On periodic responses generated by a degenerate analog neuron model with periodic inputs

Periodic responses to periodically varying stimulating pulse sequences are mathematically described for a degenerate analog neuron model. The model used was derived by Yoshizawa et al. (1982) in their investigation of the state transition of an electronic model using a tunnel diode in a degenerate case. Periodic responses to constant pulse sequences for the model were described by them. In this paper, it is shown that periodic responses to periodically varying pulse sequences for the model are identical with those which the author previously described for a discrete neuron model.     

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.     

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.     

Voltage transients in neuronal dendritic trees.

An analytical method is outlined for calculating the passive voltage transient at each point in an extensively branched neuron model for arbitrary current injection at a single branch. The method is based on a convolution formula that employs the transient response function, the voltage response to an instantaneous pulse of current. For branching that satisfies Rall's equivalent cylinder constraint, the response function is determined explicitly. Voltage transients, for a brief current injected at a branch terminal, are evaluated at several locations to illustrate the attenuation and delay characteristics of passive spread. A comparison with the same transient input terminal input, the fraction of input charge dissipated by various branches in the neuron model is illustrated. These fractions are independent of the input time course. For transient synaptic conductance change at a single branch terminal, a numerical example demonstrates the nonlinear effect of reduced synaptic driving potential. The branch terminal synaptic input is compared with the same synaptic conductance input applied to the soma on the basis of excitatory postsynaptic potential amplitude at the soma and charge delivered to the soma.     

A model of a thalamic neuron

We modify our recent three equilibrium-point model of neuronal bursting by a means of a small deformation of the nullclines in the x-y phase plane to give a model that can have as many as five equilibrium points. In this model the middle stable equilibrium point (e.p.) is separated from the outer stable and unstable e.ps by two saddle points. If the system is started at rest at the middle stable e.p. it has the following complex properties: A short suprathreshold current pulse switches the model from a silent state to a bursting state, or to give a single burst, depending on the choice of parameters. A subthreshold depolarizing current step gives a passive response at rest, but if the model is either constantly hyperpolarized or constantly depolarized, then the same current step gives different active responses. At a hyperpolarized level this consists of a burst response that shows refractoriness. At a depolarized level it consists of tonic firing with a linear frequency--current relationship. Hyperpolarization from rest is followed by post-inhibitory rebound. The model responds in a unique and characteristic way to an applied current ramp. These properties are very similar to those that have been recently recorded intracellularly from neurons in the mammalian thalamus. In the x-y phase plane our models of the repetitively firing neuron, the bursting neuron and the thalamic neuron form a progression of models in which the y nullcline in the subthreshold region is deformed once to give the burst neuron model, and a second time to give the thalamic neuron model. Each deformation can be interpreted as corresponding to the inclusion of a slow inward current in the model. As these currents are included so the associated firing properties increase in complexity.     

Modelling the isometric force response to multiple pulse stimuli in locust skeletal muscle

An improved model of locust skeletal muscle will inform on the general behaviour of invertebrate and mammalian muscle with the eventual aim of improving biomedical models of human muscles, embracing prosthetic construction and muscle therapy. In this article, the isometric response of the locust hind leg extensor muscle to input pulse trains is investigated. Experimental data was collected by stimulating the muscle directly and measuring the force at the tibia. The responses to constant frequency stimulus trains of various frequencies and number of pulses were decomposed into the response to each individual stimulus. Each individual pulse response was then fitted to a model, it being assumed that the response to each pulse could be approximated as an impulse response and was linear, no assumption were made about the model order. When the interpulse frequency (IPF) was low and the number of pulses in the train small, a second-order model provided a good fit to each pulse. For moderate IPF or for long pulse trains a linear third-order model provided a better fit to the response to each pulse. The fit using a second-order model deteriorated with increasing IPF. When the input comprised higher IPFs with a large number of pulses the assumptions that the response was linear could not be confirmed. A generalised model is also presented. This model is second-order, and contains two nonlinear terms. The model is able to capture the force response to a range of inputs. This includes cases where the input comprised of higher frequency pulse trains and the assumption of quasi-linear behaviour could not be confirmed.     

Response of a neuronal membrane to applied sinusoidal currents

The membrane model of Connor and Stevens was used to calculate the response of a neuron to an injected sinusoidal current. This stimulating current simulates the effects of cell exposure to incident time-harmonic electromagnetic fields. The theoretical results obtained with this model were compared with intracellular recordings carried out during the injection of a sinusoidal transmembrane current through a single microelectrode. Experimental and theoretical data were substantially in agreement for current amplitudes that can be induced by actual exposure conditions.     

猫体感皮层神经元对同时刺激隐神经的A类和C类纤维的反应型式

记录了麻痹猫的体感皮层(SI)神经元的自发和隐神经的A类和C类纤维传入诱发放电(A-ED和C-ED)。用NCCVF分析神经元放电。结果表明,SI区神经元对同时刺激隐神经的A类和C类纤维的反应呈多种型式:(1)A-ED和C-ED共存,包括Ⅰ.A-ED和C-ED始终相互伴随出现;Ⅱ.在刺激之初,只出现A-ED,但是,当阻断A类纤维传入并由C类纤维传入诱发神经元放电后,再同时刺激A类和C类纤维时,A-ED和C-ED便同时出现。(2)A-ED制约C-ED,特点是,只要A-ED存在,C/ED就不出现。只有阻断A类纤维传入后,C-ED才产生。(3)单一A-ED,不管在什么刺激条件下,这类神经元都只有A-ED,而不产生C-ED 结论:根据反应型式的不同,可将SI区的神经元分为Ⅰ.A类和C类纤维传入同时驱动的神经元;Ⅱ.A-ED制约C-ED的神经元;Ⅲ.只由A类纤维传入驱动的神经元。     

Extracellular transduction events under pulsed stimulation in moth olfactory sensilla

In natural conditions, pheromones released continuously by female moths are broken in discontinuous clumps and filaments. These discontinuities are perceived by flying male moths as periodic variations in the concentration of the stimulus, which have been shown to be essential for location of females. We study analytically and numerically the evolution in time of the activated pheromone-receptor (signaling) complex in response to periodic pulses of pheromone. The 13-reaction model considered takes into account the transport of pheromone molecules by pheromone binding proteins (PBP), their enzymatic deactivation in the perireceptor space and their interaction with receptors at the dendritic membrane of neurons in Antheraea polyphemus sensitive to the main pheromone component. The time-averaged and periodic properties of the temporal evolution of the signaling complex are presented, in both transient and steady states. The same time-averaged response is shown to result from many different pulse trains and to depend hyperbolically on the time-averaged pheromone concentration in air. The dependency of the amplitude of the oscillations of the signaling complex on pulse characteristics, especially frequency, suggests that the model can account for the ability of the studied type of neuron to resolve repetitive pulses up to 2 Hz, as experimentally observed. Modifications of the model for resolving pulses up to 10 Hz, as found in other neuron types sensitive to the minor pheromone components, are discussed.     

Response of a pacemaker neuron model to stochastic pulse trains

 We investigated the response of a pacemaker neuron model to trains of inhibitory stochastic impulsive perturbations. The model captures the essential aspect of the dynamics of pacemaker neurons. Especially, the model reproduces linearization by stochastic pulse trains, that is, the disappearance of the paradoxical segments in which the output firing rate of pacemaker neurons increases with inhibition rate, as the coefficient of variation of the input pulse train increases. To study the response of the model to stochastic pulse trains, we use a Markov operator governing the phase transition. We show how linearization occurs based on the spectral analysis of the Markov operator. Moreover, using Lyapunov exponents, we show that variable inputs evoke reliable firing, even in situations where periodic stimulation with the same mean rate does not. Received: 30 April 2001 / Accepted in revised form: 19 September 2001     

Possible interaction between synaptic and pacemaker mechanisms of electrical activity in bursting neurons of Helix pomatia

Membrane hyperpolarization induced by short pulses of inward current, by stimulation of the anal nerve, which leads to the appearance of a long IPSP in the neuron, and developing during the appearance of spontaneous IPSPs in the neuron was investigated in neuron RPa1 ofHelix pomatia. Short-term hyperpolarization of the neuron membrane by an inward current (10 msec) led to the development of self-maintained (regenerative) membrane hyperpolarization lasting several seconds. The amplitude and duration of regenerative hyperpolarization increased with an increase in amplitude and duration of the pulse of inward current. The time course of IPSPs arising spontaneously in the neuron and in response to stimulation of the anal nerve was similar to that of regenerative hyperpolarization evoked by a pulse of inward current. It is suggested that regenerative hyperpolarization associated with activation of endogenous mechanisms of regulation of the bursting activity of the neuron may be due not only to short-term membrane hyperpolarization of the test neuron by the electric current, but also to hyperpolarization occurring during IPSP generation.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 13, No. 1, pp. 67–74, January–February, 1981.     

Slow motor neuron stimulation of locust skeletal muscle: model and measurement

The isometric force response of the locust hind leg extensor tibia muscle to stimulation of a slow extensor tibia motor neuron is experimentally investigated, and a mathematical model describing the response presented. The measured force response was modelled by considering the ability of an existing model, developed to describe the response to the stimulation of a fast extensor tibia motor neuron and to also model the response to slow motor neuron stimulation. It is found that despite large differences in the force response to slow and fast motor neuron stimulation, which could be accounted for by the differing physiology of the fibres they innervate, the model is able to describe the response to both fast and slow motor neuron stimulation. Thus, the presented model provides a potentially generally applicable, robust, simple model to describe the isometric force response of a range of muscles.     

Reproducing bursting interspike interval statistics of the gustatory cortex

Cortical neurons in vivo generate highly irregular spike sequences. Recently, it was experimentally found that the local variation of interspike intervals, LV, is nearly constant for every spike sequence for the same neurons. On the contrary, the coefficient of variation, CV, varies over different spike sequences. Here, we first show that these characteristic features are also applicable in bursting spike sequences that are obtained from the rat gustatory cortex. Next, we show that the conventional leaky integrate-and-fire model does not fully account for reproducing these statistical features in data of real bursting spike sequences. We resolve this difficulty by proposing an alternative neuron model which is a reduction of the bursting neuron model involving the persistent sodium current. Our study implies that (1) the characteristic features of CV and LV are the results of the endogenous bursting and (2) the bursting behavior in the gustatory cortex is caused mainly by the persistent sodium current.     

Mathematical properties of responses of a neuron model

Recently, Nagumo and Sato proposed a mathematical neuron model in the form of a nonlinear difference equation and investigated its response characteristic. The result showed that the input-output relationship of the neuron model is quite complicated and takes the form of an extended Cantor's function. It also explained the unusual and unsuspected phenomenon found by Harmon in experimental studies with his transistor neuron model. — In this paper, a fraction representation of a sequence of pulses is proposed. A mathematical treatment of the same neuron model based on the representation gives the same result as in the previous paper. Moreover, many mathematical properties, including the one where the ratio of the number of 1's contained in a cycle of a sequence to the length of the cycle gives any rational number between 0 and 1, were obtained by investigating sequences generated by the model.     

A model cortical circuit for the storage of temporal sequences

Despite the fact that temporal information processing is of particular significance in biological memory systems, not much has yet been explored about how these systems manage to store temporal information involved in sequences of stimuli. A neural network model capable of learning and recalling temporal sequences is proposed, based on a neural mechanism in which the sequences are expanded into a series of periodic rectangular oscillations. Thus, the mathematical framework underlying the model, to some extent, is concerned with the Walsh function series. The oscillatory activities generated by the interplay between excitatory and inhibitory neuron pools are transmitted to another neuron pool whose role in learning and retrieval is to modify the rhythms and phases of the rectangular oscillations. Thus, a basic functional neural circuit involves three different neuron pools. The modifiability of rhythms and phases is incorporated into the model with the aim of improving the quality of the retrieval. Numerical simulations were conducted to show the characteristic features of the learning as well as the performance of the model in memory recall.     

Cholecystokinin and cholecystokinin antagonists enhance postsynaptic excitability in the dentate gyrus

The sulfated and unsulfated octapeptide cholecystokinin (CCK) sequences and the pancreatic CCK antagonists, CR 1409 and benzotript, were applied iontophoretically in the rat dentate gyrus granular layer while the response evoked by single pulse stimulation of the perforant path was recorded. The stimulating current was varied and the resulting relationship between the slope of the response (input) against the population spike amplitude (output) was used as a measure of excitability at the granule cell synapse. All four test compounds shifted the input/output curve to the left indicating an increase in postsynaptic excitability. These results thus imply that endogenous CCK acts at the central type of CCK receptor to modulate cortical input to granule cells by reducing the threshold for synaptic excitation.     

Temporally patterned pulse trains affect duration tuning characteristics of bat inferior collicular neurons

 This study examines the effect of temporally patterned pulse trains on duration tuning characteristics of inferior collicular neurons of the big brown bat, Eptesicus fuscus, under free-field stimulation conditions. Using a 50% difference between maximal and minimal responses as a criterion, the duration tuning characteristics of inferior collicular neurons determined with pulse trains of different pulse durations are described as band-pass, long-pass, short-pass, and all-pass. Each band-pass neuron discharged maximally to a specific pulse duration that was at least 50% larger than the neuron's responses to a long- and a short-duration pulse. In contrast, each long- or short-pass neuron discharged maximally to a range of long- or short-duration pulses that were at least 50% larger than the minimal responses. The number of impulses of an all-pass neuron never differed by more than 50%. When pulse trains were delivered at different pulse repetition rates, the number of short-pass and band-pass neurons progressively increased with increasing pulse repetition rates. The slope of the duration tuning curves also became sharper when determined with pulse trains at high pulse repetition rates. Possible mechanisms underlying these findings are discussed. Accepted: 25 August 1999     

Pressure sensation by an anterior pagoda neuron population distributed in multiple ganglia in the leech, Whitmania pigra

Sensory processing of pressure signals in the central nervous system of the leech, Whitmania pigra, was studied through the interaction between pressure sensory neurons and anterior pagoda neurons. The responses of anterior pagoda neurons to one pulse or a train of pulses in pressure sensory neurons were characterized by the latency and amplitude of excitatory postsynaptic potentials. Here we show that each pressure sensory neuron is able to activate all the anterior pagoda neurons throughout the leech central nervous system. The response patterns of all anterior pagoda neurons were appropriate to the pressure location: in the longitudinal direction the anterior pagoda neuron further away from the pressure sensory neuron had a smaller response with longer latency; inside each ganglion, the anterior pagoda neuron on the contralateral side had a larger response with shorter latency than that on the ipsilateral side. All anterior pagoda neurons excited by pressure sensory neurons comprised a parallel system in which each anterior pagoda neuron was independent from the others. The location information of pressure stimuli was represented through the response of all 40 anterior pagoda neurons covering the whole leech body with a specific pattern of latency and amplitude.