Biological Neuronal Networks Research Articles

Autonomous and ubiquitous in-node learning algorithms of active directed graphs and its storage behavior

The brain’s memory system is extraordinarily complex, evidenced by the multitude of neurons involved and the intricate electrochemical activities within them, as well as the complex interactions among neurons. Memory research spans various levels, from cellular and molecular to cognitive behavioral studies, each with its own focus, making it challenging to fully describe the memory mechanism. Many details of how biological neuronal networks encode, store, and retrieve information remain unknown. In this study, we model biological neuronal networks as active directed graphs, where each node is self-adaptive and relies on local information for decision-making. To explore how these networks implement memory mechanisms, we propose a parallel distributed information access algorithm based on the node scale of the active directed graph. Here, subgraphs are seen as the physical realization of the information stored in the active directed graph. Unlike traditional algorithms with global perspectives, our algorithm emphasizes global node collaboration in resource utilization through local perspectives. While it may not achieve the global optimum like a global-view algorithm, it offers superior robustness, concurrency, decentralization, and biological feasibility. We also tested network capacity, fault tolerance, and robustness, finding that the algorithm performs better in sparser network structures.

Existence and stability criteria for global synchrony and for synchrony in two alternating clusters of pulse-coupled oscillators updated to include conduction delays

Phase Response Curves (PRCs) have been useful in determining and analyzing various phase-locking modes in networks of oscillators under pulse-coupling assumptions, as reviewed in Mathematical Biosciences, 226:77–96, 2010. Here, we update that review to include progress since 2010 on pulse coupled oscillators with conduction delays. We then present original results that extend the derivation of the criteria for stability of global synchrony in networks of pulse-coupled oscillators to include conduction delays. We also incorporate conduction delays to extend previous studies that showed how an alternating firing pattern between two synchronized clusters could enforce within-cluster synchrony, even for clusters unable to synchronize themselves in isolation. To obtain these results, we used self-connected neurons to represent clusters. These results greatly extend the applicability of the stability analyses to networks of pulse-coupled oscillators since conduction delays are ubiquitous and strongly impact the stability of synchrony. Although these analyses only strictly apply to identical oscillators with identical connections to other oscillators, the principles are general and suggest how to promote or impede synchrony in physiological networks of neurons, for example. Heterogeneity can be interpreted as a form of frozen noise, and approximate synchrony can be sustained despite heterogeneity. The pulse-coupled oscillator model can not only be used to describe biological neuronal networks but also cardiac pacemakers, lasers, fireflies, artificial neural networks, social self-organization, and wireless sensor networks.

In silico modeling of reservoir-based predictive coding in biological neuronal networks on microelectrode arrays

Reservoir computing and predictive coding together yield a computational model for exploring how neuronal dynamics in the mammalian cortex underpin temporal signal processing. Here, we construct an in-silico model of biological neuronal networks grown on microelectrode arrays and explore their computing capabilities through a sine wave prediction task in a reservoir-based predictive coding framework. Our results show that the time interval between stimulation pulses is a critical determinant of task performance. Additionally, under a fixed feedback latency, pulse amplitude modulation is a favorable encoding scheme for input signals. These findings provide practical guidelines for future implementation of the model in biological experiments.

Existence and Stability Criteria for Global Synchrony and for Synchrony in two Alternating Clusters of Pulse-Coupled Oscillators Updated to Include Conduction Delays.

37N25, 39A06, 39A30, 92B25, 92C20.

(Invited) Enabling Bio-Realistic Artificial Intelligence Hardware with Neuromorphic Nanoelectronics

The exponentially improving performance of digital computers has recently slowed due to the speed and power consumption issues resulting from the von Neumann bottleneck. In contrast, neuromorphic computing aims to circumvent these limitations by spatially co-locating logic and memory in a manner analogous to biological neuronal networks [1]. Beyond reducing power consumption, neuromorphic devices provide efficient architectures for image recognition, machine learning, and artificial intelligence [2]. This talk will explore how low-dimensional nanoelectronic materials enable gate-tunable neuromorphic devices [3]. For example, by utilizing self-aligned, atomically thin heterojunctions, dual-gated Gaussian transistors have been realized, which show tunable anti-ambipolarity for artificial neurons, competitive learning, spiking circuits, and mixed-kernel support vector machines [4,5]. In addition, field-driven defect motion in polycrystalline monolayer MoS2 enables gate-tunable memristive phenomena that serve as the basis of hybrid memristor/transistor devices (i.e., ‘memtransistors’) that concurrently provide logic and data storage functions [6]. The planar geometry of memtransistors further allows multiple contacts and dual gating that mimic the behavior of biological systems such as heterosynaptic responses [7]. Moreover, control over polycrystalline grain structure enhances the tunability of potentiation and depression, which enables unsupervised continuous learning in spiking neural networks [8]. Finally, the moiré potential in asymmetric twisted bilayer graphene/hexagonal boron nitride heterostructures gives rise to robust electronic ratchet states. The resulting hysteretic, non-volatile injection of charge carriers enables room-temperature operation of moiré synaptic transistors with diverse bio-realistic neuromorphic functionalities and efficient compute-in-memory designs for low-power artificial intelligence and machine learning hardware [9].[1] V. K. Sangwan, et al., Matter, 5, 4133 (2022).[2] V. K. Sangwan, et al., Nature Nanotechnology, 15, 517 (2020).[3] M. E. Beck, et al., ACS Nano, 14, 6498 (2020).[4] M. E. Beck, et al., Nature Communications, 11, 1565 (2020).[5] X. Yan, et al., Nature Electronics, DOI: 10.1038/s41928-023-01042-7 (2023).[6] X. Yan, et al., Advanced Materials, 34, 2108025 (2022).[7] H.-S. Lee, et al., Advanced Functional Materials, 30, 2003683 (2020).[8] J. Yuan, et al., Nano Letters, 21, 6432 (2021).[9] X. Yan, et al., Nature, DOI: 10.1038/s41586-023-06791-1 (2023).

Multistability and synchronicity of memristor coupled adaptive synaptic neuronal network

Memristor coupled neuronal networks can simulate the complex interactions between neurons in biological neuronal networks. These capture the current and synaptic transmission between neurons through mathematical equations, thus reflecting the signal transmission and integration in biological neuronal networks. This paper presents a five-dimensional isomorphic memristor coupled adaptive synaptic neuron (mCASN) network using a non-ideal memristor to couple two-dimensional adaptive synaptic neurons. The theoretical analysis of equilibrium points shows that the mCASN network has many different stability types. The complex parameters-dependent bifurcation behaviors are studied using various numerical methods, and the initial state-dependent coexistence behaviors and the riddled-like basins of attraction sensitive to initial states are further revealed, which proves that the coupled network has multistability. In addition, using the normalized average synchronization error method, we reveal that the mCASN network has synchronization characteristics controlled by parameters and initial states. The complete synchronization and lag synchronization induced by the network parameters, the internal variable of the coupled memristor, and the state variable of the sub-neuron are numerically analyzed. Finally, the mCASN network is implemented using an MCU-based digital hardware platform, and the numerical results are verified.

Power consumption during forward locomotion of C. elegans: an electrical circuit simulation

Biological neuronal networks are of great interest for emerging technological approaches such as neuromorphic engineering due to their capability to efficiently process information. To understand the principles governing this energy efficiency, it is useful to investigate model organisms with small and well-characterized neuronal networks. Caenorhabditis elegans (C. elegans) is such a model organism and perfectly suited for this purpose, because its neuronal network consists of only 302 neurons whose interconnections are known. In this work, we design an ideal electrical circuit modeling this neuronal network in combination with the muscles it controls. We simulate this circuit by a run-time efficient wave digital algorithm. This allows us to investigate the energy consumption of the network occurring during locomotion of C. elegans and hence deduce potential design principles from an energy efficiency point of view. Simulation results verify that a locomotion is indeed generated. We conclude from the corresponding energy consumption rates that a small number of neurons in contrast to a high number of interconnections is favorable for consuming only little energy. This underlines the importance of interneurons. Moreover, we find that gap junctions are a more energy-efficient connection type than synapses, and inhibitory synapses consume more energy than excitatory ones. However, the energetically cheapest connection types are not the most frequent ones in C. elegans’ neuronal network. Therefore, a potential design principle of the network could be a balance between low energy costs and a certain functionality.Graphical abstractEnergy consumption rates during forward locomotion of C. elegans. a Rates for the ion channels of all neurons, and b average rates for ion channels of a single, active neuron. c Comparison of average rates with respect to the number of active sensory, motor, and interneurons. d Rates for all gap junctions and synapses, and e rates for all synapses of a specific neurotransmitter type. f Average rates for a single synaptic or gap junctions connection vs the total number of connections present for the type of connection (i.e. ACh-synapse, GABA-synapse, Glu-synapse, gap junction).

Functional Connectivity Prediction With Deep Learning for Graph Transformation.

Inferring resting-state functional connectivity (FC) from anatomical brain wiring, known as structural connectivity (SC), is of enormous significance in neuroscience for understanding biological neuronal networks and treating mental diseases. Both SC and FC are networks where the nodes are brain regions, and in SC, the edges are the physical fiber nerves among the nodes, while in FC, the edges are the nodes' coactivation relations. Despite the importance of SC and FC, until very recently, the rapidly growing research body on this topic has generally focused on either linear models or computational models that rely heavily on heuristics and simple assumptions regarding the mapping between FC and SC. However, the relationship between FC and SC is actually highly nonlinear and complex and contains considerable randomness; additional factors, such as the subject's age and health, can also significantly impact the SC-FC relationship and hence cannot be ignored. To address these challenges, here, we develop a novel SC-to-FC generative adversarial network (SF-GAN) framework for mapping SC to FC, along with additional metafeatures based on a newly proposed graph neural network-based generative model that is capable of learning the stochasticity. Specifically, a new graph-based conditional generative adversarial nets model is proposed, where edge convolution layers are leveraged to encode the graph patterns in the SC in the form of a graph representation. New edge deconvolution layers are then utilized to decode the representation back to FC. Additional metafeatures of subjects' profile information are integrated into the graph representation with newly designed sparse-regularized layers that can automatically select features that impact FC. Finally, we have also proposed new post hoc explainer of our SF-GAN, which can identify which subgraphs in SC strongly influence which subgraphs in FC by a new multilevel edge-correlation-guided graph clustering problem. The results of experiments conducted to test the new model confirm that it significantly outperforms existing state-of-the-art methods, with additional interpretability for identifying important metafeatures and subgraphs.

Artificial neural network of thermal Buoyancy and Fourier flux impact on suction/injection‐based Darcy medium surface filled with hybrid and ternary nanoparticles

AbstractThis study's main objective is to analyze the heat and velocity transfer rate with various effects such as the suction and buoyancy effects on a stretching sheet with ternary hybrid nanofluid flow via a porous medium. Ternary hybrid nanofluid is Case‐1 Ag‐TiO2 with base fluid H2O and Case‐2 CNT + Graphene + Al2O3 with base fluid H2O. Hybrid nanofluids have been used to speed up the heat transfer process, following Lie group transformations are used to transform non‐linear Partial Differential Equations (PDEs) into Ordinary Differential Equations (ODEs). The boundary value problem solver was used in conjunction with the ODE45 numerical approach to solve the resulting Ordinary differential equations. On a stretchy surface, the overall relationship between temperature, velocity, shear stress, and heat transfer rate are shown for a range of values of the significant factors. The temperature profiles have been rising with the impact of Da and fw. Utilizing streamlines and a machine learning technique to examine the flow pattern of a fluid. Artificial neurons or nodes make up a neural network, which is known as a neural network in the sense that the term is used today. A network or circuit of biological neurons is referred to as a neural network.

4Ward: A relayering strategy for efficient training of arbitrarily complex directed acyclic graphs

Thanks to their ease of implementation, multilayer perceptrons (MLPs) have become ubiquitous in deep learning applications. The graph underlying an MLP is indeed multipartite, i.e. each layer of neurons only connects to neurons belonging to the adjacent layer. In contrast, in vivo brain connectomes at the level of individual synapses suggest that biological neuronal networks are characterized by scale-free degree distributions or exponentially truncated power law strength distributions, hinting at potentially novel avenues for the exploitation of evolution-derived neuronal networks. In this paper, we present “4Ward”, a method and Python library capable of generating flexible and efficient neural networks (NNs) from arbitrarily complex directed acyclic graphs. 4Ward is inspired by layering algorithms drawn from the graph drawing discipline to implement efficient forward passes, and provides significant time gains in computational experiments with various Erdős-Rényi graphs. 4Ward not only overcomes the sequential nature of the learning matrix method, by parallelizing the computation of activations, but also addresses the scalability issues encountered in the current state-of-the-art and provides the designer with freedom to customize weight initialization and activation functions. Our algorithm can be of aid for any investigator seeking to exploit complex topologies in a NN design framework at the microscale.

Image analysis of brain cortex cells in vitro using deep learning method

The article presents a method for analyzing images of cultured cortical cells for a quantitative analysis of the parameters of development of biological neural networks using machine learning approaches. We have developed software modules for segmentation of images into cells, clusters, and neurites using the neural network model and the deep learning method; a training set of images of cultivated neurons and corresponding segmentation masks have been generated. The results were validated by analyzing the development of cultivated neurons in vitro based on the length count of neutrites at different growth stages of the culture. The developed methods for monitoring the processes of formation of biological neuronal networks based on the analysis of the neuronal growth under different conditions and on different substrates provide an opportunity to monitor the processes of stem cell differentiation in the neurogenic direction. The results can be used in monitoring the formation of organoids in bioengineering applications, as well as in modeling the processes of nerve tissue regeneration.

Symbiosis of an artificial neural network and models of biological neurons: Training and testing

In this paper, we show the possibility of creating and identifying the features of an artificial neural network (ANN), which consists of mathematical models of biological neurons. The FitzHugh–Nagumo (FHN) system is used as a paradigmatic model demonstrating basic neuron activities. First, in order to reveal how biological neurons can be embedded within an ANN, we train the ANN with nonlinear neurons to solve a basic image recognition problem with an MNIST database; next, we describe how FHN systems can be introduced into this trained ANN. After all, we show that an ANN with FHN systems inside can be successfully trained with improved accuracy comparing with first trained ANN and then with inserted FHN systems. This approach opens up great opportunities in terms of the direction of analog neural networks, in which artificial neurons can be replaced by more appropriate biological ones.

Biological neurons act as generalization filters in reservoir computing

Reservoir computing is a machine learning paradigm that transforms the transient dynamics of high-dimensional nonlinear systems for processing time-series data. Although the paradigm was initially proposed to model information processing in the mammalian cortex, it remains unclear how the nonrandom network architecture, such as the modular architecture, in the cortex integrates with the biophysics of living neurons to characterize the function of biological neuronal networks (BNNs). Here, we used optogenetics and calcium imaging to record the multicellular responses of cultured BNNs and employed the reservoir computing framework to decode their computational capabilities. Micropatterned substrates were used to embed the modular architecture in the BNNs. We first show that the dynamics of modular BNNs in response to static inputs can be classified with a linear decoder and that the modularity of the BNNs positively correlates with the classification accuracy. We then used a timer task to verify that BNNs possess a short-term memory of several 100 ms and finally show that this property can be exploited for spoken digit classification. Interestingly, BNN-based reservoirs allow categorical learning, wherein a network trained on one dataset can be used to classify separate datasets of the same category. Such classification was not possible when the inputs were directly decoded by a linear decoder, suggesting that BNNs act as a generalization filter to improve reservoir computing performance. Our findings pave the way toward a mechanistic understanding of information representation within BNNs and build future expectations toward the realization of physical reservoir computing systems based on BNNs.

Synaptic propagation in neuronal networks with finite-support space-dependent coupling.

Traveling waves of electrical activity are ubiquitous in biological neuronal networks. Traveling waves in the brain are associated with sensory processing, phase coding, and sleep. The neuron and network parameters that determine traveling waves' evolution are the synaptic space constant, synaptic conductance, membrane time constant, and synaptic decay time constant. We used an abstract neuron model in a one-dimensional network to investigate the propagation characteristics of traveling wave activity. We formulate a set of evolution equationsbased on the network connectivity parameters. Using a combination of numerical and analytical approaches, we show that these traveling waves are stable to a series of perturbations with biological relevance.

Structural Modularity Tunes Mesoscale Criticality in Biological Neuronal Networks.

Numerous studies suggest that biological neuronal networks self-organize toward a critical state with stable recruitment dynamics. Individual neurons would then statistically activate exactly one further neuron during activity cascades termed neuronal avalanches. Yet, it is unclear if and how this can be reconciled with the explosive recruitment dynamics within neocortical minicolumns in vivo and within neuronal clusters in vitro, which indicates that neurons form supercritical local circuits. Theoretical studies propose that modular networks with a mix of regionally subcritical and supercritical dynamics would create apparently critical dynamics, resolving this inconsistency. Here, we provide experimental support by manipulating the structural self-organization process of networks of cultured rat cortical neurons (either sex). Consistent with the prediction, we show that increasing clustering in neuronal networks developing in vitro strongly correlates with avalanche size distributions transitioning from supercritical to subcritical activity dynamics. Avalanche size distributions approximated a power law in moderately clustered networks, indicating overall critical recruitment. We propose that activity-dependent self-organization can tune inherently supercritical networks toward mesoscale criticality by creating a modular structure in neuronal networks.SIGNIFICANCE STATEMENT Critical recruitment dynamics in neuronal networks are considered optimal for information processing in the brain. However, it remains heavily debated how neuronal networks would self-organize criticality by detailed fine-tuning of connectivity, inhibition, and excitability. We provide experimental support for theoretical considerations that modularity tunes critical recruitment dynamics at the mesoscale level of interacting neuron clusters. This reconciles reports of supercritical recruitment dynamics in local neuron clusters with findings on criticality sampled at mesoscopic network scales. Intriguingly, altered mesoscale organization is a prominent aspect of various neuropathological diseases currently investigated in the framework of criticality. We therefore believe that our findings would also be of interest for clinical scientists searching to link the functional and anatomic signatures of such brain disorders.

Partitioned estimation methodology of biological neuronal networks with topology-based module detection

Parameter estimation of neuronal networks is closely related with information processing mechanisms in neural systems. Estimation of synaptic parameters for neuronal networks was an time consuming task. Due to complex interactions between neurons, computational efficiency and accuracy of estimation methods is relatively low. Meanwhile, inherent topological properties such as core–periphery and modular structures are not fully considered in estimation. In order to improve the efficiency and accuracy of estimation, this study proposes a two-stage PartitionMLE method which introduces detected neuronal modules as topological constraints in estimation. The proposed PartitionMLE method firstly decomposes the system into multiple non-overlapping neuronal modules, by performing topology-based module detection. Dynamic parameters including intra-modular and inter-modular parameters are estimated in two stages, using detected hubs to connect non-overlapping neuronal modules. The contributions of PartitionMLE method are two-folds: reducing estimation errors and improving the model interpretability. Experiments about neuronal networks consisting of Hodgkin–Huxley (HH) and leaky integrate-and-firing (LIF) neurons validated the effectiveness of the PartitionMLE method, with comparison to the single-stage MLE method.

Predicting in vitro single-neuron firing rates upon pharmacological perturbation using Graph Neural Networks.

Modern Graph Neural Networks (GNNs) provide opportunities to study the determinants underlying the complex activity patterns of biological neuronal networks. In this study, we applied GNNs to a large-scale electrophysiological dataset of rodent primary neuronal networks obtained by means of high-density microelectrode arrays (HD-MEAs). HD-MEAs allow for long-term recording of extracellular spiking activity of individual neurons and networks and enable the extraction of physiologically relevant features at the single-neuron and population level. We employed established GNNs to generate a combined representation of single-neuron and connectivity features obtained from HD-MEA data, with the ultimate goal of predicting changes in single-neuron firing rate induced by a pharmacological perturbation. The aim of the main prediction task was to assess whether single-neuron and functional connectivity features, inferred under baseline conditions, were informative for predicting changes in neuronal activity in response to a perturbation with Bicuculline, a GABA A receptor antagonist. Our results suggest that the joint representation of node features and functional connectivity, extracted from a baseline recording, was informative for predicting firing rate changes of individual neurons after the perturbation. Specifically, our implementation of a GNN model with inductive learning capability (GraphSAGE) outperformed other prediction models that relied only on single-neuron features. We tested the generalizability of the results on two additional datasets of HD-MEA recordings-a second dataset with cultures perturbed with Bicuculline and a dataset perturbed with the GABA A receptor antagonist Gabazine. GraphSAGE models showed improved prediction accuracy over other prediction models. Our results demonstrate the added value of taking into account the functional connectivity between neurons and the potential of GNNs to study complex interactions between neurons.

Dynamic and Functional Alterations of Neuronal Networks In Vitro upon Physical Damage: A Proof of Concept.

There is a growing technological interest in combining biological neuronal networks with electronic ones, specifically for biological computation, human-machine interfacing and robotic implants. A major challenge for the development of these technologies is the resilience of the biological networks to physical damage, for instance, when used in harsh environments. To tackle this question, here, we investigated the dynamic and functional alterations of rodent cortical networks grown in vitro that were physically damaged, either by sequentially removing groups of neurons that were central for information flow or by applying an incision that cut the network in half. In both cases, we observed a remarkable capacity of the neuronal cultures to cope with damage, maintaining their activity and even reestablishing lost communication pathways. We also observed-particularly for the cultures cut in half-that a reservoir of healthy neurons surrounding the damaged region could boost resilience by providing stimulation and a communication bridge across disconnected areas. Our results show the remarkable capacity of neuronal cultures to sustain and recover from damage, and may be inspirational for the development of future hybrid biological-electronic systems.

Objective Supervised Machine Learning-Based Classification and Inference of Biological Neuronal Networks.

The classification of biological neuron types and networks poses challenges to the full understanding of the human brain’s organisation and functioning. In this paper, we develop a novel objective classification model of biological neuronal morphology and electrical types and their networks, based on the attributes of neuronal communication using supervised machine learning solutions. This presents advantages compared to the existing approaches in neuroinformatics since the data related to mutual information or delay between neurons obtained from spike trains are more abundant than conventional morphological data. We constructed two open-access computational platforms of various neuronal circuits from the Blue Brain Project realistic models, named Neurpy and Neurgen. Then, we investigated how we could perform network tomography with cortical neuronal circuits for the morphological, topological and electrical classification of neurons. We extracted the simulated data of 10,000 network topology combinations with five layers, 25 morphological type (m-type) cells, and 14 electrical type (e-type) cells. We applied the data to several different classifiers (including Support Vector Machine (SVM), Decision Trees, Random Forest, and Artificial Neural Networks). We achieved accuracies of up to 70%, and the inference of biological network structures using network tomography reached up to 65% of accuracy. Objective classification of biological networks can be achieved with cascaded machine learning methods using neuron communication data. SVM methods seem to perform better amongst used techniques. Our research not only contributes to existing classification efforts but sets the road-map for future usage of brain–machine interfaces towards an in vivo objective classification of neurons as a sensing mechanism of the brain’s structure.

Neuronal avalanche dynamics and functional connectivity elucidate information propagation in vitro.

Cascading activity is commonly observed in complex dynamical systems, including networks of biological neurons, and how these cascades spread through the system is reliant on how the elements of the system are connected and organized. In this work, we studied networks of neurons as they matured over 50 days in vitro and evaluated both their dynamics and their functional connectivity structures by observing their electrophysiological activity using microelectrode array recordings. Correlations were obtained between features of their activity propagation and functional connectivity characteristics to elucidate the interplay between dynamics and structure. The results indicate that in vitro networks maintain a slightly subcritical state by striking a balance between integration and segregation. Our work demonstrates the complementarity of these two approaches—functional connectivity and avalanche dynamics—in studying information propagation in neurons in vitro, which can in turn inform the design and optimization of engineered computational substrates.