Purkinje neuron network (Zang et al. 2020)

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Accession:266799
Both spike rate and timing can transmit information in the brain. Phase response curves (PRCs) quantify how a neuron transforms input to output by spike timing. PRCs exhibit strong firing-rate adaptation, but its mechanism and relevance for network output are poorly understood. Using our Purkinje cell (PC) model we demonstrate that the rate adaptation is caused by rate-dependent subthreshold membrane potentials efficiently regulating the activation of Na+ channels. Then we use a realistic PC network model to examine how rate-dependent responses synchronize spikes in the scenario of reciprocal inhibition-caused high-frequency oscillations. The changes in PRC cause oscillations and spike correlations only at high firing rates. The causal role of the PRC is confirmed using a simpler coupled oscillator network model. This mechanism enables transient oscillations between fast-spiking neurons that thereby form PC assemblies. Our work demonstrates that rate adaptation of PRCs can spatio-temporally organize the PC input to cerebellar nuclei.
Reference:
1 . Zang Y, Hong S, De Schutter E (2020) Firing rate-dependent phase responses of Purkinje cells support transient oscillations. Elife [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell; Realistic Network;
Brain Region(s)/Organism: Cerebellum;
Cell Type(s): Cerebellum Purkinje GABA cell;
Channel(s):
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: NEURON; MATLAB;
Model Concept(s): Phase Response Curves; Action Potentials; Spatio-temporal Activity Patterns; Synchronization; Action Potential Initiation; Oscillations;
Implementer(s): Zang, Yunliang ; Hong, Sungho [shhong at oist.jp];
Search NeuronDB for information about:  Cerebellum Purkinje GABA cell;
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PRC_network_code
figure2
figure2B
mod
abBK.mod *
apthreshold.mod *
CaP_Raman.mod *
cdp_spiny.mod *
cdp10AIS.mod *
cdp20N_FD2.mod *
cdp4N.mod *
distr.mod *
ihnew.mod *
kv11.mod *
Kv1A.mod *
kv3.mod *
Kv34.mod *
kv4hybrid2.mod *
kv4s.mod *
mslo.mod *
nap.mod *
peak.mod *
pkjlk.mod *
rsgold.mod *
SK2.mod *
syn2.mod *
TCa.mod *
                            
: this model is built-in to neuron with suffix syn2

COMMENT
synaptic current with exponential rise and decay conductance defined by
        i = g * (v - e)      i(nanoamps), g(micromhos);
        where
         g = 0 for t < onset and
         g=amp*((1-exp(-(t-onset)/tau0))-(1-exp(-(t-onset)/tau1)))
          for t > onset
ENDCOMMENT
					       
INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)}

NEURON {
	POINT_PROCESS syn2
	RANGE onset, tau0, tau1, gmax, e, i, myv
	NONSPECIFIC_CURRENT i
}
UNITS {
	(nA) = (nanoamp)
	(mV) = (millivolt)
	(umho) = (micromho)
}

PARAMETER {
	onset=0  (ms)
	tau0=0.2 (ms)
	tau1=3.0 (ms)
	gmax=0 	 (umho)
	e=0	 (mV)
	v	 (mV)
}

ASSIGNED { i (nA)  g (umho) myv (mV)}

LOCAL   a[2]
LOCAL   tpeak
LOCAL   adjust
LOCAL   amp

BREAKPOINT {
	myv = v
        g = cond(t)
	i = g*(v - e)
}

FUNCTION myexp(x) {
	if (x < -100) {
	myexp = 0
	}else{
	myexp = exp(x)
	}
}

FUNCTION cond(x) {
	tpeak=tau0*tau1*log(tau0/tau1)/(tau0-tau1)
	adjust=1/((1-myexp(-tpeak/tau0))-(1-myexp(-tpeak/tau1)))
	amp=adjust*gmax
	if (x < onset) {
		cond = 0
	}else{
		a[0]=1-myexp(-(x-onset)/tau0)
		a[1]=1-myexp(-(x-onset)/tau1)
		cond = amp*(a[0]-a[1])
	}
}

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