expressing neurons were distinct in their autonomous and driven firing characteristics, their expression of intrinsic ion conductances, and their responsiveness to chronic 6-hydroxydopamine lesion. In summary, our data argue that parvalbumin-expressing neurons and Npas1-expressing neurons are two distinct functional classes of GPe neurons. This work revises our understanding of the GPe, and provides the foundation for future studies of its function and dysfunction.

SIGNIFICANCE STATEMENT

Until recently, the heterogeneity of the constituent neurons within the external globus pallidus (GPe) was not fully appreciated. We addressed this knowledge gap by discovering two principal GPe neuron classes, which were identified by their nonoverlapping expression of the markers parvalbumin and Npas1. Our study provides evidence that parvalbumin and Npas1 neurons have different topologies within the basal ganglia.

The domain of neuronal firing on a plane of input current and conductance

The activation of neurotransmitter receptors increases the current flow and membrane conductance and thus controls the firing rate of a neuron. In the present work, we justified the two-dimensional representation of a neuronal input by voltage-independent current and conductance and obtained experimentally and numerically a complete input-output (I/O) function. The dependence of the steady-state firing rate on the input current and conductance was studied as a two-parameter I/O function. We employed the dynamic patch clamp technique in slices to get this dependence for the whole domain of two input signals that evoke stationary spike trains in a single neuron (Ω-domain). As found, the Ω-domain is finite and an additional conductance decreases the range of spike-evoking currents. The I/O function has been reproduced in a Hodgkin-Huxley-like model. Among the simulated effects of different factors on the I/O function, including passive and active membrane properties, external conditions and input signal properties, the most interesting were: the shift of the right boundary of the Ω-domain (corresponding to the exCitation block) leftwards due to the decrease of the maximal potassium conductance; and the reduction of the Ω-domain by the decrease of the maximal sodium concentration. As found in experiments and simulations, the Ω-domain is reduced by the decrease of extracellular sodium concentration, by cooling, and by adding slow potassium currents providing interspike interval adaptation; the Ω-domain height is increased by adding color noise. Our modeling data provided a generalization of I/O dependencies that is consistent with previous studies and our experiments. Our results suggest that both current flow and membrane conductance should be taken into account when determining neuronal firing activity.

Preserved dichotomy but highly irregular and burst discharge in the basal ganglia in alert dystonic rats at rest

Despite its prevalence, the underlying pathophysiology of dystonia remains poorly understood. Using our novel tri-component classification algorithm, extracellular neuronal activity in the globus pallidus (GP), STN, and the entopeduncular nucleus (EP) was characterized in 34 normal and 25 jaundiced dystonic Gunn rats with their heads restrained while at rest. In normal rats, neurons in each nucleus were similarly characterized by two physiologically distinct types: regular tonic with moderate discharge frequencies (mean rates in GP, STN and EP ranging from 35-41 spikes/s) or irregular at slower frequencies (17-20 spikes/s), with a paucity of burst activity. In dystonic rats, these nuclei were also characterized by two distinct principal neuronal patterns. However, in marked difference, in the dystonic rats, neurons were primarily slow and highly irregular (12-15 spikes/s) or burst predominant (14-17 spikes/s), with maintained modest differences between nuclei. In GP and EP, with increasing severity of dystonia, burstiness was moderately further increased, irregularity mildly further increased, and discharge rates mildly further reduced. In contrast, these features did not appreciably change in STN with worsening dystonia. Findings of a lack of bursting in GP, STN and EP in normal rats in an alert resting state and prominent bursting in dystonic Gunn rats suggest that cortical or other external drive is normally required for bursting in these nuclei and that spontaneous bursting, as seen in dystonia and Parkinson's disease, is reflective of an underlying pathophysiological state. Moreover, the extent of burstiness appears to most closely correlate with the severity of the dystonia.

Prototypic and arkypallidal neurons in the dopamine-intact external globus pallidus

Studies in dopamine-depleted rats indicate that the external globus pallidus (GPe) contains two main types of GABAergic projection cell; so-called "prototypic" and "arkypallidal" neurons. Here, we used correlative anatomical and electrophysiological approaches in rats to determine whether and how this dichotomous organization applies to the dopamine-intact GPe. Prototypic neurons coexpressed the transcription factors Nkx2-1 and Lhx6, comprised approximately two-thirds of all GPe neurons, and were the major GPe cell type innervating the subthalamic nucleus (STN). In contrast, arkypallidal neurons expressed the transcription factor FoxP2, constituted just over one-fourth of GPe neurons, and innervated the striatum but not STN. In anesthetized dopamine-intact rats, molecularly identified prototypic neurons fired at relatively high rates and with high regularity, regardless of brain state (slow-wave activity or spontaneous activation). On average, arkypallidal neurons fired at lower rates and regularities than prototypic neurons, and the two cell types could be further distinguished by the temporal coupling of their firing to ongoing cortical oscillations. Complementing the activity differences observed in vivo, the autonomous firing of identified arkypallidal neurons in vitro was slower and more variable than that of prototypic neurons, which tallied with arkypallidal neurons displaying lower amplitudes of a "persistent" sodium current important for such pacemaking. Arkypallidal neurons also exhibited weaker driven and rebound firing compared with prototypic neurons. In conclusion, our data support the concept that a dichotomous functional organization, as actioned by arkypallidal and prototypic neurons with specialized molecular, structural, and physiological properties, is fundamental to the operations of the dopamine-intact GPe.

Using multi-compartment ensemble modeling as an investigative tool of spatially distributed biophysical balances: application to hippocampal oriens-lacunosum/moleculare (O-LM) cells

Multi-compartmental models of neurons provide insight into the complex, integrative properties of dendrites. Because it is not feasible to experimentally determine the exact density and kinetics of each channel type in every neuronal compartment, an essential goal in developing models is to help characterize these properties. To address biological variability inherent in a given neuronal type, there has been a shift away from using hand-tuned models towards using ensembles or populations of models. In collectively capturing a neuron's output, ensemble modeling approaches uncover important conductance balances that control neuronal dynamics. However, conductances are never entirely known for a given neuron class in terms of its types, densities, kinetics and distributions. Thus, any multi-compartment model will always be incomplete. In this work, our main goal is to use ensemble modeling as an investigative tool of a neuron's biophysical balances, where the cycling between experiment and model is a design criterion from the start. We consider oriens-lacunosum/moleculare (O-LM) interneurons, a prominent interneuron subtype that plays an essential gating role of information flow in hippocampus. O-LM cells express the hyperpolarization-activated current (Ih). Although dendritic Ih could have a major influence on the integrative properties of O-LM cells, the compartmental distribution of Ih on O-LM dendrites is not known. Using a high-performance computing cluster, we generated a database of models that included those with or without dendritic Ih. A range of conductance values for nine different conductance types were used, and different morphologies explored. Models were quantified and ranked based on minimal error compared to a dataset of O-LM cell electrophysiological properties. Co-regulatory balances between conductances were revealed, two of which were dependent on the presence of dendritic Ih. These findings inform future experiments that differentiate between somatic and dendritic Ih, thereby continuing a cycle between model and experiment.

Estimating parameters and predicting membrane voltages with conductance-based neuron models

Recent results demonstrate techniques for fully quantitative, statistical inference of the dynamics of individual neurons under the Hodgkin-Huxley framework of voltage-gated conductances. Using a variational approximation, this approach has been successfully applied to simulated data from model neurons. Here, we use this method to analyze a population of real neurons recorded in a slice preparation of the zebra finch forebrain nucleus HVC. Our results demonstrate that using only 1,500 ms of voltage recorded while injecting a complex current waveform, we can estimate the values of 12 state variables and 72 parameters in a dynamical model, such that the model accurately predicts the responses of the neuron to novel injected currents. A less complex model produced consistently worse predictions, indicating that the additional currents contribute significantly to the dynamics of these neurons. Preliminary results indicate some differences in the channel complement of the models for different classes of HVC neurons, which accords with expectations from the biology. Whereas the model for each cell is incomplete (representing only the somatic compartment, and likely to be missing classes of channels that the real neurons possess), our approach opens the possibility to investigate in modeling the plausibility of additional classes of channels the cell might possess, thus improving the models over time. These results provide an important foundational basis for building biologically realistic network models, such as the one in HVC that contributes to the process of song production and developmental vocal learning in songbirds.

Transgenic mouse lines subdivide external segment of the globus pallidus (GPe) neurons and reveal distinct GPe output pathways

Cell-type diversity in the brain enables the assembly of complex neural circuits, whose organization and patterns of activity give rise to brain function. However, the identification of distinct neuronal populations within a given brain region is often complicated by a lack of objective criteria to distinguish one neuronal population from another. In the external segment of the globus pallidus (GPe), neuronal populations have been defined using molecular, anatomical, and electrophysiological criteria, but these classification schemes are often not generalizable across preparations and lack consistency even within the same preparation. Here, we present a novel use of existing transgenic mouse lines, Lim homeobox 6 (Lhx6)-Cre and parvalbumin (PV)-Cre, to define genetically distinct cell populations in the GPe that differ molecularly, anatomically, and electrophysiologically. Lhx6-GPe neurons, which do not express PV, are concentrated in the medial portion of the GPe. They have lower spontaneous firing rates, narrower dynamic ranges, and make stronger projections to the striatum and substantia nigra pars compacta compared with PV-GPe neurons. In contrast, PV-GPe neurons are more concentrated in the lateral portions of the GPe. They have narrower action potentials, deeper afterhyperpolarizations, and make stronger projections to the subthalamic nucleus and parafascicular nucleus of the thalamus. These electrophysiological and anatomical differences suggest that Lhx6-GPe and PV-GPe neurons participate in different circuits with the potential to contribute to different aspects of motor function and dysfunction in disease.

The emergence of two anti-phase oscillatory neural populations in a computational model of the Parkinsonian globus pallidus

Experiments in rodent models of Parkinson's disease have demonstrated a prominent increase of oscillatory firing patterns in neurons within the Parkinsonian globus pallidus (GP) which may underlie some of the motor symptoms of the disease. There are two main pathways from the cortex to GP: via the striatum and via the subthalamic nucleus (STN), but it is not known how these inputs sculpt the pathological pallidal firing patterns. To study this we developed a novel neural network model of conductance-based spiking pallidal neurons with cortex-modulated input from STN neurons. Our results support the hypothesis that entrainment occurs primarily via the subthalamic pathway. We find that as a result of the interplay between excitatory input from the STN and mutual inhibitory coupling between GP neurons, a homogeneous population of GP neurons demonstrates a self-organizing dynamical behavior where two groups of neurons emerge: one spiking in-phase with the cortical rhythm and the other in anti-phase. This finding mirrors what is seen in recordings from the GP of rodents that have had Parkinsonism induced via brain lesions. Our model also includes downregulation of Hyperpolarization-activated Cyclic Nucleotide-gated (HCN) channels in response to burst firing of GP neurons, since this has been suggested as a possible mechanism for the emergence of Parkinsonian activity. We found that the downregulation of HCN channels provides even better correspondence with experimental data but that it is not essential in order for the two groups of oscillatory neurons to appear. We discuss how the influence of inhibitory striatal input will strengthen our results.

Synchrony in Parkinson's disease: importance of intrinsic properties of the external globus pallidus

The mechanisms for the emergence and transmission of synchronized oscillations in Parkinson's disease, which are potentially causal to motor deficits, remain debated. Aside from the motor cortex and the subthalamic nucleus, the external globus pallidus (GPe) has been shown to be essential for the maintenance of these oscillations and plays a major role in sculpting neural network activity in the basal ganglia (BG). While neural activity of the healthy GPe shows almost no correlations between pairs of neurons, prominent synchronization in the β frequency band arises after dopamine depletion. Several studies have proposed that this shift is due to network interactions between the different BG nuclei, including the GPe. However, recent studies demonstrate an important role for the properties of neurons within the GPe. In this review, we will discuss these intrinsic GPe properties and review proposed mechanisms for activity decorrelation within the dopamine-intact GPe. Failure of the GPe to desynchronize correlated inputs can be a possible explanation for synchronization in the whole BG. Potential triggers of synchronization involve the enhancement of GPe-GPe inhibition and changes in ion channel function in GPe neurons.

An interactive channel model of the Basal Ganglia: bifurcation analysis under healthy and parkinsonian conditions

Oscillations in the basal ganglia are an active area of research and have been shown to relate to the hypokinetic motor symptoms of Parkinson's disease. We study oscillations in a multi-channel mean field model, where each channel consists of an interconnected pair of subthalamic nucleus and globus pallidus sub-populations.To study how the channels interact, we perform two-dimensional bifurcation analysis of a model of an individual channel, which reveals the critical boundaries in parameter space that separate different dynamical modes; these modes include steady-state, oscillatory, and bi-stable behaviour. Without self-excitation in the subthalamic nucleus a single channel cannot generate oscillations, yet there is little experimental evidence for such self-excitation. Our results show that the interactive channel model with coupling via pallidal sub-populations demonstrates robust oscillatory behaviour without subthalamic self-excitation, provided the coupling is sufficiently strong. We study the model under healthy and Parkinsonian conditions and demonstrate that it exhibits oscillations for a much wider range of parameters in the Parkinsonian case. In the discussion, we show how our results compare with experimental findings and discuss their possible physiological interpretation. For example, experiments have found that increased lateral coupling in the rat basal ganglia is correlated with oscillations under Parkinsonian conditions.

Supersensitive presynaptic dopamine D2 receptor inhibition of the striatopallidal projection in nigrostriatal dopamine-deficient mice

The dopamine (DA) D2 receptor (D2R)-expressing medium spiny neurons (D2-MSNs) in the striatum project to and inhibit the GABAergic neurons in the globus pallidus (GP), forming an important link in the indirect pathway of the basal ganglia movement control circuit. These striatopallidal axon terminals express presynaptic D2Rs that inhibit GABA release and thus regulate basal ganglion function. Here we show that in transcription factor Pitx3 gene mutant mice with a severe DA loss in the dorsal striatum mimicking the DA denervation in Parkinson's disease (PD), the striatopallidal GABAergic synaptic transmission displayed a heightened sensitivity to presynaptic D2R-mediated inhibition with the dose-response curve shifted to the left, although the maximal inhibition was not changed. Functionally, low concentrations of DA were able to more efficaciously reduce the striatopallidal inhibition-induced pauses of GP neuron activity in DA-deficient Pitx3 mutant mice than in wild-type mice. These results demonstrate that presynaptic D2R inhibition of the striatopallidal synapse becomes supersensitized after DA loss. These supersensitive D2Rs may compensate for the lost DA in PD and also induce a strong disinhibition of GP neuron activity that may contribute to the motor-stimulating effects of dopaminergic treatments in PD.

Active decorrelation in the basal ganglia

The cytoarchitecturally-homogeneous appearance of the globus pallidus, subthalamic nucleus and substantia nigra has long been said to imply a high degree of afferent convergence and sharing of inputs by nearby neurons. Moreover, axon collaterals of neurons in the external segment of the globus pallidus and the substantia nigra pars reticulata arborize locally and make inhibitory synapses on other cells of the same type. These features suggest that the connectivity of the basal ganglia may impose spike-time correlations among the cells, and it has been puzzling that experimental studies have failed to demonstrate such correlations. One possible solution arises from studies of firing patterns in basal ganglia cells, which reveal that they are nearly all pacemaker cells. Their high rate of firing does not depend on synaptic excitation, but they fire irregularly because a dense barrage of synaptic inputs normally perturbs the timing of their autonomous activity. Theoretical and computational studies show that the responses of repetitively-firing neurons to shared input or mutual synaptic coupling often defy classical intuitions about temporal synaptic integration. The patterns of spike-timing among such neurons depend on the ionic mechanism of pacemaking, the level of background uncorrelated cellular and synaptic noise, and the firing rates of the neurons, as well as the properties of their synaptic connections. Application of these concepts to the basal ganglia circuitry suggests that the connectivity and physiology of these nuclei may be configured to prevent the establishment of permanent spike-timing relationships between neurons. The development of highly synchronous oscillatory patterns of activity in Parkinson's disease may result from the loss of pacemaking by some basal ganglia neurons, and accompanying breakdown of the mechanisms responsible for active decorrelation.

Signal enhancement in the output stage of the basal ganglia by synaptic short-term plasticity in the direct, indirect, and hyperdirect pathways

Many of the synapses in the basal ganglia display short-term plasticity. Still, computational models have not yet been used to investigate how this affects signaling. Here we use a model of the basal ganglia network, constrained by available data, to quantitatively investigate how synaptic short-term plasticity affects the substantia nigra reticulata (SNr), the basal ganglia output nucleus. We find that SNr becomes particularly responsive to the characteristic burst-like activity seen in both direct and indirect pathway striatal medium spiny neurons (MSN). As expected by the standard model, direct pathway MSNs are responsible for decreasing the activity in SNr. In particular, our simulations indicate that bursting in only a few percent of the direct pathway MSNs is sufficient for completely inhibiting SNr neuron activity. The standard model also suggests that SNr activity in the indirect pathway is controlled by MSNs disinhibiting the subthalamic nucleus (STN) via the globus pallidus externa (GPe). Our model rather indicates that SNr activity is controlled by the direct GPe-SNr projections. This is partly because GPe strongly inhibits SNr but also due to depressing STN-SNr synapses. Furthermore, depressing GPe-SNr synapses allow the system to become sensitive to irregularly firing GPe subpopulations, as seen in dopamine depleted conditions, even when the GPe mean firing rate does not change. Similar to the direct pathway, simulations indicate that only a few percent of bursting indirect pathway MSNs can significantly increase the activity in SNr. Finally, the model predicts depressing STN-SNr synapses, since such an assumption explains experiments showing that a brief transient activation of the hyperdirect pathway generates a tri-phasic response in SNr, while a sustained STN activation has minor effects. This can be explained if STN-SNr synapses are depressing such that their effects are counteracted by the (known) depressing GPe-SNr inputs.

Relating ion channel expression, bifurcation structure, and diverse firing patterns in a model of an identified motor neuron

Neurons show diverse firing patterns. Even neurons belonging to a single chemical or morphological class, or the same identified neuron, can display different types of electrical activity. For example, motor neuron MN5, which innervates a flight muscle of adult Drosophila, can show distinct firing patterns under the same recording conditions. We developed a two-dimensional biophysical model and show that a core complement of just two voltage-gated channels is sufficient to generate firing pattern diversity. We propose Shab and DmNa v to be two candidate genes that could encode these core currents, and find that changes in Shab channel expression in the model can reproduce activity resembling the main firing patterns observed in MN5 recordings. We use bifurcation analysis to describe the different transitions between rest and spiking states that result from variations in Shab channel expression, exposing a connection between ion channel expression, bifurcation structure, and firing patterns in models of membrane potential dynamics.

Preserving axosomatic spiking features despite diverse dendritic morphology

Throughout the nervous system, cells belonging to a certain electrical class (e-class)-sharing high similarity in firing response properties-may nevertheless have widely variable dendritic morphologies. To quantify the effect of this morphological variability on the firing of layer 5 thick-tufted pyramidal cells (TTCs), a detailed conductance-based model was constructed for a three-dimensional reconstructed exemplar TTC. The model exhibited spike initiation in the axon and reproduced the characteristic features of individual spikes, as well as of the firing properties at the soma, as recorded in a population of TTCs in young Wistar rats. When using these model parameters over the population of 28 three-dimensional reconstructed TTCs, both axonal and somatic ion channel densities had to be scaled linearly with the conductance load imposed on each of these compartments. Otherwise, the firing of model cells deviated, sometimes very significantly, from the experimental variability of the TTC e-class. The study provides experimentally testable predictions regarding the coregulation of axosomatic membrane ion channels density for cells with different dendritic conductance load, together with a simple and systematic method for generating reliable conductance-based models for the whole population of modeled neurons belonging to a particular e-class, with variable morphology as found experimentally.