We provide a toy example network of synaptically uncoupled model
neurons that fire tonically and receive episodic common inputs.
Since an accurate mathematical model capable of reproducing our
experimental data is still missing, we resorted to artificially
altering the PRC of a simplified model neuron, by changing its
sub-threshold voltage dynamics (alternating between a leaky and a
non-leaky LIF model).
When the units of such a network behave as perfect integrators
(i.e., phase-independent PRC, such as PCs at low firing rates),
the episodic arrival of common inputs induces an identical phase
advance across the network, leaving their low population firing
When the units display phase-dependent PRCs (i.e., such as PCs firing
at high firing rates), the same common inputs activation induces
unequal phase shifts across the network, breaking the asynchronous
state and leading to a synchronization of neuronal firing.
This phenomenon is not novel and is reminiscent of the collective
properties of perfect resonators (see: Ermentrout et al. 2007). While
this is of course only a toy model, it may helps us to illustrate the
impact of PC response properties on network-level phenomena, as a
putative way to alternatively relay downstream or ignore common
inputs, depending only on the PCs firing rate.
The "integrateAndFirePRC.py" script is a Python script with BRIAN code
to produce the figure in the "lif_prc_study.pdf" file.
The IPython Notebook version of the same script is also available.
You can launch it by doing: "ipython notebook --pylab=inline" and
loading the *.pynb file from the browser.