Synaptic Coupling Research Articles

Postnatal Development of the Circadian Rhythmicity of Human Pineal Melatonin Synthesis and Secretion (Systematic Review).

Introduction: According to current knowledge, at birth, the pineal gland and melatonin receptors are already present and the suprachiasmatic nucleus is largely functional, and noradrenaline, the key pineal transmitter, can be detected in the early foetal period. It is still unclear why the pineal gland is not able to start its own pulsatile synthesis and secretion of melatonin in the first months of life, and as a result, infants during this time are dependent on an external supply of melatonin. Method: The causes and consequences of this physiological melatonin deficiency in human infancy are examined in a systematic review of the literature, in which 40 of 115 initially selected publications were evaluated in detail. The references of these studies were checked for relevant studies on this topic. References from previous reviews by the author were taken into account. Results: The development and differentiation of the pineal gland, the pinealocytes, as the site of melatonin synthesis, and the development and synaptic coupling of the associated predominantly noradrenergic neural pathways and vessels and the associated Lhx4 homebox only occurs during the first year of life. Discussion: The resulting physiological melatonin deficiency is associated with sleep disorders, infant colic, and increased crying in babies. Intervention studies indicate that this deficiency should be compensated for through breastfeeding, the administration of nonpooled donor milk, or through industrially produced chrononutrition made from nonpooled cow's milk with melatonin-poor day milk and melatonin-rich night milk.

Synaptic coupling and synchronization for HR neural network developing a novel type II non-linear memristor, potential to neuromorphic application

Synaptic coupling and synchronization for HR neural network developing a novel type II non-linear memristor, potential to neuromorphic application

Activity patterns in ring networks of quadratic integrate-and-fire neurons with synaptic and gap junction coupling.

We consider a ring network of quadratic integrate-and-fire neurons with nonlocal synaptic and gap junction coupling. The corresponding neural field model supports solutions such as standing and traveling waves, and also lurching waves. We show that many of these solutions satisfy self-consistency equationswhich can be used to follow them as parameters are varied. We perform numerical bifurcation analysis of the neural field model, concentrating on the effects of varying gap junction coupling strength. Our methods are generally applicable to a wide variety of networks of quadratic integrate-and-fire neurons.

STED Imaging of Vesicular Endocytosis in the Synapse.

Endocytosis is a fundamental biological process that couples exocytosis to maintain the homeostasis of the plasma membrane and sustained neurotransmission. Super-resolution microscopy enables optical imaging of exocytosis and endocytosis in live cells and makes an essential contribution to understanding molecular mechanisms of endocytosis in neuronal somata and other types of cells. However, visualization of exo-endocytic events at the single vesicular level in a synapse with optical imaging remains a great challenge to reveal mechanisms governing the synaptic exo-endocytotic coupling. In this protocol, we describe the technical details of stimulated emission depletion (STED) imaging of synaptic endocytosis at the single-vesicle level, from sample preparation and microscopy calibration to data acquisition and analysis.

Investigation of Synchronization Control of the Memristive/Resistive-Coupled Neural Network with Noise Effect

This study comprehensively investigates synchronization control of the memristive- and resistive-coupled neural network with noise effect. In this context, a sub-network is constructed with three chaotic memristive Hindmarsh–Rose neurons coupled by the memristive synapses. Then, two equivalent sub-networks are linked by the diffusive resistive synapse under a distinctive global network structure including two sub-networks. Thus, a double (memristive/resistive) control mechanism is used to achieve the synchronization state. The first mechanism is the memristive synaptic coupling in each sub-network, and the second one is the diffusive resistive coupling between two sub-networks constructing the global network. The synchronization between the neurons is proven theoretically through the Lyapunov stability and Lipschitz theorems and this proof process is verified with numerical experiments. According to the theoretical and numerical results, by adjusting memristive/resistive synaptic coupling weights, a synchrony behavior is generated successfully in these sub-networks and global networks. Additionally, this paper also handles the Gaussian white noise effect on the global network to examine continuity capability and stability of synchronization. Two different frameworks are built by applying the noise with multiple noise power levels and periods to (i) one of the resistive coupling neurons in each sub-network directly and (ii) one neuron in a sub-network without direct contact with the other sub-network. With these two characteristic designs, it is proven that the second design provides more robust characteristics since it utilizes the double control mechanism, which enhances the stability throughout external interferences enabling the network to sustain synchronous states.

Well-Posedness and Regularity of Solutions to Neural Field Problems with Dendritic Processing

We study solutions to a recently proposed neural field model in which dendrites are modelled as a continuum of vertical fibres stemming from a somatic layer. Since voltage propagates along the dendritic direction via a cable equation with nonlocal sources, the model features an anisotropic diffusion operator, as well as an integral term for synaptic coupling. The corresponding Cauchy problem is thus markedly different from classical neural field equations. We prove that the weak formulation of the problem admits a unique solution, with embedding estimates similar to the ones of nonlinear local reaction–diffusion equations. Our analysis relies on perturbing weak solutions to the diffusion-less problem, that is, a standard neural field, for which weak problems have not been studied to date. We find rigorous asymptotic estimates for the problem with and without diffusion, and prove that the solutions of the two models stay close, in a suitable norm, on finite time intervals. We provide numerical evidence of our perturbative results.

Dynamic mechanisms of delay formation and propagation in neuronal astrocytic network with electromagnetic induction

A model of neuro-astrocytic coupling with electromagnetic induction has been developed to deeply investigate the genesis and propagation of Delay within networks. Delay is defined as the time neurons continue to fire after external stimulation has ceased until they reach a resting state. The findings reveal that the primary cause of Delay in the neuron-astrocyte coupling system is the role of astrocytes. We observe that within a certain range, the feedback intensity causes a fractal structure of Delay, and as the feedback from astrocytes intensifies, Delay increases indefinitely. Neurons can continue firing indefinitely post-stimulation, and we have identified the feedback threshold for this infinite Delay. Further, we observed the transmission of Delay in neuron-astrocyte networks. Subsequent neurons, which would not normally fire, begin to discharge during the transmission of Delay, a phenomenon induced by either synaptic or astrocytic coupling. Finally, with electromagnetic induction, we noted the cumulative effect of Delay in the network, leading to longer sustained firing in more distant neurons as the network extends and propagates. Our research elucidates the precise mechanisms of generation and propagation of Delay, offering insights akin to mechanisms of memory in the nervous system, potentially providing novel understandings in the field of cognitive science.

Coexistence of asynchronous and clustered dynamics in noisy inhibitory neural networks

A regime of coexistence of asynchronous and clustered dynamics is analysed for globally coupled homogeneous and heterogeneous inhibitory networks of quadratic integrate-and-fire (QIF) neurons subject to Gaussian noise. The analysis is based on accurate extensive simulations and complemented by a mean-field description in terms of low-dimensional next generation neural mass models for heterogeneously distributed synaptic couplings. The asynchronous regime is observable at low noise and becomes unstable via a sub-critical Hopf bifurcation at sufficiently large noise. This gives rise to a coexistence region between the asynchronous and the clustered regime. The clustered phase is characterised by population bursts in the γ-range (30–120 Hz), where neurons are split in two equally populated clusters firing in alternation. This clustering behaviour is quite peculiar: despite the global activity being essentially periodic, single neurons display switching between the two clusters due to heterogeneity and/or noise.

Energy consumption in the synchronization of neurons coupled by electrical or memristive synapse

The energy consumption in synapses has been an issue of great concern, and we apply the resistor to function as the electrical synapse, and the memristor is utilized as the chemical synapse. We investigate the dynamics of neurons during the synchronization, as well as the energy consumption associated with coupled channels. The numerical results revealed that two neurons with different initial values can get into a complete synchronization, regardless of whether they are coupled via resistive or memristive synapse. Furthermore, the energy consumption of electrical synaptic coupling is companied by an energy phase transition burst that causes a sharp increase or decrease in the channel energy consumption. In contrast, memristive coupling promotes steady information and energy exchange between neurons, with relatively lower energy consumption compared to electrical synaptic coupling. Meanwhile, the memconductance of the memristor is lower than that of resistive coupling, leading to a lower coupling strength when the synchronization is achieved. Furthermore, the employment of the energy switch to trigger synaptic activation or silence can effectively control synaptic activity, and neurons can spontaneously synchronize and maintain energy balance. The energy difference between chaotic neurons can cause the transitions between synchronization, desynchronization, and resynchronization. The findings may provide insights for developing genuine neural circuits and leveraging them in artificial neuron design.

Optimal input reverberation and homeostatic self-organization toward the edge of synchronization.

Transient or partial synchronization can be used to do computations, although a fully synchronized network is sometimes related to the onset of epileptic seizures. Here, we propose a homeostatic mechanism that is capable of maintaining a neuronal network at the edge of a synchronization transition, thereby avoiding the harmful consequences of a fully synchronized network. We model neurons by maps since they are dynamically richer than integrate-and-fire models and more computationally efficient than conductance-based approaches. We first describe the synchronization phase transition of a dense network of neurons with different tonic spiking frequencies coupled by gap junctions. We show that at the transition critical point, inputs optimally reverberate through the network activity through transient synchronization. Then, we introduce a local homeostatic dynamic in the synaptic coupling and show that it produces a robust self-organization toward the edge of this phase transition. We discuss the potential biological consequences of this self-organization process, such as its relation to the Brain Criticality hypothesis, its input processing capacity, and how its malfunction could lead to pathological synchronization and the onset of seizure-like activity.

Intensity- and frequency-specific effects of transcranial alternating current stimulation are explained by network dynamics

Objective. Transcranial alternating current stimulation (tACS) can be used to non-invasively entrain neural activity and thereby cause changes in local neural oscillatory power. Despite its increased use in cognitive and clinical neuroscience, the fundamental mechanisms of tACS are still not fully understood. Approach. We developed a computational neuronal network model of two-compartment pyramidal neurons (PY) and inhibitory interneurons, which mimic the local cortical circuits. We modeled tACS with electric field strengths that are achievable in human applications. We then simulated intrinsic network activity and measured neural entrainment to investigate how tACS modulates ongoing endogenous oscillations. Main results. The intensity-specific effects of tACS are non-linear. At low intensities (<0.3 mV mm−1), tACS desynchronizes neural firing relative to the endogenous oscillations. At higher intensities (>0.3 mV mm−1), neurons are entrained to the exogenous electric field. We then further explore the stimulation parameter space and find that the entrainment of ongoing cortical oscillations also depends on stimulation frequency by following an Arnold tongue. Moreover, neuronal networks can amplify the tACS-induced entrainment via synaptic coupling and network effects. Our model shows that PY are directly entrained by the exogenous electric field and drive the inhibitory neurons. Significance. The results presented in this study provide a mechanistic framework for understanding the intensity- and frequency-specific effects of oscillating electric fields on neuronal networks. This is crucial for rational parameter selection for tACS in cognitive studies and clinical applications.

Theory of Coupled Neuronal-Synaptic Dynamics

In neural circuits, synaptic strengths influence neuronal activity by shaping network dynamics, and neuronal activity influences synaptic strengths through activity-dependent plasticity. Motivated by this fact, we study a recurrent-network model in which neuronal units and synaptic couplings are interacting dynamic variables, with couplings subject to Hebbian modification with decay around quenched random strengths. Rather than assigning a specific role to the plasticity, we use dynamical mean-field theory and other techniques to systematically characterize the neuronal-synaptic dynamics, revealing a rich phase diagram. Adding Hebbian plasticity slows activity in already chaotic networks and can induce chaos in otherwise quiescent networks. Anti-Hebbian plasticity quickens activity and produces an oscillatory component. Analysis of the Jacobian shows that Hebbian and anti-Hebbian plasticity push locally unstable modes toward the real and imaginary axes, respectively, explaining these behaviors. Both random-matrix and Lyapunov analysis show that strong Hebbian plasticity segregates network timescales into two bands, with a slow, synapse-dominated band driving the dynamics, suggesting a flipped view of the network as synapses connected by neurons. For increasing strength, Hebbian plasticity initially raises the complexity of the dynamics, measured by the maximum Lyapunov exponent and attractor dimension, but then decreases these metrics, likely due to the proliferation of stable fixed points. We compute the marginally stable spectra of such fixed points as well as their number, showing exponential growth with network size. Finally, in chaotic states with strong Hebbian plasticity, a stable fixed point of neuronal dynamics is destabilized by synaptic dynamics, allowing any neuronal state to be stored as a stable fixed point by halting the plasticity. This phase of freezable chaos offers a new mechanism for working memory. Published by the American Physical Society 2024

A general description of criticality in neural network models

Recent experimental observations have supported the hypothesis that the cerebral cortex operates in a dynamical regime near criticality, where the neuronal network exhibits a mixture of ordered and disordered patterns. However, A comprehensive study of how criticality emerges and how to reproduce it is still lacking. In this study, we investigate coupled networks with conductance-based neurons and illustrate the co-existence of different spiking patterns, including asynchronous irregular (AI) firing and synchronous regular (SR) state, along with a scale-invariant neuronal avalanche phenomenon (criticality). We show that fast-acting synaptic coupling can evoke neuronal avalanches in the mean-dominated regime but has little effect in the fluctuation-dominated regime. In a narrow region of parameter space, the network exhibits avalanche dynamics with power-law avalanche size and duration distributions. We conclude that three stages which may be responsible for reproducing the synchronized bursting: mean-dominated subthreshold dynamics, fast-initiating a spike event, and time-delayed inhibitory cancellation. Remarkably, we illustrate the mechanisms underlying critical avalanches in the presence of noise, which can be explained as a stochastic crossing state around the Hopf bifurcation under the mean-dominated regime. Moreover, we apply the ensemble Kalman filter to determine and track effective connections for the neuronal network. The method is validated on noisy synthetic BOLD signals and could exactly reproduce the corresponding critical network activity. Our results provide a special perspective to understand and model the criticality, which can be useful for large-scale modeling and computation of brain dynamics.

Intra-ripple frequency accommodation in an inhibitory network model for hippocampal ripple oscillations.

Hippocampal ripple oscillations have been implicated in important cognitive functions such as memory consolidation and planning. Multiple computational models have been proposed to explain the emergence of ripple oscillations, relying either on excitation or inhibition as the main pacemaker. Nevertheless, the generating mechanism of ripples remains unclear. An interesting dynamical feature of experimentally measured ripples, which may advance model selection, is intra-ripple frequency accommodation (IFA): a decay of the instantaneous ripple frequency over the course of a ripple event. So far, only a feedback-based inhibition-first model, which relies on delayed inhibitory synaptic coupling, has been shown to reproduce IFA. Here we use an analytical mean-field approach and numerical simulations of a leaky integrate-and-fire spiking network to explain the mechanism of IFA. We develop a drift-based approximation for the oscillation dynamics of the population rate and the mean membrane potential of interneurons under strong excitatory drive and strong inhibitory coupling. For IFA, the speed at which the excitatory drive changes is critical. We demonstrate that IFA arises due to a speed-dependent hysteresis effect in the dynamics of the mean membrane potential, when the interneurons receive transient, sharp wave-associated excitation. We thus predict that the IFA asymmetry vanishes in the limit of slowly changing drive, but is otherwise a robust feature of the feedback-based inhibition-first ripple model.

Node-Wise Monotone Barrier Coupling Law for Formation Control.

We study a node-wise monotone barrier coupling law, motivated by the synaptic coupling of neural central pattern generators. It is illustrated that this coupling imitates the desirable properties of neural central pattern generators. In particular, the coupling law (1) allows us to assign multiple central patterns on the circle and (2) allows for rapid switching between different patterns via simple 'kicks'. In the end, we achieve full control by partitioning the state space by utilizing a barrier effect and assigning a unique steady-state behavior to each element of the resulting partition. We analyze the global behavior and study the viability of the design.

Statistical mechanics of learning via reverberation in bidirectional associative memories

We study bi-directional associative neural networks that, exposed to noisy examples of an extensive number of random archetypes, learn the latter (with or without the presence of a teacher) when the supplied information is enough: in this setting, learning is heteroassociative – involving couples of patterns – and it is achieved by reverberating the information depicted from the examples through the layers of the network. By adapting Guerra’s interpolation technique, we provide a full statistical mechanical picture of supervised and unsupervised learning processes (at the replica symmetric level of description) obtaining analytically phase diagrams, thresholds for learning, a picture of the ground-state in plain agreement with Monte Carlo simulations and signal-to-noise outcomes. In the large dataset limit, the Kosko storage prescription as well as its statistical mechanical picture provided by Kurchan, Peliti, and Saber in the eighties is fully recovered. Computational advantages in dealing with information reverberation, rather than storage, are discussed for natural test cases. In particular, we show how this network admits an integral representation in terms of two coupled restricted Boltzmann machines, whose hidden layers are entirely built of by grand-mother neurons, to prove that by coupling solely these grand-mother neurons we can correlate the patterns they are related to: it is thus possible to recover Pavlov’s Classical Conditioning by adding just one synapse among the correct grand-mother neurons (hence saving an extensive number of these links for further information storage w.r.t. the classical auto-associative setting). Likewise, it is enough to equip the BAM’s synaptic coupling with its transpose matrix (and alternate among these two, e.g., by introducing a clock) to let these networks be able count sequences of patterns (still preserving Detailed Balance, at difference w.r.t. the auto-associative case).

How synaptic function controls critical transitions in spiking neuron networks: insight from a Kuramoto model reduction.

The dynamics of synaptic interactions within spiking neuron networks play a fundamental role in shaping emergent collective behavior. This paper studies a finite-size network of quadratic integrate-and-fire neurons interconnected via a general synaptic function that accounts for synaptic dynamics and time delays. Through asymptotic analysis, we transform this integrate-and-fire network into the Kuramoto-Sakaguchi model, whose parameters are explicitly expressed via synaptic function characteristics. This reduction yields analytical conditions on synaptic activation rates and time delays determining whether the synaptic coupling is attractive or repulsive. Our analysis reveals alternating stability regions for synchronous and partially synchronous firing, dependent on slow synaptic activation and time delay. We also demonstrate that the reduced microscopic model predicts the emergence of synchronization, weakly stable cyclops states, and non-stationary regimes remarkably well in the original integrate-and-fire network and its theta neuron counterpart. Our reduction approach promises to open the door to rigorous analysis of rhythmogenesis in networks with synaptic adaptation and plasticity.

Macroscopic behavior of populations of quadratic integrate-and-fire neurons subject to non-Gaussian white noise.

We study macroscopic behavior of populations of quadratic integrate-and-fire neurons subject to non-Gaussian noises; we argue that these noises must be α-stable whenever they are delta-correlated (white). For the case of additive-in-voltage noise, we derive the governing equation of the dynamics of the characteristic function of the membrane voltage distribution and construct a linear-in-noise perturbation theory. Specifically for the recurrent network with global synaptic coupling, we theoretically calculate the observables: population-mean membrane voltage and firing rate. The theoretical results are underpinned by the results of numerical simulation for homogeneous and heterogeneous populations. The possibility of the generalization of the pseudocumulant approach to the case of a fractional α is examined for both irrational and fractional rational α. This examination seemingly suggests the pseudocumulant approach or its modifications to be employable only for the integer values of α=1 (Cauchy noise) and 2 (Gaussian noise) within the physically meaningful range (0;2]. Remarkably, the analysis for fractional α indirectly revealed that, for the Gaussian noise, the minimal asymptotically rigorous model reduction must involve three pseudocumulants and the two-pseudocumulant model reduction is an artificial approximation. This explains a surprising gain of accuracy for the three-pseudocumulant models as compared to the two-pseudocumulant ones reported in the literature.

Dynamic behaviors analysis of fraction-order neural network under memristive electromagnetic induction

The dynamic behaviors of coupled neurons with different mathematical representations have received more and more attention in recent years. The coupling among heterogeneous neurons can show richer dynamic phenomena, which is of great significance in understanding the function of the human brain. In this paper, we present a fraction-order heterogeneous network with three neurons, which is built by coupling an FN neuron with two HR neurons. Complex electromagnetic surroundings have meaningful physical influence on the electrical activities of neurons. To imitate the effects of electromagnetic induction on the three-neuron heterogeneous network, we introduce a fraction-order locally active memristor in the neural network. The characteristics of this memristor are carefully analyzed by pinched hysteresis loops and its locally active characteristic is proved by the power-off plot and the DC &lt;i&gt;v-i&lt;/i&gt; plot. Then, the parameter-dependent dynamic activities are investigated numerically by using several dynamical analysis methods, such as the phase diagrams, bifurcation diagrams, Lyapunov exponent spectra, and attraction basins. In addition, the network also reveals rich dynamic behaviors, including coexisting activities, anti-monotonicity phenomena, transient chaos and firing patterns, providing support for further investigating the firing patterns of the human brain. In particular, complex dynamics, including coexisting attractors, anti-monotonicity, and firing patterns, can be influenced by the order and strength of electrical synaptic coupling and electromagnetic induction. The control of the bistable state can be realized through the time feedback control method, so that the bistable state can be transformed into an ideal monostable state. The study of the fraction-order memristive neural network may expand the field of view for understanding the collective behaviors of neurons. Finally, based on the ARM platform, we give a digital implementation of the fraction-order memristive neural network, which can verify the consistency with the numerical simulation results. In the future, we will explore more interesting memristive neural networks and study different types of methods to control the firing behaviors of the networks.

Dynamics of oscillator populations globally coupled with distributed phase shifts

Globally coupled populations of oscillators are exemplary models for synchronization and the emergence of collective modes. In many cases, the nature of the global coupling is predetermined by the setup. Nevertheless, the oscillators can possess distinct properties and intrinsic noise, leading to non-identity of the system elements. The variation in natural frequencies among the oscillators is the primary source of non-identity. This feature has already been extensively studied. Our research focuses on the impact of phase shift coupling disorder. These phase lags naturally occur where the global force must propagate to reach spatially distributed elements of the population. First, we develop a phase model in the Kuramoto–Sakaguchi form for a group of quadratic integrate-and-fire neurons that are inter-connected by a synaptic current transmitted with different time delays. This occurs when each cell receives input from other cells of the ensemble with an inherent delay. From a mathematical perspective, a global force affects oscillators with different time delays, resulting in a spread of phase lags in the corresponding phase model. Assuming a weak interaction between system units, we transform to slow-varying phases and use the standard time-average procedure. Secondly, we demonstrate that a distribution of phase shifts in coupling may result from local oscillator properties, particularly when synaptic coupling of neurons incorporates a “low-pass filter” of an incoming, globally averaged synaptic field. For this purpose, we examine the classic θ-neuron model, which is frequently used to analyze the collective dynamics of a Type I neuron population. Here, we posit that neurons interact through chemical synapses, with each corresponding synaptic current forcing on the neuron satisfying the relaxation equation while having an individual, disordered value of the relaxation constant. Under this assumption of weak coupling and through the use of multiple timescale analysis, we obtain the Kuramoto-Sakaguchi model of phase oscillators which exhibit distributed phase lags. Next, we will consider the characteristics of the phase model. In the thermodynamic limit, the one-particle probability density function characterizes the continuum of phase oscillators. It evolves according to the continuity equation and possesses an exact solution in the Ott–Antonsen ansatz form at each α phase lag value. This manifold is attractive and represents a special ansatz for the expansion of a Poisson kernel in a Fourier series with respect to the phase variable, as demonstrated in other papers. Using this analytical approach, we obtain a low-dimensional depiction of the collective behavior of the system, which indicates that in the equations for macroscopic complex fields, the redefined order parameter Q(t,α) depends solely on the phase shifts α through the initial conditions. However, its dynamics remain independent. Using stability analyses in the linear approximation and reduced equations, we argue that during the dynamics process, the memory of the initial state is lost and Q(t,α)→Q(t). After Q(t) converges, the population dynamics with a distribution of phase shifts reduces to a single dynamical equation for the auxiliary order parameter Q(t), and the original order parameters are connected to it through circular moments of the phase shift distribution g(α). All theoretical concepts are confirmed through numerical calculations performed directly within the oscillatory population models under consideration.