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
figure1
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 *
                            
: nap.mod is a persistent Na+ current from
: Baker 2005, parameter assignments and formula's from page 854

NEURON {
	SUFFIX nap
    USEION na READ ena WRITE ina
	RANGE gbar,ina
:    THREADSAFE
}

UNITS {
	(S) = (siemens)
	(mV) = (millivolts)
	(mA) = (milliamp)
}
CONSTANT {
q10  =2.7
}
PARAMETER {
	gbar = 2.2630e-04 :3.7(nS)/1635(um^2)
:	ena= 65 (mV)

	A_amp = 17.235 (/ms) : A for alpha m persis
	B_amp = 27.58 (mV)
	C_amp = -11.47 (mV)

	A_bmp = 17.235 (/ms) : A for beta m persis
	B_bmp = 86.2 (mV)
	C_bmp = 19.8 (mV)
}

ASSIGNED {
	v	(mV) : NEURON provides this
	i	(mA/cm2)
	g	(S/cm2)
	tau_m	(ms)
	minf
	hinf
	ena
	ina
	qt
}

STATE { m h }

BREAKPOINT {
	SOLVE states METHOD cnexp
	g = gbar * m^3
	ina = g * (v-ena)
}

INITIAL {
qt = q10^((celsius-22 (degC))/10 (degC))
	: assume that equilibrium has been reached
	m = alpham(v)/(alpham(v)+betam(v))
}

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

FUNCTION alpham(Vm (mV)) (/ms) {
	alpham=A_amp/(1+exp((Vm+B_amp)/C_amp))
}

FUNCTION betam(Vm (mV)) (/ms) {
	betam=A_bmp/(1+exp((Vm+B_bmp)/C_bmp))
}

FUNCTION rates(Vm (mV)) (/ms) {
	tau_m = 1.0 / (alpham(Vm) + betam(Vm))/qt
	minf = 1.0/(1+exp(-(Vm+66)/5))
}













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