Purkinje cell: Synaptic activation predicts voltage control of burst-pause (Masoli & D'Angelo 2017)

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Accession:239421
"The dendritic processing in cerebellar Purkinje cells (PCs), which integrate synaptic inputs coming from hundreds of thousands granule cells and molecular layer interneurons, is still unclear. Here we have tested a leading hypothesis maintaining that the significant PC output code is represented by burst-pause responses (BPRs), by simulating PC responses in a biophysically detailed model that allowed to systematically explore a broad range of input patterns. BPRs were generated by input bursts and were more prominent in Zebrin positive than Zebrin negative (Z+ and Z-) PCs. Different combinations of parallel fiber and molecular layer interneuron synapses explained type I, II and III responses observed in vivo. BPRs were generated intrinsically by Ca-dependent K channel activation in the somato-dendritic compartment and the pause was reinforced by molecular layer interneuron inhibition. BPRs faithfully reported the duration and intensity of synaptic inputs, such that synaptic conductance tuned the number of spikes and release probability tuned their regularity in the millisecond range. ..."
Reference:
1 . Masoli S, D'Angelo E (2017) Synaptic Activation of a Detailed Purkinje Cell Model Predicts Voltage-Dependent Control of Burst-Pause Responses in Active Dendrites. Front Cell Neurosci 11:278 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network; Synapse;
Brain Region(s)/Organism: Cerebellum;
Cell Type(s): Cerebellum Purkinje GABA cell;
Channel(s): I Potassium; I K,Ca;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: NEURON;
Model Concept(s): Detailed Neuronal Models; Bursting;
Implementer(s): Masoli, Stefano [stefano.masoli at unipv.it];
Search NeuronDB for information about:  Cerebellum Purkinje GABA cell; I K,Ca; I Potassium;
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Purkinjecell_2017
mod_files
Cav2_1.mod *
Cav3_1.mod *
Cav3_2.mod *
Cav3_3.mod *
cdp5.mod *
HCN1_Angeloetal2007.mod *
Kca11.mod *
Kca22.mod *
Kca31.mod *
Kir23.mod *
Kv11.mod *
Kv15.mod *
Kv33.mod *
Kv34.mod *
Kv43.mod *
Leak.mod *
Nav16.mod *
PC_Gaba_det_vi_alfa1.mod
PURKINJE_Ampa_det_vi.mod
UBC_TRP.mod
                            
: Calcium ion accumulation with endogenous buffers, DCM and pump

COMMENT

The basic code of Example 9.8 and Example 9.9 from NEURON book was adapted as:

1) Extended using parameters from Schmidt et al. 2003.
2) Pump rate was tuned according to data from Maeda et al. 1999
3) DCM was introduced and tuned to approximate the effect of radial diffusion

Reference: Anwar H, Hong S, De Schutter E (2010) Controlling Ca2+-activated K+ channels with models of Ca2+ buffering in Purkinje cell. Cerebellum*

*Article available as Open Access

PubMed link: http://www.ncbi.nlm.nih.gov/pubmed/20981513

Written by Haroon Anwar, Computational Neuroscience Unit, Okinawa Institute of Science and Technology, 2010.
Contact: Haroon Anwar (anwar@oist.jp)

ENDCOMMENT


NEURON {
  SUFFIX cdp5
  USEION ca READ cao, cai, ica WRITE cai
  RANGE ica_pmp
  RANGE Nannuli, Buffnull2, rf3, rf4, vrat
  RANGE TotalPump

}


UNITS {
	(mol)   = (1)
	(molar) = (1/liter)
	(mM)    = (millimolar)
	(um)    = (micron)
	(mA)    = (milliamp)
	FARADAY = (faraday)  (10000 coulomb)
	PI      = (pi)       (1)
}

PARAMETER {
	Nannuli = 10.9495 (1)
	celsius (degC)
        
	cainull = 45e-6 (mM)
        mginull =.59    (mM)

:	values for a buffer compensating the diffusion

	Buffnull1 = 0	(mM)
	rf1 = 0.0134329	(/ms mM)
	rf2 = 0.0397469	(/ms)

	Buffnull2 = 60.9091	(mM)
	rf3 = 0.1435	(/ms mM)
	rf4 = 0.0014	(/ms)

:	values for benzothiazole coumarin (BTC)
	BTCnull = 0	(mM)
	b1 = 5.33	(/ms mM)
	b2 = 0.08	(/ms)

:	values for caged compound DMNPE-4
	DMNPEnull = 0	(mM)
	c1 = 5.63	(/ms mM)
	c2 = 0.107e-3	(/ms)

:       values for Calbindin (2 high and 2 low affinity binding sites)

        CBnull=	.16             (mM)
        nf1   =43.5           (/ms mM)
        nf2   =3.58e-2        (/ms)
        ns1   =5.5            (/ms mM)
        ns2   =0.26e-2        (/ms)

:       values for Parvalbumin

        PVnull  = .08           (mM)
        m1    = 1.07e2        (/ms mM)
        m2    = 9.5e-4                (/ms)
        p1    = 0.8           (/ms mM)
        p2    = 2.5e-2                (/ms)

  	kpmp1    = 3e-3       (/mM-ms)
  	kpmp2    = 1.75e-5   (/ms)
  	kpmp3    = 7.255e-5  (/ms)
	TotalPump = 1e-9	(mol/cm2)	

}

ASSIGNED {
	diam      (um)
	ica       (mA/cm2)
	ica_pmp   (mA/cm2)
	parea     (um)     : pump area per unit length
	parea2	  (um)
	cai       (mM)
	mgi	(mM)
	vrat	(1)	
}

CONSTANT { cao = 2	(mM) }

STATE {
	: ca[0] is equivalent to cai
	: ca[] are very small, so specify absolute tolerance
	: let it be ~1.5 - 2 orders of magnitude smaller than baseline level

	ca		(mM)    <1e-3>
	mg		(mM)	<1e-6>
	
	Buff1		(mM)	
	Buff1_ca	(mM)

	Buff2		(mM)
	Buff2_ca	(mM)

	BTC		(mM)
	BTC_ca		(mM)

	DMNPE		(mM)
	DMNPE_ca	(mM)	

        CB		(mM)
        CB_f_ca		(mM)
        CB_ca_s		(mM)
        CB_ca_ca	(mM)

        PV		(mM)
        PV_ca		(mM)
        PV_mg		(mM)
	
	pump		(mol/cm2) <1e-15>
	pumpca		(mol/cm2) <1e-15>

}

BREAKPOINT {
	SOLVE state METHOD sparse
}

LOCAL factors_done

INITIAL {
		factors()

		ca = cainull
		mg = mginull
		
		Buff1 = ssBuff1()
		Buff1_ca = ssBuff1ca()

		Buff2 = ssBuff2()
		Buff2_ca = ssBuff2ca()

		BTC = ssBTC()
		BTC_ca = ssBTCca()		

		DMNPE = ssDMNPE()
		DMNPE_ca = ssDMNPEca()

		CB = ssCB( kdf(), kds())   
	        CB_f_ca = ssCBfast( kdf(), kds())
       	 	CB_ca_s = ssCBslow( kdf(), kds())
        	CB_ca_ca = ssCBca( kdf(), kds())

        	PV = ssPV( kdc(), kdm())
        	PV_ca = ssPVca(kdc(), kdm())
        	PV_mg = ssPVmg(kdc(), kdm())

		
  	parea = PI*diam
	parea2 = PI*(diam-0.2)
	ica = 0
	ica_pmp = 0
:	ica_pmp_last = 0
	pump = TotalPump
	pumpca = 0
	
	cai = ca
}

PROCEDURE factors() {
        LOCAL r, dr2
        r = 1/2                : starts at edge (half diam)
        dr2 = r/(Nannuli-1)/2  : full thickness of outermost annulus,
        vrat = PI*(r-dr2/2)*2*dr2  : interior half
        r = r - dr2
}


LOCAL dsq, dsqvol  : can't define local variable in KINETIC block
                   :   or use in COMPARTMENT statement

KINETIC state {
  COMPARTMENT diam*diam*vrat {ca mg Buff1 Buff1_ca Buff2 Buff2_ca BTC BTC_ca DMNPE DMNPE_ca CB CB_f_ca CB_ca_s CB_ca_ca PV PV_ca PV_mg}
  COMPARTMENT (1e10)*parea {pump pumpca}


	:pump
	~ ca + pump <-> pumpca  (kpmp1*parea*(1e10), kpmp2*parea*(1e10))
	~ pumpca <-> pump   (kpmp3*parea*(1e10), 0)
  	CONSERVE pump + pumpca = TotalPump * parea * (1e10)
	
	ica_pmp = 2*FARADAY*(f_flux - b_flux)/parea	
	: all currents except pump
	: ica is Ca efflux
	~ ca << (-ica*PI*diam/(2*FARADAY))

	:RADIAL DIFFUSION OF ca, mg and mobile buffers

	dsq = diam*diam
		dsqvol = dsq*vrat
		~ ca + Buff1 <-> Buff1_ca (rf1*dsqvol, rf2*dsqvol)
		~ ca + Buff2 <-> Buff2_ca (rf3*dsqvol, rf4*dsqvol)
		~ ca + BTC <-> BTC_ca (b1*dsqvol, b2*dsqvol)
		~ ca + DMNPE <-> DMNPE_ca (c1*dsqvol, c2*dsqvol)
		:Calbindin	
		~ ca + CB <-> CB_ca_s (nf1*dsqvol, nf2*dsqvol)
	       	~ ca + CB <-> CB_f_ca (ns1*dsqvol, ns2*dsqvol)
        	~ ca + CB_f_ca <-> CB_ca_ca (nf1*dsqvol, nf2*dsqvol)
        	~ ca + CB_ca_s <-> CB_ca_ca (ns1*dsqvol, ns2*dsqvol)

		:Paravalbumin
        	~ ca + PV <-> PV_ca (m1*dsqvol, m2*dsqvol)
        	~ mg + PV <-> PV_mg (p1*dsqvol, p2*dsqvol)


  	cai = ca
	mgi = mg
}

FUNCTION ssBuff1() (mM) {
	ssBuff1 = Buffnull1/(1+((rf1/rf2)*cainull))
}
FUNCTION ssBuff1ca() (mM) {
	ssBuff1ca = Buffnull1/(1+(rf2/(rf1*cainull)))
}
FUNCTION ssBuff2() (mM) {
        ssBuff2 = Buffnull2/(1+((rf3/rf4)*cainull))
}
FUNCTION ssBuff2ca() (mM) {
        ssBuff2ca = Buffnull2/(1+(rf4/(rf3*cainull)))
}

FUNCTION ssBTC() (mM) {
	ssBTC = BTCnull/(1+((b1/b2)*cainull))
}

FUNCTION ssBTCca() (mM) {
	ssBTCca = BTCnull/(1+(b2/(b1*cainull)))
}

FUNCTION ssDMNPE() (mM) {
	ssDMNPE = DMNPEnull/(1+((c1/c2)*cainull))
}

FUNCTION ssDMNPEca() (mM) {
	ssDMNPEca = DMNPEnull/(1+(c2/(c1*cainull)))
}

FUNCTION ssCB( kdf(), kds()) (mM) {
	ssCB = CBnull/(1+kdf()+kds()+(kdf()*kds()))
}
FUNCTION ssCBfast( kdf(), kds()) (mM) {
	ssCBfast = (CBnull*kds())/(1+kdf()+kds()+(kdf()*kds()))
}
FUNCTION ssCBslow( kdf(), kds()) (mM) {
	ssCBslow = (CBnull*kdf())/(1+kdf()+kds()+(kdf()*kds()))
}
FUNCTION ssCBca(kdf(), kds()) (mM) {
	ssCBca = (CBnull*kdf()*kds())/(1+kdf()+kds()+(kdf()*kds()))
}
FUNCTION kdf() (1) {
	kdf = (cainull*nf1)/nf2
}
FUNCTION kds() (1) {
	kds = (cainull*ns1)/ns2
}
FUNCTION kdc() (1) {
	kdc = (cainull*m1)/m2
}
FUNCTION kdm() (1) {
	kdm = (mginull*p1)/p2
}
FUNCTION ssPV( kdc(), kdm()) (mM) {
	ssPV = PVnull/(1+kdc()+kdm())
}
FUNCTION ssPVca( kdc(), kdm()) (mM) {
	ssPVca = (PVnull*kdc())/(1+kdc()+kdm())
}
FUNCTION ssPVmg( kdc(), kdm()) (mM) {
	ssPVmg = (PVnull*kdm())/(1+kdc()+kdm())
}

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