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.     

On the role of subthreshold dynamics in neuronal signaling

The role of subthreshold dynamics in neuronal signaling is examined using periodic pulse train stimulation of the Fitzhugh-Nagumo (FN) model of nerve membrane excitability and results from the squid giant axon as an experimental data base. For a broad range of stimulus conditions the first pulse in a pulse train elicited an action potential, whereas all subsequent pulses elicited subthreshold responses, both in the axon and in the FN model. These results are not well described by the Hodgkin and Huxley 1952 model. Various different patterns of subthreshold responses, including chaotic dynamics, can be observed in both systems-the FN model and the axon-depending upon stimulus conditions. For some conditions action potentials are occasionally interspersed among the subthreshold events with randomly occurring interspike intervals. The randomness is directly attributable to the underlying subthreshold chaos-deterministic chaos-rather than to a stochastic noise source. We conclude that this mechanism may contribute to multimodal interspike interval histograms which have been observed from individual neurons throughout the nervous system.     

A presettable multichannel digital timer.

A digital timer is described which generates a number of pulses whose delays with respect to a periodic reference pulse can be independently preset by means of thumbwheel switches. The timing intervals are crystal-controlled and can be varied over a wide range--typically 0.1 ms to 99.99 s. It is shown how a pulse train of up to 46 pulses may be obtained, the delay of each pulse in the train being individually presettable. Digital integrated circuits are used throughout, except for the output stage of enhanced drive capability.     

Simulation of the excitation of quasi-plane wake waves in a plasma by a resonant sequence of laser pulses with a variable envelope

Results are presented from full-scale numerical simulations of the excitation of wake waves by a sequence of weakly relativistic laser pulses in a subcritical plasma. Computations were carried out with a 2D3V version of the SUR-CA code that is based on the local-recursive nonlocal-asynchronous algorithm of the particle-in-cell method. The parameters of a train of laser pulses were chosen to correspond to the resonant excitation of the wake field. The curvature of the envelope of the pulses was chosen to depend on the number of the pulse in the train. Numerical simulations showed that there are plane waves during the first period of the plasma wave behind the pulse train.     

Density-dependent birth rate, birth pulses and their population dynamic consequences

 In most models of population dynamics, increases in population due to birth are assumed to be time-independent, but many species reproduce only during a single period of the year. We propose a single-species model with stage structure for the dynamics in a wild animal population for which births occur in a single pulse once per time period. Using the discrete dynamical system determined by the stroboscopic map, we obtain an exact periodic solution of systems which are with Ricker functions or Beverton-Holt functions, and obtain the threshold conditions for their stability. Above this threshold, there is a characteristic sequence of bifurcations, leading to chaotic dynamics, which implies that the dynamical behaviors of the single species model with birth pulses are very complex, including small-amplitude annual oscillations, large-amplitude multi-annual cycles, and chaos. This suggests that birth pulse, in effect, provides a natural period or cyclicity that allows for a period-doubling route to chaos. Received: 13 June 2001 / Revised version: 7 September 2001 / Published online: 8 February 2002     

Temporal selectivity by single neurons in the torus semicircularis of Batrachyla antartandica (Amphibia: Leptodactylidae)

We investigated the response selectivities of single auditory neurons in the torus semicircularis of Batrachyla antartandica (a leptodactylid from southern Chile) to synthetic stimuli having diverse temporal structures. The advertisement call for this species is characterized by a long sequence of brief sound pulses having a dominant frequency of about 2000 Hz. We constructed five different series of synthetic stimuli in which the following acoustic parameters were systematically modified, one at a time: pulse rate, pulse duration, pulse rise time, pulse fall time, and train duration. The carrier frequency of these stimuli was fixed at the characteristic frequency of the units under study (n=44). Response patterns of TS units to these synthetic call variants revealed different degrees of selectivity for each of the temporal variables. A substantial number of neurons showed preference for pulse rates below 2 pulses s(-1), approximating the values found in natural advertisement calls. Tonic neurons generally showed preferences for long pulse durations, long rise and fall times, and long train durations. In contrast, phasic and phasic-burst neurons preferred stimuli with short duration, short rise and fall times and short train durations.     

Pulsatile signaling in intercellular communication. Periodic stimuli are more efficient than random or chaotic signals in a model based on receptor desensitization.

The efficiency of various patterns of pulsatile stimulation is determined in a model in which a receptor becomes desensitized in the presence of its stimulatory ligand. The effect of stochastic or chaotic changes in the duration and/or interval between successive pulses in a series of square-wave stimuli is investigated. Before addressing the effect of random variations in the pulsatile signal, we first extend the results of a previous analysis (Li, Y.X., and A. Goldbeter. 1989. Biophys. J. 55:125-145) by demonstrating the existence of an optimal periodic signal that maximizes target cell responsiveness whatever the magnitude of stimulation. As to the effect of stochastic or chaotic variations in the pulsatile stimulus, three kinds of random distributions are used, namely, a Gaussian and a white-noise distribution, and a chaotic time series generated by the logistic map. All these random distributions are symmetrically centered around the reference value of the duration or interval that characterizes the optimal periodic stimulus yielding maximal responsiveness in target cells. Stochastically or chaotically varying pulses are less effective than the periodic signal that corresponds to the optimal pattern of pulsatile stimulation. The response of the receptor system is most sensitive to changes in the time interval that separates successive stimuli. Similar conclusions hold when stochastic or chaotic signals are compared to a reference periodic stimulus differing from the optimal one, although the effect of random variations is then reduced. The decreased efficiency of stochastic pulses accounts for the observed superiority of periodic versus stochastic pulses of cyclic AMP (cAMP) in Dictyostelium amoebae. The results are also discussed with respect to the efficiency of periodic versus stochastic or chaotic patterns of hormone secretion.     

Photoresponses of Halobacterium salinarum to repetitive pulse stimuli.

Halobacterium salinarum cells from 3-day-old cultures have been stimulated with different patterns of repetitive pulse stimuli. A short train of 0.6-s orange light pulses with a 4-s period resulted in reversal peaks of increasing intensity. The reverse occurred when blue light pulses were delivered as a finite train: with a 3-s period, the response declined in sequence from the first to the last pulse. To evaluate the response of the system under steady-state conditions of stimulation, continuous trains of pulses were also applied; whereas blue light always produced a sharply peaked response immediately after each pulse, orange pulses resulted in a declining peak of reversals that lasted until the subsequent pulse. An attempt to account for these results in terms of current excitation/adaptation models shows that additional mechanisms appear to be at work in this transduction chain.     

基于复杂性度量的心率变异信号非线性分析

假设心率变异信号是累积－发放模型（Ｉｎｔｅｇｒａｔｅ－ｆｉｒｅ）与非线性动力学系统耦合产生的峰电位链（ＳｐｉｋｅＴｒａｉｎ）。以符号动力学为基础,提出利用峰电位间隔（ｉｎｔｅｒｓｐｉｋｅｉｎｔｅｒｖａｌ,ＩＳＩ）及其随机替代数据的Ｃ１、Ｃ２复杂度来定量刻划非线性动力学系统特性。结果表明：确定性驱动产生的峰电位间隔序列可以与随机性驱动产生的峰电位间隔序列区分开。因此,在噪声干扰较强的生理信号中,尤其是在不清楚非线性动力系统变量和峰电位间隔序列之间是否存在微分同胚的情况下,以复杂性度量来代替以Ｔａｋｅｎｓ嵌入定理为基础的关联维数、Ｌｙａｐｎｏｖ指数等描述动力系统特征的方法是合适的。最后通过２类共３７个个体,每个个体的心电数据为１０００个Ｒ－Ｒ间期的微分序列检验心率变异信号的非线性结构。     

Determining the degree of chaos from analysis of ISI time series in the nervous system: a comparison between correlation dimension and nonlinear forecasting methods

Two different chaotic time series analysis methods – the correlation dimension and nonlinear forecasting – are introduced and then used to process the interspike intervals (ISI) of the action potential trains propagated along a single nerve fiber of the anesthetized rat. From the results, the conclusion is drawn that compared with the correlation dimension, nonlinear forecasting is more efficient and robust for chaotic ISI time series analysis in a noisy environment. Moreover, the evolution of the correlation coefficient curves calculated from nonlinear forecasting can qualitatively give a better reflection of the unpredictability of the system's future behavior and is in good agreement with the values of the largest Lyapunov exponent that quantitatively measures the degree of chaos. Received: 19 November 1996 / Accepted in revised form: 15 September 1997     

Periodic solutions and refractory periods in the soliton theory for nerves and the locust femoral nerve

Close to melting transitions it is possible to propagate solitary electromechanical pulses which reflect many of the experimental features of the nerve pulse including mechanical dislocations and reversible heat production. Here we show that one also obtains the possibility of periodic pulse generation when the constraint for the nerve is the conservation of the overall length of the nerve. This condition generates an undershoot beneath the baseline ('hyperpolarization') and a 'refractory period', i.e., a minimum distance between pulses. In this paper, we outline the theory for periodic solutions to the wave equation and compare these results to action potentials from the femoral nerve of the locust (Locusta migratoria). In particular, we describe the frequently occurring minimum-distance doublet pulses seen in these neurons and compare them to the periodic pulse solutions.     

On reinforcement and interference between stimuli

It is shown that the current “two-factor” theory of nerve excitation can account for sustained inhibition or enhancement by a sequence of stimulus pulses, and for the decrease in the reinforcement period with each successive pulse of the train.     

Suppression of radiation damping during selective excitation of the water signal: The WANTED sequence

Summary A new pulse sequence is presented allowing the use of long selective pulses at the water frequency using standard equipment. Radiation damping is suppressed during the pulse by the use of gradient echoes programmed between the single pulses of a DANTE train. This WANTED (water-selective DANTE using gradients) sequence thus allows the observation of interactions with water without the use of special probe heads or filtering of undesired resonances. By combining the WANTED sequence with NOESY, ROESY and NOESY-GSQC experiments, we obtain selective 1D and 2D spectra fit to the observation of chemical exchange and dipolar interactions between water and protein protons.     

Band-selective editing of exchange-relay in protein-water NOE experiments

A pulse sequence is proposed which uses a train of band-selective pulses for the editing of slow chemical exchange-relay effects in experiments designed to study water-macromolecule interactions. Compared to previous methods, this experiment does not require knowledge of the exact chemical shift of the relaying labile protons and needs only the recording of a single experiment to edit the relay through different exchanging groups resonating at different frequencies. The pulse sequence has been implemented using Gaussian cascades and was applied to the study of the hydration of HEW lysozyme.     

Only noise can induce chaos in discrete populations

Motivated by the papers from Ellner and Turchin 2005 and Dennis et al. 2003 we investigate the possibility to detect chaos in noisy ecological systems. One message of our paper is that if a dynamic model is available and if this model predicts chaotic behaviour, one should consider its discrete-state, noisy version when fitting numerical predictions to observations. We emphasize that deterministic discrete-state models behave periodically, thus only the interaction of these deterministic skeletons with random noise can produce non-regular dynamics. We detect and describe a relatively sharply defined range of the noise (the grey zone) where the gradual transition from periodic to chaotic behaviour happens. This zone, the upper border of which can be predicted analytically, is identified in experimental data as well as in numerical simulations. In the grey zone the global, statistical behaviour will approach the statistics produced by the chaotic, continuous model, and in this sense we claim that noise can produce chaos.     

Traveling waves in a piecewise-linear reaction-diffusion model of excitable medium

One-dimensional autowaves (traveling waves) in excitable medium described by a piecewise-linear reaction-diffusion system have been investigated. Two main types of wave have been considered: a single pulse and a periodic sequence of pulses (wave trains). In a two-component system, oscillations are due to the second component of the reaction-diffusion system, while in a one-component system, they are caused by external periodic excitation (forcing). Using semianalytical solutions for the wave profile, the shape and velocity of autowaves have been found. It is shown that the dispersion relation for oscillating sequences of pulses has an anomalous character.     

基于混沌降噪的神经元放电峰峰间期序列分析

围绕如何来消除神经元峰峰间期序列中随机噪声影响从而提取出决定不规则性的确定性动力学关系这个问题,本文首先简要介绍峰峰间期序列样本的制备,然后着重讨论一个简单可行的混沌时间序列降噪方法的原理和算法实现,最终将该方法运用到神经元放电活动数值模拟和实验记录到的峰峰间期时间序列样本分析中。本文分析结果再次证明神经放电活动中确实存在着不规则混沌运动,而且降噪结果进一步揭示了神经电生理实验中决定混沌放电的不连续但分段光滑的单峰函数关系     

CHARACTERISTICS OF MINKE WHALE (BALAENOPTERA ACUTOROSTRATA) PULSE TRAINS RECORDED NEAR PUERTO RICO

A nine-day acoustic and visual survey was conducted off the West Indies in March 1994 to study the pulse trains that were detected on SOSUS arrays throughout winter in deep water between the West Indies and Bermuda. During the survey, pulse train sounds were consistently recorded in an area 190–350 km northeast of Puerto Rico. Vocalizing animals were never visually observed, but visual sighting conditions were often poor and observation height was low. Pulse trains occurred in two basic forms. The "speed-up" pulse train was characterized by an accelerating series of pulses with energy in the 200–400 Hz band, with individual pulses lasting 40-60 msec. Speedup pulse trains started with average pulse rates of 1.5 pulses/sec, lasted 43.7 ± 6.0 sec, and ended with average pulse rates of 2.8 pulses/sec. The less common "slow-down" pulse train was characterized by a decelerating series of pulses with energy in the 250-350 Hz band. Slow-down pulse trains started at pulse rates averaging 4.5 pulses/sec, lasted 60.9 ± 5.8 sec, and ended with average pulse rates of 2.9 pulses/sec. We believe the recorded pulse trains are from minke whales based on careful reanalysis of, and comparison to, minke whale pulse-train sounds recorded in the Caribbean by Winn and Perkins (1976).     

The dependence of impulse propagation speed on firing frequency, dispersion, for the Hodgkin-Huxley model.

Propagation speed of an impulse is influenced by previous activity. A pulse following its predecessor too closely may travel more slowly than a solitary pulse. In contrast, for some range of interspike intervals, a pulse may travel faster than normal because of a possible superexcitable phase of its predecessor's wake. Thus, in general, pulse speeds and interspike intervals will not remain constant during propagation. We consider these issues for the Hodgkin-Huxley cable equations. First, the relation between speed and frequency or interspike interval, the dispersion relation, is computed for particular solutions, steadily propagating periodic wave trains. For each frequency, omega, below some maximum frequency, omega max, we find two such solutions, one fast and one slow. The latter are likely unstable as a computational example illustrates. The solitary pulse is obtained in the limit as omega tends to zero. At high frequency, speed drops significantly below the solitary pulse speed; for 6.3 degrees C, the drop at omega max is greater than 60%. For an intermediate range of frequencies, supernormal speeds are found and these are correlated with oscillatory swings in sub- and superexcitability in the return to rest of an impulse. Qualitative consequences of the dispersion relation are illustrated with several different computed pulse train responses of the full cable equations for repetitively applied current pulses. Moreover, changes in pulse speed and interspike interval during propagation are predicted quantitatively by a simple kinematic approximation which applies the dispersion relation, instantaneously, to individual pulses. One example shows how interspike time intervals can be distorted during propagation from a ratio of 2:1 at input to 6:5 at a distance of 6.5 cm.     

Low-Dimensional Dynamics in Sensory Biology 1: Thermally Sensitive Electroreceptors of the Catfish

We report the results of a search for evidence of periodic unstableorbits in the electroreceptors of the catfish. The function of thesereceptor organs is to sense weak external electric fields. Inaddition, they respond to the ambient temperature and to the ioniccomposition of the water. These quantities are encoded by receptorsthat make use of an internal oscillator operating at the level of themembrane potential. If such oscillators have three or more degreesof freedom, and at least one of which also exhibits a nonlinearity,they are potentially capable of chaotic dynamics. By detecting theexistence of stable and unstable periodic orbits, we demonstratebifurcations between noisy stable and chaotic behavior using theambient temperature as a parameter. We suggest that the techniquedeveloped herein be regarded as an additional tool for the analysisof data in sensory biology and thus can be potentially useful instudies of functional responses to external stimuli. We speculatethat the appearance of unstable orbits may be indicative of a stateof heightened sensory awareness by the animal.