Development and transition of spiral wave in the coupled Hindmarsh-Rose neurons in two-dimensional space

The dynamics and the transition of spiral waves in the coupled Hindmarsh-Rose （H-R） neurons in two-dimensional space are investigated in the paper. It is found that the spiral wave can be induced and developed in the coupled HR neurons in two-dimensional space, with appropriate initial values and a parameter region given. However, the spiral wave could encounter instability when the intensity of the external current reaches a threshold value of 1.945. The transition of spiral wave is found to be affected by coupling intensity D and bifurcation parameter r. The spiral wave becomes sparse as the coupling intensity increases, while the spiral wave is eliminated and the whole neuronal system becomes homogeneous as the bifurcation parameter increases to a certain threshold value. Then the coupling action of the four sub-adjacent neurons, which is described by coupling coefficient D＇, is also considered, and it is found that the spiral wave begins to breakup due to the introduced coupling action from the sub-adjacent neurons （or sites） and together with the coupling action of the nearest-neighbour neurons, which is described by the coupling intensity D.

Instability and Death of Spiral Wave in a Two-Dimensional Array of Hindmarsh-Rose Neurons

Spiral wave could be observed in the excitable media, the neurons are often excitable within appropriateparameters. The appearance and formation of spiral wave in the cardiac tissue is linked to monomorphic ventriculartachycardia that can denervate into polymorphic tachycardia and ventricular fibrillation. The neuronal system oftenconsists of a large number of neurons with complex connections. In this paper, we theoretically study the transitionfrom spiral wave to spiral turbulence and homogeneous state (death of spiral wave) in two-dimensional array of theHindmarsh-Rose neuron with completely nearest-neighbor connections. In our numerical studies, a stable rotating spiralwave is developed and selected as the initial state, then the bifurcation parameters are changed to different values toobserve the transition from spiral wave to homogeneous state, breakup of spiral wave and weak change of spiral wave,respectively. A statistical factor of synchronization is defined with the mean field theory to analyze the transition fromspiral wave to other spatial states, and the snapshots of the membrane potentials of all neurons and time series of meanmembrane potentials of all neurons are also plotted to discuss the change of spiral wave. It is found that the sharpchanging points in the curve for factor of synchronization vs. bifurcation parameter indicate sudden transition fromspiral wave to other states. And the results are independent of the number of neurons we used.

FK506 contributes to peripheral nerve regeneration by inhibiting neuroinflammatory responses and promoting neuron survival

FK506(Tacrolimus)is a systemic immunosuppressant approved by the U.S.Food and Drug Administration.FK506 has been shown to promote peripheral nerve regeneration,however,its precise mechanism of action and its pathways remain unclear.In this study,we established a rat model of sciatic nerve injury and found that FK506 improved the morphology of the injured sciatic nerve,increased the numbers of motor and sensory neurons,reduced inflammatory responses,markedly improved the conduction function of the injured nerve,and promoted motor function recovery.These findings suggest that FK506 promotes peripheral nerve structure recovery and functional regeneration by reducing the intensity of inflammation after neuronal injury and increasing the number of surviving neurons.

Inhibitory gamma-aminobutyric acidergic neurons in the anterior cingulate cortex participate in the comorbidity of pain and emotion

Pain is often comorbid with emotional disorders such as anxiety and depression.Hyperexcitability of the anterior cingulate cortex has been implicated in pain and pain-related negative emotions that arise from impairments in inhibitory gamma-aminobutyric acid neurotransmission.This review primarily aims to outline the main circuitry(including the input and output connectivity)of the anterior cingulate cortex and classification and functions of different gamma-aminobutyric acidergic neurons;it also describes the neurotransmitters/neuromodulators affecting these neurons,their intercommunication with other neurons,and their importance in mental comorbidities associated with chronic pain disorders.Improving understanding on their role in pain-related mental comorbidities may facilitate the development of more effective treatments for these conditions.However,the mechanisms that regulate gamma-aminobutyric acidergic systems remain elusive.It is also unclear as to whether the mechanisms are presynaptic or postsynaptic.Further exploration of the complexities of this system may reveal new pathways for research and drug development.

Many faces of neuronal activity manipulation in Drosophila

Animals exhibit complex responses to external and internal stimuli.The information is computed by interconnected neurons that express numerous ion channels,which modulate the neuronal membrane potential.How can neuronal activity orchestrate complex motor patterns or allow learning from previous experience?To answer such questions,we need the ability not only to record,but also to modulate neuronal activity in both space(e.g.,neuronal subsets)and time.

Chaotic dynamics and its analysis of Hindmarsh-Rose neurons by Shil'nikov approach

In this paper, the relationship between external current stimulus and chaotic behaviors of a Hindmarsh–Rose(HR)neuron is considered. In order to find out the range of external current stimulus which will produce chaotic behaviors of an HR neuron, the Shil’nikov technique is employed. The Cardano formula is taken to obtain the threshold of the chaotic motion, and series solution to a differential equation is utilized to obtain the homoclinic orbit of HR neurons. This analysis establishes mathematically the value of external current input in generating chaotic motion of HR neurons by the Shil’nikov method. The numerical simulations are performed to support the theoretical results.

Small molecule inhibitor DDQ-treated hippocampal neuronal cells show improved neurite outgrowth and synaptic branching

The process of neurite outgrowth and branching is a crucial aspect of neuronal development and regeneration.Axons and dendrites,sometimes referred to as neurites,are extensions of a neuron's cellular body that are used to start networks.Here we explored the effects of diethyl(3,4-dihydroxyphenethylamino)(quinolin-4-yl)methylphosphonate(DDQ)on neurite developmental features in HT22 neuronal cells.In this work,we examined the protective effects of DDQ on neuronal processes and synaptic outgrowth in differentiated HT22cells expressing mutant Tau(mTau)cDNA.To investigate DDQ chara cteristics,cell viability,biochemical,molecular,western blotting,and immunocytochemistry were used.Neurite outgrowth is evaluated through the segmentation and measurement of neural processes.These neural processes can be seen and measured with a fluorescence microscope by manually tracing and measuring the length of the neurite growth.These neuronal processes can be observed and quantified with a fluorescent microscope by manually tracing and measuring the length of the neuronal HT22.DDQ-treated mTau-HT22 cells(HT22 cells transfected with cDNA mutant Tau)were seen to display increased levels of synaptophysin,MAP-2,andβ-tubulin.Additionally,we confirmed and noted reduced levels of both total and p-Tau,as well as elevated levels of microtubule-associated protein 2,β-tubulin,synaptophysin,vesicular acetylcholine transporter,and the mitochondrial biogenesis protein-pe roxisome prolife rator-activated receptor-gamma coactivator-1α.In mTa u-expressed HT22 neurons,we observed DDQ enhanced the neurite characteristics and improved neurite development through increased synaptic outgrowth.Our findings conclude that mTa u-HT22(Alzheimer's disease)cells treated with DDQ have functional neurite developmental chara cteristics.The key finding is that,in mTa u-HT22 cells,DDQ preserves neuronal structure and may even enhance nerve development function with mTa u inhibition.

Induced pluripotent stem cell-related approaches to generate dopaminergic neurons for Parkinson's disease

The progressive loss of dopaminergic neurons in affected patient brains is one of the pathological features of Parkinson's disease,the second most common human neurodegenerative disease.Although the detailed pathogenesis accounting for dopaminergic neuron degeneration in Parkinson's disease is still unclear,the advancement of stem cell approaches has shown promise for Parkinson's disease research and therapy.The induced pluripotent stem cells have been commonly used to generate dopaminergic neurons,which has provided valuable insights to improve our understanding of Parkinson's disease pathogenesis and contributed to anti-Parkinson's disease therapies.The current review discusses the practical approaches and potential applications of induced pluripotent stem cell techniques for generating and differentiating dopaminergic neurons from induced pluripotent stem cells.The benefits of induced pluripotent stem cell-based research are highlighted.Various dopaminergic neuron differentiation protocols from induced pluripotent stem cells are compared.The emerging three-dimension-based brain organoid models compared with conventional two-dimensional cell culture are evaluated.Finally,limitations,challenges,and future directions of induced pluripotent stem cell–based approaches are analyzed and proposed,which will be significant to the future application of induced pluripotent stem cell-related techniques for Parkinson's disease.

NOX4 exacerbates Parkinson's disease pathology by promoting neuronal ferroptosis and neuroinflammation

Parkinson's disease is primarily caused by the loss of dopaminergic neurons in the substantia nigra compacta.Ferroptosis,a novel form of regulated cell death characterized by iron accumulation and lipid peroxidation,plays a vital role in the death of dopaminergic neurons.However,the molecular mechanisms underlying ferroptosis in dopaminergic neurons have not yet been completely elucidated.NADPH oxidase 4 is related to oxidative stress,however,whether it regulates dopaminergic neuronal ferroptosis remains unknown.The aim of this study was to determine whether NADPH oxidase 4 is involved in dopaminergic neuronal ferroptosis,and if so,by what mechanism.We found that the transcriptional regulator activating transcription factor 3 increased NADPH oxidase 4 expression in dopaminergic neurons and astrocytes in an 1-methyl-4-phenyl-1,2,3,6 tetrahydropyridine-induced Parkinson's disease model.NADPH oxidase 4 inhibition improved the behavioral impairments observed in the Parkinson's disease model animals and reduced the death of dopaminergic neurons.Moreover,NADPH oxidase 4 inhibition reduced lipid peroxidation and iron accumulation in the substantia nigra of the Parkinson's disease model animals.Mechanistically,we found that NADPH oxidase 4 interacted with activated protein kinase Cαto prevent ferroptosis of dopaminergic neurons.Furthermore,by lowering the astrocytic lipocalin-2 expression,NADPH oxidase 4 inhibition reduced 1-methyl-4-phenyl-1,2,3,6 tetrahydropyridine-induced neuroinflammation.These findings demonstrate that NADPH oxidase 4 promotes ferroptosis of dopaminergic neurons and neuroinflammation,which contribute to dopaminergic neuron death,suggesting that NADPH oxidase 4 is a possible therapeutic target for Parkinson's disease.

Inhibition of the NLRP3 inflammasome attenuates spiral ganglion neuron degeneration in aminoglycoside-induced hearing loss

Aminoglycosides are a widely used class of antibacterials renowned for their effectiveness and broad antimicrobial spectrum.However,their use leads to irreversible hearing damage by causing apoptosis of hair cells as their direct target.In addition,the hearing damage caused by aminoglycosides involves damage of spiral ganglion neurons upon exposure.To investigate the mechanisms underlying spiral ganglion neuron degeneration induced by aminoglycosides,we used a C57BL/6J mouse model treated with kanamycin.We found that the mice exhibited auditory deficits following the acute loss of outer hair cells.Spiral ganglion neurons displayed hallmarks of pyroptosis and exhibited progressive degeneration over time.Transcriptomic profiling of these neurons showed significant upregulation of genes associated with inflammation and immune response,particularly those related to the NLRP3 inflammasome.Activation of the canonical pyroptotic pathway in spiral ganglion neurons was observed,accompanied by infiltration of macrophages and the release of proinflammatory cytokines.Pharmacological intervention targeting NLRP3 using Mcc950 and genetic intervention using NLRP3 knockout ameliorated spiral ganglion neuron degeneration in the injury model.These findings suggest that NLRP3 inflammasome-mediated pyroptosis plays a role in aminoglycoside-induced spiral ganglion neuron degeneration.Inhibition of this pathway may offer a potential therapeutic strategy for treating sensorineural hearing loss by reducing spiral ganglion neuron degeneration.

Effects of electric field on vibrational resonances in Hindmarsh-Rose neuronal systems for signal detection

Changes in the concentration of charged ions in neurons can generate induced electric fields,which can further modulate cell membrane potential.In this paper,Fourier coefficients are used to investigate the effect of electric field on vibrational resonance for signal detection in a single neuron model and a bidirectionally coupled neuron model,respectively.The study found that the internal electric field weakens vibrational resonance by changing two factors,membrane potential and phase-locked mode,while the periodic external electric field of an appropriate frequency significantly enhances the vibrational resonance,suggesting that the external electric field may play a constructive role in the detection of weak signals in the brain and neuronal systems.Furthermore,when the coupling of two neurons is considered,the effect of the electric field on the vibrational resonance is similar to that of a single neuron.The paper also illustrates the effect of electric field coupling on vibrational resonance.This study may provide a new theoretical basis for understanding information encoding and transmission in neurons.

FUBP3 mediates the amyloid-β-induced neuronal NLRP3 expression

Alzheimer's disease is characterized by deposition of amyloid-β,which forms extracellular neuritic plaques,and accumulation of hyperphosphorylated tau,which aggregates to form intraneuronal neurofibrillary tangles,in the brain.The NLRP3 inflammasome may play a role in the transition from amyloid-βdeposition to tau phosphorylation and aggregation.Because NLRP3 is primarily found in brain microglia,and tau is predominantly located in neurons,it has been suggested that NLRP3 expressed by microglia indirectly triggers tau phosphorylation by upregulating the expression of pro-inflammatory cytokines.Here,we found that neurons also express NLRP3 in vitro and in vivo,and that neuronal NLRP3 regulates tau phosphorylation.Using biochemical methods,we mapped the minimal NLRP3 promoter and identified FUBP3 as a transcription factor regulating NLRP3 expression in neurons.In primary neurons and the neuroblastoma cell line Neuro2A,FUBP3 is required for endogenous NLRP3 expression and tau phosphorylation only when amyloid-βis present.In the brains of aged wild-type mice and a mouse model of Alzheimer's disease,FUBP3 expression was markedly increased in cortical neurons.Transcriptome analysis suggested that FUBP3 plays a role in neuron-mediated immune responses.We also found that FUBP3 trimmed the 5′end of DNA fragments that it bound,implying that FUBP3 functions in stress-induced responses.These findings suggest that neuronal NLRP3 may be more directly involved in the amyloid-β-to–phospho-tau transition than microglial NLRP3,and that amyloid-βfundamentally alters the regulatory mechanism of NLRP3 expression in neurons.Given that FUBP3 was only expressed at low levels in young wild-type mice and was strongly upregulated in the brains of aged mice and Alzheimer's disease mice,FUBP3 could be a safe therapeutic target for preventing Alzheimer's disease progression.

Transforming growth factor-beta 1 enhances discharge activity of cortical neurons

Transforming growth factor-beta 1(TGF-β1)has been extensively studied for its pleiotropic effects on central nervous system diseases.The neuroprotective or neurotoxic effects of TGF-β1 in specific brain areas may depend on the pathological process and cell types involved.Voltage-gated sodium channels(VGSCs)are essential ion channels for the generation of action potentials in neurons,and are involved in various neuroexcitation-related diseases.However,the effects of TGF-β1 on the functional properties of VGSCs and firing properties in cortical neurons remain unclear.In this study,we investigated the effects of TGF-β1 on VGSC function and firing properties in primary cortical neurons from mice.We found that TGF-β1 increased VGSC current density in a dose-and time-dependent manner,which was attributable to the upregulation of Nav1.3 expression.Increased VGSC current density and Nav1.3 expression were significantly abolished by preincubation with inhibitors of mitogen-activated protein kinase kinase(PD98059),p38 mitogen-activated protein kinase(SB203580),and Jun NH2-terminal kinase 1/2 inhibitor(SP600125).Interestingly,TGF-β1 significantly increased the firing threshold of action potentials but did not change their firing rate in cortical neurons.These findings suggest that TGF-β1 can increase Nav1.3 expression through activation of the ERK1/2-JNK-MAPK pathway,which leads to a decrease in the firing threshold of action potentials in cortical neurons under pathological conditions.Thus,this contributes to the occurrence and progression of neuroexcitatory-related diseases of the central nervous system.

Modeling and dynamics of double Hindmarsh-Rose neuron with memristor-based magnetic coupling and time delay

The firing of a neuron model is mainly affected by the following factors:the magnetic field,external forcing current,time delay,etc.In this paper,a new time-delayed electromagnetic field coupled dual Hindmarsh-Rose neuron network model is constructed.A magnetically controlled threshold memristor is improved to represent the self-connected and the coupled magnetic fields triggered by the dynamic change of neuronal membrane potential for the adjacent neurons.Numerical simulation confirms that the coupled magnetic field can activate resting neurons to generate rich firing patterns,such as spiking firings,bursting firings,and chaotic firings,and enable neurons to generate larger firing amplitudes.The study also found that the strength of magnetic coupling in the neural network also affects the number of peaks in the discharge of bursting firing.Based on the existing medical treatment background of mental illness,the effects of time lag in the coupling process against neuron firing are studied.The results confirm that the neurons can respond well to external stimuli and coupled magnetic field with appropriate time delay,and keep periodic firing under a wide range of external forcing current.

The burden of upper motor neuron involvement is correlated with the bilateral limb involvement interval in patients with amyotrophic lateral sclerosis:a retrospective observational study

Amyotrophic lateral sclerosis is a rare neurodegenerative disease characterized by the involvement of both upper and lower motor neurons.Early bilateral limb involvement significantly affects patients'daily lives and may lead them to be confined to bed.However,the effect of upper and lower motor neuron impairment and other risk factors on bilateral limb involvement is unclear.To address this issue,we retrospectively collected data from 586 amyotrophic lateral sclerosis patients with limb onset diagnosed at Peking University Third Hospital between January 2020 and May 2022.A univariate analysis revealed no significant differences in the time intervals of spread in different directions between individuals with upper motor neuron-dominant amyotrophic lateral sclerosis and those with classic amyotrophic lateral sclerosis.We used causal directed acyclic graphs for risk factor determination and Cox proportional hazards models to investigate the association between the duration of bilateral limb involvement and clinical baseline characteristics in amyotrophic lateral sclerosis patients.Multiple factor analyses revealed that higher upper motor neuron scores(hazard ratio[HR]=1.05,95%confidence interval[CI]=1.01–1.09,P=0.018),onset in the left limb(HR=0.72,95%CI=0.58–0.89,P=0.002),and a horizontal pattern of progression(HR=0.46,95%CI=0.37–0.58,P<0.001)were risk factors for a shorter interval until bilateral limb involvement.The results demonstrated that a greater degree of upper motor neuron involvement might cause contralateral limb involvement to progress more quickly in limb-onset amyotrophic lateral sclerosis patients.These findings may improve the management of amyotrophic lateral sclerosis patients with limb onset and the prediction of patient prognosis.

Hindmarsh-Rose神经元模型的混沌控制

应用稳定性准则的混沌控制方法控制单个Hindmarsh-Rose神经元模型的混沌发放峰序列和混沌爆发运动。通过对膜电压的非线性连续-时间反馈干扰的输入,将混沌运动控制到5峰/爆发(5spikes/burst)轨道上,该轨道嵌入在混沌吸引子内。数值模拟结果显示该方法在控制HR神经元模型方面是有效的。

时滞作用下的化学突触耦合的Hindmarsh-Rose神经元同步研究

本文通过数值模拟的方法研究了化学突触耦合的Hindmarsh-Rose神经元的同步问题,以及时滞对耦合的Hindmarsh-Rose神经元同步的影响.研究发现:耦合强度能够影响化学突触的耦合神经元系统的放电活动以及耦合神经元之间的同步状态.通过调整化学突触耦合的两个Hindmarsh-Rose神经元之间的耦合强度,可以使得神经元系统从非同步状态变为同步状态.同时也发现,适当的时滞会使得两个Hindmarsh-Rose化学突触耦合神经元系统从同步状态变为非同步状态,从而破坏系统的同步活动.

Hindmarsh-Rose神经元模型的单变量控制同步与反同步

采用Hindmarsh-Rose神经元模型,研究2个神经元系统的单变量驱动响应混合同步问题,提出反馈控制与自适应控制相结合的同步策略,从理论上分析了该同步方案的可行性。数值模拟结果表明,该同步方案能使部分变量达到反同步,使其他变量达到同步,即只需要单个变量的驱动就能实现2个混沌系统的同步和反同步。

Response Ability to External Signal Enhanced by Biological Spatial Configuration in Coupled Hindmarsh-Rose Neural System

The effect of realistic topology configuration of intercellular connections on the response ability in coupled cell system is numerically investigated by using the Hindmarsh-Rose model. For the proper coupling intensity, we set the control parameter to be near the critical value, and the external stimulus is introduced to the first cell in coupled system. It is found that, on one hand, when the cells are coupled with some proper topological structures, the external stimulus could transmit through the system, and shows better response ability and higher sensitivity. On the other hand, the influence of topological configuration on the synchronous ability and selection effect of neural system are also discussed. Our results display that the topology of coupled system may play an important role in the process of signal propagation, which could help us to understand the coordinated performance of cells in tissue.

Hindmarsh-Rose神经元模型在小世界网络里的非线性耦合

研究了Hindmarsh-Rose神经元模型在小世界网络里的非线性耦合问题.通过改变邻居半径m和重连概率P来观察模型的同步问题.同步误差主要是通过解网络里的微分方程来实现的,从而揭示了该神经元模型在小世界网络里的同步规律.