A neuronal model for the discharge patterns produced by cyclic inputs

To understand the patterns of nerve impulses produced by sinusoidal stimuli, a simple model is considered which integrates input currents with a finite time constant until a threshold voltage is reached, whereupon an output pulse is produced and the process is restarted. We show here that (a) a general analytic solution exists for this model driven by sinusoidal stimuli, determining the interval between every member of the pulse train, (b) for all values of the parameters of the model a pattern exists which repeats periodically after a finite number of pulses in the absence of noise, (c) the system will approach a stable pattern which, if perturbed, will be recovered once the perturbation is removed, (d) the linear integrator or relaxation oscillator and the curren multiplier are limiting cases of this model.     

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.     

Time versus response indices affect conclusions about preference pulses

Using data from two conditions of an experiment that arranged response-contingent foods and red keylight illuminations, we compared time-indexed and response-indexed preference pulses. The interpretation of red keylight effects (relative to food effects) differed according to whether time or behaviour was used to index choice in the post-event period: preference after a red keylight was more extreme than after a food in the response pulses while preference after a food was more extreme than after a keylight in the time pulses. This was due to different response latencies following the two events in combination with a tendency for initial preference to decrease as latency increased: responding began sooner after non-foods and responding that began later, after any event, tended towards indifference. Our finding suggests that preference pulses ought to be indexed according to time since the last event delivery, particularly if the response-contingent events may result in systematically different response latencies.     

The functional sense of central oscillations in walking

 Rhythmic motor output is generally assumed to be produced by central pattern generators or, more specific, central oscillators, the rhythmic output of which can be entrained and modulated by sensory input and descending control. In the case of locomotor systems, the output of the central system, i.e., the output obtained after deafferentation of sensory feedback, shows many of the temporal characteristics of real movements. Therefore the term fictive locomotion has been coined. This article concentrates on a specific locomotor behavior, namely walking; in particular walking in invertebrates. In contrast to the traditional view, an alternative hypothesis is formulated to interpret the functional sense of these central oscillations which have been found in many cases. It is argued that the basic function of the underlying circuit is to avoid cocontraction of antagonistic muscles. Such a system operates best with an inherent period just above the maximum period observed in real walking. The circuit discussed in this article (Fig. 2) shows several properties in common with results described as “fictive walking”. It furthermore could explain a number of properties observed in animals walking in different situations. According to this hypothesis, the oscillations found after deafferentation are side effects occurring in specific artificial situations. If, however, a parameter called central excitation is large enough, the system can act as a central oscillator that overrides the sensory input completely. Received: 18 May 2001 / Accepted in revised form: 20 November 2001     

Food entrainment modifies the c-Fos expression pattern in brain stem nuclei of rats

When food is restricted to a few hours daily, animals increase their locomotor activity 2-3 h before food access, which has been termed food anticipatory activity. Food entrainment has been linked to the expression of a circadian food-entrained oscillator (FEO) and the anatomic substrate of this oscillator seems to depend on diverse neural systems and peripheral organs. Previously, we have described a differential involvement of hypothalamic nuclei in the food-entrained process. For the food entrainment pathway, the communication between the gastrointestinal system and central nervous system is essential. The visceral synaptic input to the brain stem arrives at the dorsal vagal complex and is transmitted directly from the nucleus of the solitary tract (NST) or via the parabrachial nucleus (PBN) to hypothalamic nuclei and other areas of the forebrain. The present study aims to characterize the response of brain stem structures in food entrainment. The expression of c-Fos immunoreactivity (c-Fos-IR) was used to identify neuronal activation. Present data show an increased c-Fos-IR following meal time in all brain stem nuclei studied. Food-entrained temporal patterns did not persist under fasting conditions, indicating a direct dependence on feeding-elicited signals for this activation. Because NST and PBN exhibited a different and increased response from that expected after a regular meal, we suggest that food entrainment promotes ingestive adaptations that lead to a modified activation in these brain stem nuclei, e.g., stomach distension. Neural information provided by these nuclei to the brain may provide the essential entraining signal for FEO.     

Diversity of temporal self-organized behaviors in a biochemical system.

The numerical study of a glycolytic model formed by a system of three delay-differential equations revealed a notable richness of temporal structures which included the three main routes to chaos, as well as a multiplicity of stable coexisting states. The Feigenbaum, intermitency and quasiperiodicity routes to chaos can emerge in the biochemical oscillator. Moreover, different types of birhythmicity, trirhythmicity and hard excitation emerge in the phase space. For a single range of the control parameter it can be observed the coexistence of two quasiperiodicity routes to chaos, the coexistence of a stable steady state with a stable torus, and the coexistence of a strange attractor with different stable regimes such as chaos with different periodic regimes, chaos with bursting behavior, and chaos with torus. In most of the numerical studies, the biochemical oscillator has been considered under periodic input flux being the mean input flux rate 6 mM/h. On the other hand, several investigators have observed quasiperiodic time patterns and chaotic oscillations by monitoring the fluorescence of NADH in glycolyzing yeast under sinusoidal glucose input flux. Our numerical results match well with these experimental studies.     

光对植物生物钟的调节

植物中的许多生理和生化反应都表现出一种内源的近似于24小时的昼夜节律现象,这些昼夜节律现象受生物钟的调节。高等植物的生物钟系统由输入途径、中央振荡器、输出途径以及一个阀门效应器组成。光信号通过光敏色素和隐花色素进入生物钟,使中央振荡器产生振荡,改变生物钟的输出信号,引起各种生理反应。本文综述了光信号对高等植物生物钟的调节作用和转导途径。     

Protein malnutrition of the lactating female rat: effect on maternal behaviour and spontaneous weaning of young rats

Female rats were kept on a diet with a low content of animal protein (5.5%) beginning from the 2nd day after delivery. Beginning from the 10th day after delivery their body weight was persistently lower than that of control females. Also the body weight of their young was lower than that of control animals throughout the experiment, with significant differences appearing on the 17th day of life. Spontaneous termination of maternal milk intake occurred in malnourished young 10 days later than in the controls. Retention of 85Sr in malnourished females was in keeping with their milk production. Irrespective of the differences in body weight and the quality of solid food, the malnourished young began consuming solid food at the same age and in the same relative amounts as the controls. Thus in malnourished young the period of gradual weaning was prolonged by more than to 3 weeks in contrast to 2 weeks in the controls. This is probably due to the slower extinction of the oral sucking mechanism resulting from changes in the maturation of the CNS. No changes were found in maternal behaviour (nest building and efficiency of retrieving) in malnourished females during the suckling period. However, infanticide appeared in some females during the weaning period.     

Cytosolic calcium oscillators

Many cells display oscillations in intracellular calcium resulting from the periodic release of calcium from intracellular reservoirs. Frequencies are varied, but most oscillations have periods ranging from 5 to 60 s. For any given cell, frequency can vary depending on external conditions, particularly the concentration of natural stimuli or calcium. This cytosolic calcium oscillator is particularly sensitive to those stimuli (neurotransmitters, hormones, growth factors) that hydrolyze phosphoinositides to give diacylglycerol and inositol 1,4,5-trisphosphate (Ins1,4,5P3). The ability of Ins1,4,5P3 to mobilize intracellular calcium is a significant feature of many of the proposed models that are used to explain oscillatory activity. Receptor-controlled oscillator models propose that there are complex feedback mechanisms that generate oscillations in the level of Ins1,4,5P3. Second messenger-controlled oscillator models demonstrate that the oscillator is a component of the calcium reservoir, which is induced to release calcium by a constant input of either Ins1,4,5P3 or calcium itself. In the latter case, the process of calcium-induced calcium release might be the basis of oscillatory activity in many cell types. The function of calcium oscillations is still unknown. Because oscillator frequency can vary with agonist concentration, calcium transients might be part of a frequency-encoded signaling system. When an external stimulus arrives at the cell surface the information is translated into a train of calcium spikes, i.e., the signal is digitized. Certain cells may then convey information by varying the frequency of this digital signal.     

Response characteristics of a neuron model to a periodic input

A mathematical neuron model defined by a difference equation was investigated when it was exposed to an environment of a periodic input stimulus. It is shown that pulse sequences constructed in advance by a particular method are actually realizable as the output of the system and the condition for the output sequence is also obtained with respect to the magnitude of the input. The results are interesting from a point of view of number theory.     

Synchronized oscillation in a modular neural network composed of columns

The columnar organization is a ubiquitous feature in the cerebral cortex. In this study, a neural network model simulating the cortical columns has been constructed. When fed with random pulse input with constant rate, a column generates synchronized oscillations, with a frequency varying from 3 to 43 Hz depending on parameter values. The behavior of the model under periodic stimulation was studied and the input-output relationship was non-linear. When identical columns were sparsely interconnected, the column oscillator could be locked in synchrony. In a network composed of heterogeneous columns, the columns were organized by intrinsic properties and formed partially synchronized assemblies.     

Synchronized oscillation in a modular neural network composed of columns

The columnar organization is a ubiquitous feature in the cerebral cortex. In this study, a neural network model simulating the cortical columns has been constructed. When fed with random pulse input with constant rate, a column generates synchronized oscillations, with a frequency varying from 3 to 43 Hz depending on parameter values. The behavior of the model under periodic stimulation was studied and the input-output relationship was non-linear. When identical columns were sparsely interconnected, the column oscillator could be locked in synchrony. In a network composed of heterogeneous columns, the columns were organized by intrinsic properties and formed partially synchronized assemblies.     

Pulse coupled oscillators and the phase resetting curve

Limit cycle oscillators that are coupled in a pulsatile manner are referred to as pulse coupled oscillators. In these oscillators, the interactions take the form of brief pulses such that the effect of one input dies out before the next is received. A phase resetting curve (PRC) keeps track of how much an input advances or delays the next spike in an oscillatory neuron depending upon where in the cycle the input is applied. PRCs can be used to predict phase locking in networks of pulse coupled oscillators. In some studies of pulse coupled oscillators, a specific form is assumed for the interactions between oscillators, but a more general approach is to formulate the problem assuming a PRC that is generated using a perturbation that approximates the input received in the real biological network. In general, this approach requires that circuit architecture and a specific firing pattern be assumed. This allows the construction of discrete maps from one event to the next. The fixed points of these maps correspond to periodic firing modes and are easier to locate and analyze for stability compared to locating and analyzing periodic modes in the original network directly. Alternatively, maps based on the PRC have been constructed that do not presuppose a firing order. Specific circuits that have been analyzed under the assumption of pulsatile coupling include one to one lockings in a periodically forced oscillator or an oscillator forced at a fixed delay after a threshold event, two bidirectionally coupled oscillators with and without delays, a unidirectional N-ring of oscillators, and N all-to-all networks.     

Computer simulation of reverberating spreading depression in a network of cell automata

A homogeneous network of cellular automata, representing a two-dimensional model of neural tissue, was used for simulation of periodic processes generated by spreading cortical depression. The transitional function μ and the function of the output γ of each cellular automationA at the timet is explicitly determined by its state and the input signals from 4 adjacent cells at timet-1. Computer experiments (IBM 370-135) in networks consisting of 1000 or 7200 cells illustrated the development of periodic generators due to 1) reverberation around obstacles with the perimeter exceeding the wavelength of the process: 2) reverberation in intact tissue (with zero perimeter of the obstacle); 3) formation of a stable focus of periodic activity (deterministic-stochastic oscillator). Results of computer experiments are compared with electrophysiological observations.     

A rapid and potent DNA vaccination strategy defined by in vivo monitoring of antigen expression

Induction of immunity after DNA vaccination is generally considered a slow process. Here we show that DNA delivery to the skin results in a highly transient pulse of antigen expression. Based on this information, we developed a new rapid and potent intradermal DNA vaccination method. By short-interval intradermal DNA delivery, robust T-cell responses, of a magnitude sufficient to reject established subcutaneous tumors, are generated within 12 d. Moreover, this vaccination strategy confers protecting humoral immunity against influenza A infection within 2 weeks after the start of vaccination. The strength and speed of this newly developed strategy will be beneficial in situations in which immunity is required in the shortest possible time.     

Activity in anticipation and in succession of a daily meal

When exposed, in otherwise constant conditions, to a schedule with one single meal per day, rodents anticipate the time of food availability by an increase in locomotor activity while the main circadian rhythm continues to free-run with a period different from 24 h. The anticipatory activity (AA) is considered a component which is uncoupled from the light-entrainable circadian system and controlled by a food-entrainable oscillator. In this report it is shown that, in addition to AA, sometimes a burst or band of activity appears which succeeds the feeding time (SA). AA and SA seem to belong to one another, both being controlled by the same food-entrainable oscillator. The band of activity constituted by the combination of both AA and SA, though temporarily suppressed during and immediately after the meal, follows, as a whole, the rules of entrainment as known from circadian systems.     

Role of the Pineal in the Circadian System of Birds

Pinealectomy of sparrows abolishes the free running rhythm oflocomotor activity in constant darkness. Without their pineals,sparrows still entrain to light-dark cycles and show other signsthat they retain part, but not all, of the circadian system.Interruption of either the neural input to the pineal or itsneural output, or both, does not abolish the free running rhythm.Rhythmicity can be restored to a pinealectomized bird by implantingthe pineal of a donor into the anterior chamber of its eye.A model of the circadian system controlling locomotor behavioris proposed to account for these facts. We suggest that theavian pineal contains a self-sustained oscillator, and as aconsequence, produces a rhythmic hormonal output. Circadianfluctuations of this hormone entrain a damped oscillator locatedelsewhere, which in turn drives the locomotor activity. Eachoscillator has separate access to environmental light cycles.The behavior of a pinealectomized bird is determined exclusivelyby its damped oscillator. It does not free run because it lacksthe self-sustained oscillator which, however, can be restoredby transplantation. The transplanted pineal continues its self-sustainedcircadian hormonal output which entrains the damped oscillatorand restores the system to its normal state.     

Periodic metabolic systems: Oscillations in multiple-loop negative feedback biochemical control networks

Summary For a general multiple loop feedback inhibition system in which the end product can inhibit any or all of the intermediate reactions it is shown that biologically significant behaviour is always confined to a bounded region of reaction space containing a unique equilibrium. By explicit construction of a Liapunov function for the general n dimensional differential equation it is shown that some values of reaction parameters cause the concentration vector to approach the equilibrium asymptotically for all physically realizable initial conditions. As the parameter values change, periodic solutions can appear within the bounded region. Some information about these periodic solutions can be obtained from the Hopf bifurcation theorem. Alternatively, if specific parameter values are known a numerical method can be used to find periodic solutions and determine their stability by locating a zero of the displacement map. The single loop Goodwin oscillator is analysed in detail. The methods are then used to treat an oscillator with two feedback loops and it is found that oscillations are possible even if both Hill coefficients are equal to one.