A two-variable model of somatic-dendritic interactions in a bursting neuron.

Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, ON, Canada, K1N 6N5.
Bulletin of Mathematical Biology (Impact Factor: 2.02). 10/2002; 64(5):829-60. DOI: 10.1006/bulm.2002.0303
Source: PubMed

ABSTRACT We present a two-variable delay-differential-equation model of a pyramidal cell from the electrosensory lateral line lobe of a weakly electric fish that is capable of burst discharge. It is a simplification of a six-dimensional ordinary differential equation model for such a cell whose bifurcation structure has been analyzed (Doiron et al., J. Comput. Neurosci., 12, 2002). We have modeled the effects of back-propagating action potentials by a delay, and use an integrate-and-fire mechanism for action potential generation. The simplicity of the model presented here allows one to explicitly derive a two-dimensional map for successive interspike intervals, and to analytically investigate the effects of time-dependent forcing on such a model neuron. Some of the effects discussed include 'burst excitability', the creation of resonance tongues under periodic forcing, and stochastic resonance. We also investigate the effects of changing the parameters of the model.

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    ABSTRACT: Pyramidal neurons in the electrosensory lateral line lobe (ELL) of weakly electric fish activate in an environment of time-varying electric fields, which are generated by the fish itself, while how these pyramidal neurons would behave or what kinds of firing patterns these neurons would produce under different electric fields is still unclear. In this research, the firing behaviors of ELL pyramidal neuron under DC and AC electric field stimulus are investigated in a two-compartment neuron model. By means of numerical simulations we show that firing patterns of the model ELL pyramidal neuron are much diverse under different values of DC electric field, and neuronal spike frequency exhibits a monotone decreasing trend with the linearly increased DC fields, moreover, the transition mode between these firing patterns with the variation of DC electric fields demonstrates an explicit periodic route. While for AC electric fields, neuronal firing frequency periodically transforms with the increase of AC frequency, particularly, a special transition pattern (from multi-period bursting to spiking) repeatedly appears with the change of AC frequency. Our simulation results indicate that ELL pyramidal neurons fire dynamically under the time-varying electric fields, the diversity of firing patterns and their periodic transition modes may imply the potential roles of these dynamical firings in the coding strategy of sensory information processing.
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    ABSTRACT: Bursting activity is an interesting feature of the temporal organization in many cell firing patterns. This complex behavior is characterized by clusters of spikes (action potentials) interspersed with phases of quiescence. As shown in experimental recordings, concerning the electrical activity of real neurons, the analysis of bursting models reveals not only patterned periodic activity but also irregular behavior [1] and [2]. The interpretation of experimental results, particularly the study of the influence of coupling on chaotic bursting oscillations, is of great interest from physiological and physical perspectives. The inability to predict the behavior of dynamical systems in presence of chaos suggests the application of chaos control methods, when we are more interested in obtaining regular behavior. In the present article, we focus our attention on a specific class of biophysically motivated maps, proposed in the literature to describe the chaotic activity of spiking–bursting cells [Cazelles B, Courbage M, Rabinovich M. Anti-phase regularization of coupled chaotic maps modelling bursting neurons. Europhys Lett 2001;56:504–9]. More precisely, we study a map that reproduces the behavior of a single cell and a map used to examine the role of reciprocal inhibitory coupling, specially on two symmetrically coupled bursting neurons. Firstly, using results of symbolic dynamics, we characterize the topological entropy associated to the maps, which allows us to quantify and to distinguish different chaotic regimes. In particular, we exhibit numerical results about the effect of the coupling strength on the variation of the topological entropy. Finally, we show that complicated behavior arising from the chaotic coupled maps can be controlled, without changing of its original properties, and turned into a desired attracting time periodic motion (a regular cycle). The control is illustrated by an application of a feedback control technique developed by Romeiras et al. [Romeiras FJ, Grebogi C, Ott E, Dayawansa WP. Controlling chaotic dynamical systems. Physica D 1992;58:165–92]. This work provides an illustration of how our understanding of chaotic bursting models can be enhanced by the theory of dynamical systems.
    Communications in Nonlinear Science and Numerical Simulation 01/2009; · 2.77 Impact Factor
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    ABSTRACT: Prediction and cancelation of redundant information is an important feature that many neural systems must display in order to efficiently code external signals. We develop an analytic framework for such cancelation in sensory neurons produced by a cerebellar-like structure in wave-type electric fish. Our biologically plausible mechanism is motivated by experimental evidence of cancelation of periodic input arising from the proximity of conspecifics as well as tail motion. This mechanism involves elements present in a wide range of systems: (1) stimulus-driven feedback to the neurons acting as detectors, (2) a large variety of temporal delays in the pathways transmitting such feedback, responsible for producing frequency channels, and (3) burst-induced long-term plasticity. The bursting arises from back-propagating action potentials. Bursting events drive the input frequency-dependent learning rule, which in turn affects the feedback input and thus the burst rate. We show how the mean firing rate and the rate of production of 2- and 4-spike bursts (the main learning events) can be estimated analytically for a leaky integrate-and-fire model driven by (slow) sinusoidal, back-propagating and feedback inputs as well as rectified filtered noise. The effect of bursts on the average synaptic strength is also derived. Our results shed light on why bursts rather than single spikes can drive learning in such networks "online", i.e. in the absence of a correlative discharge. Phase locked spiking in frequency specific channels together with a frequency-dependent STDP window size regulate burst probability and duration self-consistently to implement cancelation.
    Neural networks: the official journal of the International Neural Network Society 01/2013; · 1.88 Impact Factor

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