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.

A calcium-based plasticity model for predicting long-term potentiation and depression in the neocortex.

Pyramidal cells (PCs) form the backbone of the layered structure of the neocortex, and plasticity of their synapses is thought to underlie learning in the brain. However, such long-term synaptic changes have been experimentally characterized between only a few types of PCs, posing a significant barrier for studying neocortical learning mechanisms. Here we introduce a model of synaptic plasticity based on data-constrained postsynaptic calcium dynamics, and show in a neocortical microcircuit model that a single parameter set is sufficient to unify the available experimental findings on long-term potentiation (LTP) and long-term depression (LTD) of PC connections. In particular, we find that the diverse plasticity outcomes across the different PC types can be explained by cell-type-specific synaptic physiology, cell morphology and innervation patterns, without requiring type-specific plasticity. Generalizing the model to in vivo extracellular calcium concentrations, we predict qualitatively different plasticity dynamics from those observed in vitro. This work provides a first comprehensive null model for LTP/LTD between neocortical PC types in vivo, and an open framework for further developing models of cortical synaptic plasticity.

HippoUnit: A software tool for the automated testing and systematic comparison of detailed models of hippocampal neurons based on electrophysiological data.

Anatomically and biophysically detailed data-driven neuronal models have become widely used tools for understanding and predicting the behavior and function of neurons. Due to the increasing availability of experimental data from anatomical and electrophysiological measurements as well as the growing number of computational and software tools that enable accurate neuronal modeling, there are now a large number of different models of many cell types available in the literature. These models were usually built to capture a few important or interesting properties of the given neuron type, and it is often unknown how they would behave outside their original context. In addition, there is currently no simple way of quantitatively comparing different models regarding how closely they match specific experimental observations. This limits the evaluation, re-use and further development of the existing models. Further, the development of new models could also be significantly facilitated by the ability to rapidly test the behavior of model candidates against the relevant collection of experimental data. We address these problems for the representative case of the CA1 pyramidal cell of the rat hippocampus by developing an open-source Python test suite, which makes it possible to automatically and systematically test multiple properties of models by making quantitative comparisons between the models and electrophysiological data. The tests cover various aspects of somatic behavior, and signal propagation and integration in apical dendrites. To demonstrate the utility of our approach, we applied our tests to compare the behavior of several different rat hippocampal CA1 pyramidal cell models from the ModelDB database against electrophysiological data available in the literature, and evaluated how well these models match experimental observations in different domains. We also show how we employed the test suite to aid the development of models within the European Human Brain Project (HBP), and describe the integration of the tests into the validation framework developed in the HBP, with the aim of facilitating more reproducible and transparent model building in the neuroscience community.

GABA-mediated tonic inhibition differentially modulates gain in functional subtypes of cortical interneurons.

The binding of GABA (γ-aminobutyric acid) to extrasynaptic GABAA receptors generates tonic inhibition that acts as a powerful modulator of cortical network activity. Despite GABA being present throughout the extracellular space of the brain, previous work has shown that GABA may differentially modulate the excitability of neuron subtypes according to variation in chloride gradient. Here, using biophysically detailed neuron models, we predict that tonic inhibition can differentially modulate the excitability of neuron subtypes according to variation in electrophysiological properties. Surprisingly, tonic inhibition increased the responsiveness (or gain) in models with features typical for somatostatin interneurons but decreased gain in models with features typical for parvalbumin interneurons. Patch-clamp recordings from cortical interneurons supported these predictions, and further in silico analysis was then performed to seek a putative mechanism underlying gain modulation. We found that gain modulation in models was dependent upon the magnitude of tonic current generated at depolarized membrane potential-a property associated with outward rectifying GABAA receptors. Furthermore, tonic inhibition produced two biophysical changes in models of relevance to neuronal excitability: 1) enhanced action potential repolarization via increased current flow into the dendritic compartment, and 2) reduced activation of voltage-dependent potassium channels. Finally, we show theoretically that reduced potassium channel activation selectively increases gain in models possessing action potential dynamics typical for somatostatin interneurons. Potassium channels in parvalbumin-type models deactivate rapidly and are unavailable for further modulation. These findings show that GABA can differentially modulate interneuron excitability and suggest a mechanism through which this occurs in silico via differences of intrinsic electrophysiological properties.

Experimentally-constrained biophysical models of tonic and burst firing modes in thalamocortical neurons.

Somatosensory thalamocortical (TC) neurons from the ventrobasal (VB) thalamus are central components in the flow of sensory information between the periphery and the cerebral cortex, and participate in the dynamic regulation of thalamocortical states including wakefulness and sleep. This property is reflected at the cellular level by the ability to generate action potentials in two distinct firing modes, called tonic firing and low-threshold bursting. Although the general properties of TC neurons are known, we still lack a detailed characterization of their morphological and electrical properties in the VB thalamus. The aim of this study was to build biophysically-detailed models of VB TC neurons explicitly constrained with experimental data from rats. We recorded the electrical activity of VB neurons (N = 49) and reconstructed morphologies in 3D (N = 50) by applying standardized protocols. After identifying distinct electrical types, we used a multi-objective optimization to fit single neuron electrical models (e-models), which yielded multiple solutions consistent with the experimental data. The models were tested for generalization using electrical stimuli and neuron morphologies not used during fitting. A local sensitivity analysis revealed that the e-models are robust to small parameter changes and that all the parameters were constrained by one or more features. The e-models, when tested in combination with different morphologies, showed that the electrical behavior is substantially preserved when changing dendritic structure and that the e-models were not overfit to a specific morphology. The models and their analysis show that automatic parameter search can be applied to capture complex firing behavior, such as co-existence of tonic firing and low-threshold bursting over a wide range of parameter sets and in combination with different neuron morphologies.

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.

BluePyOpt: Leveraging Open Source Software and Cloud Infrastructure to Optimise Model Parameters in Neuroscience.

At many scales in neuroscience, appropriate mathematical models take the form of complex dynamical systems. Parameterizing such models to conform to the multitude of available experimental constraints is a global non-linear optimisation problem with a complex fitness landscape, requiring numerical techniques to find suitable approximate solutions. Stochastic optimisation approaches, such as evolutionary algorithms, have been shown to be effective, but often the setting up of such optimisations and the choice of a specific search algorithm and its parameters is non-trivial, requiring domain-specific expertise. Here we describe BluePyOpt, a Python package targeted at the broad neuroscience community to simplify this task. BluePyOpt is an extensible framework for data-driven model parameter optimisation that wraps and standardizes several existing open-source tools. It simplifies the task of creating and sharing these optimisations, and the associated techniques and knowledge. This is achieved by abstracting the optimisation and evaluation tasks into various reusable and flexible discrete elements according to established best-practices. Further, BluePyOpt provides methods for setting up both small- and large-scale optimisations on a variety of platforms, ranging from laptops to Linux clusters and cloud-based compute infrastructures. The versatility of the BluePyOpt framework is demonstrated by working through three representative neuroscience specific use cases.

At the Edge of Chaos: How Cerebellar Granular Layer Network Dynamics Can Provide the Basis for Temporal Filters.

Models of the cerebellar microcircuit often assume that input signals from the mossy-fibers are expanded and recoded to provide a foundation from which the Purkinje cells can synthesize output filters to implement specific input-signal transformations. Details of this process are however unclear. While previous work has shown that recurrent granule cell inhibition could in principle generate a wide variety of random outputs suitable for coding signal onsets, the more general application for temporally varying signals has yet to be demonstrated. Here we show for the first time that using a mechanism very similar to reservoir computing enables random neuronal networks in the granule cell layer to provide the necessary signal separation and extension from which Purkinje cells could construct basis filters of various time-constants. The main requirement for this is that the network operates in a state of criticality close to the edge of random chaotic behavior. We further show that the lack of recurrent excitation in the granular layer as commonly required in traditional reservoir networks can be circumvented by considering other inherent granular layer features such as inverted input signals or mGluR2 inhibition of Golgi cells. Other properties that facilitate filter construction are direct mossy fiber excitation of Golgi cells, variability of synaptic weights or input signals and output-feedback via the nucleocortical pathway. Our findings are well supported by previous experimental and theoretical work and will help to bridge the gap between system-level models and detailed models of the granular layer network.

Model cerebellar granule cells can faithfully transmit modulated firing rate signals.

A crucial assumption of many high-level system models of the cerebellum is that information in the granular layer is encoded in a linear manner. However, granule cells are known for their non-linear and resonant synaptic and intrinsic properties that could potentially impede linear signal transmission. In this modeling study we analyse how electrophysiological granule cell properties and spike sampling influence information coded by firing rate modulation, assuming no signal-related, i.e., uncorrelated inhibitory feedback (open-loop mode). A detailed one-compartment granule cell model was excited in simulation by either direct current or mossy-fiber synaptic inputs. Vestibular signals were represented as tonic inputs to the flocculus modulated at frequencies up to 20 Hz (approximate upper frequency limit of vestibular-ocular reflex, VOR). Model outputs were assessed using estimates of both the transfer function, and the fidelity of input-signal reconstruction measured as variance-accounted-for. The detailed granule cell model with realistic mossy-fiber synaptic inputs could transmit information faithfully and linearly in the frequency range of the vestibular-ocular reflex. This was achieved most simply if the model neurons had a firing rate at least twice the highest required frequency of modulation, but lower rates were also adequate provided a population of neurons was utilized, especially in combination with push-pull coding. The exact number of neurons required for faithful transmission depended on the precise values of firing rate and noise. The model neurons were also able to combine excitatory and inhibitory signals linearly, and could be replaced by a simpler (modified) integrate-and-fire neuron in the case of high tonic firing rates. These findings suggest that granule cells can in principle code modulated firing-rate inputs in a linear manner, and are thus consistent with the high-level adaptive-filter model of the cerebellar microcircuit.

The role of regularity and synchrony of cerebellar Purkinje cells for pathological nystagmus.

Previous theories assumed that the beneficial effect of the potassium channel blocker 4-aminopyridine (4-AP) for patients suffering from downbeat nystagmus (DBN) or episodic ataxia type 2 (EA2) is due to an increase of excitability of cerebellar Purkinje cells (PC). Recent experimental results using therapeutic doses of 4-AP with a mouse model of EA2 challenged the theory showing that 4-AP does not change the firing rate of PC but their regularity. Based on a mathematical model of the ocular motor and cerebellar circuitry, we show that changes in regularity have no effect without synchrony in PC firing. Together with synchronous firing, an increase in regularity may lead to a decrease in overall inhibition and may invert the inhibitory to an excitatory response due to imprinting, a novel effect of synchronized neural inhibition. Both effects are unlikely to be the causative mechanism for the success of 4-AP in treating cerebellar disorders.

Cellular and network contributions to vestibular signal processing: impact of ion conductances, synaptic inhibition, and noise.

Head motion-related sensory signals are transformed by second-order vestibular neurons (2°VNs) into appropriate commands for retinal image stabilization during body motion. In frogs, these 2°VNs form two distinct subpopulations that have either tonic or highly phasic intrinsic properties, essentially compatible with low-pass and bandpass filter characteristics, respectively. In the present study, physiological data on cellular properties of 2°VNs of the grass frog (Rana temporaria) have been used to construct conductance-based spiking cellular models that were fine-tuned by fitting to recorded spike-frequency data. The results of this approach suggest that low-threshold, voltage-dependent potassium channels in phasic and spike-dependent potassium channels in tonic 2°VNs are important contributors to the differential, yet complementary response characteristics of the two vestibular subtypes. Extension of the cellular model with conductance-based synapses allowed simulation of afferent excitation and evaluation of the emerging properties of local feedforward inhibitory circuits. This approach revealed the relative contributions of intrinsic and synaptic factors on afferent signal processing in phasic 2°VNs. Additional extension of the single-cell model to a population model allowed testing under more natural conditions including asynchronous afferent labyrinthine input and synaptic noise. This latter approach indicated that the feedforward inhibition from the local inhibitory network acts as a high-pass filter, which reinforces the impact of the intrinsic membrane properties of phasic 2°VNs on peak response amplitude and timing. Thus, the combination of cellular and network properties enables phasic 2°VNs to work as a noise-resistant detector, suitable for central processing of short-duration vestibular signals.

Functional organization of vestibular commissural connections in frog.

Central vestibular neurons receive substantial inputs from the contralateral labyrinth through inhibitory and excitatory brainstem commissural pathways. The functional organization of these pathways was studied by a multi-methodological approach in isolated frog whole brains. Retrogradely labeled vestibular commissural neurons were primarily located in the superior vestibular nucleus in rhombomeres 2/3 and the medial and descending vestibular nucleus in rhombomeres 5-7. Restricted projections to contralateral vestibular areas, without collaterals to other classical vestibular targets, indicate that vestibular commissural neurons form a feedforward push-pull circuitry. Electrical stimulation of the contralateral coplanar semicircular canal nerve evoked in canal-related second-order vestibular neurons (2 degrees VN) commissural IPSPs (approximately 70%) and EPSPs (approximately 30%) with mainly (approximately 70%) disynaptic onset latencies. The dynamics of commissural responses to electrical pulse trains suggests mediation predominantly by tonic vestibular neurons that activate in all tonic 2 degrees VN large-amplitude IPSPs with a reversal potential of -74 mV. In contrast, phasic 2 degrees VN exhibited either nonreversible, small-amplitude IPSPs (approximately 40%) of likely dendritic origin or large-amplitude commissural EPSPs (approximately 60%). IPSPs with disynaptic onset latencies were exclusively GABAergic (mainly GABA(A) receptor-mediated) but not glycinergic, compatible with the presence of GABA-immunopositive (approximately 20%) and the absence of glycine-immunopositive vestibular commissural neurons. In contrast, IPSPs with longer, oligosynaptic onset latencies were GABAergic and glycinergic, indicating that both pharmacological types of local inhibitory neurons were activated by excitatory commissural fibers. Conservation of major morpho-physiological and pharmacological features of the vestibular commissural pathway suggests that this phylogenetically old circuitry plays an essential role for the processing of bilateral angular head acceleration signals in vertebrates.

Modeling of intrinsic and synaptic properties to reveal the cellular and network contribution for vestibular signal processing.

Computational modeling of cellular and network properties of central vestibular neurons is necessary for understanding the mechanisms of sensory-motor transformation for gaze stabilization. As a first step to mathematically describe vestibular signal processing, the available physiological data of the synaptic and intrinsic properties of frog second-order vestibular neurons (2 degrees VN) were used to create a model that combines cellular and network parameters. With this approach it is now possible to reveal the particular contributions of intrinsic membrane versus emerging network properties in shaping labyrinthine afferent-evoked synaptic responses in 2 degrees VN, to simulate perturbations, and to generate hypotheses that are testable in empiric experiments.

Frequency-Domain Analysis of Intrinsic Neuronal Properties using High-Resistant Electrodes.

Intrinsic cellular properties of neurons in culture or slices are usually studied by the whole cell clamp method using low-resistant patch pipettes. These electrodes allow detailed analyses with standard electrophysiological methods such as current- or voltage-clamp. However, in these preparations large parts of the network and dendritic structures may be removed, thus preventing an adequate study of synaptic signal processing. Therefore, intact in vivo preparations or isolated in vitro whole brains have been used in which intracellular recordings are usually made with sharp, high-resistant electrodes to optimize the impalement of neurons. The general non-linear resistance properties of these electrodes, however, severely limit accurate quantitative studies of membrane dynamics especially needed for precise modelling. Therefore, we have developed a frequency-domain analysis of membrane properties that uses a Piece-wise Non-linear Electrode Compensation (PNEC) method. The technique was tested in second-order vestibular neurons and abducens motoneurons of isolated frog whole brain preparations using sharp potassium chloride- or potassium acetate-filled electrodes. All recordings were performed without online electrode compensation. The properties of each electrode were determined separately after the neuronal recordings and were used in the frequency-domain analysis of the combined measurement of electrode and cell. This allowed detailed analysis of membrane properties in the frequency-domain with high-resistant electrodes and provided quantitative data that can be further used to model channel kinetics. Thus, sharp electrodes can be used for the characterization of intrinsic properties and synaptic inputs of neurons in intact brains.

Differential dynamic processing of afferent signals in frog tonic and phasic second-order vestibular neurons.

The sensory-motor transformation of the large dynamic spectrum of head-motion-related signals occurs in separate vestibulo-ocular pathways. Synaptic responses of tonic and phasic second-order vestibular neurons were recorded in isolated frog brains after stimulation of individual labyrinthine nerve branches with trains of single electrical pulses. The timing of the single pulses was adapted from spike discharge patterns of frog semicircular canal nerve afferents during sinusoidal head rotation. Because each electrical pulse evoked a single spike in afferent fibers, the resulting sequences with sinusoidally modulated intervals and peak frequencies up to 100 Hz allowed studying the processing of presynaptic afferent inputs with in vivo characteristics in second-order vestibular neurons recorded in vitro in an isolated whole brain. Variation of pulse-train parameters showed that the postsynaptic compound response dynamics differ in the two types of frog vestibular neurons. In tonic neurons, subthreshold compound responses and evoked discharge patterns exhibited relatively linear dynamics and were generally aligned with pulse frequency modulation. In contrast, compound responses of phasic neurons were asymmetric with large leads of subthreshold response peaks and evoked spike discharge relative to stimulus waveform. These nonlinearities were caused by the particular intrinsic properties of phasic vestibular neurons and were facilitated by GABAergic and glycinergic inhibitory inputs from tonic type vestibular interneurons and by cerebellar circuits. Coadapted intrinsic filter and emerging network properties thus form dynamically different neuronal elements that provide the appropriate cellular basis for a parallel processing of linear, tonic, and nonlinear phasic vestibulo-ocular response components in central vestibular neurons.

Modelling drug modulation of nystagmus.

A better understanding of the neural and functional mechanisms underlying drug-induced changes in pathological nystagmus is likely to improve medical treatment. A treatment option for downbeat nystagmus (DBN), a common form of acquired fixation nystagmus that often occurs with cerebellar degeneration, is low doses of the potassium channel blocker 4-aminopyridine (4-AP). The upward ocular drift in DBN has a spontaneous and a vertical gaze-evoked component. Detailed analysis of the effect of 4-AP in patients showed that the drug consistently improved the gaze-evoked component, but had less effect in reducing the spontaneous drift. We show by a combination of computational modelling at the systems level and at the neuronal level how this differential effect can be investigated. We have previously postulated that DBN is caused by damage to the floccular lobe (FL). 4-AP, which has been shown to increase the excitability of Purkinje cells (PCs) in slice experiments, may thus suppress DBN by partly restoring floccular function. We simulated the effect of low concentrations of 4-AP on the cellular level using a multicompartment model of a PC, in which we changed ion channel properties to simulate damage. The transition from the cellular level to the systems level was achieved by constructing a population response. Systems level modelling predicted that the effect of 4-AP on the PCs should reduce DBN, but the predicted effect on the gaze-dependent component was less than is observed in patients. Our results suggest that the beneficial effect of 4-AP on DBN cannot be solely explained by its effect at the neuronal level of PCs, and suggests added effects at the level of the population of neurons.