Situation-Based Neuromorphic Memory in Spiking Neuron-Astrocyte Network

Mammalian brains operate in very special surroundings: to survive they have to react quickly and effectively to the pool of stimuli patterns previously recognized as danger. Many learning tasks often encountered by living organisms involve a specific set-up centered around a relatively small set of patterns presented in a particular environment. For example, at a party, people recognize friends immediately, without deep analysis, just by seeing a fragment of their clothes. This set-up with reduced "ontology" is referred to as a "situation." Situations are usually local in space and time. In this work, we propose that neuron-astrocyte networks provide a network topology that is effectively adapted to accommodate situation-based memory. In order to illustrate this, we numerically simulate and analyze a well-established model of a neuron-astrocyte network, which is subjected to stimuli conforming to the situation-driven environment. Three pools of stimuli patterns are considered: external patterns, patterns from the situation associative pool regularly presented to the network and learned by the network, and patterns already learned and remembered by astrocytes. Patterns from the external world are added to and removed from the associative pool. Then, we show that astrocytes are structurally necessary for an effective function in such a learning and testing set-up. To demonstrate this we present a novel neuromorphic computational model for short-term memory implemented by a two-net spiking neural-astrocytic network. Our results show that such a system tested on synthesized data with selective astrocyte-induced modulation of neuronal activity provides an enhancement of retrieval quality in comparison to standard spiking neural networks trained via Hebbian plasticity only. We argue that the proposed set-up may offer a new way to analyze, model, and understand neuromorphic artificial intelligence systems.

Control of movement of underwater swimmers: Animals, simulated animates and swimming robots

The control of movement in living organisms represents a fundamental task that the brain has evolved to solve. One crucial aspect is how the nervous system organizes the transformation of sensory information into motor commands. These commands lead to muscle activation and subsequent animal movement, which can exhibit complex patterns. One example of such movement is locomotion, which involves the translation of the entire body through space. Central Pattern Generators (CPGs) are neuronal circuits that provide control signals for these movements. Compared to the intricate circuits found in the brain, CPGs can be simplified into networks of neurons that generate rhythmic activation, coordinating muscle movements. Since the 1990s, researchers have developed numerous models of locomotive circuits to simulate different types of animal movement, including walking, flying, and swimming. Initially, the primary goal of these studies was to construct biomimetic robots. However, it became apparent that simplified CPGs alone were not sufficient to replicate the diverse range of adaptive locomotive movements observed in living organisms. Factors such as sensory modulation, higher-level control, and cognitive components related to learning and memory needed to be considered. This necessitated the use of more complex, high-dimensional circuits, as well as novel materials and hardware, in both modeling and robotics. With advancements in high-power computing, artificial intelligence, big data processing, smart materials, and electronics, the possibility of designing a new generation of true bio-mimetic robots has emerged. These robots have the capability to imitate not only simple locomotion but also exhibit adaptive motor behavior and decision-making. This motivation serves as the foundation for the current review, which aims to analyze existing concepts and models of movement control systems. As an illustrative example, we focus on underwater movement and explore the fundamental biological concepts, as well as the mathematical and physical models that underlie locomotion and its various modulations.

Artificial Neural Network Model with Astrocyte-Driven Short-Term Memory

In this study, we introduce an innovative hybrid artificial neural network model incorporating astrocyte-driven short-term memory. The model combines a convolutional neural network with dynamic models of short-term synaptic plasticity and astrocytic modulation of synaptic transmission. The model's performance was evaluated using simulated data from visual change detection experiments conducted on mice. Comparisons were made between the proposed model, a recurrent neural network simulating short-term memory based on sustained neural activity, and a feedforward neural network with short-term synaptic depression (STPNet) trained to achieve the same performance level as the mice. The results revealed that incorporating astrocytic modulation of synaptic transmission enhanced the model's performance.

STDP-Driven Rewiring in Spiking Neural Networks under Stimulus-Induced and Spontaneous Activity

Mathematical and computer simulation of learning in living neural networks have typically focused on changes in the efficiency of synaptic connections represented by synaptic weights in the models. Synaptic plasticity is believed to be the cellular basis for learning and memory. In spiking neural networks composed of dynamical spiking units, a biologically relevant learning rule is based on the so-called spike-timing-dependent plasticity or STDP. However, experimental data suggest that synaptic plasticity is only a part of brain circuit plasticity, which also includes homeostatic and structural plasticity. A model of structural plasticity proposed in this study is based on the activity-dependent appearance and disappearance of synaptic connections. The results of the research indicate that such adaptive rewiring enables the consolidation of the effects of STDP in response to a local external stimulation of a neural network. Subsequently, a vector field approach is used to demonstrate the successive "recording" of spike paths in both functional connectome and synaptic connectome, and finally in the anatomical connectome of the network. Moreover, the findings suggest that the adaptive rewiring could stabilize network dynamics over time in the context of activity patterns' reproducibility. A universal measure of such reproducibility introduced in this article is based on similarity between time-consequent patterns of the special vector fields characterizing both functional and anatomical connectomes.

Model of Neuromorphic Odorant-Recognition Network

We propose a new model for a neuromorphic olfactory analyzer based on memristive synapses. The model comprises a layer of receptive neurons that perceive various odors and a layer of "decoder" neurons that recognize these odors. It is demonstrated that connecting these layers with memristive synapses enables the training of the "decoder" layer to recognize two types of odorants of varying concentrations. In the absence of such synapses, the layer of "decoder" neurons does not exhibit specificity in recognizing odorants. The recognition of the 'odorant' occurs through the neural activity of a group of decoder neurons that have acquired specificity for the odorant in the learning process. The proposed phenomenological model showcases the potential use of a memristive synapse in practical odorant recognition applications.

Approaches for Memristive Structures Using Scratching Probe Nanolithography: Towards Neuromorphic Applications

This paper proposes two different approaches to studying resistive switching of oxide thin films using scratching probe nanolithography of atomic force microscopy (AFM). These approaches allow us to assess the effects of memristor size and top-contact thickness on resistive switching. For that purpose, we investigated scratching probe nanolithography regimes using the Taguchi method, which is known as a reliable method for improving the reliability of the result. The AFM parameters, including normal load, scratch distance, probe speed, and probe direction, are optimized on the photoresist thin film by the Taguchi method. As a result, the pinholes with diameter ranged from 25.4 ± 2.2 nm to 85.1 ± 6.3 nm, and the groove array with a depth of 40.5 ± 3.7 nm and a roughness at the bottom of less than a few nanometers was formed. Then, based on the Si/TiN/ZnO/photoresist structures, we fabricated and investigated memristors with different spot sizes and TiN top contact thickness. As a result, the HRS/LRS ratio, U_SET, and I_LRS are well controlled for a memristor size from 27 nm to 83 nm and ranged from ~8 to ~128, from 1.4 ± 0.1 V to 1.8 ± 0.2 V, and from (1.7 ± 0.2) × 10^-10 A to (4.2 ± 0.6) × 10^-9 A, respectively. Furthermore, the HRS/LRS ratio and U_SET are well controlled at a TiN top contact thickness from 8.3 ± 1.1 nm to 32.4 ± 4.2 nm and ranged from ~22 to ~188 and from 1.15 ± 0.05 V to 1.62 ± 0.06 V, respectively. The results can be used in the engineering and manufacturing of memristive structures for neuromorphic applications of brain-inspired artificial intelligence systems.

Information Encoding in Bursting Spiking Neural Network Modulated by Astrocytes

We investigated a mathematical model composed of a spiking neural network (SNN) interacting with astrocytes. We analysed how information content in the form of two-dimensional images can be represented by an SNN in the form of a spatiotemporal spiking pattern. The SNN includes excitatory and inhibitory neurons in some proportion, sustaining the excitation-inhibition balance of autonomous firing. The astrocytes accompanying each excitatory synapse provide a slow modulation of synaptic transmission strength. An information image was uploaded to the network in the form of excitatory stimulation pulses distributed in time reproducing the shape of the image. We found that astrocytic modulation prevented stimulation-induced SNN hyperexcitation and non-periodic bursting activity. Such homeostatic astrocytic regulation of neuronal activity makes it possible to restore the image supplied during stimulation and lost in the raster diagram of neuronal activity due to non-periodic neuronal firing. At a biological point, our model shows that astrocytes can act as an additional adaptive mechanism for regulating neural activity, which is crucial for sensory cortical representations.

Loss of neuron network coherence induced by virus-infected astrocytes: a model study

Coherent activations of brain neuron networks underlie many physiological functions associated with various behavioral states. These synchronous fluctuations in the electrical activity of the brain are also referred to as brain rhythms. At the cellular level, rhythmicity can be induced by various mechanisms of intrinsic oscillations in neurons or the network circulation of excitation between synaptically coupled neurons. One specific mechanism concerns the activity of brain astrocytes that accompany neurons and can coherently modulate synaptic contacts of neighboring neurons, synchronizing their activity. Recent studies have shown that coronavirus infection (Covid-19), which enters the central nervous system and infects astrocytes, can cause various metabolic disorders. Specifically, Covid-19 can depress the synthesis of astrocytic glutamate and gamma-aminobutyric acid. It is also known that in the post-Covid state, patients may suffer from symptoms of anxiety and impaired cognitive functions. We propose a mathematical model of a spiking neuron network accompanied by astrocytes capable of generating quasi-synchronous rhythmic bursting discharges. The model predicts that if the release of glutamate is depressed, normal burst rhythmicity will suffer dramatically. Interestingly, in some cases, the failure of network coherence may be intermittent, with intervals of normal rhythmicity, or the synchronization can disappear.

Microfluidic Bi-Layer Platform to Study Functional Interaction between Co-Cultured Neural Networks with Unidirectional Synaptic Connectivity

The complex synaptic connectivity architecture of neuronal networks underlies cognition and brain function. However, studying the spiking activity propagation and processing in heterogeneous networks in vivo poses significant challenges. In this study, we present a novel two-layer PDMS chip that facilitates the culturing and examination of the functional interaction of two interconnected neural networks. We utilized cultures of hippocampal neurons grown in a two-chamber microfluidic chip combined with a microelectrode array. The asymmetric configuration of the microchannels between the chambers ensured the growth of axons predominantly in one direction from the Source chamber to the Target chamber, forming two neuronal networks with unidirectional synaptic connectivity. We showed that the local application of tetrodotoxin (TTX) to the Source network did not alter the spiking rate in the Target network. The results indicate that stable network activity in the Target network was maintained for at least 1-3 h after TTX application, demonstrating the feasibility of local chemical activity modulation and the influence of electrical activity from one network on the other. Additionally, suppression of synaptic activity in the Source network by the application of CPP and CNQX reorganized spatio-temporal characteristics of spontaneous and stimulus-evoked spiking activity in the Target network. The proposed methodology and results provide a more in-depth examination of the network-level functional interaction between neural circuits with heterogeneous synaptic connectivity.

Social stress drives the multi-wave dynamics of COVID-19 outbreaks

The dynamics of epidemics depend on how people's behavior changes during an outbreak. At the beginning of the epidemic, people do not know about the virus, then, after the outbreak of epidemics and alarm, they begin to comply with the restrictions and the spreading of epidemics may decline. Over time, some people get tired/frustrated by the restrictions and stop following them (exhaustion), especially if the number of new cases drops down. After resting for a while, they can follow the restrictions again. But during this pause the second wave can come and become even stronger then the first one. Studies based on SIR models do not predict the observed quick exit from the first wave of epidemics. Social dynamics should be considered. The appearance of the second wave also depends on social factors. Many generalizations of the SIR model have been developed that take into account the weakening of immunity over time, the evolution of the virus, vaccination and other medical and biological details. However, these more sophisticated models do not explain the apparent differences in outbreak profiles between countries with different intrinsic socio-cultural features. In our work, a system of models of the COVID-19 pandemic is proposed, combining the dynamics of social stress with classical epidemic models. Social stress is described by the tools of sociophysics. The combination of a dynamic SIR-type model with the classical triad of stages of the general adaptation syndrome, alarm-resistance-exhaustion, makes it possible to describe with high accuracy the available statistical data for 13 countries. The sets of kinetic constants corresponding to optimal fit of model to data were found. These constants characterize the ability of society to mobilize efforts against epidemics and maintain this concentration over time and can further help in the development of management strategies specific to a particular society.

Stochastic Memristive Interface for Neural Signal Processing

We propose a memristive interface consisting of two FitzHugh–Nagumo electronic neurons connected via a metal–oxide (Au/Zr/ZrO₂(Y)/TiN/Ti) memristive synaptic device. We create a hardware–software complex based on a commercial data acquisition system, which records a signal generated by a presynaptic electronic neuron and transmits it to a postsynaptic neuron through the memristive device. We demonstrate, numerically and experimentally, complex dynamics, including chaos and different types of neural synchronization. The main advantages of our system over similar devices are its simplicity and real-time performance. A change in the amplitude of the presynaptic neurogenerator leads to the potentiation of the memristive device due to the self-tuning of its parameters. This provides an adaptive modulation of the postsynaptic neuron output. The developed memristive interface, due to its stochastic nature, simulates a real synaptic connection, which is very promising for neuroprosthetic applications.

A BCI-Based Vibrotactile Neurofeedback Training Improves Motor Cortical Excitability During Motor Imagery

In this study, we address the issue of whether vibrotactile feedback can enhance the motor cortex excitability translated into the plastic changes in local cortical areas during motor imagery (MI) BCI-based training. For this purpose, we focused on two of the most notable neurophysiological effects of MI - the event-related desynchronization (ERD) level and the increase in cortical excitability assessed with navigated transcranial magnetic stimulation (nTMS). For TMS navigation, we used individual high-resolution 3D brain MRIs. Ten BCI-naive and healthy adults participated in this study. The MI (rest or left/right hand imagery using Graz-BCI paradigm) tasks were performed separately in the presence and absence of feedback. To investigate how much the presence/absence of vibrotactile feedback in MI BCI-based training could contribute to the sensorimotor cortical activations, we compared the MEPs amplitude during MI after training with and without feedback. In addition, the ERD levels during MI BCI-based training were investigated. Our findings provide evidence that applying vibrotactile feedback during MI training leads to (i) an enhancement of the desynchronization level of mu-rhythm EEG patterns over the contralateral motor cortex area corresponding to the MI of the non-dominant hand; (ii) an increase in motor cortical excitability in hand muscle representation corresponding to a muscle engaged by the MI.

Experimental Platform to Study Spiking Pattern Propagation in Modular Networks In Vitro

The structured organization of connectivity in neural networks is associated with highly efficient information propagation and processing in the brain, in contrast with disordered homogeneous network architectures. Using microfluidic methods, we engineered modular networks of cultures using dissociated cells with unidirectional synaptic connections formed by asymmetric microchannels. The complexity of the microchannel geometry defined the strength of the synaptic connectivity and the properties of spiking activity propagation. In this study, we developed an experimental platform to study the effects of synaptic plasticity on a network level with predefined locations of unidirectionally connected cellular assemblies using multisite extracellular electrophysiology.

Spatial Memory in a Spiking Neural Network with Robot Embodiment

Cognitive maps and spatial memory are fundamental paradigms of brain functioning. Here, we present a spiking neural network (SNN) capable of generating an internal representation of the external environment and implementing spatial memory. The SNN initially has a non-specific architecture, which is then shaped by Hebbian-type synaptic plasticity. The network receives stimuli at specific loci, while the memory retrieval operates as a functional SNN response in the form of population bursts. The SNN function is explored through its embodiment in a robot moving in an arena with safe and dangerous zones. We propose a measure of the global network memory using the synaptic vector field approach to validate results and calculate information characteristics, including learning curves. We show that after training, the SNN can effectively control the robot’s cognitive behavior, allowing it to avoid dangerous regions in the arena. However, the learning is not perfect. The robot eventually visits dangerous areas. Such behavior, also observed in animals, enables relearning in time-evolving environments. If a dangerous zone moves into another place, the SNN remaps positive and negative areas, allowing escaping the catastrophic interference phenomenon known for some AI architectures. Thus, the robot adapts to changing world.

Modeling Working Memory in a Spiking Neuron Network Accompanied by Astrocytes

We propose a novel biologically plausible computational model of working memory (WM) implemented by a spiking neuron network (SNN) interacting with a network of astrocytes. The SNN is modeled by synaptically coupled Izhikevich neurons with a non-specific architecture connection topology. Astrocytes generating calcium signals are connected by local gap junction diffusive couplings and interact with neurons via chemicals diffused in the extracellular space. Calcium elevations occur in response to the increased concentration of the neurotransmitter released by spiking neurons when a group of them fire coherently. In turn, gliotransmitters are released by activated astrocytes modulating the strength of the synaptic connections in the corresponding neuronal group. Input information is encoded as two-dimensional patterns of short applied current pulses stimulating neurons. The output is taken from frequencies of transient discharges of corresponding neurons. We show how a set of information patterns with quite significant overlapping areas can be uploaded into the neuron-astrocyte network and stored for several seconds. Information retrieval is organized by the application of a cue pattern representing one from the memory set distorted by noise. We found that successful retrieval with the level of the correlation between the recalled pattern and ideal pattern exceeding 90% is possible for the multi-item WM task. Having analyzed the dynamical mechanism of WM formation, we discovered that astrocytes operating at a time scale of a dozen of seconds can successfully store traces of neuronal activations corresponding to information patterns. In the retrieval stage, the astrocytic network selectively modulates synaptic connections in the SNN leading to successful recall. Information and dynamical characteristics of the proposed WM model agrees with classical concepts and other WM models.

Spatial Properties of STDP in a Self-Learning Spiking Neural Network Enable Controlling a Mobile Robot

Development of spiking neural networks (SNNs) controlling mobile robots is one of the modern challenges in computational neuroscience and artificial intelligence. Such networks, being replicas of biological ones, are expected to have a higher computational potential than traditional artificial neural networks (ANNs). The critical problem is in the design of robust learning algorithms aimed at building a “living computer” based on SNNs. Here, we propose a simple SNN equipped with a Hebbian rule in the form of spike-timing-dependent plasticity (STDP). The SNN implements associative learning by exploiting the spatial properties of STDP. We show that a LEGO robot controlled by the SNN can exhibit classical and operant conditioning. Competition of spike-conducting pathways in the SNN plays a fundamental role in establishing associations of neural connections. It replaces the irrelevant associations by new ones in response to a change in stimuli. Thus, the robot gets the ability to relearn when the environment changes. The proposed SNN and the stimulation protocol can be further enhanced and tested in developing neuronal cultures, and also admit the use of memristive devices for hardware implementation.

Competitive Learning in a Spiking Neural Network: Towards an Intelligent Pattern Classifier

One of the modern trends in the design of human–machine interfaces (HMI) is to involve the so called spiking neuron networks (SNNs) in signal processing. The SNNs can be trained by simple and efficient biologically inspired algorithms. In particular, we have shown that sensory neurons in the input layer of SNNs can simultaneously encode the input signal based both on the spiking frequency rate and on varying the latency in generating spikes. In the case of such mixed temporal-rate coding, the SNN should implement learning working properly for both types of coding. Based on this, we investigate how a single neuron can be trained with pure rate and temporal patterns, and then build a universal SNN that is trained using mixed coding. In particular, we study Hebbian and competitive learning in SNN in the context of temporal and rate coding problems. We show that the use of Hebbian learning through pair-based and triplet-based spike timing-dependent plasticity (STDP) rule is accomplishable for temporal coding, but not for rate coding. Synaptic competition inducing depression of poorly used synapses is required to ensure a neural selectivity in the rate coding. This kind of competition can be implemented by the so-called forgetting function that is dependent on neuron activity. We show that coherent use of the triplet-based STDP and synaptic competition with the forgetting function is sufficient for the rate coding. Next, we propose a SNN capable of classifying electromyographical (EMG) patterns using an unsupervised learning procedure. The neuron competition achieved via lateral inhibition ensures the “winner takes all” principle among classifier neurons. The SNN also provides gradual output response dependent on muscular contraction strength. Furthermore, we modify the SNN to implement a supervised learning method based on stimulation of the target classifier neuron synchronously with the network input. In a problem of discrimination of three EMG patterns, the SNN with supervised learning shows median accuracy 99.5% that is close to the result demonstrated by multi-layer perceptron learned by back propagation of an error algorithm.

Astrocyte as Spatiotemporal Integrating Detector of Neuronal Activity

The functional role of astrocyte calcium signaling in brain information processing was intensely debated in recent decades. This interest was motivated by high resolution imaging techniques showing highly developed structure of distal astrocyte processes. Another point was the evidence of bi-directional astrocytic regulation of neuronal activity. To analyze the effects of interplay of calcium signals in processes and in soma mediating correlations between local signals and the cell-level response of the astrocyte we proposed spatially extended model of the astrocyte calcium dynamics. Specifically, we investigated how spatiotemporal properties of Ca²⁺ dynamics in spatially extended astrocyte model can coordinate (e.g., synchronize) networks of neurons and synapses.

Optoelectronic system for brain neuronal network stimulation

We propose an optoelectronic system for stimulation of living neurons. The system consists of an electronic circuit based on the FitzHugh–Nagumo model, an optical fiber, and a photoelectrical converter. We used this system for electrical stimulation of hippocampal living neurons in acute hippocampal brain slices (350-μm thick) obtained from a 20–28 days old C57BL/6 mouse or a Wistar rat. The main advantage of our system over other similar stimulators is that it contains an optical fiber for signal transmission instead of metallic wires. The fiber is placed between the electronic circuit and stimulated neurons and provides galvanic isolation from external electrical and magnetic fields. The use of the optical fiber allows avoiding electromagnetic noise and current flows which could affect metallic wires. Furthermore, it gives us the possibility to simulate “synaptic plasticity” by adaptive signal transfer through optical fiber. The proposed optoelectronic system (hybrid neural circuit) provides a very high efficiency in stimulating hippocampus neurons and can be used for restoring brain activity in particular regions or replacing brain parts (neuroprosthetics) damaged due to a trauma or neurodegenerative diseases.

Emergence of Relaxation Oscillations in Neurons Interacting With Non-stationary Ambient GABA

Dynamics of a homogeneous neural population interacting with active extracellular medium were considered. The corresponding mathematical model was tuned specifically to describe the behavior of interneurons with tonic GABA conductance under the action of non-stationary ambient GABA. The feedback provided by the GABA mediated transmembrane current enriched the repertoire of population activity by enabling the oscillatory behavior. This behavior appeared in the form of relaxation oscillations which can be considered as a specific type of brainwaves.

Tonic regulation of stationary asynchronous firing of a neural network

The impact of tonic conductance upon population activity was investigated. An extra tonic transmembrane current through GABA-activated extrasynaptic GABA _A -receptors was found to control stationary asynchronous firing both quantitatively and qualitatively. Quantitative regulation consisted in alterating a current level of stationary population activity while qualitative regulation manifested itself in appearance of resilient asynchronous spiking in case GABA reversal potential exceeded a certain threshold. The study was based on a modified rate model after Wilson and Cowan and backed up with a computer simulation of an explicit network model.

Dendrite and Axon Specific Geometrical Transformation in Neurite Development

We propose a model of neurite growth to explain the differences in dendrite and axon specific neurite development. The model implements basic molecular kinetics, e.g., building protein synthesis and transport to the growth cone, and includes explicit dependence of the building kinetics on the geometry of the neurite. The basic assumption was that the radius of the neurite decreases with length. We found that the neurite dynamics crucially depended on the relationship between the rate of active transport and the rate of morphological changes. If these rates were in the balance, then the neurite displayed axon specific development with a constant elongation speed. For dendrite specific growth, the maximal length was rapidly saturated by degradation of building protein structures or limited by proximal part expansion reaching the characteristic cell size.

Oscillations in a neurite growth model with extracellular feedback

We consider the influence of extracellular signalling on neurite elongation in a model of neurite growth mediated by building proteins (e.g., tubulin). The tubulin production dynamics were supplied by a function describing the influence of extracellular signalling, which can promote or depress neurite elongation. We found that this extracellular feedback could generate neurite length oscillations consisting of a periodic sequence of elongations and retractions. The oscillations prevent further outgrowth of the neurite, which becomes trapped in the non-uniform extracellular field. We analysed the characteristics of the elongation process for different distributions of attracting and repelling sources of the extracellular signalling molecules. The model predicts three different scenarios of neurite development in the extracellular field, including monotonic and oscillatory outgrowth, localised limit cycle oscillations and complete growth depression.

Experimental implementation of a biometric laser synaptic sensor

We fabricate a biometric laser fiber synaptic sensor to transmit information from one neuron cell to the other by an optical way. The optical synapse is constructed on the base of an erbium-doped fiber laser, whose pumped diode current is driven by a pre-synaptic FitzHugh–Nagumo electronic neuron, and the laser output controls a post-synaptic FitzHugh–Nagumo electronic neuron. The implemented laser synapse displays very rich dynamics, including fixed points, periodic orbits with different frequency-locking ratios and chaos. These regimes can be beneficial for efficient biorobotics, where behavioral flexibility subserved by synaptic connectivity is a challenge.

Dendritic signal transmission induced by intracellular charge inhomogeneities

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 obtain a modified cable equation. We show that charge inhomogeneities acting on a 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 signaling. We also show that membrane potential in spiny dendrites obeys the modified cable equation suggesting a crucial role of the spines in dendritic subthreshold resonance.

Bi-directional astrocytic regulation of neuronal activity within a network

The concept of a tripartite synapse holds that astrocytes can affect both the pre- and post-synaptic compartments through the Ca²⁺-dependent release of gliotransmitters. Because astrocytic Ca²⁺ transients usually last for a few seconds, we assumed that astrocytic regulation of synaptic transmission may also occur on the scale of seconds. Here, we considered the basic physiological functions of tripartite synapses and investigated astrocytic regulation at the level of neural network activity. The firing dynamics of individual neurons in a spontaneous firing network was described by the Hodgkin–Huxley model. The neurons received excitatory synaptic input driven by the Poisson spike train with variable frequency. The mean field concentration of the released neurotransmitter was used to describe the presynaptic dynamics. The amplitudes of the excitatory postsynaptic currents (PSCs) obeyed the gamma distribution law. In our model, astrocytes depressed the presynaptic release and enhanced the PSCs. As a result, low frequency synaptic input was suppressed while high frequency input was amplified. The analysis of the neuron spiking frequency as an indicator of network activity revealed that tripartite synaptic transmission dramatically changed the local network operation compared to bipartite synapses. Specifically, the astrocytes supported homeostatic regulation of the network activity by increasing or decreasing firing of the neurons. Thus, the astrocyte activation may modulate a transition of neural network into bistable regime of activity with two stable firing levels and spontaneous transitions between them.

Bistability induces episodic spike communication by inhibitory neurons in neuronal networks

Bistability is one of the important features of nonlinear dynamical systems. In neurodynamics, bistability has been found in basic Hodgkin-Huxley equations describing the cell membrane dynamics. When the neuron is clamped near its threshold, the stable rest potential may coexist with the stable limit cycle describing periodic spiking. However, this effect is often neglected in network computations where the neurons are typically reduced to threshold firing units (e.g., integrate-and-fire models). We found that the bistability may induce spike communication by inhibitory coupled neurons in the spiking network. The communication is realized in the form of episodic discharges with synchronous (correlated) spikes during the episodes. A spiking phase map is constructed to describe the synchronization and to estimate basic spike phase locking modes.

Bifurcation mechanisms of regular and chaotic network signaling in brain astrocytes

Bifurcation mechanisms underlying calcium oscillations in the network of astrocytes are investigated. Network model includes the dynamics of intracellular calcium concentration and intercellular diffusion of inositol 1,4,5-trisphosphate through gap junctions. Bifurcation analysis of underlying nonlinear dynamical system is presented. Parameter regions and principle bifurcation boundaries have been delineated and described. We show how variations of the diffusion rate can lead to generation of network calcium oscillations in originally nonoscillating cells. Different scenarios of regular activity and its transitions to chaotic dynamics have been obtained. Then, the bifurcations have been associated with statistical characteristics of calcium signals showing that different bifurcation scenarios yield qualitative changes in experimentally measurable quantities of the astrocyte activity, e.g., statistics of calcium spikes.

[Cluster associative memory formation in a three-layer network of phase oscillators]

A three-layer network model of oscillatory associative mermory is proposed. The network is capable to store binary images that can be retrieved if an appropriate stimulus has been applied. Binary images are encoded in the form of the spatial distribution of oscillatory phase clusters in-phase (+1) and anti-phase relative to the base periodic signal. The information is loaded into the network using a set of interlayer connection weights. A condition for error-free pattern retrieval has been obtained, which imposes a certain limitation on the maximal number of patterns to be stored in the memory (storage capacity). It has been shown that the capacity can be significantly increased by the generation of optimal pattern alphabet (basic pattern set). The number of stored patterns can reach values of the network size (the number of oscillators in the layer), which is significantly higher than the capacity of traditional oscillatory memory models. The dynamical and information characteristics of the retrieval process based on the optimal alphabet including the estimations of attraction basins and the admissible input pattern discrepancy for error-free retrieval have been investigated.

Spontaneous calcium signals induced by gap junctions in a network model of astrocytes

The dynamics of a network model of astrocytes coupled by gap junctions is investigated. Calcium dynamics of the single cell is described by the biophysical model comprising the set of three nonlinear differential equations. Intercellular dynamics is provided by the diffusion of inositol 1,4,5-trisphosphate (IP3) through gap junctions between neighboring astrocytes. It is found that the diffusion induces the appearance of spontaneous activity patterns in the network. Stability of the network steady state is analyzed. It is proved that the increase of the diffusion coefficient above a certain critical value yields the generation of low-amplitude subthreshold oscillatory signals in a certain frequency range. It is shown that such spontaneous oscillations can facilitate calcium pulse generation and provide a certain time scale in astrocyte signaling.

Spiking dynamics of interacting oscillatory neurons

Spiking sequences emerging from dynamical interaction in a pair of oscillatory neurons are investigated theoretically and experimentally. The model comprises two unidirectionally coupled FitzHugh-Nagumo units with modified excitability (MFHN). The first (master) unit exhibits a periodic spike sequence with a certain frequency. The second (slave) unit is in its excitable mode and responds on the input signal with a complex (chaotic) spike trains. We analyze the dynamic mechanisms underlying different response behavior depending on interaction strength. Spiking phase maps describing the response dynamics are obtained. Complex phase locking and chaotic sequences are investigated. We show how the response spike trains can be effectively controlled by the interaction parameter and discuss the problem of neuronal information encoding.

Self-referential phase reset based on inferior olive oscillator dynamics

The olivo-cerebellar network is a key neuronal circuit that provides high-level motor control in the vertebrate CNS. Functionally, its network dynamics is organized around the oscillatory membrane potential properties of inferior olive (IO) neurons and their electrotonic connectivity. Because IO action potentials are generated at the peaks of the quasisinusoidal membrane potential oscillations, their temporal firing properties are defined by the IO rhythmicity. Excitatory inputs to these neurons can produce oscillatory phase shifts without modifying the amplitude or frequency of the oscillations, allowing well defined time-shift modulation of action potential generation. Moreover, the resulting phase is defined only by the amplitude and duration of the reset stimulus and is independent of the original oscillatory phase when the stimulus was delivered. This reset property, henceforth referred to as selfreferential phase reset, results in the generation of organized clusters of electrically coupled cells that oscillate in phase and are controlled by inhibitory feedback loops through the cerebellar nuclei and the cerebellar cortex. These clusters provide a dynamical representation of arbitrary motor intention patterns that are further mapped to the motor execution system. Being supplied with sensory inputs, the olivo-cerebellar network is capable of rearranging the clusters during the process of movement execution. Accordingly, the phase of the IO oscillators can be rapidly reset to a desired phase independently of the history of phase evolution. The goal of this article is to show how this selfreferential phase reset may be implemented into a motor control system by using a biologically based mathematical model.

Emergence of chaotic attractor and anti-synchronization for two coupled monostable neurons

The dynamics of two coupled piece-wise linear one-dimensional monostable maps is investigated. The single map is associated with Poincare section of the FitzHugh-Nagumo neuron model. It is found that a diffusive coupling leads to the appearance of chaotic attractor. The attractor exists in an invariant region of phase space bounded by the manifolds of the saddle fixed point and the saddle periodic point. The oscillations from the chaotic attractor have a spike-burst shape with anti-phase synchronized spiking.

Spiking patterns emerging from wave instabilities in a one-dimensional neural lattice

The dynamics of a one-dimensional lattice (chain) of electrically coupled neurons modeled by the FitzHugh-Nagumo excitable system with modified nonlinearity is investigated. We have found that for certain conditions the lattice exhibits a countable set of pulselike wave solutions. The analysis of homoclinic and heteroclinic bifurcations is given. Corresponding bifurcation sets have the shapes of spirals twisting to the same center. The appearance of chaotic spiking patterns emerging from wave instabilities is discussed.

Selective communication and information processing by excitable systems

The phenomena of selective response of an excitable system to external pulse stimulation relating to interneuron communication and information processing problems are discussed. Subthreshold dynamics of the FitzHugh-Nagumo-like excitable system modeling of a neuron with the synaptic input is investigated. It is shown that the system response on various incoming information messages can be described by one- and two-dimensional linear and nonlinear point maps. Nonlinear integrating and resonant properties of the system are analyzed.

Theoretical and experimental study of two discrete coupled Nagumo chains

We analyze front wave (kink and antikink) propagation and pattern formation in a system composed of two coupled discrete Nagumo chains using analytical and numerical methods. In the case of homogeneous interaction among the chains, we show the possibility of the effective control on wave propagation. In addition, physical experiments on electrical chains confirm all theoretical behaviors.

Synchronization, re-entry, and failure of spiral waves in a two-layer discrete excitable system

A three-dimensional structure composed of two coupled discrete excitable lattices is considered. Each lattice (layer) is a discrete excitable subsystem and using a local model of excitation transfer and failure we have estimated the sufficient conditions for it to exhibit spiral waves. Then we show how interlayer synchronization of all motions is possible. Various effects of spiral wave synchronization, re-entry and failure are also investigated.

The emergence of form by replication

It is shown with a simple mathematical model that if a system exhibits a given form (a spatial structure) and is put in contact with another system of the same type but in a state of spatial disorder, then under certain conditions their mutual interaction as they evolve in time allows replication of form in the disordered system with a controllable degree of faithfulness.