An Adaptive Generalized Leaky Integrate-and-Fire Model for Hippocampal CA1 Pyramidal Neurons and Interneurons.

Full-scale morphologically and biophysically realistic model networks, aiming at modeling multiple brain areas, provide an invaluable tool to make significant scientific advances from in-silico experiments on cognitive functions to digital twin implementations. Due to the current technical limitations of supercomputer systems in terms of computational power and memory requirements, these networks must be implemented using (at least) simplified neurons. A class of models which achieve a reasonable compromise between accuracy and computational efficiency is given by generalized leaky integrate-and fire models complemented by suitable initial and update conditions. However, we found that these models cannot reproduce the complex and highly variable firing dynamics exhibited by neurons in several brain regions, such as the hippocampus. In this work, we propose an adaptive generalized leaky integrate-and-fire model for hippocampal CA1 neurons and interneurons, in which the nonlinear nature of the firing dynamics is successfully reproduced by linear ordinary differential equations equipped with nonlinear and more realistic initial and update conditions after each spike event, which strictly depends on the external stimulation current. A mathematical analysis of the equilibria stability as well as the monotonicity properties of the analytical solution for the membrane potential allowed (i) to determine general constraints on model parameters, reducing the computational cost of an optimization procedure based on spike times in response to a set of constant currents injections; (ii) to identify additional constraints to quantitatively reproduce and predict the experimental traces from 85 neurons and interneurons in response to any stimulation protocol using constant and piecewise constant current injections. Finally, this approach allows to easily implement a procedure to create infinite copies of neurons with mathematically controlled firing properties, statistically indistinguishable from experiments, to better reproduce the full range and variability of the firing scenarios observed in a real network.

Full-scale scaffold model of the human hippocampus CA1 area.

The increasing availability of quantitative data on the human brain is opening new avenues to study neural function and dysfunction, thus bringing us closer and closer to the implementation of digital twin applications for personalized medicine. Here we provide a resource to the neuroscience community: a computational method to generate full-scale scaffold model of human brain regions starting from microscopy images. We have benchmarked the method to reconstruct the CA1 region of a right human hippocampus, which accounts for about half of the entire right hippocampal formation. Together with 3D soma positioning we provide a connectivity matrix generated using a morpho-anatomical connection strategy based on axonal and dendritic probability density functions accounting for morphological properties of hippocampal neurons. The data and algorithms are supplied in a ready-to-use format, suited to implement computational models at different scales and detail.

A realistic morpho-anatomical connection strategy for modelling full-scale point-neuron microcircuits.

The modeling of extended microcircuits is emerging as an effective tool to simulate the neurophysiological correlates of brain activity and to investigate brain dysfunctions. However, for specific networks, a realistic modeling approach based on the combination of available physiological, morphological and anatomical data is still an open issue. One of the main problems in the generation of realistic networks lies in the strategy adopted to build network connectivity. Here we propose a method to implement a neuronal network at single cell resolution by using the geometrical probability volumes associated with pre- and postsynaptic neurites. This allows us to build a network with plausible connectivity properties without the explicit use of computationally intensive touch detection algorithms using full 3D neuron reconstructions. The method has been benchmarked for the mouse hippocampus CA1 area, and the results show that this approach is able to generate full-scale brain networks at single cell resolution that are in good agreement with experimental findings. This geometric reconstruction of axonal and dendritic occupancy, by effectively reflecting morphological and anatomical constraints, could be integrated into structured simulators generating entire circuits of different brain areas facilitating the simulation of different brain regions with realistic models.

Supervised training of spiking neural networks for robust deployment on mixed-signal neuromorphic processors.

Mixed-signal analog/digital circuits emulate spiking neurons and synapses with extremely high energy efficiency, an approach known as "neuromorphic engineering". However, analog circuits are sensitive to process-induced variation among transistors in a chip ("device mismatch"). For neuromorphic implementation of Spiking Neural Networks (SNNs), mismatch causes parameter variation between identically-configured neurons and synapses. Each chip exhibits a different distribution of neural parameters, causing deployed networks to respond differently between chips. Current solutions to mitigate mismatch based on per-chip calibration or on-chip learning entail increased design complexity, area and cost, making deployment of neuromorphic devices expensive and difficult. Here we present a supervised learning approach that produces SNNs with high robustness to mismatch and other common sources of noise. Our method trains SNNs to perform temporal classification tasks by mimicking a pre-trained dynamical system, using a local learning rule from non-linear control theory. We demonstrate our method on two tasks requiring temporal memory, and measure the robustness of our approach to several forms of noise and mismatch. We show that our approach is more robust than common alternatives for training SNNs. Our method provides robust deployment of pre-trained networks on mixed-signal neuromorphic hardware, without requiring per-device training or calibration.

A Spike-Based Neuromorphic Architecture of Stereo Vision.

The problem of finding stereo correspondences in binocular vision is solved effortlessly in nature and yet it is still a critical bottleneck for artificial machine vision systems. As temporal information is a crucial feature in this process, the advent of event-based vision sensors and dedicated event-based processors promises to offer an effective approach to solving the stereo matching problem. Indeed, event-based neuromorphic hardware provides an optimal substrate for fast, asynchronous computation, that can make explicit use of precise temporal coincidences. However, although several biologically-inspired solutions have already been proposed, the performance benefits of combining event-based sensing with asynchronous and parallel computation are yet to be explored. Here we present a hardware spike-based stereo-vision system that leverages the advantages of brain-inspired neuromorphic computing by interfacing two event-based vision sensors to an event-based mixed-signal analog/digital neuromorphic processor. We describe a prototype interface designed to enable the emulation of a stereo-vision system on neuromorphic hardware and we quantify the stereo matching performance with two datasets. Our results provide a path toward the realization of low-latency, end-to-end event-based, neuromorphic architectures for stereo vision.

Ionic Mechanisms of Impulse Propagation Failure in the FHF2-Deficient Heart.

RATIONALE: FHFs (fibroblast growth factor homologous factors) are key regulators of sodium channel (NaV) inactivation. Mutations in these critical proteins have been implicated in human diseases including Brugada syndrome, idiopathic ventricular arrhythmias, and epileptic encephalopathy. The underlying ionic mechanisms by which reduced Nav availability in Fhf2 knockout (Fhf2KO) mice predisposes to abnormal excitability at the tissue level are not well defined. OBJECTIVE: Using animal models and theoretical multicellular linear strands, we examined how FHF2 orchestrates the interdependency of sodium, calcium, and gap junctional conductances to safeguard cardiac conduction. METHODS AND RESULTS: Fhf2KO mice were challenged by reducing calcium conductance (gCaV) using verapamil or by reducing gap junctional conductance (Gj) using carbenoxolone or by backcrossing into a cardiomyocyte-specific Cx43 (connexin 43) heterozygous background. All conditions produced conduction block in Fhf2KO mice, with Fhf2 wild-type (Fhf2WT) mice showing normal impulse propagation. To explore the ionic mechanisms of block in Fhf2KO hearts, multicellular linear strand models incorporating FHF2-deficient Nav inactivation properties were constructed and faithfully recapitulated conduction abnormalities seen in mutant hearts. The mechanisms of conduction block in mutant strands with reduced gCaV or diminished Gj are very different. Enhanced Nav inactivation due to FHF2 deficiency shifts dependence onto calcium current (ICa) to sustain electrotonic driving force, axial current flow, and action potential (AP) generation from cell-to-cell. In the setting of diminished Gj, slower charging time from upstream cells conspires with accelerated Nav inactivation in mutant strands to prevent sufficient downstream cell charging for AP propagation. CONCLUSIONS: FHF2-dependent effects on Nav inactivation ensure adequate sodium current (INa) reserve to safeguard against numerous threats to reliable cardiac impulse propagation.

Open Source Brain: A Collaborative Resource for Visualizing, Analyzing, Simulating, and Developing Standardized Models of Neurons and Circuits.

Computational models are powerful tools for exploring the properties of complex biological systems. In neuroscience, data-driven models of neural circuits that span multiple scales are increasingly being used to understand brain function in health and disease. But their adoption and reuse has been limited by the specialist knowledge required to evaluate and use them. To address this, we have developed Open Source Brain, a platform for sharing, viewing, analyzing, and simulating standardized models from different brain regions and species. Model structure and parameters can be automatically visualized and their dynamical properties explored through browser-based simulations. Infrastructure and tools for collaborative interaction, development, and testing are also provided. We demonstrate how existing components can be reused by constructing new models of inhibition-stabilized cortical networks that match recent experimental results. These features of Open Source Brain improve the accessibility, transparency, and reproducibility of models and facilitate their reuse by the wider community.

A kinetic model for Brain-Derived Neurotrophic Factor mediated spike timing-dependent LTP.

Across the mammalian nervous system, neurotrophins control synaptic plasticity, neuromodulation, and neuronal growth. The neurotrophin Brain-Derived Neurotrophic Factor (BDNF) is known to promote structural and functional synaptic plasticity in the hippocampus, the cerebral cortex, and many other brain areas. In recent years, a wealth of data has been accumulated revealing the paramount importance of BDNF for neuronal function. BDNF signaling gives rise to multiple complex signaling pathways that mediate neuronal survival and differentiation during development, and formation of new memories. These different roles of BDNF for neuronal function have essential consequences if BDNF signaling in the brain is reduced. Thus, BDNF knock-out mice or mice that are deficient in BDNF receptor signaling via TrkB and p75 receptors show deficits in neuronal development, synaptic plasticity, and memory formation. Accordingly, BDNF signaling dysfunctions are associated with many neurological and neurodegenerative conditions including Alzheimer's and Huntington's disease. However, despite the widespread implications of BDNF-dependent signaling in synaptic plasticity in healthy and pathological conditions, the interplay of the involved different biochemical pathways at the synaptic level remained mostly unknown. In this paper, we investigated the role of BDNF/TrkB signaling in spike-timing dependent plasticity (STDP) in rodent hippocampus CA1 pyramidal cells, by implementing the first subcellular model of BDNF regulated, spike timing-dependent long-term potentiation (t-LTP). The model is based on previously published experimental findings on STDP and accounts for the observed magnitude, time course, stimulation pattern and BDNF-dependence of t-LTP. It allows interpreting the main experimental findings concerning specific biomolecular processes, and it can be expanded to take into account more detailed biochemical reactions. The results point out a few predictions on how to enhance LTP induction in such a way to rescue or improve cognitive functions under pathological conditions.

Fhf2 gene deletion causes temperature-sensitive cardiac conduction failure.

Fever is a highly conserved systemic response to infection dating back over 600 million years. Although conferring a survival benefit, fever can negatively impact the function of excitable tissues, such as the heart, producing cardiac arrhythmias. Here we show that mice lacking fibroblast growth factor homologous factor 2 (FHF2) have normal cardiac rhythm at baseline, but increasing core body temperature by as little as 3 °C causes coved-type ST elevations and progressive conduction failure that is fully reversible upon return to normothermia. FHF2-deficient cardiomyocytes generate action potentials upon current injection at 25 °C but are unexcitable at 40 °C. The absence of FHF2 accelerates the rate of closed-state and open-state sodium channel inactivation, which synergizes with temperature-dependent enhancement of inactivation rate to severely suppress cardiac sodium currents at elevated temperatures. Our experimental and computational results identify an essential role for FHF2 in dictating myocardial excitability and conduction that safeguards against temperature-sensitive conduction failure.

FHF-independent conduction of action potentials along the leak-resistant cerebellar granule cell axon.

Neurons in vertebrate central nervous systems initiate and conduct sodium action potentials in distinct subcellular compartments that differ architecturally and electrically. Here, we report several unanticipated passive and active properties of the cerebellar granule cell's unmyelinated axon. Whereas spike initiation at the axon initial segment relies on sodium channel (Nav)-associated fibroblast growth factor homologous factor (FHF) proteins to delay Nav inactivation, distal axonal Navs show little FHF association or FHF requirement for high-frequency transmission, velocity and waveforms of conducting action potentials. In addition, leak conductance density along the distal axon is estimated as <1% that of somatodendritic membrane. The faster inactivation rate of FHF-free Navs together with very low axonal leak conductance serves to minimize ionic fluxes and energetic demand during repetitive spike conduction and at rest. The absence of FHFs from Navs at nodes of Ranvier in the central nervous system suggests a similar mechanism of current flux minimization along myelinated axons.

A Hybrid Model for the Computationally-Efficient Simulation of the Cerebellar Granular Layer.

The aim of the present paper is to efficiently describe the membrane potential dynamics of neural populations formed by species having a high density difference in specific brain areas. We propose a hybrid model whose main ingredients are a conductance-based model (ODE system) and its continuous counterpart (PDE system) obtained through a limit process in which the number of neurons confined in a bounded region of the brain tissue is sent to infinity. Specifically, in the discrete model, each cell is described by a set of time-dependent variables, whereas in the continuum model, cells are grouped into populations that are described by a set of continuous variables. Communications between populations, which translate into interactions among the discrete and the continuous models, are the essence of the hybrid model we present here. The cerebellum and cerebellum-like structures show in their granular layer a large difference in the relative density of neuronal species making them a natural testing ground for our hybrid model. By reconstructing the ensemble activity of the cerebellar granular layer network and by comparing our results to a more realistic computational network, we demonstrate that our description of the network activity, even though it is not biophysically detailed, is still capable of reproducing salient features of neural network dynamics. Our modeling approach yields a significant computational cost reduction by increasing the simulation speed at least 270 times. The hybrid model reproduces interesting dynamics such as local microcircuit synchronization, traveling waves, center-surround, and time-windowing.

Corrigendum: Integration and regulation of glomerular inhibition in the cerebellar granular layer circuit.

[This corrects the article on p. 55 in vol. 8, PMID: 24616663.].

Action potential processing in a detailed Purkinje cell model reveals a critical role for axonal compartmentalization.

The Purkinje cell (PC) is among the most complex neurons in the brain and plays a critical role for cerebellar functioning. PCs operate as fast pacemakers modulated by synaptic inputs but can switch from simple spikes to complex bursts and, in some conditions, show bistability. In contrast to original works emphasizing dendritic Ca-dependent mechanisms, recent experiments have supported a primary role for axonal Na-dependent processing, which could effectively regulate spike generation and transmission to deep cerebellar nuclei (DCN). In order to account for the numerous ionic mechanisms involved (at present including Nav1.6, Cav2.1, Cav3.1, Cav3.2, Cav3.3, Kv1.1, Kv1.5, Kv3.3, Kv3.4, Kv4.3, KCa1.1, KCa2.2, KCa3.1, Kir2.x, HCN1), we have elaborated a multicompartmental model incorporating available knowledge on localization and gating of PC ionic channels. The axon, including initial segment (AIS) and Ranvier nodes (RNs), proved critical to obtain appropriate pacemaking and firing frequency modulation. Simple spikes initiated in the AIS and protracted discharges were stabilized in the soma through Na-dependent mechanisms, while somato-dendritic Ca channels contributed to sustain pacemaking and to generate complex bursting at high discharge regimes. Bistability occurred only following Na and Ca channel down-regulation. In addition, specific properties in RNs K currents were required to limit spike transmission frequency along the axon. The model showed how organized electroresponsive functions could emerge from the molecular complexity of PCs and showed that the axon is fundamental to complement ionic channel compartmentalization enabling action potential processing and transmission of specific spike patterns to DCN.

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.

Computational modeling predicts the ionic mechanism of late-onset responses in unipolar brush cells.

Unipolar Brush Cells (UBCs) have been suggested to play a critical role in cerebellar functioning, yet the corresponding cellular mechanisms remain poorly understood. UBCs have recently been reported to generate, in addition to early-onset glutamate receptor-dependent synaptic responses, a late-onset response (LOR) composed of a slow depolarizing ramp followed by a spike burst (Locatelli et al., 2013). The LOR activates as a consequence of synaptic activity and involves an intracellular cascade modulating H- and TRP-current gating. In order to assess the LOR mechanisms, we have developed a UBC multi-compartmental model (including soma, dendrite, initial segment, and axon) incorporating biologically realistic representations of ionic currents and a cytoplasmic coupling mechanism regulating TRP and H channel gating. The model finely reproduced UBC responses to current injection, including a burst triggered by a low-threshold spike (LTS) sustained by CaLVA currents, a persistent discharge sustained by CaHVA currents, and a rebound burst following hyperpolarization sustained by H- and CaLVA-currents. Moreover, the model predicted that H- and TRP-current regulation was necessary and sufficient to generate the LOR and its dependence on the intensity and duration of mossy fiber activity. Therefore, the model showed that, using a basic set of ionic channels, UBCs generate a rich repertoire of bursts, which could effectively implement tunable delay-lines in the local microcircuit.

Integration and regulation of glomerular inhibition in the cerebellar granular layer circuit.

Inhibitory synapses can be organized in different ways and be regulated by a multitude of mechanisms. One of the best known examples is provided by the inhibitory synapses formed by Golgi cells onto granule cells in the cerebellar glomeruli. These synapses are GABAergic and inhibit granule cells through two main mechanisms, phasic and tonic. The former is based on vesicular neurotransmitter release, the latter on the establishment of tonic γ-aminobutyric acid (GABA) levels determined by spillover and regulation of GABA uptake. The mechanisms of post-synaptic integration have been clarified to a considerable extent and have been shown to differentially involve α1 and α6 subunit-containing GABA-A receptors. Here, after reviewing the basic mechanisms of GABAergic transmission in the cerebellar glomeruli, we examine how inhibition controls signal transfer at the mossy fiber-granule cell relay. First of all, we consider how vesicular release impacts on signal timing and how tonic GABA levels control neurotransmission gain. Then, we analyze the integration of these inhibitory mechanisms within the granular layer network. Interestingly, it turns out that glomerular inhibition is just one element in a large integrated signaling system controlled at various levels by metabotropic receptors. GABA-B receptor activation by ambient GABA regulates glutamate release from mossy fibers through a pre-synaptic cross-talk mechanisms, GABA release through pre-synaptic auto-receptors, and granule cell input resistance through post-synaptic receptor activation and inhibition of a K inward-rectifier current. Metabotropic glutamate receptors (mGluRs) control GABA release from Golgi cell terminals and Golgi cell input resistance and autorhythmic firing. This complex set of mechanisms implements both homeostatic and winner-take-all processes, providing the basis for fine-tuning inhibitory neurotransmission and for optimizing signal transfer through the cerebellar cortex.

Realistic modeling of neurons and networks: towards brain simulation.

Realistic modeling is a new advanced methodology for investigating brain functions. Realistic modeling is based on a detailed biophysical description of neurons and synapses, which can be integrated into microcircuits. The latter can, in turn, be further integrated to form large-scale brain networks and eventually to reconstruct complex brain systems. Here we provide a review of the realistic simulation strategy and use the cerebellar network as an example. This network has been carefully investigated at molecular and cellular level and has been the object of intense theoretical investigation. The cerebellum is thought to lie at the core of the forward controller operations of the brain and to implement timing and sensory prediction functions. The cerebellum is well described and provides a challenging field in which one of the most advanced realistic microcircuit models has been generated. We illustrate how these models can be elaborated and embedded into robotic control systems to gain insight into how the cellular properties of cerebellar neurons emerge in integrated behaviors. Realistic network modeling opens up new perspectives for the investigation of brain pathologies and for the neurorobotic field.

The cerebellar Golgi cell and spatiotemporal organization of granular layer activity.

The cerebellar granular layer has been suggested to perform a complex spatiotemporal reconfiguration of incoming mossy fiber signals. Central to this role is the inhibitory action exerted by Golgi cells over granule cells: Golgi cells inhibit granule cells through both feedforward and feedback inhibitory loops and generate a broad lateral inhibition that extends beyond the afferent synaptic field. This characteristic connectivity has recently been investigated in great detail and been correlated with specific functional properties of these neurons. These include theta-frequency pacemaking, network entrainment into coherent oscillations and phase resetting. Important advances have also been made in terms of determining the membrane and synaptic properties of the neuron, and clarifying the mechanisms of activation by input bursts. Moreover, voltage sensitive dye imaging and multi-electrode array (MEA) recordings, combined with mathematical simulations based on realistic computational models, have improved our understanding of the impact of Golgi cell activity on granular layer circuit computations. These investigations have highlighted the critical role of Golgi cells in: generating dense clusters of granule cell activity organized in center-surround structures, implementing combinatorial operations on multiple mossy fiber inputs, regulating transmission gain, and cut-off frequency, controlling spike timing and burst transmission, and determining the sign, intensity and duration of long-term synaptic plasticity at the mossy fiber-granule cell relay. This review considers recent advances in the field, highlighting the functional implications of Golgi cells for granular layer network computation and indicating new challenges for cerebellar research.

θ-Frequency resonance at the cerebellum input stage improves spike timing on the millisecond time-scale.

The neuronal circuits of the brain are thought to use resonance and oscillations to improve communication over specific frequency bands (Llinas, 1988; Buzsaki, 2006). However, the properties and mechanism of these phenomena in brain circuits remain largely unknown. Here we show that, at the cerebellum input stage, the granular layer (GRL) generates its maximum response at 5-7 Hz both in vivo following tactile sensory stimulation of the whisker pad and in acute slices following mossy fiber bundle stimulation. The spatial analysis of GRL activity performed using voltage-sensitive dye (VSD) imaging revealed 5-7 Hz resonance covering large GRL areas. In single granule cells, resonance appeared as a reorganization of output spike bursts on the millisecond time-scale, such that the first spike occurred earlier and with higher temporal precision and the probability of spike generation increased. Resonance was independent from circuit inhibition, as it persisted with little variation in the presence of the GABAA receptor blocker, gabazine. However, circuit inhibition reduced the resonance area more markedly at 7 Hz. Simulations with detailed computational models suggested that resonance depended on intrinsic granule cells ionic mechanisms: specifically, K slow (M-like) and KA currents acted as resonators and the persistent Na current and NMDA current acted as amplifiers. This form of resonance may play an important role for enhancing coherent spike emission from the GRL when theta-frequency bursts are transmitted by the cerebral cortex and peripheral sensory structures during sensory-motor processing, cognition, and learning.