The activity of neuronal networks can exhibit periods of bursting, the properties of which remain unclear. To study the bursting dynamics of a network , we develop a new stochastic model based on synaptic properties that also accounts for afterhyperpolarization , which shapes the end of a burst. A stochastic perturbation of this system leads to a succession of bursts and interbursts and we characterize their durations using a three dimensional phase-space analysis and numerical simulations. The phase-space contains three critical points (one attractor and two saddles) separated by a two-dimensional stable manifold \Sigma. Bursting is defined by long deterministic excursions outside the basin of attraction, while the interburst duration is defined by the escape induced by random fluctuations. To characterize the distribution of the burst durations, we determine the distribution of exit points located on the two-dimensional separatrix \Sigma . In addition, we compute analytically the mean burst and AHP durations using a linearization approximation of the dynamical system . Finally, we explore how various parameters such as the network connectivity and the afterhyperpolarization characteristics influence bursting and AHP dynamics . To conclude , this new model allows us to better characterize the role of various physiological parameters on bursting dynamics .
In the absence of inhibition, excitatory neuronal networks can alternate between bursts and interburst intervals (IBI), with heterogeneous length distributions. As this dynamic remains unclear, especially the durations of each epoch , we develop here a bursting model based on synaptic depression and facilitation that also accounts for afterhyperpolarization (AHP), which is a key component of IBI. The framework is a novel stochastic three dimensional dynamical system perturbed by noise: numerical simulations can reproduce a succession of bursts and interbursts . Each phase corresponds to an exploration of a fraction of the phase-space , which contains three critical points (one attractor and two saddles) separated by a two-dimensional stable manifold \Sigma. We show here that bursting is defined by long deterministic excursions away from the attractor, while IBI corresponds to escape induced by random fluctuations. We show that the variability in the burst durations, depends on the distribution of exit points located on \Sigma that we compute using WKB and the method of characteristics . Finally, to better characterize the role of several parameters such as the network connectivity or the AHP time scale, we compute analytically the mean burst and AHP durations in a linear approximation . To conclude the distribution of bursting and IBI could result from synaptic dynamics modulated by AHP .
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and the afterhyperpolarization characteristics influence bursting and AHP dynamics
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, this new model allows us to better characterize the role of various physiological parameters on bursting dynamics
the distribution of bursting and IBI could result from synaptic dynamics modulated by AHP