While these reduced models of networks comprised of aEIF point neurons have proven very useful in the analysis of network dynamics, they are unable to distinguish basal-somatic from apical dendritic inputs and cannot account for an extracellular field because of their lack of spatial detail. Therefore, we employ a pyramidal neuron model that comprises two compartments to capture the above effects in a biophysically minimalistic way [Ladenbauer and Obermayer, 2019]. Using an analytical approach parameters are fitted to reproduce the response properties of a spatial model neuron and explore the stochastic spiking dynamics of single cells and large networks. Furthermore, a mean-field reduction is developed, based on the above Fokker-Planck approach, that allows for an accurate approximation of the firing rate dynamics of a network of coupled excitatory and inhibitory cells [Ladenbauer and Obermayer, 2019].
[Augustin et al., 2013] Augustin, M., Ladenbauer, J., and Obermayer, K. (2013). How adaptation shapes spike rate oscillations in recurrent neuronal networks. Frontiers in Computational Neuroscience.
[Augustin et al., 2017] Augustin, M., Ladenbauer, J., Baumann, F., & Obermayer, K. (2017). Low-dimensional spike rate models derived from networks of adaptive integrate-and-fire neurons: comparison and implementation. PLoS Computational Biology, 13(6), e1005545.
[Brette and Gerstner, 2005] Brette, R. and Gerstner, W. (2005). Adaptive exponential integrate-and-fire model as an effective description of neuronal activity. Journal of Neurophysiology, 94(5):3637-3642.
[Cakan and Obermayer, 2019] Cakan, C., & Obermayer, K. (2019). State-dependent effects of electrical stimulation on populations of excitatory and inhibitory neurons. arXiv preprint arXiv:1906.00676.
[Ladenbauer et al., 2013] Ladenbauer, J., Augustin, M., and Obermayer, K. (2013). How adaptation currents change threshold, gain, and variability of neuronal spiking. Journal of Neurophysiology, 111(5):939-953.
[Ladenbauer and Obermayer, 2019] Ladenbauer, J., & Obermayer, K. (2019). Weak electric fields promote resonance in neuronal spiking activity: Analytical results from two-compartment cell and network models. PLoS Computational Biology, 15(4), e1006974.
[Naud et al., 2008] Naud, R., Marcille, N., Clopath, C., and Gerstner, W. (2008). Firing patterns in the adaptive exponential integrate-and-fire model. Biological Cybernetics, 99(4-5), 335.
[Touboul and Brette, 2008] Touboul, J., and Brette, R. (2008). Dynamics and bifurcations of the adaptive exponential integrate-and-fire model. Biological Cybernetics, 99(4-5):319.