Real Neurons Research Articles

Task Learning through Stimulation-Induced Plasticity in Neural Networks

Synaptic plasticity dynamically shapes the connectivity of neural systems and is key to learning processes in the brain. To what extent the mechanisms of plasticity can be exploited to drive a neural network and make it perform some kind of computational task remains unclear. This question, relevant in a bioengineering context, can be formulated as a control problem on a high-dimensional system with strongly constrained and nonlinear dynamics. We present a self-contained procedure which, through appropriate spatiotemporal stimulations of the neurons, is able to drive rate-based neural networks with arbitrary initial connectivity towards a desired functional state. We illustrate our approach on two different computational tasks: a nonlinear association between multiple input stimulations and activity patterns (representing digit images), and the construction of a continuous attractor encoding a collective variable in a neural population. Our work thus provides a proof of principle for emerging paradigms of computation based on real neurons. Published by the American Physical Society 2024

Hippocampal synchronization in a realistic CA1 neuron model.

This work delves into studying the synchronization in two realistic neuron models using Hodgkin-Huxley dynamics. Unlike simplistic pointlike models, excitatory synapses are here randomly distributed along the dendrites, introducing strong stochastic contributions into their signal propagation. To focus on the role of different synaptic locations, we use two copies of the same neuron whose synapses are located at different distances from the soma and activated by identical Poisson distributed pulses. The synchronization is investigated through a specifically defined spiking correlation function, and its behavior is analyzed as a function of several parameters: inhibition weight, distance from the soma of one synaptic group, weight and decay time constants of the excitatory synapses.

Gated parametric neuron for spike-based audio recognition

Spiking neural networks (SNNs) aim to simulate real neural networks in the human brain with biologically plausible neurons. The leaky integrate-and-fire (LIF) neuron is one of the most widely studied SNN architectures. However, it has the vanishing gradient problem when trained with backpropagation. Additionally, its neuronal parameters are often manually specified and fixed, in contrast to the heterogeneity of real neurons in the human brain. This paper proposes a gated parametric neuron (GPN) to process spatio-temporal information effectively with the gating mechanism. Compared with the LIF neuron, the GPN has two distinguishing advantages: (1) it copes well with the vanishing gradients by improving the flow of gradient propagation; and, (2) it learns spatio-temporal heterogeneous neuronal parameters automatically. Additionally, we use the same gate structure to eliminate initial neuronal parameter selection and design a hybrid recurrent neural network-SNN structure. Experiments on two spike-based audio datasets demonstrated that the GPN network outperformed several state-of-the-art SNNs, could mitigate vanishing gradients, and had spatio-temporal heterogeneous parameters. Our work shows the ability of SNNs to handle long-term dependencies and achieve high performance simultaneously.

Multi-scale modelling of location- and frequency-dependent synaptic plasticity induced by transcranial magnetic stimulation in the dendrites of pyramidal neurons.

Repetitive transcranial magnetic stimulation (rTMS) induces long-term changes of synapses, but the mechanisms behind these modifications are not fully understood. Although there has been progress in the development of multi-scale modeling tools, no comprehensive module for simulating rTMS-induced synaptic plasticity in biophysically realistic neurons exists.. We developed a modelling framework that allows the replication and detailed prediction of long-term changes of excitatory synapses in neurons stimulated by rTMS. We implemented a voltage-dependent plasticity model that has been previously established for simulating frequency-, time-, and compartment-dependent spatio-temporal changes of excitatory synapses in neuronal dendrites. The plasticity model can be incorporated into biophysical neuronal models and coupled to electrical field simulations. We show that the plasticity modelling framework replicates long-term potentiation (LTP)-like plasticity in hippocampal CA1 pyramidal cells evoked by 10-Hz repetitive magnetic stimulation (rMS). This plasticity was strongly distance dependent and concentrated at the proximal synapses of the neuron. We predicted a decrease in the plasticity amplitude for 5 Hz and 1 Hz protocols with decreasing frequency. Finally, we successfully modelled plasticity in distal synapses upon local electrical theta-burst stimulation (TBS) and predicted proximal and distal plasticity for rMS TBS. Notably, the rMS TBS-evoked synaptic plasticity exhibited robust facilitation by dendritic spikes and low sensitivity to inhibitory suppression. The plasticity modelling framework enables precise simulations of LTP-like cellular effects with high spatio-temporal resolution, enhancing the efficiency of parameter screening and the development of plasticity-inducing rTMS protocols.

Generalized Bio-Plausible Neuron Model with Refractoriness, Frequency Adaptation and Dynamic Threshold

Real biological neurons are dynamical systems that can process a nonlinear, arbitrary input signal with a dynamic threshold voltage, exhibit refractory time, and have a smooth [Formula: see text]–[Formula: see text] curve. This paper presents a generalized bio-plausible neuron model with refractoriness, frequency adaptation, and dynamic threshold. The spiking characteristics of the generalized neuron are enhanced with less circuitry and fewer parameters compared to older circuits. The proposed silicon neuron can generate all known spiking behaviors, just like a biological neuron. The circuit is designed using a 180 nm standard CMOS process. The entire design uses 22 transistors with a total power consumption of only 2 nW for a 1 nA step current at a spike frequency of 122 Hz. The power consumption and spike frequency rate depend on the input current. The proposed neuron is also capable of displaying both Type I and Type II frequency response characteristics. In addition, our neuron model underwent Monte Carlo simulation with 1000 sample runs to assess its robustness and stability against process variations and uncertainties. The results indicate that the average energy consumption of the proposed neuron model falls within the range of 16 pJ to 68 pJ.

Neural Activity in Quarks Language: Lattice Field Theory for a Network of Real Neurons.

Brain-computer interfaces have seen extraordinary surges in developments in recent years, and a significant discrepancy now exists between the abundance of available data and the limited headway made in achieving a unified theoretical framework. This discrepancy becomes particularly pronounced when examining the collective neural activity at the micro and meso scale, where a coherent formalization that adequately describes neural interactions is still lacking. Here, we introduce a mathematical framework to analyze systems of natural neurons and interpret the related empirical observations in terms of lattice field theory, an established paradigm from theoretical particle physics and statistical mechanics. Our methods are tailored to interpret data from chronic neural interfaces, especially spike rasters from measurements of single neuron activity, and generalize the maximum entropy model for neural networks so that the time evolution of the system is also taken into account. This is obtained by bridging particle physics and neuroscience, paving the way for particle physics-inspired models of the neocortex.

A boundary element method of bidomain modeling for predicting cellular responses to electromagnetic fields

Objective. Commonly used cable equation approaches for simulating the effects of electromagnetic fields on excitable cells make several simplifying assumptions that could limit their predictive power. Bidomain or ‘whole’ finite element methods have been developed to fully couple cells and electric fields for more realistic neuron modeling. Here, we introduce a novel bidomain integral equation designed for determining the full electromagnetic coupling between stimulation devices and the intracellular, membrane, and extracellular regions of neurons. Approach. Our proposed boundary element formulation offers a solution to an integral equation that connects the device, tissue inhomogeneity, and cell membrane-induced E-fields. We solve this integral equation using first-order nodal elements and an unconditionally stable Crank–Nicholson time-stepping scheme. To validate and demonstrate our approach, we simulated cylindrical Hodgkin–Huxley axons and spherical cells in multiple brain stimulation scenarios. Main Results. Comparison studies show that a boundary element approach produces accurate results for both electric and magnetic stimulation. Unlike bidomain finite element methods, the bidomain boundary element method does not require volume meshes containing features at multiple scales. As a result, modeling cells, or tightly packed populations of cells, with microscale features embedded in a macroscale head model, is simplified, and the relative placement of devices and cells can be varied without the need to generate a new mesh. Significance. Device-induced electromagnetic fields are commonly used to modulate brain activity for research and therapeutic applications. Bidomain solvers allow for the full incorporation of realistic cell geometries, device E-fields, and neuron populations. Thus, multi-cell studies of advanced neuronal mechanisms would greatly benefit from the development of fast-bidomain solvers to ensure scalability and the practical execution of neural network simulations with realistic neuron morphologies.

A Continuous Attractor Model with Realistic Neural and Synaptic Properties Quantitatively Reproduces Grid Cell Physiology.

Computational simulations with data-driven physiological detail can foster a deeper understanding of the neural mechanisms involved in cognition. Here, we utilize the wealth of cellular properties from Hippocampome.org to study neural mechanisms of spatial coding with a spiking continuous attractor network model of medial entorhinal cortex circuit activity. The primary goal is to investigate if adding such realistic constraints could produce firing patterns similar to those measured in real neurons. Biological characteristics included in the work are excitability, connectivity, and synaptic signaling of neuron types defined primarily by their axonal and dendritic morphologies. We investigate the spiking dynamics in specific neuron types and the synaptic activities between groups of neurons. Modeling the rodent hippocampal formation keeps the simulations to a computationally reasonable scale while also anchoring the parameters and results to experimental measurements. Our model generates grid cell activity that well matches the spacing, size, and firing rates of grid fields recorded in live behaving animals from both published datasets and new experiments performed for this study. Our simulations also recreate different scales of those properties, e.g., small and large, as found along the dorsoventral axis of the medial entorhinal cortex. Computational exploration of neuronal and synaptic model parameters reveals that a broad range of neural properties produce grid fields in the simulation. These results demonstrate that the continuous attractor network model of grid cells is compatible with a spiking neural network implementation sourcing data-driven biophysical and anatomical parameters from Hippocampome.org. The software (version 1.0) is released as open source to enable broad community reuse and encourage novel applications.

Mapping model units to visual neurons reveals population code for social behaviour

The rich variety of behaviours observed in animals arises through the interplay between sensory processing and motor control. To understand these sensorimotor transformations, it is useful to build models that predict not only neural responses to sensory input1–5 but also how each neuron causally contributes to behaviour6,7. Here we demonstrate a novel modelling approach to identify a one-to-one mapping between internal units in a deep neural network and real neurons by predicting the behavioural changes that arise from systematic perturbations of more than a dozen neuronal cell types. A key ingredient that we introduce is ‘knockout training’, which involves perturbing the network during training to match the perturbations of the real neurons during behavioural experiments. We apply this approach to model the sensorimotor transformations of Drosophila melanogaster males during a complex, visually guided social behaviour8–11. The visual projection neurons at the interface between the optic lobe and central brain form a set of discrete channels12, and prior work indicates that each channel encodes a specific visual feature to drive a particular behaviour13,14. Our model reaches a different conclusion: combinations of visual projection neurons, including those involved in non-social behaviours, drive male interactions with the female, forming a rich population code for behaviour. Overall, our framework consolidates behavioural effects elicited from various neural perturbations into a single, unified model, providing a map from stimulus to neuronal cell type to behaviour, and enabling future incorporation of wiring diagrams of the brain15 into the model.

Information bottleneck-based Hebbian learning rule naturally ties working memory and synaptic updates.

Deep neural feedforward networks are effective models for a wide array of problems, but training and deploying such networks presents a significant energy cost. Spiking neural networks (SNNs), which are modeled after biologically realistic neurons, offer a potential solution when deployed correctly on neuromorphic computing hardware. Still, many applications train SNNs offline, and running network training directly on neuromorphic hardware is an ongoing research problem. The primary hurdle is that back-propagation, which makes training such artificial deep networks possible, is biologically implausible. Neuroscientists are uncertain about how the brain would propagate a precise error signal backward through a network of neurons. Recent progress addresses part of this question, e.g., the weight transport problem, but a complete solution remains intangible. In contrast, novel learning rules based on the information bottleneck (IB) train each layer of a network independently, circumventing the need to propagate errors across layers. Instead, propagation is implicit due the layers' feedforward connectivity. These rules take the form of a three-factor Hebbian update a global error signal modulates local synaptic updates within each layer. Unfortunately, the global signal for a given layer requires processing multiple samples concurrently, and the brain only sees a single sample at a time. We propose a new three-factor update rule where the global signal correctly captures information across samples via an auxiliary memory network. The auxiliary network can be trained a priori independently of the dataset being used with the primary network. We demonstrate comparable performance to baselines on image classification tasks. Interestingly, unlike back-propagation-like schemes where there is no link between learning and memory, our rule presents a direct connection between working memory and synaptic updates. To the best of our knowledge, this is the first rule to make this link explicit. We explore these implications in initial experiments examining the effect of memory capacity on learning performance. Moving forward, this work suggests an alternate view of learning where each layer balances memory-informed compression against task performance. This view naturally encompasses several key aspects of neural computation, including memory, efficiency, and locality.

Field-Programmable Analog Array Implementation of Neuromorphic Silicon Neurons with Fractional Dynamics

Silicon neurons are bioinspired circuits with the capability to reproduce the modulation through pulse-frequency observed in real neurons. They are of particular interest in closed-loop schemes to encode the control signal into pulses. This paper proposes the analog realization of neuromorphic silicon neurons with fractional dynamics. In particular, the fractional-order (FO) operator is introduced into classical neurons with the intention of reproducing the adaptation that has been observed experimentally in real neurons, which is the variation in the firing frequency even when considering a constant or periodic incoming stimulus. For validation purposes, simulations using a field-programmable analog array (FPAA) are performed to verify the behavior of the circuits.

Predictive coding networks for temporal prediction.

One of the key problems the brain faces is inferring the state of the world from a sequence of dynamically changing stimuli, and it is not yet clear how the sensory system achieves this task. A well-established computational framework for describing perceptual processes in the brain is provided by the theory of predictive coding. Although the original proposals of predictive coding have discussed temporal prediction, later work developing this theory mostly focused on static stimuli, and key questions on neural implementation and computational properties of temporal predictive coding networks remain open. Here, we address these questions and present a formulation of the temporal predictive coding model that can be naturally implemented in recurrent networks, in which activity dynamics rely only on local inputs to the neurons, and learning only utilises local Hebbian plasticity. Additionally, we show that temporal predictive coding networks can approximate the performance of the Kalman filter in predicting behaviour of linear systems, and behave as a variant of a Kalman filter which does not track its own subjective posterior variance. Importantly, temporal predictive coding networks can achieve similar accuracy as the Kalman filter without performing complex mathematical operations, but just employing simple computations that can be implemented by biological networks. Moreover, when trained with natural dynamic inputs, we found that temporal predictive coding can produce Gabor-like, motion-sensitive receptive fields resembling those observed in real neurons in visual areas. In addition, we demonstrate how the model can be effectively generalized to nonlinear systems. Overall, models presented in this paper show how biologically plausible circuits can predict future stimuli and may guide research on understanding specific neural circuits in brain areas involved in temporal prediction.

Dynamical analysis of the FitzHugh–Nagumo model with memristive synapse

Understanding the transition mechanism between different activity patterns in realistic neuron models brings forward fundamental challenges for the dynamical systems theory. The knowledge about the mechanisms can present precious predictions and intuitions for determining fundamental principles of neuron functioning. This paper aims to present a dynamic analysis of the FitzHugh–Nagumo neuron model with a memristive synapse. In this article, the effects of memristive synapse's conductance gain, applied current, and the speed of electrical signal propagation along axons and dendrites on the system's behavior and the neuron's membrane potential are investigated. Analyzes are performed by investigating bifurcation and Lyapunov exponent diagrams versus various model parameters. The physiological role of some parameters and the effect of parameter changes on the model behaviors are discussed. The results demonstrate that when no current is applied to the system, the maximum value of membrane potential is larger, and also, a lower memristive synapse conductance gain leads to a larger maximum value of membrane potential. So, it can be concluded that the neuron in an amplitude death state may be triggered and start firing by decreasing the conductance gain or not applying current.

Superficial white matter microstructural imaging method based on time-space fractional-order diffusion

Objective. Microstructure imaging based on diffusion magnetic resonance signal is an advanced imaging technique that enables in vivo mapping of the brain’s microstructure. Superficial white matter (SWM) plays an important role in brain development, maturation, and aging, while fewer microstructure imaging methods address the SWM due to its complexity. Therefore, this study aims to develop a diffusion propagation model to investigate the microstructural characteristics of the SWM region. Approach. In this paper, we hypothesize that the effect of cell membrane permeability and the water exchange between soma and dendrites cannot be neglected for typical clinical diffusion times (20 ms < t < 80 ms). We then use SpinDoctor to simulate the diffusion magnetic resonance signals of real neurons and propose a time-space fractional-order diffusion model for SWM microstructure imaging. We evaluate the validity regime of our model using numerical simulations and compare the model parameters with several state-of-the-art methods. Main results. By analyzing the simulation signals of real neuronal cells as well as diffusion magnetic resonance data from the brains of fourteen healthy human subjects, we find that the time-space fractional-order diffusion model can be used to capture the structural complexity of the tissue, indirectly through the association of time fractional exponents with restricted diffusion and space fractional exponents with perfusion and membrane permeability. Significance. The results show that the diffusion propagation model can provide new insights into the tissue architecture of the SWM.

How neuronal morphology impacts the synchronisation state of neuronal networks.

The biophysical properties of neurons not only affect how information is processed within cells, they can also impact the dynamical states of the network. Specifically, the cellular dynamics of action-potential generation have shown relevance for setting the (de)synchronisation state of the network. The dynamics of tonically spiking neurons typically fall into one of three qualitatively distinct types that arise from distinct mathematical bifurcations of voltage dynamics at the onset of spiking. Accordingly, changes in ion channel composition or even external factors, like temperature, have been demonstrated to switch network behaviour via changes in the spike onset bifurcation and hence its associated dynamical type. A thus far less addressed modulator of neuronal dynamics is cellular morphology. Based on simplified and anatomically realistic mathematical neuron models, we show here that the extent of dendritic arborisation has an influence on the neuronal dynamical spiking type and therefore on the (de)synchronisation state of the network. Specifically, larger dendritic trees prime neuronal dynamics for in-phase-synchronised or splayed-out activity in weakly coupled networks, in contrast to cells with otherwise identical properties yet smaller dendrites. Our biophysical insights hold for generic multicompartmental classes of spiking neuron models (from ball-and-stick-type to anatomically reconstructed models) and establish a connection between neuronal morphology and the susceptibility of neural tissue to synchronisation in health and disease.

Dendritic effects of tDCS insights from a morphologically realistic model neuron

Transcranial direct current stimulation (tDCS) induces subcellular compartmental-dependent polarization, maximal in the distal portions of axons and dendrites. Using a morphologically realistic neuron model, we simulated tDCS-induced membrane polarization of the apical dendrite. Thus, we investigated the differential dendritic effects of anodal and cathodal tDCS on membrane potential polarization along the dendritic structure and its subsequent effects on dendritic membrane resistance, excitatory postsynaptic potential amplitude, backpropagating action potential amplitude, input/output relations, and long-term synaptic plasticity. We further showed that the effects of anodal and cathodal tDCS on the backpropagating action potential were asymmetric, and explained this asymmetry. Additionally, we showed that the effects on input/output relations were rather weak and limited to the low-mid range of stimulation frequencies, and that synaptic plasticity effects were mostly limited to the distal portion of the dendrite. Thus, we demonstrated how tDCS modifies dendritic physiology due to the dendrite's unique morphology and composition of voltage-gated ion channels.

Rapid changes in synchronizability in conductance-based neuronal networks with conductance-based coupling.

Real neurons connect to each other non-randomly. These connectivity graphs can potentially impact the ability of networks to synchronize, along with the dynamics of neurons and the dynamics of their connections. How the connectivity of networks of conductance-based neuron models like the classical Hodgkin-Huxley model or the Morris-Lecar model impacts synchronizability remains unknown. One powerful tool to resolve the synchronizability of these networks is the master stability function (MSF). Here, we apply and extend the MSF approach to networks of Morris-Lecar neurons with conductance-based coupling to determine under which parameters and for which graphs the synchronous solutions are stable. We consider connectivity graphs with a constant non-zero row sum, where the MSF approach can be readily extended to conductance-based synapses rather than the more well-studied diffusive connectivity case, which primarily applies to gap junction connectivity. In this formulation, the synchronous solution is a single, self-coupled, or "autaptic" neuron. We find that the primary determining parameter for the stability of the synchronous solution is, unsurprisingly, the reversal potential, as it largely dictates the excitatory/inhibitory potential of a synaptic connection. However, the change between "excitatory" and "inhibitory" synapses is rapid, with only a few millivolts separating stability and instability of the synchronous state for most graphs. We also find that for specific coupling strengths (as measured by the global synaptic conductance), islands of synchronizability in the MSF can emerge for inhibitory connectivity. We verified the stability of these islands by direct simulation of pairs of neurons coupled with eigenvalues in the matching spectrum.

Dynamic Gain Decomposition Reveals Functional Effects of Dendrites, Ion Channels, and Input Statistics in Population Coding.

Modern, high-density neuronal recordings reveal at ever higher precision how information is represented by neural populations. Still, we lack the tools to understand these processes bottom-up, emerging from the biophysical properties of neurons, synapses, and network structure. The concept of the dynamic gain function, a spectrally resolved approximation of a population's coding capability, has the potential to link cell-level properties to network-level performance. However, the concept is not only useful but also very complex because the dynamic gain's shape is co-determined by axonal and somato-dendritic parameters and the population's operating regime. Previously, this complexity precluded an understanding of any individual parameter's impact. Here, we decomposed the dynamic gain function into three components corresponding to separate signal transformations. This allowed attribution of network-level encoding features to specific cell-level parameters. Applying the method to data from real neurons and biophysically plausible models, we found: (1) The encoding bandwidth of real neurons, approximately 400 Hz, is constrained by the voltage dependence of axonal currents during early action potential initiation. (2) State-of-the-art models only achieve encoding bandwidths around 100 Hz and are limited mainly by subthreshold processes instead. (3) Large dendrites and low-threshold potassium currents modulate the bandwidth by shaping the subthreshold stimulus-to-voltage transformation. Our decomposition provides physiological interpretations when the dynamic gain curve changes, for instance during spectrinopathies and neurodegeneration. By pinpointing shortcomings of current models, it also guides inference of neuron models best suited for large-scale network simulations.

Preserving Derivative Information while Transforming Neuronal Curves

The international neuroscience community is building the first comprehensive atlases of brain cell types to understand how the brain functions from a higher resolution, and more integrated perspective than ever before. In order to build these atlases, subsets of neurons (e.g. serotonergic neurons, prefrontal cortical neurons etc.) are traced in individual brain samples by placing points along dendrites and axons. Then, the traces are mapped to common coordinate systems by transforming the positions of their points, which neglects how the transformation bends the line segments in between. In this work, we apply the theory of jets to describe how to preserve derivatives of neuron traces up to any order. We provide a framework to compute possible error introduced by standard mapping methods, which involves the Jacobian of the mapping transformation. We show how our first order method improves mapping accuracy in both simulated and real neuron traces under random diffeomorphisms. Our method is freely available in our open-source Python package brainlit.

A Hyperparameter Self-Evolving SHADE-Based Dendritic Neuron Model for Classification

In recent years, artificial neural networks (ANNs), which are based on the foundational model established by McCulloch and Pitts in 1943, have been at the forefront of computational research. Despite their prominence, ANNs have encountered a number of challenges, including hyperparameter tuning and the need for vast datasets. It is because many strategies have predominantly focused on enhancing the depth and intricacy of these networks that the essence of the processing capabilities of individual neurons is occasionally overlooked. Consequently, a model emphasizing a biologically accurate dendritic neuron model (DNM) that mirrors the spatio-temporal features of real neurons was introduced. However, while the DNM shows outstanding performance in classification tasks, it struggles with complexities in parameter adjustments. In this study, we introduced the hyperparameters of the DNM into an evolutionary algorithm, thereby transforming the method of setting DNM’s hyperparameters from the previous manual adjustments to adaptive adjustments as the algorithm iterates. The newly proposed framework, represents a neuron that evolves alongside the iterations, thus simplifying the parameter-tuning process. Comparative evaluation on benchmark classification datasets from the UCI Machine Learning Repository indicates that our minor enhancements lead to significant improvements in the performance of DNM, surpassing other leading-edge algorithms in terms of both accuracy and efficiency. In addition, we also analyzed the iterative process using complex networks, and the results indicated that the information interaction during the iteration and evolution of the DNM follows a power-law distribution. With this finding, some insights could be provided for the study of neuron model training.