Subthreshold Dynamics in Periodically Stimulated Squid Giant Axons

Abstract

Action potentials resulting from periodic stimulation of nerve axons occur at intervals that are irregular at moderate stimulation frequencies. Histograms of the intervals are multimodal, as seen in stochastic resonance. At higher stimulation frequencies, the action potentials are suppressed entirely, leaving only subthreshold dynamics. Return maps constructed from data show that both types of response are governed by the same deterministic one-dimensional description, with an unstable subthreshold fixed point largely accounting for the irregular intervals at moderate stimulation frequencies.[S0031-9007(96)00200-1]

Dynamical Instability Determines the Effect of Ongoing Noise on Neural Firing

“…The values of the system parameters used in this study are a=0.753617, b=0.745338, and c=3.28076. These values are the same as those used in a prior study that showed the FN model produces responses similar to that of the squid giant axon to rapid pulsatile stimulation (Kaplan et al 1996).…”

“…A surprising feature of the response of the FN model is that it can be irregular even in the absence of ongoing noise (Ermentrout 1984;Feingold et al 1988;Lakshmanan 1988, 1994;Sato and Doi 1992;Rabinovitch et al 1994;Doi and Sato 1995;Kaplan et al 1996;Rabinovitch and Rogachevskii 1999). Here, we show that completely eliminating ongoing noise improves prominent aspects of the fit to the auditory nerve data.…”

“…The FN model has been used in many contexts, including applications involving electrical stimulation of the auditory nerve (Hochmair-Desoyer et al 1984). Most significantly for this paper, previous studies have shown that the FN model captures the main features of the squid axon's response to highrate stimulation (Sato and Doi 1992;Rabinovitch et al 1994;Doi and Sato 1995;Kaplan et al 1996). For example, temporal spiking patterns predicted by the noise-free FN model (Fig.…”

“…Dynamical instability was first demonstrated computationally in a model of atmospheric convection (Lorenz 1963), and has since been shown to occur in neural models (Aihara et al 1984;Ermentrout 1984;Feingold et al 1988;Lakshmanan 1988, 1994;Sato and Doi 1992;Rabinovitch et al 1994;Doi and Sato 1995;Kaplan et al 1996;Ichinose et al 1998;Rinzel and Ermentrout 1998;Othmer and Xie 1999;Rabinovitch and Rogachevskii 1999;Coombes and Osbaldestin 2000;Guckenheimer and Oliva 2002;Kosmidis and Pakdaman 2006;Lin 2006) and in empirical results from the squid giant axon when it is stimulated electrically at high rates Takahashi et al 1990;Kaplan et al 1996). In this study, we use a mathematical model of neuralspike generation to investigate the relative importance of the level of ongoing noise and the degree of dynamical instability in producing the neural firing irregularity observed in electrically stimulated auditory nerve fibers.…”

Period-adding bifurcations and chaos in a periodically stimulated excitable neural relaxation oscillator

“…One such instance has arisen recently that is related to the response of isolated single neurons to trains of repetitive pulsatile stimuli. It is known from several studies that with variation in the period of pulsatile stimulation an alternating pattern of period and chaotic response can be observed in a single excitable neuron [5][6][7][8][9]. In fact it is possible to observe a period adding bifurcation interspersed with windows of chaos.…”