Network dynamics of spiking neurons with adaptation

How to describe circuit level cortical dynamics? � Cortex is layered. � Few neuron types per layer. � Each type in a layer forms a population. � Populations have finite size. Here we derive a theory for such interacting populations, exploiting that neurons can be treated as quasi-renewal point processes, even in presence of spike-frequency adaptation. For a population of N neurons with � spike trains s i (t) � population activity A(t) = 1 N � N i s i (t) � inter-spike-interval (ISI) probability density P(t|ˆt) we have (cf. [4]) A(t) = � t −∞ P(t|ˆt)A(ˆ t)d ˆ t � �� � a(t) +δA(t) with fluctuations δA(t) that obey (for τ ≥ 0, conditioned on A(ˆ t < t)) �δA(t + τ)δA(t)� = N −1 a(t) δ(τ) − N −1 � t −∞ P(t + τ | ˆ t)P(t|ˆt)A(ˆ t)d ˆ t Because of synaptic coupling, external inputs and adaptation, P(t|ˆt) depends on the past activity and on time (inhomogeneous renewal point process).