Journal article Open Access

Dimensional reduction in networks of non- Markovian spiking neurons: Equivalence of synaptic filtering and heterogeneous propagation delays

Mattia, Maurizio; Biggio, Matteo; Galluzzi, Andrea; Storace, Marco

Understanding the collective behavior of the intricate web of neurons composing a brain is one of the most challenging and complex tasks of modern neuroscience. Part of this complexity resides in the distributed nature of the interactions between the network components: for instance, the neurons transmit their messages (through spikes) with delays, which are due to different axonal lengths (i.e., communication distances) and/or noninstantaneous synaptic transmission. In developing effective network models, both of these aspects have to be taken into account. In addition, a satisfactory description level must be chosen as a compromise between simplicity and faithfulness in reproducing the system behavior. Here we propose a method to derive an effective theoretical description - validated through network simulations at microscopic level - of the neuron population dynamics in many different working conditions and parameter settings, valid for any synaptic time scale. In doing this we assume relatively small instantaneous fluctuations of the input synaptic current. As a by-product of this theoretical derivation, we prove analytically that a network with non-instantaneous synaptic transmission with fixed spike delivery delay is equivalent to a network characterized by a suited distribution of spike delays and instantaneous synaptic transmission, the latter being easier to treat.

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