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
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TITLE SK2 multi-state model Cerebellum Golgi Cell Model

COMMENT
Now I have speed up the reaction rate by 3 to compensate the diffusion factor incorporated by Sergio.
Author:Sergio Solinas, Lia Forti, Egidio DAngelo
Based on data from: Hirschberg, Maylie, Adelman, Marrion J Gen Physiol 1998
Last revised: May 2007

Published in:
             Sergio M. Solinas, Lia Forti, Elisabetta Cesana, 
             Jonathan Mapelli, Erik De Schutter and Egidio D`Angelo (2008)
             Computational reconstruction of pacemaking and intrinsic 
             electroresponsiveness in cerebellar golgi cells
             Frontiers in Cellular Neuroscience 2:2
ENDCOMMENT

NEURON{
	SUFFIX SK2
	USEION ca READ cai
	USEION k READ ek WRITE ik 
	RANGE gkbar, g, ik, tcorr,scal
:    THREADSAFE
}

UNITS {
	(mA) = (milliamp)
	(mV) = (millivolt)
	(molar) = (1/liter)
	(mM) = (millimolar)
}

PARAMETER {
	celsius  (degC)
	cai (mM)
	gkbar = 0.038 (mho/cm2)
	Q10 = 2.7 (1)
	diff = 1 (1) : diffusion factor
    scal = 1
: rates ca-indipendent
	invc1 = 80e-3  ( /ms)
	invc2 = 80e-3  ( /ms)
	invc3 = 200e-3 ( /ms)

	invo1 = 1      ( /ms)
	invo2 = 100e-3 ( /ms)
	diro1 = 160e-3 ( /ms)
	diro2 = 1.2    ( /ms)

: rates ca-dipendent
	dirc2 = 200 ( /ms-mM )
	dirc3 = 160 ( /ms-mM )
	dirc4 = 80  ( /ms-mM )

}

ASSIGNED{ 
	v	(mV) 
	ek	(mV) 
	g	(mho/cm2) 
	ik	(mA/cm2) 
	invc1_t  ( /ms)
	invc2_t  ( /ms)
	invc3_t  ( /ms)
	invo1_t  ( /ms)
	invo2_t  ( /ms)
	diro1_t  ( /ms)
	diro2_t  ( /ms)
	dirc2_t  ( /ms-mM)
	dirc3_t  ( /ms-mM)
	dirc4_t  ( /ms-mM)
	tcorr	 (1)

	dirc2_t_ca  ( /ms)
	dirc3_t_ca  ( /ms)
	dirc4_t_ca  ( /ms)
} 

STATE {
	c1
	c2
	c3
	c4
	o1
	o2
}

BREAKPOINT{ 
	SOLVE kin METHOD sparse 
	g = gkbar*(o1+o2)	:(mho/cm2)
	ik = g*(v-ek)		:(mA/cm2)
} 

INITIAL{
	rate(celsius)
	SOLVE kin STEADYSTATE sparse
} 

KINETIC kin{ 
	rates(cai/diff) 
	~c1<->c2 (dirc2_t_ca, invc1_t) 
	~c2<->c3 (dirc3_t_ca, invc2_t) 
	~c3<->c4 (dirc4_t_ca, invc3_t) 
	~c3<->o1 (diro1_t, invo1_t) 
	~c4<->o2 (diro2_t, invo2_t) 
	CONSERVE c1+c2+c3+c4+o2+o1=1 
} 

FUNCTION temper (Q10, celsius (degC)) {
	temper = Q10^((celsius -23(degC)) / 10(degC)) 
}

PROCEDURE rates(cai(mM)){
	dirc2_t_ca = dirc2_t*cai
	dirc3_t_ca = dirc3_t*cai
	dirc4_t_ca = dirc4_t*cai 
} 

PROCEDURE rate (celsius(degC)) {
	tcorr = temper (Q10,celsius)*scal
	invc1_t = invc1*tcorr
	invc2_t = invc2*tcorr
	invc3_t = invc3*tcorr
	invo1_t = invo1*tcorr
	invo2_t = invo2*tcorr
	diro1_t = diro1*tcorr
	diro2_t = diro2*tcorr
	dirc2_t = dirc2*tcorr
	dirc3_t = dirc3*tcorr
	dirc4_t = dirc4*tcorr
}

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