Since the first experimental evidences of active conductances in dendrites, most neurons have been shown to exhibit dendritic excitability through the expression of a variety of voltage-gated ion channels. However, despite experimental and theoretical efforts undertaken in the last decades, the role of this excitability for some kind of dendritic computation has remained elusive. Here we show that, owing to very general properties of excitable media, the average output of a model of active dendritic trees is a highly non-linear function of their afferent rate, attaining extremely large dynamic ranges (above 50 dB). Moreover, the model yields double-sigmoid response functions as experimentally observed in retinal ganglion cells. We claim that enhancement of dynamic range is the primary functional role of active dendritic conductances. We predict that neurons with larger dendritic trees should have larger dynamic range and that blocking of active conductances should lead to a decrease of dynamic range.
The cable model is widely used in several fields of science to describe the propagation of signals. A relevant medical and biological example is the anomalous subdiffusion in spiny neuronal dendrites observed in several studies of the last decade. Anomalous subdiffusion can be modelled in several ways introducing some fractional component into the classical cable model. The Chauchy problem associated to these kind of models has been investigated by many authors, but up to our knowledge an explicit solution for the signalling problem has not yet been published. Here we propose how this solution…
The relative importance of the intrinsic and extrinsic factors determining the variety of geometric shapes exhibited by dendritic trees remains unclear. This question was addressed by developing a model of the growth of dendritic trees based on diffusion-limited aggregation process. The model reproduces diverse neuronal shapes (i.e., granule cells, Purkinje cells, the basal and apical dendrites of pyramidal cells, and the axonal trees of interneurons) by changing only the size of the growth area, the time span of pruning, and the spatial concentration of 'neurotrophic particles'. Moreover, the…
Neocortical pyramidal neurons have many dendrites, and such dendrites are capable of, in isolation of one-another, generating a neuronal spike. It is also now understood that there is a large amount of dendritic growth during the first years of a humans life, arguably a period of prodigious learning. These observations inspire the construction of a local, stochastic algorithm based on an earlier stochastic, Hebbian developmental theory. Here we investigate the neuro-computational advantages and limits on this novel algorithm that combines dendritogenesis with supervised adaptive synaptogenesis…
Neuronal morphology is an essential element for brain activity and function. We take advantage of current availability of brain-wide neuron digital reconstructions of the Pyramidal cells from a mouse brain, and analyze several emergent features of brain-wide neuronal morphology. We observe that axonal trees are self-affine while dendritic trees are self-similar. We also show that tree size appear to be random, independent of the number of dendrites within single neurons. Moreover, we consider inhomogeneous branching model which stochastically generates rooted 3-Cayley trees for the brain-wide …
Neuronal networks constitute a special class of dynamical systems, as they are formed by individual geometrical components, namely the neurons. In the existing literature, relatively little attention has been given to the influence of neuron shape on the overall connectivity and dynamics of the emerging networks. The current work addresses this issue by considering simplified neuronal shapes consisting of circular regions (soma/axons) with spokes (dendrites). Networks are grown by placing these patterns randomly in the 2D plane and establishing connections whenever a piece of dendrite falls in…
A complete single-neuron model must correctly reproduce the firing of spikes and bursts. We present a study of a simplified model of deep pyramidal cells of the cortex with active dendrites. We hypothesized that we can model the soma and its apical tuft with only two compartments, without significant loss in the accuracy of spike-timing predictions. The model is based on experimentally measurable impulse-response functions, which transfer the effect of current injected in one compartment to current reaching the other. Each compartment was modeled with a pair of non-linear differential equation…
We propose a formal mathematical model for sparse representations and active dendrites in neocortex. Our model is inspired by recent experimental findings on active dendritic processing and NMDA spikes in pyramidal neurons. These experimental and modeling studies suggest that the basic unit of pattern memory in the neocortex is instantiated by small clusters of synapses operated on by localized non-linear dendritic processes. We derive a number of scaling laws that characterize the accuracy of such dendrites in detecting activation patterns in a neuronal population under adverse conditions. We…
Dendrites are branched neuronal processes that receive input signals from other neurons or the outside world [1]. To maintain connectivity as the organism grows, dendrites must also continue to grow. For example, the dendrites in the peripheral nervous system continue to grow and branch to maintain proper coverage of their receptor fields [2, 3, 4, 5]. One such neuron is the Drosophila melanogaster class IV dendritic arborization neuron [6]. The dendritic arbors of these neurons tile the larval surface [7], where they detect localized noxious stimuli, such as jabs from parasitic wasps [8]. In …
Identify the directions of signal flows in neural networks is one of the most important stages for understanding the intricate information dynamics of a living brain. Using a dataset of 213 projection neurons distributed in different regions of Drosophila brain, we develop a powerful machine learning algorithm: node-based polarity identifier of neurons (NPIN). The proposed model is trained by nodal information only and includes both Soma Features (which contain spatial information from a given node to a soma) and Local Features (which contain morphological information of a given node). After i…
How extracellular electric fields, as generated endogenously or through transcranial brain stimulation, affect the dynamics of large neuronal populations is of great interest but not well understood. To study the collective dynamics of large populations single-compartment (point) model neurons have been proven very successful. These models, however, lack the dendritic morphology to biophysically account for the effects of electric fields, and for changes in synaptic integration due to morphology alone. Here we (i) characterize the response of a canonical spatial (ball-and-stick) model neuron t…
The nonlinear properties of the dendrites in prepositus hypoglossi neurons are involved in maintenance of eye position. The biophysical properties of these neurons are essential for the operation of the vestibular neural integrator that converts a head velocity signal to one that controls eye position. A novel method named QSA (quadratic sinusoidal analysis) for voltage clamped neurons was used to quantify nonlinear responses that are dominated by dendrites. The voltage clamp currents were measured at harmonic and interactive frequencies using specific stimulation frequencies, which act as fre…
We propose a neural network model of multi-neuron interacting system that simulates neurons to interact each other through the surroundings of neuronal cell bodies. We physically model the neuronal cell surroundings, include the dendrites, the axons and the synapses as well as the surrounding glial cells, as a collection of all kinds of oscillating modes arisen from the electric circuital environment of neuronal action potentials. By analyzing the dynamics of this neural model through the master equation approach of open quantum systems, we investigate the collective behavior of neurons. After…
Neurons are spatially extended structures that receive and process inputs on their dendrites. It is generally accepted that neuronal computations arise from the active integration of synaptic inputs along a dendrite between the input location and the location of spike generation in the axon initial segment. However, many application such as simulations of brain networks, use point-neurons --neurons without a morphological component-- as computational units to keep the conceptual complexity and computational costs low. Inevitably, these applications thus omit a fundamental property of neuronal …
A key challenge for AI is to build embodied systems that operate in dynamically changing environments. Such systems must adapt to changing task contexts and learn continuously. Although standard deep learning systems achieve state of the art results on static benchmarks, they often struggle in dynamic scenarios. In these settings, error signals from multiple contexts can interfere with one another, ultimately leading to a phenomenon known as catastrophic forgetting. In this article we investigate biologically inspired architectures as solutions to these problems. Specifically, we show that the…
Early brain connectivity development consists of multiple stages: birth of neurons, their migration and the subsequent growth of axons and dendrites. Each stage occurs within a certain period of time depending on types of neurons and cortical layers. Forming synapses between neurons either by growing axons starting at similar times for all neurons (much-overlapped time windows) or at different time points (less-overlapped) may affect the topological and spatial properties of neuronal networks. Here, we explore the extreme cases of axon formation especially concerning short-distance connectivit…
This paper presents a spike-based model which employs neurons with functionally distinct dendritic compartments for classifying high dimensional binary patterns. The synaptic inputs arriving on each dendritic subunit are nonlinearly processed before being linearly integrated at the soma, giving the neuron a capacity to perform a large number of input-output mappings. The model utilizes sparse synaptic connectivity; where each synapse takes a binary value. The optimal connection pattern of a neuron is learned by using a simple hardware-friendly, margin enhancing learning algorithm inspired by t…
The interaction between excitation and inhibition is crucial for brain computation. To understand synaptic mechanisms underlying brain function, it is important to separate excitatory and inhibitory inputs to a target neuron. In the traditional method, after applying somatic current or voltage clamp, the excitatory and inhibitory conductances are determined from the synaptic current-voltage (I-V) relation --- the slope corresponds to the total conductance and the intercept corresponds to the reversal current. Because of the space clamp effect, the measured conductance in general deviates subst…
An Operating Principle of the Cerebral Cortex, and a Cellular Mechanism for Attentional Trial-and-Error Pattern Learning and Useful Classification Extraction
Neuronal avalanche is a spontaneous neuronal activity which obeys a power-law distribution of population event sizes with an exponent of -3/2. It has been observed in the superficial layers of cortex both \emph{in vivo} and \emph{in vitro}. In this paper we analyze the information transmission of a novel self-organized neural network with active-neuron-dominant structure. Neuronal avalanches can be observed in this network with appropriate input intensity. We find that the process of network learning via spike-timing dependent plasticity dramatically increases the complexity of network structu…
NSPDI-SNN: An efficient lightweight SNN based on nonlinear synaptic pruning and dendritic integration
Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for NeuroInformation, China-Cuba Belt and Road Joint Laboratory on Neurotechnology and Brain-Apparatus Communication, School of Life Science and Technology, University of Electronic Science and Technology of China（成都脑科学研究所临床医院，教育部神经信息重点实验室，中老一带一路神经技术与脑-装置通信联合实验室，生命科学与技术学院，电子科技大学）；Academy of Medical Engineering and Translational Medicine, Tianjin University（医学工程与转化医学学院，天津大学）；School of Artificial Intelligence, Chongqing University of Education（人工智能学院，重庆教育学院）；Research Unit of NeuroInformation (2019RU035)（神经信息研究单位（2019RU035））
Refractoriness is a fundamental property of excitable elements, such as neurons, indicating the probability for re-excitation in a given time-lag, and is typically linked to the neuronal hyperpolarization following an evoked spike. Here we measured the refractory periods (RPs) in neuronal cultures and observed that an average anisotropic absolute RP could exceed 10 milliseconds and its tail 20 milliseconds, independent of a large stimulation frequency range. It is an order of magnitude longer than anticipated and comparable with the decaying membrane potential timescale. It is followed by a sh…
Power laws, that is, power spectral densities (PSDs) exhibiting 1/f^alpha behavior for large frequencies f, have commonly been observed in neural recordings. Power laws in noise spectra have not only been observed in microscopic recordings of neural membrane potentials and membrane currents, but also in macroscopic EEG (electroencephalographic) recordings. While complex network behavior has been suggested to be at the root of this phenomenon, we here demonstrate a possible origin of such power laws in the biophysical properties of single neurons described by the standard cable equation. Taking…
Signal propagation in neuronal dendrites represents the basis for interneuron communication and information processing in the brain. Here we take into account charge inhomogeneities arising in the vicinity of ion channels in cytoplasm and obtained a modified cable equation. We show that the charge inhomogeneities acting on the millisecond time scale can lead to the appearance of propagating waves with wavelengths of hundreds of micrometers. They correspond to a certain frequency band predicting the appearance of resonant properties in brain neuron signalling.
The balance between excitation and inhibition is crucial for neuronal computation. It is observed that the balanced state of neuronal networks exists in many experiments, yet its underlying mechanism remains to be fully clarified. Theoretical studies of the balanced state mainly focus on the analysis of the homogeneous Erd$\ddot{\text{o}}$s-Rényi network. However, neuronal networks have been found to be inhomogeneous in many cortical areas. In particular, the connectivity of neuronal networks can be of the type of scale-free, small-world, or even with specific motifs. In this work, we examine …
The shape and connectivity of a neuron determine its function. Modern imaging methods have proven successful at extracting such information. However, in order to analyze this type of data, neuronal morphology needs to be encoded in a graph-theoretic method. This encoding enables the use of high throughput informatic methods to extract and infer brain function. The application of graph-theoretic methods to neuronal morphological representation comes with certain difficulties. Here we report a novel, effective method to accomplish this task. The morphology of a neuron, which consists of its over…
Active inference is a normative framework for explaining behaviour under the free energy principle -- a theory of self-organisation originating in neuroscience. It specifies neuronal dynamics for state-estimation in terms of a descent on (variational) free energy -- a measure of the fit between an internal (generative) model and sensory observations. The free energy gradient is a prediction error -- plausibly encoded in the average membrane potentials of neuronal populations. Conversely, the expected probability of a state can be expressed in terms of neuronal firing rates. We show that this i…
The synaptic connectivity of cortex is plastic, with experience shaping the ongoing interactions between neurons. Theoretical studies of spike timing-dependent plasticity (STDP) have focused on either just pairs of neurons or large-scale simulations where analytic insight is lacking. A simple account for how fast spike time correlations affect both micro- and macroscopic network structure remains lacking. We develop a low-dimensional mean field theory showing how STDP gives rise to strongly coupled assemblies of neurons with shared stimulus preferences, with the connectivity actively reinforce…
We analytically study the input-output properties of a neuron whose active dendritic tree, modeled as a Cayley tree of excitable elements, is subjected to Poisson stimulus. Both single-site and two-site mean-field approximations incorrectly predict a non-equilibrium phase transition which is not allowed in the model. We propose an excitable-wave mean-field approximation which shows good agreement with previously published simulation results [Gollo et al., PLoS Comput. Biol. 5(6) e1000402 (2009)] and accounts for finite-size effects. We also discuss the relevance of our results to experiments i…
How neurons process their inputs crucially determines the dynamics of biological and artificial neural networks. In such neural and neural-like systems, synaptic input is typically considered to be merely transmitted linearly or sublinearly by the dendritic compartments. Yet, single-neuron experiments report pronounced supralinear dendritic summation of sufficiently synchronous and spatially close-by inputs. Here, we provide a statistical physics approach to study the impact of such non-additive dendritic processing on single neuron responses and the performance of associative memory tasks in …
Fluorescent nanodiamonds (FND) are carbon-based nanomaterials that can efficiently incorporate optically active photoluminescent centers such as the nitrogen-vacancy complex, thus making them promising candidates as optical biolabels and drug-delivery agents. FNDs exhibit bright fluorescence without photobleaching combined with high uptake rate and low cytotoxicity. Focusing on FNDs interference with neuronal function, here we examined their effect on cultured hippocampal neurons, monitoring the whole network development as well as the electrophysiological properties of single neurons. We obse…
We study the effects of periodic subthreshold pacemaker activity and time-delayed coupling on stochastic resonance over scale-free neuronal networks. As the two extreme options, we introduce the pacemaker respectively to the neuron with the highest degree and to one of the neurons with the lowest degree within the network, but we also consider the case when all neurons are exposed to the periodic forcing. In the absence of delay, we show that an intermediate intensity of noise is able to optimally assist the pacemaker in imposing its rhythm on the whole ensemble, irrespective to its placing, t…
Mounting evidence in neuroscience suggests the possibility of neuronal representations that individual neurons serve as the substrates of different mental representations in a point-to-point way. Combined with associationism, it can potentially address a range of theoretical problems and provide a straightforward explanation for our cognition. However, this idea is merely a hypothesis with many questions unsolved. In this paper, I will bring up a new framework to defend the idea of neuronal representations. The strategy is from micro- to macro-level. Specifically, in the micro-level, I first p…
Field closure, ice neurons, and when a dendrite is a motif
McGovern Institute for Brain Research, Massachusetts Institute of Technology（麻省理工学院麦戈文脑研究所）；The NSF AI Institute for Artificial Intelligence and Fundamental Interactions (IAIFI)（美国国家科学基金会人工智能基础相互作用研究所）
Neurons are thought of as the building blocks of excitable brain tissue. However, at the single neuron level, the neuronal membrane, the dendritic arbor and the axonal projections can also be considered an extended active medium. Active dendritic branchlets enable the propagation of dendritic spikes, whose computational functions, despite several proposals, remain an open question. Here we propose a concrete function to the active channels in large dendritic trees. By using a probabilistic cellular automaton approach, we model the input-output response of large active dendritic arbors subjecte…
This article describes the investigation of morphological variations among two set of neuronal cells, namely a control group of wild type rat cells and a group of cells of a trangenic line. Special attention is given to sigular points in the neuronal structure, namely the branching points and extremities of the dendritic processes. The characterization of the spatial distribution of such points is obtained by using a recently reported morphological technique based on forced percolation and window-size compensation, which is particularly suited to the analysis of scattered points presenting sev…
Neuronal electricality founded in murburn-thermodynamic principles: 2. Comparisons, evidenced explanations, and predictions
Amrita School of Artificial Intelligence, Coimbatore, Amrita Vishwa Vidyapeetham（阿姆利塔人工智能学院，阿姆利塔维迪亚佩塔姆大学）；Satyamjayatu: The Science & Ethics Foundation（真理至上：科学与伦理基金会）；University of Rostock（罗斯托克大学）；Wayne State University（韦恩州立大学）
This report is concerned with the relevance of the microscopic rules, that implement individual neuronal activation, in determining the collective dynamics, under variations of the network topology. To fix ideas we study the dynamics of two cellular automaton models, commonly used, rather in-distinctively, as the building blocks of large scale neuronal networks. One model, due to Greenberg \& Hastings, (GH) can be described by evolution equations mimicking an integrate-and-fire process, while the other model, due to Kinouchi \& Copelli, (KC) represents an abstract branching process, where a si…
Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College London（伦敦大学学院神经学研究所惠康神经影像中心）；VERSES AI Research Lab（VERSES人工智能研究实验室）；RIKEN Center for Brain Science（理化学研究所脑科学中心）；Nuffield Department of Clinical Neurosciences, University of Oxford（牛津大学纳菲尔德临床神经科学系）；IITB-Monash Research Academy（印度理工学院孟买分校-莫纳什大学研究学院）；Monash Biomedical Imaging, Monash University（莫纳什大学生物医学影像中心）；Cortical Labs（皮质实验室）
A model of the columnar functional organization of neocortical association areas is studied. The neuronal network is composed of many Hebbian autoassociators, or modules, each of which interacts with a relatively small number of the others. Every module encodes and stores a number of elementary percepts, or features. Memory items, or patterns, are peculiar combinations of features sparsely distributed over the multi-modular network. Any feature stored in any module can be involved in several of the stored patterns; feature-sharing is in fact source of local ambiguities and, consequently, a pot…
We present a theoretical framework using quorum-percolation for describing the initiation of activity in a neural culture. The cultures are modeled as random graphs, whose nodes are excitatory neurons with kin inputs and kout outputs, and whose input degrees kin = k obey given distribution functions pk. We examine the firing activity of the population of neurons according to their input degree (k) classes and calculate for each class its firing probability Φ_k(t) as a function of t. The probability of a node to fire is found to be determined by its in-degree k, and the first-to-fire neurons ar…
The electric activities of cortical pyramidal neurons are supported by structurally stable, morphologically complex axo-dendritic trees. Anatomical differences between axons and dendrites in regard to their length or caliber reflect the underlying functional specializations, for input or output of neural information, respectively. For a proper assessment of the computational capacity of pyramidal neurons, we have analyzed an extensive dataset of three-dimensional digital reconstructions from the NeuroMorpho.Org database, and quantified basic dendritic or axonal morphometric measures in differe…
Dynamic sampling of non-stationary spontaneous activity in dissociated neuronal networks
Graduate School of Information Science and Technology, The University of Tokyo（东京大学大学院信息理工学系研究科）；International Research Center for Neurointelligence (WPI-IRCN), The University of Tokyo（东京大学国际脑科学中心（WPI-IRCN））
Neocortical neurons have thousands of excitatory synapses. It is a mystery how neurons integrate the input from so many synapses and what kind of large-scale network behavior this enables. It has been previously proposed that non-linear properties of dendrites enable neurons to recognize multiple patterns. In this paper we extend this idea by showing that a neuron with several thousand synapses arranged along active dendrites can learn to accurately and robustly recognize hundreds of unique patterns of cellular activity, even in the presence of large amounts of noise and pattern variation. We …
Synaptic plasticity and neuron cross-talk are some of the important key mechanisms underlying formation of dynamic clusters of active neurons. The essence of this study is to model and decipher the mechanism of emergence of a task-specific functional connectivity among a population of neurons. We have used our proposed neuron activity pattern (NAP) model to define an assorted range of interactions and simulated across a 2D lattice with two-state (firing/non-firing) neurons. We observed the emergence of scale-free, hierarchically organized ordered patterns of active neurons, that we call as fun…
Spiking neurons can perform spatiotemporal feature detection by nonlinear synaptic and dendritic integration of presynaptic spike patterns. Multicompartment models of non-linear dendrites and related neuromorphic circuit designs enable faithful imitation of such dynamic integration processes, but these approaches are also associated with a relatively high computing cost or circuit size. Here, we investigate synaptic integration of spatiotemporal spike patterns with multiple dynamic synapses on point-neurons in the DYNAP-SE neuromorphic processor, which offers a complementary resource-efficient…
Experimental data have revealed that neuronal connection efficacy exhibits two forms of short-term plasticity, namely, short-term depression (STD) and short-term facilitation (STF). They have time constants residing between fast neural signaling and rapid learning, and may serve as substrates for neural systems manipulating temporal information on relevant time scales. The present study investigates the impact of STD and STF on the dynamics of continuous attractor neural networks (CANNs) and their potential roles in neural information processing. We find that STD endows the network with slow-d…
