Theory of Complex Systems and Neurophysics

Stochastic neural spiking

Single neurons are complex systems showing a spontaneous spiking activity, the statistics of which can be captured by such measures as the interspike interval density or the intervals' correlation coefficients. We use simple neuron models that incorporate some of the complicating features of the neural dynamics:

• channel noise and spike frequency adaptation (Schwalger et al. 2010, Schwalger and Lindner 2013, 2015, Shiau et al. 2015)
• up/down states (Müller-Hansen et al. 2015, Droste and Lindner 2017b)
• shot noise (Droste and Lindner 2017a)
• temporally correlated Gaussian fluctuations (Bauermeister et al. 2013, Schwalger et al. 2015)

By means of analytical calculations and numerical simulations, we study how these features of neural dynamics shape neural firing statistics. In some cases, our results also allow to conclude physiological parameters from a given firing statistics that are otherwise inaccessible (e.g. in Fisch et al. 2012 and Bauermeister et al. 2013).