Phase response curves firing rate dependency of rat purkinje neurons in vitro (Couto et al 2015)

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NEURON implementation of stochastic gating in the Khaliq-Raman Purkinje cell model. NEURON implementation of the De Schutter and Bower model of a Purkinje Cell. Matlab scripts to compute the Phase Response Curve (PRC). LCG configuration files to experimentally determine the PRC. Integrate and Fire models (leaky and non-leaky) implemented in BRIAN to see the influence of the PRC in a network of unconnected neurons receiving sparse common input.
1 . Couto J, Linaro D, De Schutter E, Giugliano M (2015) On the firing rate dependency of the phase response curve of rat Purkinje neurons in vitro. PLoS Comput Biol 11:e1004112 [PubMed]
2 . Linaro D, Couto J, Giugliano M (2014) Command-line cellular electrophysiology for conventional and real-time closed-loop experiments. J Neurosci Methods 230:5-19 [PubMed]
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Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell;
Brain Region(s)/Organism:
Cell Type(s): Cerebellum Purkinje GABA cell;
Gap Junctions:
Simulation Environment: NEURON; MATLAB; Brian; LCG; Python;
Model Concept(s): Phase Response Curves;
Implementer(s): Couto, Joao [jpcouto at];
Search NeuronDB for information about:  Cerebellum Purkinje GABA cell;
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 
coherence unaffected.
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 "" 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.