Point Neuron Models Research Articles

Studying the effect of oscillating electric field in time and space on neuronal activity using the extended point neuron model

Studying the effect of oscillating electric field in time and space on neuronal activity using the extended point neuron model

Modeling and simulation for prediction of multiple sclerosis progression

In light of extensive work that has created a wide range of techniques for predicting the course of multiple sclerosis (MS) disease, this paper attempts to provide an overview of these approaches and put forth an alternative way to predict the disease progression. For this purpose, the existing methods for estimating and predicting the course of the disease have been categorized into clinical, radiological, biological, and computational or artificial intelligence-based markers. Weighing the weaknesses and strengths of these prognostic groups is a profound method that is yet in need and works directly at the level of diseased connectivity. Therefore, we propose using the computational models in combination with established connectomes as a predictive tool for MS disease trajectories. The fundamental conduction-based Hodgkin-Huxley model emerged as promising from examining these studies. The advantage of the Hodgkin-Huxley model is that certain properties of connectomes, such as neuronal connection weights, spatial distances, and adjustments of signal transmission rates, can be taken into account. It is precisely these properties that are particularly altered in MS and that have strong implications for processing, transmission, and interactions of neuronal signaling patterns.The Hodgkin-Huxley (HH) equations as a point-neuron model are used for signal propagation inside a small network. The objective is to change the conduction parameter of the neuron model, replicate the changes in myelin properties in MS and observe the dynamics of the signal propagation across the network. The model is initially validated for different lengths, conduction values, and connection weights through three nodal connections. Later, these individual factors are incorporated into a small network and simulated to mimic the condition of MS. The signal propagation pattern is observed after inducing changes in conduction parameters at certain nodes in the network and compared against a control model pattern obtained before the changes are applied to the network. The signal propagation pattern varies as expected by adapting to the input conditions. Similarly, when the model is applied to a connectome, the pattern changes could give an insight into disease progression. This approach has opened up a new path to explore the progression of the disease in MS. The work is in its preliminary state, but with a future vision to apply this method in a connectome, providing a better clinical tool.

Dendritic filtering determines the frequency-dependent spike train correlations

Temporal correlation between neural discharge sequences induced by correlated synaptic inputs distributes widely in large population of neurons. However, how synaptic input frequency affects the spike train correlation remains largely unclear. To address this question, we use a pair of unconnected ball-and-stick (BS) model neurons of integrate-and-fire (IF) type to simulate the correlated spike trains when receiving the shared synaptic inputs with specific frequency at the distal dendrite. We derive the relevant simplified point (SP) neuron model analytically to well reproduce the BS model dynamics with suprathreshold inputs. We show that the output correlation is negatively correlated to input frequency, and this frequency-dependent correlation is modulated by dendritic morphologies and synaptic positions. Our results highlight the dependence of spike train correlation on input frequency and suggest that the dendritic filtering is a primary factor in shaping this correlation-frequency relationship using SP models and morphologically realistic model neurons. These predictions should be considered when understanding the neural population correlations. Data availabilityNo data was used for the research described in the article.

Sensitivity analysis of point neuron model simulations implemented on neuromorphic hardware.

With the ongoing growth in the field of neuro-inspired computing, newly arriving computational architectures demand extensive validation and testing against existing benchmarks to establish their competence and value. In our work, we break down the validation step into two parts-(1) establishing a methodological and numerical groundwork to establish a comparison between neuromorphic and conventional platforms and, (2) performing a sensitivity analysis on the obtained model regime to assess its robustness. We study the neuronal dynamics based on the Leaky Integrate and Fire (LIF) model, which is built upon data from the mouse visual cortex spanning a set of anatomical and physiological constraints. Intel Corp.'s first neuromorphic chip "Loihi" serves as our neuromorphic platform and results on it are validated against the classical simulations. After setting up a model that allows a seamless mapping between the Loihi and the classical simulations, we find that Loihi replicates classical simulations very efficiently with high precision. This model is then subjected to the second phase of validation, through sensitivity analysis, by assessing the impact on the cost function as values of the significant model parameters are varied. The work is done in two steps-(1) assessing the impact while changing one parameter at a time, (2) assessing the impact while changing two parameters at a time. We observe that the model is quite robust for majority of the parameters with slight change in the cost function. We also identify a subset of the model parameters changes which make the model more sensitive and thus, need to be defined more precisely.

Low-dimensional models of single neurons: a review.

The classical Hodgkin-Huxley (HH) point-neuron model of action potential generation is four-dimensional. It consists of four ordinary differential equations describing the dynamics of the membrane potential and three gating variables associated to a transient sodium and a delayed-rectifier potassium ionic currents. Conductance-based models of HH type are higher-dimensional extensions of the classical HH model. They include a number of supplementary state variables associated with other ionic current types, and are able to describe additional phenomena such as subthreshold oscillations, mixed-mode oscillations (subthreshold oscillations interspersed with spikes), clustering and bursting. In this manuscript we discuss biophysically plausible and phenomenological reduced models that preserve the biophysical and/or dynamic description of models of HH type and the ability to produce complex phenomena, but the number of effective dimensions (state variables) is lower. We describe several representative models. We also describe systematic and heuristic methods of deriving reduced models from models of HH type.

A Conductance-Based Silicon Synapse Circuit.

Neuron, synapse, and learning circuits inspired by the brain comprise the key components of a neuromorphic chip. In this study, we present a conductance-based analog silicon synapse circuit suitable for the implementation of reduced or multi-compartment neuron models. Compartmental models are more bio-realistic. They are implemented in neuromorphic chips aiming to mimic the electrical activities of the neuronal networks in the brain and incorporate biomimetic soma and synapse circuits. Most contemporary low-power analog synapse circuits implement bioinspired "current-based" synaptic models suited for the implementation of single-compartment point neuron models. They emulate the exponential decay profile of the synaptic current, but ignore the effect of the postsynaptic membrane potential on the synaptic current. This dependence is necessary to emulate shunting inhibition, which is thought to play important roles in information processing in the brain. The proposed circuit uses an oscillator-based resistor-type element at its output stage to incorporate this effect. This circuit is used to demonstrate the shunting inhibition phenomenon. Next, to demonstrate that the oscillatory nature of the induced synaptic current has no unforeseen effects, the synapse circuit is employed in a spatiotemporal spike pattern detection task. The task employs the adaptive spike-timing-dependent plasticity (STDP) learning rule, a bio-inspired learning rule introduced in a previous study. The mixed-signal chip is designed in a Taiwan Manufacturing Semiconductor Company 250 nm complementary metal oxide semiconductor technology node. It comprises a biomimetic soma circuit and 256 synapse circuits, along with their learning circuitries.

Reproducing and quantitatively validating a biologically-constrained point-neuron model of CA1 pyramidal cells.

We have attempted to reproduce a biologically-constrained point-neuron model of CA1 pyramidal cells. The original models, developed for the Brian simulator, captured the frequency-current profiles of both strongly and weakly adapting cells. As part of the present study, we reproduced the model for different simulators, namely Brian2 and NEURON. The reproductions were attempted independent of the original Brian implementation, relying solely on the published article. The different implementations were quantitatively validated, to evaluate how well they mirror the original model. Additional tests were developed and packaged into a test suite, that helped further characterize and compare various aspects of these models, beyond the scope of the original study. Overall, we were able to reproduce the core features of the model, but observed certain unaccountable discrepancies. We demonstrate an approach for undertaking these evaluations, using the SciUnit framework, that allows for such quantitative validations of scientific models, to verify their accurate replication and/or reproductions. All resources employed and developed in our study have been publicly shared via the EBRAINS Live Papers platform.

The Tripod neuron: a minimal structural reduction of the dendritic tree.

Neuron models with explicit dendritic dynamics have shed light on mechanisms for coincidence detection, pathway selection and temporal filtering. However, it is still unclear which morphological and physiological features are required to capture these phenomena. In this work, we introduce the Tripod neuron model and propose a minimal structural reduction of the dendritic tree that is able to reproduce these computations. The Tripod is a three-compartment model consisting of two segregated passive dendrites and a somatic compartment modelled as an adaptive, exponential integrate-and-fire neuron. It incorporates dendritic geometry, membrane physiology and receptor dynamics as measured in human pyramidal cells. We characterize the response of the Tripod to glutamatergic and GABAergic inputs and identify parameters that support supra-linear integration, coincidence-detection and pathway-specific gating through shunting inhibition. Following NMDA spikes, the Tripod neuron generates plateau potentials whose duration depends on the dendritic length and the strength of synaptic input. When fitted with distal compartments, the Tripod encodes previous activity into a dendritic depolarized state. This dendritic memory allows the neuron to perform temporal binding, and we show that it solves transition and sequence detection tasks on which a single-compartment model fails. Thus, the Tripod can account for dendritic computations previously explained only with more detailed neuron models or neural networks. Due to its simplicity, the Tripod neuron can be used efficiently in simulations of larger corticalcircuits. KEY POINTS: We present a neuron model, called the Tripod, with two segregated dendritic branches that are connected to an axosomatic compartment. Each branch implements inhibitory GABAergic and excitatory glutamatergic synaptic transmission, including voltage-gated NMDA receptors. Dendrites are modelled on relevant geometric and physiological parameters measured in human pyramidal cells. The neuron reproduces classical dendritic computations, such as coincidence detection and pathway selection via shunting inhibition, that are beyond the scope of point-neuron models. Under some conditions, dendritic NMDA spikes cause plateau potentials, and we show that they provide a form of short-term memory which is useful for sequence recognition. The dendritic structure of the Tripod neuron is sufficiently simple to be integrated into efficient network simulations and studied in a broad functional context.

Multiscale approach for tFUS neurocomputational modelling.

Among the non-invasive methods employed for brain stimulation, trans cranial Focused Ultrasound Stimulation (tFUS) is the technique with the best penetration into the tissues and spatial resolution. The development of computational models of US propagation in brain tissue can be useful for estimating the behaviour of neural cells subjected to mechanical stimulus due to US. This paper aims at studying the neural cell response of a cortical Regular Spiking point neuron model, for different values of stimulus Duty Cycle (DC). The main goal is to use a multiscale approach to couple the results obtained from a macroscale simulation on wave propagation in tissue, with neuron model described by Hodgkin-Huxley equations to study latency and firing rate of the RS model. The obtained results showed that latency and firing rate have slight variations along the propagation direction of the US beam, in the focal region under the skull model, for different stimulus DC.

Mapping and Validating a Point Neuron Model on Intel's Neuromorphic Hardware Loihi.

Neuromorphic hardware is based on emulating the natural biological structure of the brain. Since its computational model is similar to standard neural models, it could serve as a computational accelerator for research projects in the field of neuroscience and artificial intelligence, including biomedical applications. However, in order to exploit this new generation of computer chips, we ought to perform rigorous simulation and consequent validation of neuromorphic models against their conventional implementations. In this work, we lay out the numeric groundwork to enable a comparison between neuromorphic and conventional platforms. “Loihi”—Intel's fifth generation neuromorphic chip, which is based on the idea of Spiking Neural Networks (SNNs) emulating the activity of neurons in the brain, serves as our neuromorphic platform. The work here focuses on Leaky Integrate and Fire (LIF) models based on neurons in the mouse primary visual cortex and matched to a rich data set of anatomical, physiological and behavioral constraints. Simulations on classical hardware serve as the validation platform for the neuromorphic implementation. We find that Loihi replicates classical simulations very efficiently with high precision. As a by-product, we also investigate Loihi's potential in terms of scalability and performance and find that it scales notably well in terms of run-time performance as the simulated networks become larger.

Mapping and Validating a Point Neuron Model on Intel's Neuromorphic Hardware Loihi.

Neuromorphic hardware is based on emulating the natural biological structure of the brain. Since its computational model is similar to standard neural models, it could serve as a computational accelerator for research projects in the field of neuroscience and artificial intelligence, including biomedical applications. However, in order to exploit this new generation of computer chips, we ought to perform rigorous simulation and consequent validation of neuromorphic models against their conventional implementations. In this work, we lay out the numeric groundwork to enable a comparison between neuromorphic and conventional platforms. "Loihi"-Intel's fifth generation neuromorphic chip, which is based on the idea of Spiking Neural Networks (SNNs) emulating the activity of neurons in the brain, serves as our neuromorphic platform. The work here focuses on Leaky Integrate and Fire (LIF) models based on neurons in the mouse primary visual cortex and matched to a rich data set of anatomical, physiological and behavioral constraints. Simulations on classical hardware serve as the validation platform for the neuromorphic implementation. We find that Loihi replicates classical simulations very efficiently with high precision. As a by-product, we also investigate Loihi's potential in terms of scalability and performance and find that it scales notably well in terms of run-time performance as the simulated networks become larger.

Dual-mode dendritic devices enhanced neural network based on electrolyte gated transistors

As a fundamental component of biological neurons, dendrites have been proven to have crucial effects in neuronal activities. Single neurons with dendrite structures show high signal processing capability that is analogous to a multilayer perceptron (MLP), whereas oversimplified point neuron models are still prevalent in artificial intelligence algorithms and neuromorphic systems and fundamentally limit their efficiency and functionality of the systems constructed. In this study, we propose a dual-mode dendritic device based on electrolyte gated transistor, which can be operated to generate both supralinear and sublinear current–voltage responses when receiving input voltage pulses. We propose and demonstrate that the dual-mode dendritic devices can be used as a dendritic processing block between weight matrices and output neurons so as to dramatically enhance the expression ability of the neural networks. A dual-mode dendrites-enhanced neural network is therefore constructed with only two trainable parameters in the second layer, thus achieving 1000× reduction in the amount of second layer parameter compared to MLP. After training by back propagation, the network reaches 90.1% accuracy in MNIST handwritten digits classification, showing advantage of the present dual-mode dendritic devices in building highly efficient neuromorphic computing.

Simulation of Large Scale Neural Models With Event-Driven Connectivity Generation.

Accurate simulations of brain structures is a major problem in neuroscience. Many works are dedicated to design better models or to develop more efficient simulation schemes. In this paper, we propose a hybrid simulation scheme that combines time-stepping second-order integration of Hodgkin-Huxley (HH) type neurons with event-driven updating of the synaptic currents. As the HH model is a continuous model, there is no explicit spike events. Thus, in order to preserve the accuracy of the integration method, a spike detection algorithm is developed that accurately determines spike times. This approach allows us to regenerate the outgoing connections at each event, thereby avoiding the storage of the connectivity. Consequently, memory consumption is significantly reduced while preserving execution time and accuracy of the simulations, especially the spike times of detailed point neuron models. The efficiency of the method, implemented in the SiReNe software1, is demonstrated by the simulation of a striatum model which consists of more than 106 neurons and 108 synapses (each neuron has a fan-out of 504 post-synaptic neurons), under normal and Parkinson's conditions.

Optimization of Efficient Neuron Models With Realistic Firing Dynamics. The Case of the Cerebellar Granule Cell.

Biologically relevant large-scale computational models currently represent one of the main methods in neuroscience for studying information processing primitives of brain areas. However, biologically realistic neuron models tend to be computationally heavy and thus prevent these models from being part of brain-area models including thousands or even millions of neurons. The cerebellar input layer represents a canonical example of large scale networks. In particular, the cerebellar granule cells, the most numerous cells in the whole mammalian brain, have been proposed as playing a pivotal role in the creation of somato-sensorial information representations. Enhanced burst frequency (spiking resonance) in the granule cells has been proposed as facilitating the input signal transmission at the theta-frequency band (4–12 Hz), but the functional role of this cell feature in the operation of the granular layer remains largely unclear. This study aims to develop a methodological pipeline for creating neuron models that maintain biological realism and computational efficiency whilst capturing essential aspects of single-neuron processing. Therefore, we selected a light computational neuron model template (the adaptive-exponential integrate-and-fire model), whose parameters were progressively refined using an automatic parameter tuning with evolutionary algorithms (EAs). The resulting point-neuron models are suitable for reproducing the main firing properties of a realistic granule cell from electrophysiological measurements, including the spiking resonance at the theta-frequency band, repetitive firing according to a specified intensity-frequency (I-F) curve and delayed firing under current-pulse stimulation. Interestingly, the proposed model also reproduced some other emergent properties (namely, silent at rest, rheobase and negligible adaptation under depolarizing currents) even though these properties were not set in the EA as a target in the fitness function (FF), proving that these features are compatible even in computationally simple models. The proposed methodology represents a valuable tool for adjusting AdEx models according to a FF defined in the spiking regime and based on biological data. These models are appropriate for future research of the functional implication of bursting resonance at the theta band in large-scale granular layer network models.

Spiking neurons with spatiotemporal dynamics and gain modulation for monolithically integrated memristive neural networks

As a key building block of biological cortex, neurons are powerful information processing units and can achieve highly complex nonlinear computations even in individual cells. Hardware implementation of artificial neurons with similar capability is of great significance for the construction of intelligent, neuromorphic systems. Here, we demonstrate an artificial neuron based on NbOx volatile memristor that not only realizes traditional all-or-nothing, threshold-driven spiking and spatiotemporal integration, but also enables dynamic logic including XOR function that is not linearly separable and multiplicative gain modulation among different dendritic inputs, therefore surpassing neuronal functions described by a simple point neuron model. A monolithically integrated 4 × 4 fully memristive neural network consisting of volatile NbOx memristor based neurons and nonvolatile TaOx memristor based synapses in a single crossbar array is experimentally demonstrated, showing capability in pattern recognition through online learning using a simplified δ-rule and coincidence detection, which paves the way for bio-inspired intelligent systems.

Sparse coding with a somato-dendritic rule

Cortical neurons are silent most of the time: sparse activity enables low-energy computation in the brain, and promises to do the same in neuromorphic hardware. Beyond power efficiency, sparse codes have favourable properties for associative learning, as they can store more information than local codes but are easier to read out than dense codes. Auto-encoders with a sparse constraint can learn sparse codes, and so can single-layer networks that combine recurrent inhibition with unsupervised Hebbian learning. But the latter usually require fast homeostatic plasticity, which could lead to catastrophic forgetting in embodied agents that learn continuously. Here we set out to explore whether plasticity at recurrent inhibitory synapses could take up that role instead, regulating both the population sparseness and the firing rates of individual neurons. We put the idea to the test in a network that employs compartmentalised inputs to solve the task: rate-based dendritic compartments integrate the feedforward input, while spiking integrate-and-fire somas compete through recurrent inhibition. A somato-dendritic learning rule allows somatic inhibition to modulate nonlinear Hebbian learning in the dendrites. Trained on MNIST digits and natural images, the network discovers independent components that form a sparse encoding of the input and support linear decoding. These findings confirm that intrinsic homeostatic plasticity is not strictly required for regulating sparseness: inhibitory synaptic plasticity can have the same effect. Our work illustrates the usefulness of compartmentalised inputs, and makes the case for moving beyond point neuron models in artificial spiking neural networks.

Ring models of binocular rivalry and fusion.

When similar visual stimuli are presented binocularly to both eyes, one perceives a fused single image. However, when the two stimuli are distinct, one does not perceive a single image; instead, one perceives binocular rivalry. That is, one perceives one of the stimulated patterns for a few seconds, then the other for few seconds, and so on - with random transitions between the two percepts. Most theoretical studies focus on rivalry, with few considering the coexistence of fusion and rivalry. Here we develop three distinct computational neuronal network models which capture binocular rivalry with realistic stochastic properties, fusion, and the hysteretic transition between. Each is a conductance-based point neuron model, which is multi-layer with two ocular dominance columns (L & R) and with an idealized "ring" architecture where the orientation preference of each neuron labels its location on a ring. In each model, the primary mechanism initiating binocular rivalry is cross-column inhibition, with firing rate adaptation governing the temporal properties of the transitions between percepts. Under stimulation by similar visual patterns, each of three models uses its own mechanism to overcome cross-column inhibition, and thus to prevent rivalry and allow the fusion of similar images: The first model uses cross-column feedforward inhibition from the opposite eye to "shut off" the cross-column feedback inhibition; the second model "turns on" a second layer of monocular neurons as a parallel pathway to the binocular neurons, rivaling out of phase with the first layer, and together these two pathways represent fusion; and the third model uses cross-column excitation to overcome the cross-column inhibition and enable fusion. Thus, each of the idealized ring models depends upon a different mechanism for fusion that might emerge as an underlying mechanism present in real visual cortex.

Simple models of quantitative firing phenotypes in hippocampal neurons: Comprehensive coverage of intrinsic diversity.

Patterns of periodic voltage spikes elicited by a neuron help define its dynamical identity. Experimentally recorded spike trains from various neurons show qualitatively distinguishable features such as delayed spiking, spiking with or without frequency adaptation, and intrinsic bursting. Moreover, the input-dependent responses of a neuron not only show different quantitative features, such as higher spike frequency for a stronger input current injection, but can also exhibit qualitatively different responses, such as spiking and bursting under different input conditions, thus forming a complex phenotype of responses. In previous work, the comprehensive knowledge base of hippocampal neuron types Hippocampome.org systematically characterized various spike pattern phenotypes experimentally identified from 120 neuron types/subtypes. In this paper, we present a complete set of simple phenomenological models that quantitatively reproduce the diverse and complex phenotypes of hippocampal neurons. In addition to point-neuron models, we created compact multi-compartment models with up to four compartments, which will allow spatial segregation of synaptic integration in network simulations. Electrotonic compartmentalization observed in our compact multi-compartment models is qualitatively consistent with experimental observations. The models were created using an automated pipeline based on evolutionary algorithms. This work maps 120 neuron types/subtypes in the rodent hippocampus to a low-dimensional model space and adds another dimension to the knowledge accumulated in Hippocampome.org. Computationally efficient representations of intrinsic dynamics, along with other pieces of knowledge available in Hippocampome.org, provide a biologically realistic platform to explore the large-scale interactions of various neuron types at the mesoscopic level.

Dendritic computations captured by an effective point neuron model

Complex dendrites in general present formidable challenges to understanding neuronal information processing. To circumvent the difficulty, a prevalent viewpoint simplifies the neuronal morphology as a point representing the soma, and the excitatory and inhibitory synaptic currents originated from the dendrites are treated as linearly summed at the soma. Despite its extensive applications, the validity of the synaptic current description remains unclear, and the existing point neuron framework fails to characterize the spatiotemporal aspects of dendritic integration supporting specific computations. Using electrophysiological experiments, realistic neuronal simulations, and theoretical analyses, we demonstrate that the traditional assumption of linear summation of synaptic currents is oversimplified and underestimates the inhibition effect. We then derive a form of synaptic integration current within the point neuron framework to capture dendritic effects. In the derived form, the interaction between each pair of synaptic inputs on the dendrites can be reliably parameterized by a single coefficient, suggesting the inherent low-dimensional structure of dendritic integration. We further generalize the form of synaptic integration current to capture the spatiotemporal interactions among multiple synaptic inputs and show that a point neuron model with the synaptic integration current incorporated possesses the computational ability of a spatial neuron with dendrites, including direction selectivity, coincidence detection, logical operation, and a bilinear dendritic integration rule discovered in experiment. Our work amends the modeling of synaptic inputs and improves the computational power of a modeling neuron within the point neuron framework.

Complex Electroresponsive Dynamics in Olivocerebellar Neurons Represented With Extended-Generalized Leaky Integrate and Fire Models.

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.