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 connectivity during early development, either starting at the same time for all neurons (parallel, i.e. maximally-overlapped time windows) or occurring for each neuron separately one neuron after another (serial, i.e. no overlaps in time windows). For both cases, the number of potential and established synapses remained comparable. Topological and spatial properties, however, differed: neurons that started axon growth early on in serial growth achieved higher out-degrees, higher local efficiency, and longer axon lengths while neurons demonstrated more homogeneous connectivity patterns for parallel growth. Second, connection probability decreased more rapidly with distance between neurons for parallel growth than for serial growth. Third, bidirectional connections were more numerous for parallel growth. Finally, we tested our predictions with C. elegans data. Together, this indicates that time windows for axon growth influence the topological and spatial properties of neuronal networks opening the possibility to a posteriori estimate developmental mechanisms based on network properties of a developed network.
Axonal growth and the formation of synaptic connections are key steps in the development of the nervous system. Here we present experimental and theoretical results on axonal growth and interconnectivity in order to elucidate some of the basic rules that neuronal cells use for functional connections with one another. We demonstrate that a unidirectional nanotextured surface can bias axonal growth. We perform a systematic investigation of neuronal processes on asymmetric surfaces and quantify the role that biomechanical surface cues play in neuronal growth. These results represent an important …
Increasing experimental evidence suggests that axonal action potential conduction velocity is a highly adaptive parameter in the adult central nervous system. Yet, the effects of this newfound plasticity on global brain dynamics is poorly understood. In this work, we analyzed oscillations in biologically plausible neuronal networks with different conduction velocity distributions. Changes of 1-2 (ms) in network mean signal transmission time resulted in substantial network oscillation frequency changes ranging in 0-120 (Hz). Our results suggest that changes in axonal conduction velocity may sig…
Central neurons initiate action potentials (APs) in the axon initial segment (AIS), a compartment characterized by a high concentration of voltage-dependent ion channels and specialized cytoskeletal anchoring proteins arranged in a regular nanoscale pattern. Although the AIS was a key evolutionary innovation in neurons, the functional benefits it confers are not clear. Using a mutation of the AIS cytoskeletal protein βIV-spectrin, we here establish an in vitro model of neurons with a perturbed AIS architecture that retains nanoscale order but loses the ability to maintain a high NaV density. C…
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 …
It has recently been discovered that single neuron stimulation can impact network dynamics in immature and adult neuronal circuits. Here we report a novel mechanism which can explain in neuronal circuits, at an early stage of development, the peculiar role played by a few specific neurons in promoting/arresting the population activity. For this purpose, we consider a standard neuronal network model, with short-term synaptic plasticity, whose population activity is characterized by bursting behavior. The addition of developmentally inspired constraints and correlations in the distribution of th…
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…
Neural connectivity at the cellular and mesoscopic level appears very specific and is presumed to arise from highly specific developmental mechanisms. However, there are general shared features of connectivity in systems as different as the networks formed by individual neurons in Caenorhabditis elegans or in rat visual cortex and the mesoscopic circuitry of cortical areas in the mouse, macaque, and human brain. In all these systems, connection length distributions have very similar shapes, with an initial large peak and a long flat tail representing the admixture of long-distance connections …
Magnetic field sensing, with its recent advances, is emerging as a viable alternative to measure functional activity of single neurons in the brain by sensing action potential associated magnetic fields (APMFs). Measurement of APMFs of large axons of worms have been possible due to their size. In the mammalian brain, axon sizes, their numbers and routes, restricts using such functional imaging methods. With segmented model of mammalian pyramidal neurons, we show that the APMF of intra-axonal currents in the axon hillock are two orders of magnitude larger than other neuronal locations. Expected…
Most organisms suffer neuronal damage throughout their lives, which can impair performance of core behaviors. Their neural circuits need to maintain function despite injury, which in particular requires preserving key system outputs. In this work, we explore whether and how certain structural and functional neuronal network motifs act as injury mitigation mechanisms. Specifically, we examine how (i) Hebbian learning, (ii) high levels of noise, and (iii) parallel inhibitory and excitatory connections contribute to the robustness of the olfactory system in the Manduca sexta moth. We simulate inj…
Neural development represents not only an exciting and complex field of study, with ongoing progress, but it also became the epicentre of neuroscience and developmental biology, as it strives to describe the underlying cellular and molecular mechanisms by which the central nervous system emerges during the various levels of embryonic development phases. The nervous system is a dynamic entity, where the genetic information plays an important role in shaping the intra- and extracellular environments, which in turn offer a reliable foundation for the stem cell precursors to divide and form neuron…
We numerically investigate the influence of intrinsic channel noise on the dynamical response of delay-coupling in neuronal systems. The stochastic dynamics of the spiking is modeled within a stochastic modification of the standard Hodgkin-Huxley model wherein the delay-coupling accounts for the finite propagation time of an action potential along the neuronal axon. We quantify this delay-coupling of the Pyragas-type in terms of the difference between corresponding presynaptic and postsynaptic membrane potentials. For an elementary neuronal network consisting of two coupled neurons we detect c…
Axon guidance (AG) towards their target during embryogenesis or after injury is an important issue in the development of neuronal networks. During their growth, axons often face complex decisions that are difficult to understand when observing just a small part of the problem. In this work we propose a computational model of AG based on activity-independent mechanisms that takes into account the most important aspects of AG. The model includes the main elements (neurons, with soma, axon and growth cone; glial cells acting as guideposts) and mechanisms (attraction/repulsion guidance cues, growt…
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…
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 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…
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…
Critical brain hypothesis has been intensively studied both in experimental and theoretical neuroscience over the past two decades. However, some important questions still remain: (i) What is the critical point the brain operates at? (ii) What is the regulatory mechanism that brings about and maintains such a critical state? (iii) The critical state is characterized by scale-invariant behavior which is seemingly at odds with definitive brain oscillations? In this work we consider a biologically motivated model of Izhikevich neuronal network with chemical synapses interacting via spike-timingde…
A central problem of neuroscience involves uncovering the principles governing the organization of nervous systems which ensure robustness in brain development. The nematode Caenorhabditis elegans provides us with a model organism for studying this question. In this paper, we focus on the invariant connection structure and spatial arrangement of the neurons comprising the somatic neuronal network of this organism to understand the key developmental constraints underlying its design. We observe that neurons with certain shared characteristics - such as, neural process lengths, birth time cohort…
Synchronized bursts (SBs) with complex structures are common in neuronal cultures. Although the origin of SBs is still unclear, they have been studied for their information processing capabilities. Here, we investigate the properties of these SBs in a culture on multi-electrode array system. We find that structures of these SBs are related to the different developmental stages of the cultures. A model based on short term synaptic plasticity, recurrent connections and astrocytic recycling of neurotransmitters has been developed successfully to understand these structures. A phase diagram obtain…
This paper describes how realistic neuromorphic networks can have their connectivity fully characterized in analytical fashion. By assuming that all neurons have the same shape and are regularly distributed along the two-dimensional orthogonal lattice with parameter $Δ$, it is possible to obtain the exact number of connections and cycles of any length from the autoconvolution function as well as from the respective spectral density derived from the adjacency matrix. It is shown that neuronal shape plays an important role in defining the spatial distribution of synapses in neuronal networks. In…
When inhibitory neurons constitute about 40% of neurons they could have an important antinociceptive role, as they would easily regulate the level of activity of other neurons. We consider a simple network of cortical spiking neurons with axonal conduction delays and spike timing dependent plasticity, representative of a cortical column or hypercolumn with large proportion of inhibitory neurons. Each neuron fires following a Hodgkin-Huxley like dynamics and it is interconnected randomly to other neurons. The network dynamics is investigated estimating Bandt and Pompe probability distribution f…
The nematode Caenorhabditis elegans, with information on neural connectivity, three-dimensional position and cell linage provides a unique system for understanding the development of neural networks. Although C. elegans has been widely studied in the past, we present the first statistical study from a developmental perspective, with findings that raise interesting suggestions on the establishment of long-distance connections and network hubs. Here, we analyze the neuro-development for temporal and spatial features, using birth times of neurons and their three-dimensional positions. Comparisons…
Identifying the brain's neuronal cluster size to be presented as nodes in a network computation is critical to both neuroscience and artificial intelligence, as these define the cognitive blocks required for building intelligent computation. Experiments support many forms and sizes of neural clustering, while neural mass models (NMM) assume scale-invariant functionality. Here, we use computational simulations with brain-derived fMRI network to show that not only brain network stays structurally self-similar continuously across scales, but also neuron-like signal integration functionality is pr…
It is currently accepted that cortical maps are dynamic constructions that are altered in response to external input. Experience-dependent structural changes in cortical microcurcuts lead to changes of activity, i.e. to changes in information encoded. Specific patterns of external stimulation can lead to creation of new synaptic connections between neurons. The calcium influxes controlled by neuronal activity regulate the processes of neurotrophic factors released by neurons, growth cones movement and synapse differentiation in developing neural systems. We propose a model for description and …
Many neurons display bistability - coexistence of two firing modes such as bursting and tonic spiking or tonic spiking and silence. Bistability has been proposed to endow neurons with richer forms of information processing in general and to be involved in short-term memory in particular by allowing a brief signal to elicit long-lasting changes in firing. In this paper, we focus on bistability that allows for a choice between tonic spiking and depolarization block in a wide range of the depolarization levels. We consider the spike-producing currents in two neurons, models of which differ by the…
Continual Developmental Neurosimulation Using Embodied Computational Agents
Orthogonal Research and Education Laboratory（正交研究与教育实验室）；OpenWorm Foundation（OpenWorm基金会）；Technical University of Munich（慕尼黑工业大学）；Manipal Institute of Technology（马尼帕尔理工学院）；Plot Twisters
Topology-Dependent Emergence of Polychronous Neuronal Groups: A Recurrence-Plot Characterization
Complex Systems Modelling Graduate Program, School of Arts, Sciences and Humanities (EACH), University of São Paulo（圣保罗大学艺术与人文科学学院复杂系统建模研究生项目）；Department of Physics, Faculty of Philosophy, Sciences and Letters of Ribeirão Preto (FFCLRP), University of São Paulo（圣保罗大学里贝朗普雷图哲学、科学与文学院物理系）
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…
Dynamical wiring and rewiring in neural networks are carried out by activity-dependent growth and retraction of axons and dendrites, guided by gudance molecules, released by target cells. Experience-dependent structural changes in cortical microcurcuts lead to changes in activity, i.e. to changes in information encoded. Specific pattens of external stimulation can lead to creation of new synaptical connections between neurons. Calcium influxes controlled by neuronal activity regulates processes of neurotrophic factors release by neurons, growth cones movement and synapse differentiation in dev…
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 …
The connectome, or the entire connectivity of a neural system represented by network, ranges various scales from synaptic connections between individual neurons to fibre tract connections between brain regions. Although the modularity they commonly show has been extensively studied, it is unclear whether connection specificity of such networks can already be fully explained by the modularity alone. To answer this question, we study two networks, the neuronal network of C. elegans and the fibre tract network of human brains yielded through diffusion spectrum imaging (DSI). We compare them to th…
Phase transitions and critical behavior are crucial issues both in theoretical and experimental neuroscience. We report analytic and computational results about phase transitions and self-organized criticality (SOC) in networks with general stochastic neurons. The stochastic neuron has a firing probability given by a smooth monotonic function $Φ(V)$ of the membrane potential $V$, rather than a sharp firing threshold. We find that such networks can operate in several dynamic regimes (phases) depending on the average synaptic weight and the shape of the firing function $Φ$. In particular, we enc…
The organization of the connectivity between mammalian cortical areas has become a major subject of study, because of its important role in scaffolding the macroscopic aspects of animal behavior and intelligence. In this study we present a computational reconstruction approach to the problem of network organization, by considering the topological and spatial features of each area in the primate cerebral cortex as subsidy for the reconstruction of the global cortical network connectivity. Starting with all areas being disconnected, pairs of areas with similar sets of features are linked togethe…
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…
Message passing between components of a distributed physical system is non-instantaneous and contributes to determine the time scales of the emerging collective dynamics like an effective inertia. In biological neuron networks this inertia is due in part to local synaptic filtering of exchanged spikes, and in part to the distribution of the axonal transmission delays. How differently these two kinds of inertia affect the network dynamics is an open issue not yet addressed due to the difficulties in dealing with the non-Markovian nature of synaptic transmission. Here, we develop a mean-field di…
The advent of large scale neural computational platforms has highlighted the lack of algorithms for synthesis of neural structures to perform predefined cognitive tasks. The Neural Engineering Framework offers one such synthesis, but it is most effective for a spike rate representation of neural information, and it requires a large number of neurons to implement simple functions. We describe a neural network synthesis method that generates synaptic connectivity for neurons which process time-encoded neural signals, and which makes very sparse use of neurons. The method allows the user to speci…
The presence of diffuse Focal Axonal Swellings (FAS) is a hallmark cellular feature in many neurodegenerative diseases and traumatic brain injury. Among other things, the FAS have a significant impact on spike-train encodings that propagate through the affected neurons, leading to compromised signal processing on a neuronal network level. This work merges, for the first time, three fields of study: (i) signal processing in excitatory-inhibitory (EI) networks of neurons via population codes, (ii) decision-making theory driven by the production of evidence from stimulus, and (iii) compromised sp…
Spatially-embedded complex networks, such as nervous systems, the Internet and transportation networks, generally have non-trivial topological patterns of connections combined with nearly minimal wiring costs. However the growth rules shaping these economical trade-offs between cost and topology are not well understood. Here we study the cellular nervous system of the nematode worm C. elegans, together with information on the birth times of neurons and on their spatial locations. We find that the growth of this network undergoes a transition from an accelerated to a constant increase in the nu…
