  Neural activity exhibits a vast range of timescales that can be several fold
larger than the membrane time constant of individual neurons. Two types of
mechanisms have been proposed to explain this conundrum. One possibility is
that large timescales are generated by a network mechanism based on positive
feedback, but this hypothesis requires fine-tuning of the synaptic connections.
A second possibility is that large timescales in the neural dynamics are
inherited from large timescales of underlying biophysical processes, two
prominent candidates being adaptive ionic currents and synaptic transmission.
How the timescales of these processes influence the timescale of the network
dynamics has however not been fully explored. To address this question, we
analyze large networks of randomly connected excitatory and inhibitory units
with additional degrees of freedom that correspond to adaptation or synaptic
filtering. We determine the fixed points of the systems, their stability to
perturbations and the corresponding dynamical timescales. Furthermore, we apply
dynamical mean field theory to study the temporal statistics of the activity in
the fluctuating regime, and examine how the adaptation and synaptic timescales
transfer from individual units to the whole population. Our overarching finding
is that synaptic filtering and adaptation in single neurons have very different
effects at the network level. Unexpectedly, the macroscopic network dynamics do
not inherit the large timescale present in adaptive currents. In contrast, the
timescales of network activity increase proportionally to the time constant of
the synaptic filter. Altogether, our study demonstrates that the timescales of
different biophysical processes have different effects on the network level, so
that the slow processes within individual neurons do not necessarily induce
slow activity in large recurrent neural networks.
