Energy expenditure computation of a single bursting neuron

Antiferromagnetic artificial neuron modeling of the withdrawal reflex

Replicating neural responses observed in biological systems using artificial neural networks holds significant promise in the fields of medicine and engineering. In this study, we employ ultra-fast artificial neurons based on antiferromagnetic (AFM) spin Hall oscillators to emulate the biological withdrawal reflex responsible for self-preservation against noxious stimuli, such as pain or temperature. As a result of utilizing the dynamics of AFM neurons, we are able to construct an artificial neural network that can mimic the functionality and organization of the biological neural network responsible for this reflex. The unique features of AFM neurons, such as inhibition that stems from an effective AFM inertia, allow for the creation of biologically realistic neural network components, like the interneurons in the spinal cord and antagonist motor neurons. To showcase the effectiveness of AFM neuron modeling, we conduct simulations of various scenarios that define the withdrawal reflex, including responses to both weak and strong sensory stimuli, as well as voluntary suppression of the reflex.

Energy and synchronization between two neurons with nonlinear coupling

Consensus and synchronous firing in neural activities are relative to the physical properties of synaptic connections. For coupled neural circuits, the physical properties of coupling channels control the synchronization stability, and transient period for keeping energy diversity. Linear variable coupling results from voltage coupling via linear resistor by consuming certain Joule heat, and electric synapse coupling between neurons derives from gap junction connection under special electrophysiological condition. In this work, a voltage-controlled electric component with quadratic relation in the i-v (current-voltage) is used to connect two neural circuits composed of two variables. The energy function obtained by using Helmholtz theorem is consistent with the Hamilton energy function converted from the field energy in the neural circuit. Chaotic signals are encoded to approach a mixed signal within certain frequency band, and then its amplitude is adjusted to excite the neuron for detecting possible occurrence of nonlinear resonance. External stimuli are changed to trigger different firing modes, and nonlinear coupling activates changeable coupling intensity. It is confirmed that nonlinear coupling behaves functional regulation as hybrid synapse, and the synchronization transition between neurons can be controlled for reaching possible energy balance. The nonlinear coupling is helpful to keep energy diversity and prevent synchronous bursting because positive and negative feedback is switched with time. As a result, complete synchronization is suppressed and phase lock is controlled between neurons with energy diversity.

Dendrites and efficiency: Optimizing performance and resource utilization

The brain is a highly efficient system that has evolved to optimize performance under limited resources. In this review, we highlight recent theoretical and experimental studies that support the view that dendrites make information processing and storage in the brain more efficient. This is achieved through the dynamic modulation of integration versus segregation of inputs and activity within a neuron. We argue that under conditions of limited energy and space, dendrites help biological networks to implement complex functions such as processing natural stimuli on behavioral timescales, performing the inference process on those stimuli in a context-specific manner, and storing the information in overlapping populations of neurons. A global picture starts to emerge, in which dendrites help the brain achieve efficiency through a combination of optimization strategies that balance the tradeoff between performance and resource utilization.

Artificial Neuronal Devices Based on Emerging Materials: Neuronal Dynamics and Applications

Artificial neuronal devices are critical building blocks of neuromorphic computing systems and currently the subject of intense research motivated by application needs from new computing technology and more realistic brain emulation. Researchers have proposed a range of device concepts that can mimic neuronal dynamics and functions. Although the switching physics and device structures of these artificial neurons are largely different, their behaviors can be described by several neuron models in a more unified manner. In this paper, the reports of artificial neuronal devices based on emerging volatile switching materials are reviewed from the perspective of the demonstrated neuron models, with a focus on the neuronal functions implemented in these devices and the exploitation of these functions for computational and sensing applications. Furthermore, the neuroscience inspirations and engineering methods to enrich the neuronal dynamics that remain to be implemented in artificial neuronal devices and networks toward realizing the full functionalities of biological neurons are discussed.

Energy-efficiency computing of up and down transitions in a neural network

Spontaneous periodic up and down transitions of membrane potentials are considered to be a significant spontaneous activity of slow-wave sleep. Previous theoretical studies have shown that stimulation frequency and the dynamics of intrinsic currents have a major influence on synchronicity and firing rate of spontaneous fluctuation. Energy consumption is driven by internal spontaneous activity. However, its energy consumption and energy efficiency are not clear. Therefore, this article simulates the up and down transitions based on a neural network and discusses the energy consumption and energy efficiency. It is found that the dynamics of intrinsic currents have a great impact on the energy consumption and energy efficiency in the process. The energy consumption is influenced by the size of the period and the average power consumption of the state. The average power consumption by the up state is always greater than the consumption by the down state, and the energy consumption of the transition is more than firing. In addition, the lower average proportion of duration of the up state in the cycle leads to higher energy efficiency. Energy consumption is reduced and energy efficiency is enhanced by adjusting parameters of the network. The study helps us to understand and further explore the metabolic consumption of spontaneous activities.NEW & NOTEWORTHY We use a more biological neural network to explore energy consumption and energy efficiency of up and down transitions. Specifically, we find that average energy consumption is more than that caused by action potentials, which proves that metabolic consumption is acquired substantially in the resting state as well. We also find that energy efficiency is influenced by the proportion of duration of the up state in the cycle. These findings may further improve the economy of the nervous system.

Dopamine-Mediated Major Depressive Disorder in the Neural Circuit of Ventral Tegmental Area-Nucleus Accumbens-Medial Prefrontal Cortex: From Biological Evidence to Computational Models

Major depressive disorder (MDD) is a serious psychiatric disorder, with an increasing incidence in recent years. The abnormal dopaminergic pathways of the midbrain cortical and limbic system are the key pathological regions of MDD, particularly the ventral tegmental area- nucleus accumbens- medial prefrontal cortex (VTA-NAc-mPFC) neural circuit. MDD usually occurs with the dysfunction of dopaminergic neurons in VTA, which decreases the dopamine concentration and metabolic rate in NAc/mPFC brain regions. However, it has not been fully explained how abnormal dopamine concentration levels affect this neural circuit dynamically through the modulations of ion channels and synaptic activities. We used Hodgkin-Huxley and dynamical receptor binding model to establish this network, which can quantitatively explain neural activity patterns observed in MDD with different dopamine concentrations by changing the kinetics of some ion channels. The simulation replicated some important pathological patterns of MDD at the level of neurons and circuits with low dopamine concentration, such as the decreased action potential frequency in pyramidal neurons of mPFC with significantly reduced burst firing frequency. The calculation results also revealed that NaP and KS channels of mPFC pyramidal neurons played key roles in the functional regulation of this neural circuit. In addition, we analyzed the synaptic currents and local field potentials to explain the mechanism of MDD from the perspective of dysfunction of excitation-inhibition balance, especially the disinhibition effect in the network. The significance of this article is that we built the first computational model to illuminate the effect of dopamine concentrations for the NAc-mPFC-VTA circuit between MDD and normal groups, which can be used to quantitatively explain the results of existing physiological experiments, predict the results for unperformed experiments and screen possible drug targets.

Astrocytic modulation on neuronal electric mode selection induced by magnetic field effect

Astrocytes as well as electromagnetic induction have been primarily considered as main factors in regulating neuronal firing patterns in the recent decade. In this work, an improved neuron-astrocyte model in consideration of the modulation of astrocytes and the electromagnetic induction is employed to explore the extend to which both of the factors affect the firing modes of the neurons. The "alternation mode", defined as the alternative of neural normal spiking mode with the high-frequency bursting-like mode, clearly shows the functions of astrocytes on neurons. Moreover, the firing pattern of the neuron becomes more abnormal when astrocytes are hyper-excitable, the reason why the abnormal coupling of the astrocyte leads to the "alternation mode" of the neuron have been studied. In addition, the effect of electromagnetic induction manifests nonlinear characteristic towards neurons, complex firing modes of neurons are observed in the weaker field and a switching mode consists with quiescent and spiking mode appears when there is a higher stronger field. This approved model can reveal the normal or abnormal electric activities of neuron considered electromagnetic induction induced by the degree of excitability of the astrocyte. These results can provide potential understanding about the effects of astrocyte on neuronal activity when the coupling of electromagnetic field is considered.

Less is more: Wiring-economical modular networks support self-sustained firing-economical neural avalanches for efficient processing

The brain network is notably cost-efficient, while the fundamental physical and dynamic mechanisms underlying its economical optimization in network structure and activity have not been determined. In this study, we investigate the intricate cost-efficient interplay between structure and dynamics in biologically plausible spatial modular neuronal network models. We observe that critical avalanche states from excitation-inhibition balance under modular network topology with less wiring cost can also achieve lower costs in firing but with strongly enhanced response sensitivity to stimuli. We derive mean-field equations that govern the macroscopic network dynamics through a novel approximate theory. The mechanism of low firing cost and stronger response in the form of critical avalanches is explained as a proximity to a Hopf bifurcation of the modules when increasing their connection density. Our work reveals the generic mechanism underlying the cost-efficient modular organization and critical dynamics widely observed in neural systems, providing insights into brain-inspired efficient computational designs.

Dynamic Transitions in Neuronal Network Firing Sustained by Abnormal Astrocyte Feedback

Astrocytes play a crucial role in neuronal firing activity. Their abnormal state may lead to the pathological transition of neuronal firing patterns and even induce seizures. However, there is still little evidence explaining how the astrocyte network modulates seizures caused by structural abnormalities, such as gliosis. To explore the role of gliosis of the astrocyte network in epileptic seizures, we first established a direct astrocyte feedback neuronal network model on the basis of the hippocampal CA3 neuron-astrocyte model to simulate the condition of gliosis when astrocyte processes swell and the feedback to neurons increases in an abnormal state. We analyzed the firing pattern transitions of the neuronal network when astrocyte feedback starts to change via increases in both astrocyte feedback intensity and the connection probability of astrocytes to neurons in the network. The results show that as the connection probability and astrocyte feedback intensity increase, neuronal firing transforms from a nonepileptic synchronous firing state to an asynchronous firing state, and when astrocyte feedback starts to become abnormal, seizure-like firing becomes more severe and synchronized; meanwhile, the synchronization area continues to expand and eventually transforms into long-term seizure-like synchronous firing. Therefore, our results prove that astrocyte feedback can regulate the firing of the neuronal network, and when the astrocyte network develops gliosis, there will be an increase in the induction rate of epileptic seizures.

Memory retention in pyramidal neurons: a unified model of energy-based homo and heterosynaptic plasticity with homeostasis

The brain can learn new tasks without forgetting old ones. This memory retention is closely associated with the long-term stability of synaptic strength. To understand the capacity of pyramidal neurons to preserve memory under different tasks, we established a plasticity model based on the postsynaptic membrane energy state, in which the change in synaptic strength depends on the difference between the energy state after stimulation and the resting energy state. If the post-stimulation energy state is higher than the resting energy state, then synaptic depression occurs. On the contrary, the synapse is strengthened. Our model unifies homo- and heterosynaptic plasticity and can reproduce synaptic plasticity observed in multiple experiments, such as spike-timing-dependent plasticity, and cooperative plasticity with few and common parameters. Based on the proposed plasticity model, we conducted a simulation study on how the activation patterns of dendritic branches by different tasks affect the synaptic connection strength of pyramidal neurons. We further investigate the formation mechanism by which different tasks activate different dendritic branches. Simulation results show that compare to the classic plasticity model, the plasticity model we proposed can achieve a better spatial separation of different branches activated by different tasks in pyramidal neurons, which deepens our insight into the memory retention mechanism of brains.

Distinct regulation of bioenergetics and translation by group I mGluR and NMDAR

Neuronal activity is responsible for the high energy consumption in the brain. However, the cellular mechanisms draining ATP upon the arrival of a stimulus are yet to be explored systematically at the post-synapse. Here, we provide evidence that a significant fraction of ATP is consumed upon glutamate stimulation to energize mGluR-induced protein synthesis. We find that both mGluR and NMDAR alter protein synthesis and ATP consumption with distinct kinetics at the synaptic-dendritic compartments. While mGluR activation leads to a rapid and sustained reduction in neuronal ATP levels, NMDAR activation has no immediate impact on the same. ATP consumption correlates inversely with the kinetics of protein synthesis for both receptors. We observe a persistent elevation in protein synthesis within 5 minutes of mGluR activation and a robust inhibition of the same within 2 minutes of NMDAR activation, assessed by the phosphorylation status of eEF2 and metabolic labeling. However, a delayed protein synthesis-dependent ATP expenditure ensues after 15 minutes of NMDAR stimulation. We identify a central role for AMPK in the correlation between protein synthesis and ATP consumption. AMPK is dephosphorylated and inhibited upon mGluR activation, while it is phosphorylated upon NMDAR activation. Perturbing AMPK activity disrupts receptor-specific modulations of eEF2 phosphorylation and protein synthesis. Our observations, therefore, demonstrate that the regulation of the AMPK-eEF2 signaling axis by glutamate receptors alters neuronal protein synthesis and bioenergetics.

Upper Limit on the Thermodynamic Information Content of an Action Potential

In computational neuroscience, spiking neurons are often analyzed as computing devices that register bits of information, with each action potential carrying at most one bit of Shannon entropy. Here, I question this interpretation by using Landauer's principle to estimate an upper limit for the quantity of thermodynamic information that can be processed within a single action potential in a typical mammalian neuron. A straightforward calculation shows that an action potential in a typical mammalian cortical pyramidal cell can process up to approximately 3.4 · 1011 bits of thermodynamic information, or about 4.9 · 1011 bits of Shannon entropy. This result suggests that an action potential can, in principle, carry much more than a single bit of Shannon entropy.

Energy dependence on discharge mode of Izhikevich neuron driven by external stimulus under electromagnetic induction

Energy supply plays a key role in metabolism and signal transmission of biological individuals, neurons in a complex electromagnetic environment must be accompanied by the absorption and release of energy. In this paper, the discharge mode and the Hamiltonian energy are investigated within the Izhikevich neuronal model driven by external signals in the presence of electromagnetic induction. It is found that multiple electrical activity modes can be observed by changing external stimulus, and the Hamiltonian energy is more dependent on the discharge mode. In particular, there is a distinct shift and transition in the Hamiltonian energy when the discharge mode is switched quickly. Furthermore, the amplitude of periodic stimulus signal has a greater effect on the neuronal energy compared to the angular frequency, and the average Hamiltonian energy decreases when the discharge rhythm becomes higher. Based on the principle of energy minimization, the system should choose the minimum Hamiltonian energy when maintaining various trigger states to reduce the metabolic energy of signal processing in biological systems. Therefore, our results give the possible clues for predicting and selecting appropriate parameters, and help to understand the sudden and paroxysmal mechanisms of epilepsy symptoms.

Ionic channel blockage in stochastic Hodgkin-Huxley neuronal model driven by multiple oscillatory signals

Ionic channel blockage and multiple oscillatory signals play an important role in the dynamical response of pulse sequences. The effects of ionic channel blockage and ionic channel noise on the discharge behaviors are studied in Hodgkin-Huxley neuronal model with multiple oscillatory signals. It is found that bifurcation points of spontaneous discharge are altered through tuning the amplitude of multiple oscillatory signals, and the discharge cycle is changed by increasing the frequency of multiple oscillatory signals. The effects of ionic channel blockage on neural discharge behaviors indicate that the neural excitability can be suppressed by the sodium channel blockage, however, the neural excitability can be reversed by the potassium channel blockage. There is an optimal blockage ratio of potassium channel at which the electrical activity is the most regular, while the order of neural spike is disrupted by the sodium channel blockage. In addition, the frequency of spike discharge is accelerated by increasing the ionic channel noise, the firing of neuron becomes more stable if the ionic channel noise is appropriately reduced. Our results might provide new insights into the effects of ionic channel blockages, multiple oscillatory signals, and ionic channel noises on neural discharge behaviors.

Multiple bifurcations and coexistence in an inertial two-neuron system with multiple delays

In this paper, we construct an inertial two-neuron system with multiple delays, which is described by three first-order delayed differential equations. The neural system presents dynamical coexistence with equilibria, periodic orbits, and even quasi-periodic behavior by employing multiple types of bifurcations. To this end, the pitchfork bifurcation of trivial equilibrium is analyzed firstly by using center manifold reduction and normal form method. The system presents different sequences of supercritical and subcritical pitchfork bifurcations. Further, the nontrivial equilibrium bifurcated from trivial equilibrium presents a secondary pitchfork bifurcation. The system exhibits stable coexistence of multiple equilibria. Using the pitchfork bifurcation curves, we divide the parameter plane into different regions, corresponding to different number of equilibria. To obtain the effect of time delays on system dynamical behaviors, we analyze equilibrium stability employing characteristic equation of the system. By the Hopf bifurcation, the system illustrates a periodic orbit near the trivial equilibrium. We give the stability regions in the delayed plane to illustrate stability switching. The neural system is illustrated to have Hopf-Hopf bifurcation points. The coexistence with two periodic orbits is presented near these bifurcation points. Finally, we present some mixed dynamical coexistence. The system has a stable coexistence with periodic orbit and equilibrium near the pitchfork-Hopf bifurcation point. Moreover, multiple frequencies of the system induce the presentation of quasi-periodic behavior. The system presents stable coexistence with two periodic orbits and one quasi-periodic behavior.

Consensus of uncertain multi-agent systems with input delay and disturbances

In this paper, the problem of robust consensus for multi-agent systems affected by external disturbances is discussed. A novel consensus control is developed by using a feedback controller based on disturbance rejection and Smith predictor scheme. Specifically, the disturbance rejection performance of the uncertain multi-agent systems is improved according to the estimation of equivalent-input-disturbance and the effect of time delay in the control system is reduced via Smith predictor scheme by shifting the delay outside the feedback loop. Furthermore, by combining Lyapunov theory, matrix inequality techniques and properties of Kronecker product, a robust feedback controller for each agent is designed such that the desired consensus of the uncertain multi-agent systems affected by external disturbances can be ensured. Finally, to illustrate the validity of the designed control scheme, two numerical examples with simulation results are provided.

Temperature effect on memristive ion channels

Neuron shows distinct dependence of electrical activities on membrane patch temperature, and the mode transition of electrical activity is induced by the patch temperature through modulating the opening and closing rates of ion channels. In this paper, inspired by the physical effect of memristor, the potassium and sodium ion channels embedded in the membrane patch are updated by using memristor-based voltage gate variables, and an external stimulus is applied to detect the variety of mode selection in electrical activities under different patch temperatures. It is found that each ion channel can be regarded as a physical memristor, and the shape of pinched hysteresis loop of memristor is dependent on both input voltage and patch temperature. The pinched hysteresis loops of two ion-channel memristors are dramatically enlarged by increasing patch temperature, and the hysteresis lobe areas are monotonously reduced with the increasing of excitation frequency if the frequency of external stimulus exceeds certain threshold. However, for the memristive potassium channel, the AREA1 corresponding to the threshold frequency is increased with the increasing of patch temperature. The amplitude of conductance for two ion-channel memristors depends on the variation of patch temperature. The results of this paper might provide insights to modulate the neural activities in appropriate temperature condition completely, and involvement of external stimulus enhance the effect of patch temperature.

Spontaneous electromagnetic induction promotes the formation of economical neuronal network structure via self-organization process

Developed through evolution, brain neural system self-organizes into an economical and dynamic network structure with the modulation of repetitive neuronal firing activities through synaptic plasticity. These highly variable electric activities inevitably produce a spontaneous magnetic field, which also significantly modulates the dynamic neuronal behaviors in the brain. However, how this spontaneous electromagnetic induction affects the self-organization process and what is its role in the formation of an economical neuronal network still have not been reported. Here, we investigate the effects of spontaneous electromagnetic induction on the self-organization process and the topological properties of the self-organized neuronal network. We first find that spontaneous electromagnetic induction slows down the self-organization process of the neuronal network by decreasing the neuronal excitability. In addition, spontaneous electromagnetic induction can result in a more homogeneous directed-weighted network structure with lower causal relationship and less modularity which supports weaker neuronal synchronization. Furthermore, we show that spontaneous electromagnetic induction can reconfigure synaptic connections to optimize the economical connectivity pattern of self-organized neuronal networks, endowing it with enhanced local and global efficiency from the perspective of graph theory. Our results reveal the critical role of spontaneous electromagnetic induction in the formation of an economical self-organized neuronal network and are also helpful for understanding the evolution of the brain neural system.