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
figure4
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abBK.mod *
apthreshold.mod *
CaP_Raman.mod *
cdp_spiny.mod *
cdp10AIS.mod *
cdp20N_FD2.mod *
cdp4N.mod *
distr.mod *
ihnew.mod *
Isinunoisy.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 *
job_script *
                            
TITLE P-type calcium channel

COMMENT

According to Benton&Raman data
lower threshold but relatively large time constant compared with Sungho's model (According to Bruce Bean)
Also the ssa is steep. In this model, it is better not to shift the SSA to the left.
time speeded up by 2 times May 9 2016 (no longer)
ENDCOMMENT

NEURON {
	SUFFIX newCaP
	USEION ca READ cai, cao WRITE ica
	RANGE pcabar, ica,vshift,kt
	GLOBAL minf, taum
	GLOBAL monovalConc, monovalPerm
:	THREADSAFE
}

UNITS {
	(mV) = (millivolt)
	(mA) = (milliamp)
	(nA) = (nanoamp)
	(pA) = (picoamp)
	(S)  = (siemens)
	(nS) = (nanosiemens)
	(pS) = (picosiemens)
	(um) = (micron)
	(molar) = (1/liter)
	(mM) = (millimolar)		
}

CONSTANT {
	q10 = 3
	F = 9.6485e4 (coulombs)
	R = 8.3145 (joule/kelvin)

:	cv = 19 (mV)
:	ck = 5.5 (mV)
    cv = 30.5 (mV)
    ck = 4.113 (mV)
}

PARAMETER {
	v (mV)
	celsius (degC)

	cai (mM)
	cao (mM)
    vshift =0
	pcabar = 6e-5 (cm/s)
	monovalConc = 140 (mM)
	monovalPerm = 0
	kt=1
}

ASSIGNED {
	qt
	ica (mA/cm2)
      minf 
	taum (ms)
	T (kelvin)
	E (volt)
	zeta
}

STATE { m }

INITIAL {
	qt = q10^((celsius-22 (degC))/10 (degC))
	T = kelvinfkt( celsius )
	rates(v)
	m = minf
}

BREAKPOINT {
	SOLVE states METHOD cnexp
	ica = (1e3) * pcabar * m * ghk(v, cai, cao, 2)
}

DERIVATIVE states {
	rates(v)
	m' = (minf-m)/taum
}

FUNCTION ghk( v (mV), ci (mM), co (mM), z )  (coulombs/cm3) { 
	E = (1e-3) * v
      zeta = (z*F*E)/(R*T)	
	
	: ci = ci + (monovalPerm) * (monovalConc) :Monovalent permeability

	if ( fabs(1-exp(-zeta)) < 1e-6 ) {
	ghk = (1e-6) * (z*F) * (ci - co*exp(-zeta)) * (1 + zeta/2)
	} else {
	ghk = (1e-6) * (z*zeta*F) * (ci - co*exp(-zeta)) / (1-exp(-zeta))
	}
}

PROCEDURE rates( v (mV) ) {
	minf = 1 / ( 1 + exp(-(v+cv+vshift)/ck) )
	taum = (1e3) * taumfkt(v)/qt/kt
}

FUNCTION taumfkt( v (mV) ) (s) {
	UNITSOFF

    taumfkt = (0.0002 + 0.0007031 * exp(-((v+30+vshift)/14)^2))				:Raman data
:     taumfkt = (0.00002 + 0.00065 * exp(-((v+vshift)/40)^2))								:data from Biophysical Journal 108,2015: 578-584 David Naranjo
	UNITSON
}

FUNCTION kelvinfkt( t (degC) )  (kelvin) {
	UNITSOFF
	kelvinfkt = 273.19 + t
	UNITSON
}

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