For the construction of large-scale networks, computationally tractable, yet in a defined sense still physiologically valid neuron models are often very desirable. In particular, these models should be able to predictively reproduce physiological measurements under very different input regimes in which neurons may operate, and thus generalize well to a broad range of inputs reflecting in-vivo situations. Moreover, they should be mathematically feasible to ensure a deep understanding of the underlying processes and mechanisms responsible for network phenomena observed. Here, an approach for fast in-vitro characterization and translation of single-cell data into simple adaptive neuron models and their use in mean-field networks is presented. While the first research focus is mainly on single cells, the second one bridges to the network level.
In a first step, a method to parameter estimation mainly based on standard f-I curves which are generated from in vitro recordings is described. To achieve a fast fitting procedure, an approximation to the adaptive exponential integrate-and-fire (AdEx) neuron that allows for closed-form expressions of the firing rate upon constant step currents is derived. The resulting fitting is completely automatized and two orders of magnitude faster compared to methods based on numerical integration of the differential equations. For a wide range of different input regimes, cell types and layers of the rodent prefrontal cortex, the model could predict spike times on test traces quite accurately within the bounds of physiological reliability. In order to derive cellular parameter distributions for the construction of cortical network models, the method is applied to a large pool of experimentally recorded cells. In a next step, the 2-dimensional Fokker-Planck (FP) equation and approximations based on the retrieval of the one-dimensional FP equation for the exponential integrate-and-fire neuron are derived in order to theoretically compute the firing rate of the AdEx upon fluctuating currents. The solutions of the Fokker-Planck equations are the basis for analyzing the stability, bifurcation types, transitions or the dynamics of mean-filed network states. Theoretical predictions closely agreed with the firing rate of the simulated cells fed with in-vivo-like synaptic noise. Extensions to input currents with realistic synaptic kinetics are also provided. Furthermore, preliminary results for a mean-field network comprising different neuron types is presented.