Unifying framework for neuronal assembly dynamics.

Starting from single, spiking neurons, we derive a system of coupled differential equations for a description of the dynamics of pools of extensively many equivalent neurons. Contrary to previous work, the derivation is exact and takes into account microscopic properties of single neurons, such as axonal delays and refractory behavior. Simulations show a good quantitative agreement with microscopically modeled pools of spiking neurons. The agreement holds both in the quasistationary and nonstationary dynamical regimes, including fast transients and oscillations. The model is compared with other pool models based on differential equations. It turns out that models of the graded-response category can be understood as a first-order approximation of our pool dynamics. Furthermore, the present formalism gives rise to a system of equations that can be reduced straightforwardly so as to gain a description of the pool dynamics to any desired order of approximation. Finally, we present a stability criterion that is suitable for handling pools of neurons. Due to its exact derivation from single-neuron dynamics, the present model opens simulation possibilities for studies that rely upon biologically realistic large-scale networks composed of assemblies of spiking neurons.