神经放电节律加周期分岔序列中的簇放电到峰放电的转迁

含快慢子系统的神经元数学模型仿真预期,神经放电节律经历加周期分岔序列,可以进一步表现激变,并通过逆倍周期分岔级联进入周期1峰放电。实验调节胞外钙离子浓度,观察到从周期1簇放电开始的带有随机节律的加周期分岔到簇内有多个峰的簇放电,再经激变转迁到峰放电节律的分岔序列,提供了这种分岔序列模式实验证据。实验所见之激变表现为簇放电节律的休止期消失,放电节律变为混沌峰放电和周期峰放电。作者利用随机Chay模型更加逼真地仿真再现了实验所见的分岔序列。该实验结果验证了以前的确定性数学模型的理论预期,并利用随机理论模型仿真了其在现实神经系统的表现;揭示了一类完整的神经放电节律的转换规律。     

神经起步点自发放电节律及节律转化的分岔规律

在神经起步点的实验中观察到了复杂多样的神经放电([Ca^2 ]o)节律模式,如周期簇放电、周期峰放电、混沌簇放电、混沌峰放电以及随机放电节律等。随着细胞外钙离子浓度的降低,神经放电节律从周期l簇放电,经过复杂的分岔过程(包括经倍周期分岔到混沌簇放电、混沌簇放电经激变到混沌峰放电、以及混沌峰放电经逆倍周期分岔到周期峰放电)转化为周期l峰放电。在神经放电理论模型——Chay模型中,调节与实验相关的参数(Ca^2 平衡电位),可以获得与实验相似的神经放电节律和节律转换规律。这表明复杂的神经放电节律之间存在着一定的分岔规律,它们是理解神经元信息编码的基础。     

神经放电加周期分岔中由随机自共振引起一类新节律

当改变实验性神经起步点细胞外[Ca^2 ]时,放电节律表现出从周期1节律转换为周期4节律的加周期分岔序列。其中,周期n节律转换为周期n 1节律的过程中(n=1,2,3)存在一种新的具有交替特征的节律,该新节律为周期n簇与周期n 1簇放电的交替,并且周期n 1簇的时间间隔序列呈现出整数倍特征。确定性神经放电理论模型(chay模型)只能模拟周期n节律直接到周期n 1节律的加周期分岔序列;而随机chay模型可以模拟实验中的加周期分岔过程和新节律。进一步,新节律被确认是经随机自共振机制产生的。这不仅解释了实验现象,也将随机自共振的产生区间从以前认识到的Hopf分岔点附近扩大到加周期分岔点附近,同时扩大了噪声在神经放电和神经编码中起重要作用的参数区间。     

鳌虾口胃神经节神经元簇放电的动态离子流机制

为研究神经元自身的电活动特性(簇放电节律模式到峰放电节律模式的转迁,以及簇放电节律的离子流机制),本实验选取鳌虾口胃神经节(stomatogastric ganglion,STG)中功能上孤立的单个神经元,记录其在胞外钙离子浓度([Ca2+]o)变化和钙依赖钾离子通道阻断剂tetraethylammonium(TEA)作用下细胞内电活动的变化。当[Ca2+]o降低时,神经元膜电位水平升高,电活动模式表现为从低电位水平的静息(极化静息),到簇放电,再到峰放电,最后到高电位水平的静息(去极化静息)的转迁历程;当细胞外TEA浓度([TEA]o)增加时,神经元膜电位水平也升高,电活动模式表现为从极化静息,到簇放电,再到峰放电的转迁历程,且变化过程是可逆的。上述结果表明,不同生理状态下神经元电活动模式是复杂多样的,这种复杂多样的电活动模式随生理调节参数变化可以表现出规律性的转迁。另外,钙离子内流通过影响[Ca2+]i水平进而调节钙依赖钾电导,决定簇放电的起始与终止,这可能是簇放电产生的动态离子流机制。     

实验性神经起步点产生的整数倍簇放电节律

随机Hindmarsh-Rose模型中产生簇（bursting)放电节律是神经放电中存在随机自共振的一个重要理论证据,但是,该簇放电节律在实验中一直没有被发现。在实验性神经起步点细胞外[Ca^2 ]([Ca^2 ]o)低于周期1节律的[Ca^2 ]o时,发现了一种簇放电节律。其簇簇间期（inter-burst intervals,IBIs)呈现出与随机自共振引起的整数倍峰放电（interger multiple spiking)节律的峰峰间期类似的整数倍特征。随机Hindmarsh-Rose模型中产生的簇（bursting)放电节律也表现出类似的特征。结果验证了随机自共振簇放电的存在性,揭示该簇放电节律的统计特征。此外,该簇放电节律的参数区间以及其与整数倍峰放电节律的区别被揭示,簇放电节律的[Ca^2 ]o低于峰放电律的[Ca^2 ]o。     

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。     

周期激励下 FitzHugh-Nagumo模型的两种多峰分布放电节律

文章揭示了外界周期脉冲激励下神经元系统产生的随机整数倍和混沌多峰放电节律的关系.随机节律统计直方图呈多峰分布、峰值指数衰减、不可预报且复杂度接近1;混沌节律统计直方图呈不同的多峰分布,峰值非指数衰减、有一定的可预报性且复杂度小于1.混沌节律在激励脉冲周期小于系统内在周期且刺激强度较大时产生,参数范围较小;而随机节律在激励脉冲周期大于系统内在周期且脉冲刺激强度小时,可与随机因素共同作用而产生,产生的参数范围较大.上述结果揭示了两类节律的动力学特性,为区分两类节律提供了实用指标.     

周期激励下FHN模型的两种多峰分布放电节律

文章揭示了外界周期脉冲激励下神经元系统产生的随机整数倍和混沌多峰放电节律的关系.随机节律统计直方图呈多峰分布、峰值指数衰减、不可预报且复杂度接近1;混沌节律统计直方图呈不同的多峰分布,峰值非指数衰减、有一定的可预报性且复杂度小于1.混沌节律在激励脉冲周期小于系统内在周期且刺激强度较大时产生,参数范围较小;而随机节律在激励脉冲周期大于系统内在周期且脉冲刺激强度小时,可与随机因素共同作用而产生,产生的参数范围较大.上述结果揭示了两类节律的动力学特性,为区分两类节律提供了实用指标.     

黑质致密部神经元的反应性与放电型式的关系

通过研究黑质致密部（subastantia nigra compacta,SNc）神经元的放电型式与其对谷氨酸、多巴胺及缺氧敏感性的关系,探讨“非周期敏感”的现象在神经系统的普通性。在幼鼠的脑片胞外记录SNc神经元的自发放电,比较周期与非周期放电神经元对该三种刺激反应的敏感性,并对非周期放电神经元的动作电位峰峰间期序列（interspike interval,ISI）进行非线性动力学分析。结果表明,非周期放电神经元比周期放电神经元对上述三种缺少更敏感;非周期放电神经元的放电ISI序列含有非稳定周期轨道族,提示非周期放电存在确定的动力学机制。     

多通道在体记录技术——神经元放电与节律性场电位间的相位分析方法

本文旨在介绍神经元放电序列与节律性场电位间的相位分析方法。多通道在体记录技术能同时记录群体神经元和局部场电位的活动信号。神经元的放电活动一般表征为放电时间序列;而在局部场电位信号中,则包含有不同频率成分的周期性节律振荡。相位分析主要考察神经元放电时刻与周期性节律场电位相位间的相互关系。具体分析时,先运用Hilbert变换计算出某一频段节律场电位信号的瞬时相位值,然后再计算某一神经元放电序列中每个动作电位相对于该节律场电位的放电相位,最后通过考察这些放电相位的分布特性,来判断该神经元与该节律场电位相位间的放电相位关系。如一神经元放电序列对某种节律场电位的相位分布经统计检验不是随机的,则表明该神经元对这种节律场电位有放电锁相关系。Theta相位进动则是一种特殊的神经元放电与周期性节律场电位间的相位关系,也是海马位置细胞放电的基本特性之一。海马位置细胞在位置野内一般呈theta节律簇状放电模式,而相位进动是指每一theta波内放电的theta相位,相对上一theta波会逐渐提前。这一现象可通过对位置细胞放电的theta相位和动物实时位置使用线性模型来描述;并运用圆周线性相关分析法,计算它们之间的相关系数,从而研究位置细胞在位置野中的放电相对于theta相位的进动情况。通过相位分析,可以帮助我们了解神经元放电与节律性场电位信号间的时间信息编码特性。     

Maximum decoding abilities of temporal patterns and synchronized firings: application to auditory neurons responding to click trains and amplitude modulated white noise

Simultaneous recordings of an increasing number of neurons have recently become available, but few methods have been proposed to handle this activity. Here, we extract and investigate all the possible temporal neural activity patterns based on synchronized firings of neurons recorded on multiple electrodes, or based on bursts of single-electrode activity in cat primary auditory cortex. We apply this to responses to periodic click trains or sinusoïdal amplitude modulated noise by obtaining for each pattern its temporal modulation transfer function. An algorithm that maximizes the mutual information between all patterns and stimuli subsequently leads to the identification of patterns that optimally decode modulation frequency (MF). We show that stimulus information contained in multi-electrode synchronized firing is not redundant with single-electrode firings and leads to improved efficiency of MF decoding. We also show that the combined use of firing rate and temporal codes leads to a better discrimination of the MF.     

Ionic and neuromodulatory regulation of burst discharge controls frequency tuning

Sensory neurons encode natural stimuli by changes in firing rate or by generating specific firing patterns, such as bursts. Many neural computations rely on the fact that neurons can be tuned to specific stimulus frequencies. It is thus important to understand the mechanisms underlying frequency tuning. In the electrosensory system of the weakly electric fish, Apteronotus leptorhynchus, the primary processing of behaviourally relevant sensory signals occurs in pyramidal neurons of the electrosensory lateral line lobe (ELL). These cells encode low frequency prey stimuli with bursts of spikes and high frequency communication signals with single spikes. We describe here how bursting in pyramidal neurons can be regulated by intrinsic conductances in a cell subtype specific fashion across the sensory maps found within the ELL, thereby regulating their frequency tuning. Further, the neuromodulatory regulation of such conductances within individual cells and the consequences to frequency tuning are highlighted. Such alterations in the tuning of the pyramidal neurons may allow weakly electric fish to preferentially select for certain stimuli under various behaviourally relevant circumstances.     

Computer simulations of synchrony and oscillations evoked by two coherent inputs

Coherent oscillations have been reported in multiple cortical areas. This study examines the characteristics of output spikes through computer simulations when the neural network model receives periodic/aperiodic spatiotemporal spikes with modulated/constant populational activity from two pathways. Synchronous oscillations which have the same period as the input are observed in response to periodic input patterns regardless of populational activity. The results confirm that the output frequency of synchrony is essentially determined by the period of the repeated input patterns. On the other hand, weak periodic outputs are observed when aperiodic spikes are input with modulated populational activity. In this case, higher firing rates are necessary to input for higher frequency oscillations. The spike-timing-dependent plasticity suppresses the spikes which do not contribute to the synchrony for periodic inputs. This effect corresponds to the experimental reports that learning sharpens the synchrony in the motor cortex. These results suggest that spatiotemporal spike patterns should be entrained on modulated populational activity to transmit oscillatory information effectively in the convergent pathway.     

Response characteristics of the BVP neuron model to periodic pulse inputs.

The characteristics of the BVP neuron model response to periodic pulse stimuli are investigated. Temporal patterns of the output of the model are analyzed as a function of the stimulus intensity and period. The BVP model exhibits the same chaotic behavior, and a Cantor function-like graph of the response frequency (mean firing rate) as in electrophysiological experiments. This shows that the BVP model describes the complicated response characteristics of the neuron at least qualitatively.     

Effect of light on stochastic phase synchronization in the crayfish caudal photoreceptor

Phase synchronization between the firing of the crayfish caudal photoreceptor (CPR) and an applied periodic hydrodynamic stimulus is investigated. It is shown that the CPR firing synchronizes with a periodic stimulus over a range of frequencies corresponding to the known sensitivity range of the crayfish to hydrodynamic stimuli. This synchronization is quantified using previously developed measures of synchronization such as the synchronization index; multiple stimulus-response locking ratios occur in this system that are consistent with theoretical predictions based on the theory of synchronization of noisy oscillators. The maximal synchronization for various locking ratios is shifted to higher frequencies in the presence of light.     

Biological Experimental Observations of an Unnoticed Chaos as Simulated by the Hindmarsh-Rose Model

An unnoticed chaotic firing pattern, lying between period-1 and period-2 firing patterns, has received little attention over the past 20 years since it was first simulated in the Hindmarsh-Rose (HR) model. In the present study, the rat sciatic nerve model of chronic constriction injury (CCI) was used as an experimental neural pacemaker to investigate the transition regularities of spontaneous firing patterns. Chaotic firing lying between period-1 and period-2 firings was observed located in four bifurcation scenarios in different, isolated neural pacemakers. These bifurcation scenarios were induced by decreasing extracellular calcium concentrations. The behaviors after period-2 firing pattern in the four scenarios were period-doubling bifurcation not to chaos, period-doubling bifurcation to chaos, period-adding sequences with chaotic firings, and period-adding sequences with stochastic firings. The deterministic structure of the chaotic firing pattern was identified by the first return map of interspike intervals and a short-term prediction using nonlinear prediction. The experimental observations closely match those simulated in a two-dimensional parameter space using the HR model, providing strong evidences of the existence of chaotic firing lying between period-1 and period-2 firing patterns in the actual nervous system. The results also present relationships in the parameter space between this chaotic firing and other firing patterns, such as the chaotic firings that appear after period-2 firing pattern located within the well-known comb-shaped region, periodic firing patterns and stochastic firing patterns, as predicted by the HR model. We hope that this study can focus attention on and help to further the understanding of the unnoticed chaotic neural firing pattern.     

Dynamics of the noisy neural network

The dynamic features of interspike interval sequences and structures of spatiotemporal patterns of firing in a coupled noisy neural network are investigated. The system displays complex dynamics under periodic external stimuli. The dynamics is modulated by a periodic impulse-like synaptic current which relates to a global coupling interaction between neurons. The firings of the stimulated neurons are phase-locked to this current. In addition, the interspike interval histograms are studied for the case of frozen noise which does not change its value within a time interval once it has been distributed onto the network. It is found that the peaks in these histograms are located at integer multiples of the period of the external stimulus, and the heights of these peaks decay exponentially, which corresponds to the experimental results. Received: 12 April 1997 / Accepted in revised form: 7 May 1997