Abstract
On-off firing patterns, in which repetition of clusters of spikes are interspersed with epochs of subthreshold oscillations or quiescent states, have been observed in various nervous systems, but the dynamics of this event remain unclear. Here, we report that on-off firing patterns observed in three experimental models (rat sciatic nerve subject to chronic constrictive injury, rat CA1 pyramidal neuron, and rabbit blood pressure baroreceptor) appeared as an alternation between quiescent state and burst containing multiple period-1 spikes over time. Burst and quiescent state had various durations. The interspike interval (ISI) series of on-off firing pattern was suggested as stochastic using nonlinear prediction and autocorrelation function. The resting state was changed to a period-1 firing pattern via on-off firing pattern as the potassium concentration, static pressure, or depolarization current was changed. During the changing process, the burst duration of on-off firing pattern increased and the duration of the quiescent state decreased. Bistability of a limit cycle corresponding to period-1 firing and a focus corresponding to resting state was simulated near a sub-critical Hopf bifurcation point in the deterministic Morris—Lecar (ML) model. In the stochastic ML model, noise-induced transitions between the coexisting regimes formed an on-off firing pattern, which closely matched that observed in the experiment. In addition, noise-induced exponential change in the escape rate from the focus, and noise-induced coherence resonance were identified. The distinctions between the on-off firing pattern and stochastic firing patterns generated near three other types of bifurcations of equilibrium points, as well as other viewpoints on the dynamics of on-off firing pattern, are discussed. The results not only identify the on-off firing pattern as noise-induced stochastic firing pattern near a sub-critical Hopf bifurcation point, but also offer practical indicators to discriminate bifurcation types and neural excitability types.
Highlights
Identification of nonlinear dynamics in a single neuron or within a neuronal network is used to study neural coding mechanisms and integrated behaviors of a nervous system [1,2,3,4], and enables the depiction of complex oscillation patterns, such as periodic, chaotic or stochastic firing patterns [5,6,7,8,9,10,11,12]
Near a supercritical Hopf bifurcation point, an integer multiple firing pattern of which the interspike interval (ISI) exhibit a discrete distribution in ISIH and are approximate integer multiples of a basic ISI has been found to be induced by noise [21,22,23,24]
The dynamics of on-off firing patterns observed in three experimental models and in a theoretical stochastic ML model were investigated and compared
Summary
Identification of nonlinear dynamics in a single neuron or within a neuronal network is used to study neural coding mechanisms and integrated behaviors of a nervous system [1,2,3,4], and enables the depiction of complex oscillation patterns, such as periodic, chaotic or stochastic firing patterns [5,6,7,8,9,10,11,12]. Near a supercritical Hopf bifurcation point, an integer multiple firing pattern of which the ISIs exhibit a discrete distribution in ISIH and are approximate integer multiples of a basic ISI has been found to be induced by noise [21,22,23,24]. These stochastic firing patterns were found to be between period-1 firing and resting states as some biological parameters were changed [18,19,20,21,22,23,24]. Characteristics of the stochastic firing pattern simulated near a sub-critical Hopf bifurcation point remain unclear [25]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
