Multiplexed coding in Purkinje neuron dendrites (Zang and De Schutter 2021)

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Neuronal firing patterns are crucial to underpin circuit level behaviors. In cerebellar Purkinje cells (PCs), both spike rates and pauses are used for behavioral coding, but the cellular mechanisms causing code transitions remain unknown. We use a well-validated PC model to explore the coding strategy that individual PCs use to process parallel fiber (PF) inputs. We find increasing input intensity shifts PCs from linear rate-coders to burst-pause timing-coders by triggering localized dendritic spikes. We validate dendritic spike properties with experimental data, elucidate spiking mechanisms, and predict spiking thresholds with and without inhibition. Both linear and burst-pause computations use individual branches as computational units, which challenges the traditional view of PCs as linear point neurons. Dendritic spike thresholds can be regulated by voltage state, compartmentalized channel modulation, between-branch interaction and synaptic inhibition to expand the dynamic range of linear computation or burst-pause computation. In addition, co-activated PF inputs between branches can modify somatic maximum spike rates and pause durations to make them carry analogue signals. Our results provide new insights into the strategies used by individual neurons to expand their capacity of information processing.
1 . Zang Y, De Schutter E (2021) The Cellular Electrophysiological Properties Underlying Multiplexed Coding in Purkinje Cells. J Neurosci [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Dendrite; Neuron or other electrically excitable cell;
Brain Region(s)/Organism: Cerebellum;
Cell Type(s): Cerebellum Purkinje GABA cell;
Channel(s): I T low threshold; I Na,p; I h; I Potassium; I Sodium; I p,q; I K,Ca;
Gap Junctions:
Simulation Environment: NEURON;
Model Concept(s): Dendritic Action Potentials; Detailed Neuronal Models; Synaptic Integration; Temporal Coding; Reaction-diffusion;
Implementer(s): Zang, Yunliang ;
Search NeuronDB for information about:  Cerebellum Purkinje GABA cell; I Na,p; I T low threshold; I p,q; I h; I K,Ca; I Sodium; I Potassium;
BK_Slow.mod *
CaP.mod *
capmax.mod *
CaT.mod *
cdp_AIS.mod *
cdp_smooth.mod *
cdp_soma.mod *
cdp_spiny.mod *
ih.mod *
Kv1.mod *
kv3.mod *
kv4f.mod *
kv4s.mod *
mslo.mod *
nap.mod *
narsg.mod *
peak.mod *
pkjlk.mod *
SK2.mod *
syn2.mod *
TITLE Voltage-gated low threshold potassium current from Kv1 subunits

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

Reference: Akemann and Knoepfel, J.Neurosci. 26 (2006) 4602
Date of Implementation: April 2005


	RANGE gk, gbar, ik
	GLOBAL ninf, taun

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

	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)         

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

 	ik (mA/cm2) 
	ek (mV)
	gk  (mho/cm2)
	taun (ms)
	alphan (1/ms)
	betan (1/ms)

STATE { n h}

	qt = q10^((celsius-22 (degC))/10 (degC))
	n = ninf
	h = hinf

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

	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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