Transitions between classes of neuronal excitability and bifurcations induced by autapse

[Effect of repeated transcranial magnetic stimulation on excitability of glutaminergic neurons and gamma-aminobutyric neurons in mouse hippocampus]

Repeated transcranial magnetic stimulation (rTMS) is one of the commonly used brain stimulation techniques. In order to investigate the effects of rTMS on the excitability of different types of neurons, this study is conducted to investigate the effects of rTMS on the cognitive function of mice and the excitability of hippocampal glutaminergic neurons and gamma-aminobutyric neurons from the perspective of electrophysiology. In this study, mice were randomly divided into glutaminergic control group, glutaminergic magnetic stimulation group, gamma-aminobutyric acid energy control group, and gamma-aminobutyric acid magnetic stimulation group. The four groups of mice were injected with adeno-associated virus to label two types of neurons and were implanted optical fiber. The stimulation groups received 14 days of stimulation and the control groups received 14 days of pseudo-stimulation. The fluorescence intensity of calcium ions in mice was recorded by optical fiber system. Behavioral experiments were conducted to explore the changes of cognitive function in mice. The patch-clamp system was used to detect the changes of neuronal action potential characteristics. The results showed that rTMS significantly improved the cognitive function of mice, increased the amplitude of calcium fluorescence of glutamergic neurons and gamma-aminobutyric neurons in the hippocampus, and enhanced the action potential related indexes of glutamergic neurons and gamma-aminobutyric neurons. The results suggest that rTMS can improve the cognitive ability of mice by enhancing the excitability of hippocampal glutaminergic neurons and gamma-aminobutyric neurons.

[Analysis of nerve excitability in the dentate gyrus of the hippocampus in cerebral ischaemia-reperfusion mice]

Ischemic stroke often leads to cognitive dysfunction, which delays the recovery process of patients. However, its pathogenesis is not yet clear. In this study, the cerebral ischemia-reperfusion model was built as the experimental object, and the hippocampal dentate gyrus (DG) was the target brain area. TTC staining was used to evaluate the degree of cerebral infarction, and nerve cell membrane potentials and local field potentials (LFPs) signals were collected to explore the mechanism of cognitive impairment in ischemia-reperfusion mice. The results showed that the infarcted area on the right side of the brain of the mice in the model group was white. The resting membrane potential, the number of action potential discharges, the post-hyperpolarization potential and the maximum ascending slope of the hippocampal DG nerve cells in the model mice were significantly lower than those in the control group ( P < 0.01); the peak time, half-wave width, threshold and maximum descending slope of the action potential were significantly higher than those in the control group ( P < 0.01). The time-frequency energy values of LFPs signals in the θ and γ bands of mice in the ischemia and reperfusion groups were significantly reduced ( P < 0.01), and the time-frequency energy values in the reperfusion group were increased compared with the ischemia group ( P < 0.01). The signal complexity of LFPs in the ischemia and reperfusion group was significantly reduced ( P < 0.05), and the signal complexity in the reperfusion group was increased compared with the ischemia group ( P < 0.05). In summary, cerebral ischemia-reperfusion reduced the excitability of nerve cells in the DG area of the mouse hippocampus; cerebral ischemia reduced the discharge activity and signal complexity of nerve cells, and the electrophysiological indicators recovered after reperfusion, but it failed to reach the healthy state during the experiment period.

The important role of glial transmitters released by astrocytes in Alzheimer's disease: A perspective from dynamical modeling

This paper aims to establish a coupling model of neuronal populations and astrocytes and, on this basis, explore the possible mechanism of electroencephalography (EEG) slowing in Alzheimer's disease (AD) from the viewpoint of dynamical modeling. First and foremost, excitatory and inhibitory time constants are shown to induce the early symptoms of AD. The corresponding dynamic nature is mainly due to changes in the amplitude and frequency of the oscillatory behavior. However, there are also a few cases that can be attributed to the change of the oscillation mode caused by the limit cycle bifurcation and birhythmicity. Then, an improved neural mass model influenced by astrocytes is proposed, considering the important effects of glutamate and adenosine triphosphate (ATP) released by astrocytes on the synaptic transmission process reported in experiments. The results show that a dysfunctional astrocyte disrupts the physiological state, causing three typical EEG slowing phenomena reported clinically: the decreased dominant frequency, the decreased rhythmic activity in the α band, and the increased rhythmic activity in the δ+θ band. In addition, astrocytes may control AD when the effect of ATP on synaptic connections is greater than that of glutamate. The control rate depends on the ratio of the effect of glutamate on excitatory and inhibitory synaptic connections. These modeling results can not only reproduce some experimental and clinical results, but, more importantly, may offer a prediction of some underlying phenomena, helping to inspire the disease mechanisms and therapeutic methods of targeting astrocytes.

Three-dimensional memristive Morris-Lecar model with magnetic induction effects and its FPGA implementation

To characterize the magnetic induction flow induced by neuron membrane potential, a three-dimensional (3D) memristive Morris-Lecar (ML) neuron model is proposed in this paper. It is achieved using a memristor induction current to replace the slow modulation current in the existing 3D ML neuron model with fast-slow structure. The magnetic induction effects on firing activities are explained by the spiking/bursting firings with period-adding bifurcation and periodic/chaotic spiking-bursting patterns, and the bifurcation mechanisms of the bursting patterns are elaborated using the fast-slow analysis method to create two bifurcation sets. In particular, the 3D memristive ML model can also exhibit the homogeneous coexisting bursting patterns when switching the memristor initial states, which are effectively illustrated by the theoretical analysis and numerical simulations. Finally, a digitally FPGA-based hardware platform is developed for the 3D memristive ML model and the experimentally measured results well verify the numerical ones.

Nonlinear mechanism for the enhanced bursting activities induced by fast inhibitory autapse and reduced activities by fast excitatory autapse

The paradoxical phenomena that excitatory modulation does not enhance but reduces or inhibitory modulation not suppresses but promotes neural firing activities have attracted increasing attention. In the present study, paradoxical phenomena induced by both fast excitatory and inhibitory autapses in a "Fold/Big Homoclinic" bursting are simulated, and the corresponding nonlinear and biophysical mechanisms are presented. Firstly, the enhanced conductance of excitatory autapse induces the number of spikes per burst and firing rate reduced, while the enhanced inhibitory autapse cause both indicators increased. Secondly, with fast-slow variable dissection, the burst of bursting is identified to locate between a fold bifurcation and a big saddle-homoclinic orbit bifurcation of the fast subsystem. Enhanced excitatory or inhibitory autapses cannot induce changes of both bifurcation points, i.e., burst width. However, width of slow variable between two successive spikes within a burst becomes wider for the excitatory autapse and narrower for the inhibitory autapse, resulting in the less and more spikes per burst, respectively. Last, the autaptic current of fast autapse mainly plays a role during the peak of action potential, differing from the slow autaptic current with exponential decay, which can play roles following the peak of action potential. The fast excitatory autaptic current enhances the amplitude of the action potential and reduces the repolarization of the action potential to lengthen the interspike interval (ISI) of the spiking of the fast subsystem, resulting in the wide width of slow variable between successive spikes. The fast inhibitory autaptic current reduces the amplitude of action potential and ISI of spiking, resulting in narrow width of slow variable. The novel example of the paradoxical responses for both fast modulations and nonlinear mechanism extend the contents of neurodynamics, which presents potential functions of the fast autapse.

Repetitive transcranial magnetic stimulation enhances the neuronal excitability of mice by regulating dynamic characteristics of Granule cells' Ion channels

This study aims to explore the effects of acute high-frequency repetitive transcranial magnetic stimulation (hf-rTMS) on neuronal excitability of granule cells in the hippocampal dentate gyrus, as well as the underlying intrinsic mediating mechanisms by which rTMS regulates neuronal excitability. First, high-frequency single TMS was used to measure the motor threshold (MT) of mice. Then, rTMS with different intensities of 0 MT (control), 0.8 MT, and 1.2 MT were applied to acute mice brain slices. Next, patch-clamp technique was used to record the resting membrane potential and evoked nerve discharge of granule cells, as well as the voltage-gated sodium current (I Na) of voltage-gated sodium channels (VGSCs), transient outward potassium current (I A) and delayed rectifier potassium current (I K) of voltage-gated potassium channels (Kv). Results showed that acute hf-rTMS in both 0.8 MT and 1.2 MT groups significantly activated I Na and inhibited I A and I K compared with control group, due to the changes of dynamic characteristics of VGSCs and Kv. Acute hf-rTMS in both 0.8 MT and 1.2 MT groups significantly increased membrane potential and nerve discharge frequency. Therefore, changing dynamic characteristics of VGSCs and Kv, activating I Na and inhibiting I A and I K might be one of the intrinsic mediating mechanisms by which rTMS enhanced the neuronal excitability of granular cells, and this regulatory effect increased with the increase of stimulus intensity.

Dynamical properties of neuromorphic Josephson junctions

Neuromorphic computing exploits the dynamical analogy between many physical systems and neuron biophysics. Superconductor systems, in particular, are excellent candidates for neuromorphic devices due to their capacity to operate at great speeds and with low energy dissipation compared to their silicon counterparts. In this paper, we revisit a prior work on Josephson Junction-based neurons to identify the exact dynamical mechanisms underlying the system's neuronlike properties and reveal complex behaviors which are relevant for neurocomputation and the design of superconducting neuromorphic devices. Our paper lies at the intersection of superconducting physics and theoretical neuroscience, both viewed under a common framework-that of nonlinear dynamics theory.

Complex dynamics of hair bundle of auditory nervous system (I): spontaneous oscillations and two cases of steady states

The hair bundles of inner hair cells in the auditory nervous exhibit spontaneous oscillations, which is the prerequisite for an important auditory function to enhance the sensitivity of inner ear to weak sounds, otoacoustic emission. In the present paper, the dynamics of spontaneous oscillations and relationships to steady state are acquired in a two-dimensional model with fast variable X (displacement of hair bundles) and slow variable X a . The spontaneous oscillations are derived from negative stiffness modulated by two biological factors (S and D) and are identified to appear in multiple two-dimensional parameter planes. In (S, D) plane, comprehensive bifurcations including 4 types of codimension-2 bifurcation and 5 types of codimension-1 bifurcation related to the spontaneous oscillations are acquired. The spontaneous oscillations are surrounded by supercritical and subcritical Hopf bifurcation curves, and outside of the curves are two cases of steady state. Case-1 and Case-2 steady states exhibit Z-shaped (coexistence of X) and N-shaped (coexistence of X a ) X-nullclines, respectively. In (S, D) plane, left and right to the spontaneous oscillations are two subcases of Case-1, which exhibit the stable equilibrium point locating on the upper and lower branches of X-nullcline, respectively, resembling that of the neuron. Lower to the spontaneous oscillations are 3 subcases of Case-2 from left to right, which manifest stable equilibrium point locating on left, middle, and right branches of X-nullcline, respectively, differing from that of the neuron. The phase plane for steady state is divided into four parts by nullclines, which manifest different vector fields. The phase trajectory of transient behavior beginning from a phase point in the four regions to the stable equilibrium point exhibits different dynamics determined by the vector fields, which is the basis to identify dynamical mechanism of complex forced oscillations induced by external signal. The results present comprehensive viewpoint and deep understanding for dynamics of the spontaneous oscillations and steady states of hair bundles, which can be used to well explain the experimental observations and to modulate functions of spontaneous oscillations.

Canard solutions in neural mass models: consequences on critical regimes

Mathematical models at multiple temporal and spatial scales can unveil the fundamental mechanisms of critical transitions in brain activities. Neural mass models (NMMs) consider the average temporal dynamics of interconnected neuronal subpopulations without explicitly representing the underlying cellular activity. The mesoscopic level offered by the neural mass formulation has been used to model electroencephalographic (EEG) recordings and to investigate various cerebral mechanisms, such as the generation of physiological and pathological brain activities. In this work, we consider a NMM widely accepted in the context of epilepsy, which includes four interacting neuronal subpopulations with different synaptic kinetics. Due to the resulting three-time-scale structure, the model yields complex oscillations of relaxation and bursting types. By applying the principles of geometric singular perturbation theory, we unveil the existence of the canard solutions and detail how they organize the complex oscillations and excitability properties of the model. In particular, we show that boundaries between pathological epileptic discharges and physiological background activity are determined by the canard solutions. Finally we report the existence of canard-mediated small-amplitude frequency-specific oscillations in simulated local field potentials for decreased inhibition conditions. Interestingly, such oscillations are actually observed in intracerebral EEG signals recorded in epileptic patients during pre-ictal periods, close to seizure onsets.

Biophysical models of intrinsic homeostasis: Firing rates and beyond

In view of ever-changing conditions both in the external world and in intrinsic brain states, maintaining the robustness of computations poses a challenge, adequate solutions to which we are only beginning to understand. At the level of cell-intrinsic properties, biophysical models of neurons permit one to identify relevant physiological substrates that can serve as regulators of neuronal excitability and to test how feedback loops can stabilize crucial variables such as long-term calcium levels and firing rates. Mathematical theory has also revealed a rich set of complementary computational properties arising from distinct cellular dynamics and even shaping processing at the network level. Here, we provide an overview over recently explored homeostatic mechanisms derived from biophysical models and hypothesize how multiple dynamical characteristics of cells, including their intrinsic neuronal excitability classes, can be stably controlled.

Excitability and Threshold Mechanism for Enhanced Neuronal Response Induced by Inhibition Preceding Excitation

Postinhibitory facilitation (PIF) of neural firing presents a paradoxical phenomenon that the inhibitory effect induces enhancement instead of reduction of the firing activity, which plays important roles in sound location of the auditory nervous system, awaited theoretical explanations. In the present paper, excitability and threshold mechanism for the PIF phenomenon is presented in the Morris-Lecar model with type I, II, and III excitabilities. Firstly, compared with the purely excitatory stimulations applied to the steady state, the inhibitory preceding excitatory stimulation to form pairs induces the firing rate increased for type II and III excitabilities instead of type I excitability, when the interval between the inhibitory and excitatory stimulation within each pair is suitable. Secondly, the threshold mechanism for the PIF phenomenon is acquired. For type II and III excitabilities, the inhibitory stimulation induces subthreshold oscillations around the steady state. During the middle and ending phase of the ascending part and the beginning phase of the descending part within a period of the subthreshold oscillations, the threshold to evoke an action potential by an excitatory stimulation becomes weaker, which is the cause for the PIF phenomenon. Last, a theoretical estimation for the range of the interval between the inhibitory and excitatory stimulation for the PIF phenomenon is acquired, which approximates half of the intrinsic period of the subthreshold oscillations for the relatively strong stimulations and becomes narrower for the relatively weak stimulations. The interval for the PIF phenomenon is much shorter for type III excitability, which is closer to the experiment observation, due to the shorter period of the subthreshold oscillations. The results present the excitability and threshold mechanism for the PIF phenomenon, which provide comprehensive and deep explanations to the PIF phenomenon.

Influence of Autapses on Synchronization in Neural Networks With Chemical Synapses

A great deal of research has been devoted on the investigation of neural dynamics in various network topologies. However, only a few studies have focused on the influence of autapses, synapses from a neuron onto itself via closed loops, on neural synchronization. Here, we build a random network with adaptive exponential integrate-and-fire neurons coupled with chemical synapses, equipped with autapses, to study the effect of the latter on synchronous behavior. We consider time delay in the conductance of the pre-synaptic neuron for excitatory and inhibitory connections. Interestingly, in neural networks consisting of both excitatory and inhibitory neurons, we uncover that synchronous behavior depends on their synapse type. Our results provide evidence on the synchronous and desynchronous activities that emerge in random neural networks with chemical, inhibitory and excitatory synapses where neurons are equipped with autapses.

Numerical Bifurcation Analysis of Pacemaker Dynamics in a Model of Smooth Muscle Cells

Evidence from experimental studies shows that oscillations due to electro-mechanical coupling can be generated spontaneously in smooth muscle cells. Such cellular dynamics are known as pacemaker dynamics. In this article, we address pacemaker dynamics associated with the interaction of [Formula: see text] and [Formula: see text] fluxes in the cell membrane of a smooth muscle cell. First we reduce a pacemaker model to a two-dimensional system equivalent to the reduced Morris-Lecar model and then perform a detailed numerical bifurcation analysis of the reduced model. Existing bifurcation analyses of the Morris-Lecar model concentrate on external applied current, whereas we focus on parameters that model the response of the cell to changes in transmural pressure. We reveal a transition between Type I and Type II excitabilities with no external current required. We also compute a two-parameter bifurcation diagram and show how the transition is explained by the bifurcation structure.

Dynamical Mechanism of Hyperpolarization-Activated Non-specific Cation Current Induced Resonance and Spike-Timing Precision in a Neuronal Model

Hyperpolarization-activated cyclic nucleotide-gated cation current (I_h) plays important roles in the achievement of many physiological/pathological functions in the nervous system by modulating the electrophysiological activities, such as the rebound (spike) to hyperpolarization stimulations, subthreshold membrane resonance to sinusoidal currents, and spike-timing precision to stochastic factors. In the present paper, with increasing g_h (conductance of I_h), the rebound (spike) and subthreshold resonance appear and become stronger, and the variability of the interspike intervals (ISIs) becomes lower, i.e., the enhancement of spike-timing precision, which are simulated in a conductance-based theoretical model and well explained by the nonlinear concept of bifurcation. With increasing g_h, the stable node to stable focus, to coexistence behavior, and to firing via the codimension-1 bifurcations (Hopf bifurcation, saddle-node bifurcation, saddle-node bifurcations on an invariant circle, and saddle homoclinic orbit) and codimension-2 bifurcations such as Bogdanov-Takens (BT) point related to the transition between saddle-node and Hopf bifurcations, are acquired with 1- and 2-parameter bifurcation analysis. The decrease of variability of ISIs with increasing g_h is induced by the fast decrease of the standard deviation of ISIs, which is related to the increase of the capacity of resisting noisy disturbance due to the firing becomes far away from the bifurcation point. The enhancement of the rebound (spike) with increasing g_h builds up a relationship to the decrease of the capacity of resisting disturbance like the hyperpolarization stimulus as the resting state approaches the bifurcation point. The “typical”-resonance and non-resonance appear in the parameter region of the stable focus and node far away from the bifurcation points, respectively. The complex or “strange” dynamics, such as the “weak”-resonance for the stable node near the transition point between the stable node and focus and the non-resonance for the stable focus close to the codimension-1 and −2 bifurcation points, are discussed.

Dynamics of delay-coupled FitzHugh-Nagumo neural rings

This paper studies the dynamical behaviors of a pair of FitzHugh-Nagumo neural networks with bidirectional delayed couplings. It presents a detailed analysis of delay-independent and delay-dependent stabilities and the existence of bifurcated oscillations. Illustrative examples are performed to validate the analytical results and to discover interesting phenomena. It is shown that the network exhibits a variety of complicated activities, such as multiple stability switches, the coexistence of periodic and quasi-periodic oscillations, the coexistence of periodic and chaotic orbits, and the coexisting chaotic attractors.

Response of Electrical Activity in an Improved Neuron Model under Electromagnetic Radiation and Noise

Electrical activities are ubiquitous neuronal bioelectric phenomena, which have many different modes to encode the expression of biological information, and constitute the whole process of signal propagation between neurons. Therefore, we focus on the electrical activities of neurons, which is also causing widespread concern among neuroscientists. In this paper, we mainly investigate the electrical activities of the Morris-Lecar (M-L) model with electromagnetic radiation or Gaussian white noise, which can restore the authenticity of neurons in realistic neural network. First, we explore dynamical response of the whole system with electromagnetic induction (EMI) and Gaussian white noise. We find that there are slight differences in the discharge behaviors via comparing the response of original system with that of improved system, and electromagnetic induction can transform bursting or spiking state to quiescent state and vice versa. Furthermore, we research bursting transition mode and the corresponding periodic solution mechanism for the isolated neuron model with electromagnetic induction by using one-parameter and bi-parameters bifurcation analysis. Finally, we analyze the effects of Gaussian white noise on the original system and coupled system, which is conducive to understand the actual discharge properties of realistic neurons.