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To overcome some limits of classical neuronal models, we propose a Markovian generalization of the classical model based on Jacobi processes by introducing downwards jumps to describe the activity of a single neuron. The statistical analysis of interspike intervals is performed by studying the first passage times of the proposed Markovian Jacobi process with jumps through a constant boundary. In particular, we characterize its Laplace transform, which is expressed in terms of some generalization of hypergeometric functions that we introduce, and deduce a closed-form expression for its expectation. Our approach, which is original in the context of first-passage-time problems, relies on intertwining relations between the semigroups of the classical Jacobi process and its generalization, which have been recently established in [P. Cheridito et al., J. Ec. Polytech. - Math., 8 (2021), pp. 331--378]. A numerical investigation of the firing rate of the considered neuron is performed for some choices of the involved parameters and of the jump distributions. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Interfacing with alpha-motoneurons (MNs) is key to understand and control motor impairment and neurorehabilitation technologies. Depending on the neurophysiological condition of each individual, MN pools exhibit distinct neuro-anatomical properties and firing behaviors. Hence, the ability to assess subject-specific characteristics of MN pools is essential for unravelling the neural mechanisms and adaptations underlying motor control, both in healthy and impaired individuals. However, measuring in vivo the properties of complete human MN pools remains an open challenge. Therefore, this work proposes a novel approach based on decoding neural discharges from human MNs in vivo for driving the metaheuristic optimization of biophysically realistic MN models. First, we show that this framework provides subject-specific estimates of MN pool properties from the tibialis anterior muscle on five healthy individuals. Second, we propose a methodology to create complete pools of in silico MNs for each subject. Lastly, we show that neural-data driven complete in silico MN pools reproduce in vivo MN firing characteristics and muscle activation profiles during force-tracking tasks involving isometric ankle dorsi-flexion, at different levels of amplitude. This approach can open new avenues for understanding human neuro-mechanics and, particularly, MN pool dynamics, in a person-specific way. Thereby enabling the development of personalized neurorehabilitation and motor restoring technologies.

Interfacing with alpha-motoneurons (MNs) is key to understand and control motor impairment and neurorehabilitation technologies. Depending on the neurophysiological condition of each individual, MN pools exhibit distinct neuro-anatomical properties and firing behaviors. Hence, the ability to assess subject-specific characteristics of MN pools is essential for unravelling the neural mechanisms and adaptations underlying motor control, both in healthy and impaired individuals. However, measuring in vivo the properties of complete human MN pools remains an open challenge. Therefore, this work proposes a novel approach based on decoding neural discharges from human MNs in vivo for driving the metaheuristic optimization of biophysically realistic MN models. First, we show that this framework provides subject-specific estimates of MN pool properties from the tibialis anterior muscle on five healthy individuals. Second, we propose a methodology to create complete pools of in silico MNs for each subject. Lastly, we show that neural-data driven complete in silico MN pools reproduce in vivo MN firing characteristics and muscle activation profiles during force-tracking tasks involving isometric ankle dorsi-flexion, at different levels of amplitude. This approach can open new avenues for understanding human neuro-mechanics and, particularly, MN pool dynamics, in a person-specific way. Thereby enabling the development of personalized neurorehabilitation and motor restoring technologies. [ABSTRACT FROM AUTHOR]

Neuromorphic systems aim to provide accelerated low-power simulation of Spiking Neural Networks (SNNs), typically featuring simple and efficient neuron models such as the Leaky Integrate-and-Fire (LIF) model. Biologically plausible neuron models developed by neuroscientists are largely ignored in neuromorphic computing due to their increased computational costs. This work bridges this gap through implementation and evaluation of a single compartment Hodgkin-Huxley (HH) neuron and a multi-compartment neuron incorporating dendritic computation on the SpiNNaker, and SpiNNaker2 prototype neuromorphic systems. Numerical accuracy of the model implementations is benchmarked against reference models in the NEURON simulation environment, with excellent agreement achieved by both the fixed- and floating-point SpiNNaker implementations. The computational cost is evaluated in terms of timing measurements profiling neural state updates. While the additional model complexity understandably increases computation times relative to LIF models, it was found a wallclock time increase of only 8x was observed for the HH neuron (11x for the mutlicompartment model), demonstrating the potential of hardware accelerators in the next-generation neuromorphic system to optimize implementation of complex neuron models. The benefits of models directly corresponding to biophysiological data are demonstrated: HH neurons are able to express a range of output behaviors not captured by LIF neurons; and the dendritic compartment provides the first implementation of a spiking multi- compartment neuron model with XOR-solving capabilities on neuromorphic hardware. The work paves the way for inclusion of more biologically representative neuron models in neuromorphic systems, and showcases the benefits of hardware accelerators included in the next-generation SpiNNaker2 architecture. [ABSTRACT FROM AUTHOR]

Neuromorphic systems aim to provide accelerated low-power simulation of Spiking Neural Networks (SNNs), typically featuring simple and efficient neuron models such as the Leaky Integrate-and-Fire (LIF) model. Biologically plausible neuron models developed by neuroscientists are largely ignored in neuromorphic computing due to their increased computational costs. This work bridges this gap through implementation and evaluation of a single compartment Hodgkin-Huxley (HH) neuron and a multi-compartment neuron incorporating dendritic computation on the SpiNNaker, and SpiNNaker2 prototype neuromorphic systems. Numerical accuracy of the model implementations is benchmarked against reference models in the NEURON simulation environment, with excellent agreement achieved by both the fixed- and floating-point SpiNNaker implementations. The computational cost is evaluated in terms of timing measurements profiling neural state updates. While the additional model complexity understandably increases computation times relative to LIF models, it was found a wallclock time increase of only 8× was observed for the HH neuron (11× for the mutlicompartment model), demonstrating the potential of hardware accelerators in the next-generation neuromorphic system to optimize implementation of complex neuron models. The benefits of models directly corresponding to biophysiological data are demonstrated: HH neurons are able to express a range of output behaviors not captured by LIF neurons; and the dendritic compartment provides the first implementation of a spiking multi-compartment neuron model with XOR-solving capabilities on neuromorphic hardware. The work paves the way for inclusion of more biologically representative neuron models in neuromorphic systems, and showcases the benefits of hardware accelerators included in the next-generation SpiNNaker2 architecture.

Abstract Background Retinal circuitry provides a fundamental window to neural networks, featuring widely investigated visual phenomena ranging from direction selectivity to fast detection of approaching motion. As the divide between experimental and theoretical visual neuroscience is fading, neuronal modeling has proven to be important for retinal research. In neuronal modeling a delicate balance is maintained between bio-plausibility and model tractability, giving rise to myriad modeling frameworks. One biologically detailed framework for neuro modeling is NeuroConstruct, which facilitates the creation, visualization and analysis of neural networks in 3D. Results Here, we extended NeuroConstruct to support the generation of structured visual stimuli, to feature different synaptic dynamics, to allow for heterogeneous synapse distribution and to enable rule-based synaptic connectivity between cell populations. We utilized this framework to demonstrate a simulation of a dense plexus of biologically realistic and morphologically detailed starburst amacrine cells. The amacrine cells were connected to a ganglion cell and stimulated with expanding and collapsing rings of light. Conclusions This framework provides a powerful toolset for the investigation of the yet elusive underlying mechanisms of retinal computations such as direction selectivity. Particularly, we showcased the way NeuroConstruct can be extended to support advanced field-specific neuro-modeling.

Computational models of brain regions are crucial for understanding neuronal network dynamics and the emergence of cognitive functions. However, current supercomputing limitations hinder the implementation of large networks with millions of morphological and biophysical accurate neurons. Consequently, research has focused on simplified spiking neuron models, ranging from the computationally fast Leaky Integrate and Fire (LIF) linear models to more sophisticated non-linear implementations like Adaptive Exponential (AdEX) and Izhikevic models, through Generalized Leaky Integrate and Fire (GLIF) approaches. However, in almost all cases, these models are tuned (and can be validated) only under constant current injections and they may not, in general, also reproduce experimental findings under variable currents. This study introduces an Adaptive GLIF (A-GLIF) approach that addresses this limitation by incorporating a new set of update rules. The extended A-GLIF model successfully reproduces both constant and variable current inputs, and it was validated against the results obtained using a biophysical accurate model neuron. This enhancement provides researchers with a tool to optimize spiking neuron models using classic experimental traces under constant current injections, reliably predicting responses to synaptic inputs, which can be confidently used for large-scale network implementations., Competing Interests: Declaration of competing interest All the authors declare that no competing interests exist., (Copyright © 2024 Elsevier Inc. All rights reserved.)

Background: Retinal circuitry provides a fundamental window to neural networks, featuring widely investigated visual phenomena ranging from direction selectivity to fast detection of approaching motion. As the divide between experimental and theoretical visual neuroscience is fading, neuronal modeling has proven to be important for retinal research. In neuronal modeling a delicate balance is maintained between bio-plausibility and model tractability, giving rise to myriad modeling frameworks. One biologically detailed framework for neuro modeling is NeuroConstruct, which facilitates the creation, visualization and analysis of neural networks in 3D.Results: Here, we extended NeuroConstruct to support the generation of structured visual stimuli, to feature different synaptic dynamics, to allow for heterogeneous synapse distribution and to enable rule-based synaptic connectivity between cell populations. We utilized this framework to demonstrate a simulation of a dense plexus of biologically realistic and morphologically detailed starburst amacrine cells. The amacrine cells were connected to a ganglion cell and stimulated with expanding and collapsing rings of light.Conclusions: This framework provides a powerful toolset for the investigation of the yet elusive underlying mechanisms of retinal computations such as direction selectivity. Particularly, we showcased the way NeuroConstruct can be extended to support advanced field-specific neuro-modeling. [ABSTRACT FROM AUTHOR]

The neurons of the olivocerebellar circuit exhibit complex electroresponsive dynamics, which are thought to play a fundamental role for network entraining, plasticity induction, signal processing, and noise filtering. In order to reproduce these properties in single-point neuron models, we have optimized the Extended-Generalized Leaky Integrate and Fire (E-GLIF) neuron through a multi-objective gradient-based algorithm targeting the desired input–output relationships. In this way, E-GLIF was tuned toward the unique input–output properties of Golgi cells, granule cells, Purkinje cells, molecular layer interneurons, deep cerebellar nuclei cells, and inferior olivary cells. E-GLIF proved able to simulate the complex cell-specific electroresponsive dynamics of the main olivocerebellar neurons including pacemaking, adaptation, bursting, post-inhibitory rebound excitation, subthreshold oscillations, resonance, and phase reset. The integration of these E-GLIF point-neuron models into olivocerebellar Spiking Neural Networks will allow to evaluate the impact of complex electroresponsive dynamics at the higher scales, up to motor behavior, in closed-loop simulations of sensorimotor tasks.

Efficient and accurate large-scale networks are a fundamental tool in modeling brain areas, to advance our understanding of neuronal dynamics. However, their implementation faces two key issues: computational efficiency and heterogeneity. Computational efficiency is achieved using simplified neurons, whereas there are no practical solutions available to solve the problem of reproducing in a large-scale network the experimentally observed heterogeneity of the intrinsic properties of neurons. This is important, because the use of identical nodes in a network can generate artifacts which can hinder an adequate representation of the properties of a real network. To this aim, we introduce a mathematical procedure to generate an arbitrary large number of copies of simplified hippocampal CA1 pyramidal neurons and interneurons models, which exhibit the full range of firing dynamics observed in these cells - including adapting, non-adapting and bursting. For this purpose, we rely on a recently published adaptive generalized leaky integrate-and-fire (A-GLIF) modeling approach, leveraging on its ability to reproduce the rich set of electrophysiological behaviors of these types of neurons under a variety of different stimulation currents. The generation procedure is based on a perturbation of model's parameters related to the initial data, firing block, and internal dynamics, and suitably validated against experimental data to ensure that the firing dynamics of any given cell copy remains within the experimental range. A classification procedure confirmed that the firing behavior of most of the pyramidal/interneuron copies was consistent with the experimental data. This approach allows to obtain heterogeneous copies with mathematically controlled firing properties. A full set of heterogeneous neurons composing the CA1 region of a rat hippocampus (approximately 1.2 million neurons), are provided in a database freely available in the live paper section of the EBRAINS platform. By adapting the underlying A-GLIF framework, it will be possible to extend the numerical approach presented here to create, in a mathematically controlled manner, an arbitrarily large number of non-identical copies of cell populations with firing properties related to other brain areas., Competing Interests: Declaration of competing interest All the authors declare that no competing interests exist., (Copyright © 2024 The Author(s). Published by Elsevier Inc. All rights reserved.)

The neurons of the olivocerebellar circuit exhibit complex electroresponsive dynamics, which are thought to play a fundamental role for network entraining, plasticity induction, signal processing, and noise filtering. In order to reproduce these properties in single-point neuron models, we have optimized the Extended-Generalized Leaky Integrate and Fire (E-GLIF) neuron through a multi-objective gradient-based algorithm targeting the desired input–output relationships. In this way, E-GLIF was tuned toward the unique input–output properties of Golgi cells, granule cells, Purkinje cells, molecular layer interneurons, deep cerebellar nuclei cells, and inferior olivary cells. E-GLIF proved able to simulate the complex cell-specific electroresponsive dynamics of the main olivocerebellar neurons including pacemaking, adaptation, bursting, post-inhibitory rebound excitation, subthreshold oscillations, resonance, and phase reset. The integration of these E-GLIF point-neuron models into olivocerebellar Spiking Neural Networks will allow to evaluate the impact of complex electroresponsive dynamics at the higher scales, up to motor behavior, in closed-loop simulations of sensorimotor tasks. [ABSTRACT FROM AUTHOR]

Signal-tuned Gabor functions — Gaussian-modulated sinusoids whose parameters are determined by a spatial or spectral "tuning signal" — have previously been shown to provide a plausible model for the stimulus-dependent receptive fields and responses of the simple and complex cells of the primary visual cortex (V1). The signal-tuned responses obey Schrödinger equations, which has led to the proposal of a quantum-like model for V1 cells: by considering the squared magnitude of a particular signal-tuned wave function as a probability density, one arrives at a Poisson spiking process which appears consistent with the neurophysiological findings. Here, by incorporating Hermite-polynomial factors to the signal-tuned Gabor functions, we obtain a generalized quantum-like signal-tuned model for which further relevant properties are demonstrated, such as receptive-field coding of the stimulus and its derivatives, saturating spatial summation curves and half-wave rectification of the simple cell responses. Although only a one-dimensional approach is considered here, such properties will carry over to a two-dimensional model, in which case, as our preliminary analysis indicates, end-stopping — another important feature of cortical cells — can also be accommodated. [ABSTRACT FROM AUTHOR]

Brain neurons exhibit complex electroresponsive properties – including intrinsic subthreshold oscillations and pacemaking, resonance and phase-reset – which are thought to play a critical role in controlling neural network dynamics. Although these properties emerge from detailed representations of molecular-level mechanisms in “realistic” models, they cannot usually be generated by simplified neuronal models (although these may show spike-frequency adaptation and bursting). We report here that this whole set of properties can be generated by the extended generalized leaky integrate-and-fire (E-GLIF) neuron model. E-GLIF derives from the GLIF model family and is therefore mono-compartmental, keeps the limited computational load typical of a linear low-dimensional system, admits analytical solutions and can be tuned through gradient-descent algorithms. Importantly, E-GLIF is designed to maintain a correspondence between model parameters and neuronal membrane mechanisms through a minimum set of equations. In order to test its potential, E-GLIF was used to model a specific neuron showing rich and complex electroresponsiveness, the cerebellar Golgi cell, and was validated against experimental electrophysiological data recorded from Golgi cells in acute cerebellar slices. During simulations, E-GLIF was activated by stimulus patterns, including current steps and synaptic inputs, identical to those used for the experiments. The results demonstrate that E-GLIF can reproduce the whole set of complex neuronal dynamics typical of these neurons – including intensity-frequency curves, spike-frequency adaptation, post-inhibitory rebound bursting, spontaneous subthreshold oscillations, resonance, and phase-reset – providing a new effective tool to investigate brain dynamics in large-scale simulations.

Neuronal signals are usually characterized in terms of their discharge rate, a description inadequate to account for the complex temporal organization of spike trains. Complex temporal properties, which are characteristic of neuronal systems, can only be described with the appropriate, complex mathematical tools. Here, I apply high order structure functions to the analysis of neuronal signals recorded from parkinsonian patients during functional neurosurgery, recovering multifractal properties. To achieve an accurate model of such multifractality is critical for understanding the basal ganglia, since other non-linear properties, such as entropy, depend on the fractal properties of complex systems. I propose a new approach to the study of neuronal signals: to study spiking activity in terms of the velocity of spikes, defining it as the inverse function of the instantaneous frequency. I introduce a neural field model that includes a non-linear gradient field, representing neuronal excitability, and a diffusive term to consider the physical properties of the electric field. Multifractality is present in the model for a range of diffusion coefficients, and multifractal temporal properties are mirrored into space. The model reproduces the behavior of human basal ganglia neurons and shows that it is like that of turbulent fluids. The results obtained from the model predict that passive electric properties of neuronal activity, including ephaptic coupling, are far more relevant to the human brain than what is usually considered: passive electric properties determine the temporal and spatial organization of neuronal activity in the neural tissue.

Model-based network discovery measures, such as the brain effective connectivity, require fitting of generative process models to measurements obtained from key areas across the network. For distributed dynamic phenomena, such as generalized seizures and slow-wave sleep, studying effective connectivity from real-time recordings is significantly complicated since (i) outputs from only a subnetwork can be practically measured, and (ii) exogenous subnetwork inputs are unobservable. Model fitting, therefore, constitutes a challenging blind module identification or model inversion problem for finding both the parameters and the many unknown inputs of the subnetwork. We herein propose a novel estimation framework for identifying nonlinear dynamic subnetworks in the case of slowly-varying, otherwise unknown local inputs. Starting with approximate predictions obtained using Cubature Kalman filtering, residuals of local output predictions are utilized to improve upon local input estimates. The algorithm performance is tested on both simulated and clinical EEG of induced seizures under electroconvulsive therapy (ECT). For the simulated network, the algorithm significantly boosted the estimation accuracy for inputs and connections from noisy EEG. For the clinical data, the algorithm predicted increased subnetwork inputs during the pre-stimulus anesthesia condition. Importantly, it predicted an increased frontocentral connectivity during the generalized seizure that is commensurate with electrode placement and that corroborates the clinical hypothesis of increased frontal focality of therapeutic ECT seizures. The proposed framework can be extended to account for several input configurations and can in principle be applied to study effective connectivity within brain subnetworks defined at the microscale (cortical lamina interaction) or at the macroscale (sensory integration). [ABSTRACT FROM AUTHOR]

Neuronal signals are usually characterized in terms of their discharge rate, a description inadequate to account for the complex temporal organization of spike trains. Complex temporal properties, which are characteristic of neuronal systems, can only be described with the appropriate, complex mathematical tools. Here, I apply high order structure functions to the analysis of neuronal signals recorded from parkinsonian patients during functional neurosurgery, recovering multifractal properties. To achieve an accurate model of such multifractality is critical for understanding the basal ganglia, since other non-linear properties, such as entropy, depend on the fractal properties of complex systems. I propose a new approach to the study of neuronal signals: to study spiking activity in terms of the velocity of spikes, defining it as the inverse function of the instantaneous frequency. I introduce a neural field model that includes a non-linear gradient field, representing neuronal excitability, and a diffusive term to consider the physical properties of the electric field. Multifractality is present in the model for a range of diffusion coefficients, and multifractal temporal properties are mirrored into space. The model reproduces the behavior of human basal ganglia neurons and shows that it is like that of turbulent fluids. The results obtained from the model predict that passive electric properties of neuronal activity, including ephaptic coupling, are far more relevant to the human brain than what is usually considered: passive electric properties determine the temporal and spatial organization of neuronal activity in the neural tissue. [ABSTRACT FROM AUTHOR]

Changes in intracellular Na+ concentration ([Na+]i) are rarely taken into account when neuronal activity is examined. As opposed to Ca2+, [Na+]i dynamics are strongly affected by longitudinal diffusion, and therefore they are governed by the morphological structure of the neurons, in addition to the localization of influx and efflux mechanisms. Here, we examined [Na+]i dynamics and their effects on neuronal computation in three multi-compartmental neuronal models, representing three distinct cell types: accessory olfactory bulb (AOB) mitral cells, cortical layer V pyramidal cells, and cerebellar Purkinje cells. We added [Na+]i as a state variable to these models, and allowed it to modulate the Na+ Nernst potential, the Na+-K+ pump current, and the Na+-Ca2+ exchanger rate. Our results indicate that in most cases [Na+]i dynamics are significantly slower than [Ca2+]i dynamics, and thus may exert a prolonged influence on neuronal computation in a neuronal type specific manner. We show that [Na+]i dynamics affect neuronal activity via three main processes: reduction of EPSP amplitude in repeatedly active synapses due to reduction of the Na+ Nernst potential; activity-dependent hyperpolarization due to increased activity of the Na+-K+ pump; specific tagging of active synapses by extended Ca2+ elevation, intensified by concurrent back-propagating action potentials or complex spikes. Thus, we conclude that [Na+]i dynamics should be considered whenever synaptic plasticity, extensive synaptic input, or bursting activity are examined.

Changes in intracellular Na+ concentration ([Na+]i) are rarely taken into account when neuronal activity is examined. As opposed to Ca2+, [Na+]i dynamics are strongly affected by longitudinal diffusion, and therefore they are governed by the morphological structure of the neurons, in addition to the localization of influx and efflux mechanisms. Here, we examined [Na+]i dynamics and their effects on neuronal computation in three multi-compartmental neuronal models, representing three distinct cell types: accessory olfactory bulb (AOB) mitral cells, cortical layer V pyramidal cells, and cerebellar Purkinje cells. We added [Na+]i as a state variable to these models, and allowed it to modulate the Na+ Nernst potential, the Na+-K+ pump current, and the Na+-Ca2+ exchanger rate. Our results indicate that in most cases [Na+]i dynamics are significantly slower than [Ca2+]i dynamics, and thusmay exert a prolonged influence on neuronal computation in a neuronal type specific manner. We show that [Na+]i dynamics affect neuronal activity via three main processes: reduction of EPSP amplitude in repeatedly active synapses due to reduction of the Na+ Nernst potential; activity-dependent hyperpolarization due to increased activity of the Na+-K+ pump; specific tagging of active synapses by extended Ca2+ elevation, intensified by concurrent back-propagating action potentials or complex spikes. Thus, we conclude that [Na+]i dynamics should be considered whenever synaptic plasticity, extensive synaptic input, or bursting activity are examined. [ABSTRACT FROM AUTHOR]

Background. Datasets consisting of synthetic neural data generated with quantifiable and controlled parameters are a valuable asset in the process of testing and validating directed functional connectivity metrics. Considering the recent debate in the neuroimaging community concerning the use of these metrics for fMRI data, synthetic datasets that emulate the BOLD signal dynamics have played a central role by supporting claims that argue in favor or against certain choices. Generative models often used in studies that simulate neuronal activity, with the aim of gaining insight into specific brain regions and functions, have different requirements from the generative models for benchmarking datasets. Even though the latter must be realistic, there is a tradeoff between realism and computational demand that needs to be contemplated and simulations that efficiently mimic the real behavior of single neurons or neuronal populations are preferred, instead of more cumbersome and marginally precise ones.Methods. This work explores how simple generative models are able to produce neuronal datasets, for benchmarking purposes, that reflect the simulated effective connectivity and, how these can be used to obtain synthetic recordings of EEG and fMRI BOLD signals. The generative models covered here are AR processes, neural mass models consisting of linear and nonlinear stochastic differential equations and populations with thousands of spiking units. Forward models for EEG consist in the simple three-shell head model while the fMRI BOLD signal is modeled with the Balloon-Windkessel model or by convolution with a hemodynamic response function.Results. The simulated datasets are tested for causality with the original spectral formulation for Granger causality. Modeled effective connectivity can be detected in the generated data for varying connection strengths and interaction delays.Discussion. All generative models produce synthetic neuronal data with detectable causal effects although the relation between modeled and detected causality varies and less biophysically realistic models offer more control in causal relations such as modeled strength and frequency location.

The signal-tuned Gabor approach is based on spatial or spectral Gabor functions whose parameters are determined, respectively, by the Fourier and inverse Fourier transforms of a given 'tuning' signal. The sets of spatial and spectral signal-tuned functions, for all possible frequencies and positions, yield exact representations of the tuning signal. Moreover, such functions can be used as kernels for space-frequency transforms which are tuned to the specific features of their inputs, thus allowing analysis with high conjoint spatio-spectral resolution. Based on the signal-tuned Gabor functions and the associated transforms, a plausible model for the receptive fields and responses of cells in the primary visual cortex has been proposed. Here, we present a generalization of the signal-tuned Gabor approach which extends it to the representation and analysis of the tuning signal's fractional Fourier transform of any order. This significantly broadens the scope and the potential applications of the approach. [ABSTRACT FROM AUTHOR]

Bu makalede, nöronların simülasyonu için yeni bir bilgisayar yazılımı 'Simulron' tanıtılmaktadır. Yazılım kullanılarak gerilim-kapılı iyon kanallarına sahip uyarılabilir membranlar modellenebilmekte ve akım ve gerilim kenetleme deneyleri simüle edilebilmektedir. Program, kullanıcının iyon kanal sayısını belirlemesine ve kanalların hız fonksiyonlarını tanımlamasına izin vermektedir. Hız fonksiyonları bilinmiyorsa, program kullanıcının sürekli hal ve zaman sabiti fonksiyonlarını ayarlamasına imkan tanımaktadır. İyon kanal kapısı ve membran potansiyeli dinamiğini tanımlamak için kullanılan birinci-dereceden diferansiyel denklemler değişken zaman basamaklarına sahip ileri yönlü Euler integrasyon yöntemi kullanılarak çözülmektedir. Simülasyonun çıktıları esnek data kullanımına izin verecek şekilde tablo şablonu üzerinde gösterilmekte ve grafik olarak görüntülenebilmektedir.

Extracting the input signal of a neuron by analyzing its spike output is an important step toward understanding how external information is coded into discrete events of action potentials and how this information is exchanged between different neurons in the nervous system. Most of the existing methods analyze this decoding problem in a stochastic framework and use probabilistic metrics such as maximum-likelihood method to determine the parameters of the input signal assuming a leaky and integrate-and-fire (LIF) model. In this article, the input signal of the LIF model is considered as a combination of orthogonal basis functions. The coefficients of the basis functions are found by minimizing the norm of the observed spikes and those generated by the estimated signal. This approach gives rise to the deterministic reconstruction of the input signal and results in a simple matrix identity through which the coefficients of the basis functions and therefore the neuronal stimulus can be identified. The inherent noise of the neuron is considered as an additional factor in the membrane potential and is treated as the disturbance in the reconstruction algorithm. The performance of the proposed scheme is evaluated by numerical simulations, and it is shown that input signals with different characteristics can be well recovered by this algorithm. [ABSTRACT FROM AUTHOR]

We develop an autoregressive model framework based on the concept of Principal Dynamic Modes (PDMs) for the process of action potential (AP) generation in the excitable neuronal membrane described by the Hodgkin-Huxley (H-H) equations. The model's exogenous input is injected current, and whenever the membrane potential output exceeds a specified threshold, it is fed back as a second input. The PDMs are estimated from the previously developed Nonlinear Autoregressive Volterra (NARV) model, and represent an efficient functional basis for Volterra kernel expansion. The PDM-based model admits a modular representation, consisting of the forward and feedback PDM bases as linear filterbanks for the exogenous and autoregressive inputs, respectively, whose outputs are then fed to a static nonlinearity composed of polynomials operating on the PDM outputs and cross-terms of pair-products of PDM outputs. A two-step procedure for model reduction is performed: first, influential subsets of the forward and feedback PDM bases are identified and selected as the reduced PDM bases. Second, the terms of the static nonlinearity are pruned. The first step reduces model complexity from a total of 65 coefficients to 27, while the second further reduces the model coefficients to only eight. It is demonstrated that the performance cost of model reduction in terms of out-of-sample prediction accuracy is minimal. Unlike the full model, the eight coefficient pruned model can be easily visualized to reveal the essential system components, and thus the data-derived PDM model can yield insight into the underlying system structure and function. [ABSTRACT FROM AUTHOR]

Emerging technologies are revealing the spiking activity in ever larger neural ensembles. Frequently, this spiking is far from independent, with correlations in the spike times of different cells. Understanding how such correlations impact the dynamics and function of neural ensembles remains an important open problem.Here we describe a new, generative model for correlated spike trains that can exhibit many of the features observed in data. Extending prior work in mathematical finance, this generalized thinning and shift (GTaS) model creates marginally Poisson spike trains with diverse temporal correlation structures.We give several examples which highlight the model's flexibility and utility. For instance, we use it to examine how a neural network responds to highly structured patterns of inputs.We then show that the GTaS model is analytically tractable, and derive cumulant densities of all orders in terms of model parameters. The GTaS framework can therefore be an important tool in the experimental and theoretical exploration of neural dynamics.

The construction of biologically relevant neuronal models as well as model-based analysis of experimental data often requires the simultaneous fitting of multiple model parameters, so that the behavior of the model in a certain paradigm matches (as closely as possible) the corresponding output of a real neuron according to some predefined criterion. Although the task of model optimization is often computationally hard, and the quality of the results depends heavily on technical issues such as the appropriate choice (and implementation) of cost functions and optimization algorithms, no existing program provides access to the best available methods while also guiding the user through the process effectively. Our software, called Optimizer, implements a modular and extensible framework for the optimization of neuronal models, and also features a graphical interface which makes it easy for even non-expert users to handle many commonly occurring scenarios. Meanwhile, educated users can extend the capabilities of the program and customize it according to their needs with relatively little effort. Optimizer has been developed in Python, takes advantage of open-source Python modules for nonlinear optimization, and interfaces directly with the NEURON simulator to run the models. Other simulators are supported through an external interface. We have tested the program on several different types of problems of varying complexity, using different model classes. As targets, we used simulated traces from the same or a more complex model class, as well as experimental data. We successfully used Optimizer to determine passive parameters and conductance densities in compartmental models, and to fit simple (adaptive exponential integrate-and-fire) neuronal models to complex biological data. Our detailed comparisons show that Optimizer can handle a wider range of problems, and delivers equally good or better performance than any other existing neuronal model fitting tool. [ABSTRACT FROM AUTHOR]

Both in vivo and in vitro recordings indicate that neuronal membrane potentials can make spontaneous transitions between distinct up and down states. At the network level, populations of neurons have been observed to make these transitions synchronously. Although synaptic activity and intrinsic neuron properties play an important role, the precise nature of the processes responsible for these phenomena is not known. Using a computational model we explore the interplay between intrinsic neuronal properties and synaptic fluctuations. Model neurons of the integrate-and-fire type were extended by adding a nonlinear membrane current. Networks of these neurons exhibit large amplitude synchronous spontaneous fluctuations that make the neurons jump between up and down states, thereby producing bimodal membrane potential distributions. The effect of sensory stimulation on network responses depends on whether the stimulus is applied during an up state or deeply inside a down state. External noise can be varied to modulate the network continuously between two extreme regimes in which it remains permanently in either the up or the down state.

Emerging technologies are revealing the spiking activity in ever larger neural ensembles. Frequently, this spiking is far from independent, with correlations in the spike times of different cells. Understanding how such correlations impact the dynamics and function of neural ensembles remains an important open problem. Here we describe a new, generative model for correlated spike trains that can exhibit many of the features observed in data. Extending prior work in mathematical finance, this generalized thinning and shift (GTaS) model creates marginally Poisson spike trains with diverse temporal correlation structures. We give several examples which highlight the model's flexibility and utility. For instance, we use it to examine how a neural network responds to highly structured patterns of inputs. We then show that the GTaS model is analytically tractable, and derive cumulant densities of all orders in terms of model parameters. The GTaS framework can therefore be an important tool in the experimental and theoretical exploration of neural dynamics. [ABSTRACT FROM AUTHOR]

We propose a new variant of Volterra-type model with a nonlinear auto-regressive (NAR) component that is a suitable framework for describing the process of AP generation by the neuron membrane potential, and we apply it to input-output data generated by the Hodgkin-Huxley (H-H) equations. Volterra models use a functional series expansion to describe the input-output relation for most nonlinear dynamic systems, and are applicable to a wide range of physiologic systems. It is difficult, however, to apply the Volterra methodology to the H-H model because is characterized by distinct subthreshold and suprathreshold dynamics. When threshold is crossed, an autonomous action potential (AP) is generated, the output becomes temporarily decoupled from the input, and the standard Volterra model fails. Therefore, in our framework, whenever membrane potential exceeds some threshold, it is taken as a second input to a dual-input Volterra model. This model correctly predicts membrane voltage deflection both within the subthreshold region and during APs. Moreover, the model naturally generates a post-AP afterpotential and refractory period. It is known that the H-H model converges to a limit cycle in response to a constant current injection. This behavior is correctly predicted by the proposed model, while the standard Volterra model is incapable of generating such limit cycle behavior. The inclusion of cross-kernels, which describe the nonlinear interactions between the exogenous and autoregressive inputs, is found to be absolutely necessary. The proposed model is general, non-parametric, and data-derived. [ABSTRACT FROM AUTHOR]

Motor symptoms of Parkinson's disease are related to the excessive synchronized oscillatory activity in the beta frequency band (around 20 Hz) in the basal ganglia and other parts of the brain. This review explores the dynamics and potential mechanisms of these oscillations employing ideas and methods from nonlinear dynamics. We present extensive experimental documentation of the relevance of synchronized oscillations to motor behavior in Parkinson's disease, and we discuss the intermittent character of this synchronization. The reader is introduced to novel time-series analysis techniques aimed at the detection of the fine temporal structure of intermittent phase locking observed in the brains of Parkinsonian patients. Modeling studies of brain networks are reviewed, which may describe the observed intermittent synchrony, and we discuss what these studies reveal about brain dynamics in Parkinson's disease. The Parkinsonian brain appears to exist on the boundary between phase-locked and nonsynchronous dynamics. Such a situation may be beneficial in the healthy state, as it may allow for easy formation and dissociation of transient patterns of synchronous activity which are required for normal motor behavior. Dopaminergic degeneration in Parkinson's disease may shift the brain networks closer to this boundary, which would still permit some motor behavior while accounting for the associated motor deficits. Understanding the mechanisms of the intermittent synchrony in Parkinson's disease is also important for biomedical engineering since efficient control strategies for suppression of pathological synchrony through deep brain stimulation require knowledge of the dynamics of the processes subjected to control. [ABSTRACT FROM AUTHOR]

Abstract: Ca2+ currents in neurons and muscle cells have been classified as being one of 5 types, of which four, L, N, P/Q and R were said to be high threshold and one, T, was designated low threshold. This review focuses on quantitative aspects of L-type currents. L-type channels are now distinguished according to their structure as one of four main subtypes Cav1.1–Cav1.4. L-type calcium currents play many fundamental roles in cellular dynamical processes including control of firing rate and pacemaking in neurons and cardiac cells, the activation of transcription factors involved in synaptic plasticity and in immune cells. The half-activation potentials of L-type currents (ICaL) have been ascribed values as low as −50mV and as high as near 0mV. The inactivation of ICaL has been found to be both voltage (VDI) and calcium-dependent (CDI) and the latter component may involve calcium-induced calcium release. CDI is often an important aspect of dynamical models of cell electrophysiology. We describe the basic components in modeling ICaL including activation and both voltage and calcium dependent inactivation and the two main approaches to determining the current. We review, by means of tables of values from over 65 representative studies, the various details of the dynamical properties associated with ICaL that have been found experimentally or employed in the last 25 years in deterministic modeling in various nervous system and cardiac cells. Distributions and statistics of several parameters related to activation and inactivation are obtained. There are few reliable complete experimental data on L-type calcium current kinetics for cells at physiological calcium ion concentrations. Neurons are divided approximately into two groups with experimental half-activation potentials that are high, ≈ −18.3mV, or low, ≈ −36.4mV, which correspond closely with those for Cav1.2 and Cav1.3 channels in physiological solutions. There are very few complete experimental data on time constants of activation, those available suggesting values around 0.5–2ms. In modeling, a wide range of time constants has been employed. A major problem for quantitative studies due to lack of experimental data has been the use of kinetic parameters from one cell type for others. Inactivation time constants for VDI have been found experimentally with average 65ms. Examples of calculations of ICaL are made for linear and constant field methods and the effects of CDI are illustrated for single and double pulse protocols and the results compared with experiment. The review ends with a discussion and analysis of experimental subtype (Cav1.1–Cav1.4) properties and their roles in normal, including pacemaker, activity, and many pathological states. [Copyright &y& Elsevier]

Abstract: In this study, we examine the signal detection ability of an array of neurons with intrinsic channel fluctuation. Numerical simulations show that estimation of the input signal from the output spiking activity of the neuronal array is most accurate if a proper amount of channel noise exists. Theoretical calculation of the mutual and Fisher information confirms the effect of the noise-aided information transfer in the array, or the presence of suprathreshold stochastic resonance. These results indicate that the channel noise, which induces response variability, may play an essential role in population coding. [Copyright &y& Elsevier]

Summary: According to the most generally accepted cortico-reticular theory of absence epilepsy, sleep spindles and spike–wave discharges (SWD, characteristic hallmarks of absence epilepsy) are closely related. The present review critically evaluates this theory based on the original data obtained in WAG/Rij rat model of absence epilepsy. It is demonstrated that (1) sleep spindles and spike–wave discharges are distinguished in time–frequency domain. (2) EEG waveforms of sleep spindles and SWD are underlain by different synaptic processes, as determined with the aid of computational neuronal model of cortical field potentials. (3) Sleep spindles do not precede SWD. EEG analysis of SWD-precursor activity provides us with a clue to possible prediction of absence epilepsy episodes. Furthermore, by studying Granger causality and EEG coherence at the onset of SWD we gain more insight into the dynamics of the thalamo-cortical neuronal network associations that underlie occurrence of absence seizures. In general, spindle activity and SWD display different time–frequency characteristics as measured in cortex and thalamus, they are accompanied by different neuronal processes and require different involvement of neurotransmitters. Sleep spindles and SWD are considered as autonomous EEG phenomena, and straightforward relationship between them is doubtful. [Copyright &y& Elsevier]

Many animals, including men, use periodicity information, e.g., amplitude modulations of acoustic stimuli, as a vital cue to auditory object formation. The underlying neuronal mechanisms, however, still remain a matter of debate. Here, we mathematically analyze a model for periodicity identification that relies on the interplay of excitation and delayed inhibition. Our analytical results show how the maximal response of such a system varies systematically with the time constants of excitation and inhibition. The model reliably identifies signal periodicity in the range from about ten to several hundred Hertz. Importantly, the model relies on biologically plausible parameters only. It works best for excitatory and inhibitory neuronal couplings of equal strength, the so-called ‘balanced inhibition’. We show how balanced inhibition can serve to identify low-frequency signal periodicity and how variation of a single parameter, the inhibitory time constant, can tune the system to different frequencies. [ABSTRACT FROM AUTHOR]

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