描述神经元相互作用的非线性动力学方程的解析解

神经系统是由大量神经元构成的非线性动力系统,动力学行为十分复杂ＦＨＮ模型提供了在该系统中观察时间周期振荡这种非线性现象的实验证据．本文利用扰动法从理论上求出了ＦＨＮ模型所给出的非线性动力学方程的解析解,为进一步深入研究神经系统的动力学行为提供了理论依据     

引起神经元“非周期敏感现象”的分岔机制

实验发现神经元平均发放率变化率在放电脉冲序列串(ISI序列)呈非周期节律时普遍大于ISI呈周期节律时的平均发放率变化率,称为“非周期敏感现象”。以HR神经元模型和胰腺β-细胞模型为例,在合适的参数改变量作用下观察到了“非周期敏感现象”,并进一步讨论了平均发放率变化率与ISI序列动力学性质的关系。发现当ISI序列经历混沌-周期分岔时“非周期敏感现象”表现明显,尤其在ISI序列经历从混沌到嵌入在混沌中的周期窗口的分岔时表现最为显著。进一步的分析表明周期窗口在整个混沌带中所占测度较大,故混沌．周期分岔及从混沌到嵌入在混沌中的周期窗口分岔是引起神经元“非周期敏感现象”的一种重要动力学机制。实验结果支持上述结论。     

微弱电刺激对失眠者睡眠状况及睡眠脑电影响的初步研究

根据睡眠是由脑内亿万神经元同步振荡所刻划的观点［１］,及各种电刺激对动物睡眠影响的实验［２,３］,设计了用特定θ频率的正弦波微弱电流,刺激失眠病人颈部安眠２穴,以观察其对受试者脑电频率的客观影响。其结果是刺激后失眠病人由醒到２期的脑电记录中,θ波逐渐增加,增加了病人的总睡眠时间。这启示我们这种脑部的特殊频率微弱电流刺激,可能有引起脑部神经元群的共振现象,改变了受试者脑电中频率成分的分布特征,从而有助于失眠的治疗。这一现象是值得进一步研究的。     

电针对猫海马单细胞放电的影响

实验是在45只箭毒化浅麻醉的成年猫进行的。用强的方波串刺激施于动物的右后肢隐神经,作为伤害性刺激。以钨丝微电极记录左侧海马单细胞放电。观察电针刺激“足三里”后一定时间内海马单细胞放电的变化。观察了177个神经元,其中痛敏神经元93个(53%),痛无关神经元71个(40%),另有13个(7%)为痛抑制性神经元。电针“穴位”诱导2分钟后,在所记录的177个神经元中有35%出现抑制效应。但在93个痛敏神经元中,被针刺抑制者占57% 。还见到一部分痛反应神经元,当针刺诱导2分钟后其自发放电出现明显抑制,有的甚至停止放电,在此基础上其痛放电也受显著抑制,这种抑制现象约持续2分钟;以后逐渐恢复到针前水平(或略超过)。对其可能参与针刺镇痛活动的机制进行了讨论。     

心肌细胞自发性搏动节律的分岔和混沌现象

心脏的节律是复杂的、非线性的;其节律复杂性的起源是多层次的。实验观察了心肌细胞自发性搏动节律的模式,以及改变细胞间耦合强度时节律的转化规律。表明在以正常灌流液灌流状态下,心肌细胞表现为多种不同的节律模式,可以是周期的,也可以是非周期的。当细胞间耦合强度下降时,心肌细胞节律发生转化,并经倍周期分岔进入混沌节律。实验结果有助于更好地理解心脏节律复杂性的起源。     

由三态跃迁机制产生的两种神经放电节律

在实验性神经起步点自发放电中,发现了两种三态跃迁节律,其特征为静息、周期n及周期n+1(n=1,2)簇放电随机交替出现。应用随机Chay模型数值仿真,分别得到了与实验模型中相似的两种三态跃迁节律,这两种节律都是在两个紧邻的分岔点附近,由噪声驱动而产生的。理论分析提示,当神经元系统接近从静息经分岔到放电的临界状态,且从静息到周期n的分岔点,与从周期n到周期n+1的分岔点非常接近时,在噪声的作用下,系统运动会在静息、周期n和周期n+1三种状态之间随机跃迁,从而形成了这种三态跃迁节律。基于这种三态跃迁放电的随机共振,还有待进一步深入研究。     

海马CA1区ripple节律相关高频放电中间神经元

通过在清醒小（Mus musculus）大脑同步记录海马区单神经元放电和场电位,发现在海马CAl区存在两类-9慢波睡眠时海马特征场电位“ripple”高频振荡（100-250Hz）相关的高频放电中间神经元．这两类神经元在慢波睡眠时的放电与ripple在时间上有高度同步性,对应每个ripple振荡波,它们都有一串高频放电．其中一类中间神经元（类型Ⅰ）在一个ripple振荡波的每个子振荡周期基本有1个放电,而另一类中间神经元（类型Ⅱ）则有1-2个放电．在ripple振荡波时段,这两类中间神经元的峰值放电频率分别高达310±33．17Hz（类型Ⅰ）和410±47．61Hz（类型Ⅱ）．动物清醒活动时,这两类中间神经元的放电与海马场电位的theta节律有锁相关系,它们的最大放电概率在theta节律的波谷段．给予动物摇晃刺激时,这两类中间神经元的放电频率均会短促增加．这些研究结果显示,海马CAl区的这种高频放电中间神经元参与调节海马神经元网络的整体活动状态．     

混沌放电的可兴奋性细胞对外界刺激反应敏感的动力学机制

在大鼠损伤背根节神经元受到去甲肾上腺(NE)、四乙基胺(TEA)和高浓度钙等剌激的实验中,观察到非周期放电的神经元明显地比周期放电的神经元对外界刺激的反应敏感程度高。现有的结果表明许多非周期放电的神经元实际上表现为确定性的混沌运动,比如混沌尖峰放电、混沌簇放电以及整数倍放电等。以修正的胰腺B细胞Chay模型为例,通过对其分岔结构的分析和对构成混沌吸引子的基本骨架的不稳定周期轨道的计算,揭示了分岔、激变和混沌运动对参数敏感依赖性是该现象产生的动力学机制。同时指出以往使用平均发放率来刻划可兴奋性细胞放电活动存在的缺陷,提出了一种新的利用周期轨道信息的刻划方法。     

一类具Holling Ⅱ类功能反应的三维顺环捕食系统的研究

本文研究一类具有Holling Ⅱ类功能反应的三维顺环捕食系统,得到了其持续生存的充分条件,和当其是周期系统时,系统存在平稳振荡的判据.     

左旋千金藤啶碱的非经典安定剂特性——电生理和行为的研究

在记录神经元放电频率的实验中,发现麻醉或麻痹大鼠给予DA受体拮抗剂SPD,使VTA,SNC和DA神经元放电频率增加.但随着剂量的增加,SPD选择性地使VTA的DA神经元放电完全抑制,可被DA受体激动剂APO所翻转.提示这种抑制作用可能是DI.但SPD不抑制SNCDA神经元放电.在计数自发放电的神经元数目的实验中,观察到:慢性给予SPD21d后,大鼠VTA部位自发放电的DA神经元数目减少,有量效关系.可被APO所翻转.相反,同样给药并不影响SNC部位自发放电的DA神经元数目.当急性给予SPD时,VTA自发放电的DA神经元数目也减少,而SNC自发放电的DA细胞数不受影响.在行为实验中,SPD能抑制APO引起的定型活动,但SPD本身引起的僵住症很弱,仅能维持15min,并且无剂量依赖关系.上述结果提示:SPD选择性抑制VTADA神经元,而对SNCDA神经元的抑制作用很弱,引起的锥体外系副作用弱,可能发展成为新一代的非经典安定剂.     

藜芦碱致使大鼠背根神经节A类神经元产生触发性振荡

在大鼠L5背根节浸浴钠通道失活门阻断剂藜芦碱（veratridine),记录该背根节神经元A类单纤维传入放电。发现：浸浴藜芦碱（1．8－3μmol/L）10min后,触压皮肤感受野或刺激坐骨神经引起部分静息纤维产生高频放电,其放电峰峰间期（interspike interval,ISI)形成U字形等型式的振荡,称之为触发性振荡。刺激脉冲的间隔越大,触发该振荡所需要的刺激脉冲数也就越多;不同时程和形式的刺激引起触发性振荡的形式无明显差异;触发性振荡的后抑制时期一般为30－90s。另外,实验还观察到该触发性振荡可由同一神经刺激引起的传入冲动触发。上述结果表明,用黎芦碱处理可使初级感觉神经元产生一种触发性振荡,该振荡机制可能与触发病的发作有关。     

Inhibition synchronizes sparsely connected cortical neurons within and between columns in realistic network models

Networks of compartmental model neurons were used to investigate the biophysical basis of the synchronization observed between sparsely-connected neurons in neocortex. A model of a single column in layer 5 consisted of 100 model neurons: 80 pyramidal and 20 inhibitory. The pyramidal cells had conductances that caused intrinsic repetitive bursting at different frequencies when driven with the same input. When connected randomly with a connection density of 10%, a single model column displayed synchronous oscillatory action potentials in response to stationary, uncorrelated Poisson spike-train inputs. Synchrony required a high ratio of inhibitory to excitatory synaptic strength; the optimal ratio was 41, within the range observed in cortex. The synchrony was insensitive to variation in amplitudes of postsynaptic potentials and synaptic delay times, even when the mean synaptic delay times were varied over the range 1 to 7 ms. Synchrony was found to be sensitive to the strength of reciprocal inhibition between the inhibitory neurons in one column: Too weak or too strong reciprocal inhibition degraded intra-columnar synchrony. The only parameter that affected the oscillation frequency of the network was the strength of the external driving input which could shift the frequency between 35 to 60 Hz. The same results were obtained using a model column of 1000 neurons with a connection density of 5%, except that the oscillation became more regular.Synchronization between cortical columns was studied in a model consisting of two columns with 100 model neurons each. When connections were made with a density of 3% between the pyramidal cells of each column there was no inter-columnar synchrony and in some cases the columns oscillated 180° out of phase with each other. Only when connections from the pyramidal cells in each column to the inhibitory cells in the other column were added was synchrony between the columns observed. This synchrony was established within one or two cycles of the oscillation and there was on average less than 1 ms phase difference between the two columns. Unlike the intra-columnar synchronization, the inter-columnar synchronization was found to be sensitive to the synaptic delay: A mean delay of greater than 5 ms virtually abolished synchronization between columns.     

Responses of descending neurons to looming stimuli in the praying mantis <Emphasis Type="Italic">Tenodera aridifolia</Emphasis>

Responses to visual stimuli of some neurons that descend the nerve cord from the brain were recorded extracellularly in the mantis Tenodera aridifolia. Most of the recorded neurons showed their largest responses to looming stimuli that simulated a black circle approaching towards the mantis. The neurons showed a transient excitatory response to a gradually darkening or receding circle. The neurons showed sustained excitation to the linearly expanding stimuli, but the spike frequency decreased rapidly. The responses of the neurons were affected by both the diameter and the speed of looming stimuli. Faster or smaller looming stimuli elicited a higher peak frequency. These responses were observed in both recordings from the connective between suboesophageal and prothoracic ganglia and the connective between prothoracic and mesothoracic ganglia. There was a one-to-one correspondence of spike firing between these two recordings with a fixed delay. The neurons had the receptive field on ipsilateral side to its axon at the cervical connective. These results suggest that there is a looming-sensitive descending neuron, with an axon projecting over prothoracic ganglion, in the mantis nervous system.     

Capturing ecological complexity: OCI,a novel combination of ecological indices as applied to benthic marine habitats

The novel Overall Complexity Index (OCI) is proposed to measure ecological complexity, incorporating four complexity indices: (1) exergy and (2) throughput as extensive metrics, (3) specific exergy and (4) information as intensive metrics. Exergy and specific exergy estimate structural complexity while throughput and information functional complexity. OCI was applied to benthic habitats in a coastal marine tract encompassing a Marine Protected Area (MPA) in north-western Italy. The four individual indices did not always show homogeneous results in assigning complexity to different habitats. On the contrary, the additive measure provided by OCI showed that seagrass meadows and coralligenous reefs are in all the most complex habitats. Applying OCI provided results consistent with traditional approaches based on expert judgement, which usually attach more interest to seagrass meadows and hard bottoms with respect to soft bottoms, but expressed a synthetic, objective and quantitative approach. OCI can be mapped for management purposes, resolving the discordances evidenced by the individual indices. Ecological complexity in the study area is concentrated in some hot spots, as mapped by OCI, while the greatest part of the seafloor is occupied by low complexity habitats. Only some of these complexity hotspots are included within the Marine Protected Area, while this study suggests that high complexity areas, adjacent to the existing MPA, should be considered for protection possibly reshaping MPA's limits.     

The Quasi-Fractal Structure of Fish Brain Neurons

The box-counting method for calculating the fractal dimension (D) with the ImageJ 1.20s software is used as a tool for quantitative analysis of the neuronal morphology in the fish brain. The fractal dimension was determined for several types of neurons in the brain of two teleost species, Pholidapus dybowskii and Oncorhynchus keta. These results were compared with those obtained for some neurons of the human brain. The fractal (fractional) dimension (D), as a quantitative index of filling of two-dimensional space by the black and white image of a cell, is shown to vary from 1.22 to 1.72 depending on the type of neuron. The fractal dimension reaches its maximum in less specialized neurons that carry out a number of different functions. On the other hand, highly specialized neurons display a relatively low fractal dimension. Thus, the fractal dimension serves as a numerical measure of the spatial complexity of the neuron and correlates with the morphofunctional organization of the cell.     

A novel bursting mechanism of type a neurons in injured dorsal root ganglia

Using intracellular recording in vivo, the bursting behaviors were investigated in the neurons of chronically compressed dorsal root ganglia of the adult rat. In most cases, the first spike of a burst emerged from amplitude-increasing damped subthreshold membrane potential oscillation (SMPO) and the discharge terminated by an amplitude-decreasing damped SMPO. The rhythms of these bursting behaviors are all irregular. Since some researchers found that the stochastic dynamics can also produce similar bursting pattern, the deterministic dynamics of interevent interval (IEI) series obtained from raw membrane potential recording was detected by extraction of the hierarchy of unstable periodic orbits (UPOs) in the windowed IEI series. The results showed a number of statistically significant UPOs of order-one, order-two, and order-three. These orbits form a complex but predictable lattice of regions in which the dynamics of the bursting occurrence is deterministic. Based on a complete classification scheme, the investigated bursting can be depicted by the elliptic bursting dynamics. The significance of the finding that a neuron in the injured dorsal root ganglion has such dynamics is also discussed.     

Nonlinear Time Series Analysis of Nodulation Factor Induced Calcium Oscillations: Evidence for Deterministic Chaos?

Legume plants form beneficial symbiotic interactions with nitrogen fixing bacteria (called rhizobia), with the rhizobia being accommodated in unique structures on the roots of the host plant. The legume/rhizobial symbiosis is responsible for a significant proportion of the global biologically available nitrogen. The initiation of this symbiosis is governed by a characteristic calcium oscillation within the plant root hair cells and this signal is activated by the rhizobia. Recent analyses on calcium time series data have suggested that stochastic effects have a large role to play in defining the nature of the oscillations. The use of multiple nonlinear time series techniques, however, suggests an alternative interpretation, namely deterministic chaos. We provide an extensive, nonlinear time series analysis on the nature of this calcium oscillation response. We build up evidence through a series of techniques that test for determinism, quantify linear and nonlinear components, and measure the local divergence of the system. Chaos is common in nature and it seems plausible that properties of chaotic dynamics might be exploited by biological systems to control processes within the cell. Systems possessing chaotic control mechanisms are more robust in the sense that the enhanced flexibility allows more rapid response to environmental changes with less energetic costs. The desired behaviour could be most efficiently targeted in this manner, supporting some intriguing speculations about nonlinear mechanisms in biological signaling.     

Metabolic flux and cell cycle analysis indicating new mechanism underlying process oscillation in continuous ethanol fermentation with Saccharomyces cerevisiae under VHG conditions

Process oscillation characterized by long oscillation period and large oscillation amplitude was observed in continuous ethanol fermentation with Saccharomyces cerevisiae under very high gravity conditions. Metabolic flux analysis was applied to the fermentation system, and the results indicated that carbon flux distributions at the metabolic notes oscillated, correspondingly, and the root reason for the process oscillation was the intracellular metabolism of yeast cells. Cell cycle analysis with the flow cytometry showed that no cell-cycle-dependent synchronization of the daughter and mother cells occurred within the duration of the oscillation, and thus different mechanism existed compared with the oscillation observed in the continuous culture of Saccharomyces cerevisiae and triggered by the synchronization of the daughter and mother cells under specific conditions. Furthermore, the overall metabolic activity of the yeast cells was examined, which was found not exactly out of phase but lag behind ethanol concentration that accumulated within the fermentation system and its inhibition on the yeast cells as well, which supported the mechanistic speculation for the process oscillation: the lag response of yeast cells to ethanol inhibition.     

In Vitro Dose-Dependent Inhibition of the Intracellular Spontaneous Calcium Oscillations in Developing Hippocampal Neurons by Ketamine

Spatial and temporal abnormalities in the frequency and amplitude of the cytosolic calcium oscillations can impact the normal physiological functions of neuronal cells. Recent studies have shown that ketamine can affect the growth and development and even induce the apoptotic death of neurons. This study used isolated developing hippocampal neurons as its study subjects to observe the effect of ketamine on the intracellular calcium oscillations in developing hippocampal neurons and to further explore its underlying mechanism using Fluo-4-loaded laser scanning confocal microscopy. Using a semi-quantitative method to analyze the spontaneous calcium oscillatory activities, a typical type of calcium oscillation was observed in developing hippocampal neurons. In addition, the administration of NMDA (N-Methyl-D-aspartate) at a concentration of 100 µM increased the calcium oscillation amplitude. The administration of MK801 at a concentration of 40 µM inhibited the amplitude and frequency of the calcium oscillations. Our results demonstrated that an increase in the ketamine concentration, starting from 30 µM, gradually decreased the neuronal calcium oscillation amplitude. The inhibition of the calcium oscillation frequency by 300 µM ketamine was statistically significant, and the neuronal calcium oscillations were completely eliminated with the administration of 3,000 µM Ketamine. The administration of 100, 300, and 1,000 µM NMDA to the 1 mM ketamine-pretreated hippocampal neurons restored the frequency and amplitude of the calcium oscillations in a dose-dependent manner. In fact, a concentration of 1,000 µM NMDA completely reversed the decrease in the calcium oscillation frequency and amplitude that was induced by 1 mM ketamine. This study revealed that ketamine can inhibit the frequency and amplitude of the calcium oscillations in developing hippocampal neurons though the NMDAR (NMDA receptor) in a dose-dependent manner, which might highlight a possible underlying mechanism of ketamine toxicity on the rat hippocampal neurons during development.     

An analysis of the transitions between down and up states of the cortical slow oscillation under urethane anaesthesia

We study the dynamics of the transition between the low- and high-firing states of the cortical slow oscillation by using intracellular recordings of the membrane potential from cortical neurons of rats. We investigate the evidence for a bistability in assemblies of cortical neurons playing a major role in the maintenance of this oscillation. We show that the trajectory of a typical transition takes an approximately exponential form, equivalent to the response of a resistor–capacitor circuit to a step-change in input. The time constant for the transition is negatively correlated with the membrane potential of the low-firing state, and values are broadly equivalent to neural time constants measured elsewhere. Overall, the results do not strongly support the hypothesis of a bistability in cortical neurons; rather, they suggest the cortical manifestation of the oscillation is a result of a step-change in input to the cortical neurons. Since there is evidence from previous work that a phase transition exists, we speculate that the step-change may be a result of a bistability within other brain areas, such as the thalamus, or a bistability among only a small subset of cortical neurons, or as a result of more complicated brain dynamics.