Exponential decay characteristics of the stochastic integer multiple neural firing patterns

Abstract

Integer multiple neural firing patterns exhibit multi-peaks in inter-spike interval (ISI) histogram (ISIH) and exponential decay in amplitude of peaks, which results from their stochastic mechanisms. But in previous experimental observation that the decay in ISIH frequently shows obvious bias from exponential law. This paper studied three typical cases of the decay, by transforming ISI series of the firing to discrete binary chain and calculating the probabilities or frequencies of symbols over the whole chain. The first case is the exponential decay without bias. An example of this case was discovered on hippocampal CA1 pyramidal neuron stimulated by external signal. Probability calculation shows that this decay without bias results from a stochastic renewal process, in which the successive spikes are independent. The second case is the exponential decay with a higher first peak, while the third case is that with a lower first peak. An example of the second case was discovered in experiment on a neural pacemaker. Simulation and calculation of the second and third cases indicate that the dependency in successive spikes of the firing leads to the bias seen in decay of ISIH peaks. The quantitative expression of the decay slope of three cases of firing patterns, as well as the excitatory effect in the second case of firing pattern and the inhibitory effect in the third case of firing pattern are identified. The results clearly reveal the mechanism of the exponential decay in ISIH peaks of a number of important neural firing patterns and provide new understanding for typical bias from the exponential decay law.

Noise and Synchronization Analysis of the Cold-Receptor Neuronal Network Model

“…The corresponding data analyses suggest that noise can extend the dynamical behavior of the system [15,16]. Similar results can also be observed in experiment [17][18][19][20], which indicate that the nervous system may take advantage of the benefits of noises, including internal thermal fluctuations and external noisy inputs.…”

Dynamics of period-doubling bifurcation to chaos in the spontaneous neural firing patterns

“…In a series of studies (Ren et al 1997;Gu et al 2001Gu et al , 2003Gu et al , 2004Gu et al , 2011aWu et al 2008;Zheng et al 2009;Yang et al 2009;Wang et al 2010;Zhao et al 2010), the CCI model are used to be an experimental pacemaker to study the nonlinear dynamics of neural firing patterns, for instance, bifurcation and chaos. Experimental pacemakers were formed at the injured site of adult male Sprague-Dawley rat (200-300 g) sciatic nerve subjected to chronic ligature.…”

“…The explicit interpretation of Chay model was given in previous studies (Chay 1985;Gu et al 2001Gu et al , 2011a. v c is the reversal potential of Ca 2?…”

“…The dynamics of neural firing patterns and the bifurcations of firing patterns were of fundamental importance to the elucidation of neural coding mechanism (Braun et al 1994;Yang et al 2006). Various firing patterns, such as periodic firing, chaotic firing and stochastic resonance induced stochastic firing, were inspected in different nervous system (Chay 1985;Braun et al 1994;Ren et al 1997;Gu et al 2001Gu et al , 2003Gu et al , 2011aJia et al 2011;Du et al 2010;Guo 2011). The bifurcation process of firing patterns, such as period-adding bifurcation process with chaotic firing patterns or with stochastic firing patterns, were simulated in the theoretical models (Fan and Holden 1993;Fan and Chay 1994;Chay et al 1995) and observed in the experiments Li et al 2004;Lu et al 2009).…”

“…Three routes to chaos, period-doubling bifurcation, intermittency, and collapse of tori, were discovered in the pioneering studies on the neurons and axons, both stimulated by the external periodic stimulus (Hayashi et al 1982(Hayashi et al , 1983Aihara et al 1984;Aihara and Matsumoto 1987). In spontaneous neural firing patterns, the intermittency to chaos were observed in site of rat sciatic nerve as a pacemaker (called as an experimental neural pacemaker in a series of studies (Gu et al , 2011aWu et al 2008;Zheng et al 2009;Li et al 2004;Lu et al 2009). The intermittent chaos locates near a period-3 firing pattern, exhibiting non-smooth characteristics .…”