Class-II neurons display a higher degree of stochastic synchronization than class-I neurons

Abstract

We describe the relationship between the shape of the phase-resetting curve (PRC) and the degree of stochastic synchronization observed between a pair of uncoupled general oscillators receiving partially correlated Poisson inputs in addition to inputs from independent sources. We use perturbation methods to derive an expression relating the shape of the PRC to the probability density function (PDF) of the phase difference between the oscillators. We compute various measures of the degree of synchrony and cross correlation from the PDF's and use the same to compare and contrast differently shaped PRCs, with respect to their ability to undergo stochastic synchronization. Since the shape of the PRC depends on underlying dynamical details of the oscillator system, we utilize the results obtained from the analysis of general oscillator systems to study specific models of neuronal oscillators. It is shown that the degree of stochastic synchronization is controlled both by the firing rate of the neuron and the membership of the PRC (type I or type II). It is also shown that the circular variance for the integrate and fire neuron and the generalized order parameter for a hippocampal interneuron model have a nonlinear relationship to the input correlation.

Synchronization dynamics of two coupled neural oscillators receiving shared and unshared noisy stimuli

“…In the presence of coupling, neurons with type II PRC exhibit a higher degree of synchrony than type I PRC (results not shown, but a fair comparison can be made between Figs. 1(c) and 3(a)), which is consistent with the results of Marella and Ermentrout (2008) who considered a similar system without coupling. Unshared noise can result in asynchronous/anti-phase behavior even when the coupling is synchronous.…”

“…They also analyzed the system with moderate to strong synaptic coupling. Previous studies in uncoupled systems have shown shared noise can enhance synchrony (Teramae and Tanaka 2004;Galán et al 2007;Nakao et al 2007;Marella and Ermentrout 2008). Thus, the synchronization dynamics of two coupled neural oscillators receiving shared and unshared noise is a natural thing to study.…”

“…Shared inputs will force uncoupled neural oscillators to synchronize (Teramae and Tanaka 2004;Galán et al 2007;Nakao et al 2007;Marella and Ermentrout 2008), and the degree of synchrony increases with the amount of shared input. This has also been verified experimentally in olfactory bulb neurons by Galán et al (2006).…”

Dispersal and noise: Various modes of synchrony in ecological oscillators

“…al. [20], based on the theory of noise-induced phase synchronization [31,37,10,29,26,38,22]. The latter is an extension of phase-reduction methods to stochastic limit cycle oscillators that provides an analytical framework for studying the synchronisation of an ensemble of oscillators driven by a common randomly fluctuating input; in the case of the Moran effect such an input would be due to environmental fluctuations.…”

Efficient estimation of phase-response curves via compressive sensing

“…In a weakly coupled neural network, the PRCs of the individual neurons determine the interactions and many aspects of the network dynamics can thereby be inferred (Ermentrout et al 2001;Hansel et al 1995;Oprisan et al 2004;Smeal et al 2010;Teramae and Fukai 2008). The PRC has also been used to show how synchrony is generated within a population of uncoupled oscillators receiving common noise input (Abouzeid and Ermentrout 2009;Goldobin and Pikovsky 2005;Marella and Ermentrout 2008;Nakao et al 2005;Teramae and Tanaka 2004).…”