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
figure2C
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 *
                            
TITLE Voltage-gated low threshold potassium current from Kv1 subunits

COMMENT
The time kinetics are from the Original paper (Akeman reduce the time constatant to about 1/3);
activation curve are from original paper; inactivation data are from Stephane's paper Fig 6E 
(This current should be a combination of kv1.2 which is not sensitive to TEA and kv4.3 which is not completely blocked).
Not sure this steady state inactivation curve is right, but it would not affect the normal firing of PC. It is used to 
reproduce history dependence of development of secondary spikes. Kv4 seems not to be able to do it according to its fast inactivation kinetics.
Ik1 inactivates very slow. We set the inactivation time constant to 1000 ms. 
NEURON implementation of a potassium channel from Kv1.1 subunits
We should also refer to Gating, modulation and subunit composition of voltage-gated K+channels in dendritic inhibitory interneurones of rathippocampus
In this paper,they observe a slow delayed rectifier K current. This current is surprisingly not sensitive to 4AP,but sensitive to high does
TEA. Compared with the paper by Marco Martin 5698 • The Journal of Neuroscience, July 2, 2003 • 23(13):5698 –5707, the K currents measured in the
dendrite, about 20% of the K currents is still resistant to even 3 mM 4-AP. However, 10 mM TEA can decrease the K currents to only 10%, suggesting a K
current sensitive  to high concentration TEA instead of 4AP, similar with the work by CC Lien. I guess in the soma, there should be IK1.

Kinetic data taken from: Zerr et al., J.Neurosci. 18 (1998) 2842
Vhalf = -28.8 +/- 2.3 mV; k = 8.1 +/- 0.9 mV

The voltage dependency of the rate constants was approximated by:

alpha = ca * exp(-(v+cva)/cka)
beta = cb * exp(-(v+cvb)/ckb)

Parameters ca, cva, cka, cb, cvb, ckb
are defined in the CONSTANT block.

Laboratory for Neuronal Circuit Dynamics
RIKEN Brain Science Institute, Wako City, Japan
http://www.neurodynamics.brain.riken.jp

Reference: Akemann and Knoepfel, J.Neurosci. 26 (2006) 4602
Date of Implementation: April 2005
Contact: akemann@brain.riken.jp

ENDCOMMENT

NEURON {
	SUFFIX Kv11
	USEION k READ ek WRITE ik
	RANGE gk, gbar, ik
	GLOBAL ninf, taun
:    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

	ca = 0.12889 (1/ms)
	cva = 45 (mV)
	cka = -33.90877 (mV)

	cb = 0.12889 (1/ms)
      cvb = 45 (mV)
	ckb = 12.42101 (mV)         
}

PARAMETER {
	v (mV)
	celsius (degC)
	
	gbar = 0.011 (mho/cm2)   <0,1e9>
}


ASSIGNED {
 	ik (mA/cm2) 
	ek (mV)
	gk  (mho/cm2)
	ninf
	hinf
	taun (ms)
	tauh
	alphan (1/ms)
	betan (1/ms)
	qt
}

STATE { n h}

INITIAL {
	qt = q10^((celsius-22 (degC))/10 (degC))
	rates(v)
	n = ninf
	h = hinf
}

BREAKPOINT {
	SOLVE states METHOD cnexp
      gk = gbar * n^4 *h
	ik = gk * (v - ek)
}

DERIVATIVE states {
	rates(v)
	n' = (ninf-n)/taun
	h' = (hinf-h)/tauh 
}

PROCEDURE rates(v (mV)) {
	alphan = alphanfkt(v)
	betan = betanfkt(v)
	ninf = alphan/(alphan+betan) 
	taun = 1/(qt*(alphan + betan))
:	hinf = 0.1765+0.8235/(1+exp((v+70)/11.5))
	tauh = 1000/qt
	hinf = 1/(1+exp((v+66.16)/6.1881))
:	tauh = 1000/(1+exp((v+58.72)/3.005))/qt
}

FUNCTION alphanfkt(v (mV)) (1/ms) {
	alphanfkt = ca * exp(-(v+cva)/cka) 
}

FUNCTION betanfkt(v (mV)) (1/ms) {
	betanfkt = cb * exp(-(v+cvb)/ckb)
}





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